strategies for preventing setup errors and …
TRANSCRIPT
STRATEGIES FOR PREVENTING SETUP ERRORS AND ENHANCING TREATMENT ACCURACY TOWARD ADAPTIVE MOTION MANAGEMENT IN RADIATION
THERAPY
By
PINGFANG TSAI
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2019
© 2019 PingFang Tsai
To my beloved families
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ACKNOWLEDGMENTS
First, I would like to appreciate Dr. Chihray Liu, who always has faith in me and
give me all the freedom to explore my research. Dr. Liu always provides the best
resources available to support me in excelling in the goal. During my Ph.D. study, he
had not only taught me about the Philosophy of Doctor but also the Philosophy of Life in
many occasions. Also, Dr. Bo Lu is just like my big brother, always gives me logical
advice and helps me in any way possible. He always clears the way through to help me
see the light at the end of the tunnel. Dr. Guanghua Yan is my go-to-person when I
need someone to discuss; his calm demeanor and patience are the most valuable
characteristics that I admired. Often, he can sit down with me to look at my code or find
the root cause together; his advice is always like a key to unlock the puzzle. My external
committee member, Dr. Hongcheng Liu, provided his insights on the mathematical
concepts with his time and is always encouraging. Moreover, I want to express my
gratitude to Dr. Ying-Chao Hung, who is a professor in the department of statistics. He
guides me through statistical concepts and shares his knowledge in his specialty
without asking for anything in return. There are many colleagues that I would like to
show my gratitude, the therapist team, Ji-Yeon Park, Dr. Jonathan Li, Dr. Darren Kahler,
Dr. Jian Wu, Brendon Barraclough, Sharon Lebron, Nick Potter, Karl Mund, Haitham
Alahmad, and Jacqueline Andreozzi. With their offer along my Ph.D. journey, they
make the life merrier and the steps easier. I could not be more grateful to have such a
great team while everyone is always ready for help.
Last but not least, I would like to acknowledge my beloved families. With their
unconditional support, they allow me to have the opportunity to pursue my dream. I
certainly cannot do this alone without their love and inspiration.
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TABLE OF CONTENTS page
ACKNOWLEDGMENTS .................................................................................................. 4
LIST OF TABLES ............................................................................................................ 7
LIST OF FIGURES .......................................................................................................... 8
LIST OF ABBREVIATIONS ........................................................................................... 10
ABSTRACT ................................................................................................................... 14
CHAPTER
1 INTRODUCTION ...................................................................................................... 16
General Background ............................................................................................... 16
Overall Workflow in Radiation Therapy ................................................................... 18 Evolution of Motion Management Methods ............................................................. 19 Tracking and Imaging Modalities for Tumor Verification ......................................... 21
Review of Literatures .............................................................................................. 23 Methods to Prevent Setup Errors ..................................................................... 23
Methods to Enhance Treatment Quality ........................................................... 25 Study Objectives ..................................................................................................... 27
2 A SELF-CHECKING TREATMENT COUCH COORDINATE CALCULATION SYSTEM IN RADIOTHERAPY ............................................................................... 31
Background ............................................................................................................. 31 Materials and Methods............................................................................................ 33
Reference BB-based Calculation Method......................................................... 33
DICOM Coordinate-Based Calculation Method ................................................ 37 A Self-Checking Couch Coordinate Calculation System .................................. 38 Data Collection and Analysis ............................................................................ 40
Results .................................................................................................................... 41 Discussion .............................................................................................................. 43 Conclusions ............................................................................................................ 49
3 OVERVIEW OF THE STATISTICAL AND MATHEMATICAL CONCEPTS ................ 58
Adaptive Z-Normalization ........................................................................................ 58 Principal Component Analysis ................................................................................ 59 Singular Value Decomposition ................................................................................ 60
Singular Spectrum Analysis .................................................................................... 61
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4 TUMOR PHASE RECOGNITION BY LOCAL PRINCIPAL COMPONENT WITH MULTIVARIATE SINGULAR SPECTRUM ANALYSIS FROM CONE-BEAM TOMOGRAPHY PROJECTIONS AND EXTERNAL SURROGATES ..................... 68
Background ............................................................................................................. 68 Materials and Methods............................................................................................ 72
Raw Data Acquisition for Internal and External Signals ................................... 72 Acquisition for internal signal using CBCT ................................................. 72
Acquisition for external signal using OTS .................................................. 72 Synchronization between internal and external data .................................. 73
Tumor Phase Reconstruction Algorithm Using both External and Internal Signal ............................................................................................................ 73
Amsterdam Shroud (AS) image generating using CBCT projections ......... 73
Initial respiratory waveform extraction using Local Principal Component Analysis (LPCA) ...................................................................................... 75
Final respiratory waveform reconstruction using external surrogate information .............................................................................................. 76
LPCA-MSSA workflow ............................................................................... 79 Data Collection and Analysis ............................................................................ 80
Phantom study ........................................................................................... 80
Patient study .............................................................................................. 81 Results .................................................................................................................... 82
Phantom Study ................................................................................................. 82 Patient Study .................................................................................................... 84
Discussions ............................................................................................................. 84
Conclusions ............................................................................................................ 89
5 REFINE RESPIRATORY WAVEFORM RESULT .................................................... 102
Discriminate Type of the Respiratory Waveform ................................................... 103 Advanced Trend Curve Filtering using Instantaneous Frequency ........................ 104
6 CONCLUSIONS ....................................................................................................... 112
Summary .............................................................................................................. 112 Future Works ........................................................................................................ 113
LIST OF REFERENCES ............................................................................................. 114
BIOGRAPHICAL SKETCH .......................................................................................... 121
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LIST OF TABLES
Table page 2-1 Uncertainty of the CT scanner’s DICOM coordinate system evaluated with
patient CT scans. ................................................................................................ 55
4-1 The phase discrepancy and time accuracy of the extracted respiratory waveform compared with the reference waveform for lung patients. .................. 99
4-2 The variance distribution (%) of the principal components for each patient. ..... 100
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LIST OF FIGURES
Figure page 1-1 A linac accelerator equipped with a couch, gantry, EPID, and CBCT system. ... 29
1-2 The extracted respiratory waveform result from literatures using Local principal component analysis methods. .............................................................. 30
2-1 Ball bearings embedded couch design. .............................................................. 51
2-2 The self-checking treatment couch coordinate (TCC) calculation system with two methods. ...................................................................................................... 52
2-3 Workflow of the self-checking couch coordinate calculation system. .................. 53
2-4 Uncertainty of the CT scanner’s DICOM coordinate system evaluated by scanning the CT Couch top at various vertical and longitudinal positions. ......... 54
2-5 Accuracy of the two treatment couch coordinate calculation methods, evaluated with treatment couch coordinates determined with CBCT on the first day of treatment. .......................................................................................... 56
2-6 Deviation of the calculated treatment couch coordinates (TCCs) over the full treatment course. ................................................................................................ 57
3-1 A demonstration of how the principal component analysis from the sensor coordinates to data-centric coordinate in the principal component space. ......... 65
3-2 Process of singular value decomposition of a two-dimensional matrix. .............. 65
3-3 An example of a time series processed after singular spectrum analysis. .......... 66
3-4 The diagram displays the steps involved in obtaining the reconstructed time series through singular spectrum analysis. ......................................................... 66
3-5 Illustrate the process of forming the trajectory matrix (Y) for a time series Xt: t = 1… , N. ............................................................................................ 67
4-1 The experiment design for our study. ................................................................. 91
4-2 Tumor- Amsterdam Shroud image generation.................................................... 92
4-3 Apply Local principal component analysis (LPCA) on Tumor-Amsterdam Shroud image. .................................................................................................... 93
4-4 The grand block covariance C structures for multivariate singular spectrum analysis (MSSA). ................................................................................................ 93
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4-5 Workflow for the LPCA-MSSA algorithm ............................................................ 94
4-6 Simulation of anatomic obstructions, including hearts, ribs and other normal tissues, on a QUASARTM respiratory motion phantom. ...................................... 95
4-7 Clinical lung patient selections............................................................................ 95
4-8 A twelve breathes per minute sinusoidal waveform analyzed in power spectrum density with log scale in the frequency domain. .................................. 96
4-9 The sensitivity of LPCA only and LPCA-MSSA method with ten repeated phantom cone-beam tomography scans without any anatomic obstructions. ..... 96
4-10 Examine the robustness of the multivariate singular spectrum analysis (MSSA) algorithm where the altered external surrogate waveform and the preliminary tumor LPCA waveform were input in the MSSA to obtain the final tumor LPCA-MSSA result. .................................................................................. 97
4-11 A cardiac artifact waveform with Rando® phantom slabs. The red dash line indicates the ground truth signal from the optical tracking system...................... 98
4-12 The reconstructed waveform compared to the reference waveform with the variance percentage (%) of each principal component (PC) displayed in a bar chart.. ............................................................................................................... 101
5-1 Workflow to refine the final respiratory waveform. ............................................ 106
5-2 Detect the irregularity of a respiratory waveform. ............................................. 107
5-3 Nine decomposed reconstructed components (RC) from Patient ID 4 after applying MSSA. ................................................................................................ 108
5-4 Result comparison of LPCPA, LPCA-MSSA, and instantaneous frequency selection with the reference waveform for patient ID 4. .................................... 109
5-5 Nine decomposed reconstructed components (RC) from Patient ID 8 after applying MSSA. ................................................................................................ 110
5-6 Result comparison of LPCPA, LPCA-MSSA, and instantaneous frequency selection with the reference waveform for patient ID 8. .................................... 111
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LIST OF ABBREVIATIONS
𝐴𝑁 Adaptive z-normalization Amsterdam Shroud image
𝐴𝜎 Standard deviation filter
𝑒𝑖 ith orthogonal eigenvectors
𝑓𝑖𝑛𝑠𝑡(𝑡) Instantaneous frequency at time t
∑ Non-zero singular values
µ Mean
1D One-dimensional
2D Two-dimensional
3D Three-dimensional
4D-CBCT Four-dimensional cone-beam computed tomography
4D-CT Four-dimensional computed tomography
A Amsterdam Shroud image
AS Amsterdam Shroud
BB Ball Bearing
C Covariance matrix
CBCT Cone Beam Computed Tomography
CC Cranial-Caudal
CCW Counterclockwise
CI Confidence Interval
CT Computed Tomography
CW Clockwise
DC DICOM Coordinate
DICOM Digital Imaging and Communications in Medicine
DRR Digitally Reconstructed Radiograph
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DTS Digital Tomosynthesis
DTT Dynamic Tumor Tracking
EOF Empirical orthogonal function
EPID Electronic Portal Imaging Device
EVD Eigenvalue decomposition
FOV Field-Of-View
FT Fourier Transform
IA Intensity analysis
IGRT Image-Guided Radiation Therapy
ITV Irradiated Tumor Volume
KV Kilo-Voltage
LPCA Local Principal Component Analysis
M Embedding dimension
MLC Multi-Leaf Collimator
MRgRT Magnetic resonance-guided radiation therapy
MSSA Multivariate Singular Spectrum Analysis
MV Mega-Voltage
N Number of observations
OBI On-Board Imaging
OS Offset
OTS Optical Tracking system
P Number of variables
PC Principal Component
PCA Principal Component Analysis
POI Point-Of-Interest
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PVC Polyvinyl chloride
QA Quality Assurance
R&V Record and Verify
RC Reconstructed Component
RCC Reference Couch Coordinate
RMS Root-Mean-Square
RO-ILS Radiation Oncology Incident Learning System
RPM Real-time position management
SD Standard Deviation
SI Superior-Inferior
SQL Structured Query Language
SSA Singular Spectrum Analysis
SVD Singular Spectrum Analysis
TCC Treatment Couch Coordinate
TPS Treatment Planning System
U Left-singular vectors
V Right-singular vectors
V The eigenvectors matrix
W Window width
X A time series
𝑋𝑙(t) The 𝑙th channel of the time series and observation time at t
XVI X-ray Volume Imaging
Y Trajectory matrix of X in the univariate case
𝕐 Trajectory matrix of {𝑋𝑙(t)} in the multivariate case
λ Non-negative eigenvalue
13
σ Standard deviation
𝑃(𝑡, 𝑓) Spectrogram power spectrum for frequency f at time t
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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
STRATEGIES FOR PREVENTING SETUP ERRORS AND ENHANCING TREATMENT
ACCURACY TOWARD ADAPTIVE MOTION MANAGEMENT IN RADIATION THERAPY
By
PingFang Tsai
December 2019
Chair: Chihray Liu Cochair: Bo Lu Major: Medical Sciences – Medical Physics
Patient immobilization and prevention of gross setup errors have been the initial
key steps to deliver the radiation dose to the designated treatment area to assure the
patient radiation safety throughout the treatment course. It had been shown that there
are still several pathways that can lead to patient setup errors, and image-guided
strategies are commonly used to ensure the reproducibility of the treatment setup.
Nowadays, cone-beam computed tomography (CBCT) has become the most common
image-guided technique as a pre-treatment validation. It provides us the spatial
information to correct the patient’s treatment positions. For moving tumors, a four-
dimensional CBCT (4D-CBCT) can be used to exam moving tumor region. However,
there are some inherent factors that will affect the accuracy of the phase-sorting 4D-
CBCT. With 4D-CBCT, the tumor may not be clearly seeing, and the phase patterns
between the surrogates and tumors are not necessary to be congruent.
This dissertation provides methods preventing the setup error and improving the
accuracy of identifying the tumor phase for 4D-CBCT. The objective one is to design a
self-checking system to calculate treatment couch coordinates (TCC) before the
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commencement of the actual treatment and streamline the patient setup process. The
objective two and three are to develop a method for the tumor phase tracking from
CBCT projection images, which can recover the primary oscillation components of
tumor motion using the combined information from CBCT projection images and
external surrogates. The proof of principles and the feasibility on patients were
investigated with phantom studies in objective two and patient studies in objective three.
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CHAPTER 1 INTRODUCTION
General Background
Radiation therapy has been one of the mainstream adjuvant therapy to treat the
patient with cancers in conjunction with chemotherapy or surgery. It uses x-rays,
gamma rays, or other sources of radiation to destroy cancer cells while preserving
healthy tissue cells. Commonly, the total prescribed radiation dose was distributed into
fractionation, in which the patient received a fraction of the total prescribed dose on
different days to differentiate radiobiological responses between tumor and healthy
tissues. The delivery of radiation often required sophisticated equipment that can
accurately control the radiation beam position, beam intensity with prompt on and off
radiation beam capability. The most common machine for radiation therapy is the linear
accelerator shown in Figure 1-1, which it is capable of delivery either electron beams or
mega-voltage (MV) x-ray beams with various energy selections. The x-ray beam
production devices are mounted in the stand and the gantry. A linac accelerator gantry
can rotate within a 360-degree arc around the patient to enable different beam angles to
be aimed at the patient. The center of the rotation is defined as isocenter. Additionally, it
is crucial to confirm the radiation is delivered to the intended treatment area to ensure
the patient’s safety; thus, the pre-treatment image verification is a necessary step
before proceeding to the treatment in modern radiotherapy.
In order to perform pre-treatment image verification, a conventional linac
accelerator is equipped with the auxiliary electronic portal imaging devices (EPID),
which can acquire MV images for patient’s treatment apertures and isocenter location
verification. The digitally reconstructed radiograph (DRR) generated from simulation
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computed tomography (CT) is used to compare with the MV images for any translational
shifts. Once the change is confirmed, the couch that the patient is laying on can perform
the transformations to the updated position. The MV images, called portal verification
films, contains mainly the bony structures of the patient, central location with scales,
and the shape of the treatment aperture using multi-leaf collimators (MLC) or block.
Due to the nature of the human non-rigid body dynamics, the internal organ
position or shape varies daily. The patient’s body also has changed due to weight loss
or different filling within the individual organ; the variation results in changes in
surrounding anatomic organ location relative to the tumor region. Therefore, to ensure
the integrity of the treatment in the aspect of patient safety and treatment quality, it is
essential to have the capability to observe those changes in the internal organs.
It is not until recent years, the linac-integrated On-Board Imaging (OBI) is readily
available and commercialized as a standard extension to the existing linac accelerator.
