Towards 3D prostate cancer localization by contrast-ultrasound dispersion imagingSchalk, S.G.

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Towards 3D prostate cancer localizationby contrast-ultrasound dispersion imaging

Stefan Schalk

The research presented in this thesis was financially supported by the European Re-search Council (ERC), the Dutch Cancer Society (KWF), and the Royal NetherlandsAcademy of Arts and Sciences (KNAW).

Copyright © 2016, Stefan Schalk.Copyright of the individual chapters containing published articles belongs to the pub-lisher of the journal listed at the beginning of the respective chapters.All rights reserved. No part of this publication may be reproduced, distributed, ortransmitted in any form or by any means, including photocopying, recording, orother electronic or mechanical methods, without the prior written permission of thecopyright owner.

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A catalogue record is available from the Eindhoven University of TechnologyLibrary.ISBN: 978-90-386-4204-8

Towards 3D prostate cancer localizationby contrast-ultrasound dispersion imaging

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische UniversiteitEindhoven, op gezag van de rector magnificus prof.dr.ir. F.P.T. Baaijens,voor een commissie aangewezen door het College voor Promoties, in het

openbaar te verdedigen op woensdag 18 januari 2017 om 16:00 uur

door

Stefan Gerard Schalk

geboren te Eindhoven

Dit proefschrift is goedgekeurd door de promotoren en de samenstellingvan de promotiecommissie is als volgt:

voorzitter: prof.dr.ir. J.H. Blom1e promotor: prof.dr.ir. H. Wijkstracopromotor: dr. M. Mischileden: prof.dr. D.O. Cosgrove (Imperial College London)

prof.dr. F. Forsberg (Thomas Je�erson University)prof.dr.ir. J.M.J. den Toonder (TU Eindhoven)

adviseur: dr. H.P. Beerlage (Jeroen Bosch Ziekenhuis)

Het onderzoek dat in dit proefschrift wordt beschreven is uitgevoerd in

overeenstemming met de TU/e Gedragscode Wetenschapsbeoefening.

Summary

Towards 3D prostate cancer localization by contrast-ultrasound dispersionimaging

Prostate cancer is the most occurring type of cancer in the western world.However, due to the lack of reliable imaging techniques, typical treatment hasa radical nature (e.g., excision or radiotherapy of the whole gland), carrying anincreased risk of infections, urinary incontinence, and impotence. Moreover, standarddiagnostics, based on systematic biopsy, is invasive and has a large chance of missingtumors. For these reasons, several studies have recently been carried out to find newprostate cancer imaging techniques enabling biopsy targeting and focal treatment.One of the most promising ultrasound-based approaches is contrast-ultrasounddispersion imaging (CUDI), which exploits the microvascular di�erences betweenangiogenic and normal vasculature to distinguish between benign and malignanttissue. In particular, it aims at estimating the local dispersion of intravenously injectedultrasound contrast agents. Because the size of these contrast agents is comparableto that of red blood cells, they can travel through all the microvasculature whilestaying intravascular; they are therefore ideal for hemodynamic analysis. Acoustictime-intensity curves, reflecting the contrast concentration over time, are measuredthroughout the prostate by contrast-specific ultrasound imaging. Subsequently, localdispersion is estimated either by model fitting in the time domain or by assessmentof the similarity between neighboring time-intensity curves.

Until now, CUDI has been investigated in 2D only. For 2D CUDI, each plane inthe prostate requires a separate injection of contrast agents, making this method toocostly and time-consuming for clinical implementation. Moreover, even with multipleinjections, it is impossible to cover the full prostate volume. A 2D approach also posesimportant limitations for registration and fusion of the obtained parametric maps withlive ultrasound imaging, required e.g. for accurate biopsy targeting. In this thesis, wepropose a solution to these challenges by improvement of 2D CUDI and validationprocedures and by extending CUDI to a full 3D implementation.

ii Summary

So far, similarity for CUDI has been estimated by temporal correlation or spectralcoherence, which both assess linear similarity between time-intensity curves. In Chap-ter 2, mutual information is investigated as a more general similarity measure, alsoincorporating nonlinear similarity. The inverse relation between mutual informationand dispersion is shown by simulations. In an in-vivo study, 2D CUDI by mutual infor-mation is compared with the histology in 23 patients referred for radical prostatectomybecause of biopsy-confirmed prostate cancer. The method’s classification performanceis slightly superior, but not significantly, to that by use of linear similarity measures,and significantly better than standard perfusion parameters.

To enable extension of CUDI to 3D, the feasibility of using 3D dynamic contrast-enhanced ultrasound (DCE-US) for prostate cancer localization is investigated. Using3D DCE-US enables imaging the entire prostate using a single contrast injection,greatly improving the clinical applicability of the method. First, in Chapter 3, thetechnical feasibility of using DCE-US for 3D CUDI by similarity analysis is assessedand confirmed by characterizing the contrast dynamics and testing the method in 2patients. Next, in Chapter 4, a 3D implementation of CUDI by mutual information isintroduced and tested in 3 patients. Finally, in Chapter 5, the ability of 3D CUDI tolocalize prostate cancer is evaluated by comparing correlation, coherence, and mutualinformation maps with the outcome of systematic biopsies in 43 men. Significantdi�erences are shown between benign and malignant areas using correlation maps.

Systematic biopsies only provide a sampled representation of the presence of cancerin the prostate, which brings a risk of missing significant tumors. For this reason, ifavailable, histology after radical prostatectomy is often used as a ground truth fortraining and testing of prostate cancer imaging methods. The excised prostate istypically fixated and sliced in 3-to-4-mm thick slices in which a pathologist markscancerous tissue based on cellular di�erentiation. To construct a full 3D validationreference, an algorithm is proposed in Chapter 6 to interpolate tumor contours betweenhistology slices. Its accuracy, as well as its sensitivity to errors introduced by standardpathological procedures, are assessed in silico. When a slice thickness of 4 mm witha random Gaussian-distributed error of 0 ± 0.5 mm is applied, the average relativeerror in tumor volume does not exceed 10% and the average 90th-percentile distancebetween the original and reconstructed surface remains below 1.5 mm.

For 2D imaging, the histology slice matching the imaging plane has to be identified.However, the orientations of the imaging plane and histology slice usually do notmatch. In fact, one imaging plane may cover multiple histology slices. Also, for 3Dimaging, the positions and orientations of the histology slices have to be matchedwith their positions in the 3D data. Unfortunately, the prostate is subject to severalnon-a�ne deformations occurring during transrectal imaging and during the fixationprocess following prostatectomy. To compensate for these deformations, an elastic 3Dsurface-based registration algorithm is proposed in Chapter 7 to fuse histology withtransrectal ultrasound, providing a more reliable ground truth to validate prostatecancer imaging techniques. The method consists of three steps: an a�ne registration,

Summary iii

an elastic surface registration, and an interpolation of the surface deformations. Afteran preliminary in-vitro and in-vivo validation in Chapter 7, the proposed method ismore extensively validated in vivo in Chapter 8. The resulting registration error liesin the proximity of 2 mm, which is lower than the slicing thickness and much lowerthan the diameter of clinically significant cancer. Being shape-based, application ofthe method to other imaging modalities, such as MRI, can also be envisaged.

In conclusion, 3D CUDI could play a significant role in prostate cancer diagnosis inthe future. Being cost e�ective and applicable at the bedside, CUDI shows importantadvantages over MRI, which is currently gaining attention for prostate cancer diagnosis.Furthermore, 3D registration of ultrasound and histology facilitates the validation ofnovel imaging techniques and opens the way to the development of classifiers basedon multimodal image fusion.

iv Summary

Contents

Summary i

List of abbreviations and symbols ix

1 Introduction 11.1 Societal Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Prostate cancer . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.2 Diagnosis of prostate cancer . . . . . . . . . . . . . . . . . . 21.1.3 Treatment of prostate cancer . . . . . . . . . . . . . . . . . . 41.1.4 The need for prostate cancer imaging . . . . . . . . . . . . . 5

1.2 Current prostate cancer imaging techniques . . . . . . . . . . . . . . 61.2.1 Magnetic resonance imaging . . . . . . . . . . . . . . . . . . 61.2.2 Ultrasound . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Validation issues for emerging imaging techniques . . . . . . . . . . . 111.4 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.5 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2 Similarity analysis using mutual information 172.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.1 In vivo data acquisition . . . . . . . . . . . . . . . . . . . . . 212.2.2 CUDI by mutual information . . . . . . . . . . . . . . . . . . 212.2.3 Additional considerations . . . . . . . . . . . . . . . . . . . . 252.2.4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2.5 Validation in patients . . . . . . . . . . . . . . . . . . . . . . 28

2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.3.1 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.3.2 Patient data . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

vi Contents

2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3 Technical feasibility of 3D CUDI 393.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.2 Materials and method . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.2.1 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . 433.2.2 2D spatiotemporal similarity analysis . . . . . . . . . . . . . . 453.2.3 4D spatiotemporal similarity analysis . . . . . . . . . . . . . . 473.2.4 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.4.1 Spatiotemporal analysis . . . . . . . . . . . . . . . . . . . . . 563.4.2 Data characteristics . . . . . . . . . . . . . . . . . . . . . . . 573.4.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.6 Appendix: UCA dispersion distance . . . . . . . . . . . . . . . . . . . 603.7 Appendix: Relation between speckle size and filter parameters . . . . 60

4 3D CUDI based on mutual information 634.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.2 Material and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.2.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.2.2 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . 674.2.3 Mutual Information in 3D . . . . . . . . . . . . . . . . . . . . 674.2.4 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5 Clinical validation of 3D CUDI 715.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.2 Patients and study design . . . . . . . . . . . . . . . . . . . . . . . . 745.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6 Interpolating histopathologic data from sliced RP specimens 836.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 856.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.2.1 Histopathologic procedure . . . . . . . . . . . . . . . . . . . 876.2.2 Interpolation approach . . . . . . . . . . . . . . . . . . . . . 886.2.3 In-silico phantoms . . . . . . . . . . . . . . . . . . . . . . . . 916.2.4 Validation and quantification . . . . . . . . . . . . . . . . . . 93

Contents vii

6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 946.3.1 Slice thickness . . . . . . . . . . . . . . . . . . . . . . . . . . 946.3.2 Slice orientation . . . . . . . . . . . . . . . . . . . . . . . . . 956.3.3 Slice alignment . . . . . . . . . . . . . . . . . . . . . . . . . 956.3.4 Tumor size . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

7 3D registration of prostate data from histology and ultrasound 1017.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1037.2 Material and methods . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.2.1 Prostate anatomy . . . . . . . . . . . . . . . . . . . . . . . . 1057.2.2 Surface reconstruction . . . . . . . . . . . . . . . . . . . . . 1067.2.3 Registration algorithm . . . . . . . . . . . . . . . . . . . . . . 1087.2.4 Remeshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1147.2.5 In-vitro validation . . . . . . . . . . . . . . . . . . . . . . . . 1147.2.6 In-vivo validation . . . . . . . . . . . . . . . . . . . . . . . . 115

7.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1167.3.1 In-vitro validation . . . . . . . . . . . . . . . . . . . . . . . . 1167.3.2 In-vivo validation . . . . . . . . . . . . . . . . . . . . . . . . 119

7.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1207.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

8 Clinical validation of histology-ultrasound registration 1238.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1258.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1258.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1278.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1298.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

9 Discussion and conclusion 1359.1 Mutual information . . . . . . . . . . . . . . . . . . . . . . . . . . . 1369.2 3D CUDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1379.3 Ultrasound-histology registration . . . . . . . . . . . . . . . . . . . . 1409.4 General conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Bibliography 145

List of publications 167

Acknowledgments 171

About the author 173

viii Contents

List of abbreviations and symbols

Abbreviations

2D, 3D, 4D 2-, 3-, 4-dimensional (or dimensions)ARFI Acoustic radiation force impulse imagingAS Active surveillanceASc Anisotropic scalingAT Appearance timeAU-ROC Area under the receiving operator characteristic curveAU-TIC Area under the time-intensity curveBPH Benign prostatic hyperplasiaBPZ Border between the peripheral and central zoneCA Cryosurgical ablationCEUS Contrast-enhanced ultrasoundCT (X-ray) computed tomographyCUDI Contrast-ultrasound dispersion imagingCZ Central zoneDCE-MRI Dynamic contrast-enhanced magnetic resonance imagingDCE-US Dynamic contrast-enhanced ultrasoundDICOM Digital imaging and communication in medicineDOF Degrees of freedomDR Dynamic rangeDRE Digital rectal examinationDWI Di�usion-weighted imagingEBRT External beam radiation therapyED Erectile dysfunctionESUR European Society of Urogenital RadiologyFE Finite elementFN False negativeFP False positiveFWHM Full-width at half of the maximumHIFU High-intensity focused ultrasound

x List of abbreviations and symbols

ICP Iterative closest pointIDC Indicator dilution curveIID Independent and identically distributedISc Isotropic scalingLDRW Local density random walkLUTS Lower urinary tract symptomsmpMRI Multiparametric magnetic resonance imagingMR Magnetic resonanceMRI Magnetic resonance imagingMRSI Magnetic resonance spectroscopy imagingMutI Mutual informationMVD Microvascular densityNN Natural neighborNPV Negative predictive valueNSR Noise-to-signal ratioPCA Principal component analysisPCa Prostate cancerPET Positron emission tomographyPI Peak intensityPI-RADS Prostate imaging reporting and data system (scoring system for mpMRI)PI-RADSv2 Version 2 of PI-RADSPMF Probability mass functionPPV Positive predictive valuePSA Prostate-specific antigenPZ Peripheral zoneRBF Radial basis functionRF RadiofrequencyRMS Root mean squareROC Receiving operator characteristicRP Radical prostatectomySE Standard errorSNR Signal-to-noise ratioSNS SensitivitySPC SpecificitySPECT Single photon emission computed tomographySS Speckle sizeSWE Shear-wave elastographyT2WI T2-weighted imagingTIC Time-intensity curveTN True negativeTP True positiveTRE Target registration error, total registration errorTRUS Transrectal ultrasoundTZ Transition zoneUCA Ultrasound contrast agentUI Urinary incontinence

List of abbreviations and symbols xi

US UltrasoundWIR Wash-in rateWIT Wash-in time (or rise time)

Notation

pX(x) Probability of X = x

pX|Y (x|y) Conditional probability of X = x given Y = y

E[x] Expectation of xx Mean value of xRxx Autocorrelation of xCxx Autocovariance of xcov(•, •) CovarianceAT Transpose of AA�1 Inverse of AA \B Intersection of A and B

H(A) Hessian matrix of A|A| Determinant of A|A|v Volume of AG� Gaussian kernel with standard deviation �

H⇤ Complex conjugate of H

N (µ,�) Gaussian random noise with mean µ and standard deviation �

R(·) Reighley distributed noise

Symbols

↵ Scaling factor equal to the area under the IDC↵std Standard deviation of histology plane misorientation� Step size in the active surface algorithm� Contour�(·) Dirac delta function�t Time step⌘ External force factor in the active surface algorithm✓apex Angle between the apex of the prostate and the probe’s center line✓base Angle between the base of the prostate and the probe’s center line Dispersion-related CUDI parameter� Parameter in the active contour algorithm determining the fraction of

rEext directed normal to the model surfaceµ Mean transit time in the modified LDRW modelµn Mean of Gaussian noiseµs Mean of s⇢ Normalized spectral coherence (CUDI parameter); smoothing parameter in

RBF interpolation as defined in [1] (only in Chapter 6)

xii List of abbreviations and symbols

� Standard deviation�a Standard deviation of the additive noise�ax Axial standard deviation of a Gaussian kernel�b Blurring coe�cient�lat Lateral standard deviation of a Gaussian kernel�2n Variance of Gaussian noise

�post Standard deviation of the postprocessing filter�sp Standard deviation of the Gaussian kernel used to characterize speckle�t Standard deviation of the Gaussian kernel in Ht

⌧mem Active surface parameter controlling stretching⌧tps Active surface parameter controlling thin-plate-spline behavior⌦ Surfacea, b, c Principal axesaBA Linear conversion factor between B and A

A Acoustic intensityA0 Acoustic intensity without the presence of UCAAtb Cross-sectional area of the virtual tube used to model UCA dispersionB Number of bubblesBtot Total number of bubblesc Quantization level in a center TICC Random variable representing quantization levels in a center TICCUCA UCA concentrationC Covariance matrix of surface coordinatesC Set of quantization levels used to encode a center TICd Distance to the ultrasound transducerda, db, dc Distance to the principal axesdsl Slice thicknessD UCA dispersionE Active surface energyEint Internal active surface energyEext External active surface energyF Number of frameshsp Impulse response of Hsp

Hreg Speckle regularization filterHsp Filter characterizing the image speckle sizeHt Filter characterizing the desired speckle sizeI Mutual information (CUDI parameter)IR Reference imageIS Source imagek Quantization level in a kernel TICK Random variable representing quantization levels in kernel TICsK Alphabet used to encode kernel TICsm Mass of UCAM Connectivity matrixn Time sample indexncl Number of clusters

List of abbreviations and symbols xiii

nw Gaussian noise used to model specklenn Degrees of freedom within the negative classnp Degrees of freedom within the positive classn Surface normalN Number of kernel pixelsNc Number of occurrences of c in a center TICNk|c Number of occurrences of k in kernel pixels at time instances where C = c

Nv Number of verticesp Probability�pmin Minimum maximum node displacement (stopping criterion for the active

surface algorithm)p Surface node coordinatep0 Initial position of a surface nodepend Final position of a surface nodeP Number of observed variables in PCA analysisq Quantization level; quality measure in TetGen (only in Chapter 7)Q Number of quantization levelsr Normalized temporal correlation (CUDI parameter)s Modeled specklesa, sb, sc Scaling factor per principal axiss Active surface transformationS Scaling matrixSD Dice’s similarity coe�cientS(·) Spatial mapping of image coordinatesR

2 Determination coe�cientR Rotation matrixt Timet0 Theoretical injection time in the modified LDRW modeltarr Arrival timetw Time window lengthT Overall image coordinate transformationTaff A�ne transformationTel Elastic transformationU(·) Umbrella operatorv UCA velocitywstd Standard deviation of histology plane misalignmentx Position (1D), position in the right-left direction (3D)xim 1D position in the image�x, �y Displacement in x- and y-directionx Position (2D,3D)x0, y0, z0 Observation vectors containing x-, y-, and z-coordinatesxR Reference image coordinatesxS Source image coordinatesx(r)S Source image coordinates after rotation

Vrec Reconstructed phantom

xiv List of abbreviations and symbols

Vref Reference phantomVR Eigenvector matrix of reference image coordinatesVS Eigenvector matrix of source image coordinatesy Position in the posterior-anterior directionz Position in the base-apex directionzadd Additive noise

Chapter1Introduction

This chapter provides a background on prostate cancer and currently available imagingtechniques. Furthermore, the objectives and the outline of this thesis are given.

2 Introduction

1.1 Societal Problem

1.1.1 Prostate cancerProstate cancer is the type of cancer with the highest incidence rate and the third-ranked (second-ranked in North-America) cancer-related cause of death in males indeveloped countries [2]. The prostate is a small organ in the reproductive system,located between the bladder and the rectum (see Figure 1.1). Three major glandularregions are distinguished: the peripheral zone (PZ), the central zone (CZ), and thetransition zone (TZ) [3]. Approximately 70-80% of all prostatic carcinomas originatefrom the PZ [4]. Since the prostate, and in particular the PZ, is located directlyadjacent to the rectal wall, transrectal ultrasound (TRUS) imaging is theoreticallyvery suited for imaging of the prostate. Unfortunately, the accuracy of conventionalTRUS for prostate cancer detection is rather low [5–8].

Although the actual cause of prostate cancer is still unclear, known risk factorsare age, race, and family history [9]. Especially the link between age and presenceof prostate cancer becomes obvious from autopsy studies [10]. Around the age of30, histological detection of prostate cancer is rare. Yet, in approximately 70% to90% of men in the age between 80 and 90 years, evidence of prostate cancer wasfound during autopsy. However, because most prostate malignancies are relativelyslow-growing, men often die with prostate cancer rather than from prostate cancer.With this knowledge, it is not desirable to treat all prostatic tumors. Instead, the riskof disease-specific mortality should be predicted [8].

Tumors require an increased supply of oxygen and nutrients to grow to beyond1-2 mm in diameter [11]. In tumors of clinically significant size (0.5 cm3 [12]), a densenetwork of microvessels is formed to provide the required supplies [11]. This process,named “angiogenesis”, is considered an important prognostic marker for progression ofprostate cancer [13,14]. Through the formation of new microvessels, the microvasculardensity (MVD) increases. Moreover, angiogenic vessels are often faulty and thereforeshow di�erent characteristics with respect to normal vessels; angiogenic vessels can betortuous or saccular, can have high permeability leading to extravasating plasma, canfeature shunting vessels, and often show excessive, irregular branching [11, 15]. Allthese features can potentially be used to detect clinically significant tumors.

1.1.2 Diagnosis of prostate cancerDespite its impressive incidence and mortality rates, prostate cancer still lacks reliablediagnostics. Early detection is di�cult, because prostate cancer is usually asymp-tomatic, particularly in early stages of the disease. In only few cases, lower urinarytract symptoms (LUTS) occur in patients with prostate cancer if a tumor induces apressure increase towards the urethra [9]. Usually, suspicion is raised by an elevatedserum prostate-specific antigen (PSA) level or abnormalities found during a digitalrectal examination (DRE) [8].

Societal Problem 3

Figure 1.1: Schematic illustration of TRUS imaging in the prostate with surrounding struc-tures (left). The zonal anatomy is shown in a transversal section (right).

PSA is a protease produced by prostate epithelium to liquefy seamen [16]. Prostatecancer causes a loss of basal cells and basement membrane in the epithelium, which re-sults in a higher level of PSA in the serum. However, besides prostate cancer, elevatedPSA-levels can also be caused by other factors, such as benign prostatic hyperplasia(BPH, a benign growth of the prostate), infections, trauma, and ejaculation [9]. As aresult, the positive predictive value (PPV) of this test is as low as 30% when applyingthe commonly used threshold of 4.0 ng/mL [17]. Moreover, in over 15% of the PSAtests, prostate cancer is missed [18]. Besides the total PSA level, also the percentageof free PSA (i.e., not bound by inhibitors) was demonstrated to have diagnostic valueand is now recommended for prostate cancer screening [8, 19]. However, histologicalconfirmation is still required.

The second diagnostic test which is routinely applied, DRE, is a test in which thedoctor palpates the posterior surface of the prostate with his finger to search for sti�erregions. Because only superficial tumors can be detected in this way, there is a largechance of missing tumors [20–22]. Some researchers even advocate abandoning DREfrom clinical practice altogether [22].

Extensive randomized trials have been carried out to investigate the benefit ofmass screening for early prostate cancer detection using both PSA and DRE [23, 24].From these studies most urological societies concluded that application of wide-spreadscreening in all men would be inappropriate [8,17]. In fact, over 1000 men would haveto be screened to save one life [25, 26]. Instead, screening should only be applied tomen with an increased risk to die from prostate cancer.

Due to its high accessibility, conventional transrectal ultrasound (TRUS) imaginghas been considered for prostate cancer screening. In some cases, tumors can be seenon B-mode TRUS imaging as hypoechoic regions, but with an accuracy of 50-60% and

4 Introduction

a PPV of 6% TRUS is considered unreliable as an independent diagnostic tool [8,27].In practice, B-mode TRUS is predominantly used to check the prostate for irregularitiesand to estimate its volume [27].

As a consequence of the shortcomings of the previously described tests, prostatecancer diagnosis requires confirmation by biopsy [8]. Since the exact location of tumorsis unknown beforehand, international guidelines recommend systematic biopsy as thepreferred diagnostic tool. Typically, 10-12 biopsy cores should be taken under TRUSguidance according to a geometrical template in which each core covers a part of theprostate. Based on DRE and TRUS, extra cores can be taken from suspicious areas.In practice, TRUS guidance is usually performed manually, making it challenging tofollow the template. Being invasive, this procedure can be painful and carries a risk ofcomplications such as bleedings and infections [28,29]. Moreover, there is a significantchance of missing tumors (⇡50%), requiring a repeat biopsy if indications for prostatecancer persist [30,31]. In fact, in approximately 70% of the patients, the first prostatebiopsy has a negative outcome [32]. In 15-25% of the second biopsies, prostate canceris detected after missing the tumor in the first one [33–35].

Before a treatment plan is made, the risk of a tumor to the patient’s health shouldbe assessed. The main parameters used to make a prognosis for a prostate cancer caseare PSA level, tumor size, and Gleason score [8, 17, 36]. If a tumor is not visible byimaging, its size is estimated from the amount of positive biopsies and the percentageof tumor involvement per biopsy core. The Gleason score consists of two Gleasongrades, which indicate the level of cell di�erentiation and can be determined by mi-croscopic inspection of H&E-stained tissue [37]. A Gleason grade ranges from 1 (welldi�erentiated) to 5 (poorly di�erentiated) and strongly correlates with the aggressive-ness of prostate cancer. Typically, Gleason scores are denoted as X+Y in which X isthe most extensive pattern and Y the highest secondary pattern [38]. Often X and Yare summed, yielding an overall Gleason score between 2 and 10. However, in practice,overall Gleason scores below 6 are seldom reported [39]. In the conventional d’Amicorisk group classification, an overall Gleason score of 6 is associated with low-risk, 7with intermediate risk, and 8-10 with high-risk [40]. In a recent consensus conference,a 5-grade division (6, 3+4, 4+3, 8, 9-10) was considered more appropriate to predictdisease progression [39]. Despite the important role of the Gleason score in treatmentplanning, a retrospective study including 1116 patients showed that 38% of the sys-tematic biopsies undergrades tumors, because the index lesion or high-grade core of atumor may be missed [41]. On the other hand, tumors can also be overgraded (9%)when a small, aggressive part of a tumor is sampled.

1.1.3 Treatment of prostate cancerCurrently, the most regular treatments for confined prostate cancer are radical prosta-tectomy (RP), external beam radiation therapy (EBRT), and brachytherapy [8, 42].RP is a surgical procedure in which the entire prostate including seminal vesicles is

Societal Problem 5

removed. Because the prostate encapsulates the urethra and is surrounded by nervescrucial to the erectile function, common side-e�ects after RP are urinary incontinence(UI) and erectile dysfunction (ED) [43]. In EBRT, the prostate is usually irradiated 5days a week for 4 to 6 weeks with the goal to deliver a curative dose to the prostate, butto spare surrounding tissues [9]. This treatment is often paired with hormonal treat-ment to increase its e�cacy. Besides several mild short-term side-e�ects (e.g., urinarycomplications, rectal infections, and diarrhea), severe long term complications such asED and UI can occur as late as 6 to 8 months after treatment [42]. Brachytherapymakes use of radioactive sources which are temporarily or permanently implementedinto the prostatic tissue [44]. Side-e�ects are similar to those of EBRT.

In the past decades, several alternative treatment options for prostate cancer havebecome available, of which cryosurgical ablation (CA) and high-intensity focused ul-trasound (HIFU) are currently the most promising techniques [8, 9]. CA is a surgicalintervention aimed at killing tumor cells by freezing them at a temperature below-40 °C [45]. In contrast, HIFU damages tissue by focusing the energy of a high powerultrasound beam into a small region [46]. Complications for both of these treatmentsinclude ED, UI, urinary retention, and rectal pain [9, 46].

Although EBRT, brachytherapy, CA, and HIFU could be used to perform focaltreatment, often the entire prostate is treated due to the multifocal character ofprostate cancer and the lack of reliable imaging techniques [44, 47–50]. As a conse-quence, overtreatment is a well-known problem in patients with early-stage prostatecancer [51]. This problem led to the recommendation for active surveillance (AS) inmen with very low-risk prostate cancer [8, 17]. Instead of treating a tumor, diseaseactivity is regularly monitored through clinical tests, such as PSA, DRE, and biopsy,until signs of progression appear. However, for obvious reasons, AS comes with a riskof undertreatment.

1.1.4 The need for prostate cancer imagingThe limitations of current diagnostic and therapeutic options drove researchers tosearch for alternatives. On the diagnostic side, an imaging technique revealing tumorlocations could be used to direct the biopsy needle towards a cancerous area and inthis way increase the sensitivity of biopsies. Ideally, if a technique has a su�cientlyhigh sensitivity and specificity, it could replace biopsies altogether and reduce biopsy-specific morbidity [28, 29]. Furthermore, prostate cancer imaging could play a role indetermining the size of a tumor, which is di�cult, if not impossible, with standardsystematic biopsy. Moreover, a technique able to di�erentiate between slow-growingand aggressive tumors could improve risk stratification and reduce the current problemof overtreatment. On the therapeutic side, an accurate imaging technique could pavethe way for focal treatment options. By destroying cancerous tissue only, severecomplications such as ED and UI, associated with their radical counterparts, could bereduced.

6 Introduction

1.2 Current prostate cancer imaging techniquesCurrently, the most promising imaging techniques for early detection of prostate cancerare based on magnetic resonance imaging (MRI) and TRUS. Single photon emissioncomputed tomography (SPECT) and, in particular, positron emission tomography(PET) are also options for prostate cancer detection [52, 53]. However, their role ismainly limited to detection of bone and lymph node metastases. The limited spatialresolution and the use of ionizing radiation make them unsuited for early detection oraccurate localization [8,52,54]. PET and SPECT are often combined with computedtomography (CT) to obtain more anatomical detail. Although CT has been used tomonitor bone metastases, its performance in cancer detection is inferior to that of theother imaging modalities [52].

1.2.1 Magnetic resonance imagingThe role of MRI in prostate cancer diagnosis has substantially grown in the pastdecade [8, 55]. MRI investigates the response of atomic nuclei to electromagneticradiofrequency pulse sequences [56]. Depending on the adopted sequence, severalanatomic, functional, and metabolic parametric maps can be obtained. T2-weightedimaging (T2WI), di�usion-weighted imaging (DWI), dynamic contrast-enhanced MRI(DCE-MRI) and magnetic resonance spectroscopy imaging (MRSI) are currently themost relevant MRI-based techniques for prostate cancer imaging [55,57].

T2-weighted imaging

T2WI evaluates the transverse relaxation times of hydrogen protons and was tradi-tionally used to display the anatomy. On a T2 map, prostate cancer can typicallybe observed as an ill-defined hypointenste region, much like erased charcoal [55, 57].However, in the PZ several other conditions display features similar to those of prostatecancer [58]. Also in the TZ, prostate cancer detection is challenging due the hetero-geneous signal intensity in this region and an overlap in signal intensity with that ofprostate cancer [59]. Nonetheless, since T2WI also provides anatomical information,it is particularly useful to detect extracapsular extension of tumors [55].

Di�usion-weighted imaging

By DWI, di�usion of water molecules is measured. Because malignant tissue hasdiminished extracellular space and higher cellular density compared to normal tissue,di�usion of water molecules is restricted [11,57]. As a result, prostate cancer appearsas a darker area on DWI [55, 57]. Advantages of DWI are its high contrast betweennormal and cancerous tissue and its ability to detect invasion of tumors into theseminal vesicles. Drawbacks are its low spatial resolution (⇡2 mm) and its sensitivityto magnetic distortions.

Current prostate cancer imaging techniques 7

Magnetic resonance spectroscopy imaging

MRSI assesses the relative concentrations of several metabolites and is able to revealthe increased choline and decreased citrate levels typically encountered in cancer cells[60, 61]. A relation between choline-to-citrate ratio and lesion aggressiveness wasfound [62]. However, clinical application of MRSI is hampered by its very low spatialresolution (⇡5 mm), its long acquisition time (⇡15 min) and the high technical skillrequired from the operators [57, 60]. As a result, its applicability is mostly limited todetecting recurrence and monitoring therapy response [55].

Dynamic contrast-enhanced MRI

DCE-MRI makes use of an intravenously injected contrast medium to visualize bloodflow. Usually, gadolinium-based agents are adopted in combination with T1-weightedimaging [55,57]. These agents are small enough to pass through vessel walls and leakinto extravascular space, especially from vessels with high permeability [63, 64]. Thee�ects of angiogenesis on blood flow, for instance caused by increased MVD, increasedvessel permeability, and increased vessel tortuosity, can be observed on DCE-MRI viathe contrast medium flowing through and leaking from angiogenic vessels. Typicalmarkers for cancer are focal early enhancement and early washout [57, 65]. Besidesqualitative analysis of DCE-MRI, several quantitative methods have been developedbased on fits of the time-concentration curves [64,66–68]. From these fits, curve shapefeatures and pharmacokinetic parameters can be extracted, reflecting blood perfusionand vascular permeability. So far, DCE-MRI has proven its potential for prostate cancerdiagnosis, but its added value with respect to T2WI and DWI remains limited [65,67].

Multiparametric MRI

To benefit from the strengths of each of the imaging techniques, a diagnosis is com-monly made based on two or more MRI maps, referred to as multiparametric MRI(mpMRI). In 2012, a guideline was published by the European Society of Urogen-ital Radiology (ESUR) presenting a structured reporting system for mpMRI, calledPI-RADS [55]. Scores are assigned to T2WI, DWI, MRSI and DCE-MRI using a 5-point scale in which a 1 is assigned for very low and a 5 for very high likeliness ofthe presence of clinically significant prostate cancer. The individual PI-RADS scorescan then be summed to obtain an overall risk score. Yet, despite the introduction ofPI-RADS, interpretation of mpMRI remains di�cult and subjective, particularly in theTZ [69–71].

Recently, PI-RADS was updated to PI-RADS v2, based on clinical evidence [65].In this version, DWI is predominantly used to detect tumors in the PZ and T2W in theTZ. DCE-MRI has been given a limited role and MRSI has been removed altogether.However, based on the first comparative studies between the two PI-RADS versionsthe value of the updated scoring system seems controversial [72–74].

8 Introduction

1.2.2 UltrasoundTRUS imaging is based on pressure waves backscattered by tissue. Its relatively lowcost, high spatial resolution, and wide accessibility compared to MRI make it an impor-tant imaging modality for prostate examination. Currently, TRUS is routinely appliedto obtain anatomical information and guide prostate biopsies. For prostate cancerimaging, conventional TRUS is not su�ciently accurate [5–8]. With the aim of find-ing a cost-e�cient solution for prostate cancer diagnosis and therapy guidance, manypromising TRUS-based techniques have been developed.

Machine learning

From the early 90s on, many groups have adopted machine learning principles toultrasound radiofrequency (RF) signals or TRUS images for prostate cancer localization[75]. This development has lead to a commercialized product, HistoscanningTM (AMD,Waterloo, Belgium) [76]. Although the initial results were promising [76,77], in largerstudies the classification performance was disappointing; an area under the receiveroperating characteristic (ROC) curve of 0.58 [78] and a cancer detection rate of 13.4%[79] were reported.

Doppler

Another technique intensively tested for prostate cancer localization is Doppler imag-ing. The name refers to the Doppler principle, which causes backscattered soundwaves to shift in frequency when reflected from a moving object. By applying Dopplerimaging to blood vessels, more densely vascularized regions, such as tumors, can bevisualized. The two widely applied ultrasound Doppler techniques are color Dopplerand power Doppler. While color Doppler measures the mean frequency shift, powerDoppler integrates the entire Doppler spectrum, making it more sensitive to bloodperfusion [80]. However, its value for prostate cancer localization remains limited,mainly due to its poor sensitivity to low blood flows, typical for angiogenic microves-sels [81,82].

Elastography

Motivated by the increased sti�ness resulting from the increased cellular density intumors, several research groups started investigating elastography for prostate cancerdetection [83]. Strain elastography is a qualitative type of elastography that is availablein most commercial ultrasound machines. This technique measures the compressionand decompression of tissue caused by a push from the probe to the prostate wall. Be-cause the mechanical stress induced by the push is unknown, only relative sti�ness canbe measured by this technique. A major disadvantage is the high operator-dependency,especially in the PZ, where the push is applied [84]. Consequently, results reported inliterature show strongly varying cancer detection rates [84–87].

Current prostate cancer imaging techniques 9

To reduce the operator dependency, methods have been developed in which theexternal push is replaced by local acoustic ones [83, 88]. The two main approaches,also available in commercial ultrasound scanners, are acoustic radiation force impulseimaging (ARFI) and shear-wave elastography (SWE). ARFI applies several acousticpushes after which local tissue displacement is measured. Much like conventionalstrain imaging, the resulting strain maps represent relative sti�ness. The initial resultsfor prostate cancer detection are promising, but the available evidence is still limited[89,90].

