NOVEL APPLICATIONS OF 2D AND 3D DEFORMABLE REGISTRATION IN IMAGE

NOVEL APPLICATIONS OF 2D AND 3D DEFORMABLE

REGISTRATION IN IMAGE-GUIDED RADIATION THERAPY

_______________

A Thesis

Presented to the

Faculty of

San Diego State University

_______________

In Partial Fulfillment

of the Requirements for the Degree

Master of Science

in

Radiological Health Physics

_______________

by

Vasant Patrick Kearney

Summer 2012

iii

Copyright © 2012

by

Vasant Patrick Kearney

All Rights Reserved

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ABSTRACT OF THE THESIS

Novel Applications of 2D and 3D Deformable Registration in Image-Guided Radiation Therapy

by Vasant Patrick Kearney

Master of Science in Radiological Health Physics San Diego State University, 2012

Image-guided radiation therapy (IGRT) is clinically appealing as it offers real-time patient specific image feedback and anatomical variation adaptation. Correcting non-linear misalignment of cone-beam CT (CBCT) to simulated 4DCT projection image intra-fractionally and inter-fractionally provides an opportunity to increase precision and accuracy of target localization. Taking advantage of on-board CBCT to perform deformable image registration (DIR), implemented on GPUs, allows for real-time and retrospective anatomical tracking. Increasing the spatial congruence of the on board imager to the simulation can allow for dose escalation using hypo-fractionated regimens in addition to dose reduction to organs at risk and improved target dose coverage, increasing local control without increasing toxicity. Robust respiratory signal extraction is crucial in pulmonary lesson localization. This work demonstrates the evaluation and application of DIR implemented on GPUs as a tool for IGRT. We first evaluate the performance of a realtime lung tumor tracking technique using DIR between simulated 4DCT and CBCT projections as a means to compensate for respiratory motion. Then we assess the performance of a respiratory signal extraction technique using DIR between consecutive CBCT projections. Finally, we test lower dimensional modeling using principal component analysis (PCA) as a means for 4D thoracic reconstruction and establish a correlation between respiratory modes and PCA eigenvalue decay rate.

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TABLE OF CONTENTS

PAGE

ABSTRACT ............................................................................................................................. iv

LIST OF FIGURES ................................................................................................................ vii

ACKNOWLEDGEMENTS ..................................................................................................... xi

CHAPTER

1 INTRODUCTION OF MOTION MANAGEMENT IN IMAGE GUIDED RADIATION THERAPY ..............................................................................................1

1.1 Physiological Mechanics of Respiration ............................................................1

1.2 Motion Management Techniques ......................................................................3

1.3 Respiratory Gating .............................................................................................3

1.4 Breathing Training .............................................................................................6

1.5 Respiratory Induced Motion Artifacts in CT Acquisition and 4DCT ................7

1.6 Treatment Planning based on 4DCT ..................................................................7

1.7 Respiratory Induced Cosimetric Consequences.................................................8

1.8 IMRT and Gated IMRT .....................................................................................8

1.9 Beam Tracking ...................................................................................................9

1.10 Reducing Imaging Dose when using Internal Surrogates ..............................10

1.11 Cone Beam CT for IGRT ...............................................................................10

2 INTRODUCTION OF DEFORMABLE IMAGE REGISTRATION (DEMONS) ..................................................................................................................15

3 APPLICATIONS OF INTER-MODALITY 2D DEFORMABLE IMAGE REGISTRATION ........................................................................................................18

3.1 Rigid Registration ............................................................................................18

3.2 2D Inter-modality DIR .....................................................................................18

3.3 2D Deformation of CBCT to Planning 4DCT Projection ................................23

3.4 2D DIR from 4DCBCT to Planning 4DCT Projection ....................................26

3.5 Real-Time Lung Tumor Tracking using 2DDIR .............................................27

3.6 Tumor Tracking using 2DDIR between CBCT and CT ..................................29

3.7 Tumor Tracking using 2DDIR between 4DCBCT and CT .............................30

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3.8 Respiratory Signal Extraction from CBCT Projections ...................................33

3.9 Respiratory Signal Extraction from 4DCBCT to 4DCBCT ............................34

4 INTRODUCTION OF APPLICATION OF 3D DEFORMABLE REGISTRATION TO LUNG MOTION MODELING ...............................................43

4.1 Principal Component Analysis ........................................................................43

4.2 PCA for Pulmonary Motion .............................................................................46

4.3 Overall Summary .............................................................................................49

REFERENCES ........................................................................................................................54

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LIST OF FIGURES

PAGE

Figure 1.1. The Diaphragm is contracted downward forcing the abdomen inferior and anterior during inhalation (Right) and the external intercostals contract increasing the anterior-posterior and lateral dimensions of the thorax (Left). ..............2

Figure 1.2. Schematic of (Top) amplitude gating, and (Bottom) phase gating. The horizontal axis is time, the red line in the bottom and top sine waves represent a gating threshold, the blue vertical lines represent a gating window and indicate beam on intervals. ............................................................................................6

Figure 1.3. Varian Trilogy with a CBCT OBI in arms extended mode. ..................................11

Figure 1.4. CBCT acquisition mode. (right) Full-fan mode. The KVD is centered with x-ray axis. (Left) Half-fan mode. The KVD is shifted to one side. .............................12

Figure 1.5. CBCT images acquired from full fan mode (left) and half fan mode (right). ..........................................................................................................................13

Figure 1.6. A schematic of the CBCT geometry at half fan mode. .........................................14

Figure 2.1. Flowchart of demons algorithm (A), with down-sampling (B), where the displacement vector r depends on the method (C), implemented on GPU. .................17

Figure 3.1. CT to CBCT rigid alignment using a transverse slice (Top) and double checked using a mid coronal slice (Bottom). ...............................................................19

Figure 3.2 Raw AP CBCT projection of the thorax (Left). In air scan just prior to image acquisition (middle). Raw image with the log of the in air scan removed (Right). .........................................................................................................................19

Figure 3.3. By replacing the intensity term in the double force method with a constant the gradient terms will dominate the displacement vector. ..........................................21

Figure 3.4. The top image shows the DIR vector field with out intensity correction using standard demons algorithm. The bottom image shows the DIR vector field using the modified demons algorithm with out intensity correction. ..................22

Figure 3.5. The modified simulated image shows a bony structure mismatch (red arrow) with the ground truth (left). Local Normalization (LN) enhances the intensity congruence between the simulation and the CBCT(center). DIR in conjunction with intensity correction allows for anatomical corrections and is clearly observed on bony structures (red arrow) (right). .............................................23

Figure 3.6. AP (left) and lateral (right) are shown of patient 1 with both CBCT projections (top) and simulated intensity corrected CT projections (bottom) at end of inhale. The 4DCT image sets have a body mask that removes the couch in 3D. The portion of the DVF outside the body is set to 0. ........................................24

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Figure 3.7. AP (right) and lateral (left) are shown of patient 2 with both CBCT projections (top) and simulated intensity corrected CT projections (bottom) at end of inhale. The 4DCT image sets have a body mask that removes the couch in 3D. The portion of the DVF outside the body is set to 0. ........................................24

Figure 3.8. AP (right) and lateral (left) are shown of patient 3 with both CBCT projections (top) and simulated intensity corrected CT projections (bottom) at end of inhale. ................................................................................................................25



Figure 3.11. Plot of maximum (blue), mean (red), and standard deviation (green) for patients 1-4, and 6 in the SI (top) and tangential directions (bottom) from both the Left-Right projections (right) and Anterior-Posterior projections (left). ...............27

Figure 3.12. Plot of the mean values of two projection orientations with both components of displacement for each projection. The maximum (blue), mean (red), and standard deviation (green) for patients 1-4,and 6 are graphed with the mean of all patients displayed (Top Left). .............................................................28

Figure 3.13. The tumor home position in each patient was first delineated in the reference phase of the 4DCT image set. ......................................................................28

Figure 3.14. Patient 1 2DDIR tumor tracking vs projection number in the SI direction (Top) compared with the reference tumor position (Bottom). Projection number (Horizontal axis) vs target coordinate (Vertical). ...........................................30

Figure 3.15. Patient 2 2DDIR tumor tracking vs projection number in the SI direction (Top) compared with the reference tumor position (Bottom). Projection number (Horizontal axis) vs target coordinate (Vertical). ...........................................31

Figure 3.16. Patient 2 Sagittal (top) and Coronal (bottom) DFV from EOE to EOI. ..............31

