© 2019 nicholas joseph potter
TRANSCRIPT
FEASIBILITY STUDY OF THE FLATTENING FILTER REMOVAL DESIGN FOR CONVENTIONAL TREATMENTS USING A LINEAR ACCELERATOR
By
NICHOLAS JOSEPH POTTER
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 Nicholas Joseph Potter
To Michael Thomas Brostoski
4
ACKNOWLEDGMENTS
First, I would like to thank my advisor: Dr. Bo Lu, for his patience and teachings,
but mostly for being a role model on how to be a successful medical physicist and
person. Also, I would also like to thank him for encouraging me to pursue a Ph.D.
Second, I would also like to thank my committee members: Drs. Guanghua Yan,
Jonathan Li, Chihray Liu, David Gilland, Hongcheng Liu and Dietmar Siemann for their
guidance and support.
To my family, I would like to thank my parents for all their love and unconditional
support over the years, and helping me accomplish my goals. As well as my sister, for
always being a role model to me and granting me with one of the biggest joys in my life,
my niece Nora. I would like to thank my fiancé Alexandra, for her patience and support
throughout this journey and my dog Alfred for being the best boy. I also would like to
remember my stepfather, Michael Brostoski, who passed away during my Ph.D. studies,
after a short and courageous battle against cancer. Michael always showed strength
and courage throughout his life, and instilled in me an appreciation of quality hard work.
Lastly, I would like to acknowledge my current fellow graduate students for their
friendship and support: Mr. Karl Mund, Mr. Haitham Alahmad and Mrs. Ping-Fang Tsai.
As well as past graduate students: Drs. Jiyeon Park, Brendan Barraclough and Sharon
Lebron for being both my friends and mentors, they were instrumental in helping me
develop my clinical skills at the start of my graduate research at the cancer center.
5
TABLE OF CONTENTS page
ACKNOWLEDGMENTS .................................................................................................. 4
LIST OF TABLES ............................................................................................................ 7
LIST OF FIGURES .......................................................................................................... 8
LIST OF ABBREVIATIONS ........................................................................................... 11
ABSTRACT ................................................................................................................... 13 CHAPTER
1 INTRODUCTION .................................................................................................... 15
General Introduction ............................................................................................... 15
Linear Accelerator Design ................................................................................ 16 Intensity Modulated Radiation Therapy ............................................................ 17 Flattening-Filter-Free Photon Beams ............................................................... 21
Specific Aims .......................................................................................................... 23
2 EVALUATION OF USING FLATTENING-FILTER-FREE PHOTON BEAMS TO DELIVER CONVENTIONAL FLAT BEAMS ............................................................ 32
Background ............................................................................................................. 32
Methods and Materials............................................................................................ 34 Photon Energies and MLC Characteristics ....................................................... 35
Flat Beam Generation for a Specific Case ....................................................... 35 IMRT Techniques for Flat Beam Generation Using Pinnacle ........................... 37 Beam Flatness and Delivery Assessment ........................................................ 38
Results .................................................................................................................... 38 Flat Beam Generation for a Circular Open Field .............................................. 38 IMRT Techniques for Flat Beam Generation Using Pinnacle ........................... 39
Quantitative Flatness Assessment ................................................................... 39 Efficiency Assessment...................................................................................... 40
Discussion .............................................................................................................. 40
Summary ................................................................................................................ 43
3 FLAT BEAM MODULATION FOR FLATTENING-FILTER-FREE MACHINES UTILIZING A NOVEL DIRECT LEAF TRAJECTORY OPTIMIZATION MODEL ..... 51
Background ............................................................................................................. 51
Methods and Materials............................................................................................ 53 FFF Beam and MLC Characteristics ................................................................ 53 Direct Leaf Trajectory Model ............................................................................ 54
Dynamic MLC Delivery Constraints .................................................................. 56
6
Off Axis Ratio ................................................................................................... 58
Efficiency Control ............................................................................................. 59
Tongue and Groove Effect ............................................................................... 60 Trajectory Map Conversion for Beam Delivery ................................................. 61 Optimization Results and Delivery Assessment ............................................... 61
Results .................................................................................................................... 63 Preliminary Analysis ......................................................................................... 63
Flat Beam Generation Using Direct Aperture Optimization .............................. 63 Tongue and Groove Effect Correction .............................................................. 64 Treatment Time Comparison ............................................................................ 65 Computation Assessment ................................................................................. 65
Discussion .............................................................................................................. 66
Summary ................................................................................................................ 69
4 CLINICAL IMPLEMENTATION OF A DIRECT LEAF TRAJECTORY OPTIMIZATION MODEL ......................................................................................... 88
Background ............................................................................................................. 88
Methods and Discussion ......................................................................................... 89 General Workflow ............................................................................................. 89 Optimization and Calculation ............................................................................ 90
Dose Scaling .................................................................................................... 90 Summary ................................................................................................................ 92
5 ASSESSING THE IMAGE QUALITY OF THE ELECTRONIC PORTAL IMAGING DEVICE USING FLATTENING-FILTER-FREE PHOTON BEAMS ........ 98
Background ............................................................................................................. 98 Method and Materials ............................................................................................. 99
Electronic Portal Imaging Device ...................................................................... 99 Calibration of EPID ........................................................................................... 99 Image Quality Analysis ................................................................................... 100
Results and Discussion......................................................................................... 100 Summary .............................................................................................................. 101
6 SUMMARY AND FUTURE WORK ....................................................................... 107
LIST OF REFERENCES ............................................................................................. 112
BIOGRAPHICAL SKETCH .......................................................................................... 116
7
LIST OF TABLES
Table page 2-1 Beam shapes and field sizes utilized throughout the study. For square and
clinical fields the field size is given for the x and y direction on the CAX, for circular fields the field size corresponds to the diameter of the circle. ................ 49
2-2 The flatness of crossline and inline profiles of an FF open beam, step-and-shoot FFF and sliding window FFF beams for various field configurations ....... 49
2-3 Monitor Units for three delivery methods, including FF open beams, S&S FFF beams, and S&W FFF beams. ........................................................................... 50
2-4 Total delivery time for step-and-shoot (S&S) and sliding window (SW) delivery methods compared to FF open beam. .................................................. 50
3-1 Gamma comparison passing rates using 3%/3mm criteria for DLTO optimized flat beams and 6 MV reference beams for various field sizes. All field were measured on a diode array with max field size 30x30 cm2 at 100 SAD set-up. ........................................................................................................ 86
3-2 Quantitative flatness assessment for measure dose profiles along the crossline and inline of the central axis for modulated 6FFF beams and reference 6 MV conventional be ......................................................................... 86
3-3 Total treatment delivery time for 6FFF modulated flat beams and reference 6 MV static beams, for all fields delivered. ............................................................ 87
3-4 Optimization calculation time for the DLTO model for all fields measured throughout the study. .......................................................................................... 87
8
LIST OF FIGURES
Figure page 1-1 The components of a linac ................................................................................. 28
1-2 Components of the machine head for conventional radiotherapy including the flattening filter. .................................................................................................... 29
1-3 Generation of a one-dimensional intensity-profile for one leaf pair, with a unidirectional sweep. .......................................................................................... 30
1-4 Components of the machine head for a flattening-filter-free linac, the difference in the resulting fluence profile is demonstrated. ................................. 31
2-1 Schematic drawing of the field for a simple circular case, showing segmentation of the field. ................................................................................... 44
2-2 Schematic drawing showing MLC delivery for the first four control points of the simple analytical model. The shaded region corresponds to the area that receives a direct beam hit. .................................................................................. 44
2-3 Crossline and inline dose profiles at 10cm depth, 90 cm SSD setup for a circular field with diameter of 30 cm. Dose profiles were calculated by the TPS using the simple MU modulation model. Profiles are normalized to the CAX. ................................................................................................................... 45
2-4 Crossline profile comparisons between step-and-shoot modulated FFF beams and open FF beams. Beam configurations include square fields with field size of (a) 10x10 cm2, (c) 20x20 cm2, and (e) 30x30 cm2 and circular fields with field sizes of (b) 10cm, (d) 20 cm, and (f) 30 cm diameter. All profiles are normalized to the CAX. .................................................................... 46
2-5 Crossline profile comparison between sliding window modulated FFF beams and open FF beams. Beam configurations include square fields with field sizes of (a) 10x10 cm2, (c) 20x20 cm2, and (e) 30x30 cm2 and circular fields with field sizes of (b) 10cm, (d) 20 cm, and (f) 30 cm diameter. All profiles are normalized to the CAX. ....................................................................................... 47
2-6 Crossline and inline profile comparisons between modulated FFF beams including step-and-shoot and sliding window and a reference FF open beam for three clinical fields, (a-b) asymmetrical rectangle, (b-c) whole brain, and (d-e) mantle field. All profiles are normalized to the CAX. .................................. 48
3-1 Measurement set-up for the FFF beam off-axis-ratio. Measurement was performed using 100 cm SAD set-up, and utilizes an automated movement device ................................................................................................................. 70
9
3-2 Measured off-axis-ratio for the 6FFF beam, accounts for the slight asymmetry in the beam. ..................................................................................... 71
3-3 Effective beam on time for two different trajectories. Multiple solutions can produce the effective beam on time, utilizing two different treatment times (Time 2 > Time 1). .............................................................................................. 72
3-4 Simple example of beam eye view for the left leaf bank, showing the location for tongue and groove effect calculation. The dark strips between adjacent leaves represents the 1mm area for fluence calculation. .................................... 72
3-5 An example sliding window leaf trajectory for one individual leaf pair for a 20x20 cm2 field, showing (A) the trajectory before conversion including the control point sampling (50 control points) and (B) the resulting machine deliverable cumulative MU per MLC position...................................................... 73
3-6 Irregular field contours analyzed in our study, the following fields right referred to as Arb SW1, Arb SW2 and Arb SW3, throughout the study. ............. 74
3-7 Comparison of two relative dose profiles for a 20x20 cm2 field. Left shows the beam profile before efficiency considerations. Right, indicates the beam profile resulting from the model that included delivery efficiency. ....................... 75
3-8 Measured central axis crossline normalized dose profiles for modulated 6 FFF and 6 MV reference beams, the field sizes include 10x10 cm2 and 20x20 cm2 ..................................................................................................................... 76
3-9 Measured central axis crossline normalized dose profiles for modulated 6 FFF and 6 MV reference beams, the field sizes include 30x30 cm2 and 40x40 cm2 ..................................................................................................................... 77
3-10 Measured central axis crossline and inline normalized dose profiles for modulated 6 FFF and 6 MV reference beam for a whole brain contour. ............. 78
3-11 Measured central axis crossline and inline normalized dose profiles for modulated 6 FFF and 6 MV reference beam for an arbitrary “hourglass” contour. .............................................................................................................. 79
3-12 Asymmetrical spine field isodose line coverage for 6MV reference field and 6FFF modulated flat beam 50%, 95%, and 100% dose lines a shown. .............. 80
3-13 20x20 cm2 isodose line coverage for 6MV reference field and 6FFF modulated flat beam 50%, 95%, and 100% dose lines a shown. ....................... 81
3-14 Arbitrary field shape line coverage for 6MV reference field and 6FFF modulated flat beam 50%, 95%, and 100% dose lines a shown. ....................... 82
10
3-15 Central axis crossline normalized dose profiles for a modulated 6 FFF mantle field. The comparison of the two profiles highlights the ability to eliminate the tongue and groove effect. ................................................................................... 83
3-16 Evaluation of optimization weighting factors λ1 and λ3 represent the weighting for flatness and tongue and groove correction, respectively. .............. 84
3-17 Evaluation of optimization weighting factors λ1 and λ2 represent the weighting for flatness and efficiency, respectively. ............................................. 85
4-1 The main graphical user interface for flat beam planning. The following indicates the workflow for the software. (1) Input (2) Field Information (3) Optimization (4) Contour Display (5) Leaf Trajectory Display (6) Dose Calculation (7) Dose Display and (8) RTP Output .............................................. 94
4-2 Field input for a given RTP. The information is pulled directly from the RTP file, with dose, SSD, and depth allowing for user input. ...................................... 95
4-3 Graphical user interface showing field selection. Field section displays the contour for a given field geometry (bottom left) and if the field has been optimized displays leaf trajectories (bottom right). .............................................. 96
4-4 Dose display module of the software allows the user to inspect the isodose lines for an optimized flat field, as well as the dose profiles. .............................. 97
5-1 Simple schematic of the EPID panel configuration (layers are not to scale) ..... 103
5-2 Las Vegas aluminum phantom schematic for the electronic portal imaging device. .............................................................................................................. 103
5-3 EPID image of Las Vegas phantom for 6FFF beam following calibration using 6MV gain (Left) and 6 FFF gain (Right). ........................................................... 104
5-4 Acceptable image of holes visible for energy range 4 to 6MV. The circle represents a hole that must be visible in the image, and the x denotes a hole in the phantom, but is not necessary to be visible. ........................................... 105
5-5 EPID image of Las Vegas phantom for 6 FFF. ................................................. 106
5-6 EPID image of Las Vegas phantom for 6MV. ................................................... 106
11
LIST OF ABBREVIATIONS
1D One-dimensional
2D Two-dimensional
3D Three-dimensional
3D-CRT Three-dimensional conformal radiation therapy
CT Computed tomography
DAO Direct aperture optimization
DLTO Direct leaf trajectory optimization
DMPO Direct machine parameter optimization
DR Dose rate
EPID Electronic portal imaging device
FF Flattening filter
FFF Flattening-filter-free
FMO Fluence map optimization
GUI Graphical user interface
IMRT Intensity modulated radiation therapy
Linac Linear accelerator
MLC Multileaf collimator
MU Monitor units
MV Megavoltage
OAR Off-axis-ratio
OF Output factor
PRF Pulse repetition frequency
QA Quality assurance
ROI Region of interest
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S&S Step and shoot
SAD Source-to-axis distance
SBRT Stereotactic body radiation therapy
SRS Stereotactic radiosurgery
SSD Source-to-skin distance
SW Sliding window
T&G Tongue and groove
TPS Treatment planning system
VMAT Volumetric modulated arc therapy
13
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
FEASIBILITY STUDY OF THE FLATTENING FILTER REMOVAL DESIGN FOR
CONVENTIONAL TREATMENTS USING A LINEAR ACCELERATOR
By
Nicholas Joseph Potter
May 2019
Chair: Bo Lu Co-Chair: David R. Gilland Major: Medical Sciences
Flattening-filter-free (FFF) linear accelerators produce a fluence distribution that
is forward peaked. Various dosimetric benefits, such as increased dose rate, reduced
leakage and out of field dose has led to the growth of FFF technology in the clinic.
Published literature has suggested the idea of vendors offering dedicated FFF units
where the flattening filter (FF) is removed completely, and manipulating the beam to
deliver conventional flat radiotherapy treatments. The ability to deliver conventional flat
treatments while operating in FFF mode would simplify the machine head design as well
as decrease the quality assurance (QA) workload. This work aims to develop an
effective way to deliver modulated flat beam treatments, rather than utilizing a physical
FF.
The first part of the dissertation evaluated the practicality of modulating a beam
to compensate for the forward peaked intensity distribution of FFF beams. This led to
the development of a novel direct aperture optimization model for sliding window based
intensity modulated radiation therapy (IMRT), including efficiency control and tongue
14
and groove effect correction. The convex linearly constrained model can be solved for
global optimal solutions. In order to employ the model for clinical implementation a
planning tool was developed to assist in planning modulated flat beam treatments.