SWE, first introduced by Sarvazyan et al. [91], is based on the relation betweenshear wave speed and the shear modulus of the tissue in which the shear wave ispropagating. By making assumptions on the (in)compressibility of the imaged tissue,its Young’s modulus can be estimated. Later, ultrafast imaging [92–95] was used tofacilitate shear wave tracking [96], which lead to a real-time implementation of thistechnique [95]. A big advantage of SWE over the previously described elastographytechniques is its ability to measure absolute sti�ness, allowing a standardized thresholdto classify benign and malignant tissue. Although researchers agree that SWE bearsgreat potential for tumor localization, more studies are required to determine its actualvalue for prostate cancer diagnosis [97–100].

Contrast-enhanced ultrasound

A technique particularly suitable to visualize blood flow in microvessels is dynamiccontrast-enhanced ultrasound (DCE-US). Ultrasound contrast agents (UCAs) consistof encapsulated gas bubbles with a size between 0.5 and 10 µm, commonly referredto as “microbubbles” [101]. They are suitable for intravenous injection. Because thesize of microbubbles is comparable to that of red blood cells, they can flow throughangiogenic microvessels. Yet, unlike most contrast agents used in DCE-MRI, their sizeprevents extravascular leakage. These properties make DCE-US an excellent imagingmodality for hemodynamic analysis.

Already in 1968, it was discovered that gas bubbles could enhance ultrasonic signalsfor better identification of the mitral valve and the aortic root wall [102]. Much later,in 1990, the first microbubbles capable of crossing the pulmonary circulation werereported [103]. With respect to prostate cancer imaging, UCAs were initially usedto increase the sensitivity of Doppler imaging in microvessels to reveal angiogensis[104,105]. Nowadays, most ultrasound scanners are equipped with a contrast-specificimaging mode which exploits the nonlinear response of microbubbles to ultrasonicexcitation [105]. A DCE-US recording can be made after administration of a UCA bolusor by continuous injection [106,107]. Optionally, bubbles in the imaging plane can bedestroyed by a high-intensity ultrasound flash to appreciate and evaluate reperfusion[108,109]. The resulting contrast video is analyzed qualitatively or quantitatively.

In a qualitative analysis, DCE-US videos are inspected for areas of early, rapid,and increased enhancement [110, 111]. This approach has shown promising results

10 Introduction

for biopsy targeting, but the sensitivity (⇡70%) is not su�ciently high to replacesystematic biopsy [106, 107, 110, 112]. Moreover, this approach is hampered by agradual learning curve and high inter-observer variability [113].

To overcome the observer-related drawbacks of qualitative DCE-US and to extractcancer-specific features which are di�cult to see in unprocessed DCE-US recordings,several quantitative techniques have been developed. Most of them are based onthe backscattered acoustic intensity of DCE-US measured over time, referred to as“time-intensity curve” (TIC). For the relatively low concentrations of UCA used inDCE-US imaging, the relation between acoustic intensity and contrast concentrationis approximately linear [114].

In general, two types of parameters are extracted from TICs: parameters extracteddirectly from the TIC shape and model-based parameters. The former type of parame-ters, such as wash-in time (WIT, also referred to as rise time), wash-in rate (WIR), andpeak intensity (PI), typically feature e�ects based on timing and amplitude [115,116].For the latter approach, several models are available for both bolus and destruction-replenishment TICs [68, 109, 117–119]. Since commercial ultrasound scanners usuallyapply a logarithmic-like compression to visualize the acoustic intensity, a linearizationstep is typically required for model fitting. Additionally, the tail of a TIC has to betruncated to remove e�ects caused by blood recirculation. From the fits, hemodynamicparameters can be extracted.

Recently, a new type of microbubbles has been developed, which target angiogenicvasculature [120–122]. These microbubbles are decorated with antibodies that bind toreceptors specifically present in angiogenic vasculature. By using DCE-US, the boundmicrobubbles can be imaged to reveal tumor locations. In addition, these microbubblescan be loaded with drugs or genes which are released in situ after disrupting them byhigh acoustic pressure. Targeted microbubbles are currently still under investigationfor both cancer imaging and therapy [121,123].

A very recent development regarding UCAs is the growing interest in so-callednanodroplets [124]. When intravenously injected, they are in a liquid phase and havediameters below 1 µm. Due to their small size, they can pass trough highly perme-able angiogenic vessels and extravasate into interstitial space. After the droplets haveaccumulated there, their liquid phase can be changed into a gas phase by ultrasonicstimulation, which makes them detectable by ultrasound imaging. Also variants ofnanodroplets combined with molecular and photoacoustic imaging, as well as applica-tions in drug delivery, are being investigated [124–127].

Contrast-ultrasound dispersion imaging

Although most quantitative DCE-US approaches mainly assess blood perfusion, e�ectsof angiogenesis on perfusion are complex and may be contradicting [115, 128, 129].On the one hand, the lack of vasomotor control, the presence of arteriovenous shunts,and the increased vascular cross-sectional area have a negative e�ect on blood flow

Validation issues for emerging imaging techniques 11

resistance. On the other hand, the small vessel diameters, high tortuosity, and ex-travascular leakage may increase flow resistance. Based on the hypothesis that thesee�ects may be better reflected by blood dispersion rather than perfusion, contrastultrasound dispersion imaging (CUDI) was recently introduced [130–133].

In the initial approach to CUDI [130], a reparameterized local density random walk(LDRW) model was fitted to TICs. From these fits, a parameter = v

2/2D could be

extracted for each pixel, where v represents the blood flow and D the dispersion. Thefirst in-vivo results showed good correlation between and the presence of cancer [130].

Later, it was observed that similarity between TIC curves in a region is relatedto the value of in that region [131–133]. This observation lead to several CUDIimplementations in which the similarity between a TIC and those in a ring-shapedkernel around it was computed [131–133]. In the first implementation [131], thecorrelation between amplitude spectra of TICs was computed, referred to as ”spectralcoherence” (⇢). Misalignment between TICs due to di�erences in arrival times wereintrinsically removed by ignoring phase information.

In an improved implementation [133], a time-window was applied to each TICstarting from contrast appearance and ending before the second bolus passage. In thisway, the similarity analysis was performed on the most relevant part of the TIC. More-over, a speckle regularization filter was adopted to compensate for depth-dependencyand anisotropy of the ultrasound imaging system.

Finally, also temporal correlation (r) was adopted to assess similarity betweentime-windowed TICs [132]. In a preliminary validation by histology in 8 patients, apromising area under the ROC curve of 0.89 was achieved. In a comparison betweenCUDI and mpMRI in 11 patients, both the sensitivity (81% vs. 72%) and NPV (92%vs. 88%) were higher for CUDI [134].

1.3 Validation issues for emerging imagingtechniques

Because no reliable prostate cancer imaging technique is readily available, validation ofemerging techniques is not trivial. Generally, two types of ground truth are consideredfor validation: biopsy and RP specimens. Because the chance of missing tumors bysystematic biopsy is high [31], this does not represent a valid reference to assess sen-sitivity and specificity of new imaging techniques. Instead, prostate cancer detectionrates by targeted biopsies based on imaging are often compared with those by regularsystematic biopsies to determine the clinical value of a new technique [135–138].

When using RP specimens as a ground truth, the prostate is typically processedfollowing the recommendations for pathology reporting [139, 140]. In this procedure,the specimens are fixated, cut into 3-to-4-mm thick slices, and H&E-stained, afterwhich they are inspected for malignancy under a microscope. Compared to biopsy,less tumors are missed by the ground truth, the size of tumors can be estimated more

12 Introduction

accurately, and the assigned Gleason scores are more reliable. However, the populationin a study using RP for validation is biased towards cancer presence.

Another obstacle to overcome is the misalignment between the positions of thehistology slices and those of the imaging planes. In fact, an imaging plane can covermultiple histology slices if their orientations strongly di�er. Often, the histology sliceclosest matching the imaging plane is manually selected [66,130–133,141–143]. Thisprocedure may a�ect the integrity of a study. A workaround can be found by includingonly those tumors that are visible in multiple consecutive slices [134]. However, onlylarge tumors can be included in this way.

Besides slice selection, also prostate deformation is a problem for validation byRP. During specimen preparation, the prostate typically shrinks by approximately 15%[144, 145]. Additionally, non-a�ne deformations occur as a result of the pressureproduced by a transrectal probe or endorectal coil pushing against the posterior surfaceof the prostate and as a result of the absence of surrounding tissue after surgery.

Because of the uncertainty on the tumor location caused by all deformations, oftenvalidation is performed by dividing the imaging planes in 4 or more sectors [99, 134].In each sector, cancer presence is then compared with imaging. Another way toperform validation, which may be more accurate but less objective, is by manuallydefining benign and malignant regions in the imaging plane based on large benign andmalignant areas on the histology slice [66,130–133]. In either case, individual smallertumors cannot be considered for validation.

To perform an objective and accurate validation, registration between histologyand imaging is required. Driven by the recent boost in research in MRI-based prostatecancer imaging, several MRI-histology registration methods for the prostate have beenproposed. In some methods [146–148], alignment between MRI planes and histologyslices is assumed, which makes them non-transferable to TRUS imaging. Other ap-proaches [149–153] require additional, time-consuming steps which may interfere withthe clinical workflow.

Until now, not many studies have focused on TRUS-histology fusion. The rigid-body registration of ex-vivo TRUS performed in [154] is not suitable for in-vivo reg-istration. Another method [155] aligns TRUS and histology from ellipsoid fits afterwhich a thin-plate-spline transformation is applied to refine the registration. In [156],a technique applying a�ne transformation based on particle filtering was adopted. Forneither of the techniques proposed in [155,156], an indication of the registration errorwas reported.

1.4 ObjectiveThe flaws of current diagnosis of prostate cancer as described in Section 1.1 lead toundertreatment, overtreatment, and hamper broad adoption of focal therapy. WhereasMRI techniques seem to find their way into clinical practice, cheaper and more acces-

Outline of the thesis 13

sible ultrasound-based methods stay behind. As already mentioned, CUDI is currentlyone of the most promising ultrasound-based methods for prostate cancer localization.However, there are still some limitations to the work presented on CUDI so far.

Until now, only linear similarity has been explored. Nonlinear, statistical similaritymeasures could possibly reveal more subtle di�erences between TICs. Moreover, 2DDCE-US captures in-plane flow only, making it dependent on the direction of imaging.In addition, UCA flow is a 4D process by nature. Therefore, not all kinetics arecaptured by the 2D data.

The current implementation of CUDI requires an injection of UCA for each imagingplane. Because this process takes several minutes, it is in practice not feasible to coverthe entire prostate by 2D CUDI and tumors between imaging planes will be missed.This limitation makes it impossible to make a reliable diagnosis based on CUDI withoutinterrupting the clinical workflow.

Until now, CUDI has been validated in very small patient groups using manuallydefined contours marking benign and malignant areas. Due to the inaccuracy resultingfrom cognitive registration, only large tumors have been included in validation studies.Moreover, the inter-observer variability inherent to this type of validation could a�ectthe reproducibility.

The objective of this thesis is to bring CUDI closer to clinical use by overcomingthe mentioned limitations. In particular, the aim is to:

• improve the method’s accuracy,

• speed up the clinical workflow,

• and extend the clinical evidence.

1.5 Outline of the thesisEach chapter in this thesis consists of an article published in, or submitted to a peer-reviewed journal. An exception is Chapter 4, which has been published in the proceed-ings of the International Ultrasonics Symposium (IUS) 2015. A list of all publicationscan be found from page 167 onwards. The articles have been incorporated in this the-sis with minimal modifications (i.e., without modifying the content) and are thereforeself-contained.

In Chapter 2, the similarity approach of CUDI is extended towards non-linear simi-larity by using mutual information (I) as a similarity measure. A strategy for estimat-ing I is proposed. The relation between I and dispersion-related parameter is thenexplored by simulating TIC curves, including noise typically encountered in DCE-USimaging, while varying their respective values. Moreover, several algorithm settingsand design choices are tested both by simulation and in vivo. Finally, in a region-based validation, the classification performance of I, as well as those of r, ⇢, and

are evaluated in 23 patients referred for RP. This chapter has been published as [J4].

14 Introduction

As described in Section 1.4, the 2D implementation of CUDI was subject to severaldrawbacks which could be overcome by using 3D DCE-US. First, when using 3D DCE-US, the entire prostate can be imaged using only one bolus of UCA, strongly improvingthe clinical workflow. Second, no out-of-plane flow is missed, possibly increasing theaccuracy of CUDI. Finally, 3D imaging facilitates registration with real-time ultrasoundfor accurate biopsy guidance, with MRI datasets for multimodal characterization oflesions, and with 3D histology for accurate validation. However, the technical specifi-cations of commercially available transrectal 3D DCE-US imaging are quite di�erentthan those of 2D DCE-US imaging. In particular, the temporal and spatial resolutionare strongly a�ected. These di�erences and their e�ect on the use of 3D DCE-US forCUDI are evaluated in Chapter 3. Additionally, 3D CUDI by linear similarity (r and ⇢)is implemented as the first 3D quantitative DCE-US imaging technique for prostatecancer. The resulting parametric maps are compared with 12-core systematic biopsyand 2D CUDI in two patients. This chapter has been published as [J6].

Chapter 4 introduces a 3D implementation of CUDI based on I, described inChapter 2. A preliminary validation of the method for prostate cancer detection isperformed in 3 patients. This chapter has been published as [IC2].

To provide a first indication of the clinical value of quantitative 3D DCE-US imag-ing, in particular, 3D CUDI, the methods introduced in Chapters 3 and 4 are comparedwith systematic biopsy outcome in 43 patients. Additionally, some well-established per-fusion parameters are extracted from the TICs in the 3D DCE-US recordings. Moti-vated by the importance of the Gleason score in prostate cancer staging, the correlationbetween parameter values and Gleason scores is also investigated. This chapter hasbeen submitted for publication as [J2].

Chapters 6-8 address the validation problem for emerging prostate cancer imagingtechniques. We propose a 3D elastic registration algorithm to fuse ultrasound andhistology data obtained from RP specimens. The aim of the algorithm is to elimi-nate user-dependency and improve validation accuracy. By improving the registrationaccuracy, smaller tumors can be included in validation studies, reducing the currentvalidation bias towards larger tumors. Moreover, a wider variety of tumors in theground truth could serve machine learning applications.

Before tumors marked in histology slices can be used in a 3D registration algorithm,they have to be interpolated to obtain 3D volumes. In Chapter 6, a tumor interpolationmethod based on radial basis functions (RBF) [1, 157] is proposed. Because priorknowledge about the shape of the tumor between slices is limited, a straightforwardassumption of minimal curvature is made. The method is tested on several in-silicophantoms. In a series of simulations, the impact of tumor size and shape, slicingthickness and angle, and inter-slice misalignment on the accuracy of the reconstructedtumor is assessed. This chapter has been submitted for publication as [J1].

Following the tumor interpolation, a surface-based, elastic registration algorithmis described in Chapter 7. The prostate shapes to be registered are represented bytriangulated meshes. First, the meshes are aligned by a�ne registration. Two ap-

Outline of the thesis 15

proaches for a�ne registration are investigated: a step-wise approach and an iterativeclosest-point (ICP) algorithm [158]. In the step-wise approach, translation, rotation,and scaling are applied separately. The ICP algorithm iteratively finds correspondingpoints in the reference and source meshes, between which the distance is then min-imized. While the step-wise approach provides more deformation freedom, the ICPtends to be more robust due by remaining closer to the initial alignment. After a�neregistration, elastic registration is performed by parametric active surfaces, commonlyadopted in segmentation and motion tracking in medical images. Active surfaces cantransform from one shape to another, while keeping the nodal spreading along themesh roughly intact. In this way, most shape deformations can be tracked withoutlocally destroying the mesh, improving robustness. After elastic surface registration,surface deformations are interpolated to obtain the full 3D transformation map fromsource to reference shape. Two interpolation techniques are investigated: naturalneighbor interpolation and finite elements of uniform, nearly incompressible material.Because no additional equipment or steps are required outside routine prostate ex-aminations and RP processing, interference with the clinical workflow, encountered inmost registration methods designed for MRI, is minimized. All approaches are testedin vitro using gelatin phantoms with embedded markers, providing a 3D point-to-pointregistration error. The registration error is also assessed in vivo in 7 patients using theborder of the PZ as validation reference. This chapter has been published as [J5].

The algorithm described in Chapter 7 is more extensively validated in vivo inChapter 8 based on histology and ultrasound data from the prostates of 14 patients. Inthis validation, 3D ultrasound datasets are reconstructed from sweep videos, obtainedby scanning the prostate from base to apex. The histology slices are then reconstructedby ultrasound imaging after applying the registration method that performed bestin Chapter 7. In contrast to the work in Chapter 7, where only the border of thePZ was used, now also the urethra, cysts, and calcifications are used as validationlandmarks. In this way, most parts of the prostate are represented by the validationresults. Registration errors are evaluated per prostate section (base, mid, apex) andper landmark type. This chapter has been submitted for publication as [J3].

In Chapter 9, general conclusions and critical discussion of the work presented inthis thesis are given. Furthermore, potential future applications and research lines areproposed.

16 Introduction

Chapter2Similarity analysis using mutualinformation

The content of this chapter has been published as [J4]:

S.G. Schalk, L. Demi, N. Bouhouch, M.P.J. Kuenen, A.W. Postema, J.J.M.C.H.de la Rosette, H. Wijkstra, T.J. Tjalkens, and M. Mischi, “Contrast-enhancedultrasound angiogenesis imaging by mutual information analysis for prostate cancerlocalization,” IEEE Trans. Biomed. Eng., in press. © 2016, IEEE.

18 Similarity analysis using mutual information

AbstractObjective: The role of angiogenesis in cancer growth has stimulated research aimedat non-invasive cancer detection by blood perfusion imaging. Recently, contrastultrasound dispersion imaging was proposed as an alternative method for angiogenesisimaging. After the intravenous injection of an ultrasound-contrast-agent bolus,dispersion can be indirectly estimated from the local similarity between neighboringtime-intensity curves (TICs) measured by ultrasound imaging. Up until now, onlylinear similarity measures have been investigated. Motivated by the promising resultsof this approach in prostate cancer (PCa), we developed a novel dispersion estimationmethod based on mutual information, thus including nonlinear similarity, to furtherimprove its ability to localize PCa.

Methods: First, a simulation study was performed to establish the theoretical linkbetween dispersion and mutual information. Next, the method’s ability to localize PCawas validated in vivo in 23 patients (58 datasets) referred for radical prostatectomyby comparison with histology.

Results: A monotonic relationship between dispersion and mutual information wasdemonstrated. The in-vivo study resulted in a receiver operating characteristic (ROC)curve area equal to 0.77, which was superior (p=0.21-0.24) to that obtained bylinear similarity measures (0.74-0.75) and (p<0.05) to that by conventional perfusionparameters (0.70).

Conclusion: Mutual information between neighboring TICs can be used to indirectlyestimate contrast dispersion and can lead to more accurate PCa localization.

Significance: An improved PCa localization method can possibly lead to better grad-ing and staging of tumors, and support focal-treatment guidance. Moreover, futureemployment of the method in other types of angiogenic cancer can be considered.

Introduction 19

2.1 IntroductionProstate cancer is one of the most common forms of cancer in the world. In theUnited States it accounts for 26% and 9% of all cancer diagnoses and deaths in men,respectively [159]. To date, prostate cancer is still diagnosed using systematic biop-sies, which consist of taking a dozen of geometrically distributed specimens from theprostate using a core needle. Systematic biopsy is invasive and has a low sensitivity;moreover, it carries a risk of infection, sepsis, and bleeding [29, 160]. Due to theinability of current diagnostics to accurately localize and grade prostate cancer, thismalignancy is often treated using whole-gland treatments (e.g., radical prostatectomy,external beam radiotherapy, brachytherapy), which expose patients to severe side ef-fects such as incontinence, sexual dysfunction, and gastrointestinal toxicity [42]. Animaging technique able to detect and locate cancer at an early stage could improveboth prostate cancer diagnosis and treatment: it could lead to better staging and earlygrading of tumors, and open doors to focal treatment. However, a reliable imagingtechnique requires reliable prognostic markers.

The established link between angiogenesis (the formation of new vessels) and can-cer growth [161] has opened new horizons towards better imaging techniques. Par-ticularly, a local increase in microvascular density (MVD) as a result of angiogenesishas been considered as a prognostic marker for cancer aggressiveness and metasta-sis [162–165]. Several imaging methods aim to detect this higher MVD through araise in tissue perfusion. Most of these methods are based on dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), Doppler ultrasound imaging ordynamic contrast-enhanced ultrasound (DCE-US) [113,166–168].

Due to its real-time availability at the bedside, ultrasound o�ers a practical andcost-e�ective alternative to MRI for prostate imaging. DCE-US is especially interest-ing for tumor angiogenesis imaging, because of its ability of highlighting the low bloodflow in microvasculature. This ability results from the employment of an ultrasound-contrast agent (UCA), typically consisting of gas-filled microbubbles that can be in-jected into the blood stream. Due to their size, comparable to that of red blood cells,these microbubbles flow through the smallest microvessels and, unlike most MRI con-trast agents, do not extravasate into the interstitial space, which makes them moresuitable for hemodynamic quantification [169]. Moreover, their high echogenicity andnonlinear response to acoustic waves make it possible to enhance signals coming fromvessels while suppressing signals coming from other tissue [170].

In DCE-US imaging, typically, a sequence of images based on backscattered acous-tic intensity of microbubbles is recorded. Next, a time-intensity curve (TIC), repre-senting the evolution of the UCA concentration over time, can be produced at eachpixel and further analyzed (see Fig. 2.1).

Several methods based on DCE-US have been proposed for angiogenesis detectionby assessment of tissue perfusion. Often, quantification is performed by extractingamplitude and time features from the measured TICs. Up until now, DCE-US perfusion

20 Similarity analysis using mutual information

Figure 2.1: Acquisition of a time-intensity curve. In the sub-figures, frames of a contrast-enhanced ultrasound sequence are given (a) before wash-in, (b) after wash-in, and (c) duringwash-out of contrast agents. The unprocessed image intensity q over time (referred to as“time-intensity curve”) at the pixel indicated by the dots is given in (d). The dashed lines in(a)-(c) represent the prostate boundary.

quantification has not shown reliable angiogenesis detection results in the prostate [11].This could in part be due to the complex influence of the geometrical and structuralproperties of tumor microvessels on microvascular perfusion.

In fact, tumor microvessels di�er, both structurally and functionally, from normalvessels. Normal blood vessels are relatively straight, branch by bifurcation, and have apredictable diameter. In contrast, tumor microvessels typically show irregular branch-ing, have an unpredictable vessel diameter, high tortuosity, and contain arteriovenousshunts. Moreover, tumor microvessels can be leaky, which allows plasma to leak intothe interstitial space, contributing to a high interstitial pressure [11,162]. Whereas ar-teriovenous shunts and high microvascular density stimulate perfusion, high interstitialpressure, high tortuosity, and small vessel diameters oppose it [11,128,171].

Recently, contrast ultrasound dispersion imaging (CUDI) has been proposed as analternative method for angiogenesis imaging [130–133]. Considering the geometricalproperties of the microvascular architecture, dispersion may in fact be more suitablefor detecting angiogenic processes than perfusion.

So far, two di�erent approaches have been proposed to perform CUDI. The firstapproach estimates dispersion by fitting each TIC with a convective-dispersion modelin the time domain [130,172]. The second approach is based on an indirect estimationof dispersion, achieved by computing the similarity between neighboring TICs using

Methods 21

linear measures such as spectral coherence and temporal correlation [131–133].Motivated by the promising performances of the second approach in particular, this

paper presents a new method of dispersion estimation by using mutual informationas a similarity measure. As opposed to the linear measures, mutual information alsoallows the exploration of nonlinear connectivity between TICs [173].

The method was validated by simulation of DCE-US recordings for several dis-persion levels, while using di�erent settings. Additionally, an in-vivo validation wasperformed for prostate cancer imaging on 58 datasets from 23 patients referred for radi-cal prostatectomy (RP). The generated parametric maps were validated by comparisonwith histopathology after RP. Results were compared with other CUDI parameters andTIC features used to estimate local perfusion. A preliminary version of this work hasbeen reported in [174].

2.2 Methods

2.2.1 In vivo data acquisitionAll patient data has been recorded at the AMC University Hospital (Amsterdam, TheNetherlands) after obtaining approval from the local ethics committee and writteninformed consent from the participating patients.

After a 2.4-mL bolus of SonoVue® (Bracco, Milan, Italy) UCA had been intra-venously injected, a two-minute 2-dimensional DCE-US sequence was recorded usinga Philips iU22 (Philips Healthcare, Bothell, WA) ultrasound machine equipped witheither a C8-4v or a C10-3v transrectal transducer. Power modulation contrast imagingwas adopted at 3.5 MHz and a mechanical index equal to 0.06 was used. The dynamicrange and gain were set such that a low signal (baseline) was visible before injectingthe UCA and peak signals were prevented from clipping. All sequences were storedin Digital Imaging and Communication in Medicine (DICOM) format using losslesscompression.

For further processing, the RGB values in the color-coded DCE-US sequenceswere converted to 8-bit quantization levels, q, based on the color map used by thescanner. TICs are actually time sequences of q (see Fig. 2.1). A logarithmic relationexists between q and the backscattered acoustic intensity A [130]. Because A and theUCA concentration, CUCA, are linearly related for CUCA lower than 1 volh Sonovue®

dilution [114,130], q can be considered as a logarithmically compressed representationof CUCA.

2.2.2 CUDI by mutual informationIn the first approach presented for CUDI, UCAs were modeled to move according toa convection-dispersion process [130]. From the model, a local parameter = v

2/2D

was extracted for the TIC in each pixel (after applying spatial downsampling), in

22 Similarity analysis using mutual information

which v and D represent the UCA velocity and dispersion, respectively. Based on thesame model, the local degree of dispersion can be indirectly estimated using similaritymeasures [131–133]. This approach originates from the observation that the shapesimilarity between TICs is influenced by the local degree of dispersion. TICs obtainedfrom a low dispersion region are in fact more similar than those obtained from a regionwith a higher dispersion. The assessment of similarity between neighboring TICs cantherefore be an indirect measure of local dispersion. A monotonic relation between

and linear similarity between neighboring TICs, measured by the spectral coherence ⇢

or correlation coe�cient r, has been shown in [132,133].The more general similarity measure implemented here is mutual information,

which quantifies the degree of statistical dependency between two random variables.In contrast to ⇢ and r, mutual information is not limited to linear connectivity, andtherefore allows the exploration of non-linear relationships between TICs. For thisreason, we expect it to reveal more subtle changes in similarity, which could result inmore accurate dispersion imaging.

Before calculating the mutual information, a Wiener deconvolution filter [133]was adopted to compensate for the depth-dependency and anisotropy of the spatialresolution of the ultrasound imaging system. The filter was calibrated to regularize thespeckle size to approximately 1.6 mm as proposed in [174]. Following [174], spatialdownsampling of a factor 3⇥3 was applied, greatly decreasing the computation time.

After the preprocessing steps, TICs were aligned according to their appearance time(AT), which is defined as the time at which a filtered TIC reaches 10% of its peakvalue. As a result, estimations of similarity between TIC shapes were not disruptedby phase di�erences. The aligned TICs were then windowed using a window with alength tw. The roles of the time window were to focus on the most relevant part ofthe TIC, which contains the first UCA passage, and to reduce the computation time.

For each pixel, the similarity was estimated as the mutual information betweenthe TIC in this pixel and to those in a kernel around it. We chose the shape ofthe kernel to be ring-shaped with an inner radius of 1 mm and an outer radius of2.5 mm (see Fig. 2.2) as proposed in [131]. The inner radius should prevent a bias inmutual information caused by the imaging resolution, for which the speckle size wasregularized to 1.6 mm (yielding a correlation equal to 50% between pixels at 0.8 mmdistance from each other). The outer radius is a tradeo� between the number of TICsthat can be used to accurately estimate the mutual information and the resolution ofthe final similarity map, which should be su�cient to detect tumors at an early stage.In fact, the angiogenic switch typically occurs when a tumor grows beyond 2-3 mm indiameter [175].

In the process of computing the mutual information, four assumptions (AS1-AS4)were made to reduce the computational complexity:

AS1 time samples within a TIC are independent of each other,

AS2 the occurrence of samples in a TIC is a stationary statistical process,

Methods 23

1.0 mm

2.5 mm

Center pixelKernel pixelsKernel pixels after downsampling

Figure 2.2: The kernel used for the similarity analysis.

AS3 a TIC in the kernel is statistically dependent on the TIC in the center pixelonly,

AS4 TICs in each of the kernel pixels can be described by the same statisticalprocess.

The validity of these assumptions is discussed in Section 2.4. In the remainder of thissection, assumptions applied during the derivation of the mutual information will beindicated in brackets.

We modeled TICs in a center pixel as a set of F independent and identicallydistributed (IID) data points obtained from the random variable C (AS1 and AS2),where F is the number of frames. TICs in the N kernel pixels were considered tobe samples taken from a random variable K

N . The mutual information, indicated bysymbol I, between C and K

N could then be written as [176]

I(KN, C) =

X

kN2KN

X

c2CPKN ,C(k

N, c) log2

⇣PKN ,C(k

N, c)

PKN (kN )PC(c)

⌘ (2.1)

with

PKN (kN) =

X

c2CPKN ,C(k

N, c),

PC(c) =

X

kN2KN

PKN ,C(kN, c).

24 Similarity analysis using mutual information

Here, C = K = {0,1,...,Q� 1} where Q is the size of the alphabet (i.e., the numberof quantization levels) used to encode a TIC. It can be observed that I(K

N, C) is

dependent only on the joint distribution of KN and C. This distribution is given bythe joint probability mass function (PMF), PKN ,C(k

N, c).

The PMF contains probabilities that combinations of TIC values in the center pixeland the kernel around it occur at the same time. High values in the PMF are relatedto a higher predictability of kernel TICs from the center TIC and mutual informationis a measure of this predictability.

Using the chain rule for joint probabilities, we could rewrite PKN ,C(kN, c) as

PKN ,C(kN, c) = PC(c)PKN |C(k

N |c). (2.2)

In (2.2), PC(c) is the probability for the TIC in the center pixel to have value c andPKN |C(k

N |c) is the conditional probability of KN

= kN , given C = c. Given the

IID process describing the center TIC (AS1 and AS2), the number of occurrences Fc

of each quantization level in a TIC followed a multinomial distribution [177]. Using amaximum likelihood estimator, PC(c) could then be estimated as [177]

PC(c) =Fc

F. (2.3)

To estimate the conditional probability PKN |C(kN |c) we assumed each component

of KN to be dependent only on c (AS3). In that case, we could write PKN |C(kN |c)

as

PKN |C(kN |c) =

NY

i=1

P (ki|c), (2.4)

with ki being a quantization level in the ith TIC in the kernel.

By applying the assumption that all TICs in the kernel originate from the samestatistical process (AS4), the total number of occurrences Nk|c of a quantizationlevel k in the entire kernel in a frame for which C = c again followed a multinomialdistribution. Analogous to PC(c), the maximum likelihood estimation PKN |C(k

N |c)of PKN |C(k

N |c) was then given by

PKN |C(kN |c) =

Nk|c

NcN. (2.5)

Substituting equations (2.3) and (2.5) into (2.2) yielded the estimated PMF

PKN ,C(kN, c) =

Nc

F

Nk|c

NcN=

Nk|c

FN, (2.6)

which could be used to compute I(KN, C) in (2.1).

Methods 25

2.2.3 Additional considerationsSeveral factors can a�ect the estimation of I(KN

, C), such as the applied preprocess-ing steps, the number of quantization levels, Q, used to describe TICs, the scannersettings (e.g., gain and dynamic range), the time window tw, and the type of DCE-USdata used (linear or logarithmic). These factors should be taken into considerationbefore using the presented method and were tested in simulations and in the patientstudy.

As an additional preprocessing step, a temporal low-pass filter with a cuto� fre-quency of 0.5 Hz could be applied to increase the SNR, because the bandwidth of thefrequency spectrum of a TIC containing the UCA kinetics in the prostate is limited to0.5 Hz [131].

If the full 8-bit range is used to code the TICs, Q = 256. However, it can beadvantageous to compress the data by using a lower value for Q to avoid sparsity inPKN ,C(k

N, c).

Because the absolute quantization levels in the TIC may be influenced by thescanner settings, it may be more accurate to only look at the similarity betweenshapes of the curve. To this end, each curve can be scaled between its minimumand maximum over the Q quantization levels before running the mutual informationanalysis. We refer to this procedure as “TIC normalization”.

Instead of the logarithmically compressed TICs obtained from the DICOM files,linearized TICs can be used. Linearization requires a conversion from quantizationlevel q to acoustic intensity A, which can be realized as described in [130]. Using Q

equally spaced quantization levels, the linearized data can then again be quantized toperform a mutual information analysis. Compared to log-compressed data, a linearizedcurve results in a higher resolution for the representation of high UCA concentrationsand in a lower resolution for low concentrations. As a result, the details around the peakof a TIC could become more visible. However, linearization brings back multiplicativenoise [178–180] particularly at high quantization levels in the TIC, which may corrupta robust estimation of I.

As an example, the average PMF PKN ,C(kN, c), computed over a benign and

malignant region, using TIC normalization with Q = 64 is given in Fig. 2.3. A blurryPMF, like the one for benign tissue indicates less mutual information between thecenter and kernel TICs, whereas the higher values around the diagonal of the PMF formalignant tissue indicate higher mutual information.

2.2.4 SimulationTo investigate the relation between I and , with inversely related to the UCAdispersion, we performed a simulation study in which TICs were described by themodified local-density random walk (LDRW) model presented in [130]. The concen-

26 Similarity analysis using mutual information

Figure 2.3: Estimated PMFs PKN ,C(kN, c) averaged over (a) a benign (average I = 0.71)

and (b) a malignant tissue region (average I = 1.71) using normalized, log-compressed datawith 64 quantization levels.

tration CUCA(t) as a function of time, t, is then given by

CUCA(t) =

8<

:↵

q

2⇡(t�t0)exp(

�(t�t0�µ)2

2(t�t0)), for t > t0

0, otherwise,(2.7)

in which µ and t0 represent the mean transit time and theoretical injection time,respectively. The parameter ↵ is a scaling factor equal to the area under the curve andis set to 1 to obtain a probability density function of arrival times of single microbubblesP (tarr) = CUCA(t)|↵=1. If we discretize the time space in equal intervals with length�t (inverse to the frame rate), the number of microbubbles observed at a certaintime interval n follows a binomial distribution [180]. For a high total number ofmicrobubbles Btot and a low �t, the binomial distribution may be approximated by aPoisson distribution [181]. Here, we used Btot = 4000, in line with the values used in[180], and �t = 0.1 s, similar to the frame rate observed in DCE-US sequences. Sampleswere taken from this distribution for each n to simulate the number of microbubblesB[n].

Since the acoustic intensity A[n] is linearly related to the UCA concentration andhence to B[n] for low concentrations [114,130], A[n] can be written as

A[n] = aBAB[n] +A0, (2.8)

with A0 being the acoustic intensity when no UCA is present and aBA the linearconversion factor between the number of microbubbles and the acoustic intensity. Inthis simulation, we used aBA = 1.

Furthermore, additive Gaussian noise zadd ⇠ N (0,�2a) and Rayleigh-distributed

multiplicative noise R(•), typically present in ultrasound imaging [178, 182], wereincluded in the simulation, extending equation (2.8) to

A[n] = R(aBAB[n]) +A0 + zadd. (2.9)

Methods 27

The value of �a was set to 0.15, based on the standard deviations of A around baselinesobserved in patients.

Finally, a conversion from A[n] to quantization level q[n] was made assuming alogarithmic relation

q[n] =255

DR 10 log10(A[n]), (2.10)

where scaling of the curve is controlled by the dynamic range (DR). Here we usedDR = 25 dB, conform the dynamic range used in part of the in-vivo measurements.An example of a simulated TIC is given in Fig 2.4.

To simulate a DCE-US sequence, TICs with constant values of , µ, and t0 weregenerated in a grid of 212⇥212 pixels. The pixel size was set to 0.45 mm, similar tothe downsampled pixel size in vivo, and the temporal resolution was 1/�t = 10 Hz.Mutual information analysis was then performed on the simulated DCE-US sequenceto obtain a parametric map of I.

In a first test, we evaluated the relation of I with the dispersion-related param-eter , with special attention to its monotonicity. We simulated multiple DCE-USsequences, each time increasing the value of by 0.1 s-1 in a range from 0.1 to 1 s-1,typically encountered in patient data. The value of µ was fixed to 25 s, chosen withinthe range of values found in previous publications [130, 131]. The injection time t0

only causes time shifts in the TICs, of which the e�ect is neutralized after alignmentof the TICs according to their ATs, and its value is therefore irrelevant. After comput-ing the parametric maps, box plots were made, based on the values of I in the inner200⇥200 pixels in each map. A band of 6 pixels at each edge of the parametric mapwas removed from the analysis to exclude boundary e�ects.