Figure 3.17. Patient 3 SI tumor position vs projection number (top), with the corresponding tangential tumor position (middle), compared against the reference RPM signal (bottom). Projection number (Horizontal axis). .......................32

Figure 3.18. Patient 6 SI tumor position vs projection number (top), with the corresponding tangential tumor position (middle), compared against the reference RPM signal (bottom). Projection number (Horizontal axis). .......................33

Figure 3.19. Demonstration of 2DDIR respiratory signal extraction using SI component of motion (Top) and the corresponding reference tumor SI position (Bottom) for patient 1. Projection numbers 32 and 70 correspond to EOE, projection numbers 9, 50, and 88 correspond to EOI as determined with diaphragm position. Projection number (Horizontal axis) vs target coordinate (Vertical). .....................................................................................................................34

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Figure 3.20. 2DDIR respiratory signal using SI component of motion (Top) and the corresponding reference tumor SI position (Bottom) for patient 2. Projection numbers 4 and 30 correspond to EOE, projection numbers 18 and 41 correspond to EOI as determined with diaphragm position. Projection number (Horizontal axis) vs target coordinate (Vertical). ........................................................35

Figure 3.21. Short 2DDIR respiratory signal using SI component of motion (Top) and the corresponding ground truth tumor SI position (Bottom) for patient 3. Projection number (Horizontal axis) vs signal amplitude (Vertical axis). ...................36

Figure 3.22. Full 2DDIR respiratory signal using SI component of motion (Top) and the corresponding ground truth tumor SI position (Bottom) for patient 3. Projection number (Horizontal axis) vs signal amplitude (Vertical axis). ...................37

Figure 3.23. DDIR respiratory signal using SI component of motion (Top) and the corresponding ground truth tumor SI position (Bottom) for patient 4. Projection number (Horizontal axis) vs signal amplitude (Vertical axis). ...................38


Figure 3.25. DDIR respiratory signal using SI component of motion (Top) and the corresponding ground truth tumor SI position (Bottom) for patient 5. Projection number (Horizontal axis) vs signal amplitude (Vertical axis). ...................40

Figure 3.26. Full 2DDIR respiratory signal using SI component of motion (Top) and the corresponding ground truth tumor SI position (Bottom) for patient 5. ..................40

Figure 3.27. DDIR respiratory signal using SI component of motion (Top) and the corresponding ground truth tumor SI position (Bottom) for patient 6. ........................41


Figure 4.1. A mass on a spring moving with sinusoidal motion. Cameras A, B, and C are recording the motion of the mass from random vantage points. ............................44

Figure 4.2. Data set for motion in 2 dimensions (Right). Signal-to-noise ratio taken along the X direction (Top Left), and taken along the Y direction (Bottom Left)..............................................................................................................................45

Figure 4.3. Schematic of various motion scenarios with various degrees of redundancy. Motion with equal parts x and y motion (A). Progression towards higher degrees of redundancy as one component of motion becomes more dominant (B and C). Motion in a highly redundant state with only one directional component. .................................................................................................45

Figure 4.4. Lung mask of patient 6 (Top) and lung mask applied to the CT image with additional thresholding. ................................................................................................47

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Figure 4.5. 4DCT DIR results for patient 1. Lung tumor tracked in 3D from EOE (phase 6) to EOI (phase 9) (top left). Lung tumor tracked in from the R2 axis displaying only 1 dimension of motion in the R1 direction. Lung tumor tracked in from the R1 axis displaying only 1 dimension of motion in the R2 direction. ......................................................................................................................48

Figure 4.6. LOOCV error plotted against total number of eignevectors of the mean of all nine 4DCT phases for the masked case (Left) and the un-masked case (Right). .........................................................................................................................49

Figure 4.7. Superimposed errors between the EOE and EOI DIR and the first 3 eigenvectors of the DVF’s are represented by colored regions in the coronal slice for the unmasked case (Right) and masked case (Left) for patient 1, red regions represent the highest error and blue represents the lowest error. Maximum error is 2.3mm for the masked case and 4.2mm for the unmasked case. ..............................................................................................................................50

Figure 4.8. Coronal slice of 1st eigenvector (left) and 2nd eigenvector field (right) for masked case for patient 2. ............................................................................................50

Figure 4.9. Eigenvector (horizontal axis) with associated eigenvalue (vertical axis). ............51

Figure 4.10. Ratio of 1st and 2nd eigenvalues (Top, green dots) and 1st and 3rd eigenvalues (Top, blue dots), and the ratio of the absolute value of SI/AP components of demons output between EOE and EOI (Bottom, Red dots), and the absolute value of SI/Axial components (Bottom, purple dots), with the horizontal axis representing patient number and the vertical axis representing the unit-less ratio value. ...............................................................................................52

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ACKNOWLEDGEMENTS

I would like to recognize my advisor Dr. Laura I. Cerviño for her dedication,

guidance, patience and support through the course of all my projects. I give special thanks to

my committee members Dr. Usha Sinha, and Dr. Faramarz Valafar. I would like to

acknowledge Dr. Xiaoyu Wang (Postdoctoral Fellow) Dr. Xun Jia (Assistant Professor) Dr.

Hao Yan (Postdoctoral Fellow), Xin Zhen (Visiting Graduate), and Steve Jiang (Executive

Director) at the University of California San Diego (UCSD) Department of Radiation

Oncology, and Center for Advanced of Radiotherapy Technologies (CART), for their

contributions to my project.

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CHAPTER 1

INTRODUCTION OF MOTION MANAGEMENT

IN IMAGE GUIDED RADIATION THERAPY

A new era of radiation therapy has emerged with technological advancements, such

as intensity-modulated radiation therapy (IMRT) in conjunction with on-board imaging

modalities such as 2D X-Ray, Surface contour, and cone beam computed tomography

(CBCT). These advancements can produce highly conformal radiation therapy that allow for

more precise treatment of the tumor site with a higher level of normal tissue sparing. Intra-

fractional organ motion degrades the spatial relationship between the simulation image and

on-board image, introducing treatment errors in conformal radiotherapy. Thoracic and

abdominal lesion position can be effected dramatically by intra-fractional cardiac, muscular

skeletal, gastrointestinal, and pulmonary motion. Treatment errors introduced by organ

motion becomes more severe in hypo-fractionated stereo-tactic radiation therapy (SBRT) or

single fraction stereo-tactic radio-surgery (SRS). This chapter provides a brief history and

overview of current IGRT techniques and imaging modalities to manage respiratory motion.

1.1 PHYSIOLOGICAL MECHANICS OF RESPIRATION

The lungs are encapsulated by a fluid-filled intrapleural space anatomically located

within the thoracic cavity. Inhalation increases the volume of the thoracic cavity as air is

actively drawn into the lungs by active muscular participation, mainly the diaphragm.

Inhalation contracts the diaphragm muscle causing it to descend. This diaphragmatic

movement forces the abdomen to shift anteriorly and inferiorly to make way for the

expanding lung volume. While the diaphragm muscle increases the superior-inferior (SI)

volume of the lung, the external intercostal muscles increase the anterior-posterior volume of

the lung. The external intercostals join adjacent ribs at an oblique angle and when contracted

pull the rib cage superiorly and anteriorly increasing the circumference of the thorax during

inhalation. Figure 1.1 shows an illustration of interfractional lung expansion. During

vigorous inhalation accessory muscles of respiration such as the sternocleidomastoid,

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Figure 1.1. The Diaphragm is contracted downward forcing the abdomen inferior and anterior during inhalation (Right) and the external intercostals contract increasing the anterior-posterior and lateral dimensions of the thorax (Left).

platysma, and the scalene muscles of the neck are activated for support. Exhalation can be

both passive or active depending on the period and amplitude of respiration. Passive

exhalation is defined as quite breathing, where the lungs elasticity returns the thoracic cavity

to its pre-inhalation position, and active exhalation requires participation of the internal

intercostals and abdominal muscles.

Respiration is a sudo involuntary function, a person will continue to breathe despite

being unconscious but is also capable of controlling their breathing pattern within limits.

The primary function of respiration is to maintain normal levels of O2 and CO2 within the

blood, maintaining homeostasis. If adequate respiration is not maintained two conditions can

arise respiratory acidosis (decreased blood pH), a life threatening condition, and respiratory

alkalosis (increased blood pH). Involuntary respiration is regulated by chomoreceptors

sensitive to CO2, O2, and pH in the arterial blood. The partial pressure of CO2 is the most

dominant factor controlling the urge to breath as O2 and pH stimuli contribute less to the

period and amplitude of involuntary breathing.

