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Optimal delivery techniques for intracranial stereotactic radiosurgery using circular and multileaf collimators

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Optimal delivery techniques for intracranial stereotactic radiosurgery using circular and multileaf collimators
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Wagner, Thomas H., 1966-
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ix, 306 leaves : ill. ; 29 cm.

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Beams ( jstor )
Brain stem ( jstor )
Collimators ( jstor )
Conformity ( jstor )
Diameters ( jstor )
Dosage ( jstor )
Eggshells ( jstor )
Lesions ( jstor )
Radiosurgery ( jstor )
Radiotherapy ( jstor )
Dissertations, Academic -- Nuclear and Radiological Engineering -- UF ( lcsh )
Nuclear and Radiological Engineering thesis, Ph.D ( lcsh )
Radiosurgery ( lcsh )
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theses ( marcgt )
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Thesis:
Thesis (Ph.D.)--University of Florida, 2000.
Bibliography:
Includes bibliographical references (leaves 297-304).
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Printout.
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Vita.
Statement of Responsibility:
by Thomas H.Wagner.

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OPTIMAL DELIVERY TECHNIQUES FOR INTRACRANIAL STEREOTACTIC
RADIOSURGERY USING CIRCULAR AND MULTILEAF COLLIMATORS














By

THOMAS H. WAGNER


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


2000

















Copyright 2000

by

Thomas H. Wagner




























This work is dedicated to my loving wife and friend, Nanette P. Parratto-Wagner.












ACKNOWLEDGMENTS

I would like to express my sincere appreciation for the guidance provided me by

the members of my supervisory committee. I would especially like to thank my

committee chairman, Dr. Frank J. Bova, from whom I have learned much about medical

physics and whose mentoring has been a key component of the successes I have enjoyed

during my doctoral work. I would also like to thank and acknowledge the contributions

of Dr. Sanford L. Meeks, who has always encouraged me to go beyond simply the

academic requirements and to strive to publish my work, and of Dr. Beverly L. Brechner,

who invested much of her personal time in teaching and coaching me through elementary

topology and set theory, as well as contributing key ideas for our joint sphere packing

project. I am grateful to Dr. Willaim A. Friedman and Dr. John M. Buatti for all of the

valuable clinical feedback, mentoring, and support I have received from them during my

doctoral work and association with the University of Florida stereotactic radiosurgery

program. I also owe special thanks to Dr. Taeil Yi for contributing his ideas and for his

initial computer programming efforts in our joint sphere packing project, and to Dr.

Yunmei Chen, whose contributions played a key role towards the success of our joint

sphere-packing project. Drs. Brechner, Yi, and Chen are all from the University of

Florida Department of Mathematics. I would like to give my most sincere thanks to Dr.

Lionel G. Bouchet for many hours of insightful technical discussions about numerous

aspects of my research, and especially for his computer programming efforts towards

transferring image and anatomical structure data between the several treatment planning







systems in our lab. I am grateful to Russell D. Moore for his invaluable aid in helping me

navigate and use the myriad of Unix computer systems necessary to perform my research

work, and to Lisa Mandell for her assistance in gathering radiosurgery patient data from

the University of Florida SRS-patient database. I would like to thank Dr. Wesley E.

Bolch for his support and encouragement for the entire time I have been a graduate

student at the University of Florida, and to Dr. Kelly D. Foote for many hours of

insightful conversations about radiosurgery and neurological surgery, and for his patient

tutoring and assistance in contouring brain lesions and other intracranial structures.

Finally, I am deeply indebted to my friend and wife, Nanette, without whose support and

loving encouragement I would not have had the strength to begin, let alone complete, the

last several years of my life in graduate school.














TABLE OF CONTENTS
ACKNOWLEDGMENTS ......................................................................................... iv

A B STR A CT .................................................................................... ...viii

CHAPTERS

1 IN TRO D U CTION ......................................................................................................

Megavoltage Photon Radiotherapy And Radiosurgery .................................... ...... 1
Technical Evolution and Improvements Stereotactic Radiotherapy.......................... 5
Linear Accelerator Radiosurgery and Radiotherapy Treatment Techniques.................. 6
Technical Evolution and Improvements Linear Accelerator Radiation Delivery ....... 9
Research Problem: Comparison of SRS Treatment Methods................................... 13

2 EVALUATION OF TREATMENT PLANS ...............................................................17

D ose C alculation...................................................................................................... 18
Isodoses and Dose-volume Histograms ................................................................... 30
Physical Dose-volume Figures of Merit .............................................................. 37
Biological M odels................................................................................................... 49

3 OPTIMIZED RADIOSURGERY TREATMENT PLANNING WITH CIRCULAR
CO LLIM A TO RS .........................................................................................................57

Circular Collimator SRS Dosimetry.................................................................... 58
Single Isocenter Treatment Planning.................................................................... 60
Multiple Isocenter Radiosurgery Planning Tools .................................... ............ 70
Multiple Isocenter Radiosurgery Planning via Sphere Packing ............................... 80
Converting Sphere-Packing Arrangements to Radiosurgery Plans .......................... 94
Application to Phantom and Clinical Targets......................................... ........... ... 95
Results Phantom Targets ...................................................................................... 97
Results Clinical Targets ........................................................................................ 98
Sphere Packing as a Mulitple-Isocenter Radiosurgery Planning Tool ..................... 103
Sphere Packing Algorithm: Potential Developments ................................................. 105
C conclusion ............................................................................................................ 108

4 SHAPED BEAM SRS ............................................................................................ 109

Introduction ...................................................................... ........................................ 109
Generation of Isotropic Beam Bouquets............................................... .......... .... 111







Rotation of Beam Bouquets ........................................................................................ 127
Generation of Beam's Eye Views (BEVs).................................................................. 129
Field Shaping with Multileaf Collimators ............................................................. 134
Shaped Field D osim etry.............................................................................................. 139
Optimization of Isotropic Beam Bouquet Orientation................................................ 140
Limits on Adjusting Beam Positions from the Initial Isotropic Beam Bouquet......... 147
Appropriate Number of Beams for Use in Shaped Beam SRS Planning ................... 157
Application of Isotropic Beam Bouquets Nine Beam Plan for Meningioma .......... 162
Dynamic Arcs with MLC...................................................................................... 169
C conclusion ............................................................................................................ 172


5 INTENSITY MODULATED SRS WITH FIXED BEAMS .....................................174

Introduction........................................................................................................... 174
Intensity Modulated Radiotherapy (IMRT).............................................................. 175
IMRT Treatment Planning with CadPlan/Helios.................................................. 182
Example Nine Beam and Nine Intensity-Modulated Beams for Meningioma........ 187
Multiple Isocenters as a Special Case of IMRT.......................................................... 196

6 SRS METHODS COMPARISON ....................................................................199

Introduction........................................................................................................... 199
Clinical Example Case Data....................................................................................... 202
Comparison of Alternative SRS Treatment Delivery Methods to Multiple Isocenter
SRS with Circular Collimators ................................................................................... 268
Strengths and Weaknesses of Multiple Isocenters and IMRT.................................. 277
Applying the Results of this Research to New SRS Cases....................................... 287
C onclusions............................................................................................................ .. 289

7 CONCLUSION.........................................................................................................291

LIST OF REFERENCES.......................................................................................... 297

BIOGRAPHICAL SKETCH ...................................................................................... 305












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

OPTIMAL DELIVERY TECHNIQUES FOR INTRACRANIAL STEREOTACTIC
RADIOSURGERY USING CIRCULAR AND MULTILEAF COLLIMATORS

By

Thomas H. Wagner

August 2000


Chairman: Francis J. Bova
Major Department: Nuclear and Radiological Engineering

The University of Florida stereotactic radiosurgery (SRS) system is a well-

established system of single fraction, highly conformal linear accelerator based radiation

therapy for intracranial lesions. As originally implemented, the system is characterized

by the delivery of circular radiation beams with multiple arcs of megavoltage photon

beams all impinging on the target. The introduction of multileaf collimators (MLCs) and

computer-controlled treatment machinery offers the opportunity to plan and deliver more

complex radiation treatments that may apply dose to the target while applying less dose

to non-target tissues. There are numerous treatment techniques that may be employed

with such equipment, including multiple static fields, dynamic conformal arcing

treatments, and treatment with intensity modulated radiation therapy (IMRT) fields. This

expanded list of patient treatment options poses a new problem to the treatment planner:

determining the optimum treatment method for a given patient. Although many centers


viii







report the expanding use of these and other treatment techniques, there are few, if any,

reports that offer definitive comparisons of the major treatment techniques against one

another.

The purpose of this research was to compare radiosurgery plans using MLC static

fields, dynamic conformal arcs, and IMRT, with radiosurgery plans using circular

collimators and multiple isocenters, and to determine which of the MLC-based treatment

methods provides the best results. Representative clinical example cases from the

University of Florida radiosurgery patient database were used to examine the dosimetric

performance of each type of treatment delivery. Analysis of these clinical example cases

shows that circular collimators with multiple isocenters deliver dose distributions equal to

or better than MLC-based techniques for every example case studied. IMRT

radiosurgery treatments can yield results comparable to multiple isocenters, for cases

involving larger sized targets that would require more than about fifteen isocenters, and

for targets with relatively smooth-surfaced three-dimensional shapes. For most target

shapes, multiple isocenter dose distributions are more conformal and provide a steeper

dose falloff outside of the target than the MLC-based treatment methods. The software

tools developed for this research can also be employed in a clinically useful timeframe to

develop patient-specific optimized treatment plans to assist in this determination.












CHAPTER 1
INTRODUCTION

Megavoltage Photon Radiotherapy And Radiosurgery
Conventional external beam radiotherapy, or teletherapy, involves the

administration of radiation absorbed dose to cure disease. The general teletherapy

paradigm is to irradiate the gross lesion plus an additional volume suspected of

containing microscopic disease not visible through physical examination or imaging, to a

uniform dose level. External photon beams with peak photon energy in excess of 1 MeV

are targeted upon the lesion site by registering external anatomy and internal radiographic

anatomy to the radiation (beam) source. Due to uncertainty and errors in positioning the

patient, the radiation beam, which is directed at the lesion, may need to be enlarged to

ensure that errors and uncertainty in patient positioning do not cause the radiation beam

to miss some or all of the target. Unfortunately, enlarging the radiation beam results in a

relatively large volume of non-diseased tissue receiving a significant radiation dose in

addition to the target. For instance, adding only a 2mm rim to a 24mm diameter spherical

volume to ensure that the 24mm diameter target is covered even with a 2mm positional

error will increase the irradiated volume from 7.2 cm3 to 11.5 cm3, an increase of 60%

(Bova 1998a).