In a second test, we assessed the influence of di�erent settings for the mutualinformation analysis on the relation between I and . For each simulation, the mutualinformation analysis was executed for all combinations of settings given below, basedon the considerations described in section 2.2.3:

• tw 2 {20, 25, 30, 35} s,

• Q 2 {64, 128, 256},

• with and without applying a temporal filter,

• using q[n] or A[n],

• with and without TIC normalization.

To evaluate the performance of these settings in finding prostate cancer, we focusedon the parametric maps of I obtained from DCE-US simulations with = 0.2, = 0.3,and = 0.4 s-1. The choice for the values of was motivated by the threshold usedin vivo (i.e., = 0.3 s-1, see Table 2.1) to classify benign and malignant tissue.

Next, for each setting, two receiver operating characteristic (ROC) curves werecomputed based on the parametric maps of I. In one ROC curve, parametric maps for

28 Similarity analysis using mutual information

(a) (b)

Figure 2.4: Example of a simulated TIC ( = 0.5 s-1, µ = 25 s, t0 = 5 s) expressed as (a)acoustic intensity (linear scale) and (b) quantization level (log-compressed).

= 0.2 s-1 and for = 0.3 s-1 were considered; another ROC curve included maps for = 0.3 s-1 and = 0.4 s-1. For each ROC curve, the lowest value of representedbenign and the highest malignant tissue. The average area under the ROC curves(AU-ROC) was used as a performance metric to evaluate the capability of a settingto discriminate between normal and malignant tissue (i.e., to discriminate between = 0.2, = 0.3, and = 0.4 s-1). A schematic overview of the process describedabove is given in Fig. 2.5.

2.2.5 Validation in patientsTo validate the ability of the presented mutual information analysis to detect prostatecancer, patients with biopsy-proven cancer referred for RP were selected. For eachpatient, one or more DCE-US sequences were recorded as described in section 2.2.1,after which parametric maps of I were produced. Following RP, excised prostates wereprocessed and sliced according to [139]. Benign and malignant regions were drawnon the ultrasound image if a benign or malignant area was marked by the pathologistin the corresponding histology slice and two adjacent slices. During this process, theperson drawing the regions was blinded to DCE-US videos and parametric maps.

Overall, 35 malignant (⇡ 8.2⇥104 pixels) and 50 benign regions (⇡ 8.6⇥104 pixels)could be drawn in 58 DCE-US sequences from 23 patients. In some patients onlybenign or malignant regions had been drawn.

Because the mutual information analysis only gives useful information about tumorlocations in areas with qualitatively good TIC curves (i.e., following the LDRW model),we created three binary masks (1=include, 0=exclude) for each parametric map basedon the DCE-US sequence. Regions were drawn avoiding as many holes (i.e., zeros) inthe mask as possible and pixels which were not included by all masks were excludedfrom the validation.

The first mask was used to exclude areas in which no contrast signal was presentat all. Only pixels with a mean acoustic intensity A � 7 over the first 35 s after theAT were included. The second mask dealt with saturation: pixels for which the TIC,median-filtered over 7 time samples, contained a q > 235 were excluded. Finally, in

Methods 29

Figure 2.5: Schematic overview of the method used to estimate the ability of I to discriminatedi�erent dispersion levels around the threshold for prostate cancer. First, parametric mapsare generated for = 0.2, = 0.3, and = 0.4 s-1. From these maps, two ROC curves aregenerated of which the average area under the curves is used as a measure to define howwell I can discriminate between the di�erent values of . The dashed box in the parametricimages represents the pixels which are included in the ROC curves.

the third mask, pixels for which the correlation coe�cient, R2, of the TIC fit describedin [130] was lower than 0.8 were excluded.

We tested the mutual information analysis with a reduced set of settings, comparedwith the simulation described in Section 2.2.4, because of the large number of datasetsto analyze:

• tw 2 {25, 35} s,

• Q 2 {64, 256},

• With and without applying a temporal filter,

• Using q[n] or A[n],

• With and without TIC normalization.

To hide clinically insignificant (small) lesions [183], each of the obtained mutual in-formation maps was smoothened with a 2D Gaussian spatial filter (�post = 1.5 mm)before analyzing its classification performance. From the mutual information values inthe benign and malignant pixels, the ROC curve was obtained. The optimal threshold

30 Similarity analysis using mutual information

Table 2.1: In vivo comparison of contrast parameters. The p-values in the last columnrepresent the significance of di�erences between the areas AU-ROCs of mutual information(I) and the other parameters.

Parameter Threshold SNS SPC AU-ROC p-value

I � 1.198 0.713 0.711 0.775 N/Ar [132] � 0.369 0.690 0.689 0.747 0.24⇢ [133] � 0.800 0.679 0.673 0.743 0.21FWHM < 18.7 s 0.622 0.668 0.704 0.042WIT < 7.50 s 0.633 0.627 0.663 < 0.01 [130] � 0.298 s-1 0.606 0.619 0.651 < 0.01PI � 59.72 a.u. 0.560 0.625 0.642 < 0.01AU-TIC � 1346 a.u. 0.495 0.509 0.509 < 0.01

SNS=sensitivity, SPC=specificity, AU-ROC=area under the ROC curve,FWHM=full-width at half-maximum, WIT=wash-in time,PI=peak intensity, AU-TIC=area under the TIC.

was chosen to minimize the Euclidean distance to the top left corner of the curve,where sensitivity (SNS) and specificity (SPC) were equal to 1. Three classificationperformance measures were then computed: SNS, SPC, AU-ROC. For reference, thebest performing mutual information analysis was compared to several other DCE-US-based parameters described in literature: r [132], ⇢ [133], [130], peak intensity (PI,linearized TIC peak value), wash-in time (WIT, i.e., the time between AT and reaching95% of the TIC peak), full-width at half of the maximum (FWHM) of the TIC, andarea under the linearized TIC (AU-TIC).

To investigate the statistical significance of the di�erences in classification perfor-mance between the di�erent parameters, p-values of the di�erence in AU-ROC werecalculated. The standard error (SE) in estimating each AU-ROC was computed as de-scribed in [184]. This computation requires the degrees of freedom nn and np withinthe negative and positive class, respectively, to be known. Since neighboring pixels inparametric maps are highly dependent on each other because of spatial filtering andthe kernel used in CUDI, they could not be regarded as independent measurements.Instead, we assumed a number of independent pixels per region based on the averageregion area per class (47.0 mm2 for benign, 62.8 mm2 for malignant). Assuming roundregions and a minimum spacing between independent points of approximately 6.5 mm(kernel diameter+�post), we estimated the number of independent samples per area tobe 3 and 4, respectively. Hence, nn = 150 and np = 140. Di�erences were consideredto be significant for p < 0.05.

Results 31

0.1 0.5 11

1.5

2

2.5

3

𝜅𝜅 [s-1]

𝐼𝐼[-]

Figure 2.6: Box plots of mutual information I computed from simulated curves with increas-ing values of .

2.3 Results

2.3.1 SimulationFigure 2.6 contains box plots of I obtained by simulation as described in Section 2.2.4for increasing values of between 0.1 and 1 s-1 (the first test). Here, the CUDIsettings found to be optimal in vivo were used to compute the mutual information(i.e., tw = 35 s, Q = 64, using normalized q[n] and a temporal filter). As expected, Iis monotonically related to . This relation was also observed for other settings (notshown here), but resulted in higher standard deviations of I for small tw.

The AU-ROCs, obtained by the second simulation test (see Fig. 2.5), for di�erentsettings of CUDI by mutual information are presented in Fig. 2.7. When no temporalfilter was applied, only linearized data gave good results for each time window. In anycase, a time window of 35 s resulted in the best classification performance.

For the data preprocessed by a temporal filter, the AU-ROC increased with thelength of the time window. Again, tw = 35 s produced the highest AU-ROC. For thiswindow length, a higher number of quantization levels Q performed better than a lowerone and normalized log-compressed data performed better than the unnormalized orlinearized data.

2.3.2 Patient dataThe classification results of di�erent settings in patient data are given in Fig. 2.8. Inline with the simulation results, a time window of 35 s gave better results than one of25 s, and using this time window, normalized log-compressed data worked marginallybetter than other data types. However, in contrast to the simulation results, Q = 64

32 Similarity analysis using mutual information

0.5

0.6

0.7

0.8

0.9

1

Are

a un

der t

he R

OC

cur

ve

Q=6

4

128

256 64 128

256 64 128

256

tw = 20 s 25 s 35 s

Without temporal filter

(a)

64 128

256

30 s

[ ]Normalized [ ]Normalized [ ]

With temporal filter

0.5

0.6

0.7

0.8

0.9

1

Are

a un

der t

he R

OC

cur

ve

Q=6

4

128

256 64 128

256 64 128

256

tw = 20 s 25 s 35 s

(b)

64 128

256

30 s

Figure 2.7: Performance of mutual information in discriminating simulated curves with dif-ferent values of . We tested the influence of a temporal filter, the window length tw, thenumber of quantization levels Q, the type of DCE-US data (linear A[n] or log-compressedq[n]), and normalization of the data on the performance.

outperformed Q = 256.Table 2.1 shows the results of the in-vivo study for several CUDI and perfusion-

related parameters. In the last column, the p-values are given, obtained from thestatistical analysis comparing the AU-ROC of I with those of the other parameters.The corresponding ROC curves of the 6 best performing parameters and their operatingpoints, defined by the thresholds given in Table 2.1, are depicted in Fig. 2.9. Mutualinformation performs better than the other similarity-based parameters, though notsignificantly (p = 0.24 and p = 0.21). The di�erences between I and the other threeparameters, however, were significant (p < 0.05).

Examples of parametric maps of each of the three similarity methods in one planeare shown in Fig. 2.10. The settings used to generate the map of the mutual infor-

Discussion 33

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mation were the best performing in the in vivo validation (i.e., with temporal filter,using normalized log-compressed data, Q = 64, tw = 35 s). The corresponding histol-ogy slice with cancerous tissue marked by a pathologist is also presented. Particularlyin the near field on the patient’s right side (left in the image), I seems to be moreaccurate than r and ⇢, which tend to overestimate the size of the tumor in that area.

2.4 DiscussionIn this research, we presented an extension of CUDI by spatiotemporal analysis us-ing mutual information. In contrast to correlation or coherence, mutual informationpermits the exploration of nonlinear relationships among TICs by assessing the degreeof statistical dependence between a TIC and its surrounding TICs. In fact, mutualinformation vanishes if and only if a TIC is statistically independent to its surround-ings. However, a vanishing correlation or coherence indicates only the lack of lineardependence rather than a total independence.

The presented extension of similarity-based CUDI from linear similarity measuresto mutual information resulted in an improved capability of finding prostate cancer in23 patients. However, extension of the dataset is required to investigate if a significantimprovement between the presented method and the other similarity-based methodscan be proven.

Computing a more general similarity comes at a small computational cost, whichincreases when using more quantization levels and longer time windows. Using animplementation in MATLAB (The MathWorks, Natick, MA) on a PC with a Intel®

34 Similarity analysis using mutual information

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Figure 2.10: Parametric maps of CUDI by (a) correlation r [132], (b) coherence ⇢ [131,133],and (c) mutual information I. Subfigure (d) contains the corresponding histology slice withcancer marked in red.

CoreTM i5-2500 processor at 3.30 GHz (Intel, Santa Clara, CA) and 16 GB of randomaccess memory, the method using the settings which gave the best classification per-formance took approximately 7 to 10 minutes to complete, depending on the size ofthe prostate. In comparison, the linear similarity methods took approximately 4 to 7minutes to complete. However, no code optimization had been applied and computa-tion of both types of similarity maps can be strongly parallelized, because similaritiesin di�erent parts of the prostate can be computed simultaneously without conflict.Therefore, we expect an optimized implementation of the methods to reduce the com-

Discussion 35

putation time by several minutes, which makes it suitable for adoption into a routineprostate examination.

To validate this method, histology was used as ground truth, which is based oncell di�erentiation (Gleason score [37]). In contrast, CUDI aims at finding regionsof reduced dispersion as a result of angiogenesis. Consequently, CUDI and histologymay produce slightly di�erent tumor locations. Moreover, other pathologies a�ect-ing the microvascular structure, such as inflammation, may a�ect UCA dispersion.Quantitative information about the microvascular density or distribution in a specificarea in the prostate can be helpful for the interpretation of CUDI. To this end, im-munohistology [13] could be employed as it provides information on the microvasculararchitecture.

In-vivo validation was performed by manually drawing benign and malignant re-gions after cognitive registration of the fundamental image and histology. This vali-dation method could be improved by using an accurate image registration method toobtain a better fusion of histology and parametric maps.

From the simulation as well as the in vivo results, it can be concluded that a longertime window leads to improved classification. More data to estimate the joint PMFin (2.6) may result in a more accurate estimation of the mutual information. Thewindow length is however limited to the point at which recirculation occurs (around35 s), which generates noise independent of the local microvasculature.

According to the simulation results, applying a temporal filter reduces the capabilityof mutual information to distinguish between the critical values of . It seems that thenoise may be of value in estimating the underlying statistical process which generatedthe TICs. However, in vivo, the temporal filter improved the results. The complexityof the noise encountered in vivo might not be fully described by that modeled in thesimulation. In fact, di�erent noise statistics apply for low and high UCA concentrations[179,180]. Moreover, noise due to small movements of the probe or patient have notbeen taken into account. Therefore, the extra filtering step is required to maximallyexploit the data.

In Section 2.2.2, four assumptions were made in the computation of the mutualinformation between TICs. Each of the assumptions simplifies the statistical modeland reduces the computational complexity. In future work, one or more assumptionscould be left out to achieve more accurate mutual information estimation. Here, wediscuss the validity of these assumptions.

By considering TICs as IID processes (AS1 and AS2), time-dependency, intrinsic tothe process of UCA flowing through the vascular system, was ignored. The validity ofthese assumptions is therefore questionable. Nonetheless, they may still be useful forestimating dispersion from TIC similarity for the following reason. Mutual information,as applied in this paper, can be regarded as the predictability of kernel TIC values froma center TIC value, regardless of their position in time. Because TICs always have acertain global shape, each TIC value only occurs in certain phases of the curve. For asimilar curve shapes in the center and the kernel, a TIC value in the center will occur

36 Similarity analysis using mutual information

in the same phase as that value will occur in the kernel, making the kernel TIC valuepredictable. If a region has a lower dispersion, the values of TICs in the kernel willbe more similar in shape, hence better predictable by the values in the center. As aresult, low dispersion still results in high mutual information.

By aligning the TICs according to their ATs, the influence of in-plane flow on time-shifts between TICs is reduced. This supports the assumption that TIC values in thekernel pixels are statistically only dependent on the center TIC value at a certain timeinstance (AS3). Di�erences amongst TICs within the kernel can be a direct result ofdispersion. These di�erences lead to a more spread-out PMF of K

N and C, whichagain results in an expected lower mutual information for high dispersion.

Kernel TICs are assumed to originate from the same statistical distribution, regard-less of their position in the kernel (AS4). This assumption can be made, because thekernel covers only a relatively small area. Moreover, no a-priori information is availableabout di�erences between kernel TICs based on their position in the kernel. There is,however, a large computational benefit in applying AS4, caused by a reduction in thenumber of entries in the PMF PKN ,C(k

N, c), from which the mutual information is

calculated, by a factor N .A key hypothesis behind the presented method is that TIC shape similarity is higher

in regions with lower dispersion; lower dispersion is linked to the presence of angio-genesis, possibly due to the e�ects of increased tortuosity. Yet, other irregularities inthe vasculature may occur across the kernel, such as an area containing a larger vesselsurrounded by microvessels or a vascularized region with a necrotic core. Whereas anecrotic core does not contain any UCA and will hence be excluded from the analysis,an area containing both larger and smaller vessels could lead to heterogeneous flowpatterns. Depending on the scale at which discontinuities occur, these may introducelocal artifacts in the image. However, these can be distinguished from spatially dis-tributed similarity reflecting the presence of an angiogenic microvascular architectureindicative of clinically significant cancer. To this end, the size of the kernel was chosensuch that the larger, clinically significant tumors could be localized and most of theinsignificant tumors would not be detected.

We adopted a Wiener deconvolution filter to compensate for changes in spatialresolution of the ultrasound imaging system over depth. Unfortunately we were notable to compensate for changes in beam width in the elevational direction, whichincreases from 1.4 mm at a depth of 2 cm to 3.4 mm at 5 cm. This increase mayhave an influence on the similarity between TICs and on the validity of AS4. However,we did not observe a significant change in mutual information over depth. It maynonetheless be interesting to investigate this phenomenon further in 4D DCE-US1

recordings.The results of dispersion estimation by mutual information analysis confirm that

1In [J4] and [J6] and therefore also in Chapters 2 and 3, the term “4D DCE-US” is used insteadof “3D DCE-US”. In the other chapters, we write “3D DCE-US” to avoid inconsistency with the term“2D DCE-US”.

Conclusions 37

a reduction in dispersion, in a particular region, is an indicator of the existence ofan underlying angiogenic structure. One of the causes for the reduction in dispersionmight be the tortuosity of angiogenic vasculature, which acts against dispersion byconstraining the microbubbles within the sampling volume. However, other factors,such as arteriovenous shunts and increased microvascular density, may play a role. Thelink between dispersion and the geometrical properties of the tumor’s microvasculararchitecture must be further researched to have a better understanding on how theseparameters influence the convective-dispersion process.

The method presented here aims at finding the mutual information between localTIC shapes, which are di�cult to appreciate by naked eye. To be able to compareTIC shapes, these were aligned according to their ATs. However, information providedby ATs and mutual information may be complimentary [111, 185]; combining thesetwo features in a multiparametric approach may possibly improve the classificationperformance.

In this paper, an implementation of CUDI by similarity analysis in 2D has beendescribed. However, a pilot study has recently been conducted extending the methodto 3D and testing the feasibility of 4D DCE-US to perform such analyses using linearsimilarity measures [J6] or mutual information [IC2]. This extension makes it possibleto image the entire prostate using a single bolus of contrast agent, saving time andcosts, while increasing the patient’s comfort. Moreover, by having the full 4D UCAkinetics at our disposal, we are no longer limited to in-plane flow for our dispersionanalysis. Incorporating through-plane flow could lead to a more accurate estimationof the local dispersion.

2.5 ConclusionsUCA dispersion can be indirectly estimated from the mutual information betweenneighboring TICs as shown by a simulation study. Because low UCA dispersion reflectsthe presence of prostate cancer, mutual information can possibly be used to localizetumors. In an in-vivo validation for prostate cancer localization including 23 patients,mutual information performed better than other CUDI implementations and severalfeatures extracted from TICs commonly used to investigate tissue perfusion. Still, amore accurate estimation of the value of the presented method could be achieved byvalidating it in a larger patient group as well as other types of cancer where angiogenesisplays an important role.

38 Similarity analysis using mutual information

Chapter3Technical feasibility of 3D CUDI

The content of this chapter has been published as [J6]:

S.G. Schalk, L. Demi, M. Smeenge, D.M. Mills, K.D. Wallace,J.J.M.C.H. de la Rosette, H. Wijkstra, and M. Mischi, “4-D spatiotemporalanalysis of ultrasound contrast agent dispersion for prostate cancer localization: afeasibility study,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 62, no. 5,pp. 839-851, 2015. © 2015, IEEE.

40 Technical feasibility of 3D CUDI

AbstractCurrently, non-radical treatment for prostate cancer is hampered by the lack of reliablediagnostics. Contrast-ultrasound dispersion imaging (CUDI) has recently shown greatpotential as a prostate cancer imaging technique. CUDI estimates the local dispersionof intravenously injected contrast agents – imaged by transrectal dynamic contrast-enhanced ultrasound (DCE-US) – to detect angiogenic processes related to tumorgrowth. The best CUDI results have so far been obtained by similarity analysis of thecontrast kinetics in neighboring pixels. To date, CUDI has been investigated in 2Donly. In this paper, an implementation of 3D CUDI based on spatiotemporal similarityanalysis of 4D DCE-US is described. Di�erent from 2D methods, 3D CUDI permitsanalysis of the entire prostate using a single injection of contrast agent. To perform 3DCUDI, a new strategy was designed to estimate the similarity in the contrast kineticsat each voxel and data processing steps were adjusted to the characteristics of 4DDCE-US images. The technical feasibility of 4D DCE-US in 3D CUDI was assessedand confirmed. Additionally, in a preliminary validation in two patients, dispersionmaps by 3D CUDI were quantitatively compared to those by 2D CUDI and to 12-coresystematic biopsies with promising results.

Introduction 41

3.1 IntroductionProstate cancer is the type of cancer with the highest incidence and one of the mostprevalent cancer-related causes of death for men in the Western World [186, 187].Currently, prostate cancer is usually detected by a prostate-specific antigen (PSA)blood test or digital rectal examination (DRE) [188]. Yet, due to the low specificityof these tests, the presence of prostate cancer requires confirmation by biopsy [188],usually performed as a transrectal ultrasound (TRUS)-guided systematic biopsy, inwhich typically 6 to 16 small cores are sampled from fixed positions in the prostateaccording to a standard scheme. However, this test does not reveal the exact locationsor shapes of tumors, which might be undergraded or missed entirely [31, 41, 189].Moreover, because taking biopsies is an invasive procedure, it brings a risk of developingfever, hematuria, hematochezia, and hematospermia [29].

A minimally or non-invasive technique localizing prostate cancer could assist intargeting the biopsy needle to a suspected cancerous area and hence reducing thechance of false negatives. In this way, repeat biopsies could be avoided. Moreover,such a technique would open up possibilities to treat prostate cancer locally (e.g., byusing photodynamic therapy, focal cryoablation, or high-intensity focused ultrasound),reducing or eliminating morbidity, such as urinary incontinence or impotence, as isexperienced with radical treatment [190,191].

Currently, several imaging techniques designed to localize prostate cancer, mostlybased on MRI or ultrasound (US), are being investigated [11]. In the recent years, re-searchers have especially investigated MRI as an imaging modality to diagnose prostatecancer, due to the development of new techniques giving physiological and metabolicinformation about the gland [11, 192]. In particular, in addition to conventional T1-and T2-weighted images, di�usion-weighted MRI, dynamic contrast-enhanced MRI,and MR spectroscopy imaging can now be used to come to a more reliable diagno-sis [11, 192]. Often, some or all of the MRI techniques are combined into multi-parametric MRI (mpMRI), used for a more accurate localization of prostate can-cer [193]. Yet, despite the introduction of a standard scoring system (PI-RADS) [55],the interpretation of mpMRI datasets remains complex and subjective [194,195].

TRUS, has proven its potential as an alternative to MRI for localizing prostate can-cer, with the additional advantages of being less expensive and applicable at the bed-side. Currently, the most promising TRUS-based techniques used to localize prostatecancer are (shear-wave) elastography, color and power Doppler, and dynamic contrast-enhanced ultrasound (DCE-US). Elastography exploits the increased sti�ness of tumorswith respect to benign tissue [196–198], Doppler images can expose increased perfusioncaused by higher vascularity around tumors [11,196], and dynamic contrast-enhancedultrasound can be used to reveal angiogenesis (i.e., new microvessels required for tu-mor growth) [11, 105,199]. Although a qualitative assessment of DCE-US videos canalready assist in localizing prostate cancer [105,110,200], the slow learning curve andhigh inter-observer variability vouch for a quantitative approach [113].

42 Technical feasibility of 3D CUDI

In quantitative approaches to DCE-US imaging, in general two di�erent approachescan be distinguished. In the first approach, a single intravenous injection of aultrasound-contrast-agent (UCA) bolus is adopted and its concentration over timeis measured in the imaging plane. From the resulting indicator dilution curves (IDCs),several parameters can be extracted, such as time to peak, mean transit time, peakintensity and area under the IDC [115, 179, 201, 202]. In the second approach, a con-tinuous infusion of UCAs is applied to achieve a steady concentration in the blood.Subsequently, the UCAs in the imaging plane are disrupted by one or several US pulsesat a high mechanical index. The reperfusion of the cleared area can be recorded overtime to obtain the step response of the underlying system, from which again several pa-rameters (e.g., the initial slope) can be estimated [108,118,201,202]. The parametersobtained by each of these methods mainly give an indication of the blood perfusion.However, the e�ect of angiogenesis on blood perfusion in tumors is heterogenous: thepresence of arteriovenous shunts and the lack of vasomotor control may lead to anincreased blood flow, but this e�ect can be counterbalanced by the uneven diameter,higher tortuosity, and higher permeability of the neovessels with the last contributingto an increase in interstitial pressure [11,15].

Recently, contrast-ultrasound dispersion imaging (CUDI) has been proposed as apromising alternative to perfusion imaging to characterize changes in the structure ofmicrovessels caused by angiogenesis [130]. In CUDI, IDCs measured by DCE-US inthe prostate were originally modeled as a convection-di�usion process, based on themultipath trajectories in the microvasculature. The first approach involved fitting theconvection-di�usion model to IDCs at each pixel to find a dispersion-related parameter [130]. However, the tail of the IDC – required to find – had to be estimated fromthe first part of the IDC due to recirculation. Moreover, low signal-to-noise ratio(SNR) and dependency between model parameters can often cause estimations of to be unreliable. In more recent publications [131–133], the problem of fittingthis model to the IDCs has been overcome by an indirect assessment of dispersionbased on the similarity of IDCs in neighboring pixels. To this end, for each pixel thesimilarity was determined between the IDC in that pixel and the IDCs in a ring-shapedkernel around it, with the additional advantage of shortening the algorithm’s executiontime. Validation of CUDI involving 24 DCE-US recordings in 8 patients confirmed thesuperior accuracy of the similarity measures over IDC fitting in detecting prostatecancer [132]. Moreover, results from a more extensive, mulitcenter study including43 measurements in 24 patients indicate that CUDI outperforms the main perfusionmethods presented in literature [203].

To date, CUDI has been performed in 2D only. With the development of intra-cavitary transducers that are able to make 4D1 (3D + time) DCE-US recordings, 3DCUDI can be envisaged as a new option to detect prostate cancer. The advantages of3D over 2D CUDI are numerous: 3D CUDI can image the entire prostate with a singlebolus injection, saving time and costs, and reducing discomfort for patients; no contrastflow is missed due to out-of-plane vessels, resulting in a more accurate estimation of

Materials and method 43

the dispersion parameters; moreover, motion compensation can be applied to obtainlocal IDCs only.

This paper describes the implementation of a full 4D similarity analysis to perform3D CUDI for prostate cancer localization. To this end, the previously developed 2DCUDI technique was extended to 3D, requiring the design of a 3D kernel and recon-figuration of various parameters used in the analysis. The technical feasibility of 4DDCE-US for the implementation of 3D CUDI was evaluated with emphasis on its lim-ited spatial and temporal resolution. Additionally, the obtained 3D CUDI maps werecompared with the corresponding 2D CUDI and biopsy results in two patients.

3.2 Materials and method

3.2.1 Data acquisitionPatient data was acquired at the Academic Medical Center (AMC), University Hospitalin Amsterdam (The Netherlands) with approval of the hospital’s ethics committee.

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1In [J4] and [J6] and therefore also in Chapters 2 and 3, the term “4D DCE-US” is used insteadof “3D DCE-US”. In the other chapters, we write “3D DCE-US” to avoid inconsistency with the term“2D DCE-US”.

44 Technical feasibility of 3D CUDI

Table 3.1: Specifications of the dynamic contrast-enhanced ultrasound recordings.

2D 4D-full* 4D-narrow*

Temporal resolution (s�1) 7.5 0.26 0.34Imaging depth (mm) 50 49 31Lateral field of view (�) 146 146 146Elevational field of view (�) N/A 119 89Tx line density (lines/�) 1.1 0.37 0.37Rx line density (lines/�) 2.1 0.74 0.74Plane density (planes/�) N/A 0.85 0.85

*4D-full refers to the regular 4D DCE-US recordings,whereas 4D-narrow refers to the 4D recording with a re-duced field of view.

Patients who participated in the study signed an informed consent.For each DCE-US recording, a 2.4 mL bolus of SonoVue® (Bracco, Milan, Italy)

UCA was intravenously injected. A LOGIQ E9 (GE Healthcare, Wauwatosa, WI)ultrasound scanner equipped with an IC9-5 and RIC9-5 transrectal probe was used tomake 2D and 4D DCE-US recordings, respectively. The scanner was set to contrastmode at 4 MHz. For the 4D recordings, the BQ setting (image quality) was set to“low” to maximize the temporal resolution. To prevent destruction of microbubbles bythe ultrasound pressure, a low mechanical index (between 0.09 and 0.13) was adopted.The dynamic range and gain were set such that IDCs did not saturate. Because the4D recordings were provided in spherical coordinates, linear interpolation was appliedto obtain cartesian datasets with a voxel size of 0.25⇥0.25⇥0.25 mm3.

In total, six DCE-US recordings were made in two patients. A period of at least 5minutes was left between subsequent injections for the UCA to be cleared. In patient 1,one 2D DCE-US and two 4D DCE-US sequences were recorded. The second 4D DCE-US sequence was recorded with a reduced field of view, which was possible becauseof the small size of the prostate, increasing the volume rate. In Fig. 3.1, the averageIDC inside the prostate is plotted for each DCE-US recording. Table 3.1 summarizesthe characteristics of the di�erent types of DCE-US sequences: 2D, 4D with full fieldof view, and 4D with reduced field of view. A 25% reduction of the elevational fieldof view and a 37% reduction of the imaging depth led to a 31% increase in temporalresolution. Additionally, Table 3.1 contains the line densities in transmission (Tx) andreception (Rx) and plane densities, which were provided by GE. In patient 2, two 2DDCE-US sequences and one 4D DCE-US sequence with full field of view were recorded.

To further characterize the di�erences between 2D and 4D DCE-US, we assessedthe spatial resolution from the acquired data. In vitro experiments [131] were usedto estimate the speckle size, which is closely related to the spatial resolution. To

Materials and method 45

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estimate the speckle size for 4D DCE-US, a straightforward extension of the experimentdescribed in [131] from 2D to 3D was applied. Figure 3.2 shows the speckle size ineach direction for the adopted 2D and 4D DCE-US settings.

3.2.2 2D spatiotemporal similarity analysisIn [131–133] it was shown that a spatiotemporal similarity analysis can be used toestimate the UCA dispersion. In this method, the average similarity is estimatedbetween each IDC and those IDCs in a ring-shaped kernel [Fig. 3.3(a)] around it.A higher similarity is related to a lower dispersion D. In [131–133], the correlationbetween frequency amplitude spectra of IDCs (referred to as coherence ⇢) and thecorrelation r between IDCs in the temporal domain are used as similarity measures.

46 Technical feasibility of 3D CUDI

Figure 3.3: (a) Kernel used in 2D CUDI and (b) a cut view of the kernel used in 3D CUDI.The 3D kernel has the same inner and outer radius as the 2D kernel.

An overview of the workflow for CUDI by spatiotemporal similarity analysis – asproposed in [131–133] – is given in Fig. 3.4, in which each step is numbered from W1to W10. After recording a DCE-US image (W1), because of the anisotropic and depth-dependent nature of the speckle size (Fig. 3.2), the Wiener filter proposed in [133] wasapplied to the DCE-US images to regularize the speckle size to approximately 0.8 mm(W2). In this way, the influence of the imaging resolution on the spatiotemporal

Materials and method 47

similarity analysis is reduced. The target speckle size is a tradeo� between SNR andthe desired spatial resolution of CUDI. To save computational time, which can beespecially critical for 3D CUDI, the images are downsampled (W3) to approximatelymatch the speckle size. The noise in IDCs is reduced by a low-pass filter in the temporaldomain (W4), after which the most informative part of the curve (35 s beginning fromthe appearance time of the UCA) is extracted (W5). Because the DCE-US data isstored as a log compressed image of the backscattered acoustic intensity, the data islinearized (W6) before further processing.

Now, the data is ready for the spatiotemporal analysis (W7). For each pixel, theaverage similarity between the IDC at the investigated pixel and the IDCs in a ring-shaped kernel around it is calculated in the frequency domain (coherence ⇢) or thetime-domain (correlation r) (W8). The kernel [Fig. 3.3(a)] has an inner radius of1.0 mm and an outer radius of 2.5 mm. The inner radius has to be large enough toprevent a bias in the similarity resulting from spatial dependency caused by the imagingresolution. The outer radius is a tradeo� between the number of pixels available toestimate the dispersion parameters and the resolution in the final dispersion map,which should be small enough to detect early angiogenesis (2-3 mm [175]). Moreover,the e�ect of UCA dispersion should be visible in all kernel pixels. When assuminga blood velocity v through the capillaries of 1 mm/s [204] and a (high) value for

(= v2/2D) of 3 s-1, D = 0.17 mm2/s. The dispersion distance covered during the

time window tw of 35 s is thenp

2Dtw =p

2 · 0.17 · 35 = 3.4 mm (see Appendix 3.6),which means that all pixels in the kernel are reached by the dispersion of UCA from thecenter pixel. Finally, to facilitate visual interpretation of the similarity results, spatialGaussian filters (�post = 0.5 mm) (W9) are applied to obtain the final dispersion maps(W10).

3.2.3 4D spatiotemporal similarity analysisFirst, we applied CUDI by curve-fitting [130] to the 4D DCE-US data. However,because of the low temporal resolution, the majority of the IDCs could not be fitted(no fit or R

2< 0.75). For this reason, the CUDI methods explored in this paper

are the spatiotemporal similarity analyses obtaining the parameters coherence (⇢) andcorrelation (r). Due to the large di�erence in data characteristics (Table 3.1) between2D and 4D DCE-US, some of the steps in the workflow for the spatiotemporal similarityanalysis (Fig. 3.4) were redesigned to perform 3D CUDI.

In [133], speckle noise was modeled as white noise filtered by a Gaussian filterHsp(�ax,�lat) with constant axial standard deviation �ax and depth-dependent lateralstandard deviation �lat. Note that the orientation of the Gaussian filter follows thedirection of the imaging line. The speckle size (SS), shown in Fig. 3.2, is linearly relatedto the filter parameter � as � ⇡ 0.30·SS (see Appendix 3.7). The speckle regularizationfilter (W2) is implemented as the Wiener deconvolution of Hsp(�ax,�lat) [133]. Toapply the filter to the 4D DCE-US data, it was extended by including the standard

48 Technical feasibility of 3D CUDI

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deviation �el in the elevational direction, yielding

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⇤sp(�ax,�lat,�el)

|Hsp(�ax,�lat,�el)|2 + NSR. (3.1)

The input of the regularization filter Hreg(�t) is the standard deviation �t ofthe filter Ht(�t) corresponding to the target isotropic speckle size. NSR (noise-to-signal ratio) is a term which controls a trade-o� between the filter’s accuracy andstability. For the 4D DCE-US data, the optimal value for NSR was experimentallydetermined to be approximately 10-5. In [133], the target speckle size of the Wienerfilter was proposed to be 0.8 mm (�t = 0.25 mm) as a well-configured trade-o�between noise reduction and image resolution (i.e., the smallest tumor that can bedetected). Although the speckle size in 4D DCE-US in the lateral and elevationaldirection is much larger than that of 2D DCE-US, the Wiener filter was still able toregularize the speckle size to 0.8 mm. Therefore, no changes were made to this value.As a consequence, also the downsampling factor (W3), which depends on the spatialresolution, did not need to be changed.

The temporal filter (W4) used in 2D CUDI – a low-pass filter with a cut-o� fre-quency of 0.5 Hz, designed to remove noise from IDCs [130,131] – was removed for 3DCUDI, because the temporal resolution of 4D DCE-US was already below the cut-o�frequency. However, as explained in more detail in section 3.4.2, the temporal reso-

Materials and method 49

Table 3.2: Comparison of 2D and 3D CUDI by spatiotemporal similarity analysis.

2D CUDI 3D CUDI

Kernel shape ring shellTarget speckle size of Wiener filter (mm) 0.8 0.8Inner kernel radius (mm) 1.0 1.0Outer kernel radius (mm) 2.5 2.5Cut-o� frequency of temporal filter (Hz) 0.5 noneSize of time window (s) 35 45Std. dev. of Gaussian post-filter (mm) 0.5 0.5

lution was still su�ciently high to follow the UCA kinetics, and the cut-o� frequencycould in fact be decreased without losing relevant information. Moreover, the limita-tion in noise reduction due to the lack of time filtering was partly compensated for bythe increased amount of IDCs that could be used in the spatial filter by having a thirddimension available.

To increase the number of samples from IDCs available for the similarity analysis,we increased the window size (W5) from 35 s to 45 s. The extra data points areespecially beneficial for the coherence analysis, since the phase information is removedin this analysis. However, to find the optimal window size, more DCE-US data isneeded.