Different modes of respiration have been characterized by breathing type, either chest

or abdominal, or postural, either lateral decubitus, supine, prone, upright. Different

respiration modes can lead to different intrafractional breathing patterns and should be taken

3

into consideration. Respiratory motion of the lungs, esophagus, liver, pancreas, breast,

prostate, kidneys depend on the the type of respiratory mode and can lead to different

intrafractional target motion variation, either in the host organ, tumor cite, or implanted

fiducial marker.1-4

1.2 MOTION MANAGEMENT TECHNIQUES

Many studies have quantified intrafractional motion via fiducial implants, tumor

movement, the host organ, and surrogates. It is known that patient breathing patterns can

vary in period, and magnitude intrafractionally, which effects treatment quality.2, 5-16

Current methods to compensate for organ motion caused primarily by respiration

include tracking, radio-opaque fiducial markers implanted in the tumor site, the diaphragm as

a surrogate for tumor motion, infrared markers placed on the abdomen, and tracking the body

surface contour. These methods are used in either respiratory gating or beam tracking.17-33

Another category of respiratory compensation requires active patient participation, such as

forced shallow breath (jet ventilation) and active breath hold. These techniques require

additional therapist training and participation and may not be well tolerated by patients.

Typical lung can cancer patients have compromised lung function and may not be able to

actively participate.

1.3 RESPIRATORY GATING

Respiratory Gated radiation therapy has the potential for dose escalation to the target

and increased normal tissue sparing by decreasing the margin of the clinical target volume

(CTV) and planed target volume (PTV). Ideal patient candidates would have large

respiratory motion amplitude, and the ability to undergo breath coaching. Large respiratory

motion would increase the benefit as the relative margin size of the CTV and PTV would

decrease. The ability of the patient to provide a steady reproducible breathing cycle enhances

the congruence between the planning and on-board imaging systems.

There are two main technical aspects of gated radio-therapy. Precise tumor

localization and prompt linac gating response time. In general tumor localization is of much

greater concern but acquisition of the gating signal to the linac response may not be

ignored.34 Gating based on tumor localization has the potential to produce two types of

4

errors, false negative and false positive. False positive errors (beam off at wrong target

positions), causes overdose to the normal tissue and under dose to the target. False negative

(beam off at right target positions) increases treatment time and reduces treatment efficiency.

Japan introduced clinical gated radiotherapy for heavy ion beams in the late 1980s, in

which external surrogates were used to monitor respiration.35 Hokkaido University in

collaboration with Mitsubishi Electronics Co.,Ltd. were the first to introduce a real time

tumor tracking system which used gold markers implanted in the tumor. Respiratory gating

was first clinically introduced in the United States at the University of California, Davis

using the Varian 2100C linac. Varian Medical Systems Inc. commercialized the real-time

position management (RPM) respiratory gating system. The RM system is now widely used

clinically.36-42

We distinguish between three main gating categories. Gating based on internal

surrogates, direct detection of tumor mass in real-time, and external gating.

Internal gating based on surrogates relies correlating the motion of internal structures

apart from the tumor to derive tumor motion, such as implanted fiducial markers, and

diaphragm position. In general implanted fiducials are the most common clinical internal

surrogate. The Mitsubishi/Hokkaido RTRT system is an internal gating system routinely

used clinically. The real-time tumor tracking (RTRT) system was developed to reduce setup

error and uncertainty due to organ motion during radiation therapy.1, 35, 43-53

4 sets of diagnostic x-ray imaging systems maintain implanted fiducial localization

accuracy at all gantry angles. This system can track the implanted fiducials at a video frame

rate. This allows the linac to be gated within a given tolerance. Phantom experiments report

accuracy of tumor-tracking to within 1.5mm for targets moving up to 4cm/s with a time delay

between the recognition of the marker position and the start or stop treatment linac was 0.03

seconds.

Fiducial marker insertion into the lung is an invasive procedure with an associated

risk of infection. Many physicians are reluctant to implant markers into the lung as

puncturing the chest wall runs the risk of pnemothorax. An alternative to invasive

implantation is brochofiberscopy, in which fiducials are placed near the tumor site via the

bronchio tubes. The use of bronchofiberscopy is only feasible for peripheral lung tumors and

not safe for central lung lesions. fiducial insertion is generally only useful within two weeks

5

after implantation as fiducials tend to migrate and correlate less with tumor position during

treatments with large number of fractions.

In general the Varian RPM respiratory gating system is the most widely used external

gating tool. 4D CT scanning, cine electronic portal imaging device (EPID) treatment

verification, and patient breath coaching are used in conjunction with the RPM for precise

tumor localization through external surrogates.

To overcome patients breathing pattern fluctuation both intra- and inter-fractionally

breath coaching is crucial. It is important to maintain a high level of reproducibility and

ensure reasonable treatment times. Patients that are unable to follow breath coaching

instructions should be excluded from IGRG.

In IGRG we define the gating window to be the range of the surrogate signal. When

the surrogate is in within a particular range, it generates a gating-on signal which turns the

linac on, and when the surrogate falls outside the range, it generates a gating off signal which

stops the delivery of the beam. The gating signal is always a one dimensional on/off signal

but can be generated from multiple contributors depending on how many surrogate signals

are used. There are generally two types of gating signals that are used. External gating signal

generates a sinusoidal signal that corresponds to the anterior-posterior (AP) amplitude of

external markers, the relative amplitude of the signal is used to define the gating window.

Internal gating signal relies on the absolute position of the surrogate and is generally directly

correlated with the position of the tumor. Breathing phase derived gating based on the

external marker surrogate signal is called phase gating, while motion amplitude derived

gating signal is called amplitude or displacement gating. Breathing phase gating relies on the

periodic nature of the respiratory cycle from 0 to 360 degrees. Generally the EOE is defined

to be 0 or 360 degrees while the EOI is defined to be 180 degrees. Patient breathing is

irregular by nature and the phase value often does not correlate perfectly to the amplitude

value generated by the same surrogate. It is unclear which technique is most suited for

respiratory gating.

In order to quantify treatment efficiency we introduce the concept known as duty

cycle which is the beam-on time as compared to the total treatment time. Conventional non-

gated radiotherapy has a duty cycle of 100% while typical duty cycle for gated 3DCRT is

around 40%. Gated IMRT duty cycles can fall below 30% when using step and shoot mode

6

due to the MLC leaf motion beam off time. These vary depending on the size of the gating

window being used and the patient specific breathing style. Figure 1.2 shows a schematic of

two different breathing paterns.

Figure 1.2. Schematic of (Top) amplitude gating, and (Bottom) phase gating. The horizontal axis is time, the red line in the bottom and top sine waves represent a gating threshold, the blue vertical lines represent a gating window and indicate beam on intervals.

In respiratory gated radiation therapy there is always a trade-off between efficiency

and treatment precision. If a large gating window is used then the treatment time remains

low while a small gating window can provide a higher degree of precision in treatment.

1.4 BREATHING TRAINING

Audio and Video feedback coaches the patient helping to maintain a steady

reproducible breathing signal crucial in the implementation of the RPM system. The audio

instruction tells the patient when to breathe in and out, while the video feedback insures the

patients maintains a constant EOE and EOI by displaying the patients respiratory waveform.

Video instruction coaches respiratory amplitude while audio instruction coaches breathing

period. It has been shown that both the magnitude and period can become more stable if an

audiovisual feedback system is implemented.3, 4, 54 Typically patients is breath trained for

one hour before a CT simulation is taken. The EOE is typically trained to be in the gating

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window. If the patient is able to follow the coaching instructions then treatment is continued.

Patient specific motion magnitude is measured flouroscopically and a gating window is

determined usually allowing for 5-mm residual tumor motion.

1.5 RESPIRATORY INDUCED MOTION ARTIFACTS IN CT

ACQUISITION AND 4DCT

Motion artifacts caused by different parts of the object moving in and out of the slice

window during image acquisition distort the target volume leading to incorrect positional and

volumetric information.

Special treatment planning margins need to be considered to guarantee target volume

coverage. The GTV and an expanded margin that includes the suspected microscopic spread

to account for intrafractional respiratory motion, inter-fractional motion, and patient set up

error, the planned target volume (PTV) is obtained by expanding the clinical target volume

(CTV) as specified in the International Commission on Radiation Units and Measurement

(ICRU) report 62.55 Extended margins are necessary in non-gated treatment planning to

ensure target coverage throughout the entire respiratory cycle and consequently increases

dose to normal tissue.