It has long been known that for many cancerous diseases, a radiobiological

advantage is realized by administering the total radiation dose in small doses (fractions)

over an extended period of time. Bergonie and Tribondeau discovered this principle in

the early twentieth century by experimenting to determine the doses of x-rays to the testes






required to sterilize male goats (Hall 1994a). They discovered that they could not

administer a high enough dose of x-rays to the testicles to cause sterilization without also

causing a severe skin reaction in tissue adjacent to the testicles. However, when they

administered the x-ray dose--in small doses, given once a day over several weeks,

sterilization without an adverse skin reaction was possible. They postulated that the

testes were a model of tumor tissue, while the adjacent skin served as a model of dose-

limiting, normal tissue. Although these assumptions are now known to be false, the

conclusion was valid, that in most cases, for a given level of normal tissue toxicity, better

tumor control may be achieved with multiple dose fractions over an extended time.

In contrast to conventional, fractionated radiotherapy, stereotactic radiosurgery

(SRS) involves the administration of a relatively large, single dose of radiation (10 Gy to

20 Gy) to a small volume of disease, thereby abandoning the advantages provided by

fractionation. Lars Leksell conceived of the idea of radiosurgery in 1951 (Leksell 1951).

His original idea involved using many beams of orthovoltage x-rays converging on an

intra-cranial target to create a lesion. Leksell's idea, known as the Gamma Knife or

gamma unit, was practically implemented in 1967 using an array of 170 Co-60 sources,

each of which emitted megavoltage gamma rays through radioactive decay (Leksell

1983; Colombo 1998). The decay gamma rays were collimated with holes bored in a

large radiation shield to converge to a single point inside the patient's head. The use of

secondary collimator helmets, each with different size holes (4, 8, 14, and 18 mm

diameter), allowed for the creation of several sizes of a spherical, high dose region (Maitz

1998). Irregularly shaped lesions could be produced by "stacking" spherical regions

together to build up complex shapes. The patient's skull was positioned with sub-







millimetric precision using a minimally invasive hearing that attached to each size of

collimator helmet (Wasserman 1996).

Linear accelerators linacss) were first used for radiosurgical use in the 1980s.

Betti and Derichinsky reported using a linear accelerator with multiple fixed, isocentric

beams in 1983 (Betti 1983). Several investigators reported using multiple converging

arcs with a linac by 1985 (Colombo 1985; Hartmann 1985). By fitting an isocentric

linear accelerator with circular collimators, multiple beams and/or arcs of radiation could

be made to converge upon the machine's center of rotation, where the patient's tumor had

been positioned. By such a means, dose distributions very similar to those of the gamma

knife could be produced with megavoltage photons from a linac, rather than from the

decay of radioactive sources. A significant practical difficulty of using an isocentric

linear accelerator, however, lies in overcoming the mechanical inaccuracy of rotation

inherent in heavy rotating equipment. A common upper limit on allowable mechanical

error ("wobble") of rotational center of linear accelerator gantrys is 2mm, plus an

additional 2mm error in the treatment couch rotation accuracy. Added in quadrature, the

resultant total possible error between the expected and actual radiation isocenter can be as

high as 2.8 mm, about an order of magnitude larger than the mechanical error associated

with gamma unit treatments. If the mechanical inaccuracy of the treatment machine

cannot be resolved, the radiosurgeon would need to increase the size of the radiation

therapy beam in order to ensure that the target being treated is completely covered.

Addition of even one or two millimeters of extra margin to a radiosurgical treatment

beam has a markedly undesirable effect, however, by drastically increasing the volume

treated to the target (prescription) dose. It is therefore strongly to the radiosurgeon's






advantage to improve the mechanical and overall system accuracy in positioning the

patient, in order to allow using treatment beams of the minimum necessary size (Meeks

1998a). By reducing the volume of non-target tissue irradiated to high levels, the

likelihood of incurring a complication (adverse reaction to the radiation treatment) may

be minimized.

The University of Florida radiosurgery system was developed in the mid-1980s as

a solution to the above mentioned problem of linear accelerator radiosurgery (Friedman

1989; Friedman 1992; Meeks 1998b). By using an isocentric system, as indicated by the

arrows in Figure 1-1, to position the patient and to provide tertiary, circular collimation of

the x-ray beam, the system allows a linear accelerator to be used to deliver radiosurgical

treatments (Figure 1-2) with mechanical accuracy comparable to a gamma unit.





















Figure 1-1: University of Florida radiosurgery system : isocentric subsystem in place
under the gantry of a linear accelerator linacc).






























Figure 1-2: Time lapse photograph showing arc rotation of the linac gantry about the
patient during treatment. The patient's lesion has been positioned at the radiation
isocenter with a stereotactic hearing and the isocentric subsystem.



Technical Evolution and Improvements Stereotactic Radiotherapy
Although minimally invasive, the hearings associated with gamma unit and

linear accelerator radiosurgery make the administration of multiple radiation doses

infeasible. Some physicians have experimented with leaving the stereotactic hearing on

the patient for extended periods to allow a series of treatments over this time. Although it

is possible to overcome problems with local infection and patient discomfort, these

difficulties have generally caused other practitioners to avoid using this method of

stereotactic radiotherapy (Schwade 1990). The application of non-invasive stereotactic

localizing techniques allows easier delivery of repeated radiation treatments to a

stereotactically-located lesion. The Gil-Thomas-Cosman headframe is one example of







how this may be done, relying on a headframe which locates to the patient's head by

means of a dental mold (a "biteplate", or "biteblock"), occipital headrest, and a strap to

tightly hold the frame to the head (Reinstein 1998). Systems such as these, which

combine the functions of immobilization and positioning, tend to suffer reduced accuracy

because of immobilization forces that are inevitably applied to the reference positioning

system. Optically guided systems have been developed recently, however, which de-

couple the positioning function from the immobilization function. Such systems have

been demonstrated to provide patient positioning with smaller errors than previous

systems. One such optically guided system has demonstrated the ability to position the

patient within about 1.1 mm error at isocenter, which while not as small a positioning

error as attainable with an invasive stereotactic heading, is still significantly better than

previous systems (Bova 1997; Bova 1998b). Because of such new, non-invasive

stereotactic techniques, radiosurgery treatments can be administered in multiple fractions

(Figure 1-3). Such fractionatedd radiosurgery" is generally known as stereotactic

radiotherapy (SRT).


Linear Accelerator Radiosurgery and Radiotherapy Treatment Techniques
The major treatment techniques used to deliver linac radiosurgery treatments are

circular collimators with arcs, conformally shaped beams, and intensity modulated

radiotherapy (IMRT). Circular collimators can be used to create spherical regions of high

dose. When used with linear accelerators, the circularly collimated beam is rotated

around the target at isocenter by moving the gantry in arc mode while the patient and

treatment couch are stationary, producing a para-sagittal beam path around the target.

Betti and Derichinsky developed their linac radiosurgery system with a special chair, the







"Betti chair," which moved the patient in a side to side arc motion under a stationary

linac beam, and which produced a set of para-coronal arcs. With modem, computer

controlled linear accelerators, more complex motions other than these simple arcs are

possible. The Montreal technique, which involves synchronized motion of the patient

couch and the gantry while the radiation beam is on, is an example of this, producing a

"baseball seam" type of beam path (Wasserman 1996). The rationale of using arcs with

circular collimators is to concentrate radiation dose upon the target, while spreading the

beam entrance and exit doses over a larger volume of non-target tissue, theoretically

reducing the overall dose and toxicity to non-target tissue.











4














Figure 1-3: Patient positioned under the linear accelerator with biteblock optically guided
system. A system of stereo cameras out of the picture's field of view senses the position
of the reflective spheres attached to the biteblock in the patient's mouth. This system
allows precise and repeatable patient positioning without the need for an invasive
stereotactic hearing (shown attached to the patient in Figure 1-2). The white mask is an
immobilization aid to assist the patient in remaining motionless during the treatment.







The technique of multiple converging arcs delivered with circular collimators

produces a spherical region of high dose with a steep dose gradient, or falloff. This dose

distribution is adequate for treating a sphere or round target, but will treat a large volume

of non-target tissue to high dose if the sphere encompasses an irregularly shaped target.

Multiple spheres of varying sizes may be "stacked" together to produce a high dose

region which conforms closely to the shape of the target while still maintaining a sharp

dose gradient, as shown in Figure 1-4 (Meeks 1998b).


Figure 1-4: Conformal dose distribution produced by circular collimators and multiple
isocenters. Several isocenters, each with a set of converging arcs, have been placed near
one another to conform the composite dose distribution to the target's shape.



An alternative means of delivering a linac radiosurgery treatment is to employ

beams which are shaped to conform to the target's shape as seen from the direction of the

beam, or "beam's eye view." Conventional radiotherapy practice is to use diagnostic x-

ray radiographic or flouroscopic images of the patient obtained in a simulator session to







determine the beam's shape. In recent years, the three dimensional image sets from

computed tomography or magnetic resonance image scans have been used to construct

three-dimensional models of the patient and internal structures, such as the target. These

models of each patient structure may be used to determine the placement of radiation

beams, and to design each beam's shape.




Technical Evolution and Improvements Linear Accelerator Radiation Delivery
Both the gamma unit and early linear accelerator radiosurgery systems produced

similar sphere-like dose distributions using either multiple static, circular beams (gamma

unit) or multiple circular beams swept though several arcs (linear accelerator). However,

the linear accelerator offers additional flexibility over the gamma unit in that multiple

collimation devices may be used to produce non-circular beams, and beams with non-

uniform intensity profiles across the beam. This additional flexibility in radiation

delivery potentially offers the ability to more closely tailor the dose distribution to the

target volume with a linear accelerator than with a gamma unit. The beam shaping and

modulation devices used with linear accelerators for these purposes include custom beam

shaping blocks, wedge beam filters, custom beam compensating filters, and multi-leaf

collimators. Also, linear accelerators typically can deliver a much larger range of

radiation beam sizes, upwards to a 40 cm x 40 cm square field at 100 cm from the

radiation source.

