Quality Assurance for MagneticResonance Imaging (MRI) in

Radiotherapy

Mary Adjeiwaah

Thesis for the degree of LicentiateThesis Advisors: Tufve Nyholm PhD, Joakim Jonsson PhD, Anders

Garpebring, PhDFaculty Opponent: Rob HN Tijssen, PhD

This Project has been funded by the Schlumberger Faculty for the Future Foundation(FFTF) © Mary Adjeiwaah 2017

Medical Faculty , Department of Radiation SciencesISBN: 978-91-7601-797-5 (print)ISBN: 978-91-7601-797-5 (pdf )This work is protected in accordance with the Swedish Copyright law ( Act 1960:729)Responsible publisher under Swedish Law: Dean of the Medical FacultyPrinted by : UmU Print Service, Umeå University, Sweden, 2017Electronic version available on: http://umu.diva-portal.org/

Dedicated to my kids Awuraa and Nana who have paid the price of my decision

Contents

List of publications vii

Abbreviations ix

Popular summary xi

Populärvetenskaplig sammanfattning xiii

Acknowledgements xv

Introduction 1

1 Radiotherapy 31.1 Radiotherapy Treatment planning . . . . . . . . . . . . . . . . 3

1.1.1 Medical imaging in Radiotherapy . . . . . . . . . . . . 41.1.2 Diagnosis and Staging . . . . . . . . . . . . . . . . . . 51.1.3 Simulation and Planning . . . . . . . . . . . . . . . . 51.1.4 Dose Delivery and Tumor Localization . . . . . . . . . 51.1.5 Response Assessment and Follow up . . . . . . . . . . . 6

1.2 Aims of Study . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 MRI in Radiotherapy Treatment Planning 72.0.1 Dose calculation with MR data . . . . . . . . . . . . . 7

2.1 The Magnetic Resonance Imaging (MRI) System . . . . . . . . 92.1.1 MRI Safety . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 The Physics of Magnetic Resonance (MR) . . . . . . . . . . . . 112.2.1 Longitudinal Relaxation Time or T1 Recovery . . . . . 122.2.2 Transverse Relaxation Time or T2 Decay . . . . . . . . 132.2.3 Image Formation . . . . . . . . . . . . . . . . . . . . 142.2.4 Pulse Sequences . . . . . . . . . . . . . . . . . . . . . 152.2.5 K-Space . . . . . . . . . . . . . . . . . . . . . . . . . 162.2.6 Image Contrast . . . . . . . . . . . . . . . . . . . . . 17

3 MR Geometric Distortions 193.1 System-Related Geometric Distortions . . . . . . . . . . . . . . 19

3.1.1 B0 Field Inhomogeneity-Related Distortions . . . . . . 193.1.2 Gradient Nonlinearity-Related Distortions . . . . . . . 20

3.2 Patient-Related Geometric Distortions . . . . . . . . . . . . . . 213.2.1 Magnetic susceptibility . . . . . . . . . . . . . . . . . 213.2.2 Chemical Shift . . . . . . . . . . . . . . . . . . . . . 22

3.3 Characterizing and Correcting Geometric Distortions . . . . . 223.3.1 Bandwidth . . . . . . . . . . . . . . . . . . . . . . . 28

3.4 Impact of Distortions on RT Treatment planning . . . . . . . . 29

4 Summary of Publications 354.1 Study I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2 Paper 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5 Discussion and Conclusion 395.1 Summary and Future Works . . . . . . . . . . . . . . . . . . . 42

5.1.1 Sensitivity Analysis of Quantitative MRI in Radiotherapy 425.1.2 Designing an appropriate QA for MR-only RT . . . . . 42

I Research Papers

Author contributionsStudy I: Quantifying the effect of 3 T Magnetic Resonance Imaging

residual system distortions and patient-induced susceptibility dis-tortions on radiation therapy treatment planning for prostate cancer

Manuscript: Dosimetric Impact of MR distortions - A study on Headand Neck Cancer Patients . . . . . . . . . . . . . . . . . . . .

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List of Figures

1.1 Medical imaging modalities at each phase of the radiotherapyprocess. Modified from http://www.radiationoncology.com.au/resourcing-the-radiation-oncology-sector/essential-imaging-and-radiotherapy-techniques/

4

2.1 Proton precession due to an applied magnetic field. The intrin-sic properties of a Hydrogen proton utilized by MRI: spin [de-scribing inherent angular momentum] and magnetic moment,(a). Precession of charged particles in the direction of the appliedexternal magnetic field, (b). . . . . . . . . . . . . . . . . . . . 11

2.2 Magnetic resonance (MR) signal decay. Before the 90o radio-frequency (RF) pulse, the net magnetization (Mo) from all spinspoint in the direction of the main magnetic field (z-axis) [a]. Byapplying a 90o RF pulse, the spins gain energy and M0 is flippedinto the transverse plane to produce measurable MR signal [b]but because of local magnetic field inhomogeneities, spins get outof phase and the net magnetization returns to equilibrium. Thisrapid decay of signals induced in the receive coils is known as FreeInduction decay. . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Magnetization time curve. Longitudinal magnetization recoverygoverned by T1 relaxation time occurring at the same time as thedecay of the transverse magnetization governed by T2 relaxationtime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

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2.4 Pulse Sequence diagram for magnetic resonance image forma-tion simplified for Gradient Echo. A radio-frequency (RF) pulsecombined with the slice select gradient (Gss) selectively excitethe region of interest. The Phase (GPE) and frequency (GFE)encoding gradients are for spatial encoding of the signals. To re-phase all de-phased transverse magnetizations, additional gradi-ents (outlined in red) are applied after slice selection and beforefrequency encoding. Modified from the book, ’ MRI from Pictureto Proton’, 3rd edition [1] . . . . . . . . . . . . . . . . . . . . . 15

2.5 Filling of K-space after magnetization. After RF excitation andbefore any gradients, all encodings will be at (a). The applicationof a negative phase encoding gradient moves all data to point (b)where upon applying a frequency encoding gradient, the data issampled along Kfe, from b to d. Modified from the book, ’ MRIfrom Picture to Proton’, 3rd edition . . . . . . . . . . . . . . . . 17

3.1 Linear and Nonlinear gradients. Variations in location of signalsdue to nonlinear field gradients. . . . . . . . . . . . . . . . . . 20

3.2 Axial Images of the GE and Spectronics phantoms used in thisstudy. Computed Tomography and Gradient echo Magnetic res-onance images of the Spectronics (a & b) and GE (c & d) largefield of view spatial analysis phantoms. . . . . . . . . . . . . . . 24

3.3 Reduction in Gradient Nonlinearity distortions with 3D cor-rection. Magnitude of MR Nonlinearity distortions with radialdistance from the isocenter without 3D correction (a) and with3D correction for a spin echo sequence using a bandwidth of 488Hz/pixel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.4 Spherical harmonics (SH) up to third-order. High SH ordersresult in increasing number of modeled shapes. This in turn in-creases the likelihood to improve the B0 homogeneity. SH arearranged in orders of N with 2N + 1 terms for each order. . . . . 27

3.5 Reduction in magnitude of residual system distortions with in-creasing bandwidth. Phantom measured residual system distor-tions decreased in magnitude with increasing bandwidth from122 Hz/pixel (a) to 244 Hz/pixel after 3D correction . . . . . . 29

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3.6 Shifts due to system- and patient-induced susceptibility distor-tions. Estimated shifts at the contours of the bladder, the femoralheads, planning target volume (PTV) and rectum at bandwidthsof (a) 122 Hz/pixel, (b) 244 Hz/pixel, (c) 488 Hz/pixel in theright to left gradient readout. The boxes show the average valuesof the median (centerline) and 25% and 75% percentiles (bot-tom and top of boxes for all patients, in millimeters. The pointsabove and below each box represent the range in absolute shifts.L = left; R = right . . . . . . . . . . . . . . . . . . . . . . . . 32

3.7 Contour overlap between distorted and original CT datasets.Dice similarity coefficient (DSC) at some selected contours andthe two bandwidths studied. The mean agreement between dis-torted CT and original patient CT for all patients were above0.9 except for the spinal cord at the 122 Hz/pixel. [B-Brain, C-clinical target volume, L-left parotid, R-Right parotid, P-Planningtarget volume, S-spinal cord ] . . . . . . . . . . . . . . . . . . . 33

v

List of publications

This thesis is based on the following publication and Manuscript:

1 Quantifying the Effect of 3 T Magnetic Resonance Imaging Residual SystemDistortions and Patient-Induced Susceptibility Distortions on RadiationTherapy Treatment Planning for Prostate CancerAdjeiwaah M, Bylund M, Lundman J.A, Thellenberg Karlsson C,Jonsson JH, Nyholm TInternational Journal of Radiation Oncology • Biology • Physics (2017),doi: 10.1016/j.ijrobp.2017.10.021.

2 Dosimetric Impact of MR distortions - A study on Head and NeckCancer PatientsAdjeiwaah M, Bylund M, Lundman J.A, Zackrisson B, Söderström K,Jonsson JH, Garpebring A, Nyholm T

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Abbreviations

Acronyms

3D-CRT three dimensional conformal radiation therapy

BW bandwidth

CT Computed Tomography

dCT distorted CT

18F-FDG 18F-fluorodeoxyglucose

FID Free Induction Decay

FoV Field of View

GE Gradient Echo

HU Hounsfield unit

IMRT Intensity-Modulated Radiation Therapy

MR Magnetic Resonance

MRI Magnetic Resonance Imaging

OAR organs at risk

PET Positron Emission Tomography

PTV planning target volume

QA quality assurance

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RF Radio-Frequency

RT Radiotherapy

sCT synthetic Computed Tomography (CT)

SE Spin Echo

SNR signal-to-noise ratio

SPECT Single-Photon Emission Computed Tomography

TE Echo time

TR Repetition time

US Ultrasound

VMAT Volumetric-Modulated Arc Therapy

x

Popular summary

Magnetic resonance imaging (MRI) utilizes the magnetic properties of tissues togenerate image-forming signals. MRI has exquisite soft-tissue contrast and sincetumors are mainly soft-tissues, it offers improved delineation of the target volumeand nearby organs at risk. The proposed Magnetic Resonance-only Radiotherapy(MR-only RT) work flow allows for the use of MRI as the sole imaging modal-ity in the radiotherapy (RT) treatment planning of cancer. There are, however,issues with geometric distortions inherent with MR image acquisition processes.These distortions result from imperfections in the main magnetic field, nonlineargradients, as well as field disturbances introduced by the imaged object. In thisthesis we quantified the effect of system related and patient-induced susceptibilitygeometric distortions on dose distributions for prostate as well as head and neckcancers. Methods to mitigate these distortions were also studied.

In Study I, mean worst system related residual distortions of 3.19, 2.52 and2.08 mm at bandwidths (BW) of 122, 244 and 488 Hz/pixel up to a radial dis-tance of 25 cm from a 3 T PET/MR scanner was measured with a large field ofview (FoV) phantom. Subsequently, we estimated maximum shifts of 5.8, 2.9and 1.5 mm due to patient-induced susceptibility distortions. VMAT-optimizedtreatment plans initially performed on distorted Computed Tomography (dCT)images and recalculated on real Computed Tomography (CT) datasets resulted ina dose difference of less than 0.5%.

The magnetic susceptibility differences at tissue, metallic, air and bone in-terfaces result in local B0 magnetic field inhomogeneities. The distortion shiftscaused by these field inhomogeneities can be reduced by shimming. Study IIaimed to investigate the use of shimming to improve the homogeneity of localB0 magnetic field which will be beneficial for head and neck cancer radiother-apy applications. A shimming simulation based on spherical harmonics modelingwas developed. The spinal cord, an organ at risk and surrounded by bone and

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in close proximity to the lungs may have high susceptibility differences. In thisregion, mean pixel shifts caused by local B0 field inhomogeneities were reducedfrom 3.47± 1.22 mm to 1.35± 0.44 mm and 0.99± 0.30 mm using first andsecond order shimming respectively. This was for a bandwidth of 122 Hz/pixeland an in-plane voxel size of 1× 1 mm2. Also examined in Study II as in StudyI, was the dosimetric effect of geometric distortions on 21 Head and Neck cancertreatment plans. The dose difference in D50 at the PTV between distorted CTand real CT plans was less than 1.0%.

In conclusion, the effect of MR geometric distortions on dose plans was small.Generally, we found patient-induced susceptibility distortions were larger com-pared with residual system distortions at all delineated structures except the exter-nal contour. This information will be relevant when setting margins for treatmentvolumes and organs at risk. The current practice of characterizing MR geomet-ric distortions utilizing spatial accuracy phantoms alone may not be enough foran MR-only radiotherapy work flow. Therefore, measures to mitigate patient-induced susceptibility effects in clinical practice, especially patient-specific correc-tion algorithms are needed to complement existing distortion reduction methodssuch as high acquisition bandwidth and shimming.

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Populärvetenskapligsammanfattning

Magnetresonansbildtagning (MR) använder vävnaders magnetiska egenskaper föratt generera bildgivande signaler. MR har utmärkt mjukvävnadskontrast, och ef-tersom tumörer främst drabbar mjukvävnad bidrar MR till förbättrad utritningav behandlingsvolymer och närliggande riskorgan. Ett arbetsflöde som endast an-vänder sig av MR-bilder vid planering av strålterapi för cancerpatienter har före-slagits. Det finns dock problem med geometriska distorsioner som beror på hurMR-bilderna samlas in. Dessa distorsioner kommer från ojämnheter i magnetfäl-tet, ickelinjära gradienter och förvrängningar av magnetfältet som orsakas av detobjekt som man tar bilder av. I den här avhandlingen har vi kvantifierat effekternaav de geometriska distorsionerna från systemberoende effekter och patientindu-cerade susceptibilitetseffekter både för patienter med prostatacancer och patientermed cancer i huvud/hals-regionen. Metoder för att minska effekterna från dessadistorsioner har också studerats.