Lastly, in order to completely review the capabilities of the FFF machine design,
image quality for the electronic portal imaging device (EPID) was examined for FFF
beams. This study demonstrates that the ability to deliver conventional flat treatments is
not absent while operating in FFF mode, and the FFF beam has sufficient image quality
for portal imaging. Therefore, the complete removal of the flattening filter from the linear
accelerator design is warranted.
15
CHAPTER 1 INTRODUCTION
General Introduction
This year approximately 1.7 million people in the U.S. will be newly diagnosed
with cancer; of that around 60% will undergo radiation therapy.1,2 A large majority of
those diagnosed will receive external photon beams from a medical electron linear
accelerator.2 External beam radiation therapy involves delivering beams of high energy
x-rays through a patient. The photon beam kills cancerous cells in the beamline, as well
damages healthy cells. The tradeoff between cancer cell death and healthy tissue
damage is the fundamental compromise in radiation therapy treatment planning.
Ultimately the goal of radiation therapy is to kill cancer cells, while damaging as minimal
healthy tissue as possible, to minimize adverse later-life effects from treatment. This
can be extremely problematic for cancers that are situated in close proximity to organs
at risk, or have infiltrated healthy functioning organs.
External radiation therapy has dramatically changed/improved since its inception,
now offering a variety of advanced treatment schemes. Originally, a radiation field was
shaped by the opening of a set of metal jaws located in the linear accelerator (linac)
machine head. This mechanism only allowed square or rectangular field openings,
delivering radiation to a significant amount of healthy tissue. Consequently, treatment
techniques were developed to minimize the radiation received by healthy tissue. For
example conventional three-dimensional conformal radiation therapy (3D-CRT), which
delivers radiation to conform to the geometric shape of the radiation beam to match the
intended target as close as possible. This is achieved by utilizing different beam shapes
or “apertures”, each with a uniform intensity level. The beam can be shaped with
16
physical “blocks” that exhibit the target shape or more modernly a beam shaping device.
The multileaf collimator (MLC) consists of opposing banks of highly absorbing tungsten
leaves (20-80 total leaf pairs) that can be moved in and out of the beamline to create
complex treatment target shapes. The movement of the MLC under computer control,
can be used to modulate the beam and results in complex intensity or fluence
distributions within the target. With the advancements of adjacent technologies,
including the MLC and computed tomography (CT), the 3D-CRT treatment scheme was
further improved with the introduction of intensity modulated radiation therapy (IMRT).3
IMRT has dramatically improved treatment efficiency and offers a large improvement in
the ability to deliver complex dose distributions in the patient. The next iteration of
modulated radiation therapy is volumetric modulated arc therapy (VMAT) which is
similar to IMRT but with dynamic gantry rotation, and dose rate.
Another recent modality in radiation therapy, is the flattening-filter-free (FFF)
machine design. All previous radiation beams coming from the linear accelerator were
flattened by a physical flattening filter (FF) in the treatment head before entering the
patient. On the contrary, the FFF machine design does not attenuate the beam using a
FF before leaving the treatment head, and demonstrate a strong forward peaked
intensity distribution. FFF photon beams are the crutch of this work, and will be
extensively covered throughout this paper.
Linear Accelerator Design
The radiation beam delivered to the patient is produced in a medical linear
accelerator. Figure 1-1 shows a block diagram similar to the design of the Elekta Versa
(Elekta, Inc., Atlanta, Georgia) linac used throughout this study and the components
17
involved in the beam production. The x-ray beam production begins with the modulator
which directs electrical energy in the form of square pulses to the electron gun and
magnetron. The electron gun produces electrons via thermionic emission and sends
them into the accelerator structure. The accelerator structure is a copper tube under
vacuum, with interior copper discs where the electrons are accelerated via the
electromagnetic field of microwaves supplied by the magnetron which are also
transferred to the accelerator structure via the waveguide. A transport system of
magnets are used to bend and steer the accelerated electrons to the treatment head.
Inside the treatment head the electrons bombard a tungsten target and produce
bremsstrahlung which are highly energetic x-rays in the megavoltage (MV) range. The
resulting x-ray beam then goes through a primary collimator. The x-ray beam is then
attenuated by the flattening filter resulting in a flat intensity across the beamline. Dual
ionization chambers are used to monitor the dose and symmetry of the x-ray beam.
Finally, the beam undergoes a variety of secondary collimation such as x and y direction
collimator jaws and the MLC. The configuration of secondary collimation and the
quantity of leaves in the MLC as well as leaf thickness are linac vendor dependent. The
largest field size deliverable on our linac is 40x40 cm2 at isocenter, which is a point that
is 100 cm away from the stationary target. Figure 1-2 shows a simple schematic for the
treatment head design for the linac used throughout the study, it can be noted the MLC
acts as the beam shaping device and y-jaw.
Intensity Modulated Radiation Therapy
IMRT is credited as first “invented” in 1982 and has been extensively studied and
improved over the last 25 years.4,5 The last survey performed to investigate IMRT use in
18
the US was in 2005, and it was found that 73% of responding radiation oncologists use
IMRT clinically, compared to 2002 at 32%.6 IMRT use in the US assumingly has only
increased since 2005, and is widely utilized in nearly every US clinic.
IMRT relies on the ability to modulate the intensity of the incoming beams of
radiation. When compared to conventional uniform beam delivery, IMRT allows for a
higher degree of conformity and a more complex dose distribution within the target. In
IMRT, the beam is modulated in order to decrease the dose to critical structures or
organs, while increasing, or “focusing”, the dose on the primary target volume. This is
achieved by delivering multiple IMRT beams from desired angles, that each have their
own complex non-uniform dose distributions. The resulting dose distribution in the target
is the result of superimposing the IMRT beams delivered from multiple angles.
The calculation of the non-uniform intensities based on the dose constraints and
prescription is called inverse planning. Inverse planning originally was a two-step
process, first a fluence map optimization (FMO) is performed and then a leaf-
sequencing algorithm is applied to determine the apertures required to deliver the non-
uniform intensity distribution to the target. In the succeeding sections, we will briefly
discuss the history of inverse planning, focusing on the major milestones. Then for the
main purpose of this work we will focus on leaf sequencing algorithms for non-rotational
motor-driven MLC based IMRT, including dynamic and step and shoot delivery.
History of inverse planning: An early milestone in inverse planning was the
formulation of IMRT as an optimization problem, minimizing an objective function.7 The
use of an objective function for example the sum of squared deviations between he
delivered dose and the prescription dose has become the backbone to the IMRT
19
inverse planning process. Although an exact solution is not guaranteed, optimizing the
objective function, can lead to an “optimal” solution, originally the problem was solved
through simulated annealing.7,8 The next big milestone came when gradient decent
methods were used to solve the inverse planning problem, which led to much more
suitable computation times when compared to other solving methods.9 Various forms of
gradient descent algorithms have since become the standard of inverse planning
algorithms in commercial treatment planning systems.
Nevertheless, inverse planning solved through simulated annealing was
implemented in the commercial Peacock planning system and was used for the
planning of the first patient treatment with IMRT in 1994. Subsequently, gradient base
solution methods were implemented into an IMRT planning system, and in 1995 at
Memorial Sloan Kettering Cancer Center the first MLC-based IMRT was delivered.10 A
challenge of IMRT delivery is the compromise between fluence modulation and
managing time efficiency and leakage radiation.
Sliding window delivery: In 1992, Convery and Rosenbloom developed the
proposed dynamic delivery method that would be utilized for the first MLC-based IMRT
previously.10,11 The study concluded intensity profiles can be produced with a
unidirectional motion of MLC leaves and relatively large leaf separation referred to as
sliding window (SW), see Figure 1-3. Their work demonstrated the production of 1D
arbitrary fluence profiles; at any point x the fluence is proportional to the difference
between the time when the leaf edge of the right leaf 𝑡𝐵(𝑥) crosses that point x and
starts the irradiation, and time when the left leaf 𝑡𝐴(𝑥) crosses that same point and stops
the irradiation.11 Leaf trajectories are modeled such that, 𝑡𝐴(𝑥) − 𝑡𝑏(𝑥), equals the
20
desired fluence at every point x.11 This novel work, was further improved by Spirou and
Chui (1994) and Svensson et al (1994), and in some form is still used commercially
today.12,13 These works, found that the leaf trajectory problem has a simple analytical
solution, Equation 1-1 and Equation 1-2. Ultimately, the slope of the desired fluence
profile dictates which leaf produces the fluence, left leaf A for positive slope and right
leaf B for negative slope, represented by Equation 1-2.12 This leads to 𝑀𝐴(𝑥) and
𝑀𝐵(𝑥) the cumulative beam on time for the left and right leaf, respectively, can be
calculated directly from the desired fluence profile. The advantages of this new method
are, the solution forces one leaf of the pair to move at max leaf speed, providing the
most efficient deliver and for the first time incorporated finite leaf acceleration and
transmission through the leaves.12,13
𝐹(𝑥) = 𝑀𝑎(𝑥) − 𝑀𝑏(𝑥) (1-1)
Positive: 𝑀𝑏(𝑥𝑖+1) = 𝑀𝑏(𝑥𝑖) +∆𝑥𝑖
𝑉𝑚𝑎𝑥 , 𝑀𝑎(𝑥𝑖+1) = 𝑀𝑏(𝑥𝑖+1) + 𝐹(𝑥𝑖+1)
Negative: 𝑀𝑎(𝑥𝑖+1) = 𝑀𝑎(𝑥𝑖) +∆𝑥𝑖
𝑉𝑚𝑎𝑥 , 𝑀𝑏(𝑥𝑖+1) = 𝑀𝑎(𝑥𝑖+1) − 𝐹(𝑥𝑖+1)
(1-2)
Step and shoot delivery: This mode of IMRT delivery differs from sliding
window or dynamic delivery, due to the beam being off while the MLC leaves move from
one position to the next. In 1991, step and shoot (S&S) delivery was developed which
involves delivering a succession of field segments with a small fluence, leading to IMRT
plans that required a large number of monitor units (MU).14 S&S was further improved
and an algorithm was developed that minimized the number of MU delivered.15 The
algorithm was very similar to the dynamic algorithm previously discussed. By minimizing
MU the undesired leakage radiation can be minimized. However, the number of
21
segments is what directly affects the total treatment delivery time. The ability to
minimize the number of segments while keeping the number of MU’s as low as possible
is a much more daunting task and was not attempted until much later in 2004, and still
dictates IMRT leaf sequencing research to date.16
Since the original development of inverse planning and leaf sequencing
algorithms in the late 1980’s and early 1990’s, many works have been published
providing incremental improvements to various aspects of the IMRT planning process.
In particular, the second crutch of this work stems from one of the major modern
accomplishments “direct” optimization. As discussed the inverse planning process
typically involved first a FMO and then applied then applies one of the leaf sequencing
algorithms previously discussed. However, it was demonstrated this methodology can
be clumped together resulting in a one-step optimization scheme, which is clinically
referred to as direct aperture optimization (DAO) or direct machine parameter
optimization (DMPO).17,18 The MLC leaf positions, as well as the aperture intensities are
optimized simultaneously typically using a simulated annealing algorithm.18 The results
show that DAO can produce highly conformal step-and-shoot treatment plans and when
compared with traditional optimization strategies, demonstrates that DAO can result in a
significant reduction in both the number of beam segments and the number of monitor
units.18 The DAO model is non-convex, therefore relies on a “heuristic” approach to
solve, lacking a guaranteed global solution.
Flattening-Filter-Free Photon Beams
The bremsstrahlung distribution of megavoltage x-rays produced by the target in
a medical linear accelerator (linac) is a strongly forward peaked intensity distribution.
22
The variation in both energy and intensity across the beamline is compensated for by
introducing a FF into the treatment head. The physical filter is developed to produce a
nominally flat beam, at a designated depth below the patient surface and field size, to
accommodate the uniform dose requirement of conventional treatments. Flat dose
profiles, with uniform dose, allowed for dose calculations to be performed at a time
when computers were unavailable in the treatment planning process. Historically,
treatment planning systems (TPSs) used simple algorithms compared to today such as
the Milan-Bentley algorithm, which were based on interpolations between measured
depth dose curves and profiles, and relied on flat dose profiles.19,20 See Figure 1-2 and
1-4, which demonstrates the machine head design for a conventional linac and a FFF
linac. The resulting fluence profile for the FFF machine head design is forward peaked,
as opposed to nominally flat.
FFF linacs have been a part of radiation therapy since the 1990s. The main
interests at that time were the increased dose rate for stereotactic radiosurgery (SRS)
and/or stereotactic body radiation therapy (SBRT) treatments.21 One advantage to
removing the FF is the capability to increase the dose rate by a factor of 2-4.21-23 FFF
technology started in the clinic with the Scanditronix racetrack microtron MM50, which is
a flattening-filter-free unit. The beam properties are achieved by scanning an electron
beam on the target.24 Some linear accelerator machine designs have been developed
that remove the FF ultimately from the treatment head, including the helical
TomoTherapy unit, as well as CyberKnife system, these units are typically dedicated to
SRS.25-27
23
Including increased dose rate leading to an improvement to delivery efficiency,
many current studies have shown that FFF beams offer a variety of advantages, such
as reduced out-of-field dose, head scatter magnitude, and head scatter variation for
various field sizes, improving dose calculation accuracy.22,23,28-32 The focus for the
application of FFF technology in the clinic has shifted to IMRT in recent years, IMRT
techniques inherently do not require a flat beam profile across the beamline and the
dosimetric advantages can be utilized in IMRT planning. Therefore, modern linear
accelerator designs have been developed to offer both conventional flat and FFF
photon beams.
Specific Aims
Intensity modulated radiotherapy (IMRT) is the most important advancement in
radiation therapy since the implementation of computed tomography (CT) in the
treatment planning process, and the subsequent development of 3-dimensional
conformal radiation therapy (3D-CRT).33 IMRT revolutionized the treatment planning
process, with the introduction of inverse planning optimization. Since its inception, IMRT
has become the most commonly used modality in radiation therapy, and is partly
responsible for the emergence of many other technologies in the radiation oncology
clinic. Employing the use of a multileaf collimator (MLC) in the machine head, IMRT led
to the rapid development of many types of MLC based techniques to assist in the
delivery of the complex dosimetric distributions attributed to the modality.
IMRT results in a varying fluence profile across the beam and therefore has
revived the conversation around operating a linac in flattening-filter-free (FFF) mode,
which inherently does not have a uniform intensity across the beam. FFF linear
24
accelerators (linacs) were originally investigated for their use in stereotactic
radiosurgery (SRS) since operating in FFF mode offers an increased dose rate. In the
end, various studies found FFF beams offer many “physics” advantages which can be
extended to the treatment planning process outside of just SRS. Nevertheless, FFF
units that are not dedicated to IMRT only, require a physical flattening filter (FF) in the
treatment head to deliver conventional flat beam treatments, increasing the number of
energy modes. The complete removal of the FF from the treatment head will decrease
the number of energy modes for the unit, decreasing machine maintenance and quality
assurance. In addition, the complete removal of the flattening filter would simplify the
treatment head design. Therefore, an efficient and accurate way to deliver flat beam
profiles without the need of the flattening filter needs to be investigated.