The simplest beam-shaping device used with linear accelerators (other than the

machine's secondary collimators, which typically produce rectangular fields up to a 40

cm x 40 cm square field at the machine's isocenter) is the custom block. Such blocks are







individually constructed by pouring low melting point alloy (cerrobend) into a mold,

which is attached to a mounting tray. The edges of the apertures defined in the hardened

metal block are designed to match the divergence of the radiation beam emanating from

the treatment machine. A separate block must be manufactured for each beam that will

be used to treat the patient. Although offering the best possible match between the shape

of the target and the shape of the beam-defining aperture, the time and cost of

manufacturing such blocks limits the number of blocks and radiation beams which can be

used to treat a patient.

Wedge beam filters may be used with or without the presence of beam shaping

devices such as the custom blocks mentioned above. Wedge filters are placed in the path

of the photon beam in order to tilt the shape of the isodose distribution. This provides a

simple one-dimensional intensity modulation across the treatment field, which is often

advantageous to the treatment planner in obtaining a more homogeneous dose

distribution in the target volume. This is desirable in certain cases, for example where

the patient's anatomy changes significantly over the extent of the field. Proper placement

of a wedge filter in this case can effectively compensate for missing tissue on one side of

a treatment field. Wedges are also commonly used to reduce dose heterogeneity

("hotspots") in regions of beam overlap inside the target (Khan 1994, Ch. 11).

The idea of using a filter to modulate the beam intensity across the treatment

beam is extendable to a two-dimensional intensity modulation. A typical such 2D

compensating filter is generally used to adjust the beam intensity over a grid of small

square regions, with the goal of obtaining a uniform dose distribution in a plane near the

target. Such devices are designed for each patient, and are typically constructed by







placing differing thicknesses of dense, radiation absorbing material such as brass in a

checkerboard type pattern on a tray that is placed in the beam path. This can be done by

hand, or by use of a computer-controlled milling machine which custom machines a

single piece of radiation absorbing material into the desired shape (Purdy 1996).

Although the dose distribution around the target may be made more homogenous by such

devices, they share a disadvantage of custom blocks in excessive labor costs.

Additionally, compensators requiring manual construction can remain a source of

potential treatment errors despite quality assurance. These factors limit the usefulness

and number of fields to which such beam modifying devices may used (Hall 1961;

Sundbom 1964; Grijn 1965).

Multileaf collimators (MLCs) are mechanical beam collimating devices that can

combine some or all of the functions of beam shaping blocks, wedge filters, and custom

compensating filters discussed above (Figure 1-4). The most common type of MLC

consists of two banks of opposed leaves of radiation absorbing metal that can be moved

in a plane perpendicular to the beam's direction. The MLC can be rotated with the

treatment machine's collimator in order to align the leaves for the best fit to the target's

projected shape. The simplest use of an MLC is simply as a functional replacement for

custom made beam shaping blocks, in which the rectangular MLC edges are used to

approximate a continuous target outline shape (Figure 1-5) (Brewster 1995). However,

the MLC may be used in a more sophisticated fashion to form many different beam

shapes of arbitrary size and intensity (by varying the amount of radiation applied through

each beam aperture). In this manner, radiation fields with a similar dose profile as a

shaped, wedged field may be delivered using only the computer-controlled MLC. MLCs







can also deliver intensity modulated dose profiles similar to those achievable using

custom beam compensators, but without the disadvantages of fabrication time or of

needing to manually change a physically mounted beam filter between each treatment

field (Stemick 1998). Thus, a.computer-controlled MLC and treatment machine offer the

potential to deliver more sophisticated radiation treatments to each patient with the same

time and cost resources available. Moss investigated the efficacy of performing

radiosurgery treatments with a dynamically conforming MLC in arc mode, and concluded

that dynamic arc MLC treatments offered target coverage and normal tissue sparing

comparable to that offered by single and multiple isocenter radiosurgery (Moss 1992).

Nedzi (Nedzi 1993) showed that even crude beam shaping devices offered some

conformal benefit over single isocenter treatments with circular collimators.












r-is








Figure 1-5: Multileaf collimator (arrows) attached to the gantry of a linear accelerator.
The MLC leaves define a small square aperture in this picture.




















Figure 1-6: The narrow, rectangular MLC leaves conform the radiation field's shape to
approximate an irregularly shaped target's shape (solid line), as seen in this beam's eye
view (BEV).



Research Problem: Comparison of SRS Treatment Methods
The potential for improvement presented by some of these newer and more

sophisticated treatment delivery methods has spurred interest in their evaluation relative

to the more traditional linac SRS methods of multiple intersecting arcs and circular

collimators. These comparisons generally show that for small to medium (up to about 20

cm3) intracranial targets, multiple static beams offer acceptable conformity and target

dose homogeneity while offering a straightforward treatment planning process. Static

beam IMRT techniques generally performed comparably to or better than static beam

plans. A common conclusion by many of these investigators is that the use of multiple

isocenters with circular collimators results in a poor quality treatment plan, as evidenced

by the performance of the multiple isocenter plans they used to compare with the static

beam and IMRT plans. Even in reports more favorable to multiple isocenter linac SRS,

the investigators frequently note difficulty in achieving conformal and homogeneous

plans, and also note needing a large amount of time to plan and deliver these treatments.

Based on a number of recent comparisons of radiosurgery methods in the literature, one







could roughly expect to obtain a reasonably conformal (exposing up to about the same

volume of non-target brain tissue as target tissue to the target dose level) and

homogeneous (maximum dose not more than about twice the minimum target dose) dose

distribution for various IMRT- and mMLC treatment techniques, and moderate-to-large

sized, irregularly shaped intracranial lesions. Typical multiple isocenter plans presented

fare considerably worse, though, in terms of dose conformity, homogeneity, and in

treatment planning and delivery times (Laing 1993; Hamilton 1995; Woo 1996; Shiu

1997; Cardinale 1998; Kramer 1998; Verhey 1998).

A potential problem with these comparison studies is that they do not equitably

compare the full potential of multiple isocenter radiosurgery with circular collimators. A

qualitative inspection of the multiple isocenter dosimetric results shown in these

comparisons leads one to suspect that in many cases, sub-optimal multiple isocenter plans

are being compared with reasonably optimized static beam and dynamic MLC arcs/IMRT

plans. Although the multiple isocenter treatment plans in these comparisons in the

literature may represent a level of plan quality achievable by an average or unfamiliar

user, they do not represent the average level of plan quality in the University of Florida

experience. Unlike other evaluations readily available in the literature, an evaluation of

the best employment of an MLC in radiosurgery treatments at the University of Florida

must consider the typical quality of treatment plan that is readily achievable in the

University of Florida clinical experience.

The research problem posed is to evaluate the major SRS treatment delivery

methods that could be implemented clinically at the University of Florida, and other

institutions using the University of Florida radiosurgery system. Many claims are being







circulated about some of the newer methods mentioned earlier of employing teletherapy

beams for SRS treatment. The University of Florida radiosurgery system has

demonstrated the ability to plan and deliver tightly conformal dose distributions to

irregularly shaped targets near radiosensitive structures, while maintaining a sharp dose

gradient away from the target towards radiosensitive structures (Meeks 1998a; Meeks

1998b; Meeks 1998c; Foote 1999; Wagner 2000). While it may be attractive to

contemplate the replacement of the current circular collimator system with more

advanced and elaborate treatment delivery methods, such a decision should be based on a

reliable study.

The purpose of this research is to investigate the optimal implementation

of a multileaf collimator (MLC) system for SRS at the University of Florida. An MLC

could be employed in several different ways: 1) dynamic conformal arc treatments with

templated arc sets, 2) multiple fixed, conformal beams, and 3) multiple fixed, intensity

modulated beams. These treatment delivery options are to be compared against multiple

isocenters with circular collimators. In order to ensure a proper comparison, a reasonable

optimization strategy is employed for each treatment delivery technique to guard against

inadvertently biasing the comparison against one or the other treatment methods. To this

end, automatic planning and optimization tools were developed for multiple isocenter

SRS and for multiple static beam SRS. Due to the fewer number of variables involved,

treatment planning for dynamic MLC arc treatments will be based primarily on standard

arc templates or sets. Chapter two provides a discussion of treatment plan evaluation

techniques and tools. Chapter three is devoted to optimal treatment planning methods

with circular collimators, chapter four to shaped beam radiosurgery planning, and chapter




16


five to fixed beam IMRT planning. Chapter six is devoted to the actual comparisons of

each technique to an array of example cases, on which the guidelines and

recommendations for optimal employment of an MLC at the University of Florida are

based.












CHAPTER 2
EVALUATION OF TREATMENT PLANS

Evaluating the suitability of a stereotactic radiosurgery or radiotherapy treatment

plan requires the human planner to assimilate and analyze a vast quantity of three

dimensional dose information. Given the distribution of radiation dose in three

dimensions in the vicinity of the target, the planner must assess how well the prospective

plan accomplishes the treatment goals of uniformly irradiating the target to a high dose

level while sparing nearby radiosensitive structures from the effects of a large radiation

dose. This chapter presents currently accepted methods and tools for analyzing

stereotactic radiosurgery and radiotherapy dose distributions.

In two dimensional radiotherapy planning, doses are calculated on a two

dimensional slice in a single plane through the target, assuming that the slice chosen is

representative of the entire target region, and that the slice is semi-infinite in extent

(extends infinitely in both directions perpendicular to the plane of interest). Dose

distributions are generally displayed as isodose curves superimposed upon either the

patient contour or a single CT image slice though the region of interest. Plan evaluation

is based upon inspection of the isodose curves overlaid upon this single slice or image.

In three dimensional radiation therapy planning, evaluation of the three dimensional dose

distribution involves the processing of considerably greater amounts of information.