In the similarity analysis (W7), the ring-shaped kernel proposed in [131] was re-placed by a shell-shaped kernel [Fig. 3.3(b)] for 3D CUDI. The same as for 2D CUDI,the size of the inner sphere is determined by the imaging resolution. Since the targetspeckle size in the Wiener filter (W2) did not change compared to [132,133], we choseto keep the same dimensions also for this kernel. An overview of all parameters usedin the analysis is given in Table 3.2.

3.2.4 ValidationBecause the patients involved in this study did not undergo radical prostatectomy, nowhole-mount histology was available for validation. Since 2D CUDI by spatiotemporalanalysis has already been validated in vivo [132, 133], the 3D CUDI images werecompared to the 2D CUDI images in the corresponding planes for both patients.

Additionally, 3D CUDI was compared to histopathologic results from 12-core sys-tematic biopsies, which were taken within hours after DCE-US imaging. Tissue sampleswere acquired under TRUS guidance according to a fixed location scheme by placinga biopsy gun against the rectal wall and shooting a core needle to a maximal depthof 22 mm. Consequently, the anterior part of the prostate could not be reached bythe needle. The tissue samples with a typical length of approximately 15 mm wereanalyzed under a microscope by a pathologist and assigned a Gleason score [37] basedon their cellular di�erentiation. In addition, for each biopsy sample the percentage

50 Technical feasibility of 3D CUDI

of cancerous tissue was given. However, because the biopsy needle was guided by2D freehand US, the location and direction of the needle could not be accuratelydetermined.

For a preliminary quantitative validation of the CUDI images using the biopsyresults, 4 areas with equal width in the right-left direction were defined in each CUDIplane. Because the biopsy needle did not reach the most anterior part of the prostate,only the bottom (most posterior) 15 mm were included in these areas [Fig. 3.5(a)]. Inthis way, each area corresponds approximately to the location of one biopsy sample.Per area, the average values of r and ⇢ were compared with the pathological outcomeof the corresponding biopsy sample.

Additionally, in a quantitative coarse-to-fine validation of 3D CUDI, the parametervalues, averaged over volumes inside the prostate, were compared to the biopsy results.First, the parameter values in the entire prostate were included, after which the prostatewas divided in halves and quarters by the midplanes separating right and left, and baseand apex. Results in a finer grid could not be compared with biopsy results, due tothe large uncertainty in the biopsy locations at the base and apex. Again, only thefirst 15 mm from the most posterior point were included in this validation.

3.3 ResultsThe dispersion maps from 2D and 3D CUDI by spatiotemporal similarity analysisare shown in Figs. 3.5 to 3.7. Fig. 3.5 gives the correlation and coherence mapsfor patient 1, Figs. 3.6 and 3.7 give the same maps for imaging plane 1 and 2 inpatient 2, respectively. White areas in the coherence and correlation maps indicatepixels where no appearance time could be estimated, and therefore no time windowcould be selected. The last subfigures in each figure contain the biopsy results inthe coronal plane and give an indication of the locations in the base-apex-directionof the depicted dispersion maps (the green dashed line). Because the 2D DCE-USvideos were recorded in the mid-area of the prostate, the dispersion maps are almostperpendicular to the coronal plane.

Table 3.3 gives the quantitative comparison between the 2D and 3D CUDI mapsand the biopsy results. Based on these results, we defined for each parameter an opti-mal threshold for which the resulting sensitivity (SNS) and specificity (SPC) minimizethe function

p(1� SNS)2 + (1� SPC)2 (i.e., the Euclidian distance to the optimal

point in a receiver operating curve). The optimal thresholds and corresponding clas-sification performance are reported in Table 3.4.

In general, the 3D CUDI maps by both correlation and coherence show goodagreement with the corresponding 2D CUDI maps. Only in the second imaging planeof patient 2 (Fig. 3.7), a significant di�erence between 2D and 3D CUDI can beobserved in the transition zone. Moreover, the maps obtained by 3D CUDI agree wellwith the biopsy results, though it should be noted that the biopsy results only give an

Results 51

Figu

re3.

5:CU

DIm

aps

forp

atien

t1:

(a)

2Dan

d3D

corre

latio

nr

base

don

(b)

full

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rrow

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nce

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sed

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ore

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ive

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ples

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son

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opsy

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52 Technical feasibility of 3D CUDI

Figure 3.6: CUDI maps for patient 2, plane 1: (a) 2D and (b) 3D correlation r, (c) 2Dand (d) 3D coherence ⇢. In (e), the results from a systematic 12-core biopsy are given. Onesample (‘+’) was tested positive as a Gleason 3+3 carcinoma in <10% of the tissue, theothers were tested negative (‘-’). Additionally, the estimated location of the imaging plane isdepicted as a green dashed line. The white dashed lines in subfigure (a) indicate the biopsyareas.

indication of the sample locations, because the exact locations of the biopsy samplesare unknown (see Section 3.2.4).

In Fig. 3.8, the results of the coarse-to-fine validation for 3D CUDI are presented.The values averaged over the entire prostate for both 3D CUDI parameters in pa-tient 2 – who had only one positive biopsy – were lower then those obtained fromthe two DCE-US recordings in patient 1 with mostly positive biopsies. The resultsfrom patient 1, bolus 1, and patient 2 were obtained using the same scanner settingsand can directly be compared. For these two recordings, the parameter values in eachquarter containing only negative biopsies were lower than those containing at least onepositive biopsy.

Results 53

Figure 3.7: CUDI maps for patient 2, plane 2: (a) 2D and (b) 3D correlation r, (c) 2Dand (d) 3D coherence ⇢. In (e), the results from a systematic 12-core biopsy are given. Onesample (‘+’) was tested positive as a Gleason 3+3 carcinoma in <10% of the tissue, theothers were tested negative (‘-’). Additionally, the estimated location of the imaging plane isdepicted as a green dashed line. The white dashed lines in subfigure (a) indicate the biopsyareas.

54 Technical feasibility of 3D CUDI

Figure3.8:

Coarse-to-fineanalysis

ofthe3D

CUD

Iparameters

foreach

4DD

CE-US

recording.The

firstcolum

ncontains

them

eans±

standarddeviations

ofthe3D

CUD

Iparameters

inthe

entireprostate

(upto

15m

mfrom

them

ostposteriorpoint).In

thesecond,third,and

fourthcolum

nsthe

prostatehas

beendivided

inbase-apex,right-left,and

quarters,respectively.In

eachsetofnum

bers,thetop

row(blue)

relatesto

thecorrelation

r,andthe

bottomrow

(red)tothe

coherence⇢.

Thelastcolum

ngivesthe

biopsyresults,where

a‘+

’indicatesapositive

anda

‘-’anegative

biopsy.

Results 55

Tabl

e3.

3:Co

mpa

rison

ofth

e2D

and

3DCU

DIp

aram

eter

scor

rela

tionr

and

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renc

e⇢

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n±

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dard

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atio

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thbi

opsy

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reac

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cord

ing

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ach

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opsy

2Dr

2D⇢

3Dr

3D⇢

3Dr

3D⇢

loca

tion

resu

ltbo

lus

1bo

lus

1bo

lus

2bo

lus

2

Pat.

1rig

ht+

0.31

±0.

110.

61±

0.10

0.40

±0.

130.

40±

0.19

0.23

±0.

090.

23±

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mid

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t+

0.46

±0.

100.

75±

0.06

0.53

±0.

070.

57±

0.10

0.39

±0.

100.

49±

0.13

mid

-left

+0.

35±

0.10

0.64

±0.

100.

50±

0.08

0.54

±0.

100.

39±

0.11

0.51

±0.

18lef

t–

0.28

±0.

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60±

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0.34

±0.

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31±

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0.23

±0.

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27±

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Pat.

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±0.

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46±

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0.21

±0.

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18±

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plan

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59±

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0.30

±0.

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32±

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mid

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–0.

24±

0.14

0.63

±0.

150.

19±

0.10

0.21

±0.

11lef

t–

0.17

±0.

070.

46±

0.08

0.17

±0.

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13±

0.06

Pat.

2,rig

ht–

0.20

±0.

110.

47±

0.12

0.12

±0.

060.

10±

0.07

plan

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mid

-righ

t–

0.30

±0.

170.

62±

0.14

0.24

±0.

070.

20±

0.09

mid

-left

–0.

25±

0.16

0.55

±0.

150.

24±

0.08

0.20

±0.

10lef

t–

0.24

±0.

120.

57±

0.14

0.17

±0.

070.

13±

0.06

Pat.

=Pa

tient

.

56 Technical feasibility of 3D CUDI

Table 3.4: Classification performance of the CUDI parameters

Parameter Cancerous if Sensitivity (%) Specificity (%)

2D r � 0.31 100 (3/3) 100 (9/9)2D ⇢ � 0.61 100 (3/3) 78 (7/9)3D r � 0.37 83 (5/6) 100 (10/10)3D ⇢ � 0.36 83 (5/6) 100 (10/10)

3.4 Discussion

3.4.1 Spatiotemporal analysisIn this paper we tested the feasibility of 4D DCE-US to perform 3D CUDI, whichwas preliminarily validated by comparing the resulting dispersion maps to those by 2DCUDI and to 12-core systematic biopsy results in two patients. CUDI by spatiotemporalanalysis was performed in 2D and 3D from which the similarity parameters correlationr and coherence ⇢ were calculated. The dispersion maps of both r and ⇢ obtained by3D CUDI showed good agreement with the 2D CUDI maps from both boli of patient 1and the first bolus of patient 2 (Figs. 3.5 and 3.6), which confirmed the feasibility of4D DCE-US as an imaging technique to perform 3D CUDI. Moreover, results from 3DCUDI were consistent with the results from the biopsies.

The absolute values of the similarity parameters are di�erent for 3D CUDI withrespect to 2D CUDI, which may be explained by the di�erences in data characteristicsof the DCE-US images. In particular, the lower temporal resolution of 4D DCE-US compared to 2D DCE-US results in less data for noise suppression and likelycauses the similarity parameters to go down. On the other hand, for the 4D DCE-USimages, more data points are available for spatial filtering, expectedly increasing theSNR and consequently increasing the similarity between neighboring IDCs. Finally,the lower spatial resolution of 4D DCE-US may result in a higher similarity betweenneighboring voxels, which again is counterbalanced by the speckle regularization filter.The combined e�ect of these di�erences on the similarity parameters is di�cult topredict. However, the most important observation is the pattern being consistent in2D and 3D CUDI using separate UCA bolus injections, which implies reproducibilityof the method.

We also observed a di�erence in absolute parameter values of 3D CUDI for the tworecordings in patient 1 (Fig. 3.8). Although this might be explained by the di�erentscanner settings and DCE-US data characteristics, another explanation could relate tothe fact that two separate bolus injections were used to make the recordings. Firstly,there might have been a slight reduction in the amount of UCA that was injected inthe second recording. Secondly, some of the UCAs from the first injection might stillhave been circulating at the beginning of the second recording, despite the 5-minutewaiting period between subsequent injections. In both cases, this would result in a

Discussion 57

lower SNR and hence a lower similarity between neighboring curves due to spatiallyuncorrelated noise. However, in both recordings in patient 1, the highest parametervalues were observed at the base and the lowest in the right-apical quarter, confirmingconsistency in the relative pattern.

It is remarkable that the lowest similarity in patient 1 was observed in the quarterwith the most positive biopsy samples (Fig. 3.8). However, because in a systematicbiopsy the prostate is only sparsely sampled, there is a real possibility that tumors inthe other quarters are larger. While the scope of this paper is mainly on the feasibilityof using the 4D DCE-US recordings for 3D CUDI, future work could incorporate a moreextensive validation – including more patients or using full histology – to accuratelyquantify the correlation between 3D dispersion maps and tumor locations.

For the last dataset, plane 2 of patient 2 (Fig. 3.7), both 2D CUDI parametersshow a few enhanced areas in the transition zone, whereas the parameters calculatedby 3D CUDI are low throughout the entire image. We believe this di�erence is mainlycaused by artifacts (poor tissue suppression) in the ultrasound image (Fig. 3.9), whichcause the nonlinear response in the contrast image to be high even when no UCAis present. As a result, the similarity between IDCs in those areas is high, possiblyleading to a false positive where the biopsy results were negative. The enhanced areasare slightly larger than the artifacts, which, in our opinion, is predominantly caused bymovement of the probe or patient, and by spatial pre- and post-filtering. In the 4Dsimilarity analysis, the kernel covered a larger volume extending beyond the artifactalone. In that case, the similarity dropped and the artifact did not show in the finaldispersion maps. This is an example in which the extra information obtained by addingthe third spatial dimension into the analysis can lead to more accurate classification.

3.4.2 Data characteristicsAdditionally, we characterized the 2D and 4D DCE-US datasets with respect to tem-poral and spatial resolution. In the worst case, in which a 4D DCE-US image wasrecorded at maximum field of view, the temporal resolution was 0.26 Hz. Althoughthis number is almost a factor 30 lower than for the corresponding 2D DCE-US im-age, the resulting CUDI images show great relative agreement. An explanation forthis observation can be found by a frequency analysis of the theoretical IDC describedin [130]. The normalized power spectra of simulated IDCs with di�erent values of ,while keeping mean transit time µ constant at 20 s (typically observed in humans) isgiven in Fig. 3.10. The proposed threshold for to distinguish benign from malignanttissue lies at 0.84 s-1 [130]. However, even for = 3 s-1 – corresponding to the fastestkinetics – 99.6% of the power is located in the frequency bands below the Nyquist fre-quency of 4D DCE-US (0.13 Hz). From this, it follows that realistic IDCs can almostentirely be described by data recorded at the temporal resolution of the presented 4DDCE-US data.

The 2D DCE-US recordings have a temporal resolution which is much higher than

58 Technical feasibility of 3D CUDI

artifacts

Figure 3.9: A frame of the 2D contrast video of the second imaging plane for patient 2,before the contrast has reached the prostate. The artifacts can clearly be observed. Thecorrelation map has been overlaid on the fundamental part of the image.

the highest frequencies in the IDCs. For these recordings, a standard low-pass filterin the time domain can already increase the SNR. However, for the 4D DCE-USrecordings, the temporal resolution gives little opportunity for noise suppression byconventional linear filtering. As a result, the final 3D CUDI image is very sensitive tothe SNR of the underlying 4D DCE-US. Denoising based on dedicated noise models(as suggested in [179] or [180]) can possibly improve the method’s robustness.

Because there is limited room for noise suppression by temporal filtering, 3D CUDIcould still benefit from a higher temporal resolution. Based on the data characteristicsin Table 3.1 – considering the traveling time of the ultrasound pulses as the onlylimiting factor and assuming a pulse inversion scheme – the theoretical limit to thetemporal resolution for 4D DCE-US with full field of view is approximately 1.4 s-1.This suggests that in theory the temporal resolution could still be improved whilemaintaining the image quality.

In the far field (40 mm from the probe head), the lateral (and elevational) specklesize of 4D DCE-US is 1.8 mm, approximately twice that of 2D DCE-US (Fig. 3.2).Although it is smaller than the 2-3-mm resolution required for detection of early an-giogenesis [175], it is larger than the inner radius of the kernel used for the similarityanalysis (1 mm). Hence, the Wiener filter is not only required to compensate for thedepth-dependency of the speckle size, but also to reduce the speckle size to stay withinthe inner radius of the kernel for 3D CUDI.

3.4.3 Future workBecause only two patients were included in this pilot study, future work includes ex-tension of the patient group to be able to perform a quantitative validation, possiblycompared with histology after radical prostatectomy.

The analyses made in this study used data obtained by a commercially available

Discussion 59

Frequency (Hz)0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Pow

er s

pect

ral d

ensi

ty (n

orm

aliz

ed)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Nyquist frequency

=0.10 (s-1), 100.0% of power below Nyq. freq.=0.50 (s-1), 100.0% of power below Nyq. freq.=1.00 (s-1), 100.0% of power below Nyq. freq.=3.00 (s-1), 99.6% of power below Nyq. freq.

Figure 3.10: Normalized power spectrum of the theoretical indicator dilution curve.

machine, which was not designed for our purpose. Performance of 3D CUDI mightstill improve if the image acquisition method (e.g., the balance between spatial andtemporal resolution) is optimized for our algorithm.

Because no motion compensation has been applied to the DCE-US data before per-forming the CUDI analysis, movement of the probe relative to the patient during datarecording may result in spatial blurring of the IDCs. This may a�ect the spatial reso-lution of the resulting CUDI map. However, in most cases, it will not lead to a strongartifact in similarity because of the small local variation in IDC shape. Moreover, mo-tion of the probe is physically limited by the rectum. Considering the aforementionedremarks and the threshold of 0.5 cm3 for clinically significant tumors [139], we expecta negligible influence of motion on the diagnostic information provided by CUDI. Yet,in future work, it could be interesting to explore the e�ect of motion compensation inthe 4D DCE-US datasets on the final CUDI maps.

A 3D prostate cancer imaging technique based on TRUS can be very helpful fortaking targeted biopsies. Di�erent from targeted biopsies based on MRI [205], nomulti-modal registration technique or expensive equipment is required. Regardingultrasound-based methods, the availability of 3D data helps navigation to the lesionsfound by the prostate cancer imaging technique, and the entire prostate volume iscovered.

Because CUDI is based on di�erences in UCA dispersion caused by angiogenicmicrovasculature, this method theoretically works in any type of cancer where angio-genic growth is present. Application of the method to organs other than the prostateis therefore a logical step to make.

60 Technical feasibility of 3D CUDI

3.5 ConclusionAn extension of 2D CUDI to 3D using 4D DCE-US is proposed. We assessed thedata characteristics of the 4D DCE-US recordings and found them to be su�cient forenabling 3D CUDI by similarity analysis. The method could however benefit from anincreased temporal resolution, which could theoretically be achieved without compro-mising the image quality. Additionally, a preliminary validation of 3D CUDI in twopatients by quantitative comparison of 3D CUDI with 2D CUDI and results from 12-core systematic biopsies yielded promising results. When more extensively validated,3D CUDI could possibly be employed for targeting biopsies or focal treatment.

3.6 Appendix: UCA dispersion distanceThe dispersion of UCA through a vascular network can be modeled as particles flowingthrough an infinitely long tube with cross-sectional area Atb [130, 206]. Assuming aninitial UCA concentration CUCA(x, 0) = (m/Atb)�(x) where m is the mass of UCAand �(·) is the Dirac delta function, the UCA concentration CUCA(x, t) can be writtenas a function of the distance x downstream from the injection site and the time t afterthe injection as [206]

CUCA(x, t) =m

Atb

p4⇡Dt

exp

� (x� vt)

2

4Dt

!. (3.2)

In (3.2), conservation of mass is assumed, hence Atb

R1�1 CUCA(x, t)dx = m. If

no convection takes place (v = 0), (3.2) can be rewritten as

CUCA(x, t) =m

Atb

· 1

�p2⇡

exp

✓� x

2

2�2

◆, (3.3)

with�(t) =

p2Dt.

The last term in (3.3) can be recognized as a Gaussian probability density functionwith 0 mean and standard deviation equal to �. Consequently, at each time t, thespatial distribution of UCA is Gaussian, with standard deviation of UCA position x

equal to �(t) =p2Dt, referred to as dispersion distance.

3.7 Appendix: Relation between speckle size and fil-ter parameters

In this paper, following [133], 2D fully developed speckle s (xim) as function of thelocation xim in a US image is modeled as Gaussian noise nw (xim) with mean µn

and variance �2n, spatially filtered by a Gaussian filter Hsp (�ax,�lat) with constant

Appendix: Relation between speckle size and filter parameters 61

axial standard deviation �ax and lateral standard deviation �lat (d) dependent on theimaging depth d. The axial direction at a certain point in the US image is defined as thedirection of the US imaging line through that point and the lateral direction is definedas the direction perpendicular to the axial direction. As a result, the orientation ofthe filter changes, depending on the location in the US image. Since the 2D Gaussianfilter can be written as a convolution of two 1D Gaussian filters in the axial andlateral direction, from now on we will regard speckle in 1D (either in the axial orlateral direction) with a corresponding Gaussian filter Hsp (�sp). If hsp is the impulseresponse of Hsp (�sp) at a certain location in the US image, 1D speckle s (xim) in theneighborhood of that location can be written as

s (xim) = (nw ⇤ hsp) (xim) . (3.4)

The speckle size of s (xim) is defined as the full-width at half maximum (FWHM) ofthe autocovariance Css (�x) of s (xim) [131], defined as [207]

Css (�x) = E [(s (xim)� µs) (s (xim +�x)� µs)]

= E [s (xim) s (xim +�x)]� µ2s

= Rss (�x)� µ2s, (3.5)

where µs is the mean and Rss (�x) is the autocorrelation of s(xim). Because s (xim)

is linearly filtered wide sense stationary noise, Rss can be expressed as [207]

Rss (�x) =

Z 1

�1hsp (u)

Z 1

�1hsp (v)Rnn (�x+ u+ v) dvdu. (3.6)

In (3.6), the autocorrelation Rnn (�x) of the Gaussian noise is equal to Rnn (�x) =

µ2n+ �

2n� (�x), where �(·) is the Dirac delta function. By using the fact that the

Gaussian impulse response h integrates to 1, we can rewrite (3.6) as

Rss (�x) = µ2n+ �

2n

Z 1

�1hsp (u)hsp (�x+ u) du. (3.7)

Substituting (3.7) into (3.5) and using the fact that the mean of the noise does notchange after filtering (µs = µn) yields

Css (�x) = �2n

Z 1

�1hsp (u)hsp (�x+ u) du. (3.8)

From (3.8) it is clear that the FWHM of Css is in fact the FWHM of the convolutionof hsp with itself. The convolution of a Gaussian function (standard deviation �) withitself is again a Gaussian function with standard deviation

p2�. The FWHM of the

impulse response of a Gaussian filter with standard deviation � is equal to 2p

2 ln 2�.The FWHM of Css (or speckle size) can therefore be expressed in terms of �sp asFWHM = 4

pln 2�sp ⇡ 3.3�sp, or inversely �sp ⇡ 0.30 FWHM.

62 Technical feasibility of 3D CUDI

Chapter43D CUDI based on mutualinformation

The content of this chapter has been published as [IC2]:

S.G. Schalk, L. Demi, J.J.M.C.H. de la Rosette, P. Huang, H. Wijkstra, andM. Mischi, “3D contrast ultrasound dispersion imaging by mutual information forprostate cancer localization,” in Proc. IEEE Int. Ultrason. Symp., Taipei (Taiwan)Oct 21-24, 2015, 4 pages. © 2015, IEEE.

64 3D CUDI based on mutual information

AbstractProstate cancer (PCa) is the most occurring type of cancer in the Western World. Yet,the most common diagnostic tool, systematic biopsy, is invasive and has low sensitivity.Recently, contrast-ultrasound dispersion imaging (CUDI) by spatiotemporal similarityanalysis on contrast-enhanced ultrasound (CEUS) has been proposed as a promising,non-invasive alternative for PCa localization. It was shown that increased mutualinformation (MutI) between the indicator dilution curves in a block kernel and itscentral pixel relates to the presence of PCa. However, until now CUDI by MutI has beeninvestigated in 2D only, requiring a separate contrast injection for each imaging plane.Moreover, out-of-plane contrast flow could not be taken into account. In this work, weimplemented CUDI by MutI using 4D CEUS to overcome the aforementioned issues.We tested its feasibility to perform 3D CUDI by comparison with 12-core systematicbiopsies in 3 patients. The mean MutI for the patient with only one positive biopsysample was significantly lower than that for the other two patients with more than 6positive samples. This result encourages refinement and validation of the presentedmethod in a larger patient group.

Introduction 65

4.1 IntroductionProstate cancer (PCa) is the first type of cancer among males in the United Statesfor incidence and the second for mortality [159]. However, the typical diagnostic toolsfor PCa diagnosis, prostate-specific anitigen (PSA) blood test and systematic biopsy,have a low specificity and sensitivity, respectively [31, 42]. Moreover, being invasive,biopsies can be painful and cause infections [29].

For these reasons, researchers have been looking for a minimally invasive method tolocate PCa. One of the most promising of such methods is multi-parametric magneticresonance imaging (mpMRI) [193], which combines several MRI-based imaging tech-niques by scoring them through the PI-RADS [55] or the updated PI-RADSv2 [208]scoring system. Although mpMRI adds diagnostic value to systematic biopsies, theinterpretation of the mpMRI data remains complex and subjective [194].

Transrectal ultrasound (TRUS) has shown potential as an alternative imagingmodality for PCa detection through the development of several dedicated meth-ods [75, 76, 97, 100, 130–132, 201, 209]. Unlike MRI, TRUS is cost-e�ective, directlyapplicable at the bedside, and can be adopted without the need for support by theradiology department.

One type of TRUS-based methods involves machine learning approaches combiningfeatures extracted from RF data or gray-scale (fundamental) images [75,76]. This haslead to a commercial implementation, histoscanning [76], but a large scale study [210]reported a sensitivity and specificity of only 60% and 66%, respectively.

Other methods exploit the increased sti�ness of tumors with respect to healthytissue, of which in particular shear wave elastography imaging produced very promis-ing results with sensitivity and specificity values above 90% [97, 100]. However, thistechnique has not been validated in a large patient study, yet.

In a di�erent approach, angiogenesis (i.e., formation of new microvessels requiredfor a tumor to grow) is used as a marker for PCa. For example, Doppler ultrasound incombination with an ultrasound contrast agent (UCA) is used to reveal an enhancedperfusion as a result of angiogenesis [201,209], whereas other methods extract hemo-dynamic parameters from dynamic contrast-enhanced ultrasound (CEUS) recordingsto detect this increase in perfusion [201].

In recent work by our group [130–132], contrast ultrasound dispersion imaging(CUDI) has been developed, focusing on lower dispersion (rather than higher perfusion)as a result of properties of the microvascular architecture specific to angiogenesis(rather than increased microvascular density). A number of parameters related to thelocal dispersion of a bolus of UCAs have been explored. In an initial implementationof CUDI [130], a convection-di�usion model was fitted to individual indicator-dilutioncurves (IDCs, contrast concentration as a function of time) to obtain a dispersion-related parameter . Later, it was shown that can indirectly be estimated fromthe similarity between an IDC in a center pixel and those in an area around it [131,132], expressed in linear similarity metrics. More recently, mutual information (MutI)

66 3D CUDI based on mutual information

has been investigated in this context as a more general similarity metric, with verypromising results [174].

However, until now CUDI by MutI has been implemented using 2-dimensional (2D)CEUS imaging only. Consequently, only one plane per UCA injection can be recordedand out-of-plane contrast flow cannot be analyzed. When using a 3-dimensional (3D)probe to make 4-dimensional (4D, 3D + time) CEUS recordings, the entire prostatecan be imaged using a single contrast injection. As a results, no tumors are missedfor being outside the imaging plane and costs and time of a CEUS investigation arereduced, improving patient comfort. Moreover, since dispersion is by nature a 4Dprocess, a more accurate estimation of the contrast dispersion could be achieved, alsoaccounting for out-of-plane flow.

This paper describes a 3D implementation of CUDI by MutI. To this end, some ofthe previous design choices made for 2D CUDI had to be reconsidered and optimizedto better suit the di�erent characteristics of 4D CEUS data. The feasibility of themethod has been evaluated in three patients from two di�erent hospitals by comparingthe MutI maps with results from 12-core systematic biopsies.

4.2 Material and Methods

4.2.1 TheoryIn previous work [131, 132, 174], it was shown that an increased similarity betweenneighboring IDCs can be linked to PCa. In this context, a nonlinear similarity measure,I(K,C), was introduced based on the MutI among IDCs. This is defined as [174]

I(K,C) =

X

k2K

X

c2CPK,C(k, c) log2

⇣PK,C(k, c)

PK(k)PC(c)

⌘(4.1)

with

PK(k) =

X

c2CPK,C(k, c),

PC(c) =

X

k2KPK,C(k, c).

The random variables C and K represent the contrast levels c and k in a certainpixel (voxel in 3D) and in those in a kernel around it, respectively. The contrast levelsare logarithmically related to the UCA concentration [130]. In the 2D implementation[174], a square kernel was used and contrast levels were coded with 8-bits; in thatcase C = K = {0, 1, ..., 255}.

From (4.1), it can be observed that I is dependent only on the joint probabilitymass function (PMF) PK,C(k, c) of C and K, which, after applying the marginalization

Material and Methods 67

PK,C(k, c) = PK|C(k|c)PC(c), can eventually be approximated by [174]

PK,C(k, c) =Nk|c(k, c)

N · F , (4.2)

in which Nk|c(k, c) is the number of pixels in the kernel where K = k at time instanceswhere C = c. The variable N represents the total number of pixels in the kernel; Frepresents the number of frames in an IDC.

4.2.2 Data AcquisitionFor the 4D analysis, CEUS data were acquired from three patients referred for system-atic biopsies: two from the Academic Medical Center (AMC), University of Amsterdam(Amsterdam, The Netherlands) and one from the Second A�liated Hospital of theZhejiang University School of Medicine (Hangzhou, Zhejiang, China).

Each patient was injected with a 2.4-mL bolus of UCA SonoVue® (Bracco, Milan,Italy) to record a 2-minute CEUS volume sequence (with voxel size 0.253 mm3) usinga LOGIQ E9 ultrasound scanner (GE Healthcare) equiped with a 3D RIC5-9 probe.The scanner was used in contrast-specific mode. Furthermore, the mechanical indexwas set to a low value (0.09–0.12) to prevent UCA destruction and the imaging qualitysetting (BQ) was set to “low” to maximize the volume rate.

4.2.3 Mutual Information in 3DBefore applying the analysis described in Section 4.2.1 to the 4D CEUS data, pre-processing steps, much like those in [J6], were applied. First, the data was spatiallyfiltered using the speckle regularization filter described in [J6]. This step allowedspatial downsampling by a factor 3⇥3⇥3, strongly reducing the computation time.

The IDCs were then time-windowed to focus on the most informative part. In2D CUDI [174], the optimal window was found to be the period from 3 s before to6 s after UCA appearance (defined as the point at which the IDC reaches 10% of itspeak). Considering the low volume rate of 3D CEUS data (0.26-0.30 s-1), the windowlength was heuristically extended to 25 s, starting from UCA appearance.

Finally, to avoid a very sparse PMF as a result of the low volume rate, the numberof contrast levels was reduced from 256 to 64. As a result, C = K = {0, 1, ..., 63}.

For the CUDI analysis the square kernel used in 2D [174] was extended to 3D.However, instead of a cubic kernel, a hollow, shell-shaped kernel like the one describedin [J6] was used. This kernel does not include IDCs within 1 mm from the center IDCto avoid a bias in similarity caused by the intrinsic resolution of the imaging system.

After computing I for each voxel, a 3D Gaussian filter with a standard deviationof 0.5 mm was applied to obtain the final parametric map.

68 3D CUDI based on mutual information

Figure 4.1: Transversal cross-sections of the parametric maps of mutual information I.

4.2.4 ValidationBefore validating 3D CUDI by MutI, the three prostates were manually segmentedfrom the CEUS sequences. From each segmentation, a binary mask (representing thevoxels inside the prostate) was generated, which was eroded by 2 mm to account forsegmentation errors. These masks were then used to extract only those values fromthe parametric maps of I that were inside the prostate. Probability density functions(PDFs) of I were estimated for each prostate, based on their respective histograms.

Each patient underwent a 12-core systematic biopsy of which the outcome (numberof positive biopsies) was compared to the PDF and to the average value of I found inthat patient. Di�erences between the means of I among the patients were consideredto be significant for p < 0.05, calculated by a two-tailed Welch’s t-test. Pre-processing,post-processing, and the size of the kernel create a dependence between neighboringvalues of I unrelated to the presence of PCa. For this reason, only samples from theparametric maps at a minimum mutual distance of 10 mm were used for the statisticalanalysis.

4.3 ResultsFigure 4.1 shows the central, transversal cross section of the parametric maps of I foreach patient. The average values of I (calculated over the entire prostate) and thenumber of positive biopsies found in each patient are given in Table 4.1. As expected,in patient 1, with only one positive biopsy sample, the lowest values of I were obtained.The two patients with >50% positive biopsy samples, on the other hand, producedhigher values of I.

In Fig. 4.2(a) the estimated PDFs of I are plotted for each of the three patients. InFig. 4.2(b) the PDFs of patient 2 and 3 are combined to stress the di�erence betweenthe patient with only 1 positive biopsy sample and the patients with more than 6positive samples. The di�erence between the average values of I for the negative caseand the positive cases was significant (p < 0.001). Also, a significant di�erence was

Discussion 69

Mutual information0 0.2 0.4 0.6 0.8 1 1.2

Prob

.den

sity

0

0.5

1

1.5

2

2.5

3Patient 1Patient 2Patient 3

(a)

Prob

.den

sity

Mutual information0 0.2 0.4 0.6 0.8 1 1.2

0

0.5

1

1.5

2

2.5

3Negative casePositive cases

(b)

Figure 4.2: Probability density of mutual information I for each patient. In subfigure (b),the probability densities for patients 2 and 3 — with mostly positive biopsy samples — havebeen combined.

observed between the values of I for each set of two patients (p = 0.048 for patient 2and 3 and p < 0.001 for both other sets).

4.4 DiscussionIn this paper we presented an extension of CUDI by MutI [174] to 3D and carried outa preliminary validation with systematic biopsies in three patients from two di�erenthospitals. A significant di�erence was observed between the positive (patient 2 and 3)and negative cases (patient 1). A similar result was found for 3D CUDI using linearsimilarity measures, validated in two patients [J6].

Unexpectedly, even though the number of positive biopsies in patient 3 is higherthan in patient 2, the average MutI is higher in patient 2. An explanation can be foundin the large size of the prostate. In general, the signal-to-noise ratio (SNR) declinesfor larger distances from the probe. For large prostates this distance may have such anegative e�ect on the SNR in the far field that the similarity between IDCs significantlydecreases in that area. This decrease is also visible in Fig. 4.1. To further investigatethis hypothesis, we repeated the statistical tests including only values of I within

Table 4.1: Mutual information compared to biopsy results

Positive biopsies Gleason score (#) I (mean ± std. dev.)

Patient 1 1 of 12 3+3 (1) 0.26 ± 0.14Patient 2 7 of 12 4+3 (7) 0.61 ± 0.25Patient 3 11 of 12 4+3 (7), 3+4 (4) 0.51 ± 0.17

70 3D CUDI based on mutual information

30 mm from the tip of the probe. The average value of I for patient 2 and 3 increasedthen to 0.63 ± 0.24 and 0.57 ± 0.14, respectively. The resulting di�erence was nolonger significant (p = 0.94). When more data is available, a compensation for thise�ect could be incorporated into the method.

When interpreting the results of Table 4.1, the reader should keep in mind thattumors can be overgraded, undergraded, or missed entirely during a systematic biopsy[41,211]. Therefore, small variations in the number of positive biopsy samples and

the Gleason score determined in those samples cannot always correlate to the valuesfound by CUDI.

In a patient with a similar number of positive and negative biopsies, a higherheterogeneity in tissue type (healthy or cancerous) is expected. The PDF of patient 2in Fig. 4.2(a) is more spread out than that of patient 1 or 3, which supports thishypothesis.

Although these preliminary results are promising, more patients should be addedfor a solid statistical analysis. Moreover, including patients referred for radical prosta-tectomy makes it possible to use full histopathology as a ground truth instead of thebiopsy samples used in this work. Full histopathology provides a better characteri-zation (e.g., size and shape) of tumors. Moreover, it can potentially lead to a moreaccurate registration between parametric maps and ground truth. Both improvementswill be made in future studies.

The parameter settings for the spatial filter and the time window have now beendetermined heuristically. When more data is available, these filters will be optimizedin a more structured way, improving the classification performance of the method.

In this study, MutI has been investigated as a general measure for similarity betweenIDCs. However, other parameters reflecting the statistical dependency between IDCswill also be explored in future work.

Here and in previous work [174], the concept of using MutI between IDCs hasbeen tested for PCa localization. Because the presented method is designed to de-tect the formation of angiogenesis, it could also be applied for locating cancer whereangiogenesis plays an important role in organs other than the prostate.

4.5 ConclusionA two-dimensional method estimating the mutual information between neighboringindicator dilution curves to locate prostate cancer has been extended to three dimen-sions. This extension can possibly reduce costs and improve patient comfort, whileincreasing the method’s ability to locate tumors. The preliminary results encourageexpansion of the study to a larger dataset, also including patients referred for radicalprostatectomy. This enables further refinement and more accurate validation of themethod. The nature of the method allows application in other types of cancer in whichangiogenesis is involved.

Chapter5Clinical validation of 3D CUDI

The content of this chapter has been submitted for publication as [J2]:

S.G. Schalk, J. Huang, J. Li, L. Demi, H. Wijkstra, P. Huang, and M. Mischi,“3D quantitative contrast ultrasound for prostate cancer localization,” Eur. J.Ultrasound.

The work presented in chapter was supported by the National Natural ScienceFoundation of China.