We chose to investigate the use of modulation for flat beam production, as an
effective and easy implemented solution into the clinic. First, we established a proof of
principle by employing a simple analytical solution that aimed to compensate for the
conical intensity distribution of the FFF beam via modulation. We then looked to take
advantage of commercially available IMRT inverse planning techniques for flat beam
production, by utilizing uniform dose constraints. What became evident early on in this
work, was that beam delivery efficiency was just as important to consider as flatness, as
well as the current available two-step optimization process associated with sliding
window (SW) based IMRT was not meeting our expectations. Consequently, we needed
a direct aperture optimization (DAO) model for SW based IMRT, built from the ground
up to directly address the goals of flat beam production. The use of a DAO model for flat
beam production, at first may have seemed like overkill for such a simple dosimetric
25
goal. However, the framework offered the ability to include all MLC constraints into the
planning process as well as more modern model considerations such as efficiency
control and tongue and groove.
The FFF machine design as well as IMRT inverse planning and optimization are
thoroughly investigated throughout this work. A solution for flat beam production in the
absence of a physical FF in the machine head has been designed and implemented,
combining the dosimetric advantages of FFF beams and the ability to deliver a
conventional 3D-CRT treatment from a FFF only unit.
The ability to deliver a conventional flat beam through other means than a FF
warrants the complete removal of the FF from the linac machine design. Consequently,
this would also effect the ability to utilize 6 MV conventional flat beams for electronic
portal imaging. Electronic portal imaging devices (EPIDs) are commonly utilized for
patient setup verification prior to treatment delivery. To round out the complete
evaluation of the FFF only machine design, a study focusing on the image quality of
portal imaging in FFF mode is justified.
Evaluation of using flattening-filter-free photon beams to deliver
conventional flat beam (Specific Aim 1): In this aim, we investigate the possibility of
employing a beam modulation technique for flat beam generation using 6 FFF mode on
an Elekta Versa machine. Firstly, a linear optimization approach was employed for flat
beam generation on the largest circular field to exam the practicability of beam
modulation based method. Then, by using Pinnacle (Phillips Radiation Oncology
Systems, Phillips Healthcare) treatment planning system (TPS), two inverse planning
techniques, direct machine parameter optimization (DMPO) and sliding window (SW),
26
were tested for beam flattening on real treatment fields under FFF mode. The inverse
plans were generated based on uniform dose (to the ROI contours created using
original FF fields) optimization. Degree of flatness, and delivery efficiency for all
methods were assessed. The concept of using inverse planning techniques for FFF only
unit was concluded at the end.
Develop and implement a direct sliding window based IMRT model
(Specific Aim 2): Develop a convex, linearly constrained model, that generates leaf
trajectories and a deliverable plan for sliding window based IMRT, that accounts for all
MLC dynamic delivery constraints. This novel optimization model is called Direct Leaf
Trajectory Optimization (DLTO). The model is capable of converting all machine and
MLC constraints for sliding window based IMRT into a linear convex format, such as
minimum leaf gap, maximum leaf speed, and maximum leaf travel distance. The tongue
and groove (T&G) effect was also incorporated directly into our model in a linear convex
form, whereas other optimization models are unable to do so due to the nature of
concavity. Delivery efficiency has also been included in our DLTO models, which can
guarantee the most efficient delivery. For the study, dose distribution, machine
deliverability, and treatment time efficiency were assessed.
Design a user-friendly interface for sliding window IMRT planning (Specific
Aim 3): The purpose of this aim is to design an online system to employ our model that
will determine the leaf trajectories to deliver flat conventional beams with sliding window
based IMRT beams. The goal is to develop a quick and effective stand-alone program
for planning modulated flat treatments, detached from the treatment planning system,
allowing for dosimetry and planning freedom.
27
Assess electronic portal imaging device capabilities using flattening-filter-
free beams (Specific Aim 4): In order to conclude the ability to replace conventional
flat beams with flattening-filter-free beams, the effects of using FFF beams for EPID
based imaging must be assessed. Two of the unique features of FFF beams is an
increased dose rate, 1400 MU/min compared to 600 MU/min, and the non-flat intensity
across the beamline. The purpose of this aim is to evaluate the effect of increased dose
rate and non-flat intensity on detector response, and provide the basis on utilizing FFF
beams for EPID based imaging.
28
Figure 1-1. The components of a linac
29
Figure 1-2. Components of the machine head for conventional radiotherapy including the flattening filter.
30
Figure 1-3. Generation of a one-dimensional intensity-profile for one leaf pair, with a
unidirectional sweep.
31
Figure 1-4. Components of the machine head for a flattening-filter-free linac, the difference in the resulting fluence profile is demonstrated.
32
CHAPTER 2 EVALUATION OF USING FLATTENING-FILTER-FREE PHOTON BEAMS TO
DELIVER CONVENTIONAL FLAT BEAMS
Background
By bombarding a high-Z material target with high-energy electrons, megavoltage
X-rays are produced through the bremsstrahlung interaction process inside of the target
of a linear accelerator (linac).* This creates a forward-peaked intensity distribution of X-
rays across the beamline. By introducing a flattening filter (FF) into the beam line, a
radiotherapy linac can produce a flat beam profile at a nominal depth below the surface
of the patient. The flat beam profile is achieved by the conical shaped geometry of the
FF, which is able to reduce the relatively high intensity of the central area of the original
beam. However, the FF design itself has some major drawbacks for dosimetry. Studies
have shown that the FF contributes the majority of treatment head scatter, which results
in an increase of patient skin dose. It is also energy dependent and machine-type
dependent, which are not ideal for machine design, dosimetry and treatment planning
modeling.34,35 More importantly, introducing the FF into the beam path significantly
decreases the original dose rate due to the attenuating effect and subsequently
increases the beam delivery time.
Since beam flatness has never been a major concern for radiosurgery treatment,
the need to reduce long delivery times for radiosurgery prompted investigations into
using a flattening-filter-free (FFF) mode for SRS treatment decade’s ago3. The FFF
* "Feasibility study of using flattening-filter-free photon beams to deliver conventional flat
beams"; N Potter, S Lebron, J G.Li, C Liu, B Lu; [Published online ahead of print 2019/01/08]. Medical Dosimetry; https://doi.org/10.1016/j.meddos.2018.12.002.
Reproduced with permission from Elsevier Publishing.
33
treatment mode has been successfully implemented for LINAC-based SRS treatments
since then. Regarding the dosimetric advantages of using FFF mode, studies of
simulations and measurements22,23,28-32 suggested that the removal of the filter can
reduce out-of-field dose, head scatter magnitude, and head scatter variation for various
field sizes, and can also ultimately improve dose calculation accuracy. However, for
non-SRS treatment, the need for beam flatness outweighs the need for treatment time
reduction, especially for large field treatments. Therefore, conventional FF treatment
mode is still the desired mode for conventional 2-Dimenional (2D) and 3-Dimensional
(3D) radiotherapy treatments.19
With consideration of the pros and cons of both the FF and FFF operations,
current Linac’s keep both of the settings available, as it can provide clinicians with more
flexibility for treatments. For instance, when treating patients with intensity modulated
radiotherapy (IMRT) techniques, or 2D/3D techniques for small targets, the FFF mode
would be the favorable mode since the dose rate advantage might help decrease the
total treatment time, whereas the beam flatness would not be a consideration. By
contrast, for large target treatments using 2D/3D techniques, the FF mode would be
more favorable since the beam flatness is obviously more crucial than the delivery time
reduction. Nevertheless, keeping both modes of operation increases the workload for
machine commissioning and maintenance, as well as for routine quality assurance.
Thus, it would be ideal to completely remove the FF from the treatment head from a
machine design point-of-view, as this would significantly reduce the workload with
regard to machine maintenance and quality assurance. To successfully implement this
idea, however, it is first necessary to find a method to accurately and efficiently deliver
34
flat beams with a FFF-only mode unit. To the best of our knowledge, no studies of this
intent have yet been conducted.
In this study, we investigated the possibility of employing beam modulation
techniques for flat beam generation using the 6MV FFF mode on an Elekta Versa
(Elekta, Inc., Atlanta, Georgia) machine. First, a linear optimization approach was
employed for flat beam generation for the largest allowable circular field to examine the
practicability of beam modulation-based methods. Then, using the Pinnacle (Phillips
Radiation Oncology Systems, Phillips Healthcare) treatment planning system (TPS),
two inverse planning techniques, step-and-shoot (S&S), and sliding window (SW), were
tested and compared with one another for beam flattening for actual treatment fields
generated using the FFF mode. The inverse plans were generated based on uniform
dose (to the region of interest (ROI) contours created using the original FF fields)
optimization. Degree of flatness and delivery efficiency for all methods were ultimately
assessed. Finally, the feasibility of using inverse planning techniques to flatten a beam
for a FFF only mode unit was determined.
Methods and Materials
In this section, we first outline the establishment of a simple linear optimization
model to generate a flat beam profile for the largest circular field allowed by the
machine. The objective was to prove that flat beam profiles could be achieved for large
regular-shaped fields using a simple intensity modulation scheme. However, for fields
with arbitrary aperture shapes, a more sophisticated intensity modulation method was
required. Next, we describe how the IMRT modules of the TPS were tested for flat
beam generation for arbitrarily-shaped fields. Two IMRT techniques were employed for
35
this purpose; the S&S and the SW. Finally, the delivery and evaluation methods are
described.
Photon Energies and MLC Characteristics
The FFF mode of an Elekta Versa HD machine was used for flat beam profile
generation. It was compared to a reference conventional beam with the FF in the
beamline. The available energy of the beam that was tested was 6MV. The unit features
the Agility treatment head, which has a 160 leaf MLC (80 leaf pairs), and a 0.5 cm leaf-
width projection at isocenter with a maximum leaf speed of 6.0 cm/s and interdigitating
capability. The leaf extension limit from the carriage is 15 cm.
Flat Beam Generation for a Specific Case
Inspired by the intensity distribution of a FFF beam in the 2D plane (rotational
symmetry with conical intensity distribution), a natural thought was to compensate the
conical intensity drop-off with a reversed MU distribution modulated by the MLC to
obtain flat beams. To achieve this, we designed the following segment strategy. The
segment is started with the minimal MLC gap allowed by machine along the edge of the
field and then gradually opened by isotropically retracting the MLC in a half-circular
shape until the leaves reach the centerline of the field. The collimator is then rotated by
1800 so that the second half of the circle is irradiated in exactly the same manner. The
MUs assigned for each segment of the beam were optimized to attain the best intensity
uniformity. For this specific case study, modulated MLC segments were generated
using an in-house MATLAB (Mathworks, Natick, MA) code. It was comprised of a series
of half circle ring-shaped segments of 5 mm width increments, as Figure 2-1 indicates.
The circular field is 30cm in diameter, which is the largest circular shape allowed due to
the restriction imposed by the leaf extension limit of the carriage of the Agility head.
36
The MUs assigned to each segment were determined with a least-square optimization
scheme described as follows.
Let element xi of vector x denote the delivered MU for segment i. Let matrix A
represent the dose/MU matrix delivered to various half-ring areas by different segments,
d0 represents the desired uniform dose at 10cm depth in a large cubic water phantom.
Then x can be solved by the following constrained least-square form:
min𝑥
1
2‖𝑨 ∙ 𝒙 − 𝒅𝟎‖2
2 𝑠. 𝑡. 𝑨 ∙ 𝒙 > 𝟎 (2-1)
The element ai,j of matrix A represents the dose per MU to the center point of the ith
half-ring area along the in-plane axis, delivered by the jth segment beam. Since each
half-ring area was defined by the difference of the two consecutive segments, as
illustrated in Figure 2-1, the number of segments and number of rings must be equal.
Here, we use n to denote the number of segments or ring areas. Thus, A is an nxn
matrix. The lower half of the matrix (when 𝑖 ≥ 𝑗) represents the dose/MU contributed by
a direct beam hit as shown in Figure 2-2, as the beam is delivered segment by segment
for any jth segment the open area is the preceding ith half-rings. The non-shaded region
of Figure 2-2 corresponds to the area receiving side scatter contribution, as the area is
blocked by the MLC during the segment delivery. In this model, the MLC leakage was
not considered, as its percentage contribution is negligible.
To obtain matrix A, the planar dose delivered by each segment with 50 MU was
individually computed at 10 cm depth with 90 cm SSD by the Pinnacle (Phillips
Radiation Oncology Systems, Phillips Healthcare) TPS. The center point dose of each
half-ring area was then extracted from the planar dose files using an in-house MATLAB
code to create matrix A.To acquire the optimized MU of each segment, the interior-point
37
algorithm was facilitated to solve the optimization problem of Equation 2-1.36 The
optimized MU per segment was then imported into Pinnacle, and the beams were
analyzed for uniformity.
IMRT Techniques for Flat Beam Generation Using Pinnacle
The simple intensity-modulation scheme worked for a circular-shaped aperture
as described in the previous section. However, it would fail for an arbitrary open field
since the field shape does not have to be isotropically symmetric. Therefore, more
complex intensity-modulation schemes, which are able to optimize both segment shape
and MU, are needed. In this paper, we tested this hypothesis using two different IMRT
techniques: S&S and SW. Both of these methods have their own pros and cons.
Without limiting treatment time and control point number, the S&S IMRT technique can
achieve highly conformal plans.33 On the other hand, the SW algorithms are designed to
generate plans with better delivery efficiency since the sweep-type delivery can largely
decrease the IMRT delivery time.33
To achieve flat profiles at 10cm depth with 90 cm SSD, we created a slab-
shaped ROI at 10 cm depth as the optimization target. This ROI is perpendicular to the
beam axis with 6mm thickness. The ROI contour followed the shape of MLC-defined
open fields with 7 mm margin shrinkage to exclude the penumbra region. Maximum,
minimum and uniform dose constraints were set to 105%, 100% and 95% of prescribed
dose, respectively. The optimization parameters for step-and-shoot delivery include
maximum number of segments equal to 50, minimum segment area of 4 cm2, and
minimum segment MUs equal to 3. For sliding window conversion, the optimization
parameters included maximum control points set at 50, beam splitting minimum overlap
38
distance set at 2 cm and maximum overlap distance set at 4 cm. Apertures of circular
and square shaped fields with varied field sizes, as well as some clinical fields were
tested. The field configurations are detailed in Table 2-1. For the SW plans, when the
field size is greater than 18x18 cm2, the TPS requires a beam split due to the maximum
MLC length (20 cm extended beyond the leaf bank) restriction.
Beam Flatness and Delivery Assessment
All dose profiles for assessment were acquired through TPS dose calculation. No
physical measurement of dose profiles was performed for our study. All dose
calculations follow the same treatment setup throughout the study: 100 cm SAD set-up,
with 10cm water-equivalent depth under full scatter conditions. Crossline and inline
profiles of FFF beams generated by intensity modulation methods were assessed and
compared to their corresponding reference profiles of conventional FF open beams for
all field configurations. MU efficiencies were compared between FFF modulated beams
and FF open beams. The delivery efficiency assessment was conducted by comparing
the delivery times of modulated FFF beams with the delivery time of the corresponding
reference open FF beam.
Results
Flat Beam Generation for a Circular Open Field
The profile corresponding to the crossline central axis for the largest circular field
size (30 cm in diameter) allowed by the MLC limitation of the Agility head for beam
modulation, were measured (Figure 2-3). The MLC modulation was generated by the
method described in “Flat beam generation for a specific case”. The results indicated
that the profiles were flat with shallow dips in the middle. The dips can be attributed to
the overlapping penumbrae of the split beam edges.