The calculation of radiation absorbed dose is fundamental to radiation therapy, in

order to predict and control the radiation dose delivered to the lesion, and to non-target







regions inside the patient. This section provides a discussion of general methods of dose

calculation for radiotherapy and radiosurgery situations, followed by a presentation of

methods to evaluate the efficacy of a radiation dose distribution. The general aims of

radiotherapy and radiosurgery are simple: to deliver a high, uniform dose to the target

while minimizing the radiation dose to non-target structures. There are several tools

available to the human treatment planner to quantify the degree to which these goals are

accomplished: 1) isodose curves and distributions, 2) dose-volume histograms, 3)

physical dose-volume figures of merit, and 4) biological models of tissue response to

radiation. The following sections explain the use of each of these tools in radiation

therapy and radiosurgery treatment planning, after a discussion of methods for calculating

radiation dose distributions.




Dose Calculation
The purpose of dose calculation in radiotherapy is to be able to accurately

determine the dose to target and non-target structures inside the patient. An ideal

calculation of absorbed dose to matter in all regions of interest in megavoltage external

beam radiotherapy would correctly account for all of the interactions between the

megavoltage photons in the therapy beam and the matter in the patient. The most

accurate current methods of computing the spatial distribution of the deposition of

radiation dose involve probabilistically simulating the transport of many individual

radiation beam particles from their point of emission in the radiation source, using

random number processes (hence the name "Monte Carlo" to describe this calculation

method). Enough particles must be simulated to provide a statistically significant tally of







radiation particle interactions in each region of interest, often requiring lengthy

computing times to simulate the radiation transport of many (millions of) particles. This

dose calculation method is attractive because it is based on first principles of radiation

physics, and can therefore correctly account for any specific patient situation. However,

the amount of computation time generally required by present day computers limits its

usefulness in clinical situations.

Because of these difficulties in calculating absorbed dose distributions from first

principles of physics, the most common approach taken in radiation therapy has been to

use simpler models relying on direct measurements of dose. Typically, these models

involve using various radiation detectors to directly measure the dose distribution in a

water phantom, and applying corrections to the measured dose distributions to account

for differences between the water phantom and each actual patient situation. The dose

calculations in this report rely on such models of dose distributions. A brief discussion of

the dose calculation procedure for a rectangular solid water phantom follows, in order to

facilitate the explanation of the dose calculation process for clinical radiosurgery

situations.

The dose profile as a function of depth in a water phantom (setup shown in Figure

2-1) from a normally incident radiation beam is shown in Figure 2-2. This plot shows the

absorbed dose measured in water with a stationary radiation detector placed at the

isocenter of the linear accelerator. As the detector's depth to the water surface is

increased by adding water to the water phantom (which is a tank of water), there is a

greater thickness of water interposed between the radiation source and the detector, so

that the water absorbs more of the radiation beam. The curve is approximately







exponential in shape, but is not a pure exponential due to the non-linear variation in

scattered radiation dose to the detector with changes in water depth, and due to beam

hardening effects at greater depths. The radiation absorbed dose data measured in this

manner is commonly referred to-as "Tissue phantom ratio" (TPR) when the dose is

normalized to the dose at a particular depth (Khan 1994). TPR data is measured for each

circular radiosurgery collimator (Duggan 1998), or may be interpolated for a given

collimator from data tables of several collimators spanning a range of sizes (Surgical

Navigation Technologies 1996).










Linear accelerator
(radiation source)



\ -Colli
photos
Source to axis
distance (SAD)


Water surface






Central axis
of beam


Radiation detector at isocenter
of the linear accelerator

Figure 2-1: Schematic of setup for measuring radiation dose as a function of depth in a
water phantom


depth








1.000

S0.800

E 0.600
E
S0.400

S0.200

0.000
0 5 10 15 20 25 30
Depth to water phantom surface (cm)

Figure 2-2: Tissue-phantom ratio (TPR) curve in water phantom for a 6 MV photon beam
shaped with a 30 mm diameter circular collimator.




The dose profile in a plane perpendicular to the central axis (along the "cross

beam direction" in Figure 2-1) varies with distance from the central axis, and is thus

measured with a radiation detector as well in order to allow calculation of the radiation

dose at off-axis points. A plot of the radiation field intensity as a function of off-axis

distance, in a plane 100 cm from the radiation source, is shown in Figure 2-3 for a 30 mm

diameter circular radiosurgery collimator. This off-axis dose data is frequently

normalized to either its maximum value, or to the dose at the central axis, and is also

known as "off-axis ratio", or OAR. Like TPR data, OAR data may either be measured

for each individual radiosurgery collimator, or may be interpolated from a table of

measured OAR values for selected collimators. Due to changes in the relative dose

profile with depth (due to changes in scattered dose and beam hardening effects), OAR

profiles are usually measured at several depths in order to provide measured data under

conditions close to those for which dose is being computed.










1.000
0.900
0.800
0.700
0.600
0.500
0.400
0.300
0.200
0.100
0.000


-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Off axis distance (cm)

Figure 2-3: Off-axis ratio (OAR) curve for a single circular collimator




The last measured quantity needed to calculate dose to any point inside the water

phantom is output factor, also referred to as total scatter factor, Sc,p (Khan 1994). Sc,p

accounts for changes in the dose due to changes in the radiation field size, and to changes

from the scattered dose due to changes in the volume of phantom irradiated. Sc,p is the

ratio of dose to a reference point on the central axis of the beam, to the dose to the same

point but under standard conditions. In linear accelerator radiosurgery treatments, Sc,p is

a function only of the collimator size (diameter) used, since the linear accelerator

secondary collimators are normally placed in a constant position when using the

radiosurgery circular collimators. A plot of output factor as a function of radiosurgery

collimator size for a 6 MV linear accelerator at the University of Florida is shown in

Figure 2-4.


--a a ao M!








p









1.00

a 0.95

0.90
4 /
^ 0.85

o 0.80

0.75
5 10 15 20 25 30 35
Collimator diameter (mm)

Figure 2-4: Output factor as a function of circular radiosurgery collimator diameter for a
6MV linear accelerator at the University of Florida.


The above measured dosimetric data may be used to compute the dose to a point

in the water phantom of Figure 2-5, as given in Eq. (2-1):

r is
(2-1) Dose(P) = k -MU TPR(coll, depth(P)) OAR(P) Sc,co dists-P
Kdists-cp)

In this equation, k is the treatment machine's calibration constant, normally 0.01 Gy/MU,

MU is the number of monitor units delivered by the treatment machine, dists-cp is the

source to calibration point distance (nominally 100 cm for an isocentric machine

calibration), dists.p is the distance from the source to point P, TPR(coll, depth(P)) is the

TPR for the circular collimator being used at the depth of point P, Sc,p-coll is the total

scatter factor, or output factor, for the circular collimator being used, and OAR(P) is an

off-axis ratio representing the variation of dose away from the field's central axis (Khan

1994; Surgical Navigation Technologies 1996; Duggan 1998). Equation (2-1) provides








corrections to the measured dose data (TPR, OAR, and Scp) to account for changes in the


dose at point P from the dose to the reference point at the linear accelerator's isocenter.


If point P is moved away from the isocenter in any direction, these corrections are needed


due to changes in 1) the distance-of the dose point P from the source, 2) the distance of


dose point P from the central axis of the beam, 3) of changing collimator sizes, and 4) of


the changing water depth (attenuation) above point P. This dose model is simple and


accurate under conditions similar to the conditions under which TPR, OAR, and Sc,p were


measured, i.e.- a flat surfaced, homogeneous mass of water.


Radiation
IIOURC
1
I1"


I i

Collimated /

I
beam !




Surface I


dist4S-~P)


dit(S-CP)


Figure 2-5: Parameters for calculation of dose to point P in a water phantom from a single
radiation beam. OAD is the off-axis distance.





The simple dose model of equation (2-1) is used as the dose engine of the


University of Florida radiosurgery treatment planning system, and of most other


I depthP)
I OAD(P) 1 \
--- Isooenter
/ Isooenter


I







radiosurgery dose planning systems that utilize circular collimators. In applying equation

(2-1) to a radiosurgery treatment, one must assume that the contents of the patient's head

are homogeneous, water equivalent, and that the geometry is similar to the reference

measurement geometry shown in Figure 2-5. Since linear accelerator radiosurgery

treatments with circular collimators are delivered with arcs of radiation rather than static

beams, each arc is simulated as a set of static beams, spaced along the path of the arc.

Typically, an arc of 100 degrees is simulated as eleven static beams, spaced 10 degrees

apart (Figure 2-6). The radiation dose to any point is the sum of the doses to that point

from all of the individual beams in the arc. Likewise, the dose to any point due to

multiple arcs and isocenters is the superposition (sum) of the doses of all of the arcs

associated with each isocenter. For any arrangement of radiosurgery beams or arcs, the

dose is calculated to a grid of points spaced closely together. Isodose curves

corresponding to the locus of isodose points may be constructed by interpolation amongst

the points in the viewing plane for which dose has been computed. Dose grid point

spacing should be no further apart than 2 mm, in order to properly sample the rapidly

changing dose distributions characteristic of radiosurgery dose distributions (Schell

1995).








/
*Jy


Figure 2-6: A 100 degree arc of radiation produced by a continuously moving beam,
approximated by 11 beams spaced 10 degrees apart. Crosshairs indicate the center of
rotation (isocenter).



There are several departures from the idealized geometries shown in Figures 2-1

and 2-5 that can occur in clinical patient treatment situations, and which can potentially

lead to errors between the actual dose to a point and the dose calculated with the dose

model in equation (2-1). Inhomogeneities inside the patient or at the patient's surface can

cause significant dose errors under certain circumstances, such as for large field sizes.

An irregular (not flat) patient surface is one such example of inhomogeneity, shown in

Figure 2-7. The curvature of the patient surface causes points 1 and 2 in Figure 2-7 to lie

at different depths from the surface with respect to the beam. The resulting tissue deficit

shown will cause the photon beam to undergo less attenuation from the source to point 2

than from the source to point 1. If the TPR for central axis point 1 is used to calculate the

dose at points 1 and 2, then the dose to point 2 will be underestimated by equation (2-1),







since point 2 is not as deep as point 1 (point 2 has a numerically larger TPR than point 1).