72 Clinical validation of 3D CUDI

AbstractPurpose: To investigate the possibility of using quantitative 3D dynamic contrast-enhanced ultrasound (DCE-US), and in particular 3D contrast-ultrasound dispersionimaging (CUDI), for prostate cancer detection and localization.

Materials and Methods: 43 patients referred for 10-12-core systematic biopsyunderwent 3D DCE-US. For each 3D DCE-US recording, parametric maps of CUDI-based and perfusion-based parameters were computed. Per biopsy core, the presenceof malignancy and the Gleason score were reported. Each prostate was divided in12 sections corresponding to the biopsy locations. The 90th percentile values of theparameters in each biopsy location were compared with the biopsy outcome. Next,adjacent sections were combined into 6, 3, 2, and 1 section(s). Two validations wereperformed: one considering a section malignant if at least one core had malignancy,another if at least half of the cores were malignant. Finally, sensitivity and specificityto detect cancer were also evaluated.

Results: For CUDI by correlation (r) and wash-in time (WIT), a significantdi�erence in parameter values between benign and malignant biopsy cores wasfound (p < 0.001). For these two parameters, areas under the receiver operatingcharacteristic curve strongly increased for sections consisting of �50% malignantcores. In a left/right analysis, sensitivity and specificity were 65% and 80% for r, and57% and 77% for WIT, respectively; in a per-prostate analysis, they were 94% and50% for r, and 53% and 81% for WIT.

Conclusion: Quantitative 3D DCE-US can detect prostate cancer. We recommendfollow-up studies to investigate its value for targeting biopsies.

Introduction 73

5.1 IntroductionThe current standard method for prostate cancer (PCa) diagnosis is TRUS-guidedsystematic biopsy, usually after suspicion has been raised by digital rectal examina-tion (DRE) or an elevated serum prostate-specific antigen (PSA) level [8]. However,systematic biopsies frequently miss or under-grade tumors [41, 212]. In the latest in-ternational guidelines, multiparametric MRI (mpMRI) is recommended for patientswith persistently elevated PSA level and a prior negative biopsy session [8, 55]. How-ever, MRI investigations cannot be performed at the bedside and bring increasedcosts. Several alternative TRUS-based techniques, such as (shear-wave) elastography,computer-aided TRUS, and dynamic contrast-enhanced ultrasound (DCE-US), havebeen developed, that show promise for PCa detection [213].

In DCE-US, intravenously injected microbubbles with a size comparable to redblood cells are used as contrast agents. Although the resolution of DCE-US imag-ing is not in the range of the size of the microvasculature, the kinetics of the mi-crobubbles through the microvasculature can be captured by recording their concen-tration over time. PCa growth requires angiogenic microvasculature, which has di�er-ent structural properties (e.g., increased tortuosity, presence of arteriovenous shunts,increased permeability) resulting in di�erent microbubble kinetics [11]. Therefore,several studies have been carried out using DCE-US imaging qualitatively to detectPCa [106,107,214]. DCE-US features related to PCa are rapid contrast enhancement,increased contrast enhancement, and asymmetric flow patterns [111, 215] however,their e�ects are usually very subtle and vanish within seconds. Consequently, inter-pretation of DCE-US recordings is rather subjective when interpreted with the nakedeye. To increase objectivity and improve accuracy, the possibility of using quantitativemethods by extracting perfusion-based parameters from DCE-US recordings have beeninvestigated [113,201].

Recently, contrast-ultrasound dispersion imaging (CUDI) has been proposed as anovel approach to distinguish between angiogenic and healthy vasculature by focusingon contrast dispersion rather than perfusion [130,132,133],[J4]. In fact, it was hypoth-esized that dispersion better reflects the underlying microvascular di�erences. At theorigin of this technique, a model was fitted to acoustic time-intensity curves (TICs)in each pixel of a DCE-US recording [130]. From the fit, a dispersion-related param-eter could be extracted. Later it was shown that the similarity between neighboringTICs could be used as an indirect measure of local dispersion, which lead to betterclassification results [132, 133],[J4]. Three di�erent similarity measures were investi-gated: temporal correlation (r), spectral coherence (⇢), and mutual information (I).However, the method was still limited by the 2D nature of the recordings. Each planerequired a separate injection of microbubbles, tumors between imaging planes weremissed, and out-of-plane flow could not be observed.

Using 3D DCE-US enables imaging the vasculature in the entire prostate witha single injection of contrast agent and the inherently three-dimensional transport

74 Clinical validation of 3D CUDI

kinetics can be observed. In a recent study, the technical feasibility of 3D CUDI asthe first quantitative method using 3D DCE-US for PCa was tested in vivo in twopatients [J6]. Although the temporal resolution of 3D DCE-US recordings was too lowfor model fitting, 3D CUDI by similarity analysis was shown to be possible.

In this work, we tested the ability of quantitative 3D DCE-US, and in particular 3DCUDI by similarity analysis, for PCa detection by comparison with systematic biopsiesin 43 patients. Three similarity and four perfusion parameters were extracted from the3D DCE-US recordings. We investigated which parameters could discriminate betweenbenign and malignant tissue and made a preliminary estimation of their classificationperformance.

5.2 Patients and study designBetween January 2015 and July 2015, 9 patients, and between December 2015 andMarch 2016, 49 consecutive patients referred for systematic biopsy underwent DCE-US at the Second A�liated Hospital of Zhejiang University (SAHZU) (Hangzhou,Zhejiang, PR China). Inclusion criteria were age >18 years and referral for systematicbiopsy and DCE-US based on elevated PSA level, abnormal DRE, or lesions visiblein MRI. This study was approved by the local ethical committee and the institutionalreview board of SAHZU. Written informed consent was obtained from all participantsin the study.

After intravenous injection of 2.4 mL Sonovue® (Bracco, Milan, Italy) microbub-bles, 3D DCE-US imaging was performed using a LOGIQ E9 ultrasound scanner (GEHealthcare, Wauwatosa, WI, USA) equipped with an RIC9-5 transducer. To maxi-mize the volume rate, the imaging quality setting “B” was set to “low”. The acousticoutput power setting “AO%” was limited to “10” to prevent bubble disruption. EachDCE-US recording lasted 2 minutes and was stored in raw DICOM format. Aftertechnical evaluation of the DCE-US recordings, 13 patients were excluded (Fig. 5.1).The remaining recordings were prepared for analysis as described in [J6]. On eachof these datasets, a CUDI similarity analysis as described in [J4,J6] was performedto generate parametric maps (Fig. 5.2) of r, ⇢, and I. To enable a fair comparisonbetween the similarity measures, the same time window of 45 s, like the one describedin [J6], was used for each measure. Additionally, several perfusion parameters pro-posed in the literature [201] were extracted from the TICs at each voxel: wash-intime (WIT), peak intensity (PI), wash-in rate (WIR), and area under the TIC withinthe time window (AU-TIC). A brief description of each of the parameters is given inTable 5.1.

Systematic biopsies were performed following a 12-core protocol in which 4 coreswere taken from each of the basal, middle and apical part of the prostate. In 6 cases,1 or 2 samples were not taken from the base or apex because of the small size of theprostate. For each biopsy location, the presence of malignancy and its corresponding

Patients and study design 75

Figure 5.1: Inclusion flowchart. Protocol violations included excessive probe movement,wrong scanner settings, and untimely start of the recording. Technical complications encoun-tered were low and inconsistent sample rate and lack of contrast signal.

Table 5.1: Description of parameters obtained from 3D DCE-US recordings.

TH signParameter Symbol for mal. Description

correlation r > Cross-correlation between neighboring TICs.coherence ⇢ > Cross-correlation between the frequency

spectra of neighboring TICs.mutual information I > Mutual information between neighboring

TICs.wash-in time WIT < Time between the appearance of microbub-

bles and the peak of a TIC.peak intensity PI > Maximum linearized acoustic intensity in a

TIC.wash-in rate WIR > PI divided by WIT.area under the curve AU-TIC > Area under a linearized TIC within the ap-

plied 45-s time window.

TH: threshold; mal.: malignancy; TIC: time-intensity curve.

Gleason score were reported. In two cases, the biopsy report was inconclusive; thesepatients were excluded from the study (Fig. 5.1).

Comparison of the parametric maps with the biopsy results was done in a fine-to-coarse fashion, much like the validation performed in [J6]. First, validation wasperformed per biopsy location, dividing the manually drawn prostate into 12 sections(Fig. 5.3). To ensure that the analysis was performed on data inside the prostate, a

76 Clinical validation of 3D CUDI

Figure 5.2: Example of a parametric map of TIC correlation; (a): 3D parametric map,(b-d): transversal cross-sections at the base, middle, and apex of the prostate. The 12sections corresponding to the biopsy locations are shown in black. Gleason scores are writtenbelow each location (B = benign).

5-mm erosion was applied to the prostate boundaries prior to analysis. In addition,5-mm margins were applied between adjacent sections to prevent correlation betweenparameter values caused by the resolution of the parametric maps [J6]. Because thebiopsy needle did not reach tissue deeper than 22 mm, only voxels up to 22 mmanterior to the tip of the transducer were considered for validation. Any section for

Patients and study design 77

which the biopsy report was inconclusive was excluded from further analysis.Within each section, the 90th percentile of each parameter was computed and

compared with the biopsy outcome in that section (test 1). The 90th percentile wasused, because somewhere in a positive section an area with high parameter valuesshould occur, but not necessarily cover the entire section. For parameters for whichmalignancy would result in lower values (based on previous findings [J4]), the 10th

percentile was used. Additionally, since Gleason score is an important prognosticmarker [39], we tested parameters on their ability to di�erentiate between low grade(Gleason 6 and 7), and high grade (Gleason 8 to 10).

Subsequently, adjacent sections were combined yielding 6, 3, 2, and 1 section(s)(Fig. 5.3) (test 2). In this way, misclassification by uncertainty in the precise biopsylocation was partly removed. A section was considered malignant if at least one biopsysample within this section had a Gleason score �6. Di�erences between parametervalues in benign and malignant sections were considered to be significant for p < 0.05,determined by a Wilcoxon rank-sum test. For each parameter, receiver operatingcharacteristic (ROC) curves were generated. The area under the ROC curve wascomputed as a measure of classification performance.

In another test (test 3), the described validation was repeated on the divisions in3, 2, and 1 sections. However, this time, a section was considered malignant if atleast half of the biopsy cores were malignant and benign if all biopsy cores in it werebenign. As a result, the parameters were tested for detection of larger cancerous areas.For parameters able to identify PCa, the di�erences between benign and malignantsections were expected to grow, resulting in a larger area under the ROC curve.

A last test (test 4) was designed to estimate the sensitivity and specificity ofthe best performing parameters. In this test, each biopsy location was classified aspositive or negative following the procedure used in test 1. However, because thechance of a biopsy core missing a tumor is relatively large, validation was performedin a left/right and per-prostate analysis (i.e., dividing prostates in 2 and 1 section(s)).A section was considered benign if all biopsy cores in this section were benign; it wasconsidered malignant if at least one core was malignant. Nonetheless, if all cores ina systematic biopsy are negative, there is still a significant chance that a tumor hasbeen missed [212]. For this reason, we marked a false positive (FP) as “undecided” ifless than 20% of the biopsy locations in a benign section were classified as malignant

Figure 5.3: Division of a prostate in 12, 6, 3, 2, and 1 section(s).

78 Clinical validation of 3D CUDI

Table 5.2: Description of parameters obtained from 3D DCE-US recordings

Mean (median; range) age [years] 69 (70; 47-81)Mean (median; range) PSA [ng/mL] 23.1 (8.7; 0.3-340.0)

No malignant biopsy cores 9.8 (7.6; 1.4-21.0)At least one malignant biopsy core 34.9 (13.8; 0.3-340.0)

Highest GS per biopsy [number of patients] 43NC 26GS unknown 13 + 3 33 + 4 34 + 3 53 + 5 14 + 4 15 + 3 04 + 5 05 + 4 25 + 5 1

NC: no cancer; GS: Gleason score

(i.e., 1 biopsy location for half and 2 for full prostates). Classification thresholds forthe parameters were set to maximize Youden’s index [216].

5.3 ResultsPatients and biopsy characteristics are summarized in Table 5.2. In 17 out of 43 pa-tients (40.0%), at least one of the biopsy cores contained malignant tissue. The medianPSA level was higher for patients in which malignancy was found (13.8 ng/mL) thanfor patients without malignancy (7.6 ng/mL), although not significantly (p = 0.21).Malignancy was reported in 76 out of 507 biopsy cores (15.0%). For one biopsy core,malignancy was reported, but the Gleason score was not specified.

The area under the ROC curve (AU-ROC) and p-value for each of the parameterstested in the fine-to-coarse validation (test 1 and 2) are presented in Table 5.3. Foreach division, r resulted in the highest AU-ROC (0.57-0.67). Di�erences betweenbenign and malignant sections were significant for all but one division. Also for ⇢ andI, a significant di�erence was found in one of the divisions. However, their AU-ROCwas much lower than that of r. The best-performing perfusion parameter was WITwith AU-ROCs between 0.54 and 0.64.

The results of the second fine-to-coarse analysis (test 3) are presented in Table 5.4.Only for r and WIT, a strong increase in AU-ROC was observed. This result suggeststhat r and WIT are the parameters most suitable for discrimination between benignand malignant tissue.

Results 79

Table 5.3: Areas under ROC curves and p-values per parameter for test 1 and 2. In thesetests, malignant sections contain at least 1 malignant biopsy core. Significant di�erences areprinted in bold font.

12 sections 6 sections 3 sections(77 mal.; 431 ben.) (50 mal.; 211 ben.) (36 mal.; 95 ben.)

AU-ROC p AU-ROC p AU-ROC p

r 0.65 <0.001 0.64 <0.001 0.65 <0.01⇢ 0.56 0.045 0.57 0.059 0.58 0.080I 0.52 0.29 0.53 0.25 0.59 0.061WIT 0.64 <0.001 0.62 <0.01 0.59 0.055PI 0.51 0.40 0.50 0.50 0.50 0.53WIR 0.54 0.12 0.53 0.21 0.51 0.41AU-TIC 0.49 0.65 0.49 0.62 0.48 0.63

2 sections 1 section(23 mal.; 64 ben.) (17 mal.; 26 ben.)

AU-ROC p AU-ROC p

r 0.67 <0.01 0.57 0.22⇢ 0.58 0.14 0.52 0.44I 0.63 0.036 0.52 0.41WIT 0.59 0.096 0.54 0.35PI 0.50 0.52 0.39 0.88WIR 0.52 0.37 0.41 0.83AU-TIC 0.50 0.51 0.40 0.85

mal.: malignant; ben.: benign; AU-ROC: area under ROC curve; r: correlation;⇢: coherence; I: mutual information; WIT: wash-in time; PI: peak intensity;WIR: wash-in rate; AU-TIC: area under TIC curve.

Figure 5.4 depicts boxplots of the 90th percentile of r and 10th percentile of WITfor benign, low grade (Gleason 6 or 7), and high grade (Gleason 8-10) biopsy locations.For r, the mean ± standard deviations were 0.35 ± 0.09, 0.38 ± 0.08, and 0.41 ± 0.07,respectively. A significant increase in parameter values (p < 0.01) between benign andlow grade biopsy locations was observed. The parameter r increased also for high gradebiopsy locations increased, but this increase was not significant (p = 0.080). A similartrend (but negative) was found for WIT, whose 10th percentile values for benign, low,and high grade were 11.2 ± 2.2, 10.5 ± 2.3, and 8.4 ± 3.2, respectively. In thiscase, the di�erence between high and low grade was significant (p < 0.01), but thatbetween benign and low grade was just insignificant (p = 0.052).

The confusion matrices of the left/right and per-prostate analysis (test 4) for thetwo best performing parameters (r and WIT) are given in Table 5.5. Regarding the

80 Clinical validation of 3D CUDI

Table 5.4: Areas under the ROC curves and p-values per parameter for test 3. In thisanalysis, malignant sections contain �50% malignant cores (test 3). Significant di�erencesare printed in bold font.

3 sections 2 sections 1 section(21 mal.; 95 ben.) (13 mal.; 64 ben.) (5 mal.; 26 ben.)

AU-ROC p AU-ROC p AU-ROC p

r 0.72 <0.001 0.75 <0.01 0.77 <0.032⇢ 0.60 0.082 0.60 0.13 0.56 0.34I 0.57 0.14 0.62 0.095 0.58 0.29WIT 0.69 <0.01 0.66 0.035 0.77 0.032PI 0.46 0.72 0.52 0.41 0.45 0.64WIR 0.49 0.55 0.56 0.25 0.51 0.49AU-TIC 0.43 0.83 0.52 0.49 0.42 0.71

mal.: malignant; ben.: benign; AU-ROC: area under ROC curve; r: correlation;⇢: coherence; I: mutual information; WIT: wash-in time; PI: peak intensity;WIR: wash-in rate; AU-TIC: area under TIC curve.

Table 5.5: Confusion matrix of left/right and per-prostate cancer detection (test 4) forcorrelation (r) and wash-in time (WIT).

Left/right Per-prostateCorrelation Wash-in time Correlation Wash-in time

Pos. Neg. Pos. Neg. Pos. Neg. Pos. Neg.

Malignant 15 8 11 12 16 1 9 8Benign 11 43 7 49 11 11 4 17

Undecided 9 7 4 5

Pos.: positive; Neg.: negative.

left/right analysis, the sensitivity (SNS), specificity (SPC), positive predictive value(PPV), and negative predictive value (NPV) for r were 65%, 80%, 58%, and 84%,respectively. In the per-prostate analysis these values were 94%, 50%, 59%, and 92%.Only 1 tumor, with Gleason score 4+3, was missed in this analysis. For WIT, the SNS,SPC, PPV, and NPV were 57%, 77%, 50%, and 81% in the left/right analysis and53%, 81%, 69%, 68% in the per-prostate analysis. Using WIT, tumors were missedin 8 prostates. Their Gleason scores were 3+3 (2), 3+4 (1), 4+3 (3), 3+5 (1), and5+4 (1).

Discussion 81

Figure 5.4: Boxplots of the 90th percentile values for correlation (a) and the 10th percentilevalues for wash-in time (b) in biopsy locations grouped by Gleason grade. Outliers, indicatedby plusses, are defined as points �1.5w away from the 25-75% box with w equal to the boxsize.

5.4 DiscussionIn this study, we investigated whether and which 3D DCE-US parameters could dis-tinguish between benign and malignant prostate tissue. Both r and WIT showed asignificant di�erence between locations corresponding to benign and malignant cores.In the left/right and per-prostate analyses, r resulted in a high SNS with acceptableSPC from a clinical perspective. While r generally shows a higher SNS and NPV,WIT shows a higher SPC and PPV. Combining the two in a multiparametric approachcould exploit the benefit of both parameters. Moreover, strong indications were foundof a relation between Gleason grade and parameter values of r and WIT, which couldpotentially improve risk stratification.

In a recent study by Postema et al., probability maps based on wash-in rate statis-tics of 2D DCE-US were compared with systematic biopsy [217]. On a per-prostatebasis, a SNS of 73% and a SPC of 58% were reported. These values are in betweenthe SNS and SPC achieved by r and WIT in the present study. Xie et al. [106] usedqualitative 2D DCE-US to target cores in a 10-core biopsy to suspicious areas in 150patients. The resulting SNS and SPC stratified per patient were 86% and 56%, re-spectively. Our study shows that r can achieve comparable SNS and SPC using 3DDCE-US. Comparison of the performance of 3D DCE-US with that of mpMRI is di�-cult due to the large range in SNS (68%-94%) and SPC (21%-70%) reported in studiesinvolving biopsy naive patients [71]. We recommend performing a study applying thetwo techniques in the same patient group to evaluate the di�erences.

The validation methods applied in this study are subject to some limitations.Firstly, the value of systematic biopsy as a ground truth is limited. There is a largechance that lesions are missed, decreasing the amount of FNs and TPs, while increas-ing the amount of FPs and TNs. Although we partly compensated for this e�ect in the

82 Clinical validation of 3D CUDI

last validation by ignoring FPs for which less than 20% of the biopsy locations wereclassified as positive, the number of FNs, TPs, and TNs remains biased. Moreover,AU-ROCs in the per-biopsy analysis have probably been underestimated for parame-ters able to di�erentiate between benign and malignant locations. Secondly, becausebiopsy was guided by free-hand TRUS, the estimated location of a biopsy core did notnecessarily match its true location. For example, in the parametric map presented inFig. 5.2, the tumor was detected, but not all biopsy outcomes matched the parametervalues at their estimated locations individually. The possible misalignment betweentrue and estimated location complicated the comparison of single cores and was theprimary reason to combine multiple cores. However, the AU-ROCs did not increase forlarger sections. We may hypothesize that small tumors did not have enough influenceon the parameter values in a large region. Consequently, the definition of malignantsections to have malignancy in at least half of the cores produced an increase inAU-ROC for r and WIT.

A standard reference for PCa studies is histopathology after radical prostatectomy.However, the population represented in those studies is strongly biased towards malig-nancy. The population represented in the biopsy data in this study reflects exactly thepopulation targeted by quantitative 3D DCE-US as a diagnostic tool. Comparison withradical prostatectomy could, however, be advantageous to evaluate the ability of thetechnique to estimate tumor size and shape, also at anterior sites, and to determinehow many and which tumors are missed.

In the present study, parameter values have been directly compared with biopsyoutcome. The learning curve and inter-observer variability present in clinical practicehave not yet been accounted for and should be investigated in future studies. Werecommend comparing systematic and 3D DCE-US targeted biopsy.

5.5 ConclusionQuantitative analysis of 3D DCE-US can be used to distinguish between benign andmalignant tissue. In particular, for wash-in time and CUDI by TIC correlation, arelation between parameter value and biopsy outcome was proven. In addition, theirparameter values seem to be related to Gleason grade, although further studies arerequired to confirm this finding. We recommend future investigation of quantitative3D DCE-US for guidance of targeted biopsies as a possible alternative or addition tompMRI.

Chapter6Interpolating histopathologic datafrom sliced RP specimens

The content of this chapter has been submitted for publication as [J1]:

R.R. Wildeboer, S.G. Schalk, L. Demi, M.P.J. Kuenen, H. Wijkstra, and M. Mischi,“Tumour interpolation and three-dimensional reconstruction of radical prostatectomyspecimens after histopathologic examination,” Acad. Radiol.

The work presented in this chapter was carried out in the framework of theIMPULS2 program as a collaboration between Eindhoven University of Technologyand Philips Research.

84 Interpolating histopathologic data from sliced RP specimens

AbstractRationale and Objectives: To validate new imaging modalities for prostatecancer, images must be three-dimensionally correlated with the histological groundtruth. In this work, an interpolation algorithm is described to construct a reliablethree-dimensional reference from two-dimensional histological slices. Furthermore,the errors introduced during standard pathological procedures are quantified.

Materials and Methods: Eight clinically relevant in-silico phantoms were designedto represent di�cult-to-reconstruct tumor structures. These phantoms were subjectedto di�erent slicing procedures. Additionally, controlled errors were added to investigatethe impact of varying slicing distance, front-face orientation, and inter-slice misalign-ment on the reconstruction performance. Using a radial-basis-function interpolationalgorithm, the two-dimensional data were reconstructed in three dimensions. Theaccuracy of reconstruction was quantified by the fractional volume di�erence, thedistance between the surfaces of the reconstruction and original phantom, and theDice coe�cient.

Results: Our results demonstrate that slice thicknesses up to 4 mm can be usedto reliably reconstruct tumors of clinically significant size; the surfaces lay within a1.5-mm 90%-error margin from each other and the volume di�erence between theoriginal tumor structure and reconstruction does not exceed 10%. Dice coe�cientsabove 0.85 are preserved.

Conclusion: The presented interpolation algorithm is able to reconstruct clinicallysignificant tumor structures from two-dimensional histology slices. Errors occurringare in the order of magnitude of common registration artifacts. An inter-slice spacingof 4 mm or less is recommended during histopathology; the use of a 1.5-mm errormargin along the tumor contours can then ensure reliable mapping of the groundtruth.

Introduction 85

6.1 IntroductionImaging of prostate cancer (PCa) is still a challenge. The latest figures show that PCais the malignancy with the highest incidence and second-highest number of deathsamong Western men [218,219]. Needle biopsy is currently the only method to confirmPCa, but this technique is associated with complications [220] and underdiagnosisdue to (aggressive) foci being missed [221]. However, a large fraction of prostaticmalignancies are expected to remain clinically insignificant during the patient’s lifetime[51]. Hence, there is a substantial clinical demand to develop imaging strategies thatare su�ciently accurate to target or even avoid biopsy, and to apply tissue-preservingfocal therapy.

In recent years, several magnetic resonance (MR) and ultrasound (US) modalitieshave been investigated for targeted biopsy, among which multiparametric MR imagingand contrast-enhanced US [222]. In focal therapy, imaging is not only important forlocalizing the malignancy, but also in risk stratification and to identify insignificantlesions that do not require treatment [223]. The most recent guidelines on focaltherapy and trial design indicate that imaging is of vital importance for treatmentplanning [224, 225]. Moreover, minimally-invasive monitoring methods are requiredfor follow-up after treatment. However, to validate these techniques it is crucial toaccurately correlate the images with ground truth information from histopathology.

Histopathology involves the examination of prostate tissue after biopsy or the re-moval of the gland (radical prostatectomy, RP). During the histopathologic procedureafter RP, the specimen is usually fixated by immersion in formalin, deprived of theseminal vesicles, and sliced [139]. After the microscopic examination and marking ofmalignant areas by the pathologist, the slices are digitized. These slices serve as goldstandard for distinction between malignant and benign tissue, and allow the pathol-ogist to determine the definitive tumor grade, size, and type [139]. Usually also thetumor volume is assessed, but due to the lack of a simple measurement method it isgenerally expressed as a percentage of the entire prostate volume [226,227].

Since images and histology slices are in general not aligned, correlating the two isa complicated task. Moreover, whereas MR images are spaced in a parallel fashion,transrectal US imaging planes may di�er in orientation, especially towards basis andapex [228],[J5]. The registration process (i.e., the mapping of each location in the RPspecimen to the image) is therefore a three-dimensional (3D) problem.

Registration is also important because of the prostate deformations that occur af-ter resection. Comparing in-vivo with ex-vivo MR acquisitions, Orzcyk et al. foundthat prostates shrink on average by 19.5% [229]. This is most likely caused by the lossof vascular pressure and the absence of in-body connective tissue. The shrinkage isnot homogeneously distributed; in particular, the ratio between the anterior-posteriorand left-right dimensions decreases after RP. Deformations may also occur as a conse-quence of the handling of the specimen during fixation and slicing [230]. Furthermore,the shape of the in-vivo prostate during imaging might be altered by the pressure

86 Interpolating histopathologic data from sliced RP specimens

applied to the prostate because of the use of an endorectal coil in MR imaging [231]or a transrectal probe in US [J5].

Many 3D registration methods have been developed for a reliable matching betweenimage data and histopathology. This usually involves the use of landmarks that aremanually chosen [151], automatically identified [232], or added after resection [152,233]. Sometimes ex-vivo MR [149, 152, 233, 234] or elastographic MR images [235]are obtained to facilitate the registration to in-vivo MR. Alternatively, registrationapproaches make use of 3D-printed molds based on 3D imaging [150, 153] or thesurface contours of both histology and imaging [J5]. Reported registration errors aregenerally in the order of millimeters.

The accuracy of the validation, however, does not only depend on the ability ofthe registration algorithm to accurately restore the in-vivo prostate shape. In the firstplace, it relies on the ability to reliably reconstruct and digitize the histopathologicallyexamined RP specimen. Almost all registration techniques require a 3D model ofthe histology slices [149, 151, 153, 234],[J5]. For the model reconstruction, the tumorcontours have to be interpolated to form 3D structures. In other words, based on thetwo-dimensional (2D) slices, the entire tumor shape has to be estimated. In all ofthese steps – slicing, alignment, and tumor interpolation – errors are introduced thatcomplicate the validity of this ground truth.

Figure 6.1a-c depicts the type of errors occurring during the slicing procedure.Firstly, the sectioning process introduces variations with respect to the inter-slice dis-tance and front-face orientation (i.e., the angle of the slicing plane with respect to thelongitudinal axis of the specimen). Gibson et al. observed these to be distributed withstandard deviations of 0.5 mm and 1.1° for a 4.4-mm tissue cutting procedure [236].In a later study, standard deviations of 0.4 mm and 0.9° were found [237]. Ward etal. reported a standard deviation of only 0.2 mm for the same slice thickness [152].Many devices have been developed to standardize the slicing procedure and minimizethe errors [230]. However, 88% of the European pathologists cut the RP specimensfree-hand [238].

After slicing, the slices have to be re-aligned three-dimensionally [see Fig. 6.1(d)].This is usually performed based on block-face photographs (i.e., photos of the RPspecimen’s front face during slicing) (e.g., [149, 237]). Alignment can also be doneusing intensity matching of the slices, for example by using mutual information (e.g.,[239]). Due to the loss of similarity between slices, however, this method is generallynot usable for inter-slice spacings of more than 1 mm [228]. Also the use of naturalfeatures such as prostate contours, urethra, or ejaculatory ducts su�ers from limitedinformation redundancy and, moreover, most structures are not present in all slices[228]. Lastly, some groups use fiducial markers (sometimes in combination with ex-vivo MR imaging) to find the original alignment [154, 228, 240]. Although very smallerrors are reported, this approach is laborious and might deteriorate the specimen.The most common method, still, is manual alignment of the histological slices [148],which introduces significantly more errors than a controlled workflow [241].

Materials and methods 87

Figure 6.1: Introduction of errors during the slicing procedure of the radical prostatec-tomy specimen (in apex-base vs anterior-posterior view): (a) ideal case with equally-spaced,perfectly-aligned, parallel slices; (b) parallel slices of varying slice thickness; (c) equally-spacedslices of varying orientation; (d) equally-spaced and parallel slices that are misaligned.

For the 3D reconstruction of prostatic malignancy from the 2D slices, the interpo-lation algorithms reported in the literature range from sparsely stacking the histologicaldata imposed on the photos [149], or simply extrapolating the tumor contour over theentire slice thickness [242,243], to spline interpolations of the edges [154]. Many other2D contour-based surface-reconstruction algorithms are designed for medical purposesand might be applied to prostate cancer (e.g., [244–248]). The best choice for in-terpolation depends on the application, the reliability of the input, and the accuracyrequired. The need for a smooth interpolation instead of a step-wise approach is oftenmentioned [154,249], as well as the list of assumptions underlying 3D modeling (e.g.,about slice deformation, parallelity, and location) [237]. Moreover, actual 3D tumormodels are very di�cult to validate due to the lack of a 3D ground truth.

In this paper, we present a method to reconstruct the geometrical tumor structuresin 3D based on 2D histopathological data. Furthermore, the reconstruction errorscaused by the settings and inaccuracies of the slicing procedure are quantified. To thisend, we simulate the slicing procedure and compare the result of interpolation withRP phantoms representing a wide range of clinically relevant tumor shapes.

6.2 Materials and methods

6.2.1 Histopathologic procedureA regular prostatic pathologic examination as described in Montironi et al. is assumed[139]. In brief, the procedure involves the (a) weighting and sizing of the specimen;(b) inking of the surface to distinguish left and right; (c) (possibly) fixation by 10%

88 Interpolating histopathologic data from sliced RP specimens

neutral-bu�ered formalin bu�er injections; (d) immersion in 300 to 400 mL of formalinfor 24 h; and (e) sectioning by removing the seminal vesicles, dissecting the apical andbasal parts and step-slicing the rest of the prostate in ⇡4 mm sections perpendicularto the apex-base axis. After the sectioning procedure, (f) the slices are post-fixed for24 h; (g) front-face sections are stained and (h) histologically examined as 5-µm thickslices, either whole-mount or in quadrants. Subsequently, the pathologist prepares thehistological slices and draws contours around the malignant areas on each section.These contour data are digitized and properly aligned with respect to each other.

6.2.2 Interpolation approachThe tumor interpolation and reconstruction algorithms were implemented in MATLAB(MathWorks 2015b, Natick, MA). The program retrieves the digital 2D contours andthen consecutively (Step 1) places them in 3D space; (Step 2) determines whichcontours are likely to belong to the same lesion along several slices; (Step 3) estimatesenclosing points above or below the contours that are not connected to a contourin an adjacent slice; (Step 4) computes the distance points indicating the surface ofeach lesion using the surface normal vectors; (Step 5) interpolates the points to forma distance map using radial basis functions (RBFs) and (Step 6) constructs the lesionsurfaces at zero-distances.

Step 1: Positioning of histological data

The 2D contours of the tumor as determined during the histopathological examina-tion, which have been aligned in the x, y-plane (transverse plane), are placed a slicethickness, dsl, apart in the z-direction (longitudinal direction).

Step 2: Identification of independent lesions

Prostatic malignancies are known to be diverse and multifocal [139,243,250]. There-fore, it is important to determine whether contours in the histology set belong to thesame lesion, or to two independent lesions. In the literature, di�erent criterions areused to select the contours that are to be connected in the interpolation process: forexample, Rojas et al. used a heuristic <5 mm distance between the contours [240] andErbersdobler et al. defined <3 mm [251]. In this work, the maximum inter-contourdistance is dependent on the used slice thickness. More specifically, it is defined thatcontour �k is connected to contour �l if �l is in an adjacent slice and if at least onepoint on the area of �l is located within a distance

pdsl of the area of �k in the

x, y-plane.This criterion allows us to compute a square matrix M of which each row and

column represent a specific contour; a value of 1 is appointed to elements where

Materials and methods 89

Figure 6.2: Intermediate steps of interpolation: (a) connected contours (in blue) with topand bottom points (in red) and outward pointing normal vectors; (b) distance map point cloudwith on-surface points depicted in blue, inner o�-surface points in red and outer o�-surfacepoints in green; (c) surface plot of the RBF interpolation.

contour �k is connected to contour �l, and a value of 0 where they are not:

M(k, l) =

(1 if min(k�k(i)� �l(j)k) <

pd

0 otherwise.(6.1)

Here, k�k(i)��l(j)k is the Euclidean distance between point i on the area of contour�k and point j on the area of contour �l. Based on the connection matrix M, labelsare assigned to all groups of interconnected contours. The number of labels representsthe number of separate lesions that will be considered for interpolation individually. InFig. 6.2(a), a typical set of contours forming one lesion is depicted.

Step 3: Definition of tops and bottoms

Once the labels are assigned, the solid-tumor boundaries are defined by a specific setof 2D contours. The top and bottom of the structures, however, are not considered tobe flat. Therefore, additional top and bottom points are positioned under and abovethe lowest and upper contour, respectively.

For small contours, these top and bottom points are placed at the center of massof the adjacent contour �, half the slice thickness dsl away. This is based on theassumption that, in the absence of more information, lesions probably reach half thedistance between the contour and the next, empty slice.

Heuristically, if the average distance between the points on � and its center ofmass di�er by more than 1 mm, the contours are divided in ncl di�erent k-meansclusters for which top or bottom points are added in their center of mass at dsl/4.

90 Interpolating histopathologic data from sliced RP specimens

This number ncl depends on the standard deviation (�) in distances to the center ofmass via the heuristic expression ncl = 1 + p3�/2q. These additional points are alsovisible in Fig. 6.2(a).

Step 4: Definition of seed points using surface normal vectors

Each tumor structure is now enclosed by its contours and top and bottom points. Thiscan be viewed as a 3D point cloud defining the lesion’s surface. Following the methoddescribed by Carr et al. [1] and used by [252,253], it is possible to reconstruct the outersurface of the prostate by RBF interpolation. We refer to [1] for the mathematicalfoundations of the algorithm.

The interpolation algorithm does not only require the points on the surface (on-surface points) as input, but also points at a certain distance from the surface (o�-surface points). More specifically, it has been shown that the problem is more straight-forward to solve when two o�-surface points are defined on either side of each on-surface point. Points inside of the structure are marked with its negative distance tothe surface, whereas points on the outside have a positive distance value. Generatingsuch a set of distance points is a critical task, given the wide range of complex contourshapes. In the presented method, given the contour shapes encountered, it was pos-sible to reduce the number of points on the contour circumference to one point every⇡1 mm in order to reduce the computation time. In our case, this meant a reductionby 5/6.

Considering the typical dimensions of PCa lesions, o�-surface points are added atapproximately 1 mm on either side of the surface as shown in Fig. 6.2(b). Their posi-tions are computed using the normal vectors in the contour plane. It is not uncommonto encounter contours of which the center of mass is located outside the tumor area;therefore, their outward direction is verified by calculating the number of intersectionsbetween the normal line and the contour: an odd number of intersections in the direc-tion of the normal vector cannot occur. For all top and bottom points that are addedin the previous step, the normal vectors will point in the outward longitudinal direction[see Fig. 6.2(a)]. Since these 1-mm distances must not intersect other parts of thecontour, the algorithm might fail in reconstructing contours that have very sharp edgesor lie in a close range to each other. In these rare cases, the distance settings shouldbe adjusted.