I Artikel I mätte vi systemberoende distorsioner från en 3 T PET/MR ka-mera med ett fantom för stort Field of View (FoV). Medel för de största distor-sionerna uppmättes till 3,19, 2,52 och 2,08 mm vid bandbredder (BW) på 122,244 och 488 Hz/pixel upp till ett radiellt avstånd från isocenter på 25 cm. Destörsta förskjutningarna från patientinducerade distorsioner uppskattades till 5,8,2,9 respektive 1,5 mm. VMAT-optimerade behandlingsplaner beräknades först pådistorderade CT-bilder (dCT) och räknades sedan om på ursprungligt CT-data.Den resulterande dosskillnaden mellan de två dataseten blev mindre än 0,5%. Demagnetiska susceptibilitetsskillnaderna i gränsskikt mellan vävnad, metall, luft ochben resulterar i inhomogeniteter i det lokala statiska magnetfältet. Förskjutning-arna som orsakas av dessa inhomogeniteter kan reduceras med shimning. I ArtikelII undersökte vi användandet av shimning för att förbättra homogeniteten av det

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lokala statiska magnetfältet. Detta kommer till nytta för användning av MR vidhuvud/hals radioterapi. En simulering av shimning baserad på modeller av sfärisktharmoniska funktioner utvecklades. Ryggmärgen är ett riskorgan som ligger näralungorna och är omringat av ben, och kan därför ha höga skillnader i susceptibiliteti sin närhet. För denna region kunde medelvärdena för de pixelförskjutningar somorsakats av inhomogeniteter i det lokala statiska fältet minskas från 3, 47± 1, 22mm till 1, 35 ± 0, 44 mm och 0, 99 ± 0, 30 mm genom att använda första- re-spektive andra-ordningens shimning vid en bandbredd på 122 Hz/pixel och envoxelstorlek i planet på 1×1 mm2. I Artikel II undersöktes också den dosimetris-ka effekten av geometriska distorsioner på dosplaner för 21 patienter med cancer ihuvud/hals-regionen. Dosskillnaden mellan planer beräknade på distorderad CToch ursprunglig CT i D50 för PTV var mindre än 1,0%.

Sammanfattningsvis var effekten av geometriska distorsioner i MR-bilderna pådosplanerna små. Generellt fann vi att distorsioner från patientinducerade suscep-tibilitetseffekter var större än distorsionerna från kvarstående systemeffekter föralla utritade strukturer utom patienternas externa konturer. Vi anser att dennainformation kommer att vara relevant när man sätter säkerhetsmarginaler för be-handlingsvolymer och riskorgan. Man ser även att dagens metoder att utvärderageometriska distorsioner för MR enbart baserat på fantom för spatiell noggrann-het kanske inte räcker till för ett strålterapiarbetsflöde som enbart baseras på MR-bilder. Av denna anledning krävs utöver existerande distorsionsreducerande me-toder som hög bandbredd och shimning även metoder för att minska effektenav patientinducerade susceptibilitetseffekter, till exempel patientspecifika korrige-ringsalgoritmer.

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Acknowledgements

Throughout this work, I have received enormous support from some really impor-tant people in my life. I thank God and my parents for my faith, which constantlygives me hope and calms my soul. My dad of blessed memory has been and con-tinues to be my number one cheerleader. Though not physically here, he is myfirst go-to-person when the going gets tough. I don’t know how he does it but hestill keeps me calm and motivated. Thank you to my Mom and siblings.

Tufve, you believed in me and gave me an opportunity of a life time. You donot only care for my academic life but are also concerned about the welfare of myfamily and I thank you for that. In you I have found a good, dedicated and caringsupervisor.

Jocke, thank you for being there for me. I come to you unannounced withnumerous questions and yet you find time to answer them. Thank you for reviewson my write ups.

Anders, you take your time to explain the most complex physics phenomenain the most simplest way you can. Thank you for the many discussions we havehad on Matlab and MR physics.

Mikael, what would my academic life be without you, you are a great friend.It means a lot to me especially, when you say, ’Yes. You can do it, I have faith inYou’. I don’t know if I bother anyone more than I do to you, and yet you maketime to find all the missing spaces, commas and periods in my write-ups Thank you!.

Josef, my go-to-person when the programming gets tough, thank you for themany academic discussions we have had. Thank you for your honest opinions andfor your contributions to our review discussions.

Kristina, thank you for our academic and non-academic discussions and forthe hugs. Even in tough times we find the opportunity to see the brighter side ofthings. You are a great friend and I could not have asked for a better office-mate.

Jennifer, thank you for your strength, smile, hugs, chit-chats, and dedication

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to the collection of Starbucks city mugs.Lars, thank you for being a good fellow PhD student and for constantly re-

peating the correct pronunciation of your son’s name when I ask.Patrik, thank you for your continuous help and patience, especially during

my early days here. For fixing my computer and taking just seconds to fix Matlabcodes which I had spent days trying to fix.

To Mattias, thank you for answering all my questions about MICE and MIQAand for the many times you had to come to my office to fix issues with MICE andMIQA

Jón, thank you for the late night MR scans and the light-hearted conversationswe have had during fika and late lunch times.

Natalia, for your short time here, you have been a great emotional and aca-demic support, I will miss our chats about our families. Thank you for beingthere.

Maria, thank you for being Maria, always helpful with all administrative stuff.For your smile and words of encouragement.

My sincere thanks also go to Jonna, Anna, Nadja, Anne, Margareta, Elin,Angelica, Magnus K., Jan, Elisabet, Marita, Tommy, Jörgen, Pia, Helena, Angelicaand all the workers at CMTS for sharing this journey with me.

MR. Ali, Zainab, Amal, Jamal, Nana Aisha, Evans, Obaa Afia, Papa Yaw, Ab-dullai, Maxcell, and Jordan, you gave me a family here in Umeå and I am mostgrateful. To the home front, Thank you Solomon for your Love and for shar-ing this journey with me and our kids. You have given me the opportunity andthe room to spread my wings in order to be the woman I want to be. You havemade our current living arrangement work with your monthly visits without anycomplaints. I Love you.

To the composer of the song Daddy ist Doktor, Mama ist zuhause that got methinking about resuming my academic career, my first baby, Awuraa, you are toowise for your age. You are my little girl and yet so matured, caring and helpful.Thank you. To Nana, the little man of the house, you could not be bothered witha lot of things except maybe dinosaurs and music from One direction , Thank you.

To Awuraa and Nana, I hope that when you grow up, you will remember yourchildhood with fond memories. I also hope that the many places we have livedand the travels we have made in our quest to give you a better future will makeyou grow into better human beings, who will accept and love others as they. Andrespect the earth that God has made for us. I love you.

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Introduction

The continuous improvement in the diagnosis, staging, before- and after- treat-ment monitoring of cancers within the Radiotherapy (RT) community can beattributed to advances in medical imaging technologies. Medical imaging tech-nologies such as MRI, CT, Ultrasound (US), Positron Emission Tomography(PET), and Single-Photon Emission Computed Tomography (SPECT) are cur-rently available for use in most cancer treatment centers. The last decades haveseen the rising use of MRI in RT for treatment planning and image guidancewith the introduction of dedicated MR-only simulation scanners for RT plan-ning and hybrid MR-Linac systems [2, 3, 4, 5, 6] for clinical use. In comparisonwith ionizing radiation-based imaging, MRI provides an exceptional combinationof radiation safety and soft-tissue contrast. MRI generate images with stunningclarity of tissue boundaries and can also depict functional properties such as perfu-sion and metabolism. There are, however, issues with geometric distortions inher-ent to MR image acquisition processes hampering the integration of MRI in RT.These distortions result from imperfections in the main magnetic field, nonlineargradients as well as field disturbances introduced by the imaged object. Currentmechanisms to reduce the magnitude of geometric distortions include: (1) the useof manufacturer supplied 3D algorithms to correct gradient non-linearity distor-tions, (2) use of shim coils, which, though limited by rapid variations in the localmagnetic field, can mitigate susceptibility effects, and (3) use of high acquisitionbandwidths (BW) to reduce both system and patient related distortions, however,increasing BW compromises image quality (signal-to-noise ratio). Lastly, incor-porating acquisition sequences that are less sensitive to field inhomogeneities, suchas spin-echo protocols, could be used when necessary to reduce MR spatial inac-curacies. The move towards an MR-only radiotherapy means that existing qualityassurance (QA) measures at MR imaging centers will have to be carefully lookedat and reviewed to meet the new demands. In this thesis, we investigate the com-bined effect of system related and patient-induced susceptibility distortions on

1

radiotherapy treatment planning of prostate as well as head and neck cancers. Wealso report on mitigations aimed at reducing the effect of distortions on treatmentplanning.

2

Chapter 1

Radiotherapy

1.1 Radiotherapy Treatment planning

Cancer is a major cause of death with 8.2 million global deaths in 2012 and anestimated 14.1 million new cases per year [7]. According to the world cancerreport, 20 million new cancer cases have been predicted by the year 2025 [8].In 2011, of the 57 726 cancer cases reported in the Swedish Cancer registry, 46286 cases were people who were diagnosed for the first time [9]. Prostate cancersare the highest in men representing 32.2% of all cancers in men in 2011. Themost common cancer in women is in the breast which accounted for 30.3% ofall cancer cases among women in 2011. The continuous ageing of the Swedishpopulation accounts for 50% of the annual 2.1% and 1.5% increase in cancer casesamongst men and women reported over the last two decades. Improvements inthe accessibility of diagnostic and screening services also helps explain the increase.Also the risk of developing any form of cancer in Sweden before age 75 is about31.6% in men and 28.7% in women.

A person diagnosed with cancer will go through one or a combination oftreatments involving, surgery, chemotherapy and radiotherapy (RT). At least onein two people with cancer will at some point in their treatment go through RT[10, 11]. In RT treatment, high-energy ionizing radiation from X-ray photons,proton or electron beams are used to kill or restrain the growth of cancer cells.

Normal healthy cells do not divide as rapidly as cancer cells. Therefore whencancer cells are hit and damaged with radiation they cannot repair as effectivelyas normal cells. RT treatment, makes optimal use of the instability within tumorcells by administering prescribed doses in multiple fractions that normal cells can

3

tolerate. For example, the commonly used therapeutic dose of 2 Gy per fractionresults in overnight recovery and repair of 99% of double-strand breaks in normaltissues [12].

RT can be delivered in two ways; External or Internal. In external beam ra-diotherapy (EBRT), radiation beams from linear accelerators, cyclotrons or syn-chrotrons outside the body delivers radiation to the target region. Internal ra-diation therapy includes Brachytherapy and the use of radioactive liquids. InBrachytherapy, highly radioactive sources are placed in or near the tumor andthen removed after a short time. Alternatively, low radioactive sources known asbrachytherapy seeds are left permanently in the patient whilst their radioactivitylevels reduce to zero with time.

RT is a localized treatment regime with the primary goal to target malignanttumor cells with maximum dose while reducing dose to normal tissues. This,in turn, improves local tumor control and minimize side effects. Advances inmedical imaging technologies have made it possible to define and treat the tumorwith high precision. Dose adjustment during treatment to anatomic regions proneto movement such as the lungs and prostate are also possible. Methods such asthree dimensional conformal radiation therapy (3D-CRT), Intensity-ModulatedRadiation Therapy (IMRT), and Volumetric-Modulated Arc Therapy (VMAT)combined with image-guided radiation therapy (IGRT) increases the accuracy ofdose delivery.

1.1.1 Medical imaging in Radiotherapy

Every stage of current radiotherapy treatment process involves some form of med-ical imaging as specified in Figure 1.1.

Figure 1.1: Medical imaging modalities at each phase of the radiotherapy pro-cess. Modified from http://www.radiationoncology.com.au/resourcing-the-radiation-oncology-sector/essential-imaging-and-radiotherapy-techniques/

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1.1.2 Diagnosis and Staging

In order to optimize treatment, the correct diagnostic information about the loca-tion of the tumor and nearby organs at risk (OAR) will be required. The imagingdone at this stage is aimed at determining the location, size, extent, and stage ofthe tumor including the metastatic status of the disease. The imaging systems in-volved in diagnosing and staging the disease need to have verifiable quantitativeabilities. These qualities will be most essential when evaluating treatment responseand also for future longitudinal studies.

1.1.3 Simulation and Planning

The imaging done here is to simulate the required patient position during the ac-tual treatment. It also involves contouring of the tumor/target volume and accu-rately defining nearby organs-at-risk. For most cancer treatment centers, a CTscan is the gold standard in contouring as well as calculating the needed doseto be delivered during treatment. Tumors are mostly soft-tissues, so MRI withits superior soft-tissue contrast compared to CT might be the preferred choice.Functional imaging approaches such as PET and SPECT can also be used in de-lineating the target volume. There is strong evidence pointing to the advantagesof using multi-modal imaging through registration (CT-PET/SPECT, PET-MRIor CT-MRI fusion) techniques to accurately define the target and OAR.