For a typical adult patient with a cranial radius of curvature of about 7.5 cm, the tissue

deficit from the center of a 10x10 cm2 square field is about 1.5 cm, which corresponds to

a dose error of about 6% (for 6 MV photons attenuated at about 4% per cm of depth) at

point 2, if the TPR for central axis point 1 is used instead. The magnitude of the tissue

deficit increases as the field size increases, and decreases for smaller field sizes. For a 40

mm diameter circular field, the tissue deficit for the same radius of curvature is only

about 2.6 mm, corresponding to slightly less than a 1% dose error. The tissue deficit and

dose error for a 20 mm diameter field are only 0.6mm and 0.2%, respectively. Thus, for

small (< 40 mm diameter) radiosurgery fields, the effect of surface irregularity

(inhomogeneity) can be neglected without introducing undue error (several percent) into

the dose calculation (Ahnesjo 1999).










I '



I i
I
1 ii


Assumed flat surface
for dose model


Tissue deficit due to
surface irregularity


Figure 2-7: Tissue deficit due to an irregularity (inhomogeneity) in patient surface.






The assumption that the interior of the patient is a homogeneous, water equivalent

material can also lead to errors between the calculated (equation (2-1)) and actual dose to

a point in some cases. For instance, the dose model in equation (2-1) does not account

for the changes in beam attenuation due to differences in electron density from that of

water, such as those encountered near air cavities (e.g.- sinuses) and bone. Although

methods such as the Batho power-law correction (Khan 1994; Ahnesjo 1999) exist to

correct calculated doses for these effects, such corrections are generally not needed to







obtain sufficient calculation accuracy in stereotactic radiosurgery or radiotherapy

situations with many beams. A study by Ayyangar on two typical radiosurgery cases

compared a simple dose model similar to that of equation (2-1), with a Monte Carlo dose

model with and without inhomogeneity corrections. Not correcting the simple dose

model for the passage of the beam through the cranium caused the uncorrected dose

model to overestimate the dose by 1.5% to 2.5%, an acceptable amount of error.

Applying a TAR ratio method correction, similar to the Batho power-law correction,

reduced the dose calculation error further (Ayyangar 1998).

The small size of the beams typical of stereotactic radiosurgery and radiotherapy

allow the use of a relatively simple dose calculation model without sacrificing accuracy

of dose calculation. This simplicity is important in that it allows much faster dose

computations throughout the volume of interest, which is especially important given the

large typical numbers of beams for which dose must be calculated in radiosurgery.




Isodoses and Dose-volume Histograms
Isodose curves overlaid upon the patient's three-dimensional image set are an

important plan evaluation tool, just as in two-dimensional planning. To evaluate a three-

dimensional dose distribution by this method, however, the planner must examine the

isodose distributions in a number of planes through the target region, which can be

cumbersome for large targets occupying many planes in an image set. It is possible to

display three-dimensional renderings of three dimensional dose distributions on a flat

computer display screen, but these are also very difficult to analyze. The problem with

evaluating a three-dimensional radiosurgery dose distribution, with it's sharp dose







gradients, lies in discerning the dose received by many possibly overlapping structures

around the target. Although a number of commercially available treatment planning

systems can render three-dimensional views of arbitrary isodose volumes in various

shades of translucency, along with any structures that the user has identified, it is very

difficult to determine precise (sub-millimetric) spatial relations between the target

volume, particular isodose volumes, and radiosensitive structures. For this reason, it is

usually necessary to evaluate a large number of two dimensional isodose plots through

the region of interest to determine plan suitability. In a single two dimensional isodose

plot, one may readily determine whether a particular isodose surface coincides with the

intersection of any particular volume with the image plane, to an accuracy of within one

image pixel in the plane of interest. Even this level (within an image pixel) of visual

inspection precision can still lead to significant errors in assessing the volume of dose

coverage for small intracranial targets. Consider a 20 mm diameter spherical

radiosurgery target, for which we wish to evaluate dose coverage by inspection of an

isodose line overlaid on the image set. A 10% volume error results if the isodose line is

shifted half of one image pixel (one image pixel is 0.67 mm x 0.67 mm in a transaxial

plane for a 512 x 512 CT image acquired with a 35 cm diameter field of view) inward or

outward, which is the spatial resolution limit of our ability to discern positional shifts in

the image set. The 20 mm sphere, 4.2 cm3 volume, would apparently be equally well

covered by an isodose surface ranging in volume from 3.8 cm3 to 4.6 cm3. The volume

error problem worsens as target size decreases, and results in a 20% volume error for a 10

mm diameter target. One can imagine then the difficulty in evaluating a large number of

these isodose plots to within submillimetric image pixel resolution: on each image slice,







one must examine and remember the isodose surface which encloses the target, and

which isodose surfaces (and to which extent) intersect nearby radiosensitive structures.

This is straightforward if somewhat tedious to do on one image slice, but the difficulty is

magnified tremendously when each slice in a large region must be examined, and the

dose area information from each slice integrated with the information from all the other

image slices. A method of comparing the volumes of dose coverage that is less error-

prone is desirable.

One commonly used solution to this problem is to use dose-volume histograms

(DVHs). DVHs are a method of condensing large quantities of three dimensional dose

information into a more manageable form for analysis. The simplest type of DVH is a

"direct" histogram of volume versus dose (Lawrence 1996), as shown in Figure 2-8. This

is simply a histogram showing the number of occurrences of each dose value within a

three dimensional volume. Unfortunately, the spatial information of which specific

volumes are exposed to each dose level is lost in the process of constructing a DVH. For

this reason, DVHs are generally used clinically in conjunction with the evaluation of

multiple isodose plots as mentioned earlier.

The ideal treatment planning situation is one in which the target volume receives

a uniform dose equal to the maximum dose, and the non-target volume receives zero

dose. This would be represented in a direct DVH by having a target histogram with only

one non-zero bin at 100% dose (normalized to maximum dose), and to have a direct DVH

of the non-target volume with all dose bins receiving zero dose. Plots of ideal direct

DVHs for target and non-target volumes are shown in Figure 2-8. Figure 2-9 shows

direct DVHs for target and non-target volumes for a more typical (non-ideal)









radiosurgery dose distribution. Figure 2-10 shows direct DVHs from two hypothetical


radiosurgery plans for a radiosensitive structure.


1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
02

013
00


10 20 30 40 50 60 70 80 90 100
Relative dose


10 20 30 40 50


Relative dose


Figure 2-8: Ideal target (A) and non-target volume (B) direct DVHs. Note that in the
ideal direct DVH of the non-target volume (right side), the plot is empty, since there is no
non-target volume receiving any dose in the ideal case.


0.070

0.060

0.050

0.040

0.030

0.020

0.010

0.000
0 10 20 30 40 50 60 70 80 90 100
Dose (% of max)


FIB 0.120

0.100

0.080

0.060
a
S 0.040

0.020

0.000
0


10 20 30 40 50 60 70 80 90 100
Dose (% of max)


Figure 2-9: Typical (non-ideal) radiosurgery direct DVHs for target volume (A) and non-
target volume (B).


A 1.0

0.8

1 0.6

o 0.4

S0.2

0.0


60 70 80 90 100


--












n- 2.5

S2.0

1.5

S1.0

| 0.5

> 0.0


10.0 20.0 30.0 40.0


50.0


Dose (% max)


Figure 2-10: Direct DVHs for a radiosensitive non-target structure in two hypothetical
treatment plans


10 20 30 40 50


Dose (% max)


Figure 2-11: Cumulative DVH plot of the direct DVH data shown in Figure 2-10.









Ideal cumulative target and non-target DVHs


1.2

1.0 < .0 4 0
E
2 0.8 -
0
S--4--Target volume
S0.6 Non-target volume -----
0
It 0 .4 - -
UM-
U.
0.2 -------------- -- --------

0.0
0.0 20.0 40.0 60.0 80.0 100
Dose (percent of maximum)


.0


120.0


Figure 2-12: Ideal cumulative DVH curve for target and non-target volumes.


The purpose of plotting two DVHs on a single set of axes is to allow a direct comparison


between two or more dose distributions. In the example of Figure 2-10, "Plan 1" and


"Plan 2" are being compared with respect to the radiation dose distribution delivered to


the radiosensitive structure. As can be seen in the figure, it can difficult to evaluate


competing plans using such direct histograms (Drzymala 1991). Above about 40 units of


dose, both plans appear to be identical, but the two plans expose differing volumes of


brainstem at doses less than about 40 units. It is difficult to determine whether one plan


is better than the other from Figure 2-10. Plotting the dose-volume information in the


form of a cumulative DVH makes it simpler to evaluate two similar DVHs against one


another. A cumulative DVH is a plot of the same dose volume information as before, but


with the modification that the y value displayed for each bin x is the volume receiving >


dose x. Peaks in a direct DVH correspond to inflection points on a cumulative DVH


curve. A cumulative DVH plot of the data in Figure 2-10 is shown in Figure 2-11.


-----i

-----?
-----r

~___;







Cumulative DVHs will be used throughout the remainder of this report, unless otherwise

noted.

The information in DVHs can be used to compare rival treatment plans in many

situations. Optimal DVH curves-for target structures will be as far towards the upper

right hand corner of the plot as possible, while the optimal DVH curves for non-target

structures will be as close as possible to the lower left hand comer of the plot axes as

possible, as shown in Figure 2-12. Thus, one may readily evaluate two rival treatment

plans based upon their DVHs, if the DVH curves for each plan do not intersect, since the

more desirable curve will lie either above and to the right of the other (if it is a DVH

curve of a target volume) or below and to the left if it is a non-target volume DVH curve.

With these rules for evaluating cumulative DVHs, we can use Figure 2-11 to evaluate

Plan 1 and Plan 2 for the radiosensitive structure. Since the curve for Plan 1 always lies

below and to the left of the Plan 2 curve, and the brainstem is a non-target tissue, we can

conclude that Plan 1 is the preferred plan in order to minimize the radiation effects to the

brainstem. The relative ease of this comparison underscores the general utility of

cumulative DVHs (Figure 2-11) over direct DVHs (Figure 2-10) (Lawrence 1996;

Kutcher 1998).