Whatever surrogate or gating type is selected for respiratory-gated radiotherapy

should ideally be maintained during the simulation stage of treatment planning. For this study

we will focus on CT simulation. Typical 3D CT simulation uses a one second rotation time

using a standard FDK image reconstruction algorithm, this produces motion artifacts in areas

of the body with large motion amplitude. Two types of error are introduced with this style of

reconstruction: spatial uncertainties, which cause the tumor to appear larger than normal; and

second, the electron density voxel assignment used to calculate dose, which will be effected.

In lung lesions the electron density assigned to the tumor will be less due to averaging with

the lower density lung tissue.

1.6 TREATMENT PLANNING BASED ON 4DCT

The Organs at risk are contoured on the CT data set that is within the gating window.

The GTV and CTV are contoured in every 4DCT image set and combined to form a

composite target volume that includes the residual motion. A margin is added to the CTV to

form the PTV. The size of the margin is determined by the amount of setup error and

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additional tumor motion that is not accounted for by the 4D CT simulation. Based on the

contoured targets volumes and organs at risk a 3DCRT or IMRT treatment plan is formed.

1.7 RESPIRATORY INDUCED COSIMETRIC

CONSEQUENCES

Each voxel in the gray-scale CT image set represents an intensity that corresponds to

an attenuation coefficient. The CT simulator used in treatment planning is calibrated such

that each intensity value corresponds to an electron density. Dose is then computed at each

voxel based on the prescription dose and electron density at the corresponding voxel. Intra-

fractional organ motion causes a blurring or averaging of the intended dose distribution. In

conventional conformal radiotherapy treatments (CRT) the dose gradient at the center of the

field can be assumed to be small and can be ignored but the dose gradient at the edges of the

field is blurred by the anatomical movement near the edge of the field, effectively increasing

the beam penumbra. This effect is of greater consequence in intensity modulated radiation

therapy (IMRT) as treatment planning relies on each individual segmented field or beamlet

having a low penumbra. The interplay effect between anatomical motion and multileaf

collimator motion further exacerbates this problem.

1.8 IMRT AND GATED IMRT

IMRT has the potential to deliver a more conformal dose to the target volume while

lowering normal tissue dose as compared with CRT. Dosimetric advantages have been well

documented however IMRT demands more precise patient setup, immobilization, and staff

training.56

There are two styles of IMRT delivery “step and shot” also known as static MLC

(SMLC) and dynamic MLC (dMLC). DMLC mode continuously moves the MLC

throughout one gantry angle. SMLC involves segments or beamlets per gantry angle and

turns the beam off while transitioning between segments.57-65

QA and commissioning of IMRT requires additional time and resources. Treatment

can be planned using either forward or inverse planning for IMRT. Forward IMRT treatment

plans are generally only used for very simple cases using SMLC and are only a small step

beyond CRT. For complex plans manual forward planning becomes impractically labor

intensive and Inverse planning in used instead. Most planning systems offer inverse planning.

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Patient set up accuracy is generally verified with electronic portal imaging (EPI), which can

also be used to generate intensity maps for delivered dose.

It is common practice to treat the primary and nodal volumes with different doses per

fractions. This practice is referred to both as simultaneous modulated accelerated

radiotherapy (SMART) and simultaneous integrated boost (SIB).

Often in patient set up stable anatomic structures are preferred isocenters as the target

center of mass can be unstable. Defining the clinical target volume (CTV) and gross target

volume (gross target volume) accurately is more critical in IMRT and various forms of

immobilization are often implemented to help reproducibility.

CRT treatment delivery time is often much shorter than of non-gated IMRT. Using

the sliding window technique with a 33% duty cycle would increase a non-gated beam

delivery time of 10 minutes to a 30 minutes with gated-delivery. However one can take

advantage of the step and shot IMRT function, by synchronizing the gating beam off time to

the MLC movement we can increase the treatment time by a factor of 1.5 instead of 3 with a

33% duty cycle. This would turn a 10 minute treatment delivery into a 15 minute delivery

instead of 30 minute delivery making gated-IMRT clinically feasible.

During gated step and shoot IMRT delivery the beam-on time with the respiratory

gating window frequency distribution is not uniform. The MLC leaf movement and beam-let

time do not correspond in a one to one ratio with the gating window on/off time and produce

non uniformities that increase treatment time efficiency.

For hypo-fractionated treatments the interplay effect between the MLC leaf motion

and the target motion needs to be considered as hot spots and cold spots, to the effect of 10%

can arise inside the target volume. In highly fractionated treatments the randomness of the

beam start relative to the respiratory cycle reduces this effect to around 1%. The interplay

effect is included in gated-IMRT as the getting window always starts at the same phase or

tumor position even though only part of the respiratory cycle is used the magnitude of the

interplay effect is not reduced for highly fractionated treatments.

1.9 BEAM TRACKING

Beam tracking adapts the beam geometry and shape to dynamically contour the

moving lesion throughout the respiratory cycle.66-75 This is clinically attractive as it allows

10

for continuous beam delivery allowing for more time-efficient radio-therapy. Respiratory

gating limits beam on time to a portion of the respiratory cycle where the lesion is in line

with the conformal beam. Gating is usually performed during the end of exhale (EOE) or

end of inhale (EOI). Depending on how much of the respiratory cycle is used treatment time

can be substantially increased. Increasing treatment time can be clinically unappealing as it

allows for fewer patients per day.

For beam tracking using conventional rigid gantry based linacs, multi-leaf collimators

are used to adaptively conform the beam to the tumor shape. Cyberknife offers another

robotic radiosurgury delivery system for beam tracking.76-78 Beam tracking presents a

quality assurance challenge, much effort is needed to overcome the technical difficulties

associated with this method. Respiratory gating, although time-inefficient, is routinely used

clinically and will be the primary focus in this study.

1.10 REDUCING IMAGING DOSE WHEN USING INTERNAL

SURROGATES

The RTRT system uses 30 Hz. Efforts to decrease imaging frequency will result in

lower imaging dose. If external markers are utilized together with internal surrogates then a

predictive filter can be applied reducing the imaging frequency to as low as 5 Hz. Markers

on the patient abdomen are calibrated to internal surrogates and constantly tracked.

1.11 CONE BEAM CT FOR IGRT

Cone beam CT (CBCT) using the on-board imager (OBI) device installed on linear

accelerators (linac) allows three-dimensional (3D) online patient setup and treatment

verification for image guided radiation therapy (IGRT). CBCT enables soft tissue imaging

providing a major advantage for target localization on a daily basis. 2D localization based on

pelvic bony landmarks using portal imaging is less accurate.79

Conventional computed tomography (CT) operates in either circular or helical mode

and uses one dimensional detectors, while CBCT uses two dimensional detector arrays and

typically operates in circular mode although helical CBCT scans are a topic of ongoing

research.79-85 Many different reconstruction algorithms exist however the Feldkamp, Davis,

and Kress (FDK), reconstruction algorithm seems to be the most widely uses for circular

trajectories.86 Figure 1.3 shows a treatment Linac with a kV CBCT.

11

Figure 1.3. Varian Trilogy with a CBCT OBI in arms extended mode.

A typical CBCT OBI system consists of a kV x-ray source (KVS) and an amorphous-

silicon (a-Si) flat panel detector (KVD). The KVS and KVD are mounted on linac gantry by

two robotically controlled arms, which position the KVS and KVD orthogonal to the

treatment beam and retract when they are not in use. CBCT has two acquisition modes to

offer two different field-of-views, full-fan mode and half-fan mode as seen in Figures 1.4 and

1.5.

For the Varian OBI the x-ray tube (KVS) has two focal spots: smaller size of 0.4 mm

and larger size of 0.8 mm. The x-rays can be delivered in two modes: radiographic mode and

pulsed-fluoro. The KVD panel has a detection area of 40 cm (X) × 30 cm (Y). With the panel

set at 150 cm source-to-detector distance (SDD), the maximum superior/inferior coverage is

20 cm at the isocenter plane.

Full-fan mode is typically used to scan sites where the size is less than 24 cm such as

the cranium. Half-fan mode is typically used for sites larger than 24 cm such as full body

12

Figure 1.4. CBCT acquisition mode. (right) Full-fan mode. The KVD is centered with x-ray axis. (Left) Half-fan mode. The KVD is shifted to one side.

scans as seen in Figure 1.6. Bowtie filters for either mode can be mounted to the KVS to

modify the beam profile for less patient dose.