The OBI consists of a kilovoltage (KV) x-ray source and a KV flat panel detector, which
were located perpendicular to the MV x-ray beams as shown in Figure 1-1. The OBI
system can acquire sequential 2D KV images as known as fluoroscopy or x-ray volume
imaging (XVI) as known as the cone-beam computed tomography (CBCT). The CBCT
images offer the internal geometry of the soft tissue, bony structures, and the shape of
the external body. In addition, when it comes to treating the moving tumor regions (e.g.,
lung), it can reconstruct the 4D-CBCT images which typically sorted into ten phases per
respiratory cycle and displayed in a dynamic loop motion. The 4D-CBCT not only
contains the essential spatial information about bone and soft-tissue but also provides
temporal information about the tumor’s motion range.
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In the next section, we will review the typical workflow in radiation therapy and
what kind of challenges we might encounter and how we combat those issues with the
current state-of-art technologies.
Overall Workflow in Radiation Therapy
There are several steps involved from preparation to treatment to ensure the
integrity of the radiation treatment. In preparation for the patient’s radiation therapy, the
first step is the CT simulation. The simulation procedure involves in: (1) finalizing the
patient’s treatment position with patient-specific immobilization devices with the effort to
reproduce the patient’s treatment position at the treatment machine; (2) obtaining a
simulation three-dimensional (3D) volumetric imaging scan (e.g. computed tomography
(CT)) for treatment planning purpose; (3) establishing a temporary origin on patient’s
skin (with three points set up) for daily treatment setup up reference. The simulation CT
scan helps us gain knowledge of the internal organ and patient’s geometry; thus we can
design a customized treatment plan with optimal gantry angles and modulate beam
intensities to deliver the radiation dose while sparing the healthy tissues.
On the first day of the treatment, the radiation therapist (1) set up the patient:
set up the patient on the treatment couch with the customized immobilization devices;
(2) align the patient: with the skin tattoo origin that was created during simulation with
three points setup to correct any patient body rotation; (3) perform the translational
shifts: based on the instruction from treatment planning from skin tattoo to the updated
isocenter position; (4) the pre-treatment verification: x-ray images are acquired to
compare with the simulation CT images or DRR.
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In summary, the ultimate goals are to reproduce the patient position throughout
the treatment course, deliver the radiation beam to the intended treatment area, and to
monitor any geometry or motion range changes if possible.
In reality, as many human errors might have introduced during the patient setup
process or the patient’s condition may have changed over time due to weight loss or
respiratory pattern change. There must be a mechanism in action to prevent these
human errors and assess patient’s changes. All these uncertain elements could affect
the treatment outcome and how accurately we can deliver the radiation dose to the
tumor region and further reduce the irradiated area if possible. On top of these, it is
particularly challenging while treating a moving target area.
In the next section, we will discuss what is the techniques that are available to
manage the radiation treatment in order to support the ultimate goals that we discussed
earlier.
Evolution of Motion Management Methods
Various motion management approaches1,2 has been developed to improve the
radiation delivery accuracy to the moving target area, especially the lung region. Motion
management in the lung region is particularly essential and challenging in radiation
therapy. The reason is that the tumor moves with the patient’s respiratory cycles, which
lead to one of the primary sources of errors during radiation therapy. If the radiation is
not delivered to the intended area, it could cause harm to the surrounding healthy
tissues and eventually result in undesirable treatment outcomes and side effects.
The fact that the motion management approaches can be categorized into two
stages, pre-treatment and during treatment. In the following section, we will briefly
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introduce the motion management methods are available for lung region in clinical
practice.
At present, the most common pre-treatment motion management is using the 3D-
or 4D-CBCT images. It is widely available and easy access to most of the clinics to
observe any patient changes in geometry and even can be used for adaptive treatment
planning in the future. For during-treatment motion management, it often required
image-based verification to observe any internal body dynamic changes.
There two major tumor tracking strategies can be employed during the treatment:
(1) dynamic tumor tracking (DTT) at all time while radiation beam location is adjusted
according to the tumor location; (2) triggering the radiation beam on only when the
tumor falls in the intended treatment area. In order to perform DTT, the tumor needs to
be tracked using x-rays at most or all the time during treatment delivery.
There are two main elements that need to complement each other for DTT: One
is clear tumor location indication at all times; second is the machine capability to adjust
to the change at all times. However, the lung tumor is often in fuzzy representation in
the medical image. To apply DTT, the implanted marker is often optimal in order to have
a clear indicator for tumor location for beam aiming adjustment. Furthermore, the DTT
required a specially designed treatment machine (e.g., VERO® by BrainLab or
Cyberknife® by Accuray3), which can steering or adjusting the radiation beam at all
time. Unfortunately, it is not widely available to most of the clinics. Therefore, the
second approach by triggering the radiation beam as desired, respiratory gating, has
become the most common and accessible approach for motion management.
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The respiratory gating motion management can trigger the radiation beam based
on the patient’s phase status of the respiratory cycle. The advantage is the patient can
be in a free-breathing condition, and it is available to most of the linac accelerator
vendors. To fulfill the respiratory gating, it demands an integrated interface with the
treatment machine, which requires a signal that provides indicators for the patient’s
respiratory cycle in order to control the triggering of the radiation beam.
In the following section, we are going to outlines what is the tracking or imaging
modalities available for achieving tumor tracking or respiratory gating in order to perform
motion management for the lung patient. Similarly, we will discuss what might be the
challenges.
Tracking and Imaging Modalities for Tumor Verification
Directly tracing the lung tumor and extracting its phase information in real-time
has never been an easy task for radiation therapy society. X-ray based image
modalities, such as mega-voltage (MV) electronic portal imaging device (EPID) images4-
7 or kilo-voltage (KV) images8-13, can provide real-time two-dimensional (2D) anatomy
information in a fluoroscopy or cine mode. However, the MV EPID image is often limited
by its poor contrast and blockage by the multileaf collimator (MLC) during the treatment;
thus KV image approaches had drawn much attention by the majority of the studies.
Moreover, x-ray images are lack of contrast between tumor and surrounding tissues in
general. Also, multiple anatomic structures overlapping on the 2D image could result in
a weak and noisy extracted tumor signal, especially for images in the nearly lateral view
angles14-20.
Ultrasound images can potentially provide tumor information in real-time.
However, its implementation is restricted by detection depth, transmission medium, and
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image quality. It can be used for tumor tracking, such as abdominal or pelvis area21-24,
but the application to the lung region is currently limited to the diaphragm as a surrogate
tracking8. Magnetic resonance-guided radiation therapy (MRgRT) can provide a decent
contrast between tumor and surrounding tissue25. Nevertheless, the availability of the
MRgRT machine to most of the clinics is still limited due to the high cost and slow
availability. Even the real-time MRI tumor tracking has drawn much attention in recent
years, and it is still in the research stage26.
Due to the fuzzy features between the tumor and the surrounding healthy
tissues. There are two primary approaches to tackle the challenges: (1) use implant
surrogate in the tumor or near the tumor to improve visibility; and (2) improve the image
quality of current image modalities.
To apply the first approach, it is ideal for implementing the fiducial markers27-30 or
electromagnetic transponder beacons31-33 in the tumor region to know the exact tumor
motion during the treatment. However, it involved invasive procedures, in which the
patients may experience the risk of pneumothorax34,35 or pulmonary hemorrhage36, or
marker migration37,38. Thus, the markerless approach is preferred. Ultimately,
markerless image-guided internal tumor tracking is the optimal solution to ensure the
quality of the treatment throughout the treatment course.
The majority of the studies for markerless tumor tracking shows poor tumor
contrast and limit the angle of selection for tumor visibility. Thus, there are some studies
focused on either improving the image contrast or utilizing multiple imaging modalities to
complement with each other, including dual-energy imaging20,39-41, digital tomosynthesis
(DTS) 42-47, or MV-KV x-ray imaging48,49. Moreover, prior knowledge 4D-CBCT images
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for template matching methods9,10,12,50 are also popular in recent markerless tumor
tracking literature; thus, the algorithm can make a quick judgment of the state of the
tumor. Once the image references or templates were established, periodic image
verification by the projection or arc images is acquired by the user’s choice to observe
the internal tumor information during the treatment session. Summarizing, the prior
knowledge serves as a continuing profile monitoring indicator or baseline, and the
projection images verification serves as a verification of the condition to the internal
tumor during the treatment.
To conclude this section, the most common motion management strategy in a
combination of the treatment machines is the respiratory gating with a linac accelerator
using either KV images or CBCT images in most of the clinics. However, due to the
poor tumor visibility, the limitation of limit angle selection for real-time tumor tracking
remains unsolved.
Review of Literatures
In this section, we are going to review literature in two aspects to improve from
the current clinical workflow and recent research development. The first aspect is on
how can we improve the present patient setup process and further minimize the
possibility of a patient setup error. The second aspect is on what is the current
challenges we encounter on tumor tracking and what are the investigator’s approaches
for improving the treatment quality.
Methods to Prevent Setup Errors
Several investigators had examined the use of various approaches to minimize
the impact of position error from simulation to the daily treatment, including site-specific
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tolerance table51-54, site-specific immobilization devices indexing55, fixed couch-top
reference positions56. The site-specific tolerance table method involves setting a site-
specific tolerance for different treatment sites depending on the setup uncertainties of
the treatment sites. This information is included in the treatment field in the record and
verify (R&V) system (e.g., MOSAIQ® by Elekta or ARIA® by Varian), which is the
interface to download the treatment field parameters for the machine. However, the
shortfalls of this method include it only serves as a warning without patient-specific
standard and the treatment couch coordinate (TCC) is unknown before the treatment.
Consequently, it still results in patient setup error as the couch coordinate can be
overwritten by the operator.
For this reason, researchers establish methods to pre-calculate the patient-
specific TCC before the commencement of the treatment. Saenz et al.55 reported a
method for patient-specific couch coordinates prediction using indexed immobilization
devices. Their method relied on a radiographically visible landmark on the
immobilization device. The baseline couch coordinates (the couch coordinates when the
landmark was positioned at the treatment room isocenter) were first determined. Then
the displacement of the planned treatment isocenter relative to the landmark was used
to adjust the baseline table coordinates to obtain TCC for the patient. Overall, 86% of
their predictions were correct within 2 cm, and the mean error was under 0.1 cm, but the
standard deviation was 1.47 cm.
However, Saenz et al.’s method was dictated by the immobilization device. For
devices without a radiographically visible landmark, the method failed to predict couch
coordinates. Sueyoshi et al.56 reported a slightly different approach. Instead of using
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landmarks on the immobilization device, they used a set of fixed couch-top positions
(e.g., indexing notches of the couch-top) as the reference. Their method can be applied
with any indexed immobilization devices, as it is not immobilization device-specific. The
authors pointed out that their approach, combined with a surface-guided imaging
system AlignRT® (VisionRT, London, UK), was effective in eliminating wrong-site
treatment mistakes. Nevertheless, no quantitative analysis of the method’s accuracy
was provided in their report. Additionally, their workflow is not efficient as it consists of
several steps requiring human involvement in decision making. Therefore, there are still
needs to streamline the patient setup process to report such a solution for patient setup
automation that will present in our objective 1 in this dissertation.
Methods to Enhance Treatment Quality
Furthermore, even with an automatic patient setup system, what else will affect
patient treatment accuracy? What if the tumor within the treating area is continuously
moving? Various scientists have attempted to recover the respiratory dynamic behavior
from CBCT projection images to obtain respiratory tumor phase information. The
methods include Amsterdam Shroud (AS) method57, Intensity analysis (IA) method58,
which based simply on the pixel value summations and variations. AS method involved
in superior-inferior (SI) direction anatomic enhancements on CBCT projection image
and convert the images to an AS image to extract the respiratory signal. IA method
required to have pixel summation in both horizontal and vertical directions and using
either high-pass filter or low-pass filter to reveal the underlying respiratory information.
However, those methods still subject to the variation of pixel values on the CBCT
projection images. If there are any high-density artifacts present in the patient’s body
(e.g. surgical implants or pacemaker), the result will be highly affected. Vergalasova et
26
al.59 reported an alternative Fourier transform (FT) method in the frequency domain, but
it shows it has gantry speed dependence; it had shown the algorithm performs better
when cone beam scan at slower gantry speed. Therefore, further investigations on more
advanced methods are needed.
Yan et al.60 provided a comprehensive comparison of the methods mentioned
above (IA, AS and FT method) and proposed a statistical-based local principal
component analysis (LPCA) algorithm to extract breathing signal from the AS image. As
shown in Figure 1-2 A), the LPCA statistical method has more potential in recovery of
the respiratory waveform compared to the previous mentioned AS, IA, and FT
approaches. Chao et al.17 attempted to combat the outliers on AS image by using the
L1-Norm LPCA. The method requires two-steps, which need to run through the LPCA
method first to get the directional indication of the respiratory and then optimize through
L1-Norm LPCA. As shown in Figure 1-2 B), Chaio’s result respiratory waveform still
suffered some perturbation. And yet, the limitation of the above methods include: (1) the
extracted signal diminished or presented noise perturbation while the main internal
surrogate diaphragm is out of the projection views60; (2) Different rows of selection on
the AS image result in different results17; (3) due to anatomic obstructions on the near
lateral projection views, it still impedes the gantry angle selections for real-time in-
treatment verification.
Accordingly, owing to the challenges mentioned above, we applied another
approach called singular spectrum analysis (SSA) to recover the oscillatory components
of the extracted tumor respiratory signal and achieve noise removal at the same time in
our objective 2 and 3 in this dissertation.
27
Study Objectives
First, to establish a self-checking system to predict the patient-specific treatment
couch coordinate (TCC) in advance and evaluate our prediction accuracy. Second,
improve the 4D phase sorting by direct tumor tracking to improve the treatment
accuracy and motion management in radiation therapy. The aims will be achieved by
analyzing and accomplishing the tasks specified by the following specific objectives.
Objective 1: In this objective, we proposed a TCC self-checking system
combined with the advantages of two different calculation methods that used indexed
immobilization devices. The first method used an array of reference ball bearings (BBs)
embedded in the CT scanner’s couch-top. To obtain the patient-specific TCC, the
spatial offset of the treatment planning isocenter from the reference BB was used to
adapt the reference couch coordinates (the couch position that places reference BB at
treatment room isocenter). The second method performed a calculation using the one-
to-one mapping relationship between the CT scanner’s DICOM (Digital Imaging and
Communications in Medicine) coordinate system and the TCC system. Both methods
were used to calculate TCC, and the results were checked against each other, creating
an integrated workflow via automated self-checking. The accuracy of the calculation
system was retrospectively evaluated over six months with 275 patients (total 4969
treatment fractions), where the actual treatment position determined with CBCT was
used as references for comparison.
Objective 2: In this objective, we investigated the feasibility of extracting
respiratory pattern using local principal component analysis with multivariate singular
spectrum analysis (LPCA-MSSA) algorithm. A QUASARTM respiratory motion phantom
with a removable tumor-simulator insert was employed for the CBCT scan to acquire
28
projection images. The motion information of the external surrogate attached to the
moving part of the phantom, which was acquired by an optical tracking system (OTS)
and synchronized to CBCT projections. A comparison between LPCA only and LPCA -
MSSA methods was assessed by power spectrum analysis for a regular breathing
pattern. Furthermore, the respiratory pattern of the external surrogate was simulated
under phase shift or arbitrary amplitudes conditions to examine the robustness of the
MSSA algorithm. Finally, several anatomic obstruction scenarios were simulated by
attaching 3D printed heart model, Polyvinyl chloride (PVC) tubes and RANDO®
phantom slabs to the QUASARTM phantom respectively. Each scenario was tested with
five patient breathing patterns, including some irregular breathing patterns to mimic the
clinic scenarios. The external surrogate signal was obtained as the ground truth
reference for the phantom study. The performance of the LPCA – MSSA algorithm was
evaluated by comparing the average phase deviation, peak and valley accuracy to the
reference.
Objective 3: The purpose of this objective is to apply the LPCA- MSSA algorithm
for extracting tumor respiratory pattern on the clinical lung patients. Various tumor
locations in the lungs were selected to evaluate the versatility of the method. To
estimate the respiratory waveform for patient cases for comparison, a reference
waveform was obtained via visual verification from the attenuation images and the
tumor region AS image. The tumor LPCA- MSSA result was compared to the estimated
reference curve for its accuracy on the phase deviations and peak and valley accuracy.
In addition, for the practical clinical solution, the potential for irregular breathing and
automatic parameter selection will be discussed as the ultimate goal of this objective.