Unfortunately, it is rare for the cumulative DVH curves of rival treatment plans to

separate themselves from one another so cleanly. A more general and common

occurrence in comparing treatment plans is shown in Figure 2-13, in which the DVH

curves cross one another, perhaps more than once. The general rules above for

evaluating DVHs cannot resolve this situation, in which case we must use other means to







evaluate the treatment plans. The next section discusses physical dose volume metrics

for treatment plan comparison.


30.0
25.0
20.0
15.0
10.0
5.0
0.0


10 20 30 40
Dose (relative units)


Figure 2-13: Crossing cumulative DVH curves



Physical Dose-volume Figures of Merit
The three properties of radiosurgery and radiotherapy dose distributions which

have been correlated with clinical outcome are dose conformity, dose gradient, and dose

homogeneity (Meeks 1998a). The conformity of the dose distribution to the target

volume may be simply expressed as the ratio of the prescription isodose volume to the

target volume, frequently referred to as the PITV ratio (Shaw 1993):



(2-2) PITV = Prescription isodose volume / target volume.



Perfect conformity of a dose distribution to the target, i.e. PITV = 1.00, implies that the

prescription isodose volume exactly covers the target volume while covering no non-






target tissues. Typically, perfect conformity of the prescription isodose surface to the

target volume is not achievable, and some volume of non-target tissue must be irradiated

to the same dose level as the target, resulting in PITV ratios greater than unity. The most

conformal treatment plans are those with the lowest PITVs, if all of the plans under

comparison provide equivalent target coverage. This stipulation is necessary because the

definition of PITV does not specify how the prescription isodose is determined. It is

possible (but undesirable) to lower, and thus improve, the PITV by selecting an isodose

level which incompletely covers the target as the prescription isodose, and therefore

reduces the numerator of Eq. (2-2). Unless otherwise stated, prescription isodose levels

in the remainder of this report are selected to ensure that > 95% of the target volume

receives the prescription isodose. This ensures a more consistent basis of comparisons

for all treatment plans.

A sharp dose gradient (fall off in dose with respect to distance away from the

target volume) is an important characteristic of radiosurgery and stereotactic radiotherapy

dose distributions. Dose gradient may be characterized by the distance required for the

dose to decrease from a therapeutic (prescription) dose level to one at which no ill effects

are expected (half prescription dose).




















Figure 2-14: Transaxial, sagittal, and coronal isodose distributions for five arcs of 100
degrees each delivered with a 30 mm collimator. Isodose lines in each plane increase
from 10% to 90% in 10% increments, as indicated. The :socenter is marked with
crosshairs.


'-*--- -- -----------------~-_ -- ----------
Figure 2-15: Dose crossplots through the isocenter, corresponding to the isodose
distributions shown in Figure 2-14. The sharpest dose fall-off, from dose D to half-dose
0.5D, occurs between dose D of 80% to 0.5D = 40%, which occurs in a distance of 4.6
mm. The D to 0.5D fall-off distance is larger for 90-45% (5.1mm) and for 70-35%
(4.9mm) doses.







For illustrative purposes, a typical radiosurgical dose distribution, delivered with

five converging arcs and a 30 mm collimator to a hemispherical water phantom, is

depicted in Figures 2-14 and 2-15. The isodose surfaces in Figure 2-14 are normalized to

the point of maximum dose, such that 100% corresponds to the maximum dose. The

close proximity of the higher (50-90%) isodose lines to one another is a qualitative

measure of the steep dose gradient. A quantitative measure of gradient is obtained from

examining the dose profiles along orthogonal directions in the principal anatomical

planes (transaxial, sagittal, and coronal), as shown by cross-plots in Figure 2-15. This

figure shows the gradient between several dose levels, D, and half of D, in several

directions. The data show that for this single isocenter dose distribution, the steepest

dose gradient (distance between isodose shells of dose D to and 50% of D) occurs

between the 80% and 40% isodose shells, and is 4.6 mm for the 30 mm collimator and

five arcs. The steepest dose gradient is generally achieved between the 80% and 40%

isodose levels, and for this reason single isocenter dose distributions are prescribed to the

80% isodose shell (Meeks 1998c). The dose gradient is relatively independent of

direction (AP, Lateral, and Axial) between about the 90% and 40% isodose shells, since

the dose distribution is almost spherically symmetric between these isodose shells. Table

2-1 lists dose gradient information between the 80% and 40% isodose shells for single

isocenter dose distributions with 10 to 50 mm diameter collimators.

In general, however, radiosurgery dose distributions are not spherically

symmetric, and are tailored to fit the target's shape through manipulation of arc

parameters (Meeks 1998c), multiple isocenters, beam shaping, or intensity-modulation.

Additionally, dose distributions are often manipulated to steepen the dose gradient in the







direction of adjacent radiosensitive structures. This additional complexity makes it

necessary to complement the dose cross-plot with other methods to evaluate the dose

gradient.

Figure 2-16 illustrates this point with a hypothetical radiosurgery target

shaped like a three-dimensional letter "F", which is covered by a multiple isocenter dose

distribution using 10 mm collimators and five converging arcs at each of eight isocenters.

The 70% isodose shell, which covers the hypothetical target, represents the prescription

isodose and is shown along with the half of prescription isodose (35%), and twenty

percent of prescription isodose (14% = 0.2 x 70%). Unlike the single isocenter,

spherically symmetric dose distribution of Figures 2-14 and 2-15, the multiple isocenter

dose distribution is asymmetric, and the prescription isodose to half-prescription isodose

gradient therefore has a directional and spatial dependence. Depending on where the

dose cross-plot is centered and the direction, the distance between the prescription (70%)

and half-prescription (35%) isodose shells varies from 2 to 7 mm. In order to obtain a

representative sample average gradient distance, it would be necessary to take a large

number of gradient measurements at many points at the target's edge. However, a

method has been proposed which uses easily obtainable DVH information to generate a

numerical measure of the overall dose gradient, and which may be used with arbitrary

dose distributions.




42




















~1- *



11
Wireframe representation
of 3D target






-4' *-4' --

-- 4- 4
7^ 0,*










Figure 2-16: Irregular "F" shaped target and multiple isocenter dose distribution in
hemispherical water phantom.







The LF Index (gradient) score, or UFIg, has been proposed as a metric for

quantifying dose gradient of a stereotactic treatment plan. From treatment planning

experience at the University of Florida, it has been observed that it is possible to achieve

a dose distribution which decreases from the prescription dose level to half of

prescription dose in a distance of 3 to 4 mm away from the target. Taking this as a guide,

a gradient score UFIg may be computed as




(2-3) UFIg = 100- 00 [(REff,50%Rx REff,Rx) 0.3cm]}

where Refso%Rx is the effective radius of the half-prescription isodose volume, and RefRx

is the effective radius of the prescription isodose volume. The "effective radius" of a

volume is the radius of a sphere of the same volume, so that Reff for a volume V is given

by

_3V
(2-4) R.,

The volumes of the prescription isodose shell and the half prescription isodose

shell are obtained from a DVH of the total volume (or a sizeable volume which

completely encompasses the target volume and a volume which includes all of the half

prescription isodose shell) within the patient image dataset. The UFIg score is a

dimensionless number that exceeds 100 for dose gradients less than 3mm (steeper falloff

from prescription to half-prescription dose level), and which decreases below 100 as a

linear function of the effective distance between the prescription and half-prescription

isodose shells.







Table 2-1 summarizes dose-volume and gradient information for single isocenter

dose distributions delivered with five converging arcs and 10, 20, 30, and 50 mm circular

collimators. UFIg is calculated for each dose distribution using DVH information as

described above. Since the dosegradient for single isocenter arcing dose distributions

(with circular collimators) is achieved between the 80% and 40% isodose shells, the

volumes and effective radii of the 80% and 40% isodose shells are listed, as well as the

difference between these radii. The dose gradient is steepest for the smallest collimators

(about 10 mm diameter) with an effective distance between the 80% and 40% isodose

shells of 2.4 mm and a corresponding UFIg of 106. Dose gradient gradually worsens as

the field size collimatorr size) increases. At a 30 mm diameter field, what many consider

to be the upper limit on radiosurgery target size, the effective dose gradient is about 4.5

mm (UFIg -85).




Table 2-1: Single isocenter (five converging arcs) dose-volume and gradient information
for 10-50 mm circular collimators.
(cm3) (mm) (cm3) (mm) (mm)
Coll. Vsoo. Reff8o% V40% Reff40% Eff. Gradient UFIg
10 0.3 4.2 1.2 6.7 2.4 106
20 3.9 9.8 9.7 13.2 3.5 95
30 13.9 14.9 30.8 19.4 4.5 85
50 67.4 25.2 111.6 29.9 4.6 84









1.000
0.900
g 0.800 -
j 0.700
c 0.600
z" 0.500 -
c 0.400
| 0.300 -
0.200
0.100
0.000 -


Target
- Total volume

~-----


-_--~ -:

10 20 30 40 50 60 70 80 90 1C
Dose (% of maximum)


Figure 2-17: Target and total volume DVHs for F-shaped target in Figure 2-15.




This methodology can be applied to the dose distribution shown in Figure 2-16.

Figure 2-17 shows the DVHs for the F-shaped target volume and for a large 352 cm3

cubic volume enclosing the region of interest. From this DVH it can be seen that >95%

of the target volume receives >70% of maximum dose, which is necessary to support

selection of 70% as a prescription isodose for this target. The volume receiving 709 o of

the maximum dose is 5.2 cm3 (Rff = 10.8mm), with 22.6 cm3 (R ff= 17.5mm) receiving

35% of maximum dose. The effective dose gradient is therefore 17.5 mm 10.8 mm=

6.7 mm, corresponding to a UFIg = 62.

There is another key piece of dose-volume information contained in this DVH

(Figure 2-17), which bears on the practice of multiple isocenter radiosurgery. Table 2-2

shows the resulting prescription to half-prescription dose gradient resulting from using

various isodose shells as the prescription isodose. The important information in Table 2-


F


10






2 is that the steepest dose gradient for most (properly planned) multiple isocenter dose

distributions lies between the 70% and 35% isodose shells, with an effective distance

between the prescription and half-prescription isodose shells of 6.8 mm, corresponding to

a UFIg score of 62. Therefore, in multiple isocenter radiosurgery planning, the planner

should attempt to fit the 70% isodose shell to the target (as opposed to the 80%, 60%, or

other isodose shells) in order to maximize the dose gradient and non-target tissue sparing

(Meeks 1998c).