39
IMRT Techniques for Flat Beam Generation Using Pinnacle
Crossline profiles of S&S and SW modulated FFF beams are shown in Figure 2-
4 and Figure 2-5, respectively, along with their corresponding reference FF open beam
for regular field configurations. Crossline and inline profiles of S&S and SW FFF beams
are shown in Figure 2-6, along with the corresponding FF open beam for three different
clinical fields. For sliding window fields larger than 18cm in the MLC direction, the TPS
split the beam into two separate fields to accommodate the MLC leaf extension
limitation. The field split creates a dose spike on the flat profile at the field junction area.
Such an effect can be observed for large fields (see Figure 2-5 and Figure 2-6).
Quantitative Flatness Assessment
The computation of flatness is defined as:
𝐹𝑙𝑎𝑡𝑛𝑒𝑠𝑠 = 𝐷𝑚𝑎𝑥 − 𝐷𝑚𝑖𝑛
𝐷𝑚𝑎𝑥 + 𝐷𝑚𝑖𝑛× 100%
(2-2)
where, Dmax and Dmin are the maximum and minimum doses along the profile within the
central 80% of the field. This definition of flatness is in accordance with IEC60976.37
However, due to the nature of the intrinsic unevenness of the inline profile of the mantle
field, the flatness was computed as the average flatness of three flat portions of the
profile, as demonstrated in Figure 2-6. The quantitative flatness results are shown in
Table 2-2 for all beam configurations. For the reference FF open beams, profile flatness
is around 3-5%. For intensity modulated FFF beams, the overall flatness is better than
that of the reference open FF beam, except for the inline profiles of large FFF beams
using the SW technique, due to beam splitting. Overall, the flatness of S&S modulated
FFF beams is better than that of the SW modulated FFF beams
40
Efficiency Assessment
Table 2-3 indicates that all intensity modulated FFF beams required larger MUs
compared to FF open beams. SW beams needed more MUs than S&S beams to
achieve a similar flatness. The average MU increase was 205% for S&S delivery and
298% for SW delivery. It can also be observed that the larger the field size, the more
MUs the FFF beams required, which was expected since larger field sizes require more
modulation.
Delivery time comparison is shown in Table 2-4 for step-and-shoot and sliding
window based IMRT delivery compared to conventional FF beams. For all field
configurations, step-and-shoot beams resulted in a longer delivery time compared to
reference FF beams and sliding window beams. The largest increase in delivery time
was the clinical mantle example delivered using step-and-shoot at 11.81 times. For field
sizes less than 18 cm, sliding window modulated FFF beams resulted in a faster
delivery time compared to FF beams. For field sizes greater than 18 cm, the total
delivery time of the two split sliding window beams was within twice the delivery time of
the corresponding FF open beams.
Discussion
The largest circular field achievable with the MLC was first employed for flat
beam delivery. The results shown in Figure 2-3 indicate that the conical intensity of FFF
beams can be effectively compensated for by a reverse distribution of segment MUs for
a series of predetermined segments with a semicircular ring shape. However, this MU-
modulation method is solely performed on circular-shaped fields. For an arbitrary open
field, a more complex intensity-modulation method is required. The dip shown in the
center of the dose profile is due to overlapping penumbrae on the split beam edges, we
41
assumed the output factor is the same for all segments, however close to the beam
edge the output falls in the penumbrae region. This also suggests that a more
sophisticated modulation technique is needed to achieve better profile flatness.
Two IMRT modules (step-and-shoot and sliding window) of the Pinnacle
treatment-planning system were used to generate flat beam profiles using intensity
modulation for six regular-shaped beams and three clinical beams, as listed in Table 2-
1. The results in Table 2-2, Figure 2-4 and Figure 2-6 suggest that the step-and-shoot
technique is able to achieve a high level of flatness. The results of Table 2-2, Figure 2-5
and Figure 2-6 indicate that flat beam profiles can be achieved for field sizes less than
18x18 cm2 using the sliding window technique. However, the flatness of the beam can
be hampered for any field larger than 18 cm in the MLC direction due to beam splitting.
As demonstrated in Figure 2-5, a spike in the overlap region of the dose profile results
for large fields using the sliding window technique, due to the required split beam
delivery. Such profile spikes can lead to a much larger degree of flatness for the beams,
as Table 2-2 suggests.
As we mentioned in the introduction, the feasibility study should not only consider
the flatness, but also the delivery efficiency since a significant treatment time increase
is not ideal for conventional treatments using modulated FFF beams. Therefore, the
delivery efficiencies of modulated FFF beams were compared to their counterparts for
open FF beams. MU comparisons are listed in Table 2-3. It can be observed that the
modulation resulted in FFF beams with larger total MUs compared to the reference FF
open beams. This was expected, as modulation requires more MUs to patch the non-
flat beam profile to achieve comparable flatness. It should also be noted that the MU
42
efficiencies for SW beams are slightly better than for S&S beams in general, as the SW
technique only allows the MLC to move monotonically in one direction, which potentially
restricts the options for modulation compared to S&S beams. From a shielding
perspective, the increase in MU and subsequent increase in leakage would not require
additional shielding if the treatment room is already designed for IMRT treatments.
The comparison of the MU efficiency between modulated FFF beams and conventional
FF beams does not correlate to true delivery efficiency because the operational dose
rate in FFF mode (1400 MU/minute) is much higher than the operational dose rate for
beams using the FF (600 MU/minute). Therefore, the delivery times of the modulated
FFF and conventional FF plans were measured to assess the true delivery efficiency, as
listed in Table 2-4. The results suggest that the delivery time difference between the
IMRT beams and the reference beams was not as large as the MU efficiency difference
since the increased dose rate can compensate for the MU increase to some extent. The
results also suggest that the delivery time of the SW technique is comparable to that of
the reference FF open beam. For smaller apertures, the delivery times of SW FFF
beams are shorter than for the open FF beams due to the increased dose rate.
However, for larger beams, the delivery times of the SW FFF beams are longer than the
delivery times of the reference FF beams, but still within two times of them. The time
increase is attributed to the forced beam split required by the TPS. Alternatively, the
delivery time for larger fields could potentially be improved if beam splitting for SW
method was not required.
According to our study, it appears that both the S&S and the SW based intensity
modulation methods are able to achieve flatness that is comparable to open FF beam
43
delivery for small fields. For large field sizes, the SW method introduced dose spikes at
the center of the beam due to the beam splitting whereas the S&S method was able to
provide reasonably flat beams regardless of the field size. Regarding the delivery
efficiency, S&S delivery is very inefficient compared to FF open beam delivery. By
contrast, the study demonstrated that the SW technique has the potential to achieve a
comparable, or even faster, delivery time than that of FF open beam delivery for small
field sizes. However, due to the beam splitting requirement of the TPS, the benefits of
sliding window delivery efficiency were hindered for larger field sizes. Therefore, a more
robust and adaptable optimization technique should be pursued.
Summary
In this chapter, we investigated the possibility of employing beam modulation
techniques for flat beam generation using the 6MV FFF mode on an Elekta Versa
machine. First, a linear optimization approach was employed for flat beam generation
for the largest allowable circular field to examine the practicability of beam modulation-
based methods. Then, using the Pinnacle treatment planning system two inverse
planning techniques, step-and-shoot and sliding window were tested and compared with
one another for beam flattening for actual treatment fields generated using the FFF
mode. The inverse plans were generated based on uniform dose (to the region of
interest (ROI) contours created using the original FF fields) optimization. Degree of
flatness and delivery efficiency for all methods were ultimately assessed. This study has
shown that the concept of producing a modulated flat beam while operating in flattening-
filter-free mode is feasible. Thus, the complete removal of the flattening filter from the
gantry head is possible. However, the delivery efficiency should be improved with more
advanced beam modulation schemes for clinical utilization.
44
Figure 2-1. Schematic drawing of the field for a simple circular case, showing segmentation of the field.
Figure 2-2. Schematic drawing showing MLC delivery for the first four control points of the simple analytical model. The shaded region corresponds to the area that receives a direct beam hit.
45
Figure 2-3. Crossline and inline dose profiles at 10cm depth, 90 cm SSD setup for a
circular field with diameter of 30 cm. Dose profiles were calculated by the TPS using the simple MU modulation model. Profiles are normalized to the CAX.
46
Figure 2-4. Crossline profile comparisons between step-and-shoot modulated FFF
beams and open FF beams. Beam configurations include square fields with field size of (a) 10x10 cm2, (c) 20x20 cm2, and (e) 30x30 cm2 and circular fields with field sizes of (b) 10cm, (d) 20 cm, and (f) 30 cm diameter. All profiles are normalized to the CAX.
47
Figure 2-5. Crossline profile comparison between sliding window modulated FFF
beams and open FF beams. Beam configurations include square fields with field sizes of (a) 10x10 cm2, (c) 20x20 cm2, and (e) 30x30 cm2 and circular fields with field sizes of (b) 10cm, (d) 20 cm, and (f) 30 cm diameter. All profiles are normalized to the CAX.
48
Figure 2-6. Crossline and inline profile comparisons between modulated FFF beams
including step-and-shoot and sliding window and a reference FF open beam for three clinical fields, (a-b) asymmetrical rectangle, (b-c) whole brain, and (d-e) mantle field. All profiles are normalized to the CAX.
49
Table 2-1. Beam shapes and field sizes utilized throughout the study. For square and clinical fields the field size is given for the x and y direction on the CAX, for circular fields the field size corresponds to the diameter of the circle.
Field Shape Field Size
Square 10x10 cm2 Square 20x20 cm2 Square 30x30 cm2 Circle 10cm Circle 20cm Circle 30cm Asymmetric Rectangle 16x8 cm2 Mantle 31x38 cm2 Whole Brain 11x14 cm2
Table 2-2. The flatness of crossline and inline profiles of an FF open beam, step-and-
shoot (S&S) FFF and sliding window (SW) FFF beams for various field configurations
10 SQ
10 Circle
20 SQ 20 Circle
30 SQ 30 Circle
16x8 cm2
Mantle Whole Brain
6 MV Crossline
3.8% 4.7% 3.1% 3.8% 3.4% 3.8% 3.4% 4.7% 3.9%
6 MV Inline
4.4% 4.2% 4.4% 3.6% 3.6% 4.0% 4.4% 4.5% 4.3%
6 FFF S&S Crossline
1.6% 1.4% 1.4% 1.5% 2.5% 2.1% 2.0% 4.0% 0.8%
6 FFF S&S Inline
1.1% 1.5% 1.5% 1.8% 3.5% 2.4% 1.4% 3.9% 2.1%
6 FFF SW Crossline
3.1% 2.9% 14.4%* 2.7% 18.5%* 3.6%* 2.5% 14.5%* 2.6%
6 FFF SW Inline
1.3% 1.4% 3.4% 2.4% 5% 3.2% 1.1% 4.3% 3.3%
*For field sizes greater than 18x18cm2 the beam is split
50
Table 2-3. Monitor Units for three delivery methods, including FF open beams, S&S FFF beams, and S&W FFF beams.
Modality 10 SQ
10 Circle
20 SQ
20 Circle
30 SQ
30 Circle
16x8 cm2
Mantle
Whole Brain
6MV 657 665 599 636 573 592 652 585 652
S&S 6FFF
896 860 1309 1350 1312 1973 1150 3996 1025
SW 6FFF
1077 946 2318 1916 2848 2324 1326 2907 1092
The max control points for the optimization was set to 50 and for split beams the MU distribution is 50/50.
Table 2-4. Total delivery time for step-and-shoot (S&S) and sliding window (SW) delivery methods compared to FF open beam.
Modality 10 SQ
10 Circle
20 SQ
20 Circle
30 SQ
30 Circle
16X8 cm2
Mantle Whole Brain
S&S 6FFF
6 𝑀𝑉 𝐹𝐹 1.83 1.63 2.58 4.41 4.06 5.97 5.73 11.81 3.03
SW 6FFF
6 𝑀𝑉 𝐹𝐹 0.69 0.59 1.62 1.31 1.91 1.54 0.96 1.93 0.55
The max control points for the optimization was set to 50, the max dose rate was utilized for each delivery 6 FFF 1400 MU/min, and 6 MV 600 MU/min.
51
CHAPTER 3 FLAT BEAM MODULATION FOR FLATTENING-FILTER-FREE MACHINES UTILIZING
A NOVEL DIRECT LEAF TRAJECTORY OPTIMIZATION MODEL
Background
A natural thought would be to use intensity modulated radiotherapy (IMRT)
methods to generate flat dose maps (perpendicular to the beam axis). Our previous
feasibility study in Chapter 2, provides some insight as to whether or not current IMRT
delivery techniques (e.g. step-and-shoot, sliding window) can potentially achieve such a
goal. Although the study suggests that reasonably flat dose maps can be achieved in
most cases, some practical issues still need to be resolved prior to the full
implementation of a flattening-filter-free (FFF) only machine. From one perspective,
step-and-shoot (S&S) delivery can generate the best beam flatness with loose
segmentation number restriction. However, its delivery efficiency can be as much as
five times worse than the conventional beam for the same field size. From another
perspective, if the segment number was restricted extensively for the optimization in
order to obtain better delivery efficiency, the flatness generated by the modulated FFF
beams would become unacceptable for some cases, especially for large field sizes.
Compared to step-and-shoot delivery, the sliding window (SW) technique appears to be
a more promising delivery method for keeping both flatness and efficiency to a clinically-
acceptable level, according to our study.
When reviewing IMRT optimization schemes to develop our in-house flat beam
planning program, we naturally looked at improving the two step sliding window
planning approach, similar to the original work by Convery and Rosenbloom (1992) and
Chui and Spirou (1994), IMRT planning is outlined in Chapter 1 for reference.11,12 For
sliding window delivery the majority of treatment planning systems such as Pinnacle
52
(Phillips Radiation Oncology Systems, Phillips Healthcare), Raystation (RaySearch
Laboratories, Stockholm, Sweden), and Eclipse (Varian Medical Systems, Palo Alto,
CA) still employ some form of the two-step optimization approach.12 The scheme relies
on a fluence map optimization (FMO) and then a leaf sequencing algorithm. These
works, found that the leaf trajectory problem has a simple analytical solution, the slope
of the desired fluence profile decides which leaf produces the fluence and by forcing
one leaf to always move at max speed an efficient delivery can be planned. Convery
(1998) then introduced an extension of the algorithm that successfully enforced a
minimum leaf separation constraint, through the use of a feedback loop to correct
potential violations.38 The model could be extended to include all leaf travel constraints
and tongue and groove (T&G) effect correction. However, after examining the shear
amount of potential violations for all leaf constraints listed, the conclusion was reached
to avoid the use of iteratively applying corrections and the conversion from FMO to a
leaf sequence. The desire to mitigate the degradation of the optimal fluence due to
corrections and conversion led us to pursue a direct optimization approach.
To mitigate the drawbacks associated with the two step optimization problem,
direct aperture optimization for sliding window based IMRT was developed. Direct
aperture optimization (DAO) includes all of the multileaf collimator (MLC) constraints in
the optimization process, eliminating the need for a separate leaf sequencing step.18
DAO techniques have been employed by most commercial treatment planning systems
for step-and-shoot IMRT delivery.33 Unfortunately a direct aperture formulation for 2D
sliding window delivery has not been developed, to the best of our knowledge. The
53
challenge is to make this process time efficient, to keep the unavoidable leakage
radiation within tolerable limits and minimize tongue and groove effect.