29
Figure 1-1. A linac accelerator equipped with a couch, gantry, EPID, and CBCT system. The immobilization device on the couch is to reassure the patient’s position reproducibility. Photo Courtesy of PingFang Tsai. (September 4, 2019)
30
A B
Figure 1-2. The extracted respiratory waveform result from literatures using Local
principal component analysis methods. A) Reproduced with permission from Hao Yan, et al.60. February 11, 2013. -The breathing signals extracted by various methods (AS, IA, FT, and LPCA) B) Reproduced with permission from Ming Chao, et al.17. March 23, 2016. – Proposed adaptive robust z-normalization step and the resultant image and the corresponding extracted breathing signal.
31
CHAPTER 2 A SELF-CHECKING TREATMENT COUCH COORDINATE CALCULATION SYSTEM
IN RADIOTHERAPY
Background
Radiation therapists are usually under pressure when starting a new patient’s
treatment. * It is critical for them to correctly position a patient on a treatment couch and
move it to the treatment location. Traditionally, therapists rely on skin tattoos (reference
marks) made on a patient during CT simulation and shift instructions provided by the
computerized treatment planning system (TPS) to initiate the task. A patient is first
positioned by aligning tattoos to room lasers and is then moved with the treatment
couch according to the shift instructions. It has been shown that there are several
pathways that can lead to wrong-site treatment errors.1-3 For example, based on the
analysis of the incidences reported to the Radiation Oncology Incident Learning System
(RO-ILS), Ezzell et al.4 found that 18% of the high-priority events were attributable to
either wrong shift instructions or a wrong shift performed at treatment. Other common
pathways include (1) the patient was marked incorrectly at CT simulation (2) the patient
marks were incorrectly identified in the TPS (3) the reference image set for image-
guided radiation therapy (IGRT) was created with the wrong isocenter or the wrong
dataset. Given the number of common pathways leading to wrong-site treatment errors,
there is an urgent need for automating the patient setup process to smooth out the
workflow, mitigate the pressure on the therapists, and strengthen the first line of
defense against such errors. A critical piece of the automation, referred to in this work,
* This chapter is reprinted with permission from Wiley Publishing. (2019). “A self-checking treatment couch coordinate calculation system in radiotherapy”; P Tsai, C Liu, DL Kahler, JG Li, B Lu, G Yan; [ Published online ahead of print 2019/11/01]. Journal of Applied Clinical Medical Physics
32
is the determination of treatment couch coordinates (TCCs) before the patient is even
put onto the treatment couch. It is highly desirable to have a simple system to calculate
couch coordinates prior to the commencement of the actual treatment.
The increasing use of indexed immobilization devices presents an opportunity for
such automation. Indexed immobilization devices not only enable the patients to
reproduce and maintain their positions from CT simulation throughout the course of the
treatment, but they also provide a mechanism to relate patient position to treatment
table position through indexing. Saenz et al.5 reported a method for patient-specific
couch coordinate prediction using indexed immobilization devices. Their method relied
on a radiographically apparent landmark on the immobilization device. The baseline
couch coordinates (the couch coordinates when the landmark was positioned at the
treatment room isocenter) were first determined. Then the displacement of the planned
treatment isocenter relative to the landmark was used to adjust the baseline table
coordinates to obtain the TCCs for the patient. Overall, 86% of their predictions were
correct to within 2 cm, and the mean error was under 0.1 cm, but the standard deviation
was relatively large (1.47 cm). Additionally, their method was dictated by the
immobilization device. For devices without a radiographically apparent landmark, the
method failed to predict couch coordinates. Sueyoshi et al.6 reported a slightly different
approach. Instead of using landmarks on the immobilization device, they used a set of
fixed couch-top positions (e.g., indexing notches within the couch-top) as the reference.
Their method can be applied with any indexed immobilization device, as it is not
immobilization device-specific. The authors pointed out that their method, combined
with a surface-guided imaging system AlignRT® (VisionRT, London, UK), was effective
33
in eliminating wrong-site treatment mistakes. However, no quantitative analysis of the
method’s accuracy was provided in their report. Additionally, their workflow is not
efficient, as it consists of several steps requiring human involvement in decision making.
Several other groups7-10 reported efforts to detect setup mistakes by tightening the site-
specific tolerances for the couch coordinates. These methods, commonly known as
tolerance table approaches, do not calculate the table coordinates in advance.
Therefore, the onus remains on the therapists to figure them out while the patient is on
the treatment table.
In our opinion, an ideal method to automate the initial patient setup should have
the following features: (1) it calculates couch coordinates in advance to ease the
pressure on the therapists; (2) it is universally applicable to all treatment sites; (3) it is
not immobilization device-specific; in other words, it works with any indexed
immobilization device; (4) it offers a smooth workflow by reducing or simplifying
intermediate steps; (5) it has simple, yet rigorous, quality assurance (QA) measures to
ensure its integrity. The aim of this paper is to present a patient setup automation
solution to accomplish the above goals. We first presented two independent TCC
calculation methods, then introduced a highly automated, self-checking system that
seamlessly integrated the two methods.
Materials and Methods
Reference BB-based Calculation Method
The main idea of this method is to relate the treatment planning isocenter to the
reference ball bearings (BBs) that are embedded in the CT couch-top. The reference
couch coordinates (RCCs), i.e., the couch coordinates to position the point representing
a primary reference BB at treatment room isocenter, are predetermined. The patient-
34
specific TCCs are calculated by adjusting the RCCs according to the displacement
between the treatment planning isocenter and the primary reference BB. For this
method to work, an indexed immobilization device is used to maintain the spatial
relationship between the patient and the couch-top. With this method, the TCCs are
calculated at the treatment planning stage, significantly reducing the burden on the
therapists at the time of treatment.
Figure 2-1 A) depicts the arrangement of the BBs embedded in the CT couch-
top. All the BBs are flush with the couch surface. There are 17 BBs in six rows. In each
row, the rightmost BB (referred to as reference BB) is placed on the midline of the
couch, and the others are arranged to the left of the midline when viewed from above
the couch. There are two BBs in the most superior row, with the reference BB referred
to as the “Head BB”. The number of BBs varies in the other rows, where the reference
BB is referred to as “BB1”, “BB2”, “BB3”, “BB4” or “BB5”, with the number indicating the
number of BBs in each row. This pattern makes it easy to identify the reference BBs on
a CT scan. For example, the reference BB shows in Figure 2-1 B) can be recognized as
BB3 since there are three BBs in the row. Both the Head BB row and the BB2 row have
two BBs. They can be distinguished by the fact that, generally, the Head BB only shows
up in a head/brain scan, whereas BB2 only shows up in a lung/chest scan.
At our institution, we use an iBeam® EVO couch-top (Elekta Inc., Stockholm,
Sweden) with a Phillip Brilliance Big Bore CT simulator (Phillips Medical Systems,
Madison, WI). The same couch-top is used in each treatment room. The indexing holes
on the couch-top are labeled with a single digit or letter (Figure 2-1 A)). BB3, designated
as the primary reference BB, is located midway between the pair of “C” indexing holes.
35
The longitudinal distance between each adjacent reference BB is known, as shown in
Figure 2-1 A), from which the longitudinal offset (OSBBi,z) of the ith reference BB with
respect to BB3 can be determined. The vertical offset (OSBBi,y) and lateral offset
(OSBBi,x) are both zero since all of the reference BBs are in the same vertical and lateral
planes. The RCCs for BB3 (RCCBB3) are determined as the couch coordinates when the
treatment couch is positioned such that the midpoint of the two “C” indexing holes is
aligned with the treatment room isocenter.
The Pinnacle treatment planning system (Philips Radiation Oncology Systems,
Fitchburg, WI) is used at our institution. During treatment planning, the reference BB
closest to the treatment area is selected as the laser coordinate system origin in the CT
dataset. The arrangement of the BBs on the couch-top guarantees that at least one
reference BB is included in each patient’s CT scan. A point of interest (POI) is created
at the location of the selected reference BB. Then the DICOM (Digital Imaging and
Communications in Medicine) coordinates of this POI (DCBBi) and the planned treatment
isocenter (DCiso) are transferred from the TPS to an in-house program to calculate the
TCCs. The TCC in the lateral (TCCx), vertical (TCCy), and longitudinal (TCCz) directions
for the patient are calculated as
𝑇𝐶𝐶𝑥 = 𝑅𝐶𝐶𝐵𝐵3,𝑥 + 𝑂𝑆𝐵𝐵𝑖,𝑥 + 𝐷𝐶𝑖𝑠𝑜,𝑥 − 𝐷𝐶𝐵𝐵𝑖,𝑥
𝑇𝐶𝐶𝑦 = 𝑅𝐶𝐶𝐵𝐵3,𝑦 + 𝑂𝑆𝐵𝐵𝑖,𝑦 + 𝐷𝐶𝑖𝑠𝑜,𝑦 − 𝐷𝐶𝐵𝐵𝑖,𝑦
𝑇𝐶𝐶𝑧 = 𝑅𝐶𝐶𝐵𝐵3,𝑧 + 𝑂𝑆𝐵𝐵𝑖,𝑧 + 𝐷𝐶𝑖𝑠𝑜,𝑧 − 𝐷𝐶𝐵𝐵𝑖,𝑧
(2-1)
respectively. OSBBi,x and OSBBi,y can be omitted in the equations since they are both
zero. It is assumed that the indexing bars of the indexed immobilization device are
placed at the default locations (holes). If non-default indexing locations need to be used
36
for clinical reasons (e.g., to avoid collision), the corresponding longitudinal offset needs
to be accounted for in the equation for TCCz. Figure 2-2 A) illustrates the relationship
between the treatment planning isocenter and the reference BBs. These TCCs are
manually entered into the MOSAIQ® Record-and-Verify (R&V) system (Elekta Inc.,
Stockholm, Sweden) for each treatment beam, which are checked later during initial
chart check. If multiple isocenters are used in the treatment plan, the above process is
repeated for each treatment isocenter.
For the in-house program to apply the correct longitudinal offset (OSBBi,z), the
user needs to specify which reference BB has been selected in the TPS. Incorrect
specification leads to a calculation error of 14 cm or more in the longitudinal direction
(Figure 2-1 A)). To avoid such errors, the axial CT slice passing through the selected
reference BB is recorded as a screenshot from the TPS, and a report detailing the
user’s reference BB specification is generated by the in-house program. These two
documents are cross-checked by a physicist during the initial chart check.
Although these types of errors can be detected by the physicist during chart
checking, it is desirable to eliminate the source of error by automating the workflow. The
automation can be achieved by using the CT scanner’s DICOM coordinate system,
which will be discussed in the following sections. First, we will introduce another
calculation method that is based on CT DICOM coordinates and requires no reference
BBs (therefore, no alteration to the couch-top). Then a self-checking system combining
the advantages of the reference BB-based calculation method and the DICOM
coordinate-based calculation method will be described.
37
DICOM Coordinate-Based Calculation Method
The motivation for this method stems from an observation that we made after we
clinically implemented the reference BB-based method. The observation was that, even
though the initial couch position for each CT scan varies between patients, the DICOM
coordinates of the reference BBs in all of the CT scans have only small variations
(within 1 cm) along any axis. Considerable changes are only observed in the
longitudinal direction when the CT couch-top coordinate system is changed, which
occurs when the reset button on the scanner’s control panel is pressed. This
observation indicates that the DICOM coordinate system of the CT scanner is defined
with respect to the CT couch-top. In other words, unless changed by the operator, the
DICOM coordinate system (origin and axes) remains stationary in relation to the couch-
top. Therefore, there is a one-to-one mapping relationship between the CT DICOM
coordinate system and the treatment couch coordinate system. The TCCs to position
any point in a CT scan at the treatment room isocenter can be determined if we can do
so for a reference point (e.g., a landmark on the couch-top). Since the reference is only
needed when establishing the mapping relationship, there is no need to permanently
embed BBs into the couch-top. We temporarily taped a BB (referred to as BBt) at the
midpoint between the two “C” index holes on the couch-top and removed it after taking
a CT scan of the couch-top, from which the DICOM coordinates of BBt were determined
as DCBBt. The RCC for BBt, denoted as RCCBBt, were determined by positioning the
midpoint between the two “C” index holes on the treatment couch-top at the treatment
room isocenter. If we denote the DICOM coordinates of the treatment planning
isocenter by DCiso, the patient-specific TCCs can be calculated as,
38
𝑇𝐶𝐶𝑥 = 𝑅𝐶𝐶𝐵𝐵𝑡,𝑥 + 𝐷𝐶𝑖𝑠𝑜,𝑥 − 𝐷𝐶𝐵𝐵𝑡,𝑥
𝑇𝐶𝐶𝑦 = 𝑅𝐶𝐶𝐵𝐵𝑡,𝑦 + 𝐷𝐶𝑖𝑠𝑜,𝑦 − 𝐷𝐶𝐵𝐵𝑡,𝑦
𝑇𝐶𝐶𝑧 = 𝑅𝐶𝐶𝐵𝐵𝑡,𝑧 + 𝐷𝐶𝑖𝑠𝑜,𝑧 − 𝐷𝐶𝐵𝐵𝑡,𝑧
(2-2)
RCCBBt and DCBBt are not patient-specific. As illustrated in Figure 2-2 B), these
equations map the DICOM coordinates of any point in a CT scan directly to the
treatment room coordinates. This method also relies on the use of indexed
immobilization devices. Consistent indexing holes should be used between CT scan
and treatment. Otherwise, the longitudinal offset due to the difference in indexing holes
needs to be accounted for in the equation for TCCz.
A Self-Checking Couch Coordinate Calculation System
The advantage of the DICOM coordinate-based method over the reference BB-
based method is that it directly uses the DICOM coordinates and does not use
reference BBs embedded in the CT couch-top, which further simplifies the workflow.
However, the DICOM coordinate system can be changed unknowingly during daily
operation as the reset button on the control panel is located right next to other
frequently used buttons (e.g., buttons that move the couch in, out, up and down). This
leaves a pathway for potential errors. It is desirable to combine the advantages of the
two methods to streamline the workflow and eliminate the error pathway.
Here we introduce a self-checking treatment couch coordinate calculation system
that combines the two methods. The reference BB-based method requires the user to
specify which reference BB has been selected in the TPS. This can be a potential error
pathway as the user can potentially specify the reference BB incorrectly. The CT
scanner’s DICOM coordinate system, unless reset, remains stationary in relation to the
39
CT couch-top. Therefore, the reference BBs can be automatically distinguished based
on their DICOM coordinates. This feature can be used to automate the specification of
the reference BB. To this end, a lookup table containing all of the reference BBs’
longitudinal DICOM coordinates were stored in the in-house software. For individual
patients, the selected reference BB’s longitudinal DICOM coordinate, exported from the
TPS, is compared to the values in the lookup table to automatically determine which
reference BB has been selected. This simplifies the workflow and eliminates the error
pathway for incorrect reference BB specification. Additionally, the TCCs are calculated
with both the reference BB-based method and the DICOM coordinate-based method.
The TCCs are only manually entered into the R&V system when the numbers calculated
by the two methods agree with each other to within a specified tolerance.
The workflow for the combined method is illustrated in Figure 2-3. At CT
simulation, the therapists use predetermined indexing holes for the immobilization
devices, which can be a full-body Vac-LocTM bag mold (CIVCO, Coralville, Iowa), a half
body Vac-LocTM mold, breast boards or a Q-fix AccuFixTM device (Qfix, Avondale, PA) in
our institution. During treatment planning, the dosimetrists pick a reference BB close to
the treatment target and define a treatment planning isocenter. The DICOM coordinates
of the reference BB and the planning isocenter are transferred from the TPS to the in-
house software. The in-house software automatically detects which reference BB has
been selected and applies the corresponding offset (OSBBi, y) to calculate the TCCs. The
software also calculates the TCCs using the DICOM coordinate-based method. It then
performs a self-checking process by comparing the TCCs calculated with the two
methods. If the difference is within the specified tolerance, the results calculated with
40
the reference BB-based method are entered into the R&V system. At treatment, the
therapists use default indexing holes for the immobilization devices and load the TCCs
directly from the R&V system to set up the patient. The final treatment position is
determined using a cone-beam tomography (CBCT). In our institution, daily CBCT is
performed with the Elekta XVI linac-integrated system (Elekta Inc., Stockholm, Sweden)
for patient localization. The process to determine the TCCs is transparent to the
therapists at both CT simulation and treatment.