Table 2-2: Dose gradient variation with selection of prescription isodose shell for
multiple isocenter "F"-shaped dose distribution
Rx isodose Gradient (mm) UFIg
90 8.6 44
80 7.1 59
70 6.8 62
60 7.3 57
50 8.3 47
40 9.7 33
30 10.7 23
20 9.3 37




Dose conformity is another important characteristic of a radiosurgery treatment

plan which should be considered in plan evaluation. A means of con erting dose

conformity in terms of PITV into a conformal index score on a common scale with UFIg

has been proposed, the UFIc score. The UF Index conformall), or UFIc, is defined as




(2-5) UFIc =IO0( Target volume = (PITV)- l00.
Prescription isodose volume









The UFIc converts PITV into a numerical score expressing the degree of conformity of a

dose distribution to the target volume. UFIg score increases as the dose gradient

improves, and the UFIc score increases as dose conformity improves. Perfect conformity

(assuming the target is adequately covered) of the prescription isodose volume to the

target is indicated by a PITV = 1.00 and a UFIc = 100.

As both dose gradient and dose conformity are both important parameters in

judging a stereotactic radiosurgery or radiotherapy plan, an overall figure of merit for

judging radiosurgery plans should incorporate both of these characteristics. Since clinical

data to indicate the relative importance of conformity versus gradient is currently lacking.

an index, the UF Index (UFI) is proposed which assigns equal importance to both of these

factors. The overall UF Index score, or UFI, for a radiosurgery or radiotherapy plan is

the average of the UFIc and UFIg scores (Bova 1999).

Dose homogeneity is considered by some to be an important factor in evaluating

treatment plans. A homogeneous dose distribution throughout the target volume (target

dose within +7% and -5% of the prescribed dose to the target's periphery) is desirable for

conventional, fractionated radiotherapy (Landberg 1993). In radiosurgery, however, the

importance of a homogeneous target dose distribution is less clear. Several studies have

associated large radiosurgical dose heterogeneity (maximum dose to peripheral dose

ratio, or MDPD, > 2.0) with an increased risk of complications (Nedzi 1991; Shaw

1996). However, some radiosurgeons have hypothesized that the statistically significant

correlation between large dose inhomogeneities and complication risk may be associated

with the relatively non-conformal multiple isocenter dose distributions with which some







patients in these studies were treated, and not with dose inhomogeneity alone. One

theory is that the extreme "hot spots" associated with large dose heterogenities may be

acceptable, if the dose distribution is very conformal to the target volume and the hot spot

is contained within the target volume. Non-conformal dose distributions could easily

cause the hot spots to occur outside of the target, greatly increasing the risk of a treatment

complication. The extensive successful experience of gamma unit treatments

administered worldwide (almost all treatments with MDPD > 2.0) lends support to this

hypothesis (Flickenger 1997). Therefore, as a general principle, one strives for a

homogeoneous radiosurgery dose distribution, but this is likely not as important a factor

as conformity of the high dose region to the target volume, or the dose gradient outside of

the target.

As was shown in Tables 2-1 and 2-2, in order to maintain as steep a dose gradient

as possible, the 70% (of maximum dose ) isodose shell is generally used for planning

multiple isocenter treatments, while the 80% isodose shell is used for single isocenter

treatments. An additional benefit of selecting the 70% to 80% isodose shell, rather than

the 50% isodose shell commonly used in gamma unit radiosurgery, as the prescription

isodose is an improvement in treatment efficiency, in terms of the total number of

monitor units which must be delivered. Setting the 50% isodose shell as the prescription

isodose surface rather than 70% would require 1.4 times as many monitor units to be

given to deliver the prescription dose to the target. Also, this would impart a larger

integral dose to the patient in order to deliver the same peripheral target dose. Although

the 70% and 80% prescription isodose levels were chosen based primarily on maintaining

the steepest possible dose gradient, they represent a guideline for acceptable dose







inhomogeneity in linear accelerator radiosurgery dose planning (Meeks 1998c; Meeks

1998).




Biological Models
In planning stereotactic radiosurgery (SRS) or stereotactic radiotherapy (SRT)

treatments, the object is to minimize the dose to radiosensitive non-target structures while

covering the target with a conformal and homogenous dose distribution. In multiple

isocenter SRS planning, non-target structures are protected primarily by the steep dose

gradient inherent in stereotactic irradiation. In single isocenter SRS plans, several

techniques (arc start and stop angles, couch angles, and differential collimators) are

generally used to enhance dose conformity and to steepen the dose gradient in the

direction of especially radiosensitive structures, such as the brainstem (Meeks 1998a;

Meeks 1998; Foote 1999). Such treatment plans can be evaluated on the basis of dose

gradient and conformity, which can be determined from dose-volume histograms of the

target and surrounding volumes (Shaw 1993; Bova 1999). When multiple critical

structures are to be spared as part of the optimization process, such as in the problem of

deciding beam orientations in conformal beam SRS and SRT, the treatment plan

evaluation problem can shift away from determining obvious differences in the

conformity and gradient of competing plans. In such cases, biological indices, such as

the normal tissue complication probability (NTCP), may be used to evaluate rival

treatment plans, each of which demonstrates comparable dose gradient and conformity to

the target.







An example of this occurrence is shown in Figures 2-18(a) and 2-18(b), which

depict DVHs for the total intracranial volume ("cubic") and several radiosensitive

structures for two hypothetical radiosurgery plans. An analysis of both sets of target

DVHs (not shown) and total volume DVHs would indicate that both plans cover the

target with similar dose homogeneity (at least 95% of the target receives >69% of

maximum dose for the first plan, and >72% of maximum dose for the second plan) with

very similar dose conformity (PITVs of 1.42 and 1.40) and gradient (UFIg of 76 and 82).

However, the two plans are not equivalent, due to the doses received by the radiosensitive

structures (e.g.-brainstem, and left and right optic nerves). One can see qualitatively that

plan 2 improves (reduces) the overall dose received by these radiosensitive structures,

since the DVH curves for the left and right optic nerve are shifted downward and to the

left in Figure 2-18(b) relative to Figure 2-18(a). However, a quantitative measure of this

effect is desirable. Normal tissue complication probability (NTCP) models have been

proposed as one such quantitative measure.











- unopt-cubic
- unopt-brainstem
..----- unopt-r-optnerve
- unopt-1-optnerve


0 5 10 15 20 25 30 35 40

Dose (% of maximum)


Figure 2-18(a): DVHs for hypothetical radiosurgery plan (Plan 1).


1.0
0.9 ... ...... ._ -- opt-cubic
0.8 -*- opt-brainstem
0.7 --.... opt-r-optnerve
0.6--- .. .. -- opt-l-optnerve

0.4
0.3
0.2
0.1
0.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40 0


Dose (o of maximum)


Figure 2-18(b): DVHs for hypothetical radiosurgery plan (Plan 2).







A four-parameter model has been suggested by Lyman (Lyman 1985; Kutcher

1991) as the basis of such an NTCP figure of merit for evaluating subtle differences in

rival SRS/SRT plans. The basic four-parameter model is



1 -t
(2-6) NTCP = j Jexp 4t,
72=r, 2 t

where


(2-7) t= -TD ,
m-TDo0(v)

V
(2-8) v=-- ,and
Vgf

(2-9) TD(1) = TD(v). Vn

Here, NTCP represents the probability of complication for an organ of volume Vref

resulting from uniform irradiation of partial volume to homogeneous dose D. TDso is

the tolerance dose for whole organ irradiation at which 50% of the patients receiving this

dose encounter a 50% risk of radiation induced complication within five years after

treatment. The tolerance dose for partial organ volume, v, and the entire organ volume is

given by Eq. (2-9) (Schultheiss 1983). The quantities n and m are fitting parameters

which govern the volume and dose dependence of the NTCP model. Quantity t is a

parameterization of the number of standard deviations separating the partial volume v at

dose D from TDso. TDso, m, and n model parameters used for comparisons were taken

from curve-fits (Burman 1991) to dose-volume tolerance data in the literature (Emami

1991). Since dose distributions in SRS/SRT are almost neN er perfectly homogeneous in

the region of interest, the four-parameter model cannot be used directly as presented.






Kutcher's method (Kutcher 1991) is used to reduce each non-uniform dose volume

histogram to an equivalent volume DVH receiving the maximum dose level. This

method involves treatment of each small dose bin in the differential dose volume

histogram as a volume receiving-a uniform dose Di, which is a reasonable assumption if

the dose bin size is small enough. "Small enough" means practically using dose bins no

larger than about 2 Gy each (Kutcher 1991). The effective volume, Veff, receiving the

maximum dose Di, is found by converting the volume in each differential DVH dose bin

to an effective volume Vefi, and summing them:





(2-10) Ve = V,. D--
\ Dm



The source data cited above is applicable for NTCP calculations involving

fractionated radiotherapy under typical regimes of about 1.8-2.0 Gy per fraction on a five

day per week treatment schedule. These model parameters must be adjusted in order to

use this four parameter model to calculate NTCP for single dose radiosurgery cases. The

biologically equivalent dose formalism (BED) may be applied to make this modification

(Fowler 1989; Smith 1998), in which a BED may be calculated from any particular

fractionation scheme delivering dose D in fractions of dose d by




(2-11) BED= D. .I
a P







The BED represents a biologically effective dose for tissues with an a/p ratio of

(o/p) when delivered in fractions of dose size d. In this relation, ct and P are the

coefficients in the linear-quadratic cell survival curve (Hall 1994a; Hall 1994b). To

gauge the biological effect of two-different doses, Di and D2, given in individual fraction

doses of di and d2, respectively, one would calculate and compare the BEDs calculated

for Dl and dl, and for D2 and d2 using equation (2-11). Unit analysis of Eq. (2-11) shows

that BED has units of Gray (Gy), although to indicate that the quantity BED is

biologically effective dose rather than a physical absorbed dose, BEDs are usually

subscripted with their a/P ratio, e.g. Gy2. For the purposes of comparing rival treatment

plans, 2.0 is an acceptable default a/p ratio for normal brain and nervous tissue (Smith

1998). To use the NTCP models in equations (2-6) through (2-9) with single fraction

SRS dose distributions, the volume element in each SRS DVH dose bin must be

transformed into a biologically equivalent dose using equation (2-11), and each organ's

tolerance dose (TDso, in units of Gy) must be transformed into a biologically equivalent

single fraction BETDso. Table 2-3 summarizes NTCP model data taken from Burman

(Burman 1991) and Emani (Emami 1991) for intracranial anatomy. The radiosurgery

BED for each organ's TDso is calculated for a fractionation schedule of 2 Gy per fraction

and an a/P ratio of 2.0, in units of Gy2.