1.1.4 Dose Delivery and Tumor Localization

With the implementation of image guided radiotherapy, imaging modalities suchas cone beam CT (CBCT), MRI, etc. can be used during the delivery of doseto monitor changes in tumor and nearby organs. These changes may be due tobladder and rectal filling as well as lung movements during breathing cycles. Inbrachyterapy of gynecological cancers and high dose rate prostate brachytherapy,MRI is mostly used to ensure the accurate delivery of dose to the tumor volume.By incorporating imaging during dose delivery, the potential side effects of ra-diotherapy treatment can be greatly reduced [13]. However, CBCT have beenassociated with impaired visualization of regions with high motion and swallow-ing as well as poor soft-tissue contrast. MRI with its superior soft-tissue contrastmay offer a better option for treatment monitoring during dose delivery but, highmotion and swallowing may also be a drawback.

5

1.1.5 Response Assessment and Follow up

Response assessment involves deciding if a patient is in a remission or there isevidence of the existence of active tumor cells after radiotherapy treatment. Pos-sible tumor metastasis can also be detected during this stage. Each cancer typewill respond differently to radiotherapy based on resistance parameters such as hy-poxia, proliferation levels, and intrinsic radiation resistance at the tumor cellularlevel [14]. The use of medical imaging provides non-invasive monitoring of tu-mor changes during radiotherapy. In head and neck cancers, studies have shownsignificant reduction in unnecessary salvage surgery due to the accurate depictionof outcome when using 18F-fluorodeoxyglucose (18F-FDG) PET to assess posttreatment response [15, 16].

The relevance of imaging in radiotherapy was beautifully summed up by theCanadian Medical Physicist Harold Johns [17]:

”If you can’t see it, you can’t hit it, and if you can’t hit it, you can’t cure it.”

1.2 Aims of Study

In this study we aimed to identify risks and mitigations associated with the usageof data from MRI as the sole input for radiotherapy treatment planning of cancer.The specific aim of the two projects associated with this thesis were:

• Quantify the combined effect of scanner specific and patient-induced sus-ceptibility distortions on dose distribution. The research question is: whatbandwidth (BW) provide the best balance between reducing distortion andmaintaining image quality?

• Evaluate how objects introduced in a MR scanner affect the local Bo fielddue to differences in magnetic susceptibilities. The research question hereis: What are the benefits of linear and high order shims directed at reducinglocal Bo field imperfections?

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Chapter 2

MRI in Radiotherapy TreatmentPlanning

The success of radiotherapy depends highly on correctly delineating the target vol-ume and nearby organs at risk. The superior soft-tissue contrast provided by MRIcompared with CT makes MRI a valuable tool in radiotherapy treatment plan-ning. Since MRI uses non-ionizing radio waves of low amplitude, it is of utmostbenefit to pediatrics in the monitoring of early response and radiation inducedtissue changes [18]. There are however technical issues such as MR geometric dis-tortions and the lack of electron density information from MR data needed fordose calculations.

2.0.1 Dose calculation with MR data

With regards to electron density data, several studies have provided methods toassign electron density values to MR images for dose calculations with good results.The three main methods currently used to create synthetic CT (sCT) images fromMR data are:

1. Assignment of bulk electron densities: each segmented volume is assignedone Hounsfield unit (HU) value [19, 20, 21, 22]

2. Voxel-intensity based approach: HU values are assigned based on MR imagevoxel intensities [23, 24, 25]

3. Atlas based: a referenced dataset of co-registered MR- and CT-images aremapped to new patient MR images [26, 27, 28, 29]

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With bulk density assignment, the tissues are segmented and assigned bulkelectron density values. Lee et al. [22] compared dose plans for five prostate can-cer patients between original CT data and MR images: (i) assumed to be homoge-neous and therefore all voxels within the body contour were assigned the electrondensity of water, 3.340 × 1029 m−3, and (ii) assigned an average CT numberof 320 HU, with an equivalent electron density value of 3.874 × 1029 m−3 tosegmented bone and all other voxels assigned the electron density of water. Theyreported a dose difference of less than 2% between treatment plans of CT andMR images assigned with bulk-electron density of bone and water. However, dosecomparison between CT and MR images assumed to be homogeneous resulted ina dose difference of more than 2% .

In 2010, Jonsson et al. [21], studied the assignment of electron bulk densityvalues for different anatomic sites; pelvis, thorax, brain as well as head and neck.Ten patients for each organ site were studied. They assigned the following massdensity values to generate sCT from MR images based on the recommendationsof the ICRU 46 report [30]; 1.61 g/cm3 for whole cranium, 1.33 g/cm3 to thefemoral bones, 1.025 g/cm3 to the average soft-tissue (average value between maleand female), and lastly 0.001 g/cm3 to air. A maximum difference in the numberof monitor units needed to achieve the desired prescribed dose was 1.6% betweendose plans from CT data with and without inhomogeneity correction and bulkdensity assigned MR or CT datasets.

Other studies that have also looked at the dosimetric impact of bulk den-sity assigned MR images include Lambert et al. [31] who found a difference of1.3 ± 0.8% between CT plans and bulk density assigned MRI plans. Similarly,Prabhakar et al. [32], in 2007 investigated the feasibility of using MR data alonefor treatment plan using a cohort of 25 patients with brain tumors. They gen-erated three plans based on : (1) CT images with inhomogeneity correction, (2)CT images without inhomogeneity correction and lastly (3) MR images with thetarget assigned a uniform Hounsfield value for water. A dose difference within±2% between bulk assigned MR and CT plans was reported [32].

Recently, Persson et al. 2017, published the results of a multi-center studyinvolving four radiotherapy centers and 170 prostate cancer patients. Their studysought to validate the dosimetric accuracy of a new commercially available methodof creating sCTs by Siversson et al. [33] called the Statistical Decompositon Algo-rithm (SDA). SDA involves automatically creating sCT images from mostly T2-weighted MR data based on automatic tissue classification combined with a modelof a trained template of CT and MR materials [33]. Persson et al., reported a dose

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difference of less than 0.3% between the atlas-based sCT and original CT-basedtreatment plans from all centers.

There are also hybrid HU conversion models that for example combine atlas-and voxel intensity-based methods to create sCT’s from MR images [34, 35]. Atthe Helsinki University Central Hospital’s cancer center, a dual model HU con-version method to create sCT images from T1/T2

∗-weighted MR data has beenimplemented in their clinical MR-only RT protocol [23, 36, 37, 38, 39]. Themodel allows the heterogeneity of tissues to be represented using images from asingle MR series [36]. Korhonen et al. [38], used the dual model HU conversionin their 2013 study to convert MR intensity values within and outside bone seg-ments in an MR-only prostate treatment planning. Here, two models were used:soft tissue conversion model and bone tissue conversion model. They reported adose difference within 0.8% and an average deviation of 0.3% at the planning tar-get volume (PTV). Using the same model, Koivula et al. [36] reported a maximumabsolute dose difference of 1.8% compared with the 8.9% when using dual bulksCT and homogeneous sCT data respectively for brain tumor treatment plans.

The conclusions drawn from literature are that irrespective of the method usedin the generation of synthetic CT, dose differences between sCT and original CTto the target volume is small and that it is possible to use sCT images generatedfrom MR data to accurately calculate dose in an MR-only radiotherapy. However,caution must be taken regarding doses to organs at risk. Eilertsen et al. [40]reported differences up to 8.8% in the maximum dose to the rectum and 7.0% tothe bladder between MR and CT treatment plans. Care must therefore be takenin the calculation of dose using MR data for organs at risk since what determinesthe degree of tissue damage is not mean but rather maximum doses [40]. Theother technical challenge of MR in radiotherapy, inherent geometric distortions,will be discussed for the rest of this thesis, focusing on their causes and existing orproposed methods to reduce their impact on radiotherapy treatment planning.

2.1 The MRI System

The MR imaging system is made up of the main magnet, Radio-Frequency (RF)coils and magnetic field gradients. The main magnet is the core of the MR system.It produces a strong and homogeneous magnetic field. This is needed to alignthe protons along the direction of the magnetic field. Magnetic field strengthsare expressed in units of Tesla (T). Field strengths of up to 3 T are common andeven higher are in experimental use. MR scanners are designed to be either closed

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or open bore. The vast majority of MR scanners are of the closed bore design.The direction of the magnetic field is directed horizontally along the bore. Highfield superconducting magnets with field strengths from 1.5 T are mostly used inradiotherapy. The radio-frequency coils are made up of transmitter and receiver coils.They produce RF pulses to excite protons within tissues and detect MR signalsafter proton excitations. Though the scanner has in-built body coils, there arespecialized coils for body parts such as; head, neck, and breast in order to improvesignal-to-noise ratio (SNR).

To locate the source of MR signals from specific sections of the body that havebeen excited, magnetic field gradients are used to create momentary variations inthe magnetic field along the excited region. The gradients are responsible for thespatial encoding of MR signals. Gradients are built in the x, y and z directioninto the bore of magnet. The peak or maximum gradient strength is measuredin milliTesla per meter (mTm−1). Another important measure is the slew ratewith units of Tesla per meter per second (T/m/s). It is the peak gradient strengthdivided by the rise time. The slew rate puts limitations on the speed and otherparameters with which images are acquired. The gradients are repeatedly appliedin each pulse sequence generating the high beeping or clicking sound often heardduring scanning sections.

2.1.1 MRI Safety

As MRI is non-ionizing in contrast with X-rays and CT, there is not enough com-pelling evidence to suggest that it causes cancer [41]. The expert panel on MRsafety for the American College of Radiology has documented guidance practicefor staff and patients [42]. There are concerns about accumulation of the contrastagent gadolinium in the brain [43]. This is more of a pharmaceutical safety con-cern rather than an issue with the the magnetic field. The daily safety concernsassociated with MRI are:

• Displacement of metallic implants such as pacemakers near the static mag-netic field.

• Projectile ferromagnetic objects close to the scanner due to the strong pullof the static magnetic field.

• Excessive noise due to the force produced by currents in gradient coils inthe presence of a strong magnetic field.

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• Peripheral Nerve Stimulation (PNS) caused by the rapid switching of thegradients. PNS are more likely occur in fast imaging techniques such asecho planar imaging.

• High Specific Absorption Rate (SAR) caused by excessive exposure to RFpulses, leads to localized heating. A SAR limit of 2 Wkg−1and 4 Wkg−1

for the whole body at normal and first level operations are recommended.

2.2 The Physics of MR

Magnetic resonance imaging is based on the Nuclear Magnetic Resonance (NMR)phenomena. MRI signals are emitted when an atomic nuclei responds to radio-waves with a resonance frequency corresponding to the energy difference betweenthe spin states of the nuclei. The protons of Hydrogen, the most abundant el-ement in the human body, are mostly utilized in clinical MRI. Protons possesstwo intrinsic properties, spin and magnetic moment that are beneficial to MRI.Spin describes the inherent angular momentum of a particle. Analogous to clas-sical mechanics, charged particles with angular momentum will have a magneticmoment and will experience a torque when placed in an external magnetic field.Whilst experiencing a torque, the particles precess around the applied magneticfield as illustrated in 2.1.

Figure 2.1: Proton precession due to an applied magnetic field. The intrinsic propertiesof a Hydrogen proton utilized by MRI: spin [describing inherent angular momentum]and magnetic moment, (a). Precession of charged particles in the direction of the appliedexternal magnetic field, (b).

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The frequency with which the protons precess is proportional to the appliedmagnetic field, described by the Larmor equation:

ω0 = γB0 (2.1)

where γ is the gyromagnetic ratio with value of 42.58 MHzT−1. The Larmorfrequency of hydrogen protons is 63.86 MHz and 127.71 MHz at 1.5 T and 3 Trespectively.

To describe the dynamics of a group of spins that experience the same magneticfield strength, the magnetization vector of the spins can be used. The vector sumof these magnetization vectors is the net magnetization (Mz). At equilibrium, thenet magnetization lies in the same direction as the external magnetic field, i.e. thez-axis in conventional coordinate system, called the equilibrium magnetization(M0). Though M0 can be measured, it is very weak whilst lying parallel to B0,in the order of nT compared to for example a 3 T static magnetic field. The netmagnetization when excited to not be parallel with the external magnetic field,rotates about the z-axis with the Larmor frequency. This rotating magnetizationgives rise to a rotating magnetic field which can be detected with a receiver coil asthe signal used in MRI.

2.2.1 Longitudinal Relaxation Time or T1 Recovery

M0 is a very weak signal. However, by applying a Radio-frequency (RF) pulse, ori-ented perpendicular to B0 and oscillating at the Larmor frequency, M0 is tippedinto the xy plane. In the transverse plane, the net magnetization undergoes exci-tation. This time varying net magnetization can be measured with a receive coilsensitive to only signals perpendicular to B0. As soon as the RF pulse is switchedoff, the spins lose energy due to interactions between nearby spins. The net magne-tization gradually returns to equilibrium. The time constant describing the recov-ery of the net magnetization to 63% of its original value is known as longitudinalrelaxation or spin-lattice relaxation time, T1 . It is a random and tissue-specificprocess. The longitudinal magnetization (Mz) at time t after the 90o RF excitationpulse is given as:

Mz(t) = M0(1− e−t/T1) (2.2)

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2.2.2 Transverse Relaxation Time or T2 Decay

In the transverse plane, the spins dephase because of differences in the precessionalfrequency due to inhomogeneities in the main magnetic field. Even in a perfectlyhomogeneous magnetic field, the group of spins making up the net magnetization,experience different magnetic fields by neighboring spins. The spins then precessat different frequencies and with time will go out of phase. The phase differenceincreases with time resulting in the rapid decay of signals to nearly zero known asFree Induction Decay (FID) as illustrated in Figure 2.2.