For this study, we developed a direct aperture based optimization model to
generate flat beams using a modulated FFF beam for sliding window delivery. The
direct leaf trajectory optimization (DLTO) model incorporates all dynamic MLC
constraints into the optimization model rather than considering them only during the leaf
sequencing process. Delivery efficiency control and tongue and groove effect were also
incorporated into the optimization model. With the convexity character of the model, the
optimal solution can be guaranteed. The dose map flatness and delivery efficiency were
evaluated with the delivery results. The final conclusions are presented at the end of
this article.
Methods and Materials
We first describe the machine and MLC characteristics utilized in the study. A
general DLTO model is presented, we firstly addressed the shortfalls of the general
model. A new convex model, which incorporated all MLC constraints, was subsequently
introduced to address the shortfalls. Next we integrated two additional features,
efficiency control and tongue and groove effect, into the optimization model. For final
beam delivery, trajectory map conversion method was demonstrated. Finally, the
optimization weighting factors, beam delivery and evaluation methods for the flat beam
production are discussed.
FFF Beam and MLC Characteristics
In our study, the flattening-filter-free beam model of an Elekta Versa HD (Elekta,
Inc., Atlanta, Georgia) machine was used for flat beam profile generation. Final dose
maps were compared to its counterpart generated by a conventional beam with the FF.
54
The energy of the beam tested was 6MV with nominal dose rate 600 MU/minute for FF
beam and 1400 MU/minute for FFF beam. The unit features the Agility treatment head,
which has a 160 leaf MLC (80 leaf pairs), and a 0.5 cm leaf-width projection at isocenter
with a maximum leaf speed of 6.0 cm/s and interdigitating capability. The MLC requires
a 6 mm leaf gap for all leaf pairs, during dynamic delivery. The leaf extension limit from
a movable carriage is 15 cm into the opposing plane. Each bank of the movable
carriages cannot pass the center line of the beam. The leaf extension limit for each
individual bank is 20 cm, which is also the maximum distance between any two leaves
from the same leaf bank.
Direct Leaf Trajectory Model
The DLTO model was initially introduce by Papp and Unkelbach in 2014 for
volumetric modulated arc therapy (VMAT) optimization.39 Rather than optimizing the
fluence as the traditional FMO model does, DLTO is able to directly model the leaf
trajectories in a linear form and use them as the optimization constraints. The leaf
trajectory constraints were established based on arrival/departure time satisfaction of
each leaf pair. The convexity of the model is guaranteed by the convexity of the
objective functions and linearity of constraints. The model was briefly introduced in this
subsection as follows.
If we let 𝒅𝒊 represent the absorbed dose to voxel i and 𝒅𝒊𝑫 denote for the desired
dose to the same voxel, then the objective function f can be defined as a form of the
summation of least square approximation between absorbed dose and desired dose
over all voxels, indicated in Equation 3-1. 𝒅𝒊 can be computed as the summation of the
product of dose influence factor 𝑫𝒏𝒊𝒋 and beam intensity fluence 𝒙𝒏𝒋 over all leaf pair n
55
and bixel location j, written in Equation 3-2. Beam intensity fluence 𝒙𝒏𝒋 can be further
represented by the product of the constant dose rate DR and effective beam-on time 𝒕𝒏𝒋
at bixel j of leaf pair n, suggested in Equation 3-3.
𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑓(𝑑) = ∑ (𝑑𝑖 − 𝑑𝑖𝐷)2
𝑖
(3-1)
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑑𝑖 = ∑ ∑ 𝐷𝑛𝑖𝑗
𝐽𝑁
𝑥𝑛𝑗 (3-2)
𝑥𝑛𝑗 = 𝐷𝑅 ∙ 𝑡𝑛𝑗 (3-3)
In the above optimization model, variable 𝒅𝒊 has been successfully transferred to
variable𝒕𝒏𝒋, effective beam on time. 𝒕𝒏𝒋 can then be determined by the relationship of
the arrival/departure times between the leading leaf and the tailing leaf of the same pair,
indicated in Equation 3-4.
𝑡𝑛𝑗 = 1
2[𝑙𝑛𝑗
𝑜𝑢𝑡 − 𝑟𝑛𝑗𝑜𝑢𝑡 + 𝑙𝑛(𝑗+1)
𝑖𝑛 − 𝑟𝑛(𝑗+1)𝑖𝑛 ]
(3-4)
In Equation 3-.4, 𝒓𝒏𝒋𝒊𝒏 and 𝒓𝒏𝒋
𝒐𝒖𝒕 represent the arrival and leaving times of the
leading leaf at the boundary between bixel j-1 and j for leaf pair n, respectively.
Similarly, 𝒍𝒏𝒋𝒊𝒏 and 𝒍𝒏𝒋
𝒐𝒖𝒕, represent the arrival and leaving times of the trailing leaf at the
boundary between bixel j-1 and j for leaf pair n, respectively.
To ensure that the breakpoints in the piecewise linear leaf trajectories are
properly ordered and the trailing leaf is always behind the leading one, Equation 3-5 and
Equation 3- 6 were also added into the constraints.
0 ≤ 𝑟𝑖𝑛 ≤ 𝑟𝑜𝑢𝑡, 0 ≤ 𝑙𝑖𝑛 ≤ 𝑙𝑜𝑢𝑡 (3-5)
56
𝑟𝑖𝑛 ≤ 𝑙𝑖𝑛, 𝑟𝑜𝑢𝑡 ≤ 𝑙𝑜𝑢𝑡 (3-6)
The above MLC timing constraints enforce monotonic leaf motion in the DLTO
model and allow us to directly optimize leaf trajectories along with finding the optimal
dose distribution.
This model is a convex optimization problem as the objective function is convex
and constraints are linear. Convex optimization problems can be solved efficiently in
general and global optimal solutions are guaranteed. In principal, it can be applied to
the proposed problem, to acquire the modulation to achieve a flat beam using FFF
beam. However, the general DLTO model, only accounts for MLC travel timing
constraints with no consideration of the limits of dynamic delivery, such as leaf gap and
leaf travel limits. Therefore, the model is not a practical one, which is able to generate
deliverable plans. In addition, the model does not include delivery efficiency and tongue
and groove effect into the optimization, which is also essential to improve the final
delivery efficiency and the flatness of the dose map. Thus, to make the DLTO model
clinically feasible, more work was done in this paper. In the next three subsection, we
include all the beam delivery necessities into the model to tackle our problem while
keeping the convexity of the problem and the linearity of the constraints intact.
Dynamic MLC Delivery Constraints
The optimization model presented in the previous section can be extended to
take into account the additional dynamic delivery machine constraints while keeping the
linearity of the constraints intact. As variable j represents the distance and location
indicator for each leaf in the trajectory, we can intuitively utilize j to introduce the MLC
distance-based constraints. The added constraints include minimum leaf gap, maximum
57
leaf travel distance into opposing plane, maximum leaf travel of adjacent leaves in the
same bank, and equal beam off times for all leaf pairs, they are described as follows.
To incorporate the minimum leaf gap of opposing leaves during delivery, denoted as
Lgap, the general model of Equation 3-6 can be rewritten as Equation 3-7 to directly
enforce the leaf gap requirement. Such constraint imposes the minimum gap throughout
the entire trajectory, as well as keeps the trailing leaf behind the leading one. The range
of subscript j in Equation 3-7 should be confined by leave’s maximum travel distance
across the centerline for both banks. Thus, both starting bixel j , 𝒋𝒔𝒕𝒂𝒓𝒕 and ending bixel
j, 𝒋𝒆𝒏𝒅 are restricted to be less than the max leave travel distance, as indicated in
Equation 3-8.
𝑟𝑛𝑗𝑜𝑢𝑡 ≤ 𝑙𝑛(𝑗−𝐿𝑔𝑎𝑝)
𝑜𝑢𝑡 (3-7)
𝐿𝑒𝑓𝑡 𝐵𝑎𝑛𝑘: 𝑗𝑠𝑡𝑎𝑟𝑡 ≤ 𝑇𝑟𝑎𝑣𝑒𝑙 𝐶𝑜𝑛𝑠𝑡𝑟. 𝑎𝑛𝑑 𝑗𝑒𝑛𝑑 ≤ 𝑇𝑟𝑎𝑣𝑒𝑙 𝐶𝑜𝑛𝑠𝑡𝑟.
𝑅𝑖𝑔ℎ𝑡 𝐵𝑎𝑛𝑘: 𝑗𝑠𝑡𝑎𝑟𝑡 ≥ (−)𝑇𝑟𝑎𝑣𝑒𝑙 𝐶𝑜𝑛𝑠𝑡𝑟. 𝑎𝑛𝑑 𝑗𝑒𝑛𝑑 ≥ (−)𝑇𝑟𝑎𝑣𝑒𝑙 𝐶𝑜𝑛𝑠𝑡𝑟. (3-8)
Equation 3-9 implements the leaf carriage constraint. Those constraints will be
only enforced only if a potential violation is found due to field shape and size. In that
manner, we can customized the size of the constraints for each individual model to
acquire better computation efficiency. This is achieved by preprocessing and evaluating
the difference in starting and ending locations for each leaf trajectory for a given field
shape. A potential violation arises if the difference in starting positons, difference in
ending positons, or difference between the start and end positons is greater than the
maximum allowed distance. If a potential violation is found, then constraints will be
added to the model for each potential. The function of the introduced restrictions are
similar to Equation 3-8 as it limits the range of bixel indicator j, for a given leaf bank.
58
If |𝑗𝑆𝑛
− 𝑗𝑆𝑚
| > 𝐶𝑎𝑟𝑟. 𝐶𝑜𝑛𝑠𝑡𝑟. or |𝑗𝑆𝑛
− 𝑗𝐸𝑚
| > 𝐶𝑎𝑟𝑟. 𝐶𝑜𝑛𝑠𝑡𝑟. or |𝑗𝐸𝑛
− 𝑗𝐸𝑚
| > 𝐶𝑎𝑟𝑟. 𝐶𝑜𝑛𝑠𝑡𝑟.
Then 𝑙𝑛𝑗𝑜𝑢𝑡 ≤ 𝑙𝑚(𝑗 + 𝐶𝑎𝑟𝑟𝑖𝑎𝑔𝑒 𝐶𝑜𝑛𝑠𝑡𝑟.)
𝑜𝑢𝑡 , 𝑟𝑛𝑗𝑜𝑢𝑡 ≤ 𝑟𝑚(𝑗+ 𝐶𝑎𝑟𝑟𝑖𝑎𝑔𝑒 𝐶𝑜𝑛𝑠𝑡𝑟.)
𝑜𝑢𝑡 ∀ 𝑛 ≠ 𝑚 (3-9)
S and E in Eq. 3-9 refer to the starting and ending locations for each leaf pair,
respectively. Subscripts n and m represent the number of any two leaves in the same
bank.
By enforcing all trailing leaves “out” time be equal for the last leaf position,
Equation 3-10 can guarantee beam off times for all leaf pairs are the same. The
necessity of beam off time constraints arise from the fact that beam will stop for all leaf
pairs at the same time once the last trailing leaf stops moving.
𝑙𝑛(𝑗𝑒𝑛𝑑−𝐿𝑔𝑎𝑝 )𝑜𝑢𝑡 = 𝑙𝑚(𝑗𝑒𝑛𝑑 − 𝐿𝑔𝑎𝑝)
𝑜𝑢𝑡 (3-10)
Off Axis Ratio
During the optimization process, the FFF off-axis-ratio (OAR) is applied to the
fluence calculated by Equation 3-3, in order to account for the conical shaped drop off of
intensity for the FFF beam. Originally we used a completely symmetric OAR, that
utilized a measured 40x40 cm2 open FFF profile rotated about the central axis 360
degrees. However, to improve calculation accuracy and profile symmetry after delivery,
we measured the OAR, at 10 cm depth and 100 cm SAD set-up to apply in our
optimization model. This was performed using the Sun Nuclear IC Profiler (Sun Nuclear
Corp, Melbourne, FL.), attached to an automated movement device, see Figure 3-1 for
measurement set-up. We delivered a fully open 40x40 cm2 FFF beam, and measured
the relative dose profile along the inline of the central axis profile (vertical direction). By
59
moving the IC Profiler in 1 cm increments in each direction, measuring the inline profile
from -20 to 20, we were able to interpolate and compute a more accurate representation
of the FFF OAR. Figure 3-2 shows the measured OAR, and accounts for the slight
asymmetry of the FFF beam. The dose profiles measured throughout this study, all
display excellent profile symmetry and improved flatness across the profile.
Efficiency Control
We utilized a symmetric 20x20 cm2 square field, to initially analyze the model.
Two shortfalls were concluded from the initial analysis, the model resulted in
asymmetric leaf trajectories for a symmetric field, and small incremental segments led
to dose calculation errors due to output factor changes. The combination of the two
shortfalls also led to a large increase of MU compared to 6MV delivery. Shown in Figure
3-3, is a simple example to explain how the optimization model could calculate two
equal effective times 𝒕𝒏𝒋 for two different trajectories.
To control the delivery efficiency, two methodologies could be applied in the
original optimization scheme. One is to restrict total delivery time in a constraint format;
the other is to add a weighted delivery time term into the objective function. For this
work, we chose the second method since it not only provides the flexibility to control the
delivery efficiency by varying the weighting but also diminishes the issue of an infeasible
solution, which is unavoidable for method 1. Since the total treatment time can be
expressed as 𝒍𝒏(𝒋𝒆𝒏𝒅−𝑳𝒈𝒂𝒑 )𝒐𝒖𝒕 (the trailing leaf’s out time for the last leave position), the
objective function Equation 3-1 can be rewritten as Equation 3-11 to incorporate the
delivery efficiency control.
60
𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑓(𝑑) = 𝜆1 ∑ (𝑑𝑖 − 𝑑𝑖𝐷)2 + 𝜆2𝑙𝑛(𝑗𝑒𝑛𝑑−𝐿𝑔𝑎𝑝 )
𝑜𝑢𝑡
𝑖
(3-11)
In which 𝜆1and 𝜆2 are weighting factors for dose uniformity and delivery efficiency,
respectively.
Tongue and Groove Effect
To describe T&G effect, two extra fluence variables, 𝒙𝒏𝒋𝑳𝑻𝑮and 𝒙𝒏𝒋
𝑹𝑻𝑮,
corresponding to the T&G fluence for the left and right leaf bank respectively, were
introduced into the model. They represent the partial fluence transmission at T&G
edges (1mm strips) between adjacent leaves from both banks. The geometric location
of T&G fluence is shown in a schematic drawing as an example, demonstrated in Figure
3-4. Extending the general model, T&G fluence is calculated utilizing two new “effective
beam on times” variables for the left and right leaf bank, 𝒕𝒏𝒋𝑳𝑻𝑮and 𝒕𝒏𝒋
𝑹𝑻𝑮respectively. Thus,
Equation 3-12 and Equation 3-13 are able to approximate T&G effective beam on time
for each pair of adjacent leaves. The equations are similar to the general model.
However, it relies on the arrival and departure time of the adjacent leaf, in place of the
opposing leaf for each pair.