Beam shaping x-ray filters or compensators have been used in computed tomography

CT to modify the distribution of x-ray flux across the field of view. Compensator filters have

been used in CT for beam hardening and reduction in dose to the patient.87-91 These

compensators have been used in CBCT for scatter and heel compensation.92, 93 Initially,

compensators have been used to improve the detectability in film radiographs with the

delivery of more uniform fluence at the detector.94

Bowtie filters potentially play a larger role in scatter, beam hardening, uniform

fluence across the detector, and dose reduction. Bowtie filtration is used for improving

image uniformity, CT number accuracy, contrast, and reduction in streak artifacts and patient

dose.94

13

Figure 1.5. CBCT images acquired from full fan mode (left) and half fan mode (right).

14

Figure 1.6. A schematic of the CBCT geometry at half fan mode.

15

CHAPTER 2

INTRODUCTION OF DEFORMABLE IMAGE

REGISTRATION (DEMONS)

Deformable image registration (DIR) is very useful in the implementation of online

adaptive radiation therapy (ART). DIR is an automated image segmentation method that

transfers voxels/pixels from one image set to another. In this study we focus on intensity-

value-based DIR for pulmonary cases only. Since DIR is computationally demanding we

take advantage of a parallelized demons algorithm implemented on computer graphics

processing units GPUs to make DIR clinically useful.95 Problems that are well suited for

GPUs can be expressed as parallel computations using a programming environment such as

compute unified device architecture (CUDA). This chapter outlines various widely used

demons DIR methods and presents a new method useful in inter-modality DIR.

The demons algorithm uses displacement vectors to move the voxels in the moving

image to match the static (reference) image. In the original demos algorithm, a displacement

vector dr = (dx, dy, dz) is applied to each voxel in the moving image,

(2.1)

Is(0) and Im

(0) are the original static and moving images, respectively, and Is(n) and Im

(n) are the

static and moving images at the nth iteration. Smoothing is used to suppress noise and

preserve geometric continuity of the deformed image. We refer to the above method as the

passive force.

By including gradient information of both the static and moving image, we are able to

overcome the asymmetrical behavior of the passive force:

(2.2)

When the gradient of the static image is small, the passive force becomes inefficient,

since it uses gradient information from the static reference to determine force.14 We can

16

correct the passive force inefficiencies by using the gradient of the iteratively uploaded

moving image. This method is referred to as the active force:

(2.3)

Combining the active and passive forces we obtain the double force method:

(2.4)

By including a normalization factor α, the passive force algorithm allows the length

of the displacement vector to be adjusted adaptively in each iteration.14, 96, 97 This method is

referred to as the double force method:

(2.5)

To account for asymmetries both the static and moving images are symmetrically

deformed toward one another in each iteration.98 This method is referred to as the fast

inverse consistent demons algorithm:

(2.6)

Often in clinical cases the basic demons assumption that the displacement vector is

reasonably small or local is violated. We can reduce the magnitude of the displacement

vector with respect to voxel size by introducing a multi-scale strategy.

A typical 512*512*100 pulmonary CT image set will be down sampled by two levels

in the lateral and anterior-posterior directions. The new 128*128*100 image set will then be

deformed to give a coarse vector field that will then be propagated to the finer scales and

finally to the original image where the most detailed displacements occur. Since the

iterations at coarse scales are computationally less expensive multi-scaling can be used to

speed up computation time as well.

The basic assumption in all of the demons algorithms is that there is an intensity

connections between corresponding regions on the moving and static images. Inter-modality

17

DIR often violates this assumption. A method has been developed to deal with the intensity

inconsistency of CBCT to CT DIR.

Deformation with Intensity Simultaneously Corrected (DISC), performs an adaptive

intensity correction step on the CBCT image at every iteration step of the demons

registration.95 The DISC demons method has a patch by patch histogram normalization

procedure imbedded in the algorithm, and provides a solution to inter-modality DIR.

Gradient calculation, displacement vector, and the smoothing step of the demons algorithm,

seen in Figure 2.1, are parallelized in CUDA and run on the NVIDIA Tesla C1060 graphics

card to speed up computation time.14

Figure 2.1. Flowchart of demons algorithm (A), with down-sampling (B), where the displacement vector r depends on the method (C), implemented on GPU.

18

CHAPTER 3

APPLICATIONS OF INTER-MODALITY 2D

DEFORMABLE IMAGE REGISTRATION

Using CBCT-4DCT 2D DIR to increase the spatial congruence between the planned

image and on-board-image will allow for more precise target and normal tissue localization

and facilitate dose escalation. CBCT-4DCT 2D DIR can be used for real-time tumor-

tracking as a beam tracking or respiratory gating tool. Additionally this chapter demonstrates

2D DIR between consecutive CBCT projections as a respiratory signal extraction tool.

3.1 RIGID REGISTRATION

Alignment of the 3D CBCT reconstruction with the simulation CT is preformed to

extract the pixel resizing value and offset in the X, Y, and Z directions as seen in Figure 3.1.

Alignment is obtained by normalized cross-correlation then visually verified and manually

adjusted. After rigid alignment a simulated projection in constructed. Each pixel in the

simulated projection represents a line integral through the patient and is a summation of all

the intensity values along a path from the virtual source to the virtual imager. I = ∫I0e-u(x)xdx,

integrated from the source to image pixel. The angular step size per simulated projection

represents the total rotational degrees around the patient, typically 180 or 360, divided by the

total number of CBCT projections.

The beam profile of the CBCT is non-uniform and will yield different attenuation

values depending on the region of interest (ROI), to account for this an in-air-scan is taken

and subtracted from each projection to get a beam/imager anisotropy profile as seen in Figure

3.2.

3.2 2D INTER-MODALITY DIR

When dealing with inter-modality DIR, that is, registration between images of

different modalities, the relative intensity mismatch of the two imaging modalities must be

accounted for. The relative intensities of CBCT projections to CT simulated projections are

different due mainly to scatter. Scatter-to-primary ratio (SPR) can exceed 100% in a typical

19

Figure 3.1. CT to CBCT rigid alignment using a transverse slice (Top) and double checked using a mid coronal slice (Bottom).

Figure 3.2 Raw AP CBCT projection of the thorax (Left). In air scan just prior to image acquisition (middle). Raw image with the log of the in air scan removed (Right).

20

clinical CBCT system for radiotherapy.98, 99 Different level of noise, beam hardening effects

and motion, also contribute to the intensity inconsistency between CT and CBCT.100-105

The one-dimensional geometry to the CT detector array allows for much less scatter

contamination. Since the beam in a CT is narrow in comparison to CBCT, the CT image will

be relatively less intense toward the center of the patient and relatively laterally more intense

due to a much smaller SI beam scatter factor. Additionally when simulating a CBCT

projected image from a CT no scatter component is introduced in to the CT simulation each

pixel in the simulation is simply a line integral through the patient and does not account for

scatter in any way. Since CBCT pulmonary projections are generally large enough to capture

the whole thorax in one snap shot scatter plays a major role in pixel intensity and must be

accounted for during DIR. All DIR methods have a term as seen in figure the difference in

intensity contributes largely to the movement vector of the demons algorithm.

Modifying the demons algorithm such that the gradient terms dominate, as seen in

Figure 3.3, allows for improved inter-modality DIR spatial congruence.

However, modifying the demons algorithm as illustrated in Figure 3.3 is not sufficient

to accurately deform the moving image, as seen in Figure 3.4. A patch by patch local

intensity modulation is done to overcome the inter-modality intensity mismatch.

Intensity modulations are done patch by patch, where ICP is the Intensity corrected

patch of the new moving image, MP is the patch of the original moving image, and SP is the

patch of the static image:

ICP = MP – μ(MP)*(1 – σ[MP] +μ(SP)*(1 – σ[SP]) (3.1)

Figure 3.5 visually demonstrates the anatomical corrections that can be realized with

the implementation of local intensity value correction in conjunction with a modified double

force demons algorithm. The patient in Figure 3.5 had a large rotation and structural

deformation in the AP projections that could not be accounted for with rigid registration

alone.

This method is also used not only in inter-modality DIR but also in DIR between

CBCT to CBCT projections. As the angle changes from one projection to the next during

CBCT acquisition, the relative intensities change. However, even though the intensities of

the projections change the local patch-by-patch gradient features between neighboring

21

Figure 3.3. By replacing the intensity term in the double force method with a constant the gradient terms will dominate the displacement vector.

projections remain intact. If slow gantry rotations are used, as is the case with 4DCBCT,

then neighboring projections can be registered to each other using the above DIR technique.