Data Collection and Analysis
The variation of the CT scanner’s DICOM coordinate system from one CT scan
to another was first evaluated without a patient on the treatment couch. The CT couch-
top, which can only move in the vertical and longitudinal directions, was scanned at
various vertical positions covering its vertical range. At each vertical position, the couch-
top was moved to various longitudinal positions inside its moving range and the scan
was repeated three times. The CT scans were sent to the TPS where BB3 was
identified as a point and the variation of its DICOM coordinates was quantified.
The uncertainty of the DICOM coordinate system with a patient on the treatment
couch was retrospectively analyzed with CT scans of patients. The longitudinal position
of the couch-top varies from patient to patient, depending on the anatomical location of
the intended treatment area. The variation can cause different amounts of couch sag
that adds to the uncertainty of the DICOM coordinates. To account for the effect, we
included a wide variety of patients with diseases for different sites (e.g., brain, head and
neck, lung, pelvis, etc.). For each patient, only the reference BB selected for TCCs
calculation was included in the analysis. In this way, the uncertainty analysis of the
DICOM coordinates is relevant and meaningful to the purpose of this study.
41
The accuracy of the two calculation methods was evaluated by comparing the
calculated TCCs with the ones determined using CBCT, which were retrospectively
retrieved from the MOSAIQ database using Structured Query Language (SQL). A total
of 275 patients with 4969 treatment fractions, treated within a span of six months, were
included. The treatment sites of these patients included brain, head & neck (HN),
breast, lung, abdomen, pelvis, and extremity.
Results
The uncertainty of the CT scanner’s DICOM coordinate system, evaluated
without a patient on the treatment couch, is depicted in Figure 2-4 using a box plot. The
result is represented by the variation of BB3’s DICOM coordinates. The mean value,
(0.0, -214.9, 974.3) mm, was subtracted out from the data. The variation was within 2.0
mm in the lateral and longitudinal directions and under 5.0 mm in the vertical direction.
Table 2-1 shows the uncertainty of the CT scanner’s DICOM coordinate system
evaluated with the patient on the treatment couch. A total of 361 CT scans were
reviewed. The number of CT scans using Head BB, BB1, BB2, BB3, and BB4 as the
reference BB were 94, 22, 104, 131 and 10, respectively. BB5 (the most inferior
reference BB) is excluded from the remaining discussion since it was not selected as a
reference BB in any of these CT scans. The mean coordinates of all of the reference
BBs in the lateral and vertical directions were within 1.0 mm and 5.0 mm, respectively;
the longitudinal distance between adjacent reference BBs, evaluated by the difference
between the mean longitudinal coordinates, agreed with the physical distance to within
1.0 mm. These results validated our observation that the DICOM coordinate system is
defined by the couch-top. In the lateral direction, BB4 had the smallest uncertainty
range of 1.5 mm, and the other reference BBs had a similar uncertainty range of
42
approximately 4.0 mm. The vertical direction showed the most significant variation: the
head BB had an uncertainty range of 9.7 mm, while the other reference BBs had
uncertainty ranges between 5 mm and 9 mm. In the longitudinal direction, the
uncertainty range of all of the reference BBs was between 3.5 mm and 6.0 mm. These
results have two implications: (1) the uncertainty of the DICOM coordinate system-
based couch coordinate calculation method can be up to nearly 10.0 mm in the vertical
direction, depending on which reference is used to establish the mapping relationship;
based on this result, we use a tolerance of 10.0 mm when comparing the calculation
results of the two calculation methods, and (2) to use the reference BB’s longitudinal
DICOM coordinate to automatically identify which BB the reference BB is, a tolerance of
10.0 mm is sufficient. For example, if its longitudinal coordinate is between 964.3 mm
and 984.3 mm, the reference BB can be correctly identified as BB3.
Figure 2-5 shows the accuracy of both methods when compared to the final
treatment couch coordinates determined using CBCT on the first treatment day. The
bars and error bars represent the mean deviation and the 95% confidence interval (CI),
respectively. The analysis included 22 brain, 39 head & neck, 72 lung, 25 breast, 40
abdomen, 65 pelvis, and 12 extremity cases. The calculation was accurate, with 95% of
the coordinate calculations within 3 mm. Overall, with both methods, the most
substantial average deviations were observed for breast cases in the lateral and vertical
directions and for pelvis cases in the longitudinal direction. This can be attributed to the
fact that the treatment targets for these cases are inside soft tissue. This is especially
obvious for patients with large or pendulous breasts. For the same reason, breast,
abdomen and pelvis cases had the most significant error bars. Extremity cases also had
43
slightly larger error bars, probably due to the increased difficulty in immobilization and
the decreased setup reproducibility. The brain and head & neck cases had the best
accuracy with variations to within 5 mm in all directions. It is relatively easy to reproduce
the setup for these disease sites. Surprisingly, lung cases had good accuracy that was
similar to that of the brain and head & neck cases. The overall accuracy of the reference
BB-based and DICOM coordinate-based methods was comparable. The most
substantial difference between the two methods was observed with the pelvis cases in
the longitudinal direction, where the average deviation of the DICOM coordinate-based
method was 1.6 mm higher than that of the reference BB-based method.
Figure 2-6 shows the histograms of inter-fraction deviations for all of the cases
combined over the whole treatment courses. Note the patients were initially set up using
TCCs calculated with the reference BB-based method, then localized with daily CBCT.
The deviations reported here were essentially the shifts reported from CBCT
registration. Ninety-five percent and 99% of the coordinates were within ±1.05 cm and
±1.5 cm in the lateral direction, ±1.03 cm and ±1.56 cm in the longitudinal direction, and
±0.49 cm and ±0.87 cm in the vertical direction, respectively. A trend of increasing
deviation was observed, which is probably due to anatomical changes related to weight
loss or tissue deformation, or organ motion related to respiration, rectal/bladder filling,
etc. These results highlight the importance of daily CBCT in high precision radiotherapy.
Discussion
In this work, we proposed two TCC calculation methods: the reference BB- and
the DICOM coordinate-based methods. These methods have clear advantages and
disadvantages in terms of clinical implementation and workflow. The reference BB-
based system uses BBs that are permanently embedded in the couch-top as the
44
reference. Using these BBs has several advantages over using landmarks on
immobilization devices as described by Saenz et al.5 First, not all immobilization devices
have radiopaque landmarks that can be easily recognized on a CT scan. Second, the
landmarks on different immobilization devices are most likely different in both location
and appearance on the CT scans, which makes it difficult for TPS users to correctly
identify them. Third, the reference treatment couch coordinates vary from one type of
immobilization device to another, adding complexity to the overall workflow. Being
independent of the immobilization device, the BBs physically embedded in the couch-
top overcome all of these difficulties. The unique arrangement of the embedded BBs
makes it easy to distinguish between them, reducing the odds of misidentification. BB5
has never been used as a reference for any of our clinical CT scans since any extremity
case that may have required their use was scanned feet-first into the CT scanner bore.
The downside of this approach is the need to modify the couch-top by embedding
multiple BBs. The DICOM coordinate-based method is more straightforward since it
does not use references for individual patients. The mapping relationship from the
DICOM coordinate system to the treatment couch coordinate system can be established
with a BB temporarily taped on the CT couch-top. Therefore, unlike the reference BB-
based method, the DICOM coordinate-based method does not need couch-top
modification. An additional advantage of the DICOM coordinate-based method is the
further simplification of the workflow. While the reference BB-based method requires the
TPS user to select a reference BB for each patient, the DICOM coordinate-based
method is transparent to the TPS user. This workflow simplification helps to avoid the
potential user-introduced error associated with the reference BB-based method, where
45
the reference BB could be incorrectly specified in the in-house software. The potential
problem with the DICOM coordinate-based method is that it relies on its definition
remaining stationary to the CT couch-top, which can be changed unknowingly when the
reset button is accidentally pressed during normal operation. Such incidents are
unacceptable as the resultant errors will not be detected until another method (e.g.,
image-based patient localization) is used to verify the patient’s position. In contrast, the
reference BB-based method does not have this problem. In summary, the two methods
have equally excellent accuracy when used separately; however, they leave room for
potential errors. Stringent QA measures (e.g., physics double-check) need to be in
place when a single method is used.
The combination of the two methods gives a robust self-checking system along
with a streamlined workflow. The CT DICOM coordinate system is used to facilitate the
automatic identification of the reference BB. The self-checking is performed by
comparing the calculations from both methods. This design can detect nearly all of the
error sources analyzed above. The accidental reset of the CT DICOM coordinate
system leads to an offset in the DICOM coordinates. The software will similarly detect
such an offset. The amount of offset can be determined from the difference between a
reference BB's known DICOM coordinates and its DICOM coordinates as observed on
the CT scan. This offset is then fed into the software to complete the reference BB
identification and calculation of the couch coordinates. The CT DICOM coordinate
system can then be reset to its correction position.
The design of the combined method emphasizes workflow transparency and
simplification via automation. Traditionally, the therapists make tattoos on the patient’s
46
skin during CT simulation; the dosimetrists mark the BBs representing the location of
the tattoos in the TPS and transfer the shift instructions to the therapists for treatment;
for the treatment, the therapists perform a simple calculation to determine the couch
coordinates while the patient is on the treatment couch. This process requires human
involvement at each stage, leaving a few pathways for potential errors. In contrast, our
workflow is nearly transparent to the therapists at CT simulation and treatment. They
can focus their attention on achieving proper immobilization and patient care. As for the
dosimetrists, their sole responsibility is to find a reference BB near the treatment area
where the laser coordinate system origin is placed. Workflow simplification via
automation plays a vital role. For example, the process to create the point of interest for
the reference BB and to transfer the DICOM coordinates from the TPS to the in-house
software can be simplified as single button clicks by using an embedded software
“script”, created with the Pinnacle system scripting language. This eliminates the need
to type numbers manually, which is a typical source of error. Similarly, the automatic
identification of the reference BB in the in-house software via its DICOM coordinates
simplifies the workflow and obviates a potential error pathway. Currently, the calculated
couch coordinates need to be manually entered into the R&V system. The automation
of this step involves writing data directly into the R&V database, which is not supported
by the vendor. We envision that if the TPS vendor adopts the proposed method, the
couch coordinates can be calculated by the TPS and directly transferred to the R&V
system along with other beam parameters (e.g., gantry angle, number of monitor units,
etc.). At present, these manually-entered coordinates are rigorously checked against
the report generated by the in-house software by the physicist during the initial chart
47
check. It is worth mentioning that the calculated TCCs are only used for initial patient
setup. The final treatment position is determined with subsequent daily CBCT.
As part of our continuous quality improvement efforts, two QA measures have
been implemented to prevent or detect an accidental reset of the CT DICOM coordinate
system. First, a ring-shaped device that was custom-built with 3D printing has been
mounted on top of the CT scanner reset button. If the CT scanner needs a reset, a pen-
like object must be used to reach the reset button to press it. Second, as part of the
daily CT scanner QA, the CT couch-top is moved to align a pre-marked position with the
wall laser. The reading of the couch-top’s longitudinal position is checked against the
reference value using a 1.5 mm tolerance. After the clinical implementation of the
DICOM method a year ago, but prior to the introduction of these QA measures, the CT
DICOM coordinate system was accidentally reset twice within two months. An
accidental reset has not occurred since the QA measures were put into place. The
assumption that the DICOM coordinate system is defined with respect to the CT couch-
top plays a vital role in the proposed method. Although we validated this assumption on
our Phillip Brilliance Big Bore CT simulator, we are not sure whether this feature is
common across CT scanners from different vendors since we have no access to other
CT scanners. However, it is straightforward to check on any CT scanners using our
validation method, i.e., tape a BB on the couch-top, perform repeated CT scans with
different initial couch height and longitudinal positions, and check whether the TPS-
reported DICOM coordinates of the BB remain the same.
Note that the proposed system does not rely on the use of skin tattoos or room
lasers for patient localization. However, they are used for patient’s rotational correction,
48
especially for patients treated with body mold. Two sets of tattoos are marked on the
patient skin at two different axial planes near the abdominopelvic area (one on top and
one on either side), as conventionally done under the guidance of the CT scanner’s
laser system. The longitudinal locations of the tattoos are marked on the body mold. At
treatment, patient rotational errors can be corrected by aligning the two sets of tattoos
with treatment room laser in sequence. The therapists also align the skin tattoos with
the marks on the body mold to ensure that the patients reproduce their positions.
For inter-fractional deviations over the entire treatment course in Figure 2-6, the
bell-shaped histograms were centered around zero in the lateral and longitudinal
directions, but a 0.25 cm shift toward the negative direction was found in the vertical
direction. This was consistent with the results from day one as shown in Figure 2-5. The
deviations for most cases (except brain and extremity) in the vertical direction were
negative, while they were more balanced in the other two directions. This was probably
due to the increased couch sag with the linear accelerator as compared with the CT
scanner. We have observed increased, albeit small couch sag as the treatment couch
moves towards the gantry while the patient is on the couch. The clinical impact of this
vertical shift towards the negative direction was negligible since the final treatment
position was determined with CBCT where the registration was completed based on
actual treatment target.
In addition to preventing near-miss incidents for patient treatments, there are
three additional benefits of being able to determine couch coordinates in advance. The
first one is related to a junction area on the treatment table that has a significantly
higher beam attenuation than the rest of the table. Based on the calculated couch
49
coordinates, we can tell whether the treatment beam will pass through the junction area.
If needed, different indexing holes can be used to shift the immobilization device relative
to the table in order to move the junction out of the beam path. With our approach, this
decision can be made in the treatment planning stage, instead at the time of treatment.
The resultant offset is accounted for by adjusting the longitudinal couch coordinate
(TCCz) correspondingly. The second benefit is the avoidance of possible couch
collisions. For example, to treat targets located significantly off the patient’s midline,
large lateral couch offset is needed, which can lead to collision between the couch and
the gantry. This can be determined in advance using the calculated couch coordinates,
and the treatment planning isocenter can be shifted toward the patient’s midline to avoid
the collision. The third benefit is that the software can determine whether the TCCs
exceed the couch’s limit. If it occurs, the system offers the opportunity to remedy the
situation by using non-default indexing holes or adjusting treatment planning isocenter
position. These are all benefits that allow us to foresee and prevent potential events
that, using conventional setup methods, would only be discovered after the patient is on
the treatment couch.
Conclusions
We have proposed two TCC calculation methods and a highly automated self-
checking system. Combining the use of reference BBs physically embedded in the
couch-top and the CT scanner’s DICOM coordinates, the system calculates TCCs with
excellent accuracy in advance. The system universally applies to all treatment sites with
any indexed immobilization devices. A simple, robust, streamlined workflow is achieved
via automation, eliminating nearly all of the common error pathways. The
implementation of the system significantly eases the pressure on the therapists at the
50
time of treatment, reduces patient setup time, and enhances patient safety by
minimizing the chance of medical error events related to the patient setup.
51
A B
Figure 2-1. Ball bearings embedded couch design. A) The arrangement of ball bearings (BBs) embedded in a CT couch-top. The BBs on the midline are used as references for couch coordinate calculations; others are used to facilitate reference marker identification. B) An axial CT slice passes through a reference BB (BB3) selected as the laser coordinate system origin in the treatment planning system.
52
Figure 2-2. The self-checking treatment couch coordinate (TCC) calculation system with two methods. A) Illustration of the reference BB-based TCC calculation method. The treatment planning isocenter is related to a reference BB (BBi), which in turn is related to the primary reference BB (BB3). The displacement vector from the treatment planning isocenter to BB3 is used to adapt the reference couch coordinates (RCCs) to obtain patient-specific TCCs. B) Illustration of the DICOM coordinate-based TCC calculation method. The one-to-one mapping relationship from the CT DICOM coordinates to the TCCs is established with a reference point. The displacement vector from the treatment planning isocenter to the reference is used to adapt the RCCs to obtain TCCs.
53
Figure 2-3. Workflow of the self-checking couch coordinate calculation system.
54
Figure 2-4. Uncertainty of the CT scanner’s DICOM coordinate system evaluated by scanning the CT Couch top at various vertical and longitudinal positions. The central mark of the box plot indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the '+' symbol.
55
Table 2-1. Uncertainty of the CT scanner’s DICOM coordinate system evaluated with patient CT scans. In each scan, only the reference BB selected for the couch coordinate calculation is included in the analysis. For comparison, its uncertainty represented by BB3 without a patient on the couch is also included (last row).