𝐿𝑒𝑓𝑡 𝐵𝑎𝑛𝑘: 𝑡𝑛𝑗𝐿𝑇𝐺 =
1
2[(𝑙(𝑛+1)𝑗
𝑜𝑢𝑡 + 𝑙(𝑛+1)(𝑗+1)𝑖𝑛 ) − (𝑙𝑛𝑗
𝑜𝑢𝑡 + 𝑙𝑛(𝑗+1)𝑖𝑛 )]
𝑥𝑛𝑗𝐿𝑇𝐺 = 𝐷𝑅 ∙ 𝑡𝑛𝑗
𝐿𝑇𝐺 (3-12)
𝑅𝑖𝑔ℎ𝑡 𝐵𝑎𝑛𝑘: 𝑡𝑛𝑗𝑅𝑇𝐺 =
1
2[(𝑟𝑛𝑗
𝑜𝑢𝑡 + 𝑟𝑛(𝑗+1)𝑖𝑛 ) − (𝑟(𝑛+1)𝑗
𝑜𝑢𝑡 + 𝑟(𝑛+1)(𝑗+1)𝑖𝑛 )]
𝑥𝑛𝑗𝑅𝑇𝐺 = 𝐷𝑅 ∙ 𝑡𝑛𝑗
𝑅𝑇𝐺 (3-13)
To include the T&G effects into our objective function for minimization, Equation 3-11
will be rewritten in the following form, shown as Equation 3-14
61
𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑓(𝑑) = 𝜆1 ∑ (𝑑𝑖 − 𝑑𝑖𝐷)2 + 𝜆2𝑙𝑛(𝑗𝑒𝑛𝑑−𝐿𝑔𝑎𝑝 )
𝑜𝑢𝑡
𝑖
+ 𝜆3 ∑(𝑥𝑛𝑗𝑅𝑇𝐺 + 𝑥𝑛𝑗
𝐿𝑇𝐺)
𝑛𝑗
(3-14)
where 𝜆3 is the weighing factor tongue and groove effect term.
Trajectory Map Conversion for Beam Delivery
Prior to the delivery of the modulated FFF beams, the trajectory maps had to be
converted from “times” to “positions”. The reason for this conversion is that the final
information required for machine delivery is not the arrival/departure time of the MLC at
each position, however the positions under equal “time”/MU interval. This was easily
handled by sampling the trajectories at equidistant MU (time) intervals and recording the
position. For example, for a 50 control point delivery, the equidistant sampling for
cumulative MU would be 1/50 = 0.0202 of the total MU. An example of the pre-
conversion for one individual leaf pair trajectory demonstrating the equidistant sampling
as well as the converted leaf trajectory map has been shown in Figure 3-5. After the
conversion the result is the cumulative MU and leaf position for each control point, the
trajectory is clinically deliverable for SW based IMRT.
Optimization Results and Delivery Assessment
Optimization was performed in MATLAB (Mathworks, Natick, MA) on a Dell
Optiplex 990 (Dell Inc. Round Rock, TX) with an Intel®Core™ i5-2500 CPU @3.30GHz
processor (Intel Corporation, Santa Clara, CA) and 8GB of RAM. Optimization of the
model is performed in MATLAB, utilizing CVX: Matlab for Disciplined Convex
Programming, which is a package for specifying and solving convex programs.40,41.
Optimization times are recorded for all field geometries analyzed in the study. The times
could further be improved by using a more computational powerful computer.
62
The 2D planer dose for a conventional flat beam in a virtual water tank, was
computed by our in house software using a pencil beam algorithm, which were
subsequently used as the desired planer dose 𝒅𝒊𝑫 for the optimization for any specific
field.42 The measurement data for 2D dose maps was obtained from the MapCheck2
(SunNuclear Inc. Melbourne, FL) diode array. The measurement for profile acquisitions
was performed using the IC Profiler. The plane for dose comparison was defined at 10
cm depth with 100 cm SAD setup, both dose calculation and measurement followed this
setup throughout the study. The first portion of the study focused on the capabilities of
the optimization model and its ability to plan flat beam treatments for a variety of
geometries. Dose discrepancy between modulated FFF beams and open FF beam for
contours with field size <30x30 cm2 (field size limit for Mapcheck2 Device) were initially
analyzed using gamma analysis to evaluate the DLTO model for flat beam generation.
Clinical fields and some extreme irregular field (artificially generated) were assessed to
test the robustness of the model. The irregular field contours are shown in Figure 3-6 for
reference, the purpose of these contours is to challenge the optimization algorithm, by
presenting concave contours. Next, tongue and groove effect correction was examined
for some special cases. Comparisons between the optimization with and without the
tongue and groove effect were listed in the results section to show the efficacy of the
proposed method. Delivery time was also listed for all fields used throughout the study.
Computation time was compared for all fields used throughout. The impact of
optimization parameters were evaluated at the end of the results.
63
Results
Preliminary Analysis
As mentioned in the initial results from the optimization model, yielded less than
desirable beam profiles. The results showed asymmetric trajectories when the latter
was expected, small incremental segments resulting in dose calculation errors, and a
very bad MU efficiency. It was concluded that the model was lacking in a way to control
delivery efficiency, and ultimately the size of the aperture openings. Figure 3-7 shows
the comparison of beam profiles without (left) and with (right) the efficiency included in
the objective function, represented by Equation 3-11. Beam flatness improved as
expected, due to the trajectory utilizing larger aperture openings throughout delivery,
improving dose calculation accuracy. In addition, MU efficiency was vastly improved.
Flat Beam Generation Using Direct Aperture Optimization
For the following subsection, if the field label includes “T&G” the tongue and
groove approx. was included in the model, otherwise it is excluded, as a way to
prioritize flatness and computation efficiency. The desired dose 𝑑𝑖𝐷 refers to the
calculated planar dose for the equivalent 6MV open field. Gamma comparison passing
rates are provided in Table 3-1 for field geometries < 30x30 cm2 comparing the
measured modulated flat beam and conventional flat beam generated by the FF using
3%/3mm criteria.
The quantitative degree of flatness was analyzed for all field geometries, the
computation of flatness is defined as:
𝐹𝑙𝑎𝑡𝑛𝑒𝑠𝑠 = 𝐷𝑚𝑎𝑥 − 𝐷𝑚𝑖𝑛
𝐷𝑚𝑎𝑥 + 𝐷𝑚𝑖𝑛× 100%
(3-15)
64
where, Dmax and Dmin are the maximum and minimum doses along the profile within the
central 80% of the field. This definition of flatness is in accordance with IEC60976.37
The quantitative flatness results are shown in Table 3-2 including the reference FF
equivalent open beam.
Crossline and inline central axis relative dose profiles measured at 100 cm SAD
set-up, with the IC Profiler are provided for the simple square geometry field size 10x10
cm2 to 40x40 cm2, shown in Figure 3-8 and 3-9. Next, the model was employed for flat
beam generation of more complex fields, meant to further assess the models
capabilities. Irregular fields included whole brain, asymmetrical spine, mantle and three
arbitrary shaped fields. Additional crossline and inline relative dose profiles for the
modulated FFF beams are shown in Figure 3-10 and 3-11, along with their
corresponding reference FF open beam for two different field configurations a clinical
whole brain and an “hourglass” shape contour (Arb SW3). Isodose maps for 3 different
fields including 105% 100% and 90% isodose lines are shown in Figure 3-12, 3-13 and
3-14 to better evaluate the uniformity of dose delivered by the sliding window beam in
comparison to the equivalent 6 MV isodose map.
Tongue and Groove Effect Correction
The tongue and groove effect correction detailed in the previous section is
applied on the fields that resulted in the largest dose profile “dips” across the dose map
due to the tongue and groove design. The tradeoff of the correction is computation time
which can be seen in Table 3-4. Therefore, the correction was only applied in the
optimization model for the fields that yielded the need. In Figure 3-15, a clinical
example, the mantle field is presented with and without T&G effect correction, including
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a 6MV reference field, the dip in the dose profile without correction in Figure 3-15, is
completely removed. The deviation of flatness for the T&G effect corrected beam, is
recorded in Table 3-2.
Treatment Time Comparison
Delivery time comparison is shown in Table 3-3 for sliding window based IMRT
delivery compared to conventional FF beams. It is important to note that the modulated
FFF beams dose rate was 1400 MU/min and 6 MV reference beams dose rate was 600
MU/min. Although, modulation inherently increases MU and therefore delivery time,
when compared to static delivery, the dynamic nature of SW and increased dose rate of
FFF beams results in time efficient treatments. For all field geometries the max increase
in treatment time is 2.5%, which corresponds to an increase of 33.23 seconds.
Computation Assessment
Computation time was recorded and compared for all cases presented in the
study. Displayed in Table 3-4, is the computation time for the direct sliding window
optimization model, including overall calculation time, as well as the specific interior
point optimization algorithm time. Also shown for the mantle case is the computation
time when using the T&G model and when not, it can be seen the introduction of the
T&G model significantly increases computation time. The decision of when to use the
correction should be determined on a case by case basis. For field sizes ranging from
10x10 cm2 to 40x40 cm2 and all field geometries, the DLTO computation time is
sufficiently fast. The objective function utilized in the optimization model Equation 14,
has three parts with individual weighting factors, the desired dose difference λ1, the
treatment efficiency λ2 and T&G fluence λ3. The tradeoff between gamma comparison
66
passing rate, T&G effect correction and treatment delivery time was analyzed by
examining the effect weighting factors λ1, λ2 and λ3 have on the delivered dose maps,
shown in Figure 3-16 and Figure 3-17.
Discussion
In this study we investigated the efficacy of a novel 2-dimensional direct sliding
window based IMRT optimization model to produce a conventional flat beam treatment
through modulation. The optimization model was used to plan a variety of field
geometries ranging from 10x10 cm2 to 40x40 cm2 including clinical contours and
arbitrary field geometries The tongue and groove effect was analyzed for sliding window
delivery and a correction was added to the model in a linearly constrained, convex form.
Degree of flatness, treatment delivery efficiency, and computation efficiency were
recorded for all fields geometries mentioned in the study.
Square field geometries with field size 10x10 cm2 to 40x40 cm2 were planned
using the DLTO model. As well as a few arbitrary field geometries and three clinical
examples. All modulated flat beams analyzed exhibited acceptable uniformity and
overall comparable flatness to a beam produced with the FF. Multiple fields were
measured on a diode array and compared via gamma analysis to their FF counterpart,
with nearly all fields having 100% agreement (Table 3-1). For the fields analyzed,
particularly, the field geometries that are not simple squares, the outer edges of the field
have a 1-3% discrepancy in measured dose when compared to the optimized dose
map. This dose difference can be attributed to the output factor assumption, the model
assumes a constant output factor (OF) of 1 throughout the entire delivery. However, due
to the dynamic movement of the leaves, the edges of the field would have a different OF
67
than the central portion of the field. The field edges are either being “opened up” or
“closed on” due to the sliding window delivery. The output difference is responsible for
the shoulder region of the measured dose profiles exhibiting the largest flatness
deviation. However, it is important to note that the physical FF is designed to only
produce a flat field typically for a 10x10 cm2 field, subsequently our optimization scheme
can produce a flat field independent of field size. Therefore, it is evident that the
modulated flat beam would be more consistently flat and have less variation across size
and shape when compared to conventional beam produced with a FF. Lastly, analyzing
modulated fields, it can be noted that the flatness for the dose profiles in the MLC
movement direction (Crossline for non-rotated fields) is slightly worse than the degree of
flatness in the non-movement direction. The results for the modulated flat beams
indicate that for a variety of field geometries a comparable or better degree of flatness
to 6 MV conventional beams can be achieved.
Tongue and groove effect was successfully modeled in our optimization scheme,
giving the user the option to include the correction when deemed appropriate. The
mantle field was utilized to study T&G and our implemented correction. The measured
dose profile resulted in “dips” where the T&G fluence in the 1mm strip between adjacent
leaves calculated by Equation 3-12 and 3-13 was the largest (Figure 3-15). The largest
degree of flatness in Table 3-2, was 6.4% and can be attributed to the T&G effect. The
dose profile “dips” are completely removed when the correction is included in the
optimization of the mantle field, with proper weighting. To better understand the impact
the T&G effect correction has on the optimization, gamma comparison passing rates
(3%/3mm criteria) for the measured mantle field modulated beam and the conventional
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static beam was recorded utilizing 7 different weighting factor schemes (Equation 3-14).
The tradeoff between passing rate and T&G weighting, is shown in Figure 3-16, the
optimal weighting scheme for λ1 and λ3, is when the T&G fluence is weighted 1
magnitude larger than flatness.
As discussed flatness is not the only important variable when analyzing our
DLTO model to produce flat beams. Introducing modulation into the beam delivery will
inherently increase the total MU required to deliver an equivalent dose for static
delivery. However, due to the dynamic nature of sliding window delivery and the
increased dose rate capability of FFF beams, the impact of increased MUs on delivery
time can be reduced. Specifically 6 FFF can utilize an increased max dose rate of 1400
MU/min compared to 600 MU/min for 6 MV. By including efficiency in the optimization
model which was detailed in the previous section, we can minimize the overall delivery
time down, guaranteeing the most efficient treatment without degrading flatness. For
field sizes less than 15x15cm2 our modulated flat beam treatments can be delivered in
less time than conventional beams, shown in Table 3-3. For larger field sizes, the
increase in treatment delivery time would not interfere with typical clinical treatment
scheduling, and the max increase in time was the 40x40 cm2 indicated in Table 3-3
equal to 2.5x. Including T&G in the objective function, resulted in a negligible increase
to delivery time, also shown in Table 3-3. The tradeoff between gamma comparison
passing rate (3%/3mm criteria) and delivery efficiency was analyzed, and is shown in
Figure 3-17. For all weighing schemes, the overall delivery time only changed by 1.4s,
therefore weighting should prioritize flatness over treatment efficiency. By including the
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efficiency in the objective function (Equation 3-11) the optimization model yields
sufficient treatment times.
In terms of computing efficiency, the total calculation time which includes
compiling the constraints and model for the specific contour, as well as the interior point
optimization (solving time) was recorded for all fields, shown in Table 3-4.36 For the
majority of fields studied, the total optimization time was 30 seconds or less and the
interior point time was 2s or less. The larger the field or increased modulation resulted
in a larger optimization time. The inclusion of tongue and groove in the model increases
calculation time and has the biggest impact on interior point optimization time. The
impact of including T&G on calculation time is field specific and correlates to the overall
T&G fluence. Calculation efficiency was sufficient for all fields analyzed.
Summary
In this chapter, we developed a complete direct aperture optimization model for
sliding window based IMRT. The DLTO model incorporates all dynamic MLC constraints
rather than considering them only during the leaf sequencing process. Delivery
efficiency control and a tongue and groove effect correction, were also incorporated into
the DLTO model. With the convexity character of the model, a global optimal solution
can be guaranteed. The degree of flatness and treatment delivery time were evaluated
alongside computation efficiency. The DLTO model was capable of planning modulated
flat beam treatments for flattening-filter-free photon beams. The treatment time
efficiency and planning calculation time is acceptable for clinical practice and would not
interfere with our current treatment planning procedures.
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Figure 3-1. Measurement set-up for the FFF beam off-axis-ratio. Measurement was
performed using 100 cm SAD set-up, and utilizes an automated movement device
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Figure 3-2. Measured off-axis-ratio for the 6FFF beam, accounts for the slight asymmetry in the beam.
72
Figure 3-3. Effective beam on time for two different trajectories. Multiple solutions can
produce the effective beam on time, utilizing two different treatment times (Time 2 > Time 1).
Figure 3-4. Simple example of beam eye view for the left leaf bank, showing the
location for tongue and groove effect calculation. The dark strips between adjacent leaves represents the 1mm area for fluence calculation.