Direct tumor tracking using 4DCBCT to 4DCBCT 2DDIR cannot be achieved, as the

tangential component of the 4DCBCT deformed image is not reliable under all projection

angles. A region of lung tissue under focus may be plainly visible at some projection angles

but may be difficult or impossible to distinguish at other angles. Bony structure or couch

superposition presents a challenge in CBCT 2DDIR. Relatively low attenuating tissue such

as the lung or soft tissue can be difficult for DIR to distinguish when superimposed with

highly attenuating material such as metal or bone. Varying patient thickness with projection

angle can also present challenges in CBCT 2DDIR as the line integral from the source to the

detector may pass through varying patient thickness and create varying relative intensities.

22

Figure 3.4. The top image shows the DIR vector field with out intensity correction using standard demons algorithm. The bottom image shows the DIR vector field using the modified demons algorithm with out intensity correction.

However, when using 4DCBCT since the angle between projections is relatively small and so

registering consecutive projections using the modified demons algorithm produces accurate

deformations. The deformations may not represent physical coordinates of anatomical

structures under all circumstances in the tangential direction but the SI component of the

DVFs from 2DDIR can be used to extract a respiratory signal even in the presents of bony

structure or couch superposition.

23

Figure 3.5. The modified simulated image shows a bony structure mismatch (red arrow) with the ground truth (left). Local Normalization (LN) enhances the intensity congruence between the simulation and the CBCT(center). DIR in conjunction with intensity correction allows for anatomical corrections and is clearly observed on bony structures (red arrow) (right).

3.3 2D DEFORMATION OF CBCT TO PLANNING 4DCT

PROJECTION

Patients are rigidly aligned in lateral and AP projections. 2DDIR is performed on all

patients at EOI based on the diaphragm SI position. Respiratory phase matching is done to

ensure that displacement vector fields represent non-respiratory anatomical misalignment. In

Figures 3.6-3.10 the blue arrows represent the DVF superimposed with the static image. The

DVFs represent voxel displacement. The maximum mean and standard deviation are shown

in the SI and tangential directions in Figures 3.6-3.10. The CBCT projections for patients 1

and 2 are taken in half fan mode. Each voxel represents 1 mm in the tangential direction and

2.5 mm in the SI direction in Figures 3.6 and 3.7.

24

Figure 3.6. AP (left) and lateral (right) are shown of patient 1 with both CBCT projections (top) and simulated intensity corrected CT projections (bottom) at end of inhale. The 4DCT image sets have a body mask that removes the couch in 3D. The portion of the DVF outside the body is set to 0.

Figure 3.7. AP (right) and lateral (left) are shown of patient 2 with both CBCT projections (top) and simulated intensity corrected CT projections (bottom) at end of inhale. The 4DCT image sets have a body mask that removes the couch in 3D. The portion of the DVF outside the body is set to 0.

25

Figure 3.8. AP (right) and lateral (left) are shown of patient 3 with both CBCT projections (top) and simulated intensity corrected CT projections (bottom) at end of inhale.


26


3.4 2D DIR FROM 4DCBCT TO PLANNING 4DCT

PROJECTION

Patients 3-6 are taken with full fan mode. The Varian RPM signal was used to match

EOI CBCT projection with simulated CT projections in this case as these patients represent

the 4DCBCT patient set. Patients 3-6 have voxel spacing of 0.95mm in the tangential

direction and 2.5mm in the SI direction for Figures 3.8-3.10.

Patient 6 in Figure 3.10 had relatively large cardiac motion that can not be reliably

corrected for using 4DCT simulated projection deformable registration. DVFs near the heart

of patient 6 in the AP projections are not reliable.

Rigid offsets can be obtained using normalized cross-correlation, or manually with

only two projections. Care should be taken to ensure respiratory phase matching, as incorrect

phase can increase errors in the deformed image. Manual rigid alignment can be preformed

within minutes, and typical GPU DIR computation time was 0.3 seconds. In a 7-field IMRT

treatment, rigid offsets can be obtained and each field can be deformably registered in under

5 minutes. Figures 3.11 and 3.12 show the potential spacial accuracy gains that can be

realized with 2DDIR for non respiratory anatomical misalignment.

27

Figure 3.11. Plot of maximum (blue), mean (red), and standard deviation (green) for patients 1-4, and 6 in the SI (top) and tangential directions (bottom) from both the Left-Right projections (right) and Anterior-Posterior projections (left).

3.5 REAL-TIME LUNG TUMOR TRACKING USING 2DDIR

A tumor home position was identified in the reference phase of the 4DCT image set

as seen in Figure 3.13. The tumor position was tracked throughout the respiratory cycle

using 3D DIR. The first three PCA eigenvectors where used to extract the tumor coordinates

at each phase.

Simulated 4DCT respiratory projections were then individually registered to

pulmonary CBCT projections using a modified 2D DIR demons algorithm implemented on

GPUs. An automated global image-preprocessing algorithm of the simulated projection was

implemented to account for the relative local inter-modality intensity mismatch. The

28

Figure 3.12. Plot of the mean values of two projection orientations with both components of displacement for each projection. The maximum (blue), mean (red), and standard deviation (green) for patients 1-4,and 6 are graphed with the mean of all patients displayed (Top Left).

Figure 3.13. The tumor home position in each patient was first delineated in the reference phase of the 4DCT image set.

29

congruence of the inter-modality deformation vector field was inspected using bony

structures, diaphragm position, and tumor position, and if available RPM signal. The tumor

coordinates were then projected onto the simulated image after DIR. The demons output was

then added to the PCA derived tumor home position to obtain the deformed tumor position.

The deformed tumor position was then compared with the RPM signal generated during

CBCT acquisition. Anatomical structural congruence was compared by subtracting the

deformed image from the CBCT image.

3.6 TUMOR TRACKING USING 2DDIR BETWEEN CBCT

AND CT

Typically 660 projections were used per rotation taken with half fan mode with a

bowtie filter. This scenario allows for 11 projections per second with each projection angle

changing by about half a degree per projection. It is not typical to have an RPM signal for

CBCT so a tumor position is identified visually on each projection or by diaphragm position

interpolation for Figures 3.14 and 3.15. To decrease computation time both the simulated

projection and CBCT projection are downsampled by 1 level from 192*256 to 96*128 pixels.

This is done to allow for real time tumor tracking as computation time is no more than 0.15

seconds.

Patient 1 tumor position agrees well with the ground truth except for projections 50-

70 as seen in Figure 3.14. These projections were visually inspected and it was determined

that the relative height of the diaphragm agrees more closely with the 2DDIR tumor tracking

model than the ground truth. Patient 2 shows a strong period and phase correlation of tumor

position however there is a strong amplitude mismatch as seen in Figure 3.15. We do not

have the tumor position for this patient in the 4DCT reconstructions and it is difficult to

visually delineate in the projection image due to noise. As seen in Figure 3.16, the

displacements are on the order of 5 voxels in the SI direction.

There is a 2.5 to 1 ratio between the CBCT to simulated 4DCT SI voxel size which

corresponds to a 2 voxel SI displacement between EOE and EOI which agree more closely

with the 2DDIR model then the reference tumor position for patient 2.

30

Figure 3.14. Patient 1 2DDIR tumor tracking vs projection number in the SI direction (Top) compared with the reference tumor position (Bottom). Projection number (Horizontal axis) vs target coordinate (Vertical).

3.7 TUMOR TRACKING USING 2DDIR BETWEEN

4DCBCT AND CT

4D CBCT is accompanied with a corresponding RPM signal that is used as the

ground truth. 4D CBCT total scan acquisition time is 4 minutes, as opposed to 1 minute

conventional CBCT scan time. Our 4D CBCT scans were acquired using full fan mode with

a bowtie filter. Typically, 2200 projections are collected over 180 degrees, with about 9

projections per second with each projection angle changing by about 0.08 degrees per

projection. The ground truth was taken to be the Varian RPM signal. Only relative signal

amplitude, phase and period are compared in Figures 3.17 and 3.18. To decrease

computation time both the simulated projection and CBCT projection are downsampled by 2

levels from 384*512 to 96*128 pixels.

For Patient 3, in Figure 3.17, the SI and tangential tumor position are 90 degrees out

of phase with the RPM signal which expected as the abdomen moves anteriorly and the lungs

move inferiorly during inhalation. The tangential phase of the tumor position with respect to

31

Figure 3.15. Patient 2 2DDIR tumor tracking vs projection number in the SI direction (Top) compared with the reference tumor position (Bottom). Projection number (Horizontal axis) vs target coordinate (Vertical).