Figure 2.2: Magnetic resonance (MR) signal decay. Before the 90o radio-frequency (RF)pulse, the net magnetization (Mo) from all spins point in the direction of the main mag-netic field (z-axis) [a]. By applying a 90o RF pulse, the spins gain energy andM0 is flippedinto the transverse plane to produce measurable MR signal [b] but because of local mag-netic field inhomogeneities, spins get out of phase and the net magnetization returns toequilibrium. This rapid decay of signals induced in the receive coils is known as FreeInduction decay.

The time constant that describes the decay of the Transverse magnetization(Mxy) to equilibrium is known as spin-spin or Transverse relaxation time, T2. T2

is the time taken for the transverse magnetization to decay to 37% of its originalvalue. Transverse magnetization (Mxy) at time t after the 90o RF pulse is given

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as:

Mxy(t) = M0e−t/T2 (2.3)

Different tissues have different T2 values that are not directly dependent onthe magnetic field strength. For Gradient echo sequences, the actual observed sig-nal decay is much faster than the predefined T2 values due to inhomogeneities inthe main magnetic field. The time constant that takes into account field inhomo-geneities is known as T2

∗ (T2 star). Though T1 and T2 occur simultaneously, T2

decay is faster than T1 recovery as portrayed in Figure 2.3.

Figure 2.3: Magnetization time curve. Longitudinal magnetization recovery governed byT1 relaxation time occurring at the same time as the decay of the transverse magnetizationgoverned by T2 relaxation time.

2.2.3 Image Formation

To form an MR image would require;

• macroscopic amounts of hydrogen protons

• protons precessing at the Larmor frequency when placed in a magnetic field.

• applying an RF pulse to flip the net magnetization into the transverse plane.In the transverse plane the MR signals are strong enough to be measured

• the time constants T1 and T2 for contrast

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2.2.4 Pulse Sequences

To create MR images for diagnostic purposes, a combination of magnetic gradientsare needed to be applied at the appropriate time and in the right order to spatiallyencode the source of these signals. The combination of magnetic field gradientsand the timing of various the RF pulses referred is to as Pulse Sequences. Generally,pulse sequences haveRF pulse/s, slice selection gradients (Gss) , frequency (GFE)and phase (GPE) encoding gradients, Repetition time (TR) and Echo time (TE)as shown in figure 2.4. TR is the time between two RF excitation pulses whilst TEis the time between the 90o RF pulse and the maximum amplitude in the echo.

Figure 2.4: Pulse Sequence diagram for magnetic resonance image formation simplifiedfor Gradient Echo. A radio-frequency (RF) pulse combined with the slice select gradient(Gss) selectively excite the region of interest. The Phase (GPE) and frequency (GFE)encoding gradients are for spatial encoding of the signals. To re-phase all de-phased trans-verse magnetizations, additional gradients (outlined in red) are applied after slice selectionand before frequency encoding. Modified from the book, ’ MRI from Picture to Proton’, 3rdedition [1]

During slice selection, an RF pulse is concurrently applied with a slice selectgradient (GSS). The RF pulse when combined with any of the gradients (x, y,or z-gradients) makes the resonance condition fulfilled within the selected two-dimensional plane or slice. We can therefore selectively excite protons in multiple

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planes (transverse, oblique, sagittal or coronal) by appropriately orienting the slice-select gradients. The phase encoding gradients are turned on and off whilst waitingfor an echo. This results in the accumulation of phase shifts for protons in theselected direction. The GFE , also known as Readout gradient, is used to cause arange of Larmor frequencies along the applied regions. The range of frequenciescan be decomposed by Fourier transforms allowing the spatial localization of MRsignals. By applying two frequency encoding gradients with opposite polarity anecho is formed. If a magnetic gradient is used to create this echo, the resulting pulsesequence is known as Gradient-Echo and Spin-Echo sequence if a 180o refocusingRF pulse is used.

2.2.5 K-Space

K-space is a coordinate system where encoded information is stored in MR. Eachposition in this coordinate system, corresponds to spatial frequencies. Hence, im-ages can be obtained using the inverse Fourier transform. After spins have beenexcited by the RF pulse, the encoding corresponds to being at the center or originof k-space, point (a) on Figure 2.5. For two dimensional MR imaging, each row(Kfe) represents one sample readout at a specific phase encoding Kpe. By apply-ing a combination of phase and frequency encoding gradients, the MR signals canbe sampled in k-space based on their spatial information. Therefore any imper-fections in the gradients affect sampling in k-space which may in turn distort thefinal image.

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Figure 2.5: Filling of K-space after magnetization. After RF excitation and before anygradients, all encodings will be at (a). The application of a negative phase encoding gra-dient moves all data to point (b) where upon applying a frequency encoding gradient, thedata is sampled along Kfe, from b to d. Modified from the book, ’ MRI from Picture toProton’, 3rd edition

2.2.6 Image Contrast

Different tissues appear differently on an MR image due to their signal intensities.All body tissue types are either water-based tissues, e.g. brain, cartilage, muscle,kidney, fat-based tissues, e.g. bone marrow, fat, or fluids, e.g. Cerebrospinal Fluid(CSF), Oedema. In MRI image acquisition, we use different pulse sequences withvarying timing to produce image contrast. The choice of timing parameters, resultsin T1, T2 or proton density, -weighted images. To obtain T2-weighted imageseither with a Gradient Echo (GE) or Spin Echo (SE) sequence, a long TR andlong TE are used. Tissues with long T2 relaxation times (mostly water-based likebrain) appear bright on T2-weighted images. Due to the long TR, T2-weightedimages mostly taken with SE sequences have long acquisition times. GE sequencescan be utilized to reduce the scan time. In this case, it is no longer be T2-weightedbut rather T2

∗-weighted (refer to section 2.2.2). T1-weighted images also knownas anatomic scans have short acquisition times because of the short TR. UnlikeT2-weighted images, tissues with long T1 show up dark in T1-weighted images.

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Chapter 3

MR Geometric Distortions

To create and assign signals to their source, MRI uses a combination of strongmagnets, radio frequency pulses and magnetic gradients to establish a linear rela-tionship between resonant frequency and position. Any imperfections in any ofthese devices will result in system related MR geometric distortions. Though everyeffort is made to make modern scanners as homogeneous as possible, the patientto be scanned also introduces field perturbations into the main magnet known asPatient Related distortions.

3.1 System-Related Geometric Distortions

Two main sources of system-related distortions are inhomogeneities in the mainB0 field and nonlinearities in the gradients system. Ideally, a linear gradient su-perimposed on a homogeneous static magnetic field are needed for MR signallocalization and image formation.

3.1.1 B0 Field Inhomogeneity-Related Distortions

A highly homogeneous static magnetic field especially at the isocenter is neededfor MR image acquisitions. Inhomogeneity describes deviations from the averagevalue of the main magnetic field. It is measured in parts per million (ppm) orppm over a Diameter of Spherical Volume (DSV). Due to the large value of γ andconsidering the relationship between resonance frequency and B0, as depictedin equation 2.1, there is a significant shift in frequency even for a few ppm inB0, leading to geometric distortions and intensity variations in MR images. Forinstance, a 3 T scanner may offer a 1 ppm homogeneity over a 40 cm DSV from the

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isocenter. Thus for all spins within ±20 cm of the magnet’s isocenter, variations inmagnetic strength will not be more than 3×10−6 T, corresponding to a frequencyshift of 127.71 Hz. So for our first project, using acquisition BW of 122, 244, 488Hz/pixel and 1×1 mm pixel, pixel shifts of 1.05, 0.52, and 0.26 mm respectivelycould be attributed to magnetic field inhomogeneities. Shimming before scanningcan improve field uniformity and when combined with high BW can reduce B0

related geometric distortions.

3.1.2 Gradient Nonlinearity-Related Distortions

Ideally, the magnetic field gradients over the imaging volume should be linear tomaintain the geometric integrity of MR images. However, due to design con-straints such as the demand for gradients with high slew rate, gradient linearityreduces significantly at distances away from the magnet’s isocenter as shown inFigure 3.1. Here, an MR signal originally located at position x0 will have anapparent location of x. The effect of nonlinear gradients is increased geometricinaccuracy away from the scanner’s isocenter. At the peripheries of the scanner,distortion values of 7.4 mm at a distance of 230 mm from the isocenter due togradient nonlinearity effects for a 1 T scanner have been reported [44].

Figure 3.1: Linear and Nonlinear gradients. Variations in location of signals due tononlinear field gradients.

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3.2 Patient-Related Geometric Distortions

The patient in the scanner also introduces distortions due to magnetic susceptibil-ity and chemical shift effects.

3.2.1 Magnetic susceptibility

The differences in magnetic susceptibility between tissues relative to other anatomictissues, air, bone as well as implants, result in patient-induced susceptibility distor-tions [45]. Indeed, most biological tissues are weakly diamagnetic and thereforetheir magnetic polarities relative to the external magnetic field is in the oppositedirection. Bone and air have the lowest susceptibility whilst blood has the highest.At the boundary of tissues with different susceptibilities, a micro-gradient field iscreated. This micro-gradient field disturbs the local B0 field and speeds up de-phasing of protons on either side of the boundary. They are most severe in areaswhere there are transitions between tissue, bone, air or metallic implants. Usually,susceptibility-induced effects show up as signal loss in these areas. A measure ofpositional accuracy due to effects of magnetic susceptibility can be estimated by:

∆x =∆χB0

GR(3.1)

and GR, the Readout gradient strength is given as:

GR =BW

γFoV(3.2)

where ∆x is the shift in position, ∆χ is difference in magnetic susceptibility,B0 is the main magnetic field strength, BW is bandwidth, Field of View (FoV)is the field of view. γ, is the gyromagnetic ratio with an approximate value of42.58 MHzT−1. Thus, with the increasing magnetic strength of clinical MR sys-tems, geometric distortions associated with magnetic susceptibilities may be moreprominent. In this thesis work, we used a method proposed by Lundman et al.[46] and integrated in MICE-Toolkit, to simulate patient-induced susceptibilitydistortions. It requires the creation of a susceptibility map for each patient. Alook up table was created matching the HU values of air, fat, muscle and bonewith their corresponding susceptibility values. This look up table was then used tocreate a susceptibility map based on HU values from CT images of the patients.

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3.2.2 Chemical Shift

The slight differences in the resonant frequency of protons because of variationsin their molecular environment especially at high magnetic field strengths resultsin chemical shift. The effects of chemical shift are signal loss and distortions. Thechemical shift between water and fat molecules is about 3.5 ppm irrespective ofmagnetic field strength. Nonetheless, the shift in frequency between the protonsof these molecules increase with rising field strength. The frequency shift f due tothe resultant field perturbations (dB) is calculated as:

f = γdB (3.3)

Therefore, estimated frequency shifts will be :At 1.5 T

f = γdB (3.4)

= 42.58× 1.5× 3.5× 10−6 (3.5)≈ 224 Hz (3.6)

At 3 T

f = 42.58× 3× 3.5× 10−6 (3.7)≈ 447 Hz (3.8)

The magnitude of Patient-induced susceptibility distortions and the shift infrequency due to chemical shift effects as shown in Equation 3.1 and 3.3 is pro-portional to the strength of the main magnetic field [47] and can be reduced withincreased BW.

3.3 Characterizing and Correcting Geometric Distortions

As a QA measure, it has been recommended by The American Association of Physi-cists in Medicine (AAPM) report No.100 that system related MR distortions arequantified as part of routine quality control [48]. The report also recommendsthat MR systems dedicated to radiotherapy treatment planning purposes shoulddetermine the geometric accuracy throughout the entire imaging volume, and notrestricted to regions close to the isocenter.

Distortions due to inhomogeneities in the static magnetic field and patient-induced effects occur in the frequency encoding direction whilst gradient nonlin-earity distortions are exhibited in all directions within the scanner. In conventional

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2D MR imaging, distortions from field perturbations occur only in the readoutand slice select directions, whilst in 3D MR scans, these distortions are not foundin the slice select direction. This is because 3D MR acquisitions uses phase encod-ing in the slice select direction [48].

From Equation 3.1, we know that the amount of MR distortions is propor-tional to the the ratio of magnetic field strength combined with any perturbations(dB = B0 + δB0 + δBs) and the readout gradient strength (GR).

∆x =dB

GR(3.9)

In their work to characterize and correct MR geometric distortions, Baldwinet al. [49], showed that if frequency encoding is done in the x-axis whilst phaseencoding occur is in the y and z axes for a 3D MR scan, then the magnitude ofdistortions in each of the axes will be :

x′ = x+∆x

= x+δBGx(x, y, z)

Gx+

δB0(x, y, z)

Gx+

δBs(x, y, z)

Gx(3.10)

y′ = y +∆y

= y +δBGy(x, y, z)

Gy(3.11)

z′ = z +∆z

= z +δBGz(x, y, z)

Gz(3.12)

Where ∆x, ∆y, ∆z are the magnitude of distortions in each direction respec-tively. Gx, Gy, Gz and δBGx, δBGy, δBGy are the gradient strengths and theircorresponding nonlinearities. δB0, and δBs are the field imperfections from thestatic magnetic field and patient-induced susceptibility effects, respectively.

Based on Equations 3.10-3.12, the different sources of geometric distortionscan be quantified and separated. Distortions from field imperfections are onlyobserved in the gradient encoding direction as shown inEquation 3.10. Therefore,by reversing the polarity of the encoding gradient Gx, it is possible to separatedistortions resulting from dB0 and dBs.

To characterize distortions, phantoms embedded with structures of knownposition are utilized. The difference (∆x) between the apparent position (x′) andthe originally known position (x) which is usually obtained from CT scans gives

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the magnitude of distortions. Prott et al. [50] used phantoms to measure andcompare distortions from 27 MR units (0.2 -1.5 T field strengths) across Austria,Germany and the Netherlands.