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Figure 3-5. An example sliding window leaf trajectory for one individual leaf pair for a 20x20 cm2 field, showing (A) the trajectory before conversion including the control point sampling (50 control points) and (B) the resulting machine deliverable cumulative MU per MLC position.
(B)
(A)
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Figure 3-6. Irregular field contours analyzed in our study, the following fields right referred to as Arb SW1, Arb SW2 and Arb SW3, throughout the study.
75
Figure 3-7. Comparison of two relative dose profiles for a 20x20 cm2 field. Left shows
the beam profile before efficiency considerations. Right, indicates the beam profile resulting from the model that included delivery efficiency.
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Figure 3-8. Measured central axis crossline normalized dose profiles for modulated 6
FFF and 6 MV reference beams, the field sizes include 10x10 cm2 and 20x20 cm2
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Figure 3-9. Measured central axis crossline normalized dose profiles for modulated 6
FFF and 6 MV reference beams, the field sizes include 30x30 cm2 and 40x40 cm2
78
Figure 3-10. Measured central axis crossline and inline normalized dose profiles for
modulated 6 FFF and 6 MV reference beam for a whole brain contour.
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Figure 3-11. Measured central axis crossline and inline normalized dose profiles for
modulated 6 FFF and 6 MV reference beam for an arbitrary “hourglass” contour.
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Figure 3-12. Asymmetrical spine field isodose line coverage for 6MV reference field and 6FFF modulated flat beam 50%, 95%, and 100% dose lines a shown.
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Figure 3-13. 20x20 cm2 isodose line coverage for 6MV reference field and 6FFF modulated flat beam 50%, 95%, and 100% dose lines a shown.
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Figure 3-14. Arbitrary field shape line coverage for 6MV reference field and 6FFF modulated flat beam 50%, 95%, and 100% dose lines a shown.
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Figure 3-15. Central axis crossline normalized dose profiles for a modulated 6 FFF
mantle field. The comparison of the two profiles highlights the ability to eliminate the tongue and groove effect.
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Figure 3-16. Evaluation of optimization weighting factors λ1 and λ3 represent the weighting for flatness and tongue and groove correction, respectively.
84.0%
86.0%
88.0%
90.0%
92.0%
94.0%
96.0%
98.0%
100.0%
0.001 0.01 0.1 1 10 100 1000
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
λ1/ λ3
TG Effect Passing Rate
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Figure 3-17. Evaluation of optimization weighting factors λ1 and λ2 represent the weighting for flatness and efficiency, respectively.
80.0%
82.0%
84.0%
86.0%
88.0%
90.0%
92.0%
94.0%
96.0%
98.0%
100.0%
0.001 0.01 0.1 1 10 100 1000
39
39.2
39.4
39.6
39.8
40
40.2
40.4
40.6
λ1/ λ2
Seco
nd
s
Delivery Time Passing Rate
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Table 3-1. Gamma comparison passing rates using 3%/3mm criteria for DLTO optimized flat beams and 6 MV reference beams for various field sizes. All field were measured on a diode array with max field size 30x30 cm2 at 100 SAD set-up.
Field Gamma Passing Rate(%) 3%/3mm
10x10 cm2 100.0 Spine 15x6 cm2 100.0 20x20 cm2 100.0 30x30 cm2 99.8 Arb SW1 100.0 Arb SW2 100.0 Arb SW3 100.0 Whole Brain 100.0
Table 3-2. Quantitative flatness assessment for measure dose profiles along the
crossline and inline of the central axis for modulated 6FFF beams and reference 6 MV conventional be
Field 6 FFF Cr-Plane
6FFF In-Plane
6 MV Cr-Plane
6MV In-Plane
10x10 cm2 2.9 2.5 3.0 3.8 15x6 cm2 2.7 3.3 3.3 3.9 20x20 cm2 2.8 2.5 3.1 4.0 30x30 cm2 2.6 2.4 3.2 4.3 Arb SW1 3.4 3.3 3.8 3.4 Arb SW2 2.6 3.4 3.5 3.1 Arb SW3 2.8 2.9 3.1 5.4 Whole Brain 3.1 2.8 3.9 4.3 Mantle 6.4 3.5 4.7 4.5 Mantle T&G 3.8 3.4 4.7 4.5
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Table 3-3. Total treatment delivery time for 6FFF modulated flat beams and reference 6 MV static beams, for all fields delivered.
Field SW 6FFF (s) Static 6 MV (s) SW 6FFF/6 MV
10x10 cm2 23.40 26.0 0.90 20x20 cm2 32.03 23.9 1.34 30x30 cm2 44.00 23.0 1.91 40x40 cm2 55.23 22.0 2.50 Arb SW1 28.14 25.0 1.13 Arb SW2 34.19 23.9 1.43 Arb SW3 22.99 26.7 0.86 Whole Brain 17.20 23.8 0.73 15x6 cm2 21.56 26.2 0.82 Mantle 33.80 22.6 1.49 Mantle T&G 39.42 22.6 1.74
Table 3-4. Optimization calculation time for the DLTO model for all fields measured
throughout the study.
Field Calculation Time (s) Interior Point Time (s)
10x10 cm2 16.032648 0.95 20x20 cm2 19.316858 1.37 30x30 cm2 25.352494 1.98 40x40 cm2 80.154531 2.28 Arb SW1 19.063774 1.28 Arb SW2 21.735680 1.89 Arb SW3 17.556734 1.15 Whole Brain 16.590719 1.06 15x6 cm2 24.759497 1.12 Mantle 28.209213 2.29 Mantle T&G 34.294071 5.54
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CHAPTER 4 CLINICAL IMPLEMENTATION OF A DIRECT LEAF TRAJECTORY OPTIMIZATION
MODEL
Background
A direct aperture optimization (DAO) model was developed for sliding window
(SW) based intensity modulated radiation therapy (IMRT) in Chapter 3. The overall goal
of the direct leaf trajectory optimization (DLTO) model is to accurately and efficiently
plan a modulated flat beam treatment, for a flattening-filter-free photon beam. In order to
employ the DLTO model in a clinical setting a graphical user interface (GUI) needs to be
developed to assist in flat beam planning and provide a simple workflow. When
developing the planning tool we set out to address two goals, create an easy to use and
understandable interface and to be completely detached and independent from the
treatment planning system.
First of all, the software will be able to communicate directly to our clinic’s
Radiation Oncology Information System, Mosaiq (Elekta, Inc., Atlanta, Georgia) through
the use of the Radiation Treatment Plan (RTP) file structure, which is used to
communicate with Mosaiq and our treatment planning system. Therefore we can directly
input the field contours and treatment plan parameters generated by a physician or
dosimetrist on Mosaiq, into our planning tool. The optimization module will allow the
user to select specific fields for optimization, providing flexibility for treatment plans with
multiple beams types and past treatment courses. Tongue and groove can be included
in the optimization on a field by field basis. Secondly, it is important to provide the user
a way to visualize the resulting dose distribution for the modulated flat beam. Therefore,
a dose calculation function was included in the software, developed in house it can
calculate the absolute dose of the field to compare with measurement after delivery. By
89
including the dose calculation functionality we were able to extend the capabilities of our
planning program to generate a flat beam treatment at any depth, source-to-skin
distance (SSD), and prescription dose. The modulated flat beam dose distribution can
be analyzed using simple tools providing absolute dose profile display and an isodose
map for a given field. Lastly, the optimized leaf trajectories are converted to a clinically
deliverable sliding window based IMRT, and is amended to the patients RTP file. It is
important to utilize Mosaiq and the record and verify (R&V) system to validate the SW
beam parameters and machine constraints before delivery.
Developed in this chapter is a planning tool to employ the DLTO model
developed in Chapter 3 for flat beam planning utilizing a FFF beam. The following
software was developed to allow for direct leaf trajectory optimization, dose calculation
and RT plan generation.
Methods and Discussion
General Workflow
The following workflow outlines the steps required and the options a user has
when planning modulated flat beam treatments for a FFF photon beam using our
planning tool, see Figure 4-1.
1. The physician or dosimetrist draws the contour(s) for conventional flat beam treatment on Mosaiq and exports the MLC position and treatment course information for the static field geometry. Output from Mosaiq is the Radiation Treatment Plan .RTP file.
2. The RTP file is imported into our in-house planning program, by pressing the Open button and selecting the desired RTP file. Information is displayed for user verification includes MRN, Name, Field ID, Energy, MU, Dose, SSD, and Depth. As well as a status indicator “Incomplete”, “Optimized”, or “Calculated” (Figure 4-2).
3. The user can then choose which fields are to undergo optimization and which to include tongue and groove in the optimization. Once the fields are selected press the “Optimize” button to begin, a status bar will indicate the progress of the optimization.
90
4. When optimization is complete the leaf trajectories can be viewed in the display window to initially view the leaf trajectories. The control points can be analyzed individually or the full sliding window delivery can be visualized (Figure 4-3).
5. Dose calculation can be performed immediately following optimization, and is only available for fields that have undergone optimization by pressing the Dose Calculation button. The SSD, depth, and dose can be adjusted by the user prior to calculation. Once a field reaches “Complete” status any changes to SSD, depth or dose will result in a dose scaling calculation.
6. For any selected field that has reached “Complete” status pressing the Dose Display button will bring up a separate window. The user can analyze crossline and inline dose profiles across the contour and an isodose map (Figure 4-4).
7. Lastly, for any field that has reached a ‘Complete” status the RTP file will be amended and ready for import back into Mosaiq, by pressing the Write RTP button.
Optimization and Calculation
Optimization of the DLTO model outlined Chapter 3 is performed in MATLAB,
utilizing CVX: Matlab for Disciplined Convex Programming, which is a package for
specifying and solving convex programs.40,41. Optimization results are clinically
deliverable leaf trajectories for a sliding window based IMRT beam that result in a
uniform relative dose across the beam.
The 2D planer dose for our modulated flat beam in a virtual water tank at 90cm
SSD and 10cm depth, was computed by our in house software using a pencil beam
algorithm.42
Dose Scaling
The result of the optimization and calculation module, is the 2D planar dose at 10
cm depth and 90 cm SSD, for our modulated flat beam. One of the advantages
discussed in Chapter 3 for our proposed method as opposed to using a physical
flattening filter, is opportunity to deliver a flat beam at any desired depth and field size.
As opposed to the physical FF which is developed to produce a nominally flat beam at
91
only one designated field size and depth (10x10 cm2 at 10cm depth). To accomplish this
goal a dose scaling module was developed for our planning tool. It is important to note,
dose scaling is different than the absolute dose calculation performed after optimization
for our sliding window beam and overall is a much simpler calculation.
The first objective is to calculate the required MU to deliver the prescribed dose
for a 6 MV beam with our equivalent field size, at a desired depth and SSD. The
difficulty, is calculating the equivalent nominal field size, 𝑭𝑺𝒄 due to the contours not
always being simple square geometries, we utilized some ingenuity to accomplish this
task and the tool at our disposal, our in-house dose calculation software.
Using Equation 4-1 we can calculate the dose per MU, 𝒌 represents the machine
calibration factor for the linac (cGy/MU), utilizing the Tissue Phantom Ratio 𝑻𝑷𝑹, the
collimator scatter factor 𝑺𝒄, the phantom scatter factor 𝑺𝒑 and inverse square correction.
𝐷𝑜𝑠𝑒
𝑀𝑈= 𝑘 ∙ 𝑇𝑃𝑅(𝐹𝑆𝑑, 𝑑) ∙ 𝑆𝑐(𝐹𝑆𝑐) ∙ 𝑆𝑝(𝐹𝑆𝑑) ∙ (
𝑆𝑆𝐷𝑐𝑎𝑙 + 𝑑𝑐𝑎𝑙
𝑆𝑆𝐷𝑑 + 𝑑)
2
(4-1)
As mentioned, we need the equivalent field size 𝑭𝑺𝒄 for our patient specific
contour and then the field size at desired depth 𝑭𝑺𝒅. We calculate the absolute dose for
a 10x10 cm2 6 MV beam using an arbitrary MU, then we calculate the 2D planar dose
for a 6 MV beam for the patient specific field contour with the same arbitrary MU as the
10x10 cm2 beam. The ratio of the central axis point dose, is the output factor change
due to the patient specific contour. Utilizing the calculated output factor and tabulated
data for relative output factors 𝑺𝒄,𝒑 and correlated equivalent square field size we can
determine our patient specific contour equivalent field size 𝑭𝑺𝒄.
Once we have obtained our nominal equivalent field size for our patient specific
contour, we can obtain our field size at desired depth d. Using simple geometry we
92
convert the nominal equivalent field size 𝑭𝑺𝒄, though Equation 4-2, resulting in the field
size at desired depth, 𝑭𝑺𝒅.
𝐹𝑆𝑑 = 𝑆𝑆𝐷𝑑 + 𝑑
𝑆𝑆𝐷𝑐𝑎𝑙 + 𝑑𝑐𝑎𝑙∙ 𝐹𝑆𝑐
(4-2)
Next, we can obtain the tissue phantom ratio, 𝑻𝑷𝑹(𝑭𝑺𝒅, 𝒅) at the equivalent field
size and depth, from a lookup table. Once again, we can utilize the relative output factor
data 𝑺𝒄,𝒑 and the calculated nominal equivalent field size as well as the equivalent field
size at depth d, we can obtain the values for 𝑺𝒄(𝑭𝑺𝒄) and 𝑺𝒑(𝑭𝑺𝒅). The dose per MU is
calculated from Equation 4-1, combined with the prescription dose, we calculate the
required number of MU to deliver the prescribed dose for a 6MV beam for the patient
specific contour at depth d and SSDd.
Finally, we calculate once again the planar dose at 90 SSD and 10 cm depth for
6MV applying the new MU value obtained from Equation 4-1. The ratio of the central
axis point dose for 6 MV and the calculated sliding window beam dose calculated at 90
cm SSD and 10cm depth is the MU scaling factor calculated by Equation 4-3 for the
sliding window beam. Using the scaling factor, we can obtained the MU required to
deliver the prescribed dose at depth d, SSDd and equivalent field size 𝑭𝑺𝒅 for the sliding
window beam.
𝑀𝑈𝑆𝑊 = 𝐷𝑜𝑠𝑒 6𝑀𝑉
𝐷𝑜𝑠𝑒6𝐹𝐹𝐹∙ 𝑀𝑈6𝑀𝑉
(4-3)
Summary
A planning tool was developed to assist the treatment planner flat beam
generation using sliding window based IMRT. The DLTO model developed in Chapter 3
is implemented to plan accurate, efficient and machine deliverable modulated flat
93
beams. The workflow process begins by importing the physician drawn contour into the
program. The software employs the DLTO model to generate machine deliverable
sliding window trajectories, and then utilizes another in-house program to calculate the
absolute dose of the field. The following trajectories are written into readable files that
will be communicated to Mosaiq for verification and delivery. The software also includes
the ability to add tongue and groove correction to the optimization model and various
dose analysis tools including dose profiles and isodose line display.
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Figure 4-1. The main graphical user interface for flat beam planning. The following indicates the workflow for the software. (1) Input (2) Field Information (3) Optimization (4) Contour Display (5) Leaf Trajectory Display (6) Dose Calculation (7) Dose Display and (8) RTP Output
(1) (2) (3)
(4)
(6) (7) (8)
(5)
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Figure 4-2. Field input for a given RTP. The information is pulled directly from the RTP file, with dose, SSD, and depth allowing for user input.