Figure 3.16. Patient 2 Sagittal (top) and Coronal (bottom) DFV from EOE to EOI.

32

Figure 3.17. Patient 3 SI tumor position vs projection number (top), with the corresponding tangential tumor position (middle), compared against the reference RPM signal (bottom). Projection number (Horizontal axis).

the RPM signal depends on its location within the thorax and can be both in phase or 90

degrees out of phase. The jagged peaks and troughs represent cardiac influenced motion.

The amplitude is generally low, no larger than 1mm, for cardiac motion.

For Patient 6, in Figure 3.18, the SI tumor position is 90 degrees out of phase with the

RPM signal which expected as the abdomen moves anteriorly and the lungs move inferiorly

during inhalation. The jagged peaks and troughs represent cardiac influenced motion. The

cardiac motion amplitude is considerable for this patient.

Accurate real-time modeling of cardiac motion is not possible with this method as the

time frame for 2DDIR is 0.15 seconds. Overall there is a good congruence between the RPM

signal and the tumor position in regards to phase and period.

Generally real-time tumor tracking can be accomplished reliably in some projections

and not in others. Projection angles that allow for good lung contrast will providing

33

Figure 3.18. Patient 6 SI tumor position vs projection number (top), with the corresponding tangential tumor position (middle), compared against the reference RPM signal (bottom). Projection number (Horizontal axis).

relatively minimal couch, cardiac, or bony structure interference are good candidates for

2DDIR real-time lung tumor tracking.

3.8 RESPIRATORY SIGNAL EXTRACTION FROM CBCT

PROJECTIONS

Lung tumors are first identified on the reference 4DCT image set then projected onto

the simulated CBCT projection. The simulated projection is then deformably registered to

the ground truth CBCT projection. The tumor site location is visually validated on a

projection angle with few obstructions. Consecutive CBCT projections are then deformably

registered to each other to obtain a new set of tumor coordinates for each successive

projection. Two different scenarios were studied, CBCT and 4DCBCT. CBCT projections

were collected from 0 to 360 degrees with a total acquisition time of 1 minute.

Typically 660 projections were used per rotation taken with half fan mode with a

bowtie filter. This scenario allows for 11 projections per second with each projection angle

34

changing by about half a degree per projection. It is not typical to have an RPM signal for

CBCT so a tumor position is identified visually on each projection or by diaphragm position

interpolation for Figures 3.19 and 3.20.

Figure 3.19. Demonstration of 2DDIR respiratory signal extraction using SI component of motion (Top) and the corresponding reference tumor SI position (Bottom) for patient 1. Projection numbers 32 and 70 correspond to EOE, projection numbers 9, 50, and 88 correspond to EOI as determined with diaphragm position. Projection number (Horizontal axis) vs target coordinate (Vertical).

For patient 1 in Figure 3.19, the incongruity in signal amplitude at projections 50-70

was inspected visually and found to agree more closely with the 2DDIR signal.

For patient 2 in Figure 3.20, the local EOI was visually inspected to correspond to

projection 18 using the diaphragm as a visual surrogate. Visual inspection of the EOE and

EOI using the diaphragm agrees much more closely with the 2DDIR signal then with the

ground truth. Additionally, the 2DDIR signal is much smoother with a more regular period.

3.9 RESPIRATORY SIGNAL EXTRACTION FROM 4DCBCT

TO 4DCBCT

A 4D CBCT is accompanied with a corresponding RPM signal that is used as the

ground truth. 4D CBCT total scan acquisition time is 4 minutes, as opposed to 1 minute

35

Figure 3.20. 2DDIR respiratory signal using SI component of motion (Top) and the corresponding reference tumor SI position (Bottom) for patient 2. Projection numbers 4 and 30 correspond to EOE, projection numbers 18 and 41 correspond to EOI as determined with diaphragm position. Projection number (Horizontal axis) vs target coordinate (Vertical).

conventional CBCT scan time. Our 4D CBCT scans were acquired using full fan mode with

a bowtie filter. Typically, 2200 projections are collected over 180 degrees, with about 9

projections per second with each projection angle changing by about 0.08 degrees per

projection. The ground truth was taken to be the Varian RPM signal. Only relative signal

amplitude, phase and period are compared for Figures 3.21-3.28.

Patient 3 in Figure 3.21, the 2DDIR respiratory signal agrees well with the ground

truth. The below baseline RPM signal amplitude observed at projection 160 was visual

inspected and was found to not correspond to below baseline diaphragm height. The 2DDIR

signal agrees more closely with observed diaphragm height in this region. The gagged lines

that can be observed near EOI or EOE from projections 110 to 150 are due to cardiac motion.

Cardiac motion will compromise the respiratory signal for projections where the hearth is

superimposed with the tumor site.

36

Figure 3.21. Short 2DDIR respiratory signal using SI component of motion (Top) and the corresponding ground truth tumor SI position (Bottom) for patient 3. Projection number (Horizontal axis) vs signal amplitude (Vertical axis).

The 2DDIR signal follows the same phase and period as the RPM signal but is

subject to baseline shift for patient 3 as seen in Figure 3.22.

Patient 4 in Figure 3.23, had very strong cardiac interference, as seen in the relatively

high frequency, low amplitude signal superimposed with the respiratory signal.


subject to a baseline shift for patient 4 as seen in Figure 3.24. Strong Cardiac interference

causes the jagged curves during EOE and EOI in the 2DDIR signal.


subject to a baseline shift for patient 5 as seen in Figures 3.25 and 3.26.


subject to a baseline shift for patient 6 as seen in Figures 3.27 and 3.28. There are scenarios

where 2DDIR seems to more closely correspond to visually inspected diaphragmatic motion

37

Figure 3.22. Full 2DDIR respiratory signal using SI component of motion (Top) and the corresponding ground truth tumor SI position (Bottom) for patient 3. Projection number (Horizontal axis) vs signal amplitude (Vertical axis).

than the RPM signal, however 2DDIR can be subject to a baseline shift and should be either

locally normalized or low pass filtered.

38

Figure 3.23. DDIR respiratory signal using SI component of motion (Top) and the corresponding ground truth tumor SI position (Bottom) for patient 4. Projection number (Horizontal axis) vs signal amplitude (Vertical axis).

39


40

Figure 3.25. DDIR respiratory signal using SI component of motion (Top) and the corresponding ground truth tumor SI position (Bottom) for patient 5. Projection number (Horizontal axis) vs signal amplitude (Vertical axis).

Figure 3.26. Full 2DDIR respiratory signal using SI component of motion (Top) and the corresponding ground truth tumor SI position (Bottom) for patient 5.

41

Figure 3.27. DDIR respiratory signal using SI component of motion (Top) and the corresponding ground truth tumor SI position (Bottom) for patient 6.

42


43

CHAPTER 4

INTRODUCTION OF APPLICATION OF 3D

DEFORMABLE REGISTRATION TO LUNG

MOTION MODELING

Principal component analysis (PCA) is used to lower the dimensionality of noisy

periodic motion. This chapter will focus on PCA for pulmonary motion modeling by

filtering out cardiac, DIR, and CT error in an effort to volumetrically reconstruct the lung at

each respiratory phase.

Pulmonary motion induced by respiration introduces uncertainties in organ motion

and the tumor home position. There are two basic models for compensating for noisy

respiratory motion. So far, the most popular method used is single point derived motion

usually taking the tumor center of mass to by the point of interest. Modeling the motion of

the entire lung is less common. Based on the work of the entire lung motion can be derived

from a sparse subset of the lung using PCA.15

Previous studies have tracking tumor regression using dominant inter-fractional

eigenmodes rely on the patient’s ability to reliably perform active breath-hold technique.106

Image-guided radiotherapy (IGRT) is a means for managing the complex geometric

variability of the thorax such as respiration-induced tumor motion, tumor growth and

regression. Classification of intrafractional eigenmodes could prove potentially useful in

developing a classification scheme of inter-fractional free-breathing.107, 108

4.1 PRINCIPAL COMPONENT ANALYSIS

PCA provides a means to reduce a complex data set to a lower dimension to reveal

the sometimes hidden, simplified structure. Consider a mass on a spring undergoing simple

sinusoidal motion in 1D. Monitor motion from 3 naive viewing angles as seen in Figure 4.1.