Reference BB set Lateral direction Vertical direction Longitudinal direction
Mean± SD
(mm)
(max-min)
(mm)
Mean± SD
(mm)
(max-min)
(mm)
Mean± SD
(mm)
(max-min)
(mm)
Head BB (N=94) 0.7±1.0 3.6 -221.7±1.7 9.7 274.2±1.0 4.5
BB1 (N=22) 0.3±1.1 4.0 -218.6±1.6 6.5 693.2±1.2 3.5
BB2 (N=104) 0.5±0.9 4.0 -218.0±1.7 8.8 834.2±1.1 5.3
BB3 (N=131) -0.3±0.9 4.1 -217.9±1.8 7.8 973.3±1.2 6.0
BB4 (N=10) -0.2±0.5 1.5 -216.1±1.6 5.5 1184.1±1.1 3.5
BB5 (N=0) -- -- -- -- -- - -
BB3
(No patient)
0.0±0.6 1.8 -214.9±0.9 4.5 974.3±0.4 2.0
Abbreviations: N= Number of patients; SD= standard deviation
56
Figure 2-5. Accuracy of the two treatment couch coordinate calculation methods, evaluated with treatment couch coordinates determined with CBCT on the first day of treatment. The whisker indicates the 95% confidence interval.
57
Figure 2-6. Deviation of the calculated treatment couch coordinates (TCCs) over the full treatment course. At each fraction, the patients were initially set up with the calculated TCCs, then localized with daily CBCT. Reported here are the daily shifts from CBCT registration.
58
CHAPTER 3 OVERVIEW OF THE STATISTICAL AND MATHEMATICAL CONCEPTS
In this chapter, we will briefly introduce the statistical and mathematical concepts
that are exploited in the following chapters. Each section covers the topic of adaptive z-
normalization, principal component analysis (PCA), singular value decomposition
(SVD), and singular spectrum analysis (SSA). Each method assists us in achieving
objective 2 and 3 in order to enhance treatment accuracy for adaptive motion
management through CBCT projection images.
Adaptive Z-Normalization
Due to the variation of the patient’s body thickness during a 360-degree CBCT
scan, the representation of the pixel value may vary depending on the radiological path
length. Thus, we applied the adaptive z- normalization suggests by Chao et al.17 to
improve the uniformity of the foreground and background of the composited Amsterdam
Shroud(AS) image which provides us more consistent pixel values across the image
composited from the original CBCT projection images. Each pixel of the AS image (A) is
assessed by convolving with a Gaussian filter G to find the average values for each
pixel (𝐴𝐺) as shown in Eq. (3-1).
𝐴𝐺 = 𝐀 ∗ 𝐺 (3-1)
The Gaussian filter with a kernel size of 10 and a standard deviation of 5 was
used in this study. Also, the standard deviation (σ) for each pixel is computed by
applying the standard deviation filter (𝐴𝜎) of 3 x 3 neighborhood. The adapted z-
normalization AS image (𝐴𝑁) is then computed as in Eq. (3-2)
59
𝐴𝑁 = (𝐴 − 𝐴𝐺)/( 𝐴𝜎 + 𝜇(𝐴𝜎)) + 𝐴𝑎𝑙𝑙 (3-2)
Where / is the element-wise division; 𝜇(𝐴𝜎) is the mean value of the 𝐴𝜎 image;
𝐴𝑎𝑙𝑙 is the mean value of A. After applying the adaptive z- normalization, the foreground
and background homogeneity on the AS image has improved across all frames in both
vertical and horizontal directions. Therefore, the AS image after adaptive z-
normalization is then ready to be processed for the next step.
Principal Component Analysis
Principal Component Analysis (PCA) is invented in 1901 by Karl Perason61; it
was later developed and named by Harold Hotelling62 in the 1930s. PCA is a statistical
method that utilized the orthogonal linear transformation to convert the dataset from its
sensor coordinates to the data-centric coordinates in the principal component space
using linear projections. The principal component space can display the axis that
represents the linearly uncorrelated variables of the data. The transformation is defined
in such a way that the first principal component has the largest possible variance and
each succeeding component in turn as the highest variance possible under the
constraint that it is orthogonal to the preceding components.63 For instance, Figure 3-1
shows a random generated 2D Gaussian distribution where is in an ellipse shape which
contains two major unequal length axis with black arrows that are orthogonal to each
other in the original sensor coordinate (X and Y). After the PCA, the data set is linearly
transformed to principal component (PC) space, now the two axes of the original axis
are best presented with PC1 and PC2 in principal space. However, it a real-world data,
the dataset might have more than two or three variables, so the visualization of the
60
original dataset in higher dimension may not be possible. Thus, there is a need to
reduce the redundancy by lower the dimensional manifold representation of the data in
order to interpret them to the most valuable/related variables in the whole dataset.
In finding the principal component axes, PCA minimizes the redundancy of the
resulting transformed data (by ending up data that is uncorrelated), minimizes the mean
squared error between original and transformed/reduced data, and maximize the
retained variance of the data. The method to obtain the principal components involves
in the decomposition of a covariance C. If the C is a symmetric and square matrix,
eigenvalue decomposition (EVD) in linear algebra can be used to obtain the principal
components. During the decomposition, the eigenvalues and eigenvectors are acquired.
The eigenvalues present the variance of the data on the principal component axis, and
eigenvectors can be interpreted as an orthogonal axis defined by the data. If C is not a
square matrix, the singular value decomposition (SVD) is utilized to obtain the
eigenvalues and eigenvectors from the covariance C. The concept of SVD will be
explained in the next section.
Singular Value Decomposition
There are many widely used SVD applications, such as data reduction method in
machine learning, least-squares linear regression, image compression, and denoising
data.64 The singular values play an essential role where the matrix is a transformation
from one vector space to a different vector space, even possibly with a different
dimension. Moreover, the SVD can extract the essence of how to rotate the data in
space to have the best representation of each principal component axis. In general,
SVD is a matrix decomposition method, also known as matrix factorization, which
describes a given matrix using its constituent elements for a real or complex matrix. It is
61
a generalization of the eigendecomposition of a positive semidefinite normal matrix (e.g.
a symmetric matrix with positive eigenvalues). A nonnegative eigenvalue (λ),𝜆 ≥ 0, is
also a singular value. In here, we will only discuss the real matrix situation, as our data
is the real-world data with the real number.
As shown in Figure 3-2, the SVD procedure decomposes the covariance matrix
into three elements: the left-singular vectors (U), the non-zero singular values (∑), and
the right-singular vectors (V). The U contains the orthonormal eigenvector of CCT, and it
represents the counterclockwise (CCW) rotation of the data; the V contains the
orthonormal eigenvector of CTC, and it represents the clockwise(CC) rotation of the
data. (∙)𝑇 denotes the transpose of a matrix. On the diagonal entries of ∑ are the square
root of the non-zero eigenvalues of both CCT and CCT. Once the covariance C is
decomposed, and the related eigenvalues and eigenvectors were obtained, it can assist
us to find the principal axes of the data in both the PCA and singular spectrum analysis
(SSA).
Singular Spectrum Analysis
Singular Spectrum Analysis (SSA) extended the use of PCA to the time series,
which represents the data point evolved with time. As described by Groth et al.65, SSA
is widely used in climate change66,67, economics68, or geophysics69,70. It has abilities to
solve the time series for change point detection, noise removal, periodicity extraction,
and detect the trend or oscillating65, et cetera. It uses empirical orthogonal function
(EOF) which is similar to PCA, except that the EOF approach finds both spatial and
temporal patterns of the time series. Mathematically, EOFs are eigenvectors of the
covariance matrix of a dataset; it is designed to reduce the dimensionality of the dataset
in order to simplify the interpretation of complex observations and can be an aid in the
62
decomposition of time series into a sum of components, each having a meaningful
interpretation. Figure 3-3 displays an example of a time series processed after SSA, a
rather complex and noisy impression of a time series was able to be recovered to a
meaningful underlying structure by SSA.
As shown in Figure 3-4, SSA predominantly consists of four steps involved in
decomposition the primary principles. The steps including (1) embedding to form a
trajectory matrix and subsequently to form a covariance matrix; (2) decomposition to
find the eigenvectors and eigenvalues of the trajectory matrix; (3) grouping to find the
vectors of principal components (PCs); (4) diagonal averaging to find the reconstructed
components (RCs) to recover to the original time series data length. The detailed steps
of SSA are explained as follows.
First, we are going to describe how to form a covariance matrix from a time series
for SSA. As shown in Figure 3-5, considering a one-dimensional time series X with N
observations denoted by 𝐗 = {𝑋𝑡: 𝑡 = 1… ,𝑁}. Each X has a chosen embedding window
dimension (M) to estimate the time-delayed embedding matrix - a trajectory matrix Y,
which is a diagonalized constant matrix that has equal element 𝑥𝑖𝑗 on the skew diagonals
where 𝑖 + 𝑗 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 and 𝐾 = 𝑁 − 𝑀 + 1. Note that Y here represents the evolution of
time series X with a caterpillar length M69.
𝐘 =
[ 𝑥1 𝑥2 𝑥3 ⋯ 𝑥𝑀
𝑥2 𝑥3 𝑥4 ⋯ 𝑥𝑀+1
𝑥3 𝑥4 𝑥5 ⋯ 𝑥𝑀+2
⋮ ⋮ ⋮ ⋱ ⋮𝑥𝐾 𝑥𝐾+1 𝑥𝐾+2 ⋯ 𝑥𝑁 ]
(3-3)
Second, assume that Y is normalized, the covariance matrix of Y (C), which
represents the covariance between 𝑋𝑡 and 𝑋𝑡+𝜏 for all 𝜏 = 0,… ,𝑀 − 1, is estimated by
63
C= 𝐘′𝐘/(𝑁 − 𝑀 + 1) where (∙)′ indicates the transpose of a matrix. Thus, the
eigenvalues and eigenvectors can be obtained by performing singular value
decomposition (SVD) of the covariance matrix C. Since C is a symmetric and positive
semi-definite matrix, let us denote its ordered eigenvalues by 𝜆1 ≥ 𝜆2 ≥ ⋯ ≥ 𝜆𝑘 ≥ 0 and
the corresponding orthogonal eigenvectors by𝑒1, 𝑒2, … , 𝑒𝐾. Let 𝐷 = max(𝑖: 𝜆1 > 0)(i.e.
the number of non-zero eigenvalues) and define the matrix.
𝑽𝑴,𝑫 = [𝑒1: … : 𝑒𝐷] =
[ 𝑣1,1 𝑣2,1 ⋯ 𝑣𝐷,1
𝑣1,2 𝑣2,2 ⋯ 𝑣𝐷,2
𝑣1,3 𝑣2,3 ⋯ 𝑣𝐷,3
⋮ ⋮ ⋱ ⋮𝑣1,𝑀 𝑣2,𝑀 ⋯ 𝑣𝐷,𝑀]
(3-4)
and 𝑉𝑗 = 𝐘𝑗′𝑒𝑗/√𝜆𝑗 for all 𝑗 = 1,… , 𝐷. Denote 𝐘𝑗 = √𝜆𝑗𝑒𝑗𝑉𝑗
′, then the SVD of Y can
be written as
𝐘 = 𝐘1 + 𝐘2 + ⋯+ 𝐘𝐷 (3-5)
Third, the grouping step corresponds to splitting the matrix Y into disjoint groups
and summing the matrices within each group into a principal component (PC) matrix.
Once Eq. (3-5) is obtained the grouping step will partition the index set {1, 2…, D into m
disjoint subsets, say, 𝐶1, 𝐶2, … , 𝐶𝑚 𝑤ℎ𝑒𝑟𝑒 𝑚 ≤ 𝐷. This yields a grouped matrix
decomposition
𝐘 = 𝐘𝐶1+ 𝐘𝐶2
+ ⋯+ 𝐘𝐶𝑚
(3-6)
Lastly, applying the so-called Hankelization procedure to all components in Eq.
(3-6) – that is the trajectory matrix corresponding to the series obtained by averaging
the diagonal elements (see the book by Nina Golyandina et al.71, 2001, Chapter 6,
Section 2), we obtain the approximation
64
𝑥𝑡 = ∑ �̃�t(𝑘)
𝑚
𝑘=1
(3-7)
where �̃�(𝑘) = (�̃�1(𝑘)
, … , �̃�𝑁(𝑘)
) corresponds to the matrix 𝑌𝑐𝑘 , 𝑘 = 1,… ,𝑚.
The primary benefit of exploiting the SSA in our study is that it can be used as a
model-free technique so that can be applied to non-stationary time series. In other
words, SSA can adapt to a patient’s dynamic change due to various respiratory patterns
during the treatment. Also, this approach is suitable for the actual clinical situation while
baseline shift or irregular respiratory pattern of the patient might be presented. For the
above reasons, it gives us the motivation for a model-free direct tumor tracking for a
more realistic adaptive application.
65
Figure 3-1. A demonstration of how the principal component analysis from the sensor coordinates to data-centric coordinate in the principal component space. Photo Courtesy of Pingfang Tsai. (September 4, 2019)
Figure 3-2. Process of singular value decomposition of a two-dimensional matrix. Reprinted with permission from Wikipedia Website, https://en.wikipedia.org/wiki/Singular_value_decomposition (September 4, 2019).64
66
Figure 3-3. An example of a time series processed after singular spectrum analysis. The purple curve is the original time series, and the red curve is the reconstructed time series after singular spectrum analysis. (Reprinted with permission from Nina Golyandina, et al., Singular Spectrum Analysis for Time Series, Springer, 2013, Chapter 2, Section 2.72)
Figure 3-4. The diagram displays the steps involved in obtaining the reconstructed time series through singular spectrum analysis.
67
Figure 3-5. Illustrate the process of forming the trajectory matrix (Y) for a time series {𝑋𝑡: 𝑡 = 1… ,𝑁}.
68
CHAPTER 4 TUMOR PHASE RECOGNITION BY LOCAL PRINCIPAL COMPONENT WITH
MULTIVARIATE SINGULAR SPECTRUM ANALYSIS FROM CONE-BEAM TOMOGRAPHY PROJECTIONS AND EXTERNAL SURROGATES
Background
Radiation therapy requires precise dose delivery to the intended treatment area.*
Accurate treatment delivery to lung cancers is particularly challenging as the tumor is
continuously moving along with the respiratory cycles during the treatment. Respiratory-
induced tumor motion is one of the potential sources of error in lung radiation therapy.
Many motion management approaches1,2 have been developed to improve the delivery
accuracy to the lung tumors. Respiratory gating73 is one of them. Respiratory gating
controls the radiation beam on-and-off depended on whether the tumor is inside or
outside the treatment fields during the treatment. It often uses either external or internal
surrogates to trigger the beam74-77. However, respiratory phase inconsistency between
the tumor and surrogates are not uncommon and largely depends on the tumor location
and patient respiratory pattern17,60,78,79. Thus, the ability to accurately extracting the
phase correlation between the tumor and surrogates becomes crucial to ensure
accurate gating-based delivery. 4D-CBCT is another contemporary technique for
respiratory motion management. As 4D-CBCT images include both spatial and temporal
information of tumor and surround anatomy, they allow the clinician to determine the
tumor motion range and make subsequently clinical decision for tumor alignment.
Tumor phase information also plays a crucial role in the imaging reconstruction process
* This chapter is reprinted with permission from Wiley Publishing (2019). “Tumor Phase Recognition by local principal component with multivariate singular spectrum analysis from cone-beam tomography projections and external surrogates”, P Tsai, G Yan, C Liu, Y Hung, D Kahler, JY Park, JG Li, B Lu; Medical Physics; [under review]
69
of 4D-CBCT. Correct phase sorting can significantly reduce the motion artifact of the
reconstructed images of each phase.
Directly tracing the lung tumor and extracting its phase information has never
been an easy task for radiation therapy society, majorly due to the incapability of decent
tumor-soft tissue distinction of traditional image modalities (e.g., kilo-voltage (KV) x-ray
images, mega-voltage (MV) x-ray images, CBCT images, ultrasound images, etc.).
Recently, Magnetic resonance-guided radiation therapy (MRgRT) provides the potential
to extract tumor motion, benefited from good contrast between tumor and surrounding
tissue of the MR images25. However, the availability of the MRgRT machine to most of
the clinics is still limited due to the high cost and limited production. Most of tumor
tracking capabilities of MRgRT is still in the research stage26. An alternative strategy for
tumor phase extraction is to extract tumor phase information using surrogate
information in lieu of the tumor itself. Two major methodologies using such strategy
have been widely developed and applied. One is to use external surrogate information
to extract the phase information, whereas the other one is to use internal surrogate
information. Since most of the external surrogate information can be acquired by
readily available detection devices such as pressure sensors, infrared cameras, etc., it
had become much more popular than the internal surrogate-based mechanism in
routine clinics. Typical external surrogate acquisition system includes the bellow system
(Phillips Healthcare, Cleveland, OH, USA), real-time position management (RPM)
system (Varian Medical Systems, Palo Alto, CA, USA), Brainlab ExacTrac system
(BrainLab, Munich, Germany), AlignRT® system (Vision RT, London, England) and etc.