96
Figure 4-3. Graphical user interface showing field selection. Field section displays the contour for a given field geometry (bottom left) and if the field has been optimized displays leaf trajectories (bottom right).
97
Figure 4-4. Dose display module of the software allows the user to inspect the isodose lines for an optimized flat field, as well as the dose profiles.
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CHAPTER 5 ASSESSING THE IMAGE QUALITY OF THE ELECTRONIC PORTAL IMAGING
DEVICE USING FLATTENING-FILTER-FREE PHOTON BEAMS
Background
The benefits of the modern advancements in radiation therapy rely on the
accuracy of dose delivery, therefore it is crucial to be able to validate the alignment of a
patient before delivery. Electronic portal imaging devices (EPIDs) are regularly utilized
for the evaluation of geometrical accuracy in radiation therapy and provide an effective
way to acquire portal images frequently and reduce setup errors.43 EPID’s provide
clinicians with the ability to perform patient setup verification, organ and target motion
studies, compensator design and verification, treatment machine QA and patient
dosimetry.44
Focusing on image quality, contrast is examined for EPID use in the clinic. All
present day EPIDs provide 1% or better contrast resolution for larger objects > 5mm.44
The Las Vegas phantom is a contrast-detail phantom that can be utilized for EPID
acceptance testing and routine image quality evaluations.45,46 The suggested procedure
by manufactures to evaluate image quality is to have a human observer determine how
many holes of the Las Vegas phantom are visible on a given portal image.
In order to provide a complete evaluation of the flattening-filter-free (FFF)
machine design and subsequently remove the flattening filter (FF) from the treatment
head. The effect of FFF beams on portal image quality and acceptance testing for
EPIDs must be assessed. FFF beams can operate at an increased dose rate, 1400
MU/min compared to 600 MU/min and therefore can saturate the imager. A recent study
for portal dosimetry using FFF beams demonstrated the Elekta iViewGT (Elekta, Inc.,
Atlanta, Georgia) amorphous silicon (aSi) portal imager does not saturate for an open
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field at a dose rate of 800 MU/min.47 In this study we evaluate the calibration procedure
provided by the manufacturer for the Elekta iViewGT for 6FFF imaging, using a dose
rate of 800 MU/min. Then, a comparison of image quality for acceptance testing
between 6 FFF and 6 MV is conducted to conclude if a FFF only unit can provide the
same imaging capabilities as a conventional beam produced with a FF.
Method and Materials
Electronic Portal Imaging Device
Measurements were performed using the iViewGT aSi panel attached to an
Elekta Versa linac. The detector is 26x26 cm in size, but utilizes a 24x24 cm for clinical
imaging to protect the instrumentation on the detector edges. Figure 5-1 is simple
mockup of the detector configuration which includes multiple layers of buildup, a
scintillation layer, and photodiode array. The detector relies on a triggering system that
utilizes the electron gun pulse to sync the reading of image data, in between radiation
pulses. All images were acquired in single exposure mode.
Calibration of EPID
In order to calibrate the EPID for 6 FFF, we followed the guidelines for system
set up and calibration provided in the iViewGT Corrective Maintenance Manual provided
by Elekta.48 The following is the simple explanation of the calibration procedure we
performed.
1. A bad pixel map needs to be recorded, this is not done open an energy by energy basis and is consistent for all the available energies on the linac.
2. Next, an offset calibration is done by utilizing the service function for the EPID panel and is done for 6 MV and 6 FFF separately, by delivering a “dark image”.
3. Then, gain calibration is performed for each energy. Due to the saturation of the panel at max dose rate for 6 FFF we utilized a single level gain calibration as
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opposed to the multi-level gain procedure which requires a delivery at max dose rate. A flood field of max size 26x26 cm is delivered for 100 MU.
4. Finally, the radiation synchronization calibration is performed, this is done by delivering a full open field 26x26 cm, 100 MU at a desired Pulse Repetition Frequency (PRF) or dose rate.
Image Quality Analysis
FFF portal images were analyzed for image quality at a dose rate of 800 MU/min,
utilizing the Customer Acceptance Tests and Corrective Maintenance Manual provided
by Elekta.48,49 The Las Vegas Phantom, shown in Figure 5-2, is used for both
acceptance testing and quality assurance of the system. The test is very simple and
involves delivering a 100 MU, 12x12 cm2 field, wedge OUT to the phantom and visually
inspecting the portal image for the number of holes visible. Figure 5-3, shows the
required visible holes for a beam in the energy range 4-6 MV to be considered
acceptable. The 6FFF phantom image was also compared by user inspection to the
phantom image for a 6 MV beam, and the number of visible holes were compared.
Results and Discussion
The calibration of the panel for a FFF beam was performed in straightforward
manner, following the steps in the manual. The biggest difference in calibration between
the 6 MV beam and the 6 FFF beam is the gain correction. The effect of the forward
peaked intensity of the 6 FFF beam can be seen in Figure 5-4, resulting in a darkening
of the central portion of the image when compared to the periphery. This was easily
corrected for utilizing the FFF beam in calibration process. However, the introduction of
the FFF gain correction introduced a slight artifact into the image called “shadow
banding”, this is seen on the right side image in Figure 5-4, as the thin light lines
uniformly placed across the image.
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We referred to the Corrective Maintenance Manual to address the shadow
banding in the image. Different than a synchronization issue, the shadow banding is not
PRF dependent, and is caused by the frequencies of the digital accelerator pulsing and
the a-Si panel acquisition. The procedure to correct or lessen the shadow banding in the
image is to take the gain image correction at various energy signatures. If exhausting all
the available energy signatures does not remove the shadow banding from the gain
correction, the manual suggests to choose the value of that results in the best image.48
The image presented in this chapter utilized the energy signature that resulted in the
best qualitative image. Nevertheless, the shadow banding artifact could not be
completely removed from the FFF gain correction.
Figure 5-4, shows the requirement for passing the acceptance testing criteria for
holes visible in the energy range 4 to 6 MV. Due to the novelty of 6 FFF imaging there is
not an example for an acceptable image for FFF beams. Figure 5-5, shows our best
image of the Las Vegas Phantom for 6 FFF portal imaging, the image would be
considered acceptable and when compared to 6 MV (Figure 5-6) offers qualitatively
similar image quality.
Summary
The image quality of the electronic portal imaging device was evaluated and
characterized using a FFF photon beam focusing on contrast. The portal image quality
was compared for 6 FFF and 6 MV beams. The calibration of the panel can be
performed in straight forward manner for FFF beams, however the complete removal of
the shadow banding effect due to the gain correction was not successful. Though, the 6
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FFF image still would be sufficient for passing the acceptance test criteria for the EPID
panel.
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Figure 5-1. Simple schematic of the EPID panel configuration (layers are not to scale)
Figure 5-2. Las Vegas aluminum phantom schematic for the electronic portal imaging
device.
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Figure 5-3. EPID image of Las Vegas phantom for 6FFF beam following calibration
using 6MV gain (Left) and 6 FFF gain (Right).
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Figure 5-4. Acceptable image of holes visible for energy range 4 to 6MV. The circle
represents a hole that must be visible in the image, and the x denotes a hole in the phantom, but is not necessary to be visible.
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Figure 5-5. EPID image of Las Vegas phantom for 6 FFF.
Figure 5-6. EPID image of Las Vegas phantom for 6MV.
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CHAPTER 6 SUMMARY AND FUTURE WORK
The goal of this research was to investigate and evaluate the flattening filter
removal design for conventional treatments using a linear accelerator. First, the proof of
concept was investigated utilizing commercially available intensity modulated radiation
therapy (IMRT) inverse planning techniques, step and shoot (S&S) and sliding window
(SW) delivery. Focusing on degree of flatness and delivery efficiency, the two
techniques were evaluated for viability for our approach. Next, a novel direct leaf
trajectory optimization (DLTO) model was developed. The optimization model
successfully included all dynamic multileaf collimator constraints required for sliding
window delivery. As well as, efficiency control and a tongue and groove (T&G)
approximation, formulated in a linearly constrained convex form. Then, a graphical user
interface was developed to employ the optimization model to assist in flat beam
planning. The planning tool offers the user a stand-alone experience from the
commercial treatment planning system. Providing the ability to calculate the absolute
dose for the modulated flat beam treatments at any given depth, source-to-skin distance
and prescription dose, as well as quantitative dose analysis tools. Finally, the image
quality of a FFF portal image was evaluated and compared to a conventional portal
image, to complete the evaluation of the FFF machine design.
Specific Aim 1: We demonstrated that a conventional flat beam can be
delivered while operating in FFF mode. We evaluated two IMRT techniques for viability
including S&S and SW based IMRT. The approaches were evaluated for degree of
flatness and delivery efficiency. Despite the slight improvement in degree of flatness,
the delivery efficiency for the S&S technique was unacceptable; this led us to a full-time
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pursuit of SW based IMRT. This study led to proof of concept however, commercial
treatment planning for SW optimization had some inherent shortfalls for our proposed
method. Therefore, we pursued the development of a novel direct aperture optimization
(DAO) model for SW based IMRT.
Specific Aim 2: Based on the conclusions of SA1, a DAO model was developed
for SW based IMRT. By incorporating all dynamic MLC leaf constraints directly into the
model in a convex linearly constrained from, we can guarantee an optimal solution.
Eliminate the two-step conversion method typically associated inverse planning in the
process. Additionally, it was apparent after SA1 that delivery efficiency was just as
important as degree of flatness for the viability of our approach. Therefore, we
successfully included an efficiency control in the optimization model. Lastly, to further
improve the dose uniformity and flatness of the field, we developed a convex
approximation for T&G fluence modeling. The developed model provided us with the
ability to plan clinically deliverable leaf trajectories for flat beam production.
Specific Aim 3: The DLTO model developed in SA2 was clinically implemented
using an in-house developed planning tool. To assist in treatment planning an easy-to-
use workflow was developed to employ the DLTO model. Streamlined to communicate
directly with current clinical workflow, the program reads in the treatment parameters
and the patient specific contour, and then allows the user to optimize leaf trajectories
that would deliver a flat dose distribution to the contour. Dose calculation is performed
and provides flexibility for SSD, depth, and prescription dose. Dose analysis tools are
provided to the user. Lastly, the program provides a clinically deliverable beam plan for
import back into the radiation oncology management system.
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Specific Aim 4: Finally, to complete the evaluation of the FFF machine design,
the effect of a FFF beam on the electronic portal imaging devices (EPIDs) image quality
was analyzed. Focusing on contrast, the portal image quality was compared for 6 FFF
and 6 MV beams. The calibration of the panel can be performed in a straight forward
manner for FFF beams. It was concluded that FFF portal images provides comparable
image quality to 6MV. The FFF portal image would be able to pass the acceptance test
criteria provided by the EPIDs manufacturer.
Future work: In this project we developed a novel approach for flat beam
production that does not rely on a physical flattening filter. Therefore we have simplified
the linac treatment head design. To accomplish this goal a direct aperture optimization
(DAO) model was developed for sliding window (SW) based intensity modulated
radiation therapy (IMRT). The model was capable of accomplishing the goals of the
project, however it can be further improved. Mainly focusing on the output factor change
due to the leaves sweeping across the fields. In our model we assumed an output factor
of 1 for all segments or control points in the delivery. Accuracy of the optimization and
calculation can be improved by determining a control point dependent output factor
based on the aperture shape. In result, improving the agreement between the measured
and optimized dose.
The planning tool for this work, was developed to assist the treatment planner
and provide an online system separate from the treatment planning system. The idea
behind this was to provide the ability to efficiently and effectively plan conventional
treatments outside the bounds of the typical treatment planning workflow. Providing
independence and flexibility for same day treatment planning, or weekend/night
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planning. The input and output phase could be improved to make it easier for someone
to communicate with Mosaiq, by developing a more streamlined process, with less user
intervention. The dose distribution analysis tools could also be upgraded to provide
more quantitative and qualitative information to help determine the plan quality.
Portal imaging using a flattening-filter-free (FFF) beam could also be improved.
Due to limitations in user control over the calibration procedure, we could not fully
remove the shadow banding effect from the FFF gain image. Although, the image
quality was acceptable and comparable to 6 MV, the shadow banding artifact could
cause issues when imaging true patient anatomy.
As for the future outlook of this work, the most worthwhile conclusions were
reached when developing the DAO model. A few key developments have the
opportunity to be further expanded on and applied outside the scope of this dissertation.
First, the DAO model included a novel efficiency constraint, which led to the ability to
deliver conventional flat beams with field size less than 15x15 cm2, in a faster time than
static 6 MV delivery for the same uniform dose and contour. This is due to the ability to
operate at a dose rate of 1400 MU/min for FFF beams as compared to 600 MU/min for
6 MV. A current research focus in radiation therapy, pertains to developing ways to
improve dose delivery and accuracy. Various inconsistencies can arise during treatment
such as alignment variations from patient motion or anatomy changes due to breathing
during treatment. For example, a technique utilized for treating the left breast requires a
breath hold when delivering the tangent fields, in order to limit dose to the heart and
keep it out of the beam path. However, the patient’s ability to hold their breath for a long
duration could be difficult, which depends strongly on the treatment time. We believe the
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treatment time savings associated with our DAO model has the possibility to improve
techniques that require a breath hold for the delivery of a smaller conventional field.
Improvements to dose delivery accuracy due to patient motion, may also be possible
due to the faster delivery time of certain field sizes. Ultimately, less treatment time
typically results in less chance of patient motion.
Secondly, the optimization model developed for this work was with a focus on flat
beam production, however it is still a complete SW based IMRT model. Further
investigation employing the model for typical IMRT planning is warranted. A comparison
of the plan quality between our DAO model and the current two-step SW planning
technique would provide insight on the overall capabilities of the model developed for
this work. The efficiency constraint would allow our model to compete with the great
efficiency of the two-step SW technique. By including all MLC constraints in the
optimization problem, we believe our optimized fluence would have less degradation
from the “gold standard” or optimal fluence, when compared to non-direct planning.
Lastly, the original inspiration behind the model was direct leaf trajectory
optimization for VMAT planning. Now that a full suite of constraints were developed and
true clinically deliverable sliding window beams have been achieved. The SW model
could be reapplied back into VMAT planning. It would be interesting to see how the TG
effect correction and efficiency constraint could be utilized in a VMAT optimization
scheme.
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BIOGRAPHICAL SKETCH
Nicholas J. Potter was born in Wilkes–Barre, Pennsylvania. He spent his
childhood with his parents and sister in Wilkes-Barre, PA. He graduated from Elmer L.
Meyers (High School) in May 2010 and then enrolled at The Pennsylvania State
University. He graduated from that academic institution with a Bachelor of Science in
nuclear engineering in 2014.
In 2014 he started his medical physics graduate coursework at the University of
Florida in the Department of Biomedical Engineering. The program later transferred to
the Department of Medical Sciences in the College of Medicine. In 2016, he passed the
first part of his American Board of Radiology certification. During his master’s, he began
working with Dr. Bo Lu who later became his doctoral advisor. In May 2016 he obtained
his Master of Science degree in medical physics and passed his qualifier exam in June
2016. He was awarded the University of Florida’s Graduate School Fellowship Award
that same year. In August 2016, he started his doctoral research.
He received his Ph.D. from the University of Florida in the spring of 2019 and
started in the residency program at the same institution in the summer of 2019. His
current research interests include treatment planning optimization, flattening-filter-free
photon beams and 3D printing applications in radiation oncology.