We obtain three data sets that have of the motion of the mass at the end of the spring

giving six dimensions of motion. We can lower the dimensionality of this data set by

computing the most meaningful basis to re-express this noisy data set. The hope is that this

new basis will filter out the noise and reveal a hidden structure. If x is the unit basis vector

44

Figure 4.1. A mass on a spring moving with sinusoidal motion. Cameras A, B, and C are recording the motion of the mass from random vantage points.

along the x-axis and Original basis- Position (2,2) in x and y. We find another basis, which

is a linear combination of the original basis, that best re-expresses the data set. 2√2 in the (√2

, √2 ) direction and 0 in the perpendicular direction. If we let Y be a m x n matrix related by

a linear transformation P. X is the original recorded data set and Y is a re-representation of

that data set. PX=Y. P is a rotation and stretch which transforms X into Y. By assuming

linearity the problem reduces to finding the appropriate change of basis. The row vectors

{p1,...,pm} in this transformation will become the principal components of X. By

maximizing the variance along P we simultaneously maximize the signal to noise ratio as

seen in Figure 4.2. Figure 4.3 demonstrates basis selection effects motion redundancy.

PCA assumes all basis vectors are orthonormal. Select a normalized direction in m-

dimensional space along which the variance in x is maximized. Save this vector as pi1. Find

another direction along which variance is maximized, however, because of the

orthonormality condition, restrict the search to all directions perpendicular to all previous

45

Figure 4.2. Data set for motion in 2 dimensions (Right). Signal-to-noise ratio taken along the X direction (Top Left), and taken along the Y direction (Bottom Left).

Figure 4.3. Schematic of various motion scenarios with various degrees of redundancy. Motion with equal parts x and y motion (A). Progression towards higher degrees of redundancy as one component of motion becomes more dominant (B and C). Motion in a highly redundant state with only one directional component.

46

selected directions. Save this vector as pi. Repeat this procedure until m vectors are selected.

The resulting ordered set of p’s are the principal components.

4.2 PCA FOR PULMONARY MOTION

Intra-fractional deformable image registration (DIR) is performed on 4DCT scans of

lung cancer patients. Principal component analysis is conducted on a set of 10 deformation

vector fields for each patient both with and without a lung mask.

The lung and body masks in Figure 4.4 are generated using intensity thresholding,

“imfill” to fill small holes, ‘imdilate’, to further fill holes, and “bwareaopen” to remove from

the image all connected components that have fewer than a threshold number of pixels.

Grey-scale-based deformable image registration (DIR) from end-of-exhale (EOE) to

end-of-inhale (EOI) thoracic 4DCT was performed on nine phases. Principle component

analysis (PCA) was performed on the set of nine deformation vector fields that resulted from

DIR. Using the 1st two dominant eigenmodes of 4DCT using gray-scale-based deformable

image registration volumetric reconstructions are evaluated in a lung both a lung masked

case and body masked case. Figure 4.5 demonstrates DIR lung tumor tracking in the 4DCT

and shows the 2 most dominant eigenvectors.

Leave one out cross validation (LOOCV) was used to test the accuracy of the PCA

model using a single observation from the original sample as the validation data, and the

remaining observations as the training data as seen in Figures 4.6. This is repeated such that

each observation in the sample is used once as the validation data.

In our study eigenvalues typically decay by a factor of 10 between the 1st and 2nd

eigenvectors for pulmonary inter-fractional free-breathing 4DCT in the masked cases. Large

errors are present in the very center of the thorax as cardiac motion is out of phase with

respiratory motion and cannot be reliably modeled on 4DCT’s sorted using respiratory

surrogates as seen in Figure 4.7.

The first two dominant eigenmodes of PCA are shown in Figure 4.8, where the red

arrows indicate the direction and magnitude of the eigenmodes, down sampled by a factor of

4.

The two first principal components are consistent amongst patients. Inter-fractional

eigenmode comparison may provide a means to track tumor regression and breathing pattern

47

Figure 4.4. Lung mask of patient 6 (Top) and lung mask applied to the CT image with additional thresholding.

or physiological changes. We expect that patients with more dominant diaphragmatic

respiration will allow for more delineated eigenmode classification.

In this study 3 types of breathing modes are classified based on the absolute value

4DCT DIR DFV components: SI mode, along the couch axis; AP mode along the vertical

axis; and axial mode, which is orthogonal to the SI axis. While the SI mode will always

dominate, the scale of its dominance over other breathing modes changes from patient to

48

Figure 4.5. 4DCT DIR results for patient 1. Lung tumor tracked in 3D from EOE (phase 6) to EOI (phase 9) (top left). Lung tumor tracked in from the R2 axis displaying only 1 dimension of motion in the R1 direction. Lung tumor tracked in from the R1 axis displaying only 1 dimension of motion in the R2 direction.

patient based on intrafractional respiratory motion. We compare the dominance of the SI

mode over the other two modes to the decay rate of the eigenvalues for each patient.

The decay rate of eigenvalues, as seen in Figures 4.9, are correlated with the modal

classification scheme that is demonstrated in Figure 4.10.

A correlation can be seen between the eigenvalue ratios and the demons output ratios.

All patients except patient 4 exhibit a strong correlation between modal dominance and

eigenvalue decay rate. A higher order of modal dominance in SI/Axial and SI/AP breathing

modes correlate to a more dominant 1st PCA dimension.

Patient 4 in Figure 4.10, is oriented on the table at an angle tilted slightly off of the

couch axis. The chest of patient 4 is elevated above the waste, this will change the

49

Figure 4.6. LOOCV error plotted against total number of eignevectors of the mean of all nine 4DCT phases for the masked case (Left) and the un-masked case (Right).

coordinates of respiratory motion. In this study we assume the SI direction to be parallel to

the couch but this is not the case for patient 4.

Eigenvalues between the first and second dominant respiratory modes decay rapidly

for all patients as seen in Figure 4.10. Intra-fractional LOOCV maximum error is on the

order of 1mm inside the lung and 4-6mm for the whole thorax for all patients using the first

two dominant eigenmodes as seen in Figure 4.7. Eigenvalue decay is fastest for patients

where diaphragm motion is relatively large in magnitude. The first two eigenmodes

generally demonstrate a strong but smooth superior-inferior motion component with a lesser

lateral and anterior-posterior component, while subsequent less dominant eigenmodes

produce more random directional eigenvector fields.

4.3 OVERALL SUMMARY

For patient set up error correction, amongst the 5 patient cohort the mean maximum

deformation displacement was 10.25 mm with a mean mean deformation displacement of

50

Figure 4.7. Superimposed errors between the EOE and EOI DIR and the first 3 eigenvectors of the DVF’s are represented by colored regions in the coronal slice for the unmasked case (Right) and masked case (Left) for patient 1, red regions represent the highest error and blue represents the lowest error. Maximum error is 2.3mm for the masked case and 4.2mm for the unmasked case.

Figure 4.8. Coronal slice of 1st eigenvector (left) and 2nd eigenvector field (right) for masked case for patient 2.

51

Figure 4.9. Eigenvector (horizontal axis) with associated eigenvalue (vertical axis).

1.874mm +/- 1.717mm as seen in Figure 3.12. In addition to the spacial-accuracy

improvement that 2DDIR offers over conventional CBCT reconstruction rigid offset

alignment, a dose reduction is inherent in this technique as it allows for only 2 projection

angles to be used at a 2 levels of down sampling. When lower spacial resolutions are used

pixels as is the case with two levels of down sampling 1:16, 16 pixels can be grouped

together to reduce the signal-to-noise ratio.

2DDIR for direct tumor tracking is a strong tool for projections where tumor contrast

is strong. In projections where cardiac signal interference is strong smoothing or predictive

trending may be required for compensation. As typical computation time is on the order of

0.1 seconds for using the NVIDIA Tesla C1060 graphics card, this method currently allows

for 10 frames per second. Currently the entire image is used, however, decreasing the

window for DIR computation centered around the tumor will dramatically increase

computation time.

52

Figure 4.10. Ratio of 1st and 2nd eigenvalues (Top, green dots) and 1st and 3rd eigenvalues (Top, blue dots), and the ratio of the absolute value of SI/AP components of demons output between EOE and EOI (Bottom, Red dots), and the absolute value of SI/Axial components (Bottom, purple dots), with the horizontal axis representing patient number and the vertical axis representing the unit-less ratio value.

53

CBCT to CBCT consecutive projection DIR allows for respiratory signal extraction

and can be used as a retrospective analysis tool, gating tool or a phase sorting tool.

PCA decay rate correlates well with breathing mode except for patient 4 as seen in

Figure 4.10. There is a trade off between removing noise and maintaining accurate

respiratory motion while lowering the dimensionality of respiratory motion. This study has

demonstrated the utility of the respiratory modal dominance as a means to asses lower

dimensionality strength.

54

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