The information extracted by those system contains the distinct oscillation of respiratory
70
cycles. And yet, it has intrinsic discrepancy as the phase patterns between external
surrogates and internal tumor or anatomic structures are not necessary to be congruent,
which was observed in several literatures17,60,78. On the contrary, internal surrogate-
based methods can potentially overcome such drawbacks. Ideally, if the surrogate is
proximal or even inside the tumor, the phase information detected can be directly
treated as the phase information of the tumor. Such attempts have been made by
implanting fiducial markers27-30 or electromagnetic transponder beacons31-33 into the
tumor region, then using x-ray image modalities or radiofrequency to track them,
respectively. However, the implanting procedures are invasive, which can cause the risk
of pneumothorax34,35 or pulmonary hemorrhage36. The implanted surrogate can also
experience migration throughout the treatment37,38.
Considering the practicability of marker implanting methods, markerless methods
have been developed. Many researchers have attempted to recover the internal
respiratory phase information using CBCT projections. The strategies include intensity-
based methods, such as Amsterdam Shroud (AS) method57, intensity analysis (IA)
method58, frequency-domain methods, such as Fourier transform method (FT) 80, as
well as the statistical-based method, such as local principal component analysis (LPCA)
algorithm60 and a two-step L1-norm LPCA method17. All those methods can effectively
recover the phase information during the imaging with the identifiable surrogate
information. The LPCA statistical method is more robust than intensity-based methods
in general60. It cannot only discover the underlying structure of the dataset but also
provides the flexibility of choosing the principal components and discards the source of
noise or outlier at the same time. Nevertheless, the limitation of the above methods is
71
apparent. First, due to the weakness of tumor phase information in the original
projections, surrogate with strong and distinct signal (e.g. diaphragm) have to be
included in order to extract the distinct and dependable phase information. However,
this process can make the extracted phase information be internal-surrogate-like rather
than true tumor phase information. In addition, once the surrogate diaphragm
disappears from the projection views, the extracted result is affected. The discrepancy
largely depends on relative anatomical location between tumor and surrogate as well as
respiratory physiology, as we discussed. Second, missing surrogate information from
the images due to poor contrast, anatomical obstruction, or imaging cutout, can also
significantly undermine the quality of the phase signal reconstruction for those
approaches.
In this study, we proposed an innovative method to overcome the disadvantage
of current surrogate methods by combining both external and internal surrogate
information. Internal surrogate data were acquired using cropped CBCT projection
within the tumor area only. LPCA method was then adopted for initial signal extraction.
The external surrogate was acquired by recording infrared marker movement using an
infrared camera system. Singular spectrum analysis (SSA) method was followed to
further remove the small un-wanted skin movement due to the highly sensitive signal
from the infrared system. Then, we applied multivariate singular spectrum analysis
(MSSA) method to combine the oscillatory information from both the external surrogate
and the internal features to recover the tumor respiratory cycles in all projection angles
of views. With the assistance of external motion information, this method can recover
the tumor phase information even when the internal signal is not strong enough to be
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detected. The validation experiment with phantom study and the feasibility of applying
our method on clinical lung patients were also investigated in this work.
Materials and Methods
In this section, the details of the equipment and methodology used for internal
and external signal acquisitions were first introduced. An innovative phase
reconstruction algorithm using acquired signals were then described systematically. The
evaluation methods tested on both phantoms and patients were depicted at the end.
Raw Data Acquisition for Internal and External Signals
Acquisition for internal signal using CBCT
CBCT projections were used as the raw data to reconstruct the internal signal.
An Elekta Versa HDTM linac accelerator (Elekta Inc., Stockholm, Sweden) featured with
an x-ray volume imaging (XVI) system was utilized for CBCT scan. As shown in Figure
4-1 A), XVI system consists of a kilovoltage (KV) x-ray source and a KV flat-panel
detector mounted on the linac gantry. A typical 360-degree acquisition for a full CBCT
scan takes about two minutes to accomplish and received around 700 projection
images. Each projection image with 512x512 pixels was acquired with the 40.96 cm KV
image receptor (pixel size: 0.8mm).The sampling rate is around 0.183 second per
projection.
Acquisition for external signal using OTS
In our study, the external surrogate of testing objects was represented by an
infrared marker attached to the surface of the testing object (either phantoms or
patients) and its real-time position was captured by the optical tracking system (OTS)
with a pair of infrared camera mounted on the vault ceiling, as shown in Figure 4-1 B).
For phantoms, the infrared reflective marker was attached to the outside of the
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phantom’s movable insert shown in Figure 4-1 A) and C); for patients, an infrared
reflective marker was placed on the skin surface of the abdominal region where is
approximately 5cm inferior to the xiphoid process and at the midline of the patient.
Synchronization between internal and external data
The acquisition of the temporal correlation between internal and external data is
crucial for our signal processing algorithm for precise tumor phase reconstruction. To do
so, an additional reflective marker was attached to the KV flat-panel shown in Figure 4-1
A). Since the correlation between the gantry angle and panel marker position can be
empirically determined, the correspondence between the gantry angle of projection
acquisition and surface marker position during the scan can be indirectly established by
simultaneously tracing the KV panel marker and the surface external surrogate marker.
With the help of CBCT acquisition log file, one to one correspondence between
projection and its acquired gantry angle was extracted. Accordingly, the final correlation
between acquired projection images and its corresponding surface marker position
during the scan was ultimately determined.
Tumor Phase Reconstruction Algorithm Using both External and Internal Signal
Amsterdam Shroud (AS) image generating using CBCT projections
In this work, an AS image using CBCT projection was initially generated for
tumor phase information extraction. The procedures suggested by the several
literatures17,60 was applied here for this purpose and described as follows. First, each
projection image is converted to intensity image (inverse image) and then to attenuation
image by taking the logarithm of the intensity image to improve the image contrast and
tumor visibility. Second, the cranial-caudal (CC) derivative image was generated from
the attenuation image in order to enhance the anatomic features of the image. Third, the
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tumor region of the images was cropped for column array generation. Fourth, an initial
AS image is formed in a column-based manner, which arranges by the order of the
cropped projection image was received. Last, to improve the homogeneity of the AS
images, the final AS images were generated by applying the adaptive z- normalization
process to the initial AS images, suggested by Chao et al.17. An illustration of the image
process steps has been demonstrated in Figure 4-2 B). The details for the adaptive z-
normalization step can be referred to Chao et al.10 ‘s work and will not be repeated here.
It should be noticed that the distinction between our method and other common
methods is the region-of-interest (ROI) selection of the projection images for column ray
generation in step 3. Unlike other methods using the whole projection images, we only
employed the cropped ROI in the tumor region shown in Figure 4-2. The rationale
behind is to minimize the impact of the signal interference from surrounding anatomic
structures (e.g. diaphragm) and/or non-human tissue artifacts (e.g. pacemaker, implants
or treatment couch top) on the initial signal extraction. The size and location of the
region-of-interested (ROI) were determined by the patient-specific tumor location, tumor
size and tumor motion range estimated from the simulation four-dimensional computed
tomography (4D-CT). The center location of the ROI on the projection image was
defined as the projection point of the centroid of the internal tumor volume (ITV) on the
projection images. The ROI is defined as the rectangle which covers the ITV projection
on the CBCT projection images with 5 mm expansion on both sides. Tumor- AS image
after adaptive z-normalization is then ready for phase signal extraction.
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Initial respiratory waveform extraction using Local Principal Component Analysis (LPCA)
In the next stage, in order to obtain the respiratory waveform, it is required to
apply an approach to extract the signal from the AS image. Even though Yan’s
statistical LPCA method60 is particularly affected by the pixel intensity of the surrounding
structures, especially the diaphragm. In addition, in the majority of the clinical patient
cases, the tumor was obstructed by multiple anatomic structures that were not
discussed in Yan’s original work. Nevertheless the potential problems, we
adapted/employed the LPCA algorithm approach proposed by Yan et al.60 to extract the
initial respiratory waveform. The algorithm essentially uses a sliding-window fashion to
implement LPCA on the AS image. The idea is briefly introduced as follows in Figure 4-
3.
First, a LPCA column window width (W) is selected, and the window moves
sequentially by one column along the horizontal direction on the Tumor-AS image. For
the first window, the eigenvectors associated with the first PC was selected as the
principal direction since it reflects the most significant variance of the data and the PC
scores were used as the extracted signal for columns 1 to [W/2]+1. To ensure the
continuity of the extracted curve on the following windows, the correlation of each of the
first five PCs with the PC obtained from the previous window was calculated.
Subsequently, the PC has the highest correlation is selected as the principal direction
for the current step, and the corresponding PC score at the center column is selected as
the extracted signal for this column. To keep the principal direction consistent with the
one obtained from the previous step, a sign reverse might be necessary (since the PCA
cannot distinguish the positive or negative direction). The directional information was
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fed in from the real-time external surrogate signal by OTS in this study. Last, the last
window is from N-W +1 to N, the scores were used as the data points for the last
window. The end result is a time series of the tumor respiratory waveform, we called the
tumor LPCA signal. In this study, we chose the W from one to three breathing cycles as
suggested by Yan et al.60.
Final respiratory waveform reconstruction using external surrogate information
According to the previous session, the initial respiratory waveform obtained using
LPCA could potentially present some inconsistent and perturbed patterns, especially at
the observation window formed by the lateral projection views. However, unlike internal
signal, this phenomenon is not presented in the external surrogate signal as no
obstruction is presented in the way between the surrogate (fiducial marker) and the
detection system (IR camera). Thus, if we can utilize an external signal to assist with
the recovery of the internal tumor oscillation by correlating two signals in a time serial
pattern, the unperturbed internal signal can be conceivably reconstructed. Following
such ideology, a statistic method, called multivariate singular spectrum analysis (MSSA)
was introduced in this study to achieve this goal. Detail algorithm is provided as
followed.
First, let us define the initial respiratory waveform from LPCA as a one-
dimensional time series denoted by 𝐗 = {𝑥𝑡 ∶ 𝑡 ϵ 1, … ,𝑁}, where t represents the
observation of the time serial from No. 1 to No. N with an equal time interval (gantry
angle); 𝑥𝑡 represents the magnitude at the observation 𝑡. Then, a trajectory matrix Y is
created by stacking K number of X subseries, namely 𝑋𝑖, i is from 1 to K, which
possesses M number of consecutive observations and offset starting elements, as
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indicated in Eq. 4-1. M is an embedding time-delayed dimension, typically, 1 to 3
breathing cycles, and 𝐾 = 𝑁 − 𝑀 + 1.
𝐘 =
[ 𝑋1
𝑋2
𝑋3
⋮𝑋𝑘]
=
[ 𝑥1 𝑥2 𝑥3 ⋯ 𝑥𝑀
𝑥2 𝑥3 𝑥4 ⋯ 𝑥𝑀+1
𝑥3 𝑥4 𝑥5 ⋯ 𝑥𝑀+2
⋮ ⋮ ⋮ ⋱ ⋮𝑥𝐾 𝑥𝐾+1 𝑥𝐾+2 ⋯ 𝑥𝑁 ]
(4-1)
The structure of matrix Y innately correlates the underlying oscillation respiratory
pattern as the time evolved, which is able to capture the signature of the dynamical
behavior of the time series for our study.
Applying the same method, we can construct a time series and its corresponding
trajectory matrix for the external surrogate signal as well. Now, two channels of time
series are created in our study: Channel one is the external surrogate signal from OTS
denoted by 𝑿𝟏(𝒕); channel two is the preliminary result from LPCA step denoted by
X2(𝑡). Y1 and Y2 are the corresponding trajectory matrix, respectively. Now, a grand
covariance matrix between the two time series can be formed using Eq. 4-2, as
illustrated in Figure 4-4.
𝐂 = 𝕐′𝕐/(𝑁 − 𝑀 + 1), as 𝕐 = [𝐘𝟏, 𝐘𝟐] (4-2)
where (∙)′ indicates the transpose of a matrix.
Matrix C represents the covariance between 𝑋𝑡 and 𝑋𝑡+𝜏 with time lag of 𝜏 =
0, … , 𝑀 − 1. It includes auto and cross-covariance from both of time series
X1(t) and X2(t). More specifically, four-quadrant submatrix of C: C(1,1),C(2,1), C(2,1)
and C(2,2) represent the covariance between neighbor observations of X1(𝑡) and itself,
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neighbor observation of X1(𝑡) and its X2(𝑡) counterpart, neighbor observation of X2(𝑡)
and its X1(𝑡) counterpart, and neighbor observation of X2(𝑡) and itself, respectively.
Second, the eigenvalues and eigenvectors of C were obtained by performing
singular value decomposition (SVD). Since C is a symmetric and positive semi-definite
matrix, let us denote its ordered eigenvalues by 𝜆1 ≥ 𝜆2 ≥ ⋯ ≥ 𝜆𝑑 ≥ 0 and the
corresponding orthogonal eigenvectors by 𝑒1, 𝑒2, … , 𝑒𝑑. Let 𝐷 = max{𝑖: 𝜆𝑖 > 0} (i.e. the
number of eigenvalues) and define the matrix for eigenvectors (V).
𝐕 = [𝑒1: … : 𝑒𝐷] =
[ 𝑣1,1 𝑣2,1 ⋯ 𝑣𝐷,1
𝑣1,2 𝑣2,2 ⋯ 𝑣𝐷,2
𝑣1,3 𝑣2,3 ⋯ 𝑣𝐷,3
⋮ ⋮ ⋱ ⋮𝑣1,2𝑀 𝑣2,2𝑀 ⋯ 𝑣𝐷,2𝑀]
(4-3)
After the orthogonal eigenvectors were obtained, the principal component (PC)
can be calculated by projecting the data 𝕐 onto linearly uncorrelated orthogonal axes in
the principal component space. This is the grouping step where it was disjointed into 𝐷
subsets. Thus, each principal component can be calculated by Eq. 4-4.
𝐏𝐂𝑗 = 𝕐𝑒𝑗 (𝑗 = 1,… , 𝐷) (4-4)
To reconstruct the trajectory matrix 𝕐(𝑟) possessing only most dominant PCs, an
invert projection method was used as Eq. 4-5 and 4-6 shown. Each PC (𝐏𝐂𝑗) is projected
back to the original data-centric coordinates first. It yields the 𝕐𝒋 denoted as following
𝕐𝒋 = [ 𝐘𝟏𝒋, 𝐘𝟐𝒋] = 𝐏𝐂𝒋𝑒𝑗′ = 𝕐𝑒𝑗𝑒𝑗
′ (4-5)
Then, linear combination of the invert projected principal component yields the
best approximation of 𝕐 as ‖𝕐 − 𝕐(𝑟)‖ is minimum.
𝕐(𝑟) = [𝕐𝟏(𝑟) , 𝕐𝟐(𝑟)] = ∑ 𝕐𝑗
m
𝑗=1= ∑ [ 𝐘𝟏𝒋, 𝐘𝟐𝒋]
𝑚
𝑗=1 (4-6)
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where 𝒎 (𝒎 ≤ 𝐷 ) represents the index of the first m number of most dominant
PCs.
The selection of 𝒎 is based on the weight of each PC. It required the summation
of its corresponding eigenvalue normalized to the summation of the total eigenvalues be
greater than a threshold (𝑇) range from 0.9 to 0.99, which was manually chosen for
each case. It can be expressed mathematically as Eq. 4-7.
min {𝑚: ∑ 𝜆𝑖
𝑚𝑖=1
∑ 𝜆𝑗𝐷𝑗=1
≥ 𝑇} (4-7)
Lastly, we reconstruct internal tumor waveform 𝐗𝟐(𝑟)from 𝕐𝟐(𝑟)using
Hankelization procedure. Detail procedure doesn’t repeated here. Interested reader can
refer to Golyandina et al.71
LPCA-MSSA workflow
To summarize our LPCA-MSSA approach, the workflow is depicted in Figure 4-5.