Step 5: Interpolation by radial basis functions

Based on the set of distance points, the interpolation algorithm is used to computea so-called 3D distance map. In this map, the distance to the lesion’s surface at anylocation can be found. In order to create a smooth distance map, each distance pointis allowed to deviate from its original value. The extent of this deviation is controlledby a smoothing parameter, ⇢, which is heuristically set to 0.001 [1].

Materials and methods 91

Step 6: Isosurfacing of the distance map

Since the distance map contains the interpolated distance to the lesion’s surface atevery location, the shape of the lesion is now defined by all locations at which the mapis equal to zero. An example of the interpolation result is shown in Fig. 6.2(c).

6.2.3 In-silico phantomsIn order to quantify the interpolation errors, the entire slicing and reconstructionprocess was simulated using digital phantoms. This does not only solve the absenceof a 3D ground truth volume in vivo and in vitro, but it also enabled us to separatelystudy the e�ects of variations in slice thickness, front-face orientation, and alignment.Furthermore, it allows many di�erent experiments on a single phantom. Obviously,it is of paramount importance that the phantom designs represent the spectrum offrequently encountered PCa shapes as well as possible.

Over the years, several distribution maps have been created that show that PCa ismost often found in the peripheral zone (74%) and, therefore, in the lower, posteriorregions of the prostate [240, 243, 250, 254]. Lesions often have predictable smoothshapes, especially since small lesions are known to spread along the prostatic andzonal boundaries (94%) [243]. Most lesions of more than 1 mL in volume (83%) arefound to be roughly diamond-shaped in longitudinal (apex-base) direction [243].

A large majority (83%) of the RP specimens exhibits multiple foci [250]. In thesecases, the non-index (i.e., not largest) PCa foci most often (69%) occur on the oppositeside of the index-tumor [243]. Furthermore, transition-zone tumors are almost alwaysassociated with well di�erentiated peripheral index tumors [250]. In general, the indexlesion determines the prognosis [223].

Typically, PCa lesions of >0.5 mL are considered clinically significant [223, 243].It was found by Frimmel et al. that the tumor volume in resected prostates is, onaverage, 3.67 mL. Based on their volume, the lesions were subdivided in small (0.3to 1.6 mL), medium (1.6 to 3.6 mL) and large (3.8 to 36.2 mL) tumors [254]. Inthis work, the focus is on the small and medium-sized structures, because small fociare most frequently found [250]. Moreover, large tumors are more easily interpolatedbecause they appear in more histological slices and slicing errors are relatively smallcompared to their size.

With the aim of representing clinically relevant shapes, we designed eight di�erenttumor structures that are generally di�cult to interpolate (see Fig. 6.3). Phantom A1(total tumor volume of 2.1 mL) consists of four spheres of 10 mm in diameter, repre-senting the most confined shape of clinically significant size (0.5 mL). Phantoms A2(1.1 mL) and A3 (0.44 mL) contain the same architecture of spheres with sub-clinicallyrelevant diameters of 8 mm and 6 mm, respectively. Phantom B (3.4 mL) consistsof two independent lesions of significant size that are more than 3 mm but less than5 mm apart; this is the smallest significant gap for which two tumors are consideredindependent [251]. Phantom C (1.7 mL) consists of two similarly-sized structures

92 Interpolating histopathologic data from sliced RP specimens

Figure 6.3: Depiction of the 3D prostate-tumor phantoms used in this work. All phantomshave a 24⇥17⇥20-mm radii ellipsoid prostate boundary. (A1-3) consist of four sphericallesions with a radius of 5, 4, and 3 mm, respectively; (B) represents two clinically relevanttumor foci with a gap of less than 5 mm in between; (C) contains two tumor foci withdi�erent orientation with respect to the longitudinal plane; (D) consists of two semi-toroidstructures; (E) harbors a semi-toroid with another structure in between; (F) contains a singlestructure with a hole.

of which one is oriented along the slicing direction and the other one is oriented inthe transverse plane. Since both structures are slightly tilted, errors occurring due tothe “shear e�ect” are elegantly shown. This e�ect indicates the inability to identifyill-alignment in interpolating 2D-slices [228]. Phantom D (3.3 mL) harbors two semi-toroid structures that appear as two separate contours in some slices, whereas they arejoined in others. Phantom E (2.6 mL) contains similar structures, but now anotherunconnected structure is added. Lastly, phantom F (3.0 mL) shows a single tumorstructure with a hole. These last three phantoms verify the validity of the decisionrule in connecting contours [240].

Materials and methods 93

Figure 6.4: Virtual slicing procedure; (a) slicing of the digital phantom (6 mm); (b) simulatedhistological slices; (c) resulting reconstruction of the original phantom based on the slices.

Prostate outlines were added to the phantoms in order to show how the tumordimensions relate to the size of a typical prostate. It concerns an ellipsoid shape of48 mm, 34.2 mm, and 40 mm along the main axes. After triangulation, the structurehas a volume of 31.9 mL, which is equal to the average volume of RP specimens [254].

6.2.4 Validation and quantificationThe phantoms depicted in Fig. 6.3 underwent a virtual slicing procedure by computingthe cross-sections of the phantom with planes that were positioned a slice thicknessdsl apart in the longitudinal (z) direction. For each simulation, these locations wereall randomly displaced according to a normal distribution with a standard deviationof 0.5 mm, that is, the largest reported in the literature [236]. In order to quantifythe e�ect of misorientation, the planes were placed under an angle 0 ± ↵std° aroundto the y-axis. The errors resulting from misalignments were assessed by randomdisplacements 0 ± wstd mm in the x- and y-directions. Subsequently, the phantomcontours were extracted, interpolated, and reconstructed assuming a perfect slicingprocedure with the given slice thickness (i.e., no displacements, misorientation, andmisalignments). An example of a slicing and reconstruction procedure is shown inFig. 6.4.

Each simulation sequence was executed 15 times to show the e�ect of the ran-domness and to rule out incidental findings. Simulations in which the interpolationalgorithm failed to find a closed solution were excluded (<4%). To assess the qual-ity of the reconstruction, the fractional volume di�erence (FVD) was calculated: thevolume di�erence between reconstruction (Vrec) and original phantom (Vref ) as afraction of the original phantom volume:

FVD = (|Vrec|v � |Vref |v)/|Vref |v. (6.2)

in which |V|v represents the volume of V.In addition, the reconstruction errors were quantified by the distance between the

outer surface of the original phantom and that of the reconstruction along the original

94 Interpolating histopathologic data from sliced RP specimens

Figure 6.5: Mean fractional volume di�erence (FVD), 90th percentile value of the errordistance and Dice coe�cient of 15 sectioning simulations of Phantom A1-F versus the slicedistance dsl ± 0.5 mm. The error bars indicate the standard deviation among the results.

point’s normal vector. More specifically, the 90th percentile of the reconstruction errorsare mentioned. This means that 90% of the points on the original surface and thecorresponding reconstruction surface are within an error margin of the given value.

Lastly, the overlap between reference and reconstruction was studied using theDice coe�cient (SD), which defines the relative volume shared by reconstruction andreference as follows [234]:

SD = 2(|Vrec \Vref |v)/(|Vrec|v + |Vref |v). (6.3)

6.3 Results

6.3.1 Slice thicknessFigure 6.5 depicts the interpolation performance versus the slice thicknessdsl ± 0.5 mm. It is observed that, for slice thickness up to 4 mm, the means and stan-dard deviations of the performance measures stay virtually constant. They exhibit errormargins below 1.5 mm, FVD within 10% from baseline, and Dice coe�cient above0.85 (see gray regions). Some tumor designs appear to be generally more di�cult to

Results 95

interpolate. From slice thicknesses >4 mm, the performance measures and standarddeviations degrade rapidly and are less predictable. This is because the position ofthe slices with respect to the tumor structure is increasingly important; for example, asmall deviation in an 8-mm slicing sequence might lead to missing entire tumor foci.

6.3.2 Slice orientationTo quantify the e�ect of non-parallel slicing, the angle of the transversal cross-sectionsin a 4-mm equidistant slicing sequence was randomly adjusted by 0 ± ↵std° aroundthe y-axis. In Fig. 6.6, it is shown that an increasing ↵std does not result in a largedi�erence in means with respect to the parallel sequence, but it a�ects the standarddeviations of the results. This is due to an equal probability of cross-sections appearingsomewhat larger or somewhat smaller than they should.

Figure 6.6: Mean fractional volume di�erence (FVD), 90th percentile value of the errordistance and Dice coe�cient of 15 sectioning simulations of Phantom A1-F with 4-mm slicesoriented under an angle of 0 ± ↵std° as function of the standard deviation. The error barsindicate the standard deviation among the results.

96 Interpolating histopathologic data from sliced RP specimens

Figure 6.7: Mean fractional volume di�erence (FVD), 90th percentile value of the errordistance and Dice coe�cient of 15 sectioning simulations of Phantom A1-F with parallel4-mm slices that are misaligned in the transverse plane by �x = �y = 0 ± wstd mmas function of the misalignment standard deviation. The error bars indicate the standarddeviation among the results.

6.3.3 Slice alignmentThe interpolation requires the 2D contours to be spatially aligned in 3D in order toreconstruct the original shape. Due to the sparsity of the data in the longitudinaldirection, misalignment is a recurring problem in 3D reconstruction which is di�cultto identify or avoid without additional information. As can be seen in Fig. 6.7, dis-placements of 0 ± wstd mm in the x, y-plane a�ect the Dice coe�cient to a largerextent than the other performance measures. This is because reconstructed structuresmay maintain their original shape and volume, while shifting from the original position.Random misalignment of more than 1.5 mm introduces large performance drops.

6.3.4 Tumor sizeConsidering only the spherical phantoms (A1-A3), roughly the same e�ects as for theother designs are seen. It becomes clear from Fig. 6.8 that the errors are generallylargest for the smallest lesions, as well as the variety (standard deviations) in theirresults. Therefore, sub-clinically relevant structures smaller than 0.25 mL are not

Discussion 97

Figure 6.8: Mean fractional volume di�erence (FVD), 90th percentile value of the errordistance (90th P%), and Dice coe�cient of 15 sectioning simulations of Phantom A1-A3 with(a) parallel slicing distances of dsl ± 0.5 mm, (b) 4-mm slicing under an angle 0 ± ↵std°,and (c) misalignments in the transverse plane by �x = �y = 0 ± wstd mm.

expected to be well interpolated for large inter-slice spacings of �4 mm.

6.4 DiscussionBecause of the demand for imaging validation and the development of 3D imagingmodalities, an accurate 3D model from the RP specimen becomes increasingly impor-tant. Nowadays, validation with histopathology is performed by matching 2D imagingplanes with corresponding 2D histological slices, or by registration of the 3D vol-umes [148]. Because histological slices and imaging planes cannot be considered to becompletely overlapping and aligned, the second approach is favorable, provided thatthe 3D reconstruction is su�ciently accurate.

In this work, we described and tested a RBF-based algorithm to reconstruct thetumor structures from a series of 2D histopathologic slices. Using in-silico phan-toms representing frequently encountered tumor structures, we demonstrated thatslice thicknesses up to 4 mm can be used to reconstruct tumors of clinically significantsize with an appreciable accuracy; the surfaces deviate within a 1.5 mm 90%-errormargin, the volume di�erence between reference and reconstruction does not exceed

98 Interpolating histopathologic data from sliced RP specimens

10%, and a Dice coe�cient above 0.85 is maintained.This study was performed in silico, as it enabled us to repeat the slicing procedure

with di�erent values and ensured a valid ground truth. This way, it was possible torule out incidental findings caused by fortunate or unfortunate positioning of the sliceswith respect to the lesions. Preferably, the tumor appears in as many cross-sections aspossible, so that the overall tumor shape is best represented. Since the tumor shapeis not known beforehand, the suitability of the set of contours depends on the initialslicing location. It should therefore be noted that there is an intrinsic variation in theoutcomes of every slicing procedure.

A limitation of the procedure is that the occurrence of errors was simulated as arandom process. Depending on the details of the histopathology procedure, systematicerrors can be expected in slicing and alignment. For example, one might find thestandard deviation of the angle to be dependent on slice thickness or location in theprostate. However, when making use of cutting devices, this error remains constant.Also the slicing direction (i.e., apex-base or vice versa) might have an influence; dueto the cumulative errors in slice thickness, the location of the first slice could be moreaccurate than the last one. Furthermore, it was observed that slicing itself mightintroduce tears, deformations and inconsistencies that are not modeled here [230].

Since the algorithm uses criteria regarding inter-contour connection and top andbottom heights, the procedure can be optimized to best suit the evaluation at hand.The false positive or false negative volumes can be reduced by using a more conserva-tive or loose decision rule, respectively. Ultimately, more elaborate and robust decisionrules can be devised that take into account the lesion volumes and contour shapes.

Since 4-mm slicing distances were found to be su�cient, the algorithm does notrequire the pathologist to perform a more elaborate and laborious protocol for thehistological examination. Furthermore, although the computation time for interpola-tion depends on the number of contours and data points, the reconstruction generallytakes around 1-2 min (using one core on a 3.40-GHz quad-core processor personalcomputer).

Whereas slight deviations in front-face angle did not substantially alter the recon-struction for clinically significant PCa lesions, the inter-slice misalignment significantlya�ected the interpolation performance. This underlines the need for an alignmentstrategy such as the use of fiducial markers or block-face photographs. Recent align-ment strategies have shown to reduce misalignment distances to 0.6 mm [228].

It was demonstrated that the errors made in tumor interpolation are in the sameorder of magnitude as the registration errors (e.g., 1.1 mm [152], 0.71 mm [233],2-3 mm [151], 0.82 mm [232], 2.26-3.74 mm [149], 3.1 mm [235], 1.5-2.1 mm [J5]).Nevertheless, the total error in matching histopathologically-confirmed tumor struc-tures with images is not simply an addition of these errors. Especially in elasticregistration, the registration process might even compensate for misalignments in in-terpolation. Since tumors tend to spread along the prostatic capsule [243], especiallysurface-based registration algorithms could correct tumor misalignments. In any case,

Discussion 99

the quantified errors of this study indicate that caution should be taken in interpretingthe histopathological data within 1.5 mm from delineated borders of areas marked asmalignant.

Despite some debate, the total tumor volume is generally regarded as a valuableprognostic marker [226, 227], particularly for biochemical recurrence after RP [255].Current protocols include extensive stereological methods to estimate the volume, butthese methods have some well-known limitations in labor and time involved [227]. Thepresented interpolation method is found to estimate the volumes with less than 10%o�set for the average standard histopathology protocol.

Furthermore, the technique is not limited to the prostate alone and might be usedfor other small organs, in particular those that do not have usable internal naturalmarkers. Similar reconstruction protocols have been developed for the (animal) brain[246]. However, the optimal slicing thickness, location of seed points and decisionrules should be tailored to the dimensions and requirements of that organ.

In conclusion, we presented a 3D interpolation algorithm that is able to reconstructPCa tumor structures based on 2D histopathologic slices. It was demonstrated that aninter-slice distance up to 4 mm permits reliable use of 3D histology as gold standard.A good reconstruction of the 3D tumor shape enables the validation of cancerousrepresentation in novel imaging modalities with high precision. With accurate tumorlocalization, the validation is no longer limited to large tumors or quadrants. Morepatients may be enrolled in studies when tumors of all shapes and sizes can be reliablyused for validation, increasing the statistical outcomes of the validation.

100 Interpolating histopathologic data from sliced RP specimens

Chapter73D registration of prostate data fromhistology and ultrasound

The content of this chapter has been published as [J5]:

S.G. Schalk, A.W. Postema, T.A. Saidov, L. Demi, M. Smeenge,J.J.M.C.H. de la Rosette, H. Wijkstra, and M. Mischi, “3D surface-based reg-istration of ultrasound and histology in prostate cancer imaging,” Comput. Med.Imaging Graph., vol. 47, pp. 29-39, 2016. © 2015, Elsevier.

102 3D registration of prostate data from histology and ultrasound

AbstractSeveral transrectal ultrasound (TRUS)-based techniques aiming at accurate localiza-tion of prostate cancer are emerging to improve diagnostics or to assist with focaltherapy. However, precise validation prior to introduction into clinical practice is re-quired. Histopathology after radical prostatectomy provides an excellent ground truth,but needs accurate registration with imaging. In this work, a 3D, surface-based, elasticregistration method was developed to fuse TRUS images with histopathologic results.To maximize the applicability in clinical practice, no auxiliary sensors or dedicatedhardware were used for the registration. The mean registration errors measured invitro and in vivo were 1.5 ± 0.2 and 2.1 ± 0.5 mm, respectively.

Introduction 103

7.1 IntroductionProstate cancer (PCa) is the type of cancer with the highest incidence and secondhighest mortality among males in the United States [159]. Despite the statistics of thiscancer type, the main diagnostic technique, systematic biopsy, has major drawbacks.Firstly, being invasive, it can cause infections and hematuria [28]. Secondly, tumorscan be missed by the biopsy needle [256], resulting in poor sensitivity of this diagnostictool. Thirdly, tumors can be undergraded when the more aggressive region of a tumoris missed [41], leading to undertreatment. Moreover, because of the lack of reliablelocalization methods, PCa is often overtreated out of precautionary considerations[51,257], increasing risk of urinary incontinence and impotence [51].

To overcome these limitations, several methods aiming at non-invasive PCa lo-calization are currently under development. Determining the exact location of PCawould decrease the number of biopsies and the chance of missing cancerous tissueby use of targeted biopsies [258]. In addition, it can enable imaging-targeted focaltherapy as a treatment option [258,259]. Currently, most studies involving PCa local-ization are based on magnetic resonance (MR) imaging [66,168,260]. However, stud-ies using transrectal ultrasound (TRUS)-based methods – such as computer-assistedTRUS [75, 261], (shear-wave) elastography [83, 97, 99, 198], and dynamic contrast-enhanced ultrasound [217],[J6] – also show promising results. TRUS has the advan-tages over MR of being less expensive, widely used for targeting biopsies, and directlyapplicable by urologists.

Because of the lack of a medical imaging modality revealing the exact location ofcancerous tissue in the prostate, histopathologic analysis after radical prostatectomy(RP, excision of the prostate) is frequently used as a gold standard for validation ofnew imaging techniques [132, 141, 143, 168, 262, 263]. Usually, the excised prostate issectioned into 3- to 4-mm-thick slices, after which the separate slices are compared withthe images used for PCa localization [140]. However, due to the di�erent orientation ofthe imaging planes and the histology slices, one image could span multiple histologyplanes. Deformation of the prostate caused by pressure from transrectal probe ordue to surgery and preparation for histopathologic analysis can further complicateaccurate validation. Moreover, the histology slice corresponding to the image has tobe manually selected, endangering the objectivity of the validation. A 3-dimensional(3D) registration method could assist in making an objective and accurate comparisonbetween the PCa imaging technique and the gold standard.

Extensive work has already been done on in-vivo MR-pathology mapping of theprostate, which is a challenging task, because of the deformation due to surgery andto preparation of the tissue for histologic analysis. In some methods [146, 147], thehistology slices corresponding to the MR slices are manually selected after which 2Dregistration is applied. In another approach [148], the algorithm tries to find thecorresponding slices automatically prior to their registration. However, in TRUS, thehistology slices are typically not aligned with the imaging planes.

104 3D registration of prostate data from histology and ultrasound

In other studies, fiducial markers [151, 152], manually outlined natural landmarks[151], and a 3D-printed mold of the prostate [150, 153, 262] were used to assist withthe registration. Some researchers [149, 152] used ex-vivo MR images to break downthe registration into smaller steps. Although improving the registration accuracy, theextra steps could conflict with the clinical workflow in most hospitals.

In contrast to MR-histology registration, only few research groups have made at-tempts to register prostate ultrasound (US) imaging with histology. Taylor et al. [154]implemented a semi-automatic 6-degrees-of-freedom (DOF) rigid body registration al-gorithm to match the surface of an excised prostate imaged by US with the surfaceof the same prostate after fixation for histology. The registration was used for valida-tion of a cancer detection method using sonoelastography. However, the registrationaccuracy was estimated completely ex vivo. In [155], the authors described a methodfor elastic registration of a prostate recorded by in-vivo TRUS imaging and histology.An ellipsoid fit and the position of the urethra were used to align the images by a�netransformation, but no information on the registration error was given. Recently, atechnique was proposed in [156] to jointly align histology slices to intra-operative 3DUS by a�ne transformations using particle filtering. Again, except for the area overlapbetween the registered histology slices and the corresponding cross-sections in US, noinformation was provided on the accuracy of the method.

This paper describes a new method to elastically register TRUS and histology in3D for validation or training of TRUS-based PCa imaging techniques. TRUS-histologyregistration is a challenging task for reasons concerning both TRUS and histology. Themain challenges concerning TRUS are summarized below:

• the orientations of the TRUS imaging planes are unknown without use of addi-tional sensors;

• usually, no reliable natural landmarks are visible in both TRUS imaging andhistology to assist with the registration;

• introduction of the transrectal probe causes a local posterior deformation,

whereas these are the biggest obstacles concerning histology:

• for histological analysis, the prostate is cut into 3- to 4-mm-thick slices, providingpoor resolution in that direction;

• after excision, the prostate is relieved from pressure caused by surrounding organsand tissue, resulting in a deformation;

• fixation of the prostate after RP causes a volume decrease [144].

To avoid the need of landmarks or a high level of detail, which are lacking inB-mode TRUS, the method presented here is surface-based, requiring prostate shapeinformation only. Both the a�ne and local deformations of the prostate as a result

Material and methods 105

of the probe pressure and deformation after excision are taken into account. Apartfrom acquiring the prostate shapes, no manual intervention is required during theregistration process. Moreover, being independent of the underlying imaging modal-ity, application of the method in validation of PCa imaging techniques using othermodalities (e.g., MR or CT) could be a feasible option.

In other work related to surface-based, elastic registration of prostates, Crouch etal. [264] estimated boundary displacements by minimizing deformation energy. Afterthat, a uniform nearly-incompressible material with linear elasticity was assumed toestimate internal deformation. Lee et al. [265] developed a technique for a jointestimation of elasticity and deformation of organs and tested it on ten prostates.Parameters describing the mechanical properties and forces acting on the boundary ofthe prostate were optimized through minimization of the distance between the prostatesurfaces to register.

The method presented in this paper does not rely on the underlying patient-specificmechanical properties, which may be di�cult to determine during an examination andmay change during the fixation process as part of the preparation for histopathologicanalysis. Moreover, values for Young’s modulus of prostate tissue found in literaturevary in order from 10 to 100 kPa [266–270]; additionally, varying values of sti�nessamong di�erent prostate zones were reported [266]. For these reasons, internal defor-mation is estimated based on shape di�erence only. In this way, the method can beapplied using data obtained during a routine prostate examination by TRUS imagingwithout the use of specialized equipment or training.

Because of the 2D nature of TRUS imaging as commonly used in clinical practice,an additional step consisted of the construction of a 3D surface model based on theprostate contours in multiple 2D TRUS images. The reconstruction of 3D surfacesfrom 2D images can be performed in various ways [230, 252, 271, 272] and is not thefocus of this paper. However, for completeness, the method we designed for our studyis also described.

In an in-vitro experiment, the registration algorithm’s accuracy was assessed in2 gelatin phantoms with fiducial markers. Additionally, in an in-vivo experiment,we used the border between the peripheral and central zone (BPZ) to estimate themethod’s target registration error (TRE) in 7 patients. To the authors’ knowledge,no quantitative in-vivo validation has yet been reported for 3D registration betweenTRUS and histology.

7.2 Material and methods

7.2.1 Prostate anatomyThe prostate is part of the male reproductive system and is located between the bladderand the rectum. A schematic overview of the prostate anatomy is given in Fig. 7.1, inwhich the position of the TRUS imaging probe has also been drawn. This illustration

106 3D registration of prostate data from histology and ultrasound

Figure 7.1: Schematic illustration of the prostate with surrounding structures (left) and atransversal cut showing the zonal anatomy (right).

indicates the locations of the base and apex, and posterior and anterior side, whichare frequently mentioned throughout this paper. In addition, a schematic overview ofthe zonal anatomy is shown in a transversal plane.

7.2.2 Surface reconstructionTRUS

To perform 3D registration of TRUS and histology shapes, 3D triangulated meshesof the prostate shapes in both modalities were constructed. First, a TRUS video ofthe prostate, from now on referred to as “transversal sweep video”, was recorded invivo using a Philips iU22 US scanner (Philips Healthcare, Bothell, WA) with an end-fire probe in B-mode by inserting the probe rectally until it reached the prostate andsteadily rotating it to move its tip from base to apex. Additionally, a longitudinalimage in the mid-sagittal plane, which is perpendicular to the images in the sweepvideo, was recorded. The prostate boundaries were manually outlined by an expert inapproximately 30 of the frames in the transversal video, as shown for one frame inFig. 7.2(a), which would be used to construct the 3D model.

From the longitudinal image, the angles ✓base and ✓apex of the first and lasttransversal frames with the probe center line were determined (Fig. 7.3). The centerof rotation was initially chosen as indicated in Fig. 7.3. To estimate the angles of theother frames, linear interpolation was applied; i.e., a constant angular velocity of theprobe was assumed. The manually drawn contours were then positioned in a 3D Eu-clidian space. After visual comparison of the positioned contours with the longitudinalimage [Fig. 7.2(b)], the center of rotation could be moved vertically, and ✓base and

Material and methods 107

Figure 7.2: Schematic overview of the construction and registration of the prostate shapemodels obtained from ultrasound and histology. (a) One frame of the transversal sweepvideo with outlined prostate contour. (b) Longitudinal image with prostate contours fromthe transversal video. (c) Final surface mesh of the prostate obtained from TRUS imaging(after remeshing). (d) Macro-photo of prostate slices prepared for histology with canceroustissue marked in red. (e) Positioning of the prostate contours and tumors in 3D. (f) Resultingsurface mesh of the prostate obtained from histology (after remeshing).

✓apex could be adjusted.A triangulated mesh was created by connecting vertices on neighboring contours

[Fig. 7.2(c)]. Finally, thin caps were added to the base and apex to prevent sharpedges at the first and last contours.

Histology

Because histopathologic analysis of the prostate after excision was used as a gold stan-dard, patients were only included in this study if they were diagnosed with PCa andunderwent RP. After RP, the prostate was submerged in a formalin solution for approx-imately 24 h, possibly producing the side-e�ect of prostate shrinkage [144]. Then, thedistal caps of the prostate were removed by a transversal cut at approximately 4 mmfrom the apex and base. The remaining prostate was then transversally sectioned inslices with a thickness of 4 mm and prepared for microscopic examination.

A macro-photo of all slices was taken [example shown in Fig. 7.2(d)], in which

108 3D registration of prostate data from histology and ultrasound

Figure 7.3: Illustration of the angles ✓base and ✓apex of the first and last frame of thetransversal sweep video in a longitudinal image. The initial estimation of the center ofrotation of the TRUS probe has also been indicated.

the prostate contours were drawn. Additionally, any tumors found by histopathologywere added to the photo in red. By manually aligning the slices with the contoursand placing them behind each other with 4 mm distance in between [Fig. 7.2(e)], a3D prostate shape (including tumors) was reconstructed. A triangulated mesh wasobtained by linear connection between vertices in adjacent slices [Fig. 7.2(f)]. Finally,the distal caps of the prostate, which had been cut o� before, were measured andadded to the base and apex of the model to close it.

7.2.3 Registration algorithmAn image registration process can in general be described as the search for the spatialmapping S(x) that best aligns a source image IS with a reference image IR by movingthe image coordinates x:

IR(x) = IS(S(x)). (7.1)

The registered image IR is an estimation of IR. In our case, the source image wasthe histology prostate model and the reference image was the TRUS prostate model.

Our registration algorithm consisted of three steps:

1. an a�ne, global registration,

2. an elastic surface registration,

3. an internal registration, which interpolates the deformation of the surface in step2 to the inner volume.

In step 1, we accounted for the global di�erence in position, orientation and size byan a�ne mapping, whereas the local deformations, as a result of probe pressure and

Material and methods 109

radical prostatectomy, were compensated for in step 2 and 3 by an elastic mapping.The total mapping function was the concatenation of the a�ne and elastic mapping,Taff and Tel, respectively:

T (x) = Tel(Taff (x)). (7.2)

Step 1: a�ne registration

The a�ne registration globally aligned the prostate model and served as initializationfor the subsequent steps, which made it a very crucial step. We tested two di�erentapproaches: an iterative closest point (ICP) algorithm [158] and a stepwise method inwhich translation, rotation and scaling were implemented as sequential steps. As aninitialization to both approaches, the midpoints – defined as the means xR and xS ofthe surface vertex coordinates of the reference and source models, respectively – werealigned by translating the source model.

The ICP algorithm [158] iteratively finds corresponding vertices on the prostatemodels and minimizes the root-mean-square (RMS) distance between those verticesby transforming the source model. In [158], where only rigid body transformations(translation + rotation) were considered, a direct solution [273] for the minimumRMS was applied.

Besides a rigid body transformation, we also tested two non-rigid transformations:a rigid body transformation followed by an isotropic scaling (ISc) and a rigid bodytransformation followed by an anisotropic scaling (ASc). Scaling was implemented tocompensate for volume di�erence and global shape changes, mainly due to operationson the prostate after excision. Moreover, it provided a close match of the prostatesurfaces as initialization for the elastic surface registration in the next step. To findthe minimum RMS for the non-rigid transformations, we used a Levenberg-Marquardtoptimizer [274,275].

In the stepwise approach to a�ne registration, first, the three main axes of bothshapes were estimated by principal component analysis (PCA) of the surface vertexcoordinates, as elaborated in [276]. Numerically, the principal components were com-puted as the eigenvectors of the symmetric P ⇥ P covariance matrix C of the P

observed variables, which in our case was defined as:

C =

2

4cov(xO,xO) cov(xO,yO) cov(xO, zO)cov(yO,xO) cov(yO,yO) cov(yO, zO)cov(zO,xO) cov(zO,yO) cov(zO, zO)

3

5 , (7.3)

with cov(•, •) represented the covariance operator and xO, yO, and zO the observationvectors containing the x-, y-, z-components of the model vertices x.

Let VR and VS be the 3⇥ 3 orthonormal matrix containing by column the eigen-vectors (sorted by eigenvalue) of the covariance matrices for the reference and sourcemodels, respectively. These matrices represent the orientations of the models, but arenot uniquely defined, because of the possible inverse direction of the eigenvectors. We

110 3D registration of prostate data from histology and ultrasound

could, however, assume a reasonable initial alignment, because both models were sim-ilarly obtained by stacking contours from apex to base. For this reason, we swappedthe columns in VR and VS such that the largest absolute values in each column wereon the diagonal, and multiplied any column by �1 for which the entry on the diagonalwas negative. By doing this, we limited the rotation angle to 90

�.Having found the orientations VR and VS , a rotation matrix R, which transforms

VS into VR was obtained by:

R = VRV�1S

= VRVT

S. (7.4)

The individual coordinates xS of the source surface model are now registered bycombining the translation and rotation:

x(r)S

= R(xS � xS) + xR. (7.5)

Scaling (ISc or ASc) was implemented as the next step in the stepwise method.Mathematically, the source surface coordinates were pre-multiplied by a scaling matrixS:

S =

2

4sa 0 0

0 sb 0

0 0 sc

3

5 . (7.6)

For ISc (sa = sb = sc), the scaling factor was chosen such that the volumes of themodels were equal after scaling. In the ASc approach, the scaling factors sa, sb, andsc were estimated by projecting the surface nodes of each model onto each principalaxis a, b, c of that model and calculating the ratio between the root mean squareddistances da, db, and dc between the coordinates projected on these axes to the modelcenter:

sa =daR

daS

, sb =dbR

dbS

, sc =dcR

dcS

. (7.7)

The subscripts R and S in (7.7) refer to the reference and source models, respectively.The complete a�ne transformation for the stepwise approach was found by com-

bining all previous steps:

Taff (x) = VRSVT

S(x� xS) + xR. (7.8)

Step 2: elastic surface registration

For elastic registration of the surfaces, we used a parametric active contour model,based on the algorithms described in [277–279], commonly used for segmentationor motion tracking in medical images (see e.g. [280–282]). One advantage of thistechnique is its capability to project nodes from the source model onto the referencemodel while maintaining a natural spreading of the nodes. Another advantage is theintrinsic smoothing of the surface, which makes the registration less susceptible to

Material and methods 111

irregularities in the prostate models. The main steps of this algorithm are describedbelow; for a detailed description, the reader is referred to [279].

Registration is performed by minimizing an energy functional

E =

Z

⌦(Eint(s) + Eext(s))dA (7.9)

by applying a transformation s : ⌦ ⇢ R2 ! R3 to a surface ⌦ [279]. Eint representsthe internal energy, defined by the surface material properties, whereas the externalenergy Eext is defined by the reference image IR. In our case, IR was a binary voxelimage of the TRUS reference volume with a resolution of 1/3 mm per voxel. Theinternal and external energy are calculated by [279]

Eint(s) =

3X

i=1

⌧memkrsik22 + ⌧tps(kr2sik22 � 2|H(si)|), (7.10)

Eext(s) = �⌘k(r[G�b ⇤ IR])(s)k2, (7.11)

in which si denotes the i-th spatial component of s, H(·) represents the Hessian matrix,G�b is a 3D Gaussian kernel with standard deviation �b, and ⌘ is the external forcefactor, determining the weight of the external force [279]. The parameters ⌧mem and⌧tps control the surface properties and accomplish a membrane-like or a thin-plate-likebehavior, respectively.

A local minimum of (7.9) can be found by the iterative solution

pi+1 = pi + �(⌧memU(pi)� ⌧tpsU2(pi)

� �(n ·rEext(pi))n

� (1� �)rEext(pi)), (7.12)

in which pi contains the coordinates of a surface node in the ith iteration and � is

the step size of each iteration. The operator U(·) represents the Umbrella function asdefined in [279].

Forces tangent to the mesh surface can cause self-intersection within the mesh. Toprevent the surface mesh from self-intersecting, the external force vector, rEext, wasreplaced in (7.12) by a weighted sum of the external force vector and the vertex normalvector n as suggested in [279]. The parameter � 2 [0, 1] determines the influence ofthe image force relative to the surface normal.

The algorithm stops when the maximum node displacement per step size falls below�pmin. After the algorithm had stopped, we defined the elastic mapping Tel(p0) ofeach node position of the initial surface mesh to be the displacement pend � p0 ofthat vertex at the end of the algorithm.

The parameter values were empirically optimized based on the registration of theprostate models of 5 test patients. First, the standard deviation of the Gaussian filter�b was set to a value such that the blurred reference image entirely covered the source

112 3D registration of prostate data from histology and ultrasound

model. Next, a value for � was chosen su�ciently large to prevent self-intersection,but as low as possible to keep disturbance of the external energy field to a minimum.The parameters ⌧mem, ⌧tps, ⌘, and � were heuristically determined to achieve a fastconvergence, while keeping the registration smooth and stable. All parameter valuesare summarized in Table 7.1.

Step 3: internal registration

To estimate the elastic transformation Tel for the interior of the prostate, the surfacevertex displacements found by the elastic surface registration were interpolated. Wetested two di�erent ways of interpolating the vertex displacements.

The first method was a finite element (FE) approach assuming a linearly-elastic,nearly-incompressible material (Young’s modulus 25 kP, Poisson’s ratio 0.495), similarto the material properties used in [264, 283]. To this end, a tetrahedral mesh wasgenerated using TetGen 1.4.3 [284] with the quality measure q set to its maximumvalue (i.e., 18).

In the second method, we used a natural neighbor (NN) interpolation method [285]to interpolate the surface displacements in each dimension separately. This methodis based on the Voronoi diagram of the coordinates at which the displacements tobe interpolated are known. To obtain the displacement at a new coordinate, a newVoronoi diagram is constructed around this coordinate. The interpolated value isthen calculated as the weighted sum of the displacements at the coordinates whoseold Voronoi cells overlap the Voronoi cell of the new coordinate to obtain a smoothinterpolation. This technique has the advantage over FE-based methods that nointernal mesh has to be generated and no prior knowledge about the mechanicalproperties of the underlying material is required or used.

To find the complete deformation field of the prostate, the a�ne and elastic de-formations were concatenated by applying (7.2). Tumors found by histology couldnow be reconstructed in the analyzed TRUS plane by mapping all points of the tumormodel to their corresponding positions in the TRUS model according to (7.1).