Though most MR centers are provided with manufacturer-specific spatial ac-curacy phantoms for routine quality control purposes, there are also commerciallyavailable phantoms [51, 52]. In Study I, we used a GE spatial analysis phantomand a commercial phantom by Spectronics Medical AB to characterize gradientnonlinearity distortions. The CT and MR images of the two phantoms are shownin Figure 3.2

(a) (b)

(c) (d)

Figure 3.2: Axial Images of the GE and Spectronics phantoms used in this study. Com-puted Tomography and Gradient echo Magnetic resonance images of the Spectronics (a& b) and GE (c & d) large field of view spatial analysis phantoms.

For the purposes of research, phantoms have also been developed dependingon the aims of the study. Stanescu et al. [29] and Baldwin et al. [49] developedgrid sheets phantom filled with water-based solutions, whilst Doran et al. [53]

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and Tanner et al. [54] made phantoms with long fluid-filled tubes. Similarly,Mallozzi et al. [55] developed a spherical phantom embedded with an array of165 spheres filled with copper sulfate solution to characterize system related dis-tortions. Phantoms for specific anatomic regions like the pelvis [56] and head[57] have also been developed to measure distortions within such regions. Tanneret al. [54] developed a phantom to quantify distortions within the whole pelvicregion. The tube-based linearity phantom measured maximum distortions of upto 16 mm from a 1.5 T scanner corresponding to distortions within the pelvicvolume.

For all phantoms constructed to quantify MRI distortions, it is importantthat, the phantom materials do not produce additional distortions due to object-induced susceptibility effects. Using a phantom made of Polymethyl methacrylate(PMMA), Tanner et al. [54] attributed apparent shifts of up to 3 mm to magneticsusceptibility effects between air-PMMA interfaces. They could not correct forthese.

Several studies have characterized gradient nonlinearity distortions by usinglarge FoV phantoms [44, 49, 52, 58, 59, 60, 61, 62]. The conclusion from Baldwinet al. [49] and Price et al. [44] was that, the major source of geometric distortionsin MR images is from nonlinear gradients. Subsequently, gradient nonlinearitydistortions have also been demonstrated to be stable over time [44, 60, 63].

If system based distortions are known, a correction process through transfor-mation functions such as spherical harmonics [48], tri-linear interpolation [64],splines [65] among others can be adequately used to reduce these distortions. Ven-dor supplied gradient distortion correction algorithms can greatly reduce pixeldisplacements due to distortions. A study by Mah et al. [66] investigating systemdistortions on a 0.23 T scanner reported reduced maximum distortions from 40mm to 30 mm at radial distances above 200 mm from the isocenter when using3D correction. Sun et al. [56] investigated distortions from a 3 T scanner by usinga liquid filled pelvic shaped phantom. They reported maximum distortions of 7.5mm across the pelvis reducing to 2.6 mm and 1.7 mm by using the vendor sup-plied 2D and 3D correction algorithms respectively. Additionally, investigationsby Tavares et al. [57] showed that by using the vendor supplied 3D correction, av-erage distortions measured with a head-modeled phantom decreased to 2.75 mmfrom 3.7 mm for a 3 T scanner.

In Study I, we studied the reduction in gradient nonlinearity distortions whenusing the manufacturer supplied 3D algorithm as shown in Figure 3.3. At a band-width of 488 Hz/pixel, the worst observed distortions at radial distance of more

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than 250 mm from the isocenter decreased from 63.73 mm to 16.62 mm with3D correction for a 3 T MR scanner.

(a) (b)

Figure 3.3: Reduction in Gradient Nonlinearity distortions with 3D correction. Mag-nitude of MR Nonlinearity distortions with radial distance from the isocenter without 3Dcorrection (a) and with 3D correction for a spin echo sequence using a bandwidth of 488Hz/pixel.

Unlike gradient nonlinearity distortions, patient induced distortions cannotbe determined in advance because of variations in individual patient anatomies.Therefore, manufacturer supplied correction softwares do not correct for distor-tions caused by these imperfections in the static magnetic field. However, postprocessing methods such as B0 field mapping [67, 68], and reverse gradient po-larity [47, 69] have been proposed to measure and correct field inhomogeneitydistortions.

B0 field mapping is based on the notion that each MR signal has a phase andan amplitude [67]. Therefore, at each voxel position x, the phase acquired φ isproportional to the local field variation dB0 and the echo time (TE) [70]:

φ(x⃗, TE) = φ0 − γ · dB0(x⃗) · TE (3.13)

where γ is the gyromagnetic ratio = 42.58 MHzT−1. By taking several MR scanswith different echo times (TEs), the phase offset φ0 is removed and the phasedifference in dB0 can be calculated as :

dB0(x⃗) =∆φ(x⃗, TE)

γ∆TE(3.14)

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In Study II, we used spherical harmonics (SH) modeling to create the basisfunctions required to correct and improve local field inhomogeneities introducedby a patient in an MR scanner. The series of harmonics are shown in Figure 3.4.

Figure 3.4: Spherical harmonics (SH) up to third-order. High SH orders result in in-creasing number of modeled shapes. This in turn increases the likelihood to improve theB0 homogeneity. SH are arranged in orders of N with 2N + 1 terms for each order.

For this study, we used local B0 field inhomogeneity maps obtained througha method proposed by Lundman et al. [46] to create SH basis functions needed tocorrect patient-induced susceptibility field imperfections. Mean Pixel shifts dueto local B0 field inhomogeneities could be significantly reduced. For example, inthe spinal cord, mean estimated pixel shifts due to local B0 field inhomogeneitiesdecreased from 3.47±1.22 mm to 0.99±0.30 mm at 122 Hz/pixel after secondorder shimming. In 2013, Wang et al. [71] published the first study character-izing object-induced distortions at high field strengths using clinical patient data.They utilized the field mapping method proposed by Jezzard and Balaban 1995[67] to identify the source, location and magnitude of displacements caused byB0 field inhomogeneities from a 3 T MRI scanner. Their study involved MRbrain images of 19 patients. Using a bandwidth of 180 Hz/pixel, 86.9% of theestimated displacements were less than 0.5 mm and 0.1% were more than 2 mm.Maximum distortion of <4 mm were measured at tissue-air interfaces. This studyconcluded that voxel shifts caused by susceptibility effects in the brain are smallat 3 T. However because of variations in individual patient anatomies, constantmonitoring for potential localized shifts was recommended.

Another method proposed by Chang and Fitzpatrick [47] corrects for fieldinhomogeneities arising from the main magnet and objects being imaged. It re-

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quires the acquisition of images of the same object but with reversed polarity ofthe readout gradients. From Equation 3.10, and according to Baldwin et al. [49],values of x′ for positive and negative gradient readouts will therefore be:

x′+ = x+

δBGx(x, y, z)

Gx+

δB0(x, y, z)

Gx+

δBs(x, y, z)

Gx

x′− = x+

δBGx(x, y, z)

Gx− δB0(x, y, z)

Gx− δBs(x, y, z)

Gx(3.15)

Distortions from imperfections in the main magnetic field and patient-inducedsusceptibility effects will thus be the displacement in the average value of x′:

x′+ − x

′−

2=

δB0(x, y, z)

Gx+

δBs(x, y, z)

Gx(3.16)

Subsequently, the distortions due to gradient non-linearity in the x-direction canbe calculated by subtracting Equation 3.16 from the total magnitude of distortions(∆x) obtained in Equation 3.10. By knowing the measured distortions, ∆x, ∆y,∆z, a correction can be made through interpolation [53]. Distortions do notonly result in pixel displacements but also signal intensity variations. Intensitydistortions are caused by either stretching or compression of image voxels leadingto volume and shape changes. To compensate for such effects, an image intensityscale factor known as the Jacobian (J ) is multiplied by the image corrected byinterpolation (Idistorted) to achieve the desired signal intensity [53, 47].

Icorrected(x, y, z) = J(x, y, z)Idistorted(x, y, z) (3.17)

3.3.1 Bandwidth

Bandwidth, also referred to as the sampling bandwidth determines the rate atwhich encodings are sampled. Increasing the sampling bandwidth, decreases thesampling time which may decrease TE and T2∗ contrast. The chemical shift dif-ference between water and fat remains the same at a given gradient strength anddoes not change because of variations in bandwidth. However, a reduced band-width increases the pixel shifts caused by chemical shifts. For example on a 3 Tscanner, the chemical shift difference between fat and water is approximately 447Hz, and when using an image matrix of 512× 512 and a sampling bandwidth of125 kHz, pixel shifts caused by chemical shift effect will be approximately 2 pixels

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(125,000/512 ≈ 244 Hz/pixel, 447/244 ≈ 2). If the bandwidth is halved, theneach pixel represents 122 Hz, and a chemical shift of 447 Hz at 3 T correspondsapproximately to 4 pixels. It is obvious that the geometric accuracy of MR im-ages increases with increasing gradient readout bandwidth. However, increasingbandwidth decreases SNR.

In Study I, we studied the effect of bandwidth on reducing distortions. Theresults showed a decrease of one and half fold in measured mean distortions whenbandwidth was increased from 122 Hz/pixel to 244 Hz/pixel as displayed in Figure3.5. We also reported a two fold decrease in estimated maximum patient-inducedsusceptibility distortions (5.8 to 1.9 mm) from a bandwidth of 122 Hz/pixel to244 Hz/pixel .

(a) (b)

Figure 3.5: Reduction in magnitude of residual system distortions with increasing band-width. Phantom measured residual system distortions decreased in magnitude with in-creasing bandwidth from 122 Hz/pixel (a) to 244 Hz/pixel after 3D correction

3.4 Impact of Distortions on RT Treatment planning

Two of the major technical drawbacks of a MR-only radiotherapy as mentionedearlier are MR images suffering from geometric distortions and the lack of electrondensity information for dose calculations (Section 2.0.1). As discussed earlier, theimpact of using MR data for dose calculations has been extensively studied andthe conclusion is that the effect is small. In a similar manner, the effect of MRgeometric distortions on dose calculations have also been explored in literature.In 1999, Prott et al. [50] did a large multi-center study investigating the effect of

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distortions on MR images used for radiotherapy treatment planning. Their studyinvolved 27 units with MRI systems having field strengths from 0.1 to 1.5 T andfrom different manufacturers [72]. Their study did not involve patient data insteadthey created similar fictitious PTV and OAR on both distorted and distortion free-images of a phantom. They reported that the PTV and OAR deviated by up to±3% and ±8% respectively on the reference CT images compared to the MR im-ages. By comparing the 3D plans made on both image datasets, they found thatgeometric distortions caused a variation of ±0.5% in the maximum dose. Theyalso observed in the OAR that 25% of all dose calculations showed an increasein the irradiated volumes on the MR data compared to the reference image [50].Though they found this to be clinically significant, they also agreed that the irra-diated volumes were small in comparison with the total volumes. They thereforeconcluded that since MR gradient nonlinearity distortions increase with growingdistance from the isocenter, the dosimetric effects of distortions for tumors in thebrain and head and neck region will be minor compared to tumors located in thebreast, thoracic wall and abdomen [73]. To investigate the influence of residualand patient related distortions on whole breast IMRT, Walker et al. [74] alteredpatient CT images and delineated structures with distortion maps. The distortionmaps they used were obtained from a 3 T closed- and a 1 T open-bore scannerand generated by deformable registration between phantom CT and MR images.They compared IMRT plans initially optimized on the distorted CT and recom-puted on original CT images. They found that plans made with CTs distortedwith distortion maps from residual system distortions alone had minimal impacton dose plan. However, plans from 8 out of the 18 patients’ CTs distorted withcombined residual and patient related distortions were considered clinically unac-ceptable [74]. The conclusion therefore was that for whole-breast IMRT, the com-bined effect of residual and patient related distortions may result in unacceptabledose distributions [74]. For this study they measured maximum residual systemdistortions of 7.88 mm and 11.87 mm on the 3 T and 1 T scanners respectively.A recent study published in 2017 by Gustafsson et al. [52] specifically looked atthe effect of system related distortions from MR on dose distribution and on RTdelineated structures for 10 prostate cancer patients. They initially made VMATprostate treatments plans on original CT and later on distorted CT images. Subse-quently, the inverse of the displacement maps used to create the distorted CTs wasthen applied on the distorted CT dose plans to obtain a dose distribution in thesame geometry as the original patient CT images. When they compared the origi-nal CT dose distribution with the inversed distorted CT plans, they found a mean

30

percentage dose difference of less than 0.02% and a deviation of less than 0.2% forthe delineated structures. Based on their findings, they concluded that by com-bining a high bandwidth sequence with 3D correction, MR distortions producedno clinically relevant effect on dose distribution and RT structure deformations[52].

In Study I and II, we examined the effect of residual system and patient-induced susceptibility distortions on prostate as well as head and neck cancer treat-ment plans. To isolate the effect of MR distortions on dose plans, displacementfields from residual system and simulated patient-induced susceptibility distor-tions were combined and used to deform original patient CT images to form dis-torted CT images (dCT). We first made optimized VMAT dose plans on the dis-torted CT images. The field parameters from the optimized plans were then copiedto the CT data to recompute new dose plans. We evaluated dosimetric effects atdifferent bandwidths and gradient readout directions. From the two projects wefound a mean dose difference of less than 0.5% and median dose difference of lessthan 1.0% at the PTV for the first and second projects respectively. Whilst evalu-ating the residual system and patient-induced susceptibility effects, we found thatpatient-induced susceptibility distortions were high compared to residual systemdistortions at the contours of all delineated structures studied shown in Figure 3.6(results of Study I) except at the external contour (results from Study II). It wasconcluded that though shifts occurring at the contours due to patient-induced sus-ceptibility distortions were high compared with those from the system, the effectson dose distributions were minimal.