First, the tumor ROI size is determined from the simulation 4D-CT images before
treatment and is taking the maximum tumor dimension and tumor motion range into
account. Second, during CBCT acquisition, the OTS is employed to capture the real-
time signal from the KV panel and external surrogate reflective marker. At the
meanwhile, the CBCT acquisition information file (_Frame.xml) and the OTS log file
(.log) were collected to obtain the co-occurrence of CBCT scan with the external
surrogate signal. Once the projection image is available from the CBCT scan, the
appropriate image processing is performed and then assemble in the order it was
received to a tumor region-based AS image (Tumor-AS image). Third, based on the
estimated respiration rate from an external surrogate signal, LPCA is performed on the
Tumor-AS image with the pre-determined LPCA window width to obtain the preliminary
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tumor LPCA signal. Four, we used MSSA to recover the tumor respiratory waveform
which the respiratory oscillation was recovered and noise principal components were
discarded in full 360-degree angles. In this step, the input signals were the preliminary
tumor LPCA time series and the external surrogated time series processed by SSA. The
reason for SSA is that the collected external surrogate signal is often sensitive to the
minor un-wanted motion on the patient’s skin; thus the external surrogate signal was
processed using SSA with embedding dimension (M) equal to ten to remove the
variation of such noise. Therefore, we can ensure we do not input an unfavorable and
noisy external surrogate signal before proceeding to the MSSA steps. In the final step,
the internal tumor respiratory waveform can be recovered for this treatment.
Data Collection and Analysis
Phantom study
A QUASARTM 4D respiratory motion phantom (Modus Medical Devices Inc.,
London, Canada) was employed for respiratory simulations. The signal received from
the infrared-reflective marker on the movable insert was used as the ground truth; the
extracted tumor motion signal from CBCT projection images is considered as the
reconstructed waveform. Our method was assessed in four different aspects. (1) The
reconstructed results between LPCA and our method LPAC-MSSA were compared in
the frequency domain using power spectrum analysis for a sinusoidal respiratory motion
case, (2) The sensitivity on CBCT scanning uncertainty was tested for waveforms
reconstructed by both LPCA-MSSA and LPCA methods using ten repeated CBCT
scans. Peak-Valley time differences and phase discrepancy from the ground truth
among repeated scans were analyzed. (3) The robustness test of LPCA-MSSA method
on the phase shift and amplitude variation of the external surrogate was also performed.
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Three arbitrary phase shifts and three amplitude variations were applied to the original
external surrogate signal (12 BPM sinusoidal waveform) for testing purposes.(4) The
influence of anatomic structures obstruction to the waveform reconstruction was finally
assessed. Three anatomic obstruction scenarios were simulated. The first scenario was
to simulate the obstruction by heart with a solid-filled three-dimensional (3D) printed
heart placed at the side of the phantom. The second scenario was to simulate the ribs
obstruction by placing the Polyvinyl Chloride (PVC) tubes on the top and two sides of
the phantom arranged in a parallel fashion. The third scenario was to simulate the
multiple human-tissue perturbations in the lung region by placing Rando® phantom
slabs around the QUASARTM 4D phantom. Figure 4-6 demonstrated the placement of
various simulated structures. Five respiratory patterns, including sinusoidal, cardiac-
artifact, jitter-artifact, triangular, typical fast breathing waveform, were applied to each
obstruction scenarios to ensure the versatility of our method. The extracted tumor
LPCA-MSSA results were then compared to ground truths.
Patient study
Eight patient cases with various tumor sizes and locations inside lungs were
investigated in this study. Two of them have artificial implant of high density materials
proximate to lung areas, which are shown in CBCT projection images of Figure 4-7. The
tumor size varies from 1.5 to 5.5 cm, and the tumor motion range is from 3.5 to 20 mm.
Unlike phantom study of which internal tumor motion can be accurately simulated and
confirmed, the true tumor motions of patients is unknown. However, a reference tumor
motion waveform can still be extracted by tracing the tumor position on the projection
images using the following procedures. First, the window and level of each projection
image were adjusted individually in order to display the best visibility of the tumor on
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each projection. Then, the superior and the inferior pixel of the tumor were identified on
each projection. The center position (average between inferior and superior position)
subsequently mapped onto Tumor-AS image. The reference waveform of the center of
the tumor was finally established by tracing tumor center projection on the Tumor-AS
image.
The congruency between the reference waveform and the extracted waveform
was examined with respect to overall phase discrepancy (%), expiration phase
discrepancy (%), peak accuracy (seconds), and valley accuracy (seconds). In addition,
we evaluated the percentage of variance (%) and the number of PCs required while
applying LPCA-MSSA algorithm for various respiratory pattern.
Results
Phantom Study
The comparison of LPCA only method versus our approach (LPCA-MSSA) was
shown in Figure 4-8 using power spectrum density with a logarithm scale in the
frequency domain. Our LPCA- MSSA method not only matches the overall trend line
matches with the ground truth but also preserves the primary frequency (~ 0.2) of the
signal. Moreover, the area under the matched frequency (~0.2) for the LPCA-MSSA
method is larger than the LPCA only method, which implied the majority of the portion of
the waveform is recovered to match with the ground truth respiratory waveform
frequency by using LPCA-MSSA approach. For the sensitivity of the CBCT scanning
uncertainties, Figure 4-9 shows the LPCA-MSSA method presents smaller uncertainties
than the LPCA only method when compared to the ground truth in both time accuracy in
A) and phase discrepancy in B). Each group contains 10 colored dots where one dot
represents the result from one CBCT scan when compared to the ground truth.
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Moreover, the 95% confidence interval (CI) for LPCA-MSSA approach was ± 0.1
seconds in time accuracy and ± 3.4% for overall phase discrepancy. On top of this, the
most distinct difference between the two methods falls in the expiration phase
discrepancy, the LPCA only method has 95% CI of ± 9.8 % and LPCA-MSSA method
has 95% CI of ± 0.4%.
For examining the robustness of our algorithm, Figure 4-10 shows that the
internal tumor LPCA- MSSA waveform is not affected by the amplitude variation or
phase shift of the surrogate signal, which can be an external surrogate or other internal
anatomic structures in a clinical application. Among all the scenarios that we have
tested for the effect of phase shift and arbitrary amplitude variations, the recovered
internal tumor signal has peak and valley accuracy -0.009± 0.18 seconds compared
with the ground truth, and there was merely no time delay found.
Figure 4-11 displayed one of the sample waveforms from the anatomic
obstruction experiment, the LPCA- MSSA method not only significantly mitigates the
impact of the noise on the nearly lateral projection views where were indicated in the
rectangle area but also preserve the trend and the oscillation of the waveform compared
to the LPCA only method. By exploiting the LPCA-MSSA method, the tumor underlying
oscillation feature was recovered despite the disturbance from the overlapping anatomic
structures. Moreover, the extracted LPCA-MSSA respiratory patterns agreed with the
ground truth observed by the OTS. Among all the anatomic obstruction simulations and
with all the respiratory waveforms were tested, the extracted LPCA – MSSA signal had
expiration phase deviation 1.59± 1.98 %, peak accuracy -0.12±0.28 second, and valley
accuracy 0.01±0.15 second compared with the ground truth.
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Patient Study
The LPCA window width (W), number of observations (N), depends on the
degree of anatomic obstructions and the respiratory cycle length; the number of
variables (P) relies on the ROI size on the vertical direction, which is related to the
tumor size and motion range. Thus, the parameters requires is manually optimized by
the user. Table 4-1 shows the result for all the patient cases, and the overall extracted
LPCA-MSSA waveform compared to the reference waveform had overall phase
discrepancy -1.05±3.0 %, expiration phase discrepancy -1.55±1.45%, peak accuracy
0.04±0.13 seconds, and valley accuracy -0.01±0.15 seconds. All phase discrepancies
were within ±5% for all cases, and the peak-valley accuracy was within 0.3 seconds. In
addition, Table 4-2 shows the variance distribution of each PC was selected for final
waveform reconstruction; it shows that all the patients contain around 80 percent of the
variance on their first PC. The number of PC was used for reconstruction is depending
on the complexity of the waveform. The total percentage of variance needed ranged
from 89%-98% (2 – 9 principal components) for all the cases in this study. Figure 4-12
shows the reconstructed waveform and the variance distribution of each PC for patient
ID 4 and 6. It illustrates the LPCA-MSSA approach successfully recovered the
respiratory oscillation information from the LPCA only method, and it captures the trend
of the waveform as well.
Discussions
Based on the results presented in the previous section, it suggested that the
LPCA-MSSA algorithm can recognize tumor phase with adequate time and phase
accuracy in both phantom and patient studies. The MSSA approach is widely used in
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economics68 or geophysics66,67,69,70; it has abilities to solve the time series for change
point detection, noise removal, periodicity extraction, and detect the trend or
oscillating65. The major advantages of MSSA for our study are: (1) it can be used as a
model-free technique; (2) it can be applied to non-stationary time series. Those pros are
especially beneficial to the dynamic change of the patient’s respiratory pattern where
baseline shift or irregular respiratory waveform might be presented.
By employing the MSSA method for tumor respiratory waveform reconstruction, it
is capable of handling all the clinical scenarios we had simulated. The LPCA-MSSA
method shows superior performance compared to LPCA only method in terms of CBCT
scanning uncertainties and overlapping anatomic obstructions in the phantom study.
The possible cause of the CBCT scanning uncertainties in Figure 4-9 is due to the
position of the tumor varies for each scan when the CBCT acquisition started. In other
words, the tumor position had different relationships with the overlapping anatomic
structures for each scan. Thus, each scan had a minor difference in pixel values
presentation on the Tumor-AS image for this statistical-based method. In addition,
Figure 4-10 shows the MSSA uses its data to create a covariance matrix without any
presumed model to find the multiple meaningful principal component directions in terms
of variance. When the PCs were back-projected to the data-centric coordinates with
linear transformation, the final result was not affected by the external surrogate phase
shift or amplitude variation. This result represents the external surrogate only assist us
in finding the correct representation of the oscillation, the final result still recovered by
the internal tumor signal itself. Moreover, even though Figure 4-11 B) shows we had
successfully reconstructed the tumor respiratory oscillation by using LPCA-MSSA
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approach, but the trend of the waveform was captured as well. In this case, the trend
pattern may not be the vital feature that we want to recover. Therefore, de-trend of the
curve is suggested as future work to the possible improvement.
For the patient study, LPCA-MSSA approach shows excellent results, but we
may still need to determine what is clinically acceptable for the patients. In fact, the
typical human respiratory cycle is 3-5 second and each respiratory cycle is divided into
ten phases for respiratory gating application. In order to have less than one phase shift
inaccuracy, the reasonable criteria for clinical use are that the phase has less than one-
tenth of the breathing cycle and time accuracy has less than one-tenth of the average
breathing cycle. For example, the expected criteria for a 4-second breathing cycle
waveform would have 0.4 seconds criteria for the time accuracy and less than 10%
phase discrepancy. Therefore, in this study, among all the patients we validated, the
time accuracy and the phase discrepancy were all within the expected standards.
In this study, the LPCA window width and MSSA embedding were manually
optimized by the user. The case-specific LPCA window width (W) and MSSA
embedding dimension (M) are ranged from 1 to 4 respiratory cycles. The number of
PCs was chosen depending on the characteristics and the complexity of the patient’s
respiratory patterns. The regular respiratory waveform can be recovered by 90 percent
of variance. In contrast, the irregular waveform we defined here as the breathing cycle
length and relative amplitude are constantly changed during the observation period.
Thus, the complex respiratory waveform required nearly 99% percentage of variance as
it contains more underlying behaviors. Moreover, the trend of the waveform was
captured with the LPCA-MSSA approach. In other words, if it only retrieves the trend of
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the waveform from the irregular waveform, which may be misleading in our application.
In summary, for a highly irregular respiratory pattern, it is essential to include the
principal components with those small and similar variance percentages to recover
more complex underlying features were captured.
In the following section, we will address some of the limitations and drawbacks of
other existed literature compared to our approach. Yan et al.60 had shown the LPCA has
more potential in the recovery of the respiratory signal compared to the previous
mentioned AS, IA, and FT approaches. The drawbacks of using the whole projection AS
image will be discussed as follows. First, the whole projection AS image contains a
mixture of multiple organ motion information across the lungs and result in different
extracted results with different rows of selection on the AS image as shown in Yan et
al.60 and Chao et al.17. Second, the performance of the result is compromised not only
when the diaphragm is not in the view of the projection images but also when the
features of the diaphragm or other human-made structures (e.g. couch or immobilization
devices or pacemaker) have relative enhance pixel values than the tumor itself.
Moreover, when the anatomic organs are not located at the isocenter, the mixture of the
organ motion waveform representation does not maintain in the same vertical height on
the whole projection AS image due to beam divergence, thus the correlation coefficient
calculation would be affected using the LPCA method since the most notable variance
change across all the variables instead of maintaining on the same variables (same
axes).
In conclusion, the major benefits of including only the tumor region AS image are:
(1) by excluding those outlier’s pixel values, the LPCA is relatively stable compared to
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utilizing the whole projection images81; (2) the variables (P) can be less than the
observations (N), so we do not lose degree of freedom to ensure the covariance matrix
is full-ranked. The number of variables used depends on the number of pixels were
included in the ROI which depends on the tumor size and tumor motion range. For
some patient cases, we have to reduce the number of pixels by averaging the
neighboring pixels in the vertical direction on the Tumor-AS image to maintain the 𝑃 ≤
𝑁 relationship.
Furthermore, the advantage of using local window width selection is that the
patient’s respiratory cycle is more semi-periodic; in other words, the frequency of patient
respiration may change over time. The local window selection only captures the
characteristics of the local neighboring projections. If a longer window size was used,
the discrepancy between the reference waveform and the extracted signal was
observed in the clinical scenario cases. Currently, the window selection for LPCA
method is optimized by the user. The disadvantages of the LPCA only framework
include: (1) it is very sensitive to the window width as it depends on the degree of
anatomic obstruction on the first couple breathing cycles where are usually the nearly
lateral projection views of the CBCT scan; (2) it only keeps the first most dominant PC.
(3) The window width only can be an odd number. If the first window did not capture the
correction principal component direction, the rest of the window is based on the
principal component direction on the first window where might be misleading. Whereas;
the MSSA approach gives us the freedom of how many PCs that we want to preserve.
The percentage of the total variances was chosen is based on the degree of irregularity
on patient’s respiratory patterns; the more irregular of the pattern requires higher
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confidence interval (more PCs) to include a more complex underlying structure of the
original respiratory waveform.
The further improvements can be implemented as following: (1) apply the
MSSA method directly on the Tumor-AS image by the 2D extension of MSSA82, since it
enables us to capture multiple series to provide the correct indicator on the principal
directions. (2) De-trend the time series before processing the MSSA or extract only the
PCs that contain the oscillation within the range of the human respiratory cycle. Due to
the trend of the waveform is affected by the degree of the anatomic obstruction on the
nearly lateral projection views which may not be the realistic trend representation of the
tumor respiratory waveform that we ought to capture. (3) Establish criteria to distinguish
the degree of irregularity on the waveform for automatic local window width selection.
For the future application, our approach can be used for an adaptive online
application as the directional information is feed in real-time by OTS and both LPCA and
MSSA window width is within 1- 3 breathing cycles (3-15 seconds) which implied it
could extract the phase information and take action promptly. In addition, the MSSA can
be applied to a broad sense of application; it can be used in any monitoring time series
regardless of the image modalities were used. In this study, only one OTS reflective
marker was used as a respiratory oscillation indicator for continuous monitoring during
the treatment. Similarly, other available modalities, such as the external surface
detection imaging83 or internal ultrasound tracking8 can potentially provide essential
information in help with the tumor phase recognition by applying the MSSA algorithm.
Conclusions
The LPCA-MSSA algorithm is capable of recognizing tumor phase information in
all angles of views was developed. With the aid of oscillation information of external
90
surrogate and neighboring information of preliminary internal tumor signal, the
prediction accuracy was significantly improved compared to LPCA only algorithm. Most
importantly, with sufficient accuracy, it enables us to use it as the ground for 4D-CBCT
reconstruction, respiratory gating treatment, and other clinic implementations, which
require accurate tumor phase information.