Table 7.1: Parameter values in the active contour algorithm

Symbol Description Value

�pmin Stopping criterion [mm] 0.03⌧mem Resists stretching 0.01⌧tps Resists bending 0.1� Time step 0.5�b Reference image blurring coe�cient [mm] 1.67⌘ External force factor 3� Normal force factor 0.2

Material and methods 113

Figure 7.4: Schematic side-view of the phantom used for in-vitro validation.

Figure 7.5: A gelatin phantom while scanning in position 2.

Implementation

The registration algorithm described in this section was implemented in MATLAB8.4.0.150421 (The MathWorks, Natick, MA) on a PC using an Intel® Core i5-2500processor running at 3.3 GHz (Intel, Santa Clara, CA) with 16 GB RAM. Our im-plementation of the ICP algorithm in MATLAB was based on functions written byKroon [286] and by Wilm and Kjer [287], available at MATLAB Central [288]. Forthe parametric active contour model, we modified code written by Kroon [289]. Allother methods were implemented using original code.

114 3D registration of prostate data from histology and ultrasound

7.2.4 RemeshingOur registration method works best with prostate models containing triangulatedmeshes in which the vertices are as uniformly spaced as possible (i.e., the lengthsof all edges are approximately equal). It results in a more reliable orientation esti-mation for the a�ne registration, because each part of the surface is approximatelyequally represented in the PCA and ICP algorithms, and the active contour algorithmused for elastic surface registration showed more stable behavior with respect to self-intersection.

To obtain uniform meshes, a remesh algorithm using the non-adaptive part ofthe method described in [290] was applied to each of the surface models obtainedfrom both histology and TRUS. This iterative method uses front propagation to findthe location on the surface with the longest geodesic distance to all vertices thatare already in the mesh; a new vertex is then inserted at that location. In this way,vertices are equally distributed over the surface, which leads to an uniform mesh. Thenumber of vertices Nv in the mesh is a trade-o� between computational speed andaccurate representation of the prostate shape (hence higher registration accuracy forirregular surfaces). For our surface models we used Nv = 2000, which was su�cientto reproduce the encountered prostate deformations.

7.2.5 In-vitro validationBecause natural landmarks are not always present in both histology and TRUS, an in-vitro experiment, using phantoms with fiducial markers, was designed to quantitativelyassess the registration error of the presented methods. Two gelatin phantoms ofthe prostate were produced and embedded in a gelatin surrounding (Figs. 7.4 and7.5), based on the design presented in [291]. Di�erent from [291], we chose to usegelatin as phantom material, because it suited the scope of our experiments and waseasier to handle. The gelatin was constructed such that the prostate phantom wasapproximately three times sti�er than the surrounding gel.

To be able to distinguish the prostate phantom from the surrounding gel in TRUSB-mode images, a small amount of graphite powder was added to the prostate phantomas a scattering agent. Furthermore, in each phantom, 9 clay markers with a diameterof 3-5 mm were added for assessment of the TRE. A hole on the side (50 mm in diam-eter), large enough to accommodate and rotate a TRUS end-fire probe, representedthe rectum, enabling simulation of TRUS imaging during a prostate examination (po-sition 2). Alternatively, the prostate could be scanned from the top (position 1) toobtain images at a di�erent angle than in position 1 and without phantom deformationdue to pressure by the probe head, and therefore providing images that could representthe histology.

In this experiment, we used an iU22 (Philips Healthcare, Bothell, WA) US scannerwith a 3D endocavity probe (3D9-3v) to exclude model construction from this val-idation. Each phantom was first scanned from position 1 to acquire an image of a

Material and methods 115

“histology” phantom. Subsequently, each phantom was scanned with the same probefrom position 2, while pushing the probe against the phantom to acquire a “TRUS”image. The latter scan was repeated 6 times with varying strength and location ofthe force applied on the phantom to test the robustness of the registration algorithmagainst varying deformations.

In each 3D US image, the phantom’s contour and markers were manually seg-mented to construct 2000-node surface meshes with markers inside. For each phantom,all “TRUS” meshes (reference) were registered with the “histology” mesh (source) us-ing the proposed algorithms. The TRE was defined to be the distance between amarker in the reference mesh to the same marker in the registered mesh. Resultswere stored after a�ne and elastic registration to evaluate the performance of theindividual steps. The registration accuracy and execution time were compared for thedi�erent methods described in Section 7.2.3. The statistical significance (p-value) ofthe results was evaluated by two-sided Wilcoxon signed rank tests for paired data andby two-sided Wilcoxon rank sum tests for unpaired data.

The described in-vitro experiment focused on validation of the registration algo-rithm only, leaving out the construction of the model from 2D images and deformationsdue to surgery and the fixation process.

7.2.6 In-vivo validationIn 7 patients, (parts of) the border between the peripheral and central zone (BPZ) ofthe prostate (see Fig. 7.1) was visible both in the histology and TRUS images. Thesepatients were therefore selected for in-vivo validation using the BPZs as landmarks toevaluate the TRE. In two patients, two ultrasound recordings were made at di�erentdates and were both included. As a result, a total of 9 prostate model sets were usedfor validation. Di�erent from the in-vitro experiments, the in-vivo validation includedmodel construction and the e�ect of deformation after surgery.

The BPZ was manually drawn in the TRUS and histology images by an expert,after which 3D models were reconstructed as described in Section 7.2.2. Betweenthe images, the BPZ was interpolated using a linear radial basis function with noisereduction [1, 157]. The constructed models were then registered. The TRE wasdetermined by calculating the normals to the surface of the registered (histology) BPZand finding the point at which it intersected with the reference (TRUS) surface. Thedistance between the histology and TRUS surfaces along a surface normal was definedto be the TRE at that point. However, because TRUS and histology showed alsoBPZ parts that were not corresponding, the corresponding parts had to be defined forthe validation. Parts of the BPZ for which no intersection point was found along thesurface normal were considered to be non-corresponding, and were therefore ignored.Statistical analysis of the results was done in a similar way as described in Section7.2.5.

Because the models were constructed by stacking contours from base to apex, as

116 3D registration of prostate data from histology and ultrasound

Figure 7.6: Registration of phantom models (containing 9 landmarks) imaged in position1 (blue) and in position 2 (red). (a) A�ne registration by the ICP algorithm using a rigidtransformation with anisotropic scaling. (b) The same a�ne registration followed by elasticregistration using NN interpolation.

described in Section 7.2.2, the patient models already had a similar orientation. Forthis reason, the TRE was also determined for registration without applying rotation inthe stepwise a�ne transformation.

7.3 Results

7.3.1 In-vitro validationAn example of the registered phantom models with markers after a�ne and elasticregistration is shown in Figure 7.6. The model shapes showed already good agreementafter a�ne registration, but a slight mismatch could be observed due to deformationby the imaging probe. After elastic registration, the two models almost completelyoverlapped, as expected.

In Table 7.2, the TREs are summarized for each registration method. For eachmeasurement, the means and standard deviations were computed over all markers(9 per phantom). Then, the means and standard deviations were computed over allmeasurements (6 per phantom). Rotation by PCA resulted in an average TRE of over

Results 117

(c)

(a)

(d)

(b)

Reference landmarkAffinely registered landmarkReference prostate contourAffinely registered prostate contour

Reference landmarkElastically registered landmarkReference prostate contourElastically registered prostate contour

Figure 7.7: Registration in one patient included in the validation. Red represents TRUS,blue represents histology. Subfigure (a) shows the result of the a�ne registration using theICP algorithm with anisotropic scaling. Subfigure (b) shows the elastic registration using NNinterpolation, after applying the same a�ne registration as in (a). In (c) and (d), cross-cutsare shown at the planes indicated in (a) and (b), respectively.

8 mm for phantom 1, but below 2 mm for phantom 2. The reason for this di�erenceresides in the observation that, di�erent from phantom 2, no clear second main axisperpendicular to the first main axis could be distinguished for phantom 1. The ICPmethod performed well in both phantoms. No significant di�erence was observed withrespect to the mean TRE after applying elastic registration (p 2 [0.93, 0.97]) using FEinterpolation, and for NN interpolation the mean TRE was even significantly higher(p < 0.001) for each ICP method.

The computation time for any of the a�ne registration methods was negligiblecompared to the computation time of the elastic registration techniques. Also, thetype of scaling used in the a�ne registration step had little influence on the compu-tation time required for the elastic registration. Using NN instead of FE for internalregistration reduced the computation time by approximately a factor 10.

118 3D registration of prostate data from histology and ultrasoundTable

7.2:Results

ofthein-vitro

validation:m

ean±

standarddeviation

–com

putedoverallm

easurements

–ofcom

putationtim

e,mean

TRE,and

standarddeviation

(inbrackets)

oftheTRE

computed

over9m

arkersperm

easurement.

Method

Computation

TRETRE

TREtim

e(s)

phantom1

(mm

)phantom

2(m

m)

overall(mm

)

PCA0.0

±0.0

8.0±

2.5(1.8

±0.5)

1.4±

0.4(0.5

±0.2)

4.7±

3.9(1.1

±0.8)

PCA+

NN

17.4±

1.08.3

±2.7

(1.6±

0.4)1.5

±0.4

(0.5±

0.2)4.9

±4.0

(1.1±

0.7)PCA

+FE

175.9±

4.78.6

±3.0

(1.3±

0.2)1.6

±0.5

(0.5±

0.1)5.1

±4.2

(0.9±

0.5)

PCA+

ISc0.3

±0.0

8.0±

2.5(1.8

±0.5)

1.4±

0.4(0.5

±0.2)

4.7±

3.9(1.1

±0.8)

PCA+

ISc+

NN

17.1±

1.28.3

±2.7

(1.6±

0.4)1.5

±0.4

(0.5±

0.2)4.9

±4.0

(1.1±

0.7)PCA

+ISc

+FE

170.1±

5.68.6

±3.0

(1.3±

0.2)1.6

±0.5

(0.5±

0.1)5.1

±4.2

(0.9±

0.5)

PCA+

ASc0.0

±0.0

8.1±

2.6(1.7

±0.5)

1.4±

0.4(0.5

±0.1)

4.8±

3.9(1.1

±0.7)

PCA+

ASc+

NN

16.9±

0.78.4

±3.0

(1.6±

0.4)1.4

±0.4

(0.4±

0.2)4.9

±4.1

(1.0±

0.7)PCA

+ASc

+FE

167.9±

0.78.6

±3.0

(1.3±

0.2)1.5

±0.4

(0.5±

0.1)5.1

±4.2

(0.9±

0.5)

ICPrigid

0.5±

0.31.7

±0.2

(0.8±

0.3)1.3

±0.1

(0.5±

0.1)1.5

±0.3

(0.7±

0.3)ICP

rigid+

NN

17.2±

0.91.8

±0.2

(0.9±

0.3)1.3

±0.1

(0.5±

0.1)1.6

±0.3

(0.7±

0.3)ICP

rigid+

FE168.7

±6.2

1.7±

0.2(1.1

±0.3)

1.3±

0.1(0.4

±0.1)

1.5±

0.2(0.8

±0.4)

ICPrigid

+ISc

0.4±

0.01.7

±0.3

(0.8±

0.3)1.2

±0.1

(0.5±

0.1)1.5

±0.3

(0.7±

0.3)ICP

rigid+

ISc+

NN

17.1±

0.61.9

±0.3

(0.9±

0.3)1.3

±0.1

(0.5±

0.1)1.6

±0.3

(0.7±

0.3)ICP

rigid+

ISc+

FE169.7

±5.4

1.7±

0.2(1.1

±0.3)

1.3±

0.1(0.4

±0.1)

1.5±

0.2(0.7

±0.4)

ICPrigid

+ASc

0.7±

0.11.7

±0.2

(0.8±

0.2)1.2

±0.1

(0.4±

0.1)1.5

±0.3

(0.6±

0.3)ICP

rigid+

ASc+

NN

16.9±

0.61.8

±0.2

(0.9±

0.2)1.3

±0.1

(0.4±

0.1)1.5

±0.3

(0.7±

0.3)ICP

rigid+

ASc+

FE169.6

±4.7

1.7±

0.2(1.1

±0.2)

1.2±

0.1(0.5

±0.1)

1.5±

0.3(0.8

±0.4)

ISc0.3

±0.0

3.5±

0.6(1.2

±0.1)

3.2±

0.4(1.3

±0.3)

3.4±

0.5(1.2

±0.2)

ISc+

NN

16.8±

0.53.3

±0.5

(1.3±

0.2)3.2

±0.4

(1.1±

0.3)3.2

±0.5

(1.2±

0.2)ISc

+FE

171.8±

3.03.5

±0.5

(1.5±

0.2)3.6

±0.4

(1.1±

0.3)3.5

±0.4

(1.3±

0.3)

ASc0.0

±0.0

3.6±

0.6(1.3

±0.1)

3.2±

0.4(1.2

±0.3)

3.4±

0.5(1.3

±0.2)

ASc+

NN

16.5±

0.73.3

±0.6

(1.4±

0.2)3.1

±0.4

(1.1±

0.3)3.2

±0.5

(1.2±

0.3)ASc

+FE

170.8±

4.03.6

±0.5

(1.3±

0.1)3.7

±0.4

(1.1±

0.3)3.6

±0.4

(1.3±

0.4)

Results 119

Table 7.3: Results of the in-vivo validation: mean ± standard deviation – computed overall measurements – of computation time, mean TRE, and standard deviation (in brackets) ofthe TRE computed within a measurement.

Method computation TRE (mm)time (s)

PCA + ISc 0.2 ± 0.0 3.0 ± 0.6 (2.0 ± 0.8)PCA + ISc + NN 37.9 ± 7.7 2.7 ± 1.0 (1.9 ± 1.3)PCA + ISc + FE 160.0 ± 8.4 3.6 ± 1.7 (2.8 ± 1.6)

PCA + ASc 0.0 ± 0.0 2.9 ± 0.7 (2.0 ± 0.9)PCA + ASc + NN 37.2 ± 7.2 2.5 ± 0.9 (1.8 ± 1.1)PCA + ASc + FE 162.7 ± 10.5 3.6 ± 1.7 (3.0 ± 1.9)

ICP rigid + ISc 0.3 ± 0.1 2.4 ± 0.5 (1.6 ± 0.5)ICP rigid + ISc + NN 37.6 ± 8.4 2.2 ± 0.6 (1.5 ± 0.5)ICP rigid + ISc + FE 161.4 ± 12.7 2.9 ± 0.9 (2.3 ± 0.8)

ICP rigid + ASc 0.4 ± 0.1 2.4 ± 0.7 (1.6 ± 0.7)ICP rigid + ASc + NN 35.8 ± 7.7 2.2 ± 0.6 (1.6 ± 0.6)ICP rigid + ASc + FE 162.3 ± 7.3 2.7 ± 0.7 (2.0 ± 0.7)

ISc 0.3 ± 0.0 2.6 ± 0.6 (1.6 ± 0.5)ISc + NN 43.5 ± 6.1 2.2 ± 0.5 (1.4 ± 0.4)ISc + FE 174.2 ± 18.2 2.9 ± 1.3 (2.2 ± 1.0)

ASc 0.0 ± 0.0 2.5 ± 0.5 (1.6 ± 0.5)ASc + NN 42.0 ± 6.8 2.1 ± 0.5 (1.4 ± 0.3)ASc + FE 175.9 ± 18.5 2.8 ± 1.2 (2.4 ± 1.0)

7.3.2 In-vivo validationTable 7.3 gives the TREs per method based on 9 TRUS-histology registrations in 7patients (see Section 7.2.6). The results for the methods without scaling are omitted,because in some cases the shape di�erences between the reference and source modelwere too large after rigid registration only. In those cases, parts of the source modelwere not covered by the blurred reference image in the elastic surface registration. Inthose uncovered parts, elastic registration did not work and, consequently, the internaldeformations could not be computed.

The mean TRE was lower for the ICP methods than for the PCA methods. Thisdi�erence was significant for the transformation including ISc (p < 0.027), but not sig-nificant for ASc (p = 0.074). Applying elastic registration using NN interpolation aftera�ne registration decreased the TRE significantly for rigid ICP + ISc and rigid ICP +ASc (p < 0.01) and insignificantly for the other methods (p 2 [0.055, 0.20]). Inter-

120 3D registration of prostate data from histology and ultrasound

(b)

(c)

(a)

(d)

Reference prostate contourAffinely registered prostate contour

Reference prostate contourElastically registered prostate contour

Figure 7.8: Registration of 2 prostate models containing a tumor (yellow). Red representsTRUS, blue represents histology. Subfigure (a) shows the result of the a�ne registrationusing the ICP algorithm with anisotropic scaling. Subfigure (b) shows the elastic registrationusing NN interpolation, after applying the same a�ne registration as in (a). In (c) and (d),cross-cuts are shown at the planes indicated in (a) and (b), respectively.

polation by FE even increased the TRE, although not significantly (p 2 [0.13, 0.65]).When applying only scaling without automatic rotation in the a�ne step, the perfor-mance of the stepwise registration was similar to the performance of the methods usingICP as an a�ne registration step. The computation time for the NN interpolation waslonger than in Table 7.2 (p < 0.001), because the BPZ contained more points toregister than the 9 fiducial markers used in the phantom experiments. An example ofa registration of two models using one of the best performing methods (ICP rigid +ASc followed by NN) is given in Fig. 7.7.

7.4 DiscussionThe phantom experiments resulted in a mean TRE of 1.5 mm for the best performingmethod; in vivo, this value was 2.1 mm. This error is acceptable for most clinicalpurposes, since tumors are considered clinically significant when their volumes exceed0.5 cm3 [183]. Assuming a spherical shape, this yields a tumor diameter of 10 mm.

Discussion 121

TREs were comparable with the results presented in the literature [264,265], in whichsurface-based registration was applied to prostates imaged in di�erent modalities.However, in [264, 265], registration was not performed between in-vivo and ex-vivoimages, bypassing the deformation due to surgery.

In the phantom experiments, TREs due to model construction or to deformationcaused by surgery and preparation of the prostate for histopathologic analysis werenot included. Although these di�erences were included in the in-vivo study, the TREsin that study were only approximately 1 mm larger than those in the in-vitro study.This suggests that the error introduced by our method used for model construction isrelatively small.

From the lower standard deviations in the TREs in both the in-vitro (Table 7.2) andthe in-vivo experiments (Table 7.3), it can be concluded that the ICP method is morerobust in a�ne registration than the PCA-based method. The reason can possiblybe found in the fact that the PCA method tries to find three main axes like those inan ellipsoid. Because the shape of the prostate in TRUS can be deformed drasticallyat the posterior side by the pressure of the probe head on the prostate, it does notresemble an ellipsoid-like shape anymore. In this case, the three orthogonal main axesto estimate the orientation of the prostate model cannot be correctly defined.

Surprisingly, in vivo, registration without applying automatic rotation performedsimilar to the ICP methods. Because both models were constructed by stacking slicesfrom base to apex, they had already been reasonably well-aligned before applying theregistration algorithm. The same a-priori information could be applied in the validationof some PCa techniques using other imaging modalities, such as MRI, where histologyslices and imaging planes are already well aligned before registration.

When comparing in-vitro average TREs (Table 7.2) for a�ne ICP and elasticregistration, only small di�erences were observed (< 0.1 mm). An explanation forthis result could be that most of the deformation could already be covered by thea�ne registration. Errors in drawing the contours of the phantoms and markers wereprobably larger than the improvement that could be made by elastic registration.In our in-vivo experiments, the elastic registration followed by NN interpolation didresult in a small decrease in TRE for each a�ne registration method. The FE method,however, resulted in higher TREs. The deformation at the surface defined by theelastic surface registration of the a�nely registered models probably did not representrealistic boundary conditions for a physics-based model. A more general interpolationmethod, such as the NN interpolation, could then result in lower TRE.

Although the di�erences between the TREs for a�ne and elastic registration weresmall, the di�erences can be larger close to the surface. An example of the registrationof histopathology and TRUS using an a�ne and an elastic method is given in Fig. 7.8.In this case, the deformation at the posterior surfaces – caused by probe pressure– could not be compensated for by an a�ne transformation. As a result, part ofthe registered tumor lied outside the prostate and could therefore not be used forvalidation or training of a PCa imaging technique. Applying an elastic registration

122 3D registration of prostate data from histology and ultrasound

using NN interpolation solved this issue.Because the location of the BPZ in between histology slices was unknown and had

to be interpolated, an inaccuracy in the estimation of the TRE in the in-vivo validationwas possibly introduced. Moreover, the orientation of the BPZ is largely parallel tothe apex-base axis. Because the TREs were estimated based on the surface normalsof the BPZ, the influence of registration errors in that direction on the final TREwas smaller than in other directions. Fiducial point landmarks could provide a moreaccurate reference for TRE estimation, but can be di�cult to apply during a regularTRUS examination.

Although outside the scope of this work, a method was given to construct 3Dprostate models from a transversal sweep video. The presented method requires man-ual delineation of the prostate contours to obtain the most accurate models and regis-tration. However, an accurate (semi-)automatic segmentation could assist in makingthis step less time-consuming. Moreover, the accuracy of the model construction couldbenefit from using a 3D US probe to minimize the error made by the conversion from2D sweep video to 3D US.

The presented method does not rely on the mechanical properties of the prostateand, therefore, assumes a homogeneous material. The prostate, however, consists ofdi�erent zones with di�erent sti�ness [266]. Moreover, tumors are known to be sti�erthan healthy prostate tissue [266]. When the location of the central zone and thetumors are known, it could be worth applying varying sti�ness settings in the internalregistration step to reduce the TRE.

7.5 ConclusionsSeveral methods, directly applicable in clinical practice, for 3D, a�ne and elastic,surface-based registration of prostate models obtained by TRUS imaging and histologywere compared both in vitro and in vivo. Experiments using two gelatin phantomswith fiducial markers resulted in a mean TRE of 1.5 ± 0.2 mm for the best performingmethod. The mean TRE obtained from validation in 7 patients was 2.1 ± 0.5, which isbelow the slicing thickness in histology or the size of clinically significant tumors. TheICP algorithm proved to be a robust approach for a�ne registration, whereas rotationusing a PCA approach frequently resulted in large TREs. For the elastic registration,the NN interpolation outperformed a FE approach assuming linearly elastic material.Because the algorithm used for registration is independent of the adopted imagingtechnique, applications for imaging modalities other than TRUS (such as MR) can beenvisaged.

Chapter8Clinical validation ofhistology-ultrasound registration

The content of this chapter has been submitted for publication as [J3]:

A.W. Postema, S.G. Schalk, M. Mischi, J.J.M.C.H. de la Rosette, and H. Wijkstra,“3D registration improves transrectal ultrasound to resection pathology matching forprostate cancer imaging validation,” BJU Int.

124 Clinical validation of histology-ultrasound registration

AbstractObjectives: To validate a 3D elastic registration technique for matching ultrasound(US) imaging and radical prostatectomy specimen pathology.

Materials and methods: From our database we identified 14 patients with clearnatural landmarks. All landmarks were discussed between 3 investigators and onlyaccepted with unanimous consensus. Additional landmarks were added, also onthe premise of unanimous consensus. Using a 3D surface-based elastic registrationmethod, we registered US images to the pathology slices and identified the landmarklocation in both. For each landmark, xy-plane registration errors were calculated bymeasuring distance, z-axis registration error was estimated in 2 mm increments.

Results: In 7 patients, the original landmarks were rejected by the consensuspanel; the 7 remaining original landmarks were unanimously accepted. Twenty-eightadditional landmarks were identified and all 14 included cases had at least 1 usablelandmark. The median registration error of the original landmarks was 3.6 mm(range: 1.1 to 5.9 mm). The mean registration error per-patient was below 2 mm in43% (3/7) of cases and below 4 mm in 57% (4/7) of cases. Including all additionallandmarks, the median registration error was 1.9 mm (range: 0.5 to 5.9 mm) and themean registration error per-patient was below 2 mm in 64% (9/14) and below 4 mmin 78% (11/14) of cases.

Conclusion: With the proposed method, registration errors are in the range of onepathology slice thickness, below the threshold for clinically significant disease andsmaller than manual matching achieves. Therefore, the proposed method can improvethe US to pathology matching in imaging validation studies.

Introduction 125

8.1 IntroductionAccurate imaging is required to improve prostate cancer diagnostics towards targetedbiopsies and to enable focal therapy approaches [222, 292]. Several advanced ultra-sound (US) technologies such as dynamic contrast enhanced-ultrasound (DCE-US)and (shear wave) elastography have shown promise to provide the needed increases inaccuracy, and their development is ongoing [185]. Reliable validation of these imag-ing techniques requires accurate comparison with corresponding histopathology, andtherefore accurate registration between imaging and pathology. Several factors thatcomplicate US and pathology matching are the di�erences in plane angulation, defor-mations and shrinking caused by prostatectomy specimen processing and the defor-mation caused by the ultrasound probe during image acquisition [293]. Many of thesefactors also hold true for magnetic resonance imaging (MRI) to pathology matching.Furthermore, the manual allocation of pathology slices and imaging planes to prostateregions is di�cult and subjective [J5]. Many authors compensate for pathology toimaging mismatch by summarizing planes or taking results from neighboring prostateregions into consideration [294, 295]. However, this procedure leaves uncertainty onwhether over or under compensation occurs. This uncertainty in matching imagingand pathology contributes to the variability in the results that are reported in prostatecancer imaging [296]. It is therefore important that an improved, more objectivemethod of matching pathology and imaging with known approximate registration er-ror becomes available. Recently a 3D elastic registration method for ultrasound andpathology was proposed by Schalk et al. [J5]. In two ex vivo models they achieved amean registration error of 1.5 ± 0.2 mm and in 7 in vivo models they achieved a reg-istration error of 2.1 ± 0.5 mm using the peripheral zone/transitional zone (PZ/TZ)border as landmark. In the present study we aim to further validate this method invivo by using clear natural landmarks of varying shape, size and location.

8.2 MethodsFrom our database of pre-operative ultrasound scans and postoperative analysis ofradical prostatectomy specimens we selected patients on the basis of having easilyidentifiable landmarks in both pathology and imaging that could be used to validateour registration method. These data are derived from two institutional review boardapproved protocols in which patients were only included after informed consent wasobtained. During a consensus meeting between two engineers and one clinician with aresearch focus on prostate imaging (HW, SS and AP), each landmark was discussed.Landmarks were used for analysis only when there was unanimous agreement on thecorrespondence between the landmark in the US sweep and the pathology slices. Be-sides the original landmarks on the basis of which the patients were selected, additionallandmarks were added when the panel could unanimously agree on them. These ad-ditional landmarks were either point shaped (e.g., the urethra) or line shaped (e.g.,

126 Clinical validation of histology-ultrasound registration

PZ/TZ border or urethra).We used the anisotropic scaling + natural neighbor interpolation method detailed

in Schalk et al. for US to pathology registration [J5]. In short, this method entailsbuilding a 3D model of the prostate from the transversal base-to-apex transrectal2D US sweep. In each sweep video, the prostate contour was manually delineatedand the contours were stacked using the sagittal sweep video for guidance. In thiscohort, we used a Philips iU22 US scanner (Philips Healthcare, Bothell, WA) withan end-fire endocavity probe. After formalin fixation, the prostatectomy specimenwas sliced in 4 mm transversal slices. The prostate contours were delineated on amacro photograph displaying all pathology slices. Stacking of these contours allowsbuilding the 3D pathology model. The 3D US and pathology models were registeredin a three step process: a global rigid registration accounting for di�erences in sizeand orientation followed by a surface-based elastic registration accounting for localdeformations caused by e.g. probe pressure and pathology specimen processing. Inthe final step, elastic internal registration interpolates the deformation of the surfaceto the interior of the prostate. After registration, we rendered virtual US planescorresponding with the real pathology slices, identified the landmarks in both andcompared the location of the landmarks. We chose to generate virtual US slicesmatching real pathology slices instead of the other way around because the pathologydata is sparser due to the 4 mm slice thickness.

For each landmark, we calculated the registration errors in mm as the distancebetween the landmarks in the xy-plane. The original landmarks were areas for whichthe centroid was determined and this point was used for calculation of the registrationerror. For point shaped landmarks, we calculated an xy distance between the pointin pathology and the same point in the US slice. To determine the registration errorbetween line-shaped landmarks, for all points on the US landmark the minimum dis-tances to the histology landmark were determined and averaged over the entire line.The same computation was made vice versa, i.e., using the minimum distance fromhistology to US landmark. The registration error was then defined as the mean of thetwo acquired distances called the mean mean minimum distance (Fig. 8.1). Becausethe pathology slices are approximately 4 mm thick, we judged z-axis registration in halfslice (approximately 2 mm) increments. When the US and pathology landmarks wereregistered to the same plane, the z-axis error was set to be 0. When the landmarks inthe rendered US planes were located one plane besides the correct pathology plane,the z-axis error was set to 4 mm. The total registration error (TRE) was calculatedas the hypotenuse between xy-plane distance and z-axis error. We calculated whetherthe median TRE di�ered between landmark type and location.

The three primary results of this study are the median TRE for the original land-marks only, with inclusion of the additional point shaped landmarks and with inclusionof all additional landmarks. After including the additional landmarks in the analysis,we averaged the TREs within each patient to account for the varying number of land-marks per patient and the dependency of these landmarks on the same registration

Results 127

Figure 8.1: Left: the pathology slice with an original area shaped landmark (1) and aline shaped landmark (2) both delineated in blue. Middle: after ultrasound to pathologyregistration, this pathology plane was rendered and landmarks are delineated in red. Right:the two images are projected on top of each other and xy-plane registration error is calculated.

result. Both the per-patient averaged TREs and the TREs for the separate landmarkswill be presented.

8.3 ResultsFrom our database, 14 cases were selected for having natural landmarks visible inboth the US sweeps and pathology slices. During the consensus meeting, there wasno unanimous agreement on the correspondence between the original landmark in thepathology specimen and the US sweep of 4 patients. In three further patients, theoriginal landmark was discarded because they could not be delineated precisely andprecise delineation of the landmarks is a prerequisite for calculation of the registrationerror. Of the 7 remaining original landmarks, 5 could be identified in the correctpathology slice and the z-axis error was therefore judged to be 0. The other 2 originalUS landmarks were registered one slice before or after the pathology landmark. Forthese patients, the z-axis error was estimated to be 4 mm. The median TRE for theoriginal landmarks was 3.6 mm ranging from 1.1 mm to 5.9 mm. All original landmarksare described in Table 8.1. During the consensus meeting, additional landmarks wereagreed upon by the panel. With the inclusion of the additional landmarks, all 14included cases had at least 1 usable landmark and a maximum of 6. Mostly, theseadditional landmarks included clearly visible borders between the PZ and the TZ (lineshaped landmark) or the urethra (either line or point shaped landmark) (Table 8.2).After inclusion of the 11 additional point shaped landmarks, the median TRE changedto 3.4 mm with a range of 0.5 mm to 5.9 mm. When also the 17 line shaped landmarksare included the median TRE becomes 1.9 mm with a range of 0.5 mm to 5.9 mm.A graphical depiction of all data di�erentiated by landmark type and clustered per-patient is provided in Fig. 8.2. In Table 8.3, all data is categorized by TRE for alllandmarks separately and clustered per-patient.

The boxplots for the TRE for the three landmark types (original landmarks, addi-tional point landmarks and additional line landmarks) are depicted in Fig. 8.3. From

128 Clinical validation of histology-ultrasound registration

Table 8.1: Description of original landmarks with total registration errors or reason to excludethe landmark from the analysis.

Patient Description Location TRE (mm) Reason to exlcude

1 apical bulge apex - unclear delineation2 cyst mid 1.63 apical bulge apex - unclear delineation4 cyst mid-apex - no consensus on identification5 cyst mid-apex - no consensus on identification6 cyst apex - no consensus on identification7 cyst apex 3.68 calcification base 1.29 cystic region apex 5.910 cyst base 4.411 cyst mid 5.112 cyst mid 1.113 cyst apex - no consensus on identification14 cyst apex - unclear delineation

TRE: Target registration error.

Figure 8.2: Total registration errors of all landmarks plotted in per-patient clusters. Theyellow circles represent the original landmarks, the red circles represent the secondary pointshaped landmarks and the green circles the secondary line shaped landmarks.

the boxplots it can be seen that on average, the original landmarks had the highestregistration errors and the line shaped landmarks the lowest. Most of the landmarkswere situated in the mid or mid-apical planes, only 4 landmarks were located in the farapex or far base. Three of these landmarks had an above average registration error andone had a below average registration error (Fig. 8.3). Because of the small numberof landmarks in this analysis, no statistical tests were applied to assess di�erences inregistration errors depending on landmark type or location.

Discussion 129

Table 8.2: Additional landmarks agreed upon during consensus meeting.

Patient Landmark Description Location xy error (mm)

1 1 urethra (point) mid 0.51 2 urethra (point) mid-apex 0.52 2 urethra (line) mid 2.4*2 3 urethra (point) mid-apex 1.32 4 urethra (line) mid 2.23 1 urethra (point) mid-apex 4.73 2 PZ/TZ border (line) mid-base 0.2*3 3 urethra (point) mid 4.34 1 urethra (point) mid 1.25 1 urethra (line) mid-apex 0.1*5 2 PZ/TZ border (line) mid-apex 2.0*6 1 PZ/TZ border (line) mid 0.1*6 2 urethra (line) mid-apex 2.2*8 2 urethra (point) mid 0.28 3 urethra (line) mid 0.4*8 4 urethra (point) mid 0.78 5 PZ/TZ border (line) mid 0.3*8 6 urethra (point) mid-apex 2.512 2 PZ/TZ border (line) mid 2.7*13 1 PZ/TZ border (line) mid 1.1*13 2 urethra (point) mid 2.313 3 urethra (line) mid 0.6*13 4 urethra (line) mid-base 1.5*13 5 urethra (point) mid-apex 4.513 6 urethra (line) mid-apex 1.6*14 1 PZ/TZ border (line) mid-apex 0.3*14 2 PZ/TZ border (line) mid 1.0*14 3 PZ/TZ border (line) mid 0.4*

*Mean mean minimum distance.

8.4 DiscussionOur results show that the overall TRE for all types of landmarks is less than 4 mmin over three quarters of cases and less than 6 mm in all cases. This means theregistration error is smaller than the thickness of one pathology slice in most casesand similar to or smaller than the sampling density of transperineal template biopsiesin all cases. The classical definition of the size of a significant tumor focus is 0.5 mL,which in a sphere means a radius of 4.9 mm [12]. Total registration errors were belowthat threshold in all but 2 original landmarks, which exceeded it by 0.2 and 1.0 mm.

In imaging validation studies using radical prostatectomy specimens as reference

130 Clinical validation of histology-ultrasound registration

Table 8.3: Categorized total registration errors for di�erent combinations of landmarks sep-arately (top) and clustered per-patient (bottom).

Total registration errorLandmark Type 0-2 mm (%) 2-4 mm (%) 4-6 mm (%)

All landmarks separatelyoriginal landmarks 3 (43%) 1 (14%) 3 (43%)add. point-point landmarks 6 (55%) 2 (18%) 3 (27%)add. line-shaped landmarks 13 (77%) 4 (24%) 0 (0%)original + point-shaped landmarks 9 (50%) 3 (17%) 6 (33%)all landmarks 22 (63%) 7 (20%) 6 (17%)

Landmarks clustered per patientoriginal landmarks only 3 (43%) 1 (14%) 3 (43%)original + point-shaped landmarks 5 (45%) 2 (18%) 4 (36%)all landmarks 9 (64%) 2 (14%) 3 (21%)

add.: additional.

Figure 8.3: Total registration error di�erentiated by landmark type (left) and location (right).

standard, current methods to account for plane angulation and plane allocation mis-match between imaging and pathology often involve aggregating multiple planes, re-sulting in a registration uncertainty of multiple plane thicknesses [294,295]. With ourproposed method the uncertainty in registration is therefore smaller, allowing moreaccurate validation. Another benefit of the proposed method lies in that the observersdo not have to manually allocate imaging and pathology planes to certain prostateregions, removing a source of subjectivity and variability. The registration error ofthe original landmarks and additional point shaped landmarks is above the averagereported by Schalk et al. [J5] while the registration error for line shaped landmarks islower than that reported in that paper. This may indicate the influence of landmark

Discussion 131

shape or registration error definition on the results.In our study we did not perform statistical testing to evaluate the di�erences in

TRE between landmark types due to the small sample size. However, Fig. 8.3 indicatesthere may be a trend towards line shaped landmarks giving better results. Our methodof using the minimal distance between the lines for calculation of the registration errormay explain this e�ect.

Because the pathology slices were approximately 4 mm thick, pathology infor-mation was only available every 4 mm. The z-axis registration error was thereforeestimated in 0.5 slice or 2 mm increments, which may have led to both over- and un-derestimation of TREs. Furthermore, the pathology slice thickness was assumed basedon our hospital specimen processing protocol, but small variations may have occurred.Of the 14 cases selected for inclusion, only 7 original landmarks were taken into thisanalysis. This is the result of the very strict quality assessment of the landmarks. Whenduring the consensus meeting one of the investigators was not completely convincedof the quality of the landmark, the landmark was discarded. To accurately validate theproposed method we considered quality of the landmarks, the de facto reference test,to be crucial, warranting strict quality assessment at the cost of inclusion numbers. Itis important to realize that the landmarks are only used for validation. The elastic reg-istration method relies on the prostate surface contour alone. Therefore, no landmarksare required while using this technique to match (suspected) tumor locations.