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Figure 3.6: Shifts due to system- and patient-induced susceptibility distortions. Esti-mated shifts at the contours of the bladder, the femoral heads, planning target volume(PTV) and rectum at bandwidths of (a) 122 Hz/pixel, (b) 244 Hz/pixel, (c) 488 Hz/pixelin the right to left gradient readout. The boxes show the average values of the median(centerline) and 25% and 75% percentiles (bottom and top of boxes for all patients, inmillimeters. The points above and below each box represent the range in absolute shifts.L = left; R = right

In the second project we used the Dice similarity coefficient to examine con-tour overlap between distorted CT (dCT) and original CT delineated structuresas displayed in Figure 3.7. A value of one means a perfect agreement whilst zeroshows the opposite. We found average values above 0.9 for all structures exceptthe spinal cord at 122 Hz/pixel, which had an average of 0.85± 0.06 .

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0.80

0.85

0.90

0.95

1.00

B C L P R SDelineated Structures

Dic

e S

imila

rity

Inde

x (D

SC

)

Bandwidth (Hz/pixel)

122488

Figure 3.7: Contour overlap between distorted and original CT datasets. Dice similaritycoefficient (DSC) at some selected contours and the two bandwidths studied. The meanagreement between distorted CT and original patient CT for all patients were above 0.9except for the spinal cord at the 122 Hz/pixel. [B-Brain, C-clinical target volume, L-leftparotid, R-Right parotid, P-Planning target volume, S-spinal cord ]

33

Chapter 4

Summary of Publications

4.1 Study I

Quantifying the Effect of 3 T Magnetic Resonance Imaging Residual SystemDistortions and Patient-Induced Susceptibility Distortions on RadiationTherapy Treatment Planning for Prostate CancerAdjeiwaah M, Bylund M, Lundman J.A, Thellenberg Karlsson C,Jonsson J.H, Nyholm TInternational Journal of Radiation Oncology • Biology • Physics (2017),doi: 10.1016/j.ijrobp.2017.10.021.

Aim: Investigate the effect of MR system and patient-induced susceptibilitydistortions from a 3 T scanner on dose distributions for prostate cancers.

Materials and methods: Displacement vector fields were generated by addingphantom measured residual system distortions from a 3 T scanner and simulatedpatient-induced susceptibility distortions at bandwidths (BW) of 122, 244 and488 Hz/pixel and gradient readout in the right/left (R/L) and anterior/posterior(A/P) directions. Computed tomography (CT) images of 17 patients and the clin-ically delineated structures were distorted using the displacement vector fields, giv-ing distorted CT (dCT) images. Subsequently, volumetric arc therapy (VMAT)optimized plans were generated on dCT images and the field arrangements fromthe optimized plans were copied to the CT data sets to calculate new dose dis-tributions. The dose distributions were evaluated based on clinically establishedacceptance dose volume criteria. We used pairwise two-one sided equivalence teststo compare the dCT and CT dose distributions.

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Results: Maximum residual mean distortions of 3.19 mm at a radial distanceof 25 cm, and maximum mean patient-induced susceptibility shifts of 5.8 mmwere found using the lowest BW of 122 Hz/pixel. There was a dose differenceof less than 0.5% between distorted and undistorted treatment plans. The 90%confidence interval of the mean difference between the dCT and CT treatmentplans were all within an equivalence interval of (-0.5, 0.5) for all investigated planquality measures.

Conclusions: Patient-induced susceptibility distortions at high field strengthsin a closed bore MR scanners are larger than residual system distortions after usingvendor supplied 3D correction for all studied contours. However, errors in dosedue to disturbed patient outline and shifts caused by patient-induced susceptibilityeffects are below 0.5%.

4.2 Paper 2

Dosimetric Impact of MR distortions - A study on Head and NeckCancer PatientsAdjeiwaah M, Bylund M, Lundman J.A, Zackrisson B, Söderström K,Jonsson J.H, Garpebring A, Nyholm T

Aim: Evaluate the dosimetric impact of MR geometrical distortions on Headand Neck cancers for a 3 T MR scanner and assess through simulations the use ofhigh order shimming to reduce local B0 field inhomogeneities.

Materials and Methods: Residual system distortions from a 3 T scanner anddistortions from simulated patient-induced susceptibility effects were used to de-form 21 Head and Neck cancer patient CT to create distorted CT (dCT) datasets.We compared dose plans initially optimized on the dCT and recomputed on CTdata to assess the dosimetric impact of distortions on dose distributions. The sus-ceptibility value of gold was assigned to dental implants to quantitatively measurethe magnitude of object-induced susceptibility distortions. To reduce the effect oflocal B0 field inhomogeneities due to magnetic susceptibility differences betweendental implants, tissue, bone, and air interfaces, we modeled patient-specific shim-ming through spherical harmonics simulations.

Results: Phantom measured worst residual distortions at a radial distance of200 mm (400 mm FoV) using BWs of 122 and 488 Hz/pixel were 10.92 (meanobserved distortion: 3.08 mm) and 9.59 mm (mean observed distortion: 1.94mm) respectively. Mean maximum shifts from patient-induced susceptibility ef-

36

fects were 7.33±0.46 and 1.93±0.12 mm at the studied bandwidths. Estimatedpixel shifts due to B0 field inhomogeneities at the spinal cord using first and sec-ond order shimming were reduced from 3.47±1.22 mm to 1.35±0.44 mm and0.99± 0.30 mm respectively for a bandwidth of 122 Hz/pixel using 1× 1 mm2

in-plane voxel size. Mean dose difference in D50 at the PTV and spinal cord were0.21 ± 0.66% and 2.87 ± 5.97% at 122 Hz/pixel. At 488 Hz/pixel the differ-ences were reduced to 0.12±0.33% and 1.4±4.99% at the PTV and spinal cordrespectively.

Conclusions: The effect of geometric distortions on MR data used for radio-therapy treatment planning of head and neck cancers is small. However, the dosi-metric accuracy in regions with increased combined magnetic susceptibility andresidual system distortions may not be acceptable. The use of high order shimmingmay improve the geometrical accuracy of MR images.

37

Chapter 5

Discussion and Conclusion

According to the AAPM report on Comprehensive QA for radiation oncology,MR systems dedicated to radiotherapy would require geometric accuracy within2 mm [75]. To fully integrate MRI in the radiotherapy work flow, the geometri-cal accuracy needs to be guaranteed. The major sources of geometric distortionsare imperfections in the main magnetic field, gradient nonlinearities and magneticsusceptibility differences as well as chemical shift effects. In this thesis, we have in-vestigated the impact of residual system and patient-induced susceptibility effectson prostate as well as head and neck cancer radiotherapy treatment plans. We alsofocused on methods to improve the geometric accuracy of MR images.

In Study I and II, we used combined displacement maps from phantom mea-sured residual system distortions and that of simulated patient-induced suscep-tibility distortions to distort original patient CT images. In distorting the CTdatasets with displacement vector fields it was possible to:

• estimate the magnitude of shifts occurring at delineated contours due tosystem and patient-induced susceptibility distortions

• isolate the effect of geometric distortions on prostate as well as head andneck cancer VMAT plans. This was achieved by comparing treatment plansmade with geometrically inaccurate dCT images and geometrically accurateCT datasets by transferring plan parameters from the optimized distortedCT plans to the original patient CT images to recalculate new dose plans.

We found that though patient-induced susceptibility distortions were larger thanresidual system distortions at all delineated structures except the external contour,their combined dosimetric effect within the treated region was still less 1%. The

39

dose difference found between dCT and CT plans is within the findings fromprevious studies that have also looked at the impact of distortions on dose dis-tributions at different anatomic sites [50, 52, 74, 56, 76, 66]. Bandwidth, whencarefully selected bearing in mind the limit set on it by SNR and combined withvendor supplied 3D correction algorithms could reduce the level of distortions inMR images.

In study II, we also investigated through simulations local B0 field inhomo-geneities introduced by the patient and how their effect can be reduced by shim-ming. Preliminary results show that shimming could improve the homogeneityof local B0 field imperfections introduced by the patient. The magnitude of im-provements however, depended on whether or not the whole patient volume orsome selected region was shimmed. It also depended on presence of tissue, air,bone as well as dental implants/fillings in the vicinity of the shimmed region. Formost patients and regardless of the volume shimmed, gains were obtained in themean residual magnetic field homogeneity values. The argument to whether ornot incorporate high order shimming in MR-only RT will depend on the MR ap-plication. For 3 T scanners a field uniformity of the order of 10 ppm peak-to-peakin a 50 cm spherical diameter volume would be required [77]. Most scanners areequipped with first order shim coils that utilizes the gradient systems for shim-ming. This, when utilized before each patient scan could improve magnetic fieldhomogeneity. For applications such as MR spectroscopy and balance steady statesequences, high order shimming could be beneficial.

In this thesis, we found that regions with large combined system and patient-induced susceptibility distortions may have unacceptable dosimetric results as alsoreported by Walker et al. [74]. For example in the head and neck treatment plan-ning, the large magnitude of combined system and patient-induced susceptibilitydistortions relative to the small volume of the spinal cord may have reflected inthe low dice similarity coefficient at 122 Hz/pixel. This may have accounted forthe large dose difference and deviations in dose volume parameters between dis-torted and undistorted dose plans in this structure. However, a combination ofhigh bandwidth, shimming and the use of appropriate set up margins may reducethe effect of distortions on dose distribution in such regions. A study by Breen etal. [78] reported that there was a 99% probability to maintain the maximum dosewithin the spinal cord below 45 Gy with a 6 mm margin.

Due to the different patient cohorts imaged with MR scanners, pixel band-widths of not less than 440 Hz/pixel on a 3 T scanner is recommended for thepurpose of radiotherapy image acquisitions. This corresponds to 440 Hz/mm, for

40

an in-plane image voxel size of 1× 1 mm2. At this bandwidth, the water/fat shiftwill be within 1 voxel and system related as well as patient-induced susceptibil-ity distortions will approximately be of the same magnitude. Liney et al. [79]also recommended that for radiotherapy purposes, MR image acquisition pixelbandwidths should not be less than twice the water/fat shift (i.e.220 Hz at 1.5 Tand 440 Hz at 3 T). It is however, worth noting that by doubling pixel size, themagnitude of distortions will also be doubled if the bandwidth per pixel is keptconstant.

The method used in this study may have some limitations since it relied onsimulations and CT instead of MR data. It was assumed that the phantom mea-sured only system distortions and so we did not take into account potential sus-ceptibility distortions. However, object-induced distortions for this phantom hasbeen reported to be < 0.5 mm [52]. The patient cohort used in this thesis workmay not fully represent the different cancer patients at MR radiotherapy centers.This will include patients with hip implants. However, the patients used in bothprojects may be representative enough to make the outcomes of this study valu-able to the MR-only RT community. Chemical shift was also not quantified inthis study but based on the recommended bandwidth it may contribute up to 0.9pixel shifts to the overall patient-related distortions. In using simulations instead ofdirect measurements to estimate patient-induced susceptibility distortions, distor-tions from intrinsic B0 field inhomogeneities was not counted twice when systemand patient-induced susceptibility distortions were added.

In conclusion, the combined effect of system related and patient-induced sus-ceptibility distortions from spin-echo based sequences on head and neck as wellas prostate cancer VMAT treatment plans was small and within the 3-5% overallaccuracy required for RT dose delivery [80]. Therefore, with appropriate choiceof image acquisition parameters, MR images even with inherent geometrical maybe considered acceptable for radiotherapy purposes. We mostly found the mag-nitude of patient-induced susceptibility distortions to be larger compared withresidual system distortions at all delineated structures except the external contour.This is could be very relevant when setting margins for treatment volumes andorgans at risk in an MR-only RT. The current practice of characterizing MR ge-ometric distortions utilizing spatial accuracy phantoms alone may not be enoughfor an MR-only radiotherapy work flow. Therefore, measures to mitigate patient-induced susceptibility effects in clinical practice such as patient-specific correctionalgorithms are needed to complement existing distortion reduction methods suchas high acquisition bandwidth and shimming.

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5.1 Summary and Future Works

The increasing using of MR for radiotherapy purposes would require a review ofcurrent quality control procedures. To ensure the geometrical integrity of MRimages, a system to characterize both system and patient-related MR geometricdistortions may arguably be an important QA measure. Therefore integrating thequantification of geometric distortions using large field of phantoms as part of rou-tine quality control for MR scanners used for RT purposes is highly recommended.The methods presented in this thesis will be useful in determining the magnitude ofdistortion shifts at different anatomic sites. Utilizing vendor-supplied 3D correc-tion algorithms during image acquisitions is strongly recommended to reduce theeffect of residual system distortions. Subsequently, the use of appropriately highbandwidth in addition to linear or high order shimming depending on availabilitywould reduce the effects of patient-induced susceptibility distortions. Questionsthat needs further probing after this thesis are;

1. How to deal with the propagation of errors due to distortions in imagedatasets used for quantitative maps?

2. how to design QA procedures for an MR-only RT?

5.1.1 Sensitivity Analysis of Quantitative MRI in Radiotherapy

The use of quantitative T1, T2, diffusion and perfusion maps will play a major rolein radiotherapy. These quantitative maps are based on a model that is fitted to a setof images. These images are however not immune to the challenges associated withMRI: image quality and geometric distortions. This means that the quantitativemaps obtained from these images may be flawed. The question therefore is: whatwill be the appropriate trade-off between distortions and MR quantitative imaging inthe radiotherapy setting?