91
Figure 4-1. The experiment design for our study. Photo Courtesy of Pingfang Tsai (September 4, 2019) A) The cone-beam tomography system with KV x-ray source and KV flat panel detector were shown. Infrared reflective markers were attached on the side of KV flat panel, and the phantom motion insert, respectively. B) An optical tracking system (OTS) equipped with two infrared cameras to capture the real-time positions of the reflective markers. C) a QUASARTM respiratory motion phantom where the motion direction is indicated with the white arrow and the red circle indicated the location of the attached infrared-reflective marker which is served as the ground truth for the phantom study.
A
B
C
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Figure 4-2. Tumor- Amsterdam Shroud image generation. A) The image processing steps from the original projection image to a column array where only the pixel values within the tumor region-of-interest were summed. B) Assembling each column array by the order the projection image was received to form a Tumor-AS image and the result after applying adaptive z-normalization.
A
B
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Figure 4-3. Apply Local principal component analysis (LPCA) on Tumor-Amsterdam Shroud image. Note that N is the total number of projections, W is the LPCA window width, and P is the variable depends on the selected tumor ROI size. W is the window width while performing LPCA, then the number of observations is equal to W in this case.
Figure 4-4. The grand block covariance C structures for multivariate singular spectrum analysis (MSSA). Y1 and Y2 are the trajectory matrix of time series 𝑋1(𝑡) and
time series 𝑋2(𝑡), respectively.
94
Figure 4-5. Workflow for the LPCA-MSSA algorithm
95
Figure 4-6. Simulation of anatomic obstructions, including hearts, ribs and other normal
tissues, on a QUASARTM respiratory motion phantom. Photo Courtesy of Pingfang Tsai. (September 4, 2019)
Figure 4-7. Clinical lung patient selections. A) Tumor locations in the lungs of the selected clinical patients. B) Two of the selected patients present high-density material in the arm implant (Patient 1) or a pacemaker (Patient 3) where the gray box indicates where the tumor location is.
A B
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Figure 4-8. A twelve breathes per minute sinusoidal waveform analyzed in power spectrum density with log scale in the frequency domain. The arrow indicates where the peak location that matches the frequency of the original breathing waveform.
Figure 4-9. The sensitivity of LPCA only and LPCA-MSSA method with ten repeated phantom cone-beam tomography scans without any anatomic obstructions. Each circle indicates the discrepancy between the extracted signal from the algorithm and the ground truth for each scan. A) Peak accuracy versus valley accuracy in seconds B) Overall phase discrepancy versus expiration phase discrepancy in the percentage.
A B
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Figure 4-10. Examine the robustness of the multivariate singular spectrum analysis (MSSA) algorithm where the altered external surrogate waveform and the preliminary tumor LPCA waveform were input in the MSSA to obtain the final tumor LPCA-MSSA result. A) The result of tumor LPCA-MSSA waveform compared to the ground truth (lower panel), while there is a 35% phase shift on the altered external surrogate signal. B) The result of tumor LPCA-MSSA waveform compared to the ground truth (lower panel), while there is a gradual amplitude variation on the altered external surrogate signal.
A
B
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Figure 4-11. A cardiac artifact waveform with Rando® phantom slabs. The red dash line indicates the ground truth signal from the optical tracking system. A) The result of LPCA only method compared with the ground truth. The black dash boxes indicate where the nearly lateral projection angles are. B) The result of LPCA-MSSA method compared with the ground truth.
A
B
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Table 4-1. The phase discrepancy and time accuracy of the extracted respiratory waveform compared with the reference waveform for lung patients.
Patient ID
Tumor location
No. of PCs
used
Average Breathing
cycle (second)
Average phase
discrepancy (%)
Average expiration
phase discrepancy
(%)
Average peak
accuracy (second)
Average valley
accuracy (second)
1 LLL 2 2.9 0.84 -1.25 -0.03 0.07 2 LML 4 3.8 -4.86 0.38 0.2 0.2 3 LML 4 3.8 -1.84 -4.42 0.06 -0.1 4 LUL 9 3.9 4.01 -2.47 -0.06 -0.09 5 RLL 5 3.1 1.59 -1.23 -0.05 -0.08 6 RML 4 3.3 -1.95 -1.92 0.07 -0.01 7 RML 4 2.6 -1.96 -0.3 0.05 0.04 8 RUL 9 4.9 -4.2 -1.2 0.20 0.12
Mean±SD -1.05±3.0 -1.55±1.45 -0.04±0.13 -0.01±0.15 Abbreviation: LLL: Left lower lung; LML: left middle lung: LUL: Left upper lung; RLL: right lower lung; RML: right middle lung; RUL: right upper lung; SD: standard deviation; PCs: principal components
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Table 4-2 The variance distribution (%) of the principal components for each patient. The PC was ordered in descending order based on their eigenvalues. Only the PCs in bold were used for the final respiratory waveform reconstruction, and the sum of confidence interval (CI) of those PCs was shown in the last two rows.
Patient ID
1 2 3 4 5 6 7 8
Variance distribution (%)
PC1 80.74 83.86 82.34 87.85 81.70 83.06 83.35 76.56
PC2 11.14 5.13 2.61 3.40 5.30 5.44 4.40 3.79
PC3 6.34 4.89 2.56 3.20 4.97 5.13 4.35 3.76 PC4 0.95 0.95 1.92 0.89 1.34 1.04 3.36 2.98
PC5 0.34 0.76 1.90 0.84 1.29 0.90 1.79 2.51
PC6 0.19 0.70 1.07 0.74 1.16 0.81 0.74 2.48 PC7 0.1 0.65 0.96 0.45 0.60 0.64 0.42 1.24 PC8 0.06 0.63 0.94 0.35 0.56 0.39 0.32 0.96 PC9 0.06 0.57 0.43 0.28 0.42 0.28 0.32 0.94
Number of PCs used 2 4 4 9 5 4 4 9
Confidence interval 91.9 94.8 89.4 98.0 94.6 94.7 95.5 95.2 Abbreviation: PC: principal component; CI: confidence interval
101
A
B
Figure 4-12. The reconstructed waveform compared to the reference waveform with the variance percentage (%) of each principal component (PC) displayed in a bar chart. A) Patient ID4: PC1 to PC9 were used for LPCA-MSSA reconstruction. B) Patient ID6: PC1 to PC4 were used for LPCA-MSSA reconstruction. The right upper panel displays the LPCA only compared with the reference waveform; the right lower panel displays the LPCA-MSSA method compared with the reference waveform.
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CHAPTER 5 REFINE RESPIRATORY WAVEFORM RESULT
In Chapter 4, the parameters used to generate the respiratory waveform results
were manually optimized by the user. Even though it has achieved decent accuracy in
terms of the phase and time accuracy, there is still a need to automate the process for
the ultimate clinical application. Therefore, this chapter aims to explore the possibility to
automate the parameter selection process in order to refine the respiratory waveform
result. It is essential to distinguish the type of respiratory waveform to know the
complexity of the waveform and then further take the required actions. Furthermore, the
overall trend of the respiratory waveform was also captured based on the result in
chapter 4. It could be affected by the degree of variation on the internal anatomic
obstruction or the skin movement of the patient. Therefore, in this chapter, we will
automate the variance percentage selection by distinguishing the type of respiratory
waveform and further filtering out the trend curve.
Figure 5-1 shows our proposed automatic workflow after we obtain the initial
respiratory waveform from the LPCA step. The first section of this chapter will explain
the method to define the complexity of the waveform pattern and then further classified
to different waveform type as shown in Figure 5-1 level 1. In the second section of this
chapter, we will focus on how to determine if each reconstructed component truly
represents a reasonable respiratory cycle for a two minutes CBCT scan and excluded
the reconstructed components that only contain the trend of the waveform which is not
within the typical respiratory cycle shown in Figure 5-1 level 2.
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Discriminate Type of the Respiratory Waveform
It is crucial to discriminate the type of respiratory waveform so that we can
automate the variance percentage selection. As the gradual amplitude variations and
phase shift on the external surrogate signal do not affect the final respiratory result as
described in chapter 4. We defined the irregularity of the respiratory pattern in two
aspects;
(1) Abrupt change waveform: we defined the abrupt change as the sudden
amplitude change on the time series, which may cause by the patient’s coughing. The
abrupt change is determined by both root-mean-square (RMS) in Eq. 5-1 and standard
deviation (σ) in Eq. 5-2. Each time data points 𝑥𝑖 was evaluated by dividing the original
time series into two section with indexed from m to n. If detecting both RMS and σ
change occurred in the time series, we categorize this time series as abrupt change
waveform.
∑ ∆(𝑥𝑖; 𝜒([𝑥𝑚, … , 𝑥𝑛])) = (𝑛 − 𝑚 + 1)𝑙𝑜𝑔 (1
𝑛 − 𝑚 + 1∑ 𝑥𝑟
2
𝑚
𝑟=𝑛
)
𝑛
𝑖=𝑚
(5-1)
∑ ∆(𝑥𝑖; 𝜒([𝑥𝑚, … , 𝑥𝑛])) = (𝑛 − 𝑚 + 1)𝑙𝑜𝑔 ∑ 𝜎2([𝑥𝑚, … , 𝑥𝑛])
𝑛
𝑖=𝑚
𝑛
𝑖=𝑚
(5-2)
The detail methods of these change point detection can be found in the
literatures.84,85
(2) Irregular waveform: We considered the breathing cycle change due to the
perpetually respiratory cycle length change. The criteria we defined for the cycle change
is when the breathing cycle change for more than 1 second compared to the median
breathing cycle length of the time series. In Figure 5-2 plotted the examples of abrupt
104
change waveform and irregular waveform detection. After we distinguish the type of
respiratory waveform, then we can take action on the next step.
Advanced Trend Curve Filtering using Instantaneous Frequency
In Figure 5-1, the level 2 workflow includes two main steps. First, a specific
variance percentage was selected with a different type of respiratory waveform for
MSSA. Second, each reconstructed component was processed with instantaneous
frequency to exclude the particular time series that is below the typical human
respiratory cycle where might be only the trend of the original respiratory waveform.
Only the RC has the median instantaneous frequency higher than 0.1 Hz (100mHz) is
selected for reconstructing the final refined respiratory waveform.
The instantaneous frequency of a nonstationary signal is a time-varying
parameter that relates to the average of the frequencies present in the signal as it
evolves. The frequency (f) of vibratory motion is defined as the number of oscillations
per unit time.86,87 It essentially computes the spectrogram power spectrum 𝑃(𝑡, 𝑓) and
use the spectrum as a time-frequency distribution. We estimate of the instantaneous
frequency as the first conditional spectral moment of the time-frequency distribution of
the input signal. The estimated instantaneous frequency can be written as
𝑓𝑖𝑛𝑠𝑡(𝑡) =∫ 𝑓 𝑃(𝑡, 𝑓)𝑑𝑓
∞
0
∫ 𝑃(𝑡, 𝑓)𝑑𝑓∞
0
(5-3)
In this chapter, we demonstrated patient ID 4 and ID 8 cases from chapter 4 as
examples as those patient’s respiratory waveforms were classified as the irregular
waveform where it consisted of variation on the respiratory cycles. There were nine
principal components for Patient ID 4 selected in the MSSA step. As shown in Figure 5-
105
3, after each reconstructed component was evaluated with the instantaneous frequency
criteria, RC 2, 3, 5, 6, 8, and 9 were automatically selected for reconstructing the final
respiratory waveform. Figure 5-4 shows the result of Patient ID4 when comparing with
the reference waveform; the lower panel shows the result of automated RC selection
has significantly improved. Similarly, in Figure 5-5 shows patient ID 8 has nine PCs in
the MSSA step; after instantaneous frequency criteria, the RC 2, 3, 4, 5, and 6 were
automatically selected for reconstructing the final respiratory waveform. Figure 5-6
shows the automated RC selection result for Patient ID8 when compared to the
reference waveform at the lower panel.
106
Figure 5-1. Workflow to refine the final respiratory waveform.
107
A
B
Figure 5-2. Detect the irregularity of a respiratory waveform. A) The abrupt change respiratory waveform. B) Respiratory cycle change of the respiratory waveform.
108
A
B
Figure 5-3. Nine decomposed reconstructed components (RC) from Patient ID 4 after applying MSSA. A) The instantaneous frequency estimate of the reconstructed components. B) As shown in red boxes, RC 2, 3, 5, 6, 8, and 9 were selected for final waveform reconstruction after instantaneous frequency selection.
109
Figure 5-4. Result comparison of LPCPA, LPCA-MSSA, and instantaneous frequency selection with the reference waveform for patient ID 4.
110
A
B
Figure 5-5. Nine decomposed reconstructed components (RC) from Patient ID 8 after applying MSSA. A) The instantaneous frequency estimate of the reconstructed components. B) As shown in red boxes, RC 2, 3, 4, 5, and 6 were selected for final waveform reconstruction after instantaneous frequency selection.
111
Figure 5-6. Result comparison of LPCPA, LPCA-MSSA, and instantaneous frequency selection with the reference waveform for patient ID 8.
112
CHAPTER 6 CONCLUSIONS
Summary
In Chapter 2, we demonstrated the strategies to streamline the patient setup
process to prevent the potential patient setup error by developed a self-checking
treatment couch coordinate system. It is the essential first step before each treatment
and the crucial element throughout the radiation treatment course to ensure the
patient’s safety.
In Chapter 4, we have applied the direct internal tumor tracking from CBCT
projection images with LPCA- MSSA algorithm, which can recover the primary
oscillation components of tumor respiratory waveform using the combined information
from CBCT projection images and external surrogates. We incorporated LPCA to obtain
the initial respiratory waveform information and use the MSSA algorithm to select the
multiple dominant variance components. Thus, the LPCA – MSSA algorithm can
recover the oscillation of the internal tumor signal with the assisted of the external
surrogate signal. Our method can extract complete tumor breathing patterns during
CBCT projections without the limit on the angle of projection views and provide high
accuracy in terms of phase and peak-valley accuracy of the extracted curve. The
proposed method not only mitigates the impact of pixel value outliers outside of the
tumor region but also provides noise removal ability by MSSA. This study opens the
door for tumor tracking on CBCT projections for adaptive gating radiation therapy.
In this dissertation, we not only had successfully improved the current patient
setup workflow as an error prevention mechanism and take another step further to
implement LPCA-MSSA method to enhance the treatment accuracy.
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Future Works
A couple of areas in our current works can be improved for future works. First, for
the patient setup process, even though our self-checking method provides an initial
reference treatment couch coordinate that was utilized throughout the treatment, We
have noticed that the possibility of significant deviation as the treatment progress.
Therefore, in the future, we should continue collecting patient data and establish a more
meaningful alert level when the CBCT couch shift deviates from the original treatment
couch coordinate for each treatment site.
Second, as we mentioned in Chapter 4 about the sensitive of the window size in
the LPCA step, the main reason is that our case only kept 1D time series during the
LPCA step. In other words, reduce the vertical multi-dimension, which depends on the
number of pixels in the vertical direction, to one dimension (one value) that has the best
variance representation of the data. However, there is more information that is available
on the original 2D tumor-AS image. Therefore, in order to improve our method, we will
explore the possibility of applying the two-dimensional extension of the MSSA on the AS
image based on the literature82, and it can keep multiple decomposed time series
directly from the image, instead of trying to recover the oscillation after the fact. It gives
us opportunities to preserve the valuable information we need in advance and further
reduce the sensitive on the window size selection on the current method. Furthermore,
once the method achieved toward a one-step 2D extension MSSA, we would like to
research the possibility of utilizing our method for the patient respiratory monitoring
during the treatment.
114
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BIOGRAPHICAL SKETCH
Pingfang Tsai was born in Taipei, Taiwan. She spent her childhood with her
parents and older brother in Taipei. In May 2003, she received her Bachelor of Science
degree in medical imaging and radiological sciences from Chang Gung University in
Taiwan. Following graduation, she studied aboard in the United States of America to
pursue her master's degree in nuclear and radiological engineering in the medical
physics program. She ultimately received her Master of Science degree in April 2005 at
the University of Florida.
After years of working experience as a medical physicist in the hospital, she had
passed the American Board of Radiology certification in therapeutic medical physics
and the Medical Dosimetrist Certification Board as a certified medical dosimetrist. She
felt the need to enhance her critical thinking and to develop her research expertise.
Thus, she decided to come back to Gainesville for her Ph.D. study. In 2016, she started
her Ph.D. study at the University of Florida in medical physics and obtained her Ph.D.
degree in December 2019.
Her main research interests are in image-guided adaptive radiation therapy and
streamline the patient setup workflow. She will continue her career path in medical
physics to master the skills and be an independent clinical- and research-oriented
medical physicist.