As opposed to the original landmarks, which were mostly cysts, all secondarylandmarks run through multiple prostate planes. Therefore, one cannot conclude thatif the US landmark is visible in the corresponding pathology slice, the z-axis error mustbe within one slice thickness. However, because of the curved trajectory of both theurethra and the PZ/TZ border, the z-axis error will already be partly expressed byxy-plane displacement.

The landmarks in this study are not distributed randomly over the slices. Theoriginal landmarks, mostly cysts, are spread throughout the prostate but the urethrallandmarks tend to be centrally located within a pathology slice. However, the medianTRE changed from 3.6 mm to 3.4 mm after inclusion of the additional point shapedlandmarks indicating that this is only a small e�ect.

A landmark’s location on the z-axis may influence the registration error as indi-cated by Fig. 8.3. This suggests that the proposed registration method shows lowerperformance in the far base or apex. However, with only 4 landmarks in the far base orfar apex, this sample is too small to draw definite conclusions on this matter. It mustbe noted that all landmarks in the far base and apex were original and point-shapedlandmarks, which in this sample also had above average TREs. The ultimate methodof validating the proposed registration method would be incorporating markers placedin vivo that are visible in both the US model and the pathology slices. However, weacknowledge the practical and ethical di�culties with setting up such a study. Wetherefore believe that our current method of using natural landmarks is a suitable wayof showing the value of the technique. Another interesting method to reduce the mis-

132 Clinical validation of histology-ultrasound registration

match occurring with imaging to pathology correlation is the use of patient-specific 3Dprinted molds [293]. However, this method is only suitable for cross-sectional imagingtechniques such as MRI and computed tomography.

Based on our current results, we believe that our method represents an opportunityto improve the accuracy of US imaging to pathology correlation for the purpose ofvalidating novel imaging techniques. However, there are several steps that can beundertaken to improve the accuracy of the method, enhancing its potential. The3D model of the pathology could be improved by more standardized processing ofthe radical prostatectomy specimens, ensuring perfectly parallel slices of exactly equalthickness. The slice thickness can be reduced to improve z-axis localization of tumors.In our own institution we have started using a device that allows cutting perfectlyparallel 3 mm slices (Fig. 8.4). The holes that are caused by the needles while usingthe device are visible in the pathology slides and can therefore be used to guide thestacking of the planes. The accuracy of the 3D model of the imaging using the USsweeps could be improved by substituting the manual base to apex sweep with amechanized sweep or rotation. Also, some US scanner and probe configurations allowthe acquisition of 3D volumes directly, which can remove one source of error in theregistration process [199]. The first steps in PCa detection oriented US imaging in 3Dhave been undertaken [263],[J6].

Figure 8.4: Prostate cutting device used at our institution to ensure the specimen is cut inperfectly parallel 3 mm slices. The prostate is suspended on the needles (left hand side) inthe desired orientation. The specimen is then sliced through the slits that are spaced 3 mmapart. After each slice is cut, the needles can be retracted in 3 mm steps to allow cuttingthe next slice while holding the prostate in place.

Conclusion 133

8.5 ConclusionUsing the registration protocol proposed by Schalk et al., registration errors between2D ultrasound imaging and standard pathology slices can be achieved that are smallerthan the threshold of a clinically significant tumor and smaller than the thickness of astandard pathology plane. This signifies a marked improvement to frequently employedmethods of correlating imaging and pathology for validation purposes.

134 Clinical validation of histology-ultrasound registration

Chapter9Discussion and conclusion

This chapter provides a critical discussion and general conclusions of the work presentedin this thesis. Furthermore, suggestions for potential applications and future researchare given.

136 Discussion and conclusion

In this work, improvements for CUDI as a reliable prostate cancer imaging techniquehave been investigated with the aim to bring this technique closer to clinical use. Inparticular, the goals of this thesis were to:

• improve the method’s accuracy,

• speed up the clinical workflow,

• and extend the clinical evidence.

Highly accessible and reliable imaging could lead to more accurate diagnosis andpatient-tailored treatment. To realize the envisaged advancements, first, mutual in-formation was explored as a more general similarity measure for CUDI by similarityanalysis. Second, the feasibility of using 3D DCE-US for 3D CUDI and a 3D im-plementation of CUDI has been realized and tested in vivo. Finally, options for 3Dregistration of ultrasound and histopathological data, obtained after RP, have beenexplored. Each of these aspects is discussed separately in the following sections.

9.1 Mutual informationIt was hypothesized that by exploring statistical connectivity between TICs in the formof mutual information (I) the inclusion of non-linear similarity could expose moresubtle di�erences between TICs than r and ⇢. As a result, adopting I could lead tohigher accuracy of CUDI. However, the similarity analysis by r and ⇢ is based on themonotonic relation between the applied similarity measure and the dispersion-relatedparameter , providing a physical meaning to the parametric maps provided by CUDI.This rises the question whether this relation also holds for I. In Chapter 2, we confirma monotonic increase in I for increasing values of .

To evaluate whether using I actually leads to more accurate prostate cancer imag-ing, an in-vivo study in 23 patients was carried out. Mutual information was comparedwith the other CUDI parameters (r, ⇢, ) and with standard perfusion parameters(FWHM, WIT, PI, AU-TIC). Several conclusions could be drawn from the results ofthis study:

• Classification performance is better when using I instead of using the measuresfor linear similarity (r and ⇢). However, di�erences are small and were notsignificant in this dataset.

• All similarity parameters performed significantly better than the perfusion pa-rameters and the CUDI parameter . Yet, a combination of parameters may stilladd to the diagnostic value of a single one.

• The AU-ROCs found for r and ⇢ (0.75 and 0.74) were much lower than thosefound in [132] (0.89 and 0.88). This di�erence may be due to the larger amount

3D CUDI 137

of patients included in this study, resulting in more accurate estimation of theclassification performance. Based on the AU-ROCs found in this study andconsidering the limitations of 2D CUDI, it can be concluded that all similarity-based implementations of 2D CUDI have diagnostic value, but cannot be usedas a stand-alone diagnostic tool.

In contrast to the 2D implementation, in 3D CUDI, I did not result in better distinctionbetween benign and malignant tissue than r. One of the causes could reside in thesparse representation of center TICs in the PMF due to the large set of quantizationlevels (C = {0, 1, ...,Q� 1}) used to encode them. Sparsity in the PMF leads toine�ective estimation of I. In the original implementation, Q = 64 is used for both thecentral and kernel TICs. In a future implementation, a lower amount of quantizationlevels for the center TIC could be considered to reduce the method’s dependency onnoise in the center TIC. In general, the settings for 3D CUDI by I should still beoptimized on a larger dataset, preferably on histopathologic data from RP specimens,to achieve the best classification performance.

9.2 3D CUDIIn this thesis, 3D DCE-US recordings were shown to be suitable for 3D CUDI analysis.Moreover, a significant di�erence in values of r between benign and malignant tissuewas demonstrated. Particularly interesting was the correlation between r and theGleason score, which is an important factor in treatment planning. Overtreatment iscurrently a well-known problem in prostate cancer care [51], which may be reduced ifmore information on the aggressiveness of a detected tumor is available.

By implementing CUDI in 3D, several limitations of 2D CUDI were taken away.The most important advantage of 3D CUDI over its 2D counterpart is the possibility toanalyze the entire prostate with a single UCA injection. It greatly improves the clinicalapplicability of the method, making it potentially a valid alternative to MRI for prostatecancer localization. However, before the step towards the clinic can be considered,more extensive validation by targeted biopsies and RP specimens is required.

Currently, the most widely investigated prostate cancer imaging technique ismpMRI. The performance of mpMRI-based targeted biopsy for prostate cancer de-tection reported in the literature varies largely, depending on the way of interpretingthe individual parametric maps, the applied definition for significant prostate cancer,and the adopted reference standard. In a comparison between 5 studies [71], sensitiv-ities range from 68% to 100%, specificities from 21% to 85%. The median sensitivityen specificity were 92% and 42%, respectively, for comparable methodology. Thesevalues are similar to the ones (94% and 50%) found in the per-prostate analysis inChapter 5. It should be noted that the validation in Chapter 5 was purely quantita-tive and uses systematic biopsies as reference standard. Also in an earlier comparisonbetween 2D CUDI and mpMRI in the same patients [134], the performance of the two

138 Discussion and conclusion

techniques did not di�er much. To be able to fairly compare 3D CUDI and mpMRI, asimilar, but prognostic study should be carried out in which both techniques are testedin the same patients.

In this thesis, the DCE-US parameters have been evaluated individually. How-ever, because some of the parameters are based on dispersion and some on perfusion,combining both types of complementary information in a classifier may lead to im-proved cancer localization. A recent study performed by our group [297] confirmedthis hypothesis. In addition, elastography could provide additional complementaryinformation about tumor locations. Available evidence suggests that combining sev-eral ultrasound modalities leads to improved diagnostic performance [185]. Especiallythe promising initial results of SWE for prostate cancer localization [97–100] makea multiparametric approach involving 3D DCE-US imaging and SWE an interestingpath to investigate. For similar reasons, a multimodal method combining the benefitsof the aforementioned ultrasound-based techniques with mpMRI could be interesting.Although the advantages of the low cost and high accessibility of ultrasound imagingare lost by adding MRI, each of the imaging techniques (DCE-US, SWE, T2WI, DWI,DCE-MRI) reveals di�erent aspects related to tumor formation (abnormal blood flow,increased elasticity, extracapsular extension, di�erent cellular architecture, decreasedwater content, and increased vessel permeability). Moreover, MRI does not su�er fromsome of the di�culties encountered in ultrasound imaging, such as acoustic shadow-ing and decreased SNR in the anterior part of the prostate. A well-designed classifieror scoring protocol combining all imaging techniques may therefore further improveprostate cancer diagnosis.

A hypothesized advantage of 3D CUDI over 2D CUDI is a higher accuracy dueto the 4D nature of the UCA kinetics being represented by the data. In this thesis,CUDI profits from this property by employing a 3D kernel in the similarity analysis.Due to the di�erent reference standards used for validation of 2D and 3D CUDI, it isnot possible to draw a conclusion on this hypothesis based on the evidence presentedin Chapters 4 and 5. However, the AU-ROCs of r resulting from the validation of3D CUDI for larger tumors (Table 2.1) and those found for 2D CUDI (Table 5.4) areof the same order (0.72-0.77 vs. 0.75). The 4D data may yet be exploited furtherby designing data-specific methods, for example by solving the convection-di�usionequation in 3D or by estimating 3D flow patterns, as was recently proposed for 2DDCE-US in [298].

Whereas the performance of r and ⇢ were similar in 2D CUDI, the performanceof ⇢ in 3D CUDI was much worse than that of r. An explanation for this findingcould reside in the fact that by using the frequency spectrum, only half of the amountof data points can be used to compute ⇢ compared to the number of data pointsavailable to compute the temporal correlation r. Given the limited temporal resolutionof 3D DCE-US (⇡0.25 s-1), a robust estimation of ⇢ is not possible. It is thereforenot recommended to use ⇢ for 3D CUDI. Surprisingly, the AU-ROCs for the WIT inTICs obtained by 3D DCE-US are similar to those of r, although this result is not

3D CUDI 139

supported by the 2D analysis. Taking into account the low volume rate of 3D DCE-US, this finding is even more remarkable. Further investigation is required to find anexplanation for this result.

While it is not possible to compensate for out-of-plane motion in 2D DCE-USimaging, the step towards 3D DCE-US enables motion compensation in all directions.The CUDI analyses were performed without applying any motion compensation. Asa result, the clinicians were required to keep the transducer stable in a fixed positionrelative to the prostate for 2 minutes while imaging. Even for very skilled operators,such a task may be challenging. Besides, a recording can be corrupted by patientmovement. To improve the accuracy and to make 3D CUDI more accessible for less-experienced centers, motion compensation should be considered as a part of futureimplementations.

In Chapter 3, the speckle size in 2D and 3D DCE-US recordings was determinedas a measure of spatial resolution. The speckle size found for the axial direction wasthe same in 2D and 3D DCE-US imaging. This result can be expected, since the axialresolution is mainly determined by the ultrasound pulse length. The lateral specklesize can be approximated by a linear function of the distance from the transducer(Fig. 3.2). In contrast to the speckle size in the axial direction, the lateral specklesize in 3D DCE-US recordings was 1.5 to 2 times larger than that in 2D. In this case,spatial resolution may have been traded for temporal resolution by decreasing the linedensity (Table 3.1). The speckle size in 3D DCE-US imaging was approximately thesame in the lateral and elevational direction. The values found in the speckle analysisfor 2D DCE-US are similar to those found in [133].

One of the preprocessing steps in 2D and 3D CUDI is a speckle regularization filterapplied to the entire DCE-US sequence. Also, because the values in the kernel of thisfilter have to be recomputed per position in the DCE-US image, the computationalload of this step is large. The aim of the filter is to prevent a bias in similarity valuescaused by the depth-dependency of the lateral spatial resolution of the ultrasoundimaging system. However, the SNR is lower at longer distance from the probe due toultrasound attenuation in the prostate tissue. The resulting lower similarity values arenot compensated for. To reduce the computational cost caused by the speckle filter andto compensate for attenuation, it may be beneficial to investigate the combined e�ectof spatial resolution and attenuation on the final CUDI maps. Instead of applying aspeckle filter to the entire DCE-US sequence, a depth-dependent compensation factormay then be applied to the parametric maps.

In a recent publication [299], the feasibility of transabdominal DCE-US for TICfitting has been investigated. Quality of fits in transrectal and abdominal DCE-USdata were comparable. In this context, it could be interesting to apply abdominal DCE-US for 3D CUDI in the prostate. The ability of focusing in the elevational directionand the possibility of receive beamforming techniques of matrix transducers couldlead to a better spatial or temporal resolution, respectively [300], possibly allowingmore accurate assessment of the UCA kinetics. In addition, abdominal imaging is

140 Discussion and conclusion

less invasive than TRUS, adding to the patient’s comfort. On the downside, dealingwith motion may be more challenging when using abdominal ultrasound and the lowersignal-to-noise ratio at the posterior side of the prostate, which is further away fromthe transducer in abdominal imaging, may hamper tumor detection in the PZ.

The studies presented in this thesis focus on prostate cancer. However, CUDI aimsat detecting tumors featuring angiogenic growth, which also occurs in other organs,such as the liver or the breast [301]. Against this background, a possible role for 3DCUDI in cancer diagnosis in those organs could be envisaged.

Although it is hypothesized that CUDI reveals angiogenesis, this hypothesis hasnot yet been proven. Until now, CUDI has been compared with histopathology basedon cell di�erentiation. To evaluate the missing link between CUDI and angiogenesis,several options can be considered. In one approach, CUDI could be validated againstimmunohistology [162]. In a small study, several DCE-US parameters, including theCUDI parameter ⇢, were tested against immunohistology in 14 mice injected withxenograft models of two human prostate cancer types with di�erent microvasculardistribution [302]. Both by immunohistology and CUDI, the two tumor types could bedistinguished, indicating a relation between the miscrovascular distribution and CUDI.However, the process of obtaining immunohistology is quite expensive. Alternatively,one of the recently developed angiographic imaging techniques [303, 304] could serveas a ground truth. Not long ago, a study has been launched as part of a collabora-tion between our group and the University of North Carolina, comparing CUDI andangiography in xenograft mouse models. Initial results based on 3 mice suggest theexistence of a correlation between angiogenesis and CUDI [305].

Another hypothesis still to be proven states that dispersion rather than perfusionis the most relevant parameter for angiogenic imaging. In this thesis, the parameter(directly or indirectly) assessed by CUDI is = v

2/2D, in which v and D represent the

local blood velocity and dispersion, respectively. Although the name of the methodsuggests that dispersion is imaged, in fact, a combination of v and D is evaluated.In recent work [306], an alternative approach to CUDI is presented by which v and D

can be separated using Wiener system identification. Results from this study, including25 patients, show that both v and D may contain diagnostic value.

9.3 Ultrasound-histology registrationTo reduce inter-observer variability inherent to region-based validation and to allowinclusion of smaller tumors, a method for validation of prostate cancer imaging tech-niques by histopathologhy after RP has been proposed. The method includes a 3Dreconstruction of tumors outlined in histology slices and an elastic registration algo-rithm fusing them with imaging. For validation of 2D imaging, cross sections of the 3Dregistered tumors can be merged with the imaging plane. Additionally, a full 3D groundtruth is available for validation of 3D imaging. Because the method is shape-based and

Ultrasound-histology registration 141

slots for parallel slicing

plateau for prostate accomodation

needle template

needles

Figure 9.1: Schematic drawing (left) and picture (right) of the device designed for accurateslicing of radical prostatectomy specimens.

does not rely on the underlying imaging modality, also applications in MRI-histologyfusion for validation of MRI of prostate cancer, and ultrasound-ultrasound fusion forbiopsy guidance can be considered.

When using a standard histology slicing thickness of 4 mm, the expected interpo-lation error lies within 1.5 mm. The registration error strongly depends on the positionin the prostate, but in most cases errors remain below 4 mm with a median registrationerror around 2 mm. The threshold for clinical significant cancer is often defined at0.5 cm3 [12], which yields a diameter of 10 mm assuming a spherical tumor shape.With a cumulative error of 3.5 mm, significant cancers can be validated by the groundtruth obtained by this method. However, registration errors do not necessarily add toand could even compensate for some of the interpolation errors.

The presented method does not yet provide a complete validation framework.Some of the steps required in the process have not yet been extensively investigated andrequire optimization. In the simulations presented in Chapter 6, especially accurate in-plane alignment of the slices proved to be important. Additional errors are introducedwhen slices have irregular thickness or are cut under di�erent angles. In the prostatemodels used in this thesis, slices were aligned manually. Because this approach isprone to the aforementioned errors, a dedicated cutting device has now been designedfor accurate histology reconstruction (Fig. 9.1). The same landmark template can becreated throughout the prostate by puncturing it with parallel needles guided by theholes in the front plates. The prostate is then cut into 3-mm thick parallel slices usingthe equally spaced slots. The holes left by the needles can easily be annotated, afterwhich automatic reconstruction of the histology model is possible. Apart from insertingthe needles, no additional steps interfering with clinical routine are required. In futurestudies, the device can be used for more accurate histology model construction toreduce registration errors.

142 Discussion and conclusion

The ultrasound prostate models used in Chapters 7 and 8 are constructed bymanually estimating the angle between the first and last frames in transversal sweepvideos on which the models are based. Also, the center of rotation can be manuallyadjusted. All parameters are estimated by visual comparison of the model with theprostate contour in a sagittal ultrasound image. This process is rather arbitrary anda�ects the registration error. Recently, a di�erent approach has been tested in whicha 3D TRUS dataset is constructed from 2 perpendicular TRUS sweep videos. In aframe of a sagittal video, the intersection lines with frames of a transversal videoare estimated by maximizing the Pearson cross-correlation between image intensities.In this way, the individual frames of the sweep videos can be positioned in 3D toobtain a full 3D TRUS dataset. Preliminary validation in 4 patients by comparingthe reconstructed 3D TRUS dataset with those obtained by a 3D TRUS transducerresulted in an average Jaccard index of 0.79. This work has been presented in [IC4].In an unpublished test, 6 natural landmarks were defined in both 3D TRUS sets ofone patient. After rigid registration by minimizing the root-mean-squared distancebetween corresponding landmarks, a submillimeter residual was left. If imaging by 3DTRUS is not possible, this technique could be considered for accurate 3D constructionof 2D TRUS data without the need for additional sensors to track probe movement.

For validation of 2D TRUS-based prostate cancer imaging, the imaging planeshould be registered with the reconstructed 3D TRUS image. This step introducesanother registration error which should be taken into account. Registration couldbe realized manually or automatically, for example by optimizing the similarity (e.g.,cross-correlation or mutual information) between image intensities in 2D B-mode and3D TRUS.

The prostate models require the prostate contour to be known from the ultrasoundand histology data. Whereas the number of contours to be drawn in histology slicesis limited, drawing contours in a full 3D TRUS dataset can be quite time-consuming.Moreover, the contours can be unclear due to shadowing and ambiguous boundariesin the TRUS image. Adoption of one of the many available (semi-)automatic prostatesegmentation techniques [307] can save time and reduce the inter-observer variability.

In Chapter 8, the largest registration errors were encountered in the base and theapex. Several reasons can explain this finding. The histology was sliced from based toapex by which the basal and apical caps are removed. Since the caps were not includedduring model reconstruction, the size and shape of the caps had to be estimatedafterwards and added to the model. Moreover, in TRUS the prostate contours at thebase are di�cult to define due to the presence of the seminal vesicles and the contoursat the apex are often hard to distinguish from the surrounding tissue. These obstaclesconfirm the need for more accurate reconstruction of the histopathology and morereliable prostate segmentation. Furthermore, an error in the rotational misalignmentbetween prostate models estimated during the a�ne registration introduces largererrors at the boundaries of the prostate than in the middle.

In the current implementation of the registration method, the prostate was treated

General conclusion 143

as a mechanically homogeneous medium. In reality, the TZ is generally sti�er than thePZ and tumors are sti�er than healthy tissue. By incorporating this knowledge in theregistration algorithm, registration errors may be further reduced. To this end, the 3Dtumor shapes found by the interpolation method discussed in Chapter 6 can be used.However, defining the zonal anatomy would still require dedicated segmentation.

9.4 General conclusionA small improvement in the accuracy of 2D CUDI was realized by applying mutualinformation as a similarity measure. Clinical evidence for the performance of 2D CUDIwas extended by validation in a larger patient group. However, the results do not justifyindependent employment of the method for cancer diagnosis. A strong improvementin the clinical applicability of CUDI was realized by extending it to 3D. Results from avalidation study with systematic biopsy suggest the classification performance of 3DCUDI to be similar to that of 2D CUDI and mpMRI. Moreover, 3D CUDI providesinformation about tumor aggressiveness. When a larger 3D DCE-US dataset including3D histology becomes available, the current implementations of 3D CUDI could befurther improved, e.g., by optimizing the length of the time window, by adjustingthe number of quantization levels used to compute I, or by implementing a spatialfilter compensating for attenuation e�ects. A combination of 3D CUDI with otherultrasound-based parameters or mpMRI could also be considered to achieve moreaccurate diagnosis. Additionally, a 3D registration method was realized fusing prostatemodels reconstructed from histology and imaging. The resulting registration errorswere well below the diameter of clinically significant tumors. This method enables moreaccurate and more objective validation of CUDI and other prostate cancer imagingtechniques in future studies by using 3D histopathology from RP specimens as referencestandard.

144 Discussion and conclusion

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List of publications

Book chapters[B1] M. P. Schmid, L. Beaulieu, N. Nesvacil, B. R. Pieters, A. W. Postema, S. G. Schalk,

F. A. Siebert, and H. Wijkstra, “Ultrasound in brachytherapy,” in Emerging Technolo-gies in Brachytherapy, CRC Press, ch. 14, in press.

Journal articles[J1] R. R. Wildeboer, S. G. Schalk, L. Demi, M. P. J. Kuenen, H. Wijkstra, and M. Mischi,

“Tumour interpolation and three-dimensional reconstruction of radical prostatectomyspecimens after histopathologic examination,” Acad. Radiol., submitted.

[J2] S. G. Schalk, J. Huang, J. Li, L. Demi, H. Wijkstra, P. Huang, and M. Mischi, “3Dquantitative contrast ultrasound for prostate cancer localization,” Eur. J. Ultrasound,submitted.

[J3] A. W. Postema, S. G. Schalk, M. Mischi, J. J. M. C. H. de la Rosette, and H. Wijkstra,“3D registration improves transrectal ultrasound to resection pathology matching forprostate cancer imaging validation,” BJU Int., submitted.

[J4] S. G. Schalk, L. Demi, N. Bouhouch, M. P. J. Kuenen, A. W. Postema, J. J. M. C. H.de la Rosette, H. Wijkstra, T. J. Tjalkens, and M. Mischi, “Contrast-enhanced ultra-sound angiogenesis imaging by mutual information analysis for prostate cancer local-ization,” IEEE Trans. Biomed. Eng., in press.

[J5] S. G. Schalk, A. W. Postema, T. A. Saidov, L. Demi, M. Smeenge, J. J. M. C. H.de la Rosette, H. Wijkstra, and M. Mischi, “3D surface-based registration of ultrasoundand histology in prostate cancer imaging,” Comput. Med. Imaging Graph., vol. 47, pp.29-39, 2016.

[J6] S. G. Schalk, L. Demi, M. Smeenge, D. M. Mills, K. D. Wallace, J. J. M. C. H.de la Rosette, H. Wijkstra, and M. Mischi, “4-D spatiotemporal analysis of ultra-sound contrast agent dispersion for prostate cancer localization: a feasibility study,”IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 62, no. 5, pp. 839-851, 2015.Featured in “Editors’ Selection of Articles in IEEE TUFFC – April 2016 Edition.”

168 List of publications

International conference contributions[IC1] M. Mischi, S. Turco, R. J. G. van Sloun, S. G. Schalk, L. Demi,

J. J. M. C. H. de la Rosette, and H. Wijkstra, “Contrast ultrasound dispersion imag-ing in prostate cancer: an update,” in proc. 21st European Symposium on UltrasoundContrast Imaging, Rotterdam (The Netherlands), Jan 21-22, 2016, pp. 134-135.

[IC2] S. G. Schalk, L. Demi, J. J. M. C. H. de la Rosette, P. Huang, H. Wijkstra,and M. Mischi, “3D contrast ultrasound dispersion imaging by mutual informationfor prostate cancer localization,” in proc. IEEE International Ultrasonics Symposium,Taipei (Taiwan), Oct 21-24, 2015, 4 pages.

[IC3] M. Mischi, S. G. Schalk, M. Smeenge, L. Demi, J. J. M. C. H. de la Rosette, andH. Wijkstra, “3D contrast-ultrasound dispersion imaging for prostate cancer localiza-tion: a feasibility study,” 8th International Symposium on Focal Therapy and Imagingin Prostate and Kidney Cancer, Noordwijk (The Netherlands), Jun 21-23, 2015.

[IC4] S. G. Schalk, C. Chen, L. Demi, A. W. Postema, J. J. M. C. H. de la Rosette,H. Wijkstra, and M. Mischi, “Feasibility of 3D TRUS reconstruction by two perpen-dicular 2D sweep videos,” 8th International Symposium on Focal Therapy and Imagingin Prostate and Kidney Cancer, Noordwijk (The Netherlands), Jun 21-23, 2015.

[IC5] M. Mischi, S. G. Schalk, L. Demi, J. J. M. C. H. de la Rosette, and H. Wijkstra,“Feasibility of 3D contrast ultrasound dispersion imaging for prostate cancer localiza-tion,” 30th Annual Meeting of the Engineering and Urology Society, New Orleans (LA,USA), May 16, 2015.

[IC6] S. G. Schalk, L. Demi, A. W. Postema, J. J. M. C. H. de la Rosette, H. Wijkstra,and M. Mischi, “3D TRUS reconstruction based on perpendicular 2D sweep videos,”30th Annual Meeting of the Engineering and Urology Society, New Orleans (LA, USA),May 16, 2015.

[IC7] S. G. Schalk, L. Demi, M. Smeenge, J. J. M. C. H. de la Rosette, H. Wijkstra,and M. Mischi, “3D contrast-ultrasound dispersion imaging by mutual informationanalysis in prostate cancer,” in proc. 20th European Symposium on Ultrasound ContrastImaging, Rotterdam (The Netherlands), Jan 22-23, 2015, pp. 125-128. Best poster inthe category “New Directions II” – winner.

[IC8] S. G. Schalk, L. Demi, M. Smeenge, J. J. M. C. H. de la Rosette, H. Wijkstra,and M. Mischi, “Three-dimensional contrast-ultrasound dispersion imaging for prostatecancer localization, a feasibility study,” in proc. IEEE International Ultrasonics Sym-posium, Chicago (IL, USA), Sept 3-6, 2014, pp. 616-619.

[IC9] S. G. Schalk, L. Demi, M. Smeenge, J. J. M. C. H. de la Rosette, H. Wijkstra,and M. Mischi, “Four-dimensional spatiotemporal analysis of ultrasound-contrast-agentdispersion for localizing prostate cancer,” Le TOURS de MircoBulles: Targeted Ultra-sound Contrast Imaging and Drug Delivery, Tours (France), May 19-20, 2014.

[IC10] S. G. Schalk, M. Mischi, T. A. Saidov, M. Smeenge, J. J. M. C. H. de la Rosette,and H. Wijkstra, “Ultrasound-histology registration for validation of prostate cancerimaging techniques,” 6th International Symposium on Focal Therapy and Imaging inProstate and Kidney Cancer, Noordwijk (The Netherlands), May 29-31, 2013.

List of publications 169

[IC11] S. G. Schalk, M. Mischi, T. A. Saidov, and H. Wijkstra, “3D registration of histologyand ultrasound data for validation of prostate cancer imaging,” in proc. SPIE 8669,Medical Imaging 2013: Image Processing, Mar 13, 2013, 10 pages, ID: 86692T.

[IC12] M. Mischi, S. G. Schalk, T. A. Saidov, M. Smeenge, M. P. Laguna Pes,J. J. M. C. H. de la Rosette, and H. Wijkstra, “3D ultrasound-histology mappingfor validation of prostate cancer imaging methods,” in proc. 2nd Meeting of the EAUSection of Urological Imaging (ESUI), Berlin (Germany), Oct 19-20, p. 20.

[IC13] M. Mischi, S. G. Schalk, M. Smeenge, F. Brughi, T. A. Saidov, M. P. J. Kuenen,R. P. Kuipers, M. P. Laguna Pes, J. J. M. C. H. de la Rosette, and H. Wijkstra,“Registration of ultrasound and histology data for validation of emerging prostatecancer imaging techniques,” in proc. 27th Annual Meeting of the Engineering andUrology Society, Atlanta (GA, USA), May 19, 2012, p. 79.

[IC14] M. Mischi, M. P. J. Kuenen, T. A. Saidov, S. G. Schalk, W. Scheepens, andH. Wijkstra, “New developments in prostate cancer localization by contrast ultrasounddispersion imaging,” in proc. 17th European Symposium on Ultrasound Contrast Imag-ing, Rotterdam (The Netherlands), Jan 19-20, 2012, pp. 16-18.

Regional conference contributions[RC1] S. G. Schalk, L. Demi, M. Smeenge, J. J. M. C. H. de la Rosette, P. Huang,

H. Wijkstra, and M. Mischi, “3D contrast ultrasound dispersion imaging by mutualinformation for prostate cancer localization,” IEEE West European Student and YoungProfessionals Congress, Eindhoven (The Netherlands), May 20-24, 2015.

[RC2] S. G. Schalk, M. Smeenge, J. J. M. C. H. de la Rosette, H. Wijkstra, and M. Mischi,“Registration of ultrasound and histology images for validation of prostate-cancer imag-ing techniques,” IEEE-SBE Symposium on Advancing Healthcare 2014, Feb 18, 2014.Best poster award – 2nd place.

[RC3] S. G. Schalk, M. Mischi, T. A. Saidov, and H. Wijkstra, “3D ultrasound-histologyregistration for validation of prostate cancer imaging methods,” in proc. 4th DutchBiomedical Engineering Conference, Egmond aan Zee (The Netherlands), Jan 25-26,2013, p. 234.

170 List of publications

Acknowledgments

One of the questions asked to me during the first meeting I had with Massimo Mischiand Hessel Wijkstra about starting a graduation project in their group was: “What isit that you like about prostates so much?” I did not know anything about prostatesat that time, but today, 6 years later, the importance of developing better imagingtechniques for prostate cancer has become very clear to me. During those years, manypeople helped me directly and indirectly with my research and it is my pleasure tothank each one of you in these acknowledgments.

First and foremost I would like to thank Massimo Mischi and Hessel Wijkstrafor giving me the opportunity to work on this project and their support finishing it.Massimo, your enormous drive and endless energy have helped me to stay motivatedwith this dissertation as a result. Hessel, you always stimulate engineers to get involvedwith the clinical side of the research we do. Through the close collaboration with theAMC, I learned a lot about the problems that come with applying new techniques inclinical practice.

Next, I want to thank the postdocs. Tamerlan Saidov, your help with my firstarticle, which eventually became my second article, and with the Mozzarella and gelatinexperiments are much appreciated. Especially the trip to the slaughterhouse to collectpig prostates I will remember. And of course I will not (and cannot, if only becauseof his inescapable presence) forget the other postdoc, Libertario Demi. I am surelygoing to miss the scientific discussions, the lunch break lectures about food, and theconfidence-boosting squash games. And I hope we can someday follow up on the greatdiving trip to Green Island.

In the past years, many other PhDs (Maarten, Gianna, Simona, Yuan, Ruud,Rogier, Anastasia) were part of the prostate cancer project. I enjoyed working witheach of you, but I would especially like to thank you for the fun times around workinghours. The after-work borrels at Walhalla provided the sometimes needed pressuredeflation and the two IUS conferences in Chicago and Taipei were unforgettable (withSimona as our tour guide).

Engineers can design techniques to improve health care, but without clinicians

172 Acknowledgments

applying them, they are useless. In this respect I want to show my appreciation toMartijn, Arnoud (both AMC) and Maudi (Jeroen Bosch Ziekenhuis) for the time ande�ort invested in collecting the best possible data to train and validate new methods.In line with this I would also like to thank Jean de la Rosette (AMC) and HarrieBeerlage (Jeroen Bosch Ziekenhuis) for providing the platform for this research withintheir respective hospitals.

In the final year of my project, I had the opportunity to visit the Second A�liatedHospital of Zhejiang University in Hangzhou (China) for three months. Because Iwent there alone, I was very grateful for the hospitable reception I received, literallyfrom the first jet-lagged day. Thank you, prof. Huang for making me feel welcome,for providing the best possible working environment, and especially for giving me theopportunity to experience Chinese culture. Also, thanks to Jia Li and Jing Huang andthe other doctors for the many hours spent making contrast-ultrasound recordings,collecting histopathology results, and performing calibration experiments. And finally,my stay would have been very lonely without the nights out with Messi (Tao) andYoung, the occasional trips with Lili and her friends, the weekly football games, andthe movies with Meiju, so thank you for the good times.

Of course, I would also like to thank my parents and sisters for their endlessconfidence in me, especially when my spirit was low. A cappuccino and a place torelax after a disappointing day can work miracles (yes, they also taste fine in theevening despite what some of the people mentioned earlier in this acknowledgmentmay say).

En tenslotte, dankjewel, lieve Suzanne. Met jou heb ik ieder succesje in mijnonderzoek kunnen delen, maar jij hebt me ook elke keer van de grond geraapt alsik het even niet meer zag zitten. Je bent zelfs twee keer voor mij naar de anderekant van de wereld gereisd. Ik ben blij dat ik jou sinds vorig jaar o�cieel mijn vrouwkan noemen en hoop nog veel leuke en mooie momenten met jou mee te kunnen maken.

— Stefan

About the author

Stefan Schalk was born in Eindhoven, the Netherlands, on June15, 1984. After completing pre-university education at Eckart-college in Eindhoven, he studied Electrical Engineering at Eind-hoven University of Technology where he received his MSc. de-gree in 2011. As part of the study, he completed a 4-monthinternship working on system identification of an unmannedair vehicle at the University of Canterbury, Chirstchurch, NewZealand. He graduated in the Biomedical Diagnostics group ona project about registration of histology and ultrasound data for

validation of prostate cancer imaging techniques in close collaboration with the AMCuniversity hospital in Amsterdam, the Netherlands. He then continued as a PhD can-didate in the same group carrying out a project on prostate cancer localization bycontrast ultrasound dispersion imaging (CUDI) of which the results are presented inthis dissertation. In the last year of his research, he acquired a budget from the RoyalNetherlands Academy of Arts and Sciences (KNAW) for a 3-month stay at the SecondA�liated Hospital of Zhejiang University (SAHZU), Hangzhou, PR China. There, hecollected the 3D dynamic contrast-ultrasound data required complete his work andlaid the foundation for a collaboration with SAHZU for future studies. The work pre-sented in this thesis has led to several international journal publications, of which onewas featured in the “Editors’ pick of IEEE Transactions on Ultrasonics, Ferroelectrics,and Frequency Control”. Furthermore, the pilot study on 3D CUDI based on mutualinformation was awarded the prize for “Best Poster in the Category New DirectionsII” at the 20th European Symposium on Ultrasound Contrast Imaging.