5.1.2 Designing an appropriate QA for MR-only RT

The move towards an MR-only RT would require additional QA activities to com-plement existing MRI QA procedures [81]. This will be necessary in order tomaintain high accuracy, prevent failures due to personnel and patient activities,as well as machine performance failures [81]. This would include among othersthorough and perhaps mandatory regular characterization of geometric accuracytolerable for each scanner. The question is can the long term monitoring of MR

42

discrepancies and analysis provide the needed information to develop an adequate QAprocedure for dedicated MRI-only radiotherapy scanners?

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Bibliography

[1] W. McRobbie, A. E. Moore, J. M. Graves, MRI: From Picture to Proton,,Cambridge University Press, 2017.URL www.cambridge.org/9781107643239

[2] M. Köhler, T. Vaara, M. V. Grootel, R. Hoogeveen, R. Kemppainen,S. Renisch, MR-only simulation for radiotherapy planning treatment plan-ning, Tech. rep. (2015).

[3] L. G. W. Kerkmeijer, C. D. Fuller, H. M. Verkooijen, M. Verheij, A. Choud-hury, K. J. Harrington, C. Schultz, A. Sahgal, S. J. Frank, J. Goldwein, K. J.Brown, B. D. Minsky, M. van Vulpen, The MRI-Linear Accelerator Consor-tium: Evidence-Based Clinical Introduction of an Innovation in RadiationOncology Connecting Researchers, Methodology, Data Collection, QualityAssurance, and Technical Development, Frontiers in Oncology 6 (October)(2016) 1–6. doi:10.3389/fonc.2016.00215.

[4] P. J. Keall, M. Barton, S. Crozier, The Australian Magnetic ResonanceImaging-Linac Program, Seminars in Radiation Oncology 24 (3) (2014)203–206. doi:10.1016/j.semradonc.2014.02.015.URL http://dx.doi.org/10.1016/j.semradonc.2014.02.015

[5] J. J. W. Lagendijk, B. W. Raaymakers, M. van Vulpen, The MagneticResonance Imaging-Linac System, Seminars in Radiation Oncology 24 (3)(2014) 207–209. doi:10.1016/j.semradonc.2014.02.009.URL http://dx.doi.org/10.1016/j.semradonc.2014.02.009

[6] S. Mutic, J. F. Dempsey, The ViewRay System: Magnetic Resonance-Guided and Controlled Radiotherapy, Seminars in Radiation Oncology24 (3) (2014) 196–199. doi:10.1016/j.semradonc.2014.02.008.URL http://dx.doi.org/10.1016/j.semradonc.2014.02.008

45

[7] J. Ferlay, I. Soerjomataram, R. Dikshit, S. Eser, C. Mathers, M. Re-belo, D. M. Parkin, D. Forman, F. Bray, Cancer incidence and mor-tality worldwide: Sources, methods and major patterns in GLOBO-CAN 2012, International Journal of Cancer 136 (5) (2015) E359–E386.doi:10.1002/ijc.29210.

[8] B. W. Stewart, C. P. Wild, World cancer report 2014, World Health Orga-nization (2014) 1–2doi:9283204298.

[9] A. Åberg, J. Ericsson, L. Holmbergg, B. L. Rozell, Cancer Incidence in Swe-den 2011 Cancerförekomst i Sverige 2011, 2012.

[10] L. J. Schreiner, Dosimetry in modern radiation therapy: limitationsand needs, Journal of Physics: Conference Series 56 (2006) 1–13.doi:10.1088/1742-6596/56/1/001.

[11] N. Usmani, F. Foroudi, J. Du, C. Zakos, H. Campbell, P. Bryson,W. J. Mackillop, An evidence-based estimate of the appropriate rate ofutilization of radiotherapy for cancer of the cervix, International Jour-nal of Radiation Oncology Biology Physics 63 (3) (2005) 812–827.doi:10.1016/j.ijrobp.2005.03.025.

[12] A. Brahme, Accurate Description of the Cell Survival and Biological Effectat Low and High Doses and LET’s, Journal of radiation research 52 (2011)389–407.

[13] W. H. Choi, J. Cho, Evolving clinical cancer radiotherapy: Concerns re-garding normal tissue protection and quality assurance, Journal of KoreanMedical Science 31 (2016) S75–S87. doi:10.3346/jkms.2016.31.S1.S75.

[14] J. Bussink, C. M. van Herpen, J. H. Kaanders, W. J. Oyen, PET-CTfor response assessment and treatment adaptation in head and neck can-cer, The Lancet Oncology 11 (7) (2010) 661–669. doi:10.1016/S1470-2045(09)70353-5.

[15] P. Bhatnagar, M. Subesinghe, C. Patel, R. Prestwich, A. F. Scarsbrook, Func-tional imaging for radiation treatment planning, response assessment, andadaptive therapy in head and neck cancer., Radiographics : a review pub-lication of the Radiological Society of North America, Inc 33 (7) (2013)1909–29. doi:10.1148/rg.337125163.URL http://www.ncbi.nlm.nih.gov/pubmed/24224586

46

[16] X. Geets, M. Tomsej, J. A. Lee, T. Duprez, E. Coche, G. Cosnard,M. Lonneux, V. Grégoire, Adaptive biological image-guided IMRT withanatomic and functional imaging in pharyngo-laryngeal tumors: Im-pact on target volume delineation and dose distribution using heli-cal tomotherapy, Radiotherapy and Oncology 85 (1) (2007) 105–115.doi:10.1016/j.radonc.2007.05.010.

[17] P. K. Spiegel, The First Clinical X-ray Made in America-100 years, AmericanJournal of Roentgenology 95 (164) (1995) 241–243.

[18] M. A. Schmidt, G. S. Payne, Radiotherapy planning using MRI, Physicsin Medicine & Biology 60 (22) (2015) R323–R361. doi:10.1088/0031-9155/60/22/R323.

[19] A. L. Chin, A. Lin, S. Anamalayil, B.-k. K. Teo, Feasibility and limitationsof bulk density assignment in MRI for head and neck IMRT treatment plan-ning, Journal of Applied Clinical Medical Physics 15 (5) (2014) 100–111.

[20] J. Korhonen, M. Kapanen, J. Keyrilainen, T. Seppala, L. Tuomikoski,M. Tenhunen, Absorbed doses behind bones with MR image-based dosecalculations for radiotherapy treatment planning., Medical physics 40 (1)(2013) 011701. doi:10.1118/1.4769407.URL http://www.ncbi.nlm.nih.gov/pubmed/23298071

[21] J. H. Jonsson, M. G. Karlsson, M. Karlsson, T. Nyholm, Treatment planningusing MRI data: an analysis of the dose calculation accuracy for differenttreatment regions., Radiation oncology (London, England) 5 (1) (2010) 62.doi:10.1186/1748-717X-5-62.URL http://www.ro-journal.com/content/5/1/62

[22] Y. K. Lee, M. Bollet, G. Charles-Edwards, M. A. Flower, M. O. Leach,H. McNair, E. Moore, C. Rowbottom, S. Webb, Radiotherapy treatmentplanning of prostate cancer using magnetic resonance imaging alone., Ra-diotherapy and oncology 66 (2) (2003) 203–216.URL http://www.ncbi.nlm.nih.gov/pubmed/12648793

[23] L. Koivula, Intensity-based dual model method for generation of syntheticCT images from standard T2-weighted MR images - generalized techniquefor four different MR scanners, Radiotherapy and Oncology (2017) 7–13doi:10.1016/j.radonc.2017.10.011.URL https://doi.org/10.1016/j.radonc.2017.10.011

47

[24] J. M. Edmund, H. M. Kjer, K. Van Leemput, R. H. Hansen, J. A. Andersen,D. Andreasen, A voxel-based investigation for MRI-only radiotherapy of thebrain using ultra short echo times, Physics in Medicine and Biology 59 (23)(2014) 7501–7519. doi:10.1088/0031-9155/59/23/7501.

[25] M. Kapanen, M. Tenhunen, T1/T2*-weighted MRI provides clinically rel-evant pseudo-CT density data for the pelvic bones in MRI-only based ra-diotherapy treatment planning, Acta Oncologica 52 (3) (2013) 612–618.doi:10.3109/0284186X.2012.692883.

[26] H. Arabi, N. Koutsouvelis, M. Rouzaud, R. Miralbell, H. Zaidi, Atlas-guided generation of pseudo-CT images for MRI-only and hybrid PET–MRI-guided radiotherapy treatment planning, Physics in Medicine and Bi-ology 61 (17) (2016) 6531–6552. doi:10.1088/0031-9155/61/17/6531.

[27] J. Sjölund, D. Forsberg, M. Andersson, H. Knutsson, Generating pa-tient specific pseudo-CT of the head from MR using atlas-based re-gression, Physics in Medicine and Biology 60 (2) (2015) 825–839.doi:10.1088/0031-9155/60/2/825.

[28] J. A. Dowling, J. Lambert, J. Parker, O. Salvado, J. Fripp, A. Capp,C. Wratten, J. W. Denham, P. B. Greer, An atlas-based electron den-sity mapping method for magnetic resonance imaging (MRI)-alone treat-ment planning and adaptive MRI-based prostate radiation therapy, Interna-tional Journal of Radiation Oncology Biology Physics 83 (1) (2012) e5–e11.doi:10.1016/j.ijrobp.2011.11.056.URL http://dx.doi.org/10.1016/j.ijrobp.2011.11.056

[29] T. Stanescu, H. S. Jans, K. Wachowicz, B. G. Fallone, Investigation of a 3Dsystem distortion correction method for MR images (12 2009).

[30] W. GRDR, I. Wilson, Photon, Electron, Proton and Neutron InteractionData for Body Tissues. ICRU Report 46 Bethesda, Maryland 1992. 26.

[31] J. Lambert, P. B. Greer, F. Menk, J. Patterson, J. Parker, K. Dahl, S. Gupta,A. Capp, C. Wratten, C. Tang, M. Kumar, J. Dowling, S. Hauville,C. Hughes, K. Fisher, P. Lau, J. W. Denham, O. Salvado, MRI-guidedprostate radiation therapy planning: Investigation of dosimetric accuracyof MRI-based dose planning., Radiotherapy and oncology : journal of theEuropean Society for Therapeutic Radiology and Oncology 98 (3) (2011)330–4. doi:10.1016/j.radonc.2011.01.012.

48

[32] R. Prabhakar, P. K. Julka, T. Ganesh, A. Munshi, R. C. Joshi, G. K. Rath,Feasibility of using MRI alone for 3D radiation treatment planning in braintumors, Japanese Journal of Clinical Oncology 37 (6) (2007) 405–411.doi:10.1093/jjco/hym050.

[33] C. Siversson, F. Nordström, T. Nilsson, T. Nyholm, J. Jonsson,A. Gunnlaugsson, L. E. Olsson, Technical Note: MRI only prostate ra-diotherapy planning using the statistical decomposition algorithm, MedicalPhysics 42 (10) (2015) 6090–6097. doi:10.1118/1.4931417.

[34] M. Hofmann, I. Bezrukov, F. Mantlik, P. Aschoff, F. Steinke, T. Beyer,B. J. Pichler, B. Scholkopf, MRI-Based Attenuation Correction for Whole-Body PET/MRI: Quantitative Evaluation of Segmentation- and Atlas-Based Methods, Journal of Nuclear Medicine 52 (9) (2011) 1392–1399.doi:10.2967/jnumed.110.078949.

[35] M. S. R. Gudur, W. Hara, Q.-T. Le, L. Wang, L. Xing, R. Li, A unifyingprobabilistic Bayesian approach to derive electron density from MRI for radi-ation therapy treatment planning, Physics in Medicine and Biology 59 (21)(2014) 6595–6606. doi:10.1088/0031-9155/59/21/6595.

[36] L. Koivula, L. Wee, J. Korhonen, Feasibility of MRI-only treatment planningfor proton therapy in brain and prostate cancers: Dose calculation accuracyin substitute CT images, Medical Physics 43 (8Part1) (2016) 4634–4642.doi:10.1118/1.4958677.URL http://doi.wiley.com/10.1118/1.4958677

[37] J. Korhonen, M. Kapanen, J. Keyriläinen, T. Seppälä, L. Tuomikoski,M. Tenhunen, Influence of MRI-based bone outline definition errors on ex-ternal radiotherapy dose calculation accuracy in heterogeneous pseudo-CTimages of prostate cancer patients, Acta Oncologica 53 (8) (2014) 1100–1106. doi:10.3109/0284186X.2014.929737.

[38] J. Korhonen, M. Kapanen, J. Keyriläinen, T. Seppälä, M. Tenhunen, A dualmodel HU conversion from MRI intensity values within and outside of bonesegment for MRI-based radiotherapy treatment planning of prostate cancer,Medical Physics 41 (1) (2013) 011704. doi:10.1118/1.4842575.URL http://doi.wiley.com/10.1118/1.4842575

49

[39] M. Kapanen, J. Collan, A. Beule, T. Seppälä, K. Saarilahti, M. Tenhunen,Commissioning of MRI-only based treatment planning procedure for exter-nal beam radiotherapy of prostate., Magnetic resonance in medicine 70 (1)(2013) 127–135. doi:10.1002/mrm.24459.URL http://www.ncbi.nlm.nih.gov/pubmed/22886780

[40] K. Eilertsen, L. Nilsen Tor Arne Vestad, O. Geier, A. Skretting, Asimulation of MRI based dose calculations on the basis of radiother-apy planning CT images, Acta Oncologica 47 (7) (2008) 1294–1302.doi:10.1080/02841860802256426.

[41] V. Hartwig, G. Giovannetti, N. Vanello, M. Lombardi, L. Landini, S. Simi,Biological effects and safety in magnetic resonance imaging: A review, Inter-national Journal of Environmental Research and Public Health 6 (6) (2009)1778–1798. doi:10.3390/ijerph6061778.

[42] E. Kanal, A. J. Barkovich, C. Bell, J. P. Borgstede, W. G. Bradley, J. W.Froelich, J. R. Gimbel, J. W. Gosbee, E. Kuhni-Kaminski, P. A. Larson, J. W.Lester, J. Nyenhuis, D. J. Schaefer, E. A. Sebek, J. Weinreb, B. L. Wilkoff,T. O. Woods, L. Lucey, D. Hernandez, ACR guidance document on MRsafe practices: 2013, Journal of Magnetic Resonance Imaging 37 (3) (2013)501–530. doi:10.1002/jmri.24011.

[43] E. Kanal, M. F. Tweedle, Residual or retained gadolinium: practical implica-tions for radiologists and our patients., Radiology 275 (3) (2015) 630–634.doi:10.1148/radiol.2015150805.

[44] R. G. Price, M. Kadbi, J. Kim, J. Balter, I. J. Chetty, C. K. Glide-Hurst,Technical Note: Characterization and correction of gradient nonlinearityinduced distortion on a 1.0 T open bore MR-SIM, Medical Physics 42 (10)(2015) 5955–5960. doi:10.1118/1.4930245.

[45] J. F. Schenck, The role of magnetic susceptibility in magnetic resonanceimaging: MRI magnetic compatibility of the first and second kinds., Medi-cal physics 23 (6) (1996) 815–50. doi:10.1118/1.597854.

[46] J. A. Lundman, M. Bylund, A. Garpebring, C. Thellenberg Karlsson, T. Ny-holm, Patient-induced susceptibility effects simulation in magnetic reso-nance imaging, Physics and Imaging in Radiation Oncology 1 (2017) 41–45.doi:10.1016/j.phro.2017.02.004.

50

[47] H. Chang, J. M. Fitzpatrick, A Technique for Accurate Magnetic ResonanceImaging in the Presence of Field Inhomogeneities, IEE transactions on med-ical Imaging 11 (3) (1992) 319–329.

[48] A. Janke, H. Zhao, G. J. Cowin, G. J. Galloway, D. M. Doddrell, Use ofspherical harmonic deconvolution methods to compensate for nonlinear gra-dient effects on MRI images, Magnetic Resonance in Medicine 52 (1) (2004)115–122. doi:10.1002/mrm.20122.

[49] L. N. Baldwin, A. Tg, K. Wachowicz, S. D. Thomas, R. Rivest, B. G. Fallone,Characterization , prediction , and correction of geometric distortion in 3 TMR images, Medical Physics (2007) 388–399doi:10.1118/1.2402331.

[50] F.-j. Prott, U. Haverkamp, H. Eich, A. Resch, O. Micke, A.-R. Fischedick,N. Willich, R. Pötter, Effect of Distortions and Asymmetry in MR Imageson Radiotherapeutic Treatment Planning, International journal of cancer.90 (November 1999) (2000) 46–50.

[51] E. Persson, C. Gustafsson, F. Nordström, M. Sohlin, A. Gunnlaugsson,K. Petruson, N. Rintelä, K. Hed, L. Blomqvist, B. Zackrisson, T. Ny-holm, L. E. Olsson, C. Siversson, J. Jonsson, MR-OPERA – A Multi-center/multi-vendor validation of MRI-only prostate treatment planningusing synthetic CT images, International Journal of Radiation Oncol-ogy*Biology*Physicsdoi:10.1016/j.ijrobp.2017.06.006.

[52] C. Gustafsson, F. Nordström, E. Persson, J. Brynolfsson, L. E. Olsson, As-sessment of dosimetric impact of system specific geometric distortion in anMRI only based radiotherapy workflow for prostate, Physics in Medicine &Biology 62 (2017) 2976–2989. doi:10.1088/1361-6560/aa5fa2.

[53] S. J. Doran, L. Charles-edwards, S. A. Reinsberg, A complete distortion cor-rection for MR images : I . Gradient warp correction, Physics in medicineand biology 50 (2005) 1343–1361. doi:10.1088/0031-9155/50/7/001.

[54] S. F. Tanner, D. J. Finnigan, V. S. Khoo, P. Mayles, D. P. Dearnaley, M. O.Leach, Radiotherapy planning of the pelvis using distortion corrected MRimages: the removal of system distortions., Physics in medicine and biology45 (8) (2000) 2117–2132. doi:10.1088/0031-9155/45/8/305.

51

[55] R. Mallozzi, J. Gunter, J. C. Jack, J. Levy, D. Blezek, Phantom-Based Eval-uation of Gradient Nonlinearity for Quantitative Neurological MRI Stud-ies, Proceedings 14th Scientific Meeting, International Society for MagneticResonance in Medicine 14 (2006) 1364.

[56] J. Sun, J. Dowling, P. Pichler, F. Menk, D. Rivest-Henault, J. Lambert,J. Parker, J. Arm, L. Best, J. Martin, J. W. Denham, P. B. Greer, MRI simula-tion: end-to-end testing for prostate radiation therapy using geometric pelvicMRI phantoms, Physics in Medicine and Biology 60 (8). doi:10.1088/0031-9155/60/8/3097.

[57] W. M. Tavares, F. Tustumi, C. Da Costa Leite, L. F. Gamarra, E. Amaro,M. J. Teixeira, E. T. Fonoff, An image correction protocol to reduce dis-tortion for 3-T stereotactic MRI, Neurosurgery 74 (1) (2014) 121–126.doi:10.1227/NEU.0000000000000178.

[58] D. Wang, W. Strugnell, G. Cowin, D. M. Doddrell, R. Slaughter,Geometric distortion in clinical MRI systems Part I: evaluation usinga 3D phantom., Magnetic resonance imaging 22 (9) (2004) 1211–21.doi:10.1016/j.mri.2004.08.012.

[59] T. M. kawanaka Akira, Estimation of static magnetic field and gradient fieldsfrom NMR image, Physics 871.

[60] T. Mizowaki, Y. Nagata, K. Okajima, M. Kokubo, Y. Negoro, N. Araki,M. Hiraoka, Reproducibility of geometric distortion in magnetic resonanceimaging based on phantom studies, Radiotherapy and Oncology 57 (2)(2000) 237–242. doi:10.1016/S0167-8140(00)00234-6.

[61] T. Sumanaweera, S. Napel, G. Glover, S. Song, Quantification of the geo-metric accuracy of MRI in tissue: a new approach using MRI itself, 1993IEEE Conference Record Nuclear Science Symposium and Medical ImagingConference (1993) 1789–1793doi:10.1109/NSSMIC.1993.373600.

[62] M. M. Breeuwer, M. Holden, W. Zylka, Detection and correction of geo-metric distortion in 3D MR images, Medical Imaging 2001 4322 (February)(2001) 1110–1120. doi:10.1117/12.430986.

[63] M. Ahmed, M. Schmidt, A. Sohaib, C. Kong, K. Burke, C. Richardson,M. Usher, S. Brennan, A. Riddell, M. Davies, K. Newbold, K. J. Har-

52

rington, C. M. Nutting, The value of magnetic resonance imaging in tar-get volume delineation of base of tongue tumours - A study using flex-ible surface coils, Radiotherapy and Oncology 94 (2) (2010) 161–167.doi:10.1016/j.radonc.2009.12.021.URL http://dx.doi.org/10.1016/j.radonc.2009.12.021

[64] D. Wang, D. M. Doddrell, G. Cowin, A novel phantom and method forcomprehensive 3-dimensional measurement and correction of geometric dis-tortion in magnetic resonance imaging, Magnetic Resonance Imaging 22 (4)(2004) 529–542. doi:10.1016/j.mri.2004.01.008.

[65] Z. Caramanos, V. S. Fonov, S. J. Francis, S. Narayanan, G. B. Pike,D. L. Collins, D. L. Arnold, Gradient distortions in MRI: Char-acterizing and correcting for their effects on SIENA-generated mea-sures of brain volume change, NeuroImage 49 (2) (2010) 1601–1611.doi:10.1016/j.neuroimage.2009.08.008.URL http://dx.doi.org/10.1016/j.neuroimage.2009.08.008

[66] D. Mah, M. Steckner, A. Hanlon, G. Freedman, B. Milestone, R. Mitra,H. Shukla, B. Movsas, E. Horwitz, P. P. Väisänen, G. E. Hanks, MRI sim-ulation: effect of gradient distortions on three-dimensional prostate can-cer plans, Int. J. Radiation Oncology Biol. Phys. 53 (3) (2002) 757–765.doi:10.1016/S0360-3016(02)02782-7.

[67] P. Jezzard, R. S. Balaban, Correction for geometric distortion in echo planarimages from B0 field variations, Magnetic Resonance in Medicine 34 (1)(1995) 65–73. doi:10.1002/mrm.1910340111.URL http://dx.doi.org/10.1002/mrm.1910340111

[68] R. Cusack, M. Brett, K. Osswald, An Evaluation of the Use of MagneticField Maps to Undistort Echo-Planar Images, NeuroImage 142 (18) (2003)127–142. doi:10.1006/nimg.2002.1281.

[69] M. A. Moerland, R Beersma, R. Bhagwandien, H. K. Wijredeman, C. J. G.Bakker, Analysis and correction of geometric distortions in 1 . 5 T magneticresonance images for use in radiotherapy treatment planning, Phys. Med.Biol 40 (1995) 1651–1664.

[70] C. Juchem, R. de Graaf, B0 magnetic field homogeneity and shimming forin vivo magnetic resonance spectroscopy, Analytical Biochemistry (2016) 1–13doi:10.1016/j.ab.2016.06.003.

53

[71] H. Wang, J. Balter, Y. Cao, Patient-induced susceptibility effect on geo-metric distortion of clinical brain MRI for radiation treatment planning ona 3T scanner, Physics in Medicine and Biology 58 (3) (2013) 465–477.doi:10.1088/0031-9155/58/3/465.

[72] F. J. Prott, U. Haverkamp, N. Willich, A. Resch, U. Stöber, R. Pötter,Comparison of imaging accuracy at different MRI units based on phan-tom measurements, Radiotherapy and Oncology 37 (3) (1995) 221–224.doi:10.1016/0167-8140(95)01657-0.

[73] L. R. Schad, H.-H. Ehricke, B. Wowra, G. Layer, R. Engenhart, H.-U.Kauczor, H.-J. Zabel, G. Brix, W. J. Lorenz, Correction of spatial distortionin magnetic resonance angiography for radiosurgical treatment planning ofcerebral arteriovenous malformations, Magnetic Resonance Imaging 10 (4)(1992) 609–621. doi:https://doi.org/10.1016/0730-725X(92)90012-O.

[74] A. Walker, P. Metcalfe, G. Liney, V. Batumalai, K. Dundas, C. Glide-hurst,G. P. Delaney, M. Boxer, M. L. Yap, J. Dowling, D. Rivest-henault, E. Pog-son, MRI geometric distortion : Impact on tangential whole-breast IMRT,Journal of Applied Clinical Medical Physics 17 (5) (2016) 7–19.

[75] G. J. Kutcher, L. Coia, M. Gillin, W. F. Hanson, S. Leibel, R. J. Morton, J. R.Palta, J. A. Purdy, L. E. Reinstein, G. K. Svensson, M. Weller, L. Wingfield,Comprehensive QA for Radiation Oncology: Report of AAPM Task GroupNo.40, Medical Physics 21 (4) (1994) 581–618.

[76] B. Petersch, J. Bogner, A. Fransson, T. Lorang, R. Pötter, Effects of ge-ometric distortion in 0.2T MRI on radiotherapy treatment planning ofprostate cancer., Radiotherapy and oncology : journal of the EuropeanSociety for Therapeutic Radiology and Oncology 71 (1) (2004) 55–64.doi:10.1016/j.radonc.2003.12.012.

[77] T. C. Cosmus, M. Parizh, Advances in whole-body MRI magnets, IEEETransactions on Applied Superconductivity 21 (3 PART 2) (2011) 2104–2109. doi:10.1109/TASC.2010.2084981.

[78] S. L. Breen, T. Craig, A. Bayley, B. O’Sullivan, J. Kim, D. Jaf-fray, Spinal cord planning risk volumes for intensity-modulatedradiation therapy of head-and-neck cancer, International Journalof Radiation Oncology*Biology*Physics 64 (1) (2006) 321–325.doi:https://doi.org/10.1016/j.ijrobp.2005.08.038.

54

[79] G. P. Liney, M. a. Moerland, Magnetic resonance imaging acquisition tech-niques for radiotherapy planning., Seminars in radiation oncology 24 (3)(2014) 160–8. doi:10.1016/j.semradonc.2014.02.014.

[80] D. Thwaites, Accuracy required and achievable in radiotherapy dosime-try: have modern technology and techniques changed our views?,Journal of Physics: Conference Series 444 (1). doi:10.1088/1742-6596/444/1/012006.

[81] E. S. Paulson, B. Erickson, C. Schultz, X. A. Li, B. Erickson, C. Schultz,X. A. Li, Comprehensive MRI simulation methodology using a dedicatedMRI scanner in radiation oncology for external beam radiation treatmentplanning Comprehensive MRI simulation methodology using a dedicatedMRI scanner in radiation oncology for external beam radi, Medical physics28 (2015). doi:10.1118/1.4896096.URL http://dx.doi.org/10.1118/1.4896096