Table 2-3: NTCP model data for intracranial sites
TD50(1)
n m (Gy)
Brain (a)-_ 0.25 0.15 60
Brainstem ta) 0.16 0.14 65

Brainstem (b) 0.04 0.15 65
Lens (a) 0.3 0.27 18
Optic nerve (a) 0.25 0.14 65
Source:(a) (Burman 1991), (b) (Meeks 2000)



Although these models and data represent a commonly accepted method for

modeling the biological response of tissues to irradiation, the data used to fit the model

parameters remain sparse and somewhat uncertain (Zaider 1999). For the intracranial

anatomical sites listed in Table 2-3, the brain is the organ with the greatest amount of

clinical data, a total of six data points. The lens and optic nerve models are fitted for only

two data points corresponding to 5% and 50% complication probabilities for irradiation

of each entire organ. Thus, computing NTCP values with the four-parameter model is

possible, but even under the whole organ irradiation conditions under which the model

was created, significant interpolation between clinically observed data points is

necessary. For conditions of partial organ irradiation, calculation of NTCP values would

involve significant extrapolation beyond observed data (Burman 1991). For these

reasons, complication probabilities calculated by this means are intended to serve only as

a guide for evaluating rival treatment plans, and not for use as absolute probabilities of

complication (Kutcher 1996). A previous study of such simple biological models has




56


shown that it is possible to use them in the ranking of rival treatment plans, despite

uncertainties in the model parameters (Kutcher 1991).












CHAPTER 3
OPTIMIZED RADIOSURGERY TREAT MENT PLANNING WITH CIRCULAR
COLLIMATORS

This chapter presents the methods used in planning optimized single and multiple

isocenter radiosurgery treatments with circular collimators. Single isocenter LINAC

radiosurgery with evenly spaced arcs produces essentially spherical dose distributions at

high isodose levels (70-80%). To avoid covering excessive volumes of non-target tissue

to the prescription dose, however, the high dose region must be shaped to fit individual

targets. The high dose region near a single isocenter can be manipulated (within limits)

into a variety of ellipsoidal shapes that closely conform to a target's shape. For

irregularly shaped lesions, and those with an ellipsoidal shape in the transaxial plane,

however, multiple isocenters must be used to obtain a conformal dose distribution for

radiosurgery (Friedman 1998; Meeks 1998c).

The University of Florida radiosurgery planning algorithm, shown in Figure 3-1,

(Friedman 1998; Meeks 1998c) provides the basis for the treatment planning methods

outlined in this chapter. This algorithm organizes the tools (optimization variables)

available to the radiosurgery planner to efficiently generate conformal radiosurgery plans

that provide appropriate sparing of non-target tissues. The first step of the algorithm is to

determine whether the targeted lesion is adjacent to a radiosensitive structure. If so,

single isocenter arc parameters (presented in a later section) are adjusted to steepen the

dose gradient in the direction of the radiosensitive structure, if possible. If the lesion is

very irregular in shape or is an ellipsoid with the major axis aligned along the anterior-







posterior direction, multiple isocenters are used to conform the dose distribution to the

shape of the lesion. Due to the difficulty of standardizing this multiple isocenter planning

process, the major emphasis in this chapter is on a geometrically based and automated

method (sphere packing, developed in a joint project with the University of Florida

Department of Mathematics) which attempts to generate conformal multiple isocenter

dose distributions.




University of Florida
Treatment Planning Algorithm for Optimizaeton

IThe d' t a p cenP to a single, stationar ea tat is saed it ura

/ ,
circular collimator of diameter "coll" is computed at any point in the stereotactic space by,
\C3 l:cii i 3rucgture nrtte Cr sci nr^,r m^ i, ..*.:.-l ^R3CC *





























(3-1) Dose(P) = k MU TPR(coll,depth(P)) OAR(P) Sc.p-col dists-P
ilie"3: r; 'L1'A 5. lirfb' ?nLI Ir '! '


/ .


S,1 3 ':*"C r i :C<;
j A;xi: C:i e t *' i"..:So


OosO S ieC', ion

Figure 3-1: University of Florida radiosurgery planning algorithm







Circular Collimator SRS Dosimetry
The dose at any point P due to a single, stationary beam that is shaped with a

circular collimator of diameter "coll" is computed at any point in the stereotactic space by



(3-1) Dose(P) = k MU. TPR(coll, depth(P)). OAR(P). S .p_*on. dists-p
C dists-cp,)







as sho\%n in Figure 3-2. In Eq. (3-1), k is the treatment machine's calibration constant,

normally 0.01 Gy MU, MU is the number of monitor units delivered with the beam, dists-

cp is the source to calibration point distance (nominally 100cm for an isocentric machine

calibration), dists.p is the distance from the source to point P, TPR(coll, depth(P)) is the

tissue-phantom ratio for the circular collimator being used at the depth of point P, S,p-co1l

is the total scatter factor, or output factor, for the circular collimator being used, and

OAR(P) is an off-axis ratio representing the variation of dose away from the field's

central axis (Khan 1994; Surgical Navigation Technologies 1996; Duggan 1998). Data

tables of measured TPR and Sc, values for all circular collimators in use are maintained

and directly used by the treatment planning system for dose calculation at each point.

Dose distributions can be determined by a) computing the dose to each point (from each

beam) in a grid of points in the viewing planes selected by the user, or b) to a grid of

points in a three dimensional region. Each arc of radiation, formed by rotation of the

gantry about the patient with the radiation beam on, is accurately modeled as a series of

stationary beams spaced approximately 10 degrees apart. Thus, a 100-degree arc is

approximated by spacing eleven beams 10 degrees apart (Figure 2-6). The dose

algorithm assumes the patient to be water equivalent, and each beam to be perpendicular

to the patient's surface. Determination of the patient's surface and the depths for each

central axis dose point is derived from the three-dimensional stereotactic computed

tomography (CT) image set of the patient. The dose calculation falls into the "three

dimensional imaging, one dimensional dose calculation" classification discussed in

Chapter 2. Although somewhat simple, this process is rapid and provides sufficient

accuracy for radiosurgery dose calculations (Schell 1995).




60


Radiation










Surface
t \

P


depth(P)
OAD(P) S













Single Isocenter Treatment Planning
A single isocenter with multiple converging arcs may be used to create a spherical

dose distribution close in size to the diameter of the circular collimator. This type of

treatment produces a conformal dose distribution for spherical or near-spherically shaped

targets. The standard set of fourteen circular collimators used at the University of Florida

covers a range of sizes from 5mm to 40mm (5, 10, 12, 14, ..., 30, 35, and 40 mm )

diameter, projected at 100cm from the radiation source, allowing the planner to closely

match the diameter of the dose distribution to the target. As discussed in Chapter 2,

because the steepest dose gradient for single isocenter dose distributions lies between the

80% and 40% isodose shells, a collimator size should be chosen which covers the target

with the 80% isodose shell. This will ensure the steepest possible dose gradient between

the prescription and half-prescription isodose shells. A standard set of nine convenrent
t \
Surface / \

__ __OAP ....








Figure 3-2: Radiosurgery beam dose calculation for dose at point P.





Single Isocenter Treatment Planning
A single isocenter with multiple converging arcs may be used to create a spherical

dose distribution close in size to the diameter of the circular collimator. This type of

treatment produces a conformal dose distribution for spherical or near-spherically shaped

targets. The standard set of fourteen circular collimators used at the University of Florida

covers a range of sizes from 5mm to 40mm (5, 10, 12, 14, ..., 30, 35, and 40 mm )

diameter, projected at 100cm from the radiation source, allowing the planner to closely

match the diameter of the dose distribution to the target. As discussed in Chapter 2,

because the steepest dose gradient for single isocenter dose distributions lies between the

80% and 40% isodose shells, a collimator size should be chosen which covers the target

with the 80% isodose shell. This will ensure the steepest possible dose gradient between

the prescription and half-prescription isodose shells. A standard set of nine convergent







arcs (specific parameters listed in Table 3-1, in terms of International Electrotechnical

Commission (IEC) couch and gantry angles (IEC 1996)), is shown in a perspective view

in Figure 3-2, and is generally used as a basis for generating single isocenter dose

distributions. Couch and gantry angles are illustrated in Figures 3-3 through 3-6. An AP

xiew of a standard nine-arc set, delivered to an approximately spherical target with an

eighteen-millimeter collimator, is shown in Figure 3-7 along with the resultant isodose

distribution. Each arc is weighted equally with respect to dose to isocenter. The couch

angles are chosen to approximate an even and symmetrical beam distribution over the 2x

steradian solid angle above the patients head, while avoiding parallel opposed beams

which would adversely affect the dose gradient (Meeks 1998a; Meeks 1998b; Meeks

1998c).






Table 3-1: Couch and gantry angles for standard University of Florida nine arc set.
(Angles are in accordance with IEC standards).
Gantry Gantry
Couch Start Stop
10 130 30
30 130 30
50 130 30
70 130 30
350 230 330
330 230 330
310 230 330
290 230 330
270 230 330













as a starting point for single isocenter radiosurgery plans. Each equally weighted arc

4- .4..-








spans 100 degrees of gantry rotation at one of nine couch angles.



Gantry 0 degrees
Gantry
rotation









Couch rotation



Couch 0 degrees


Figure 3-4: Schematic depiction of couch and linac gantry angles. The linear accelerator
couch and gantry are positioned in the "home" position, couch at 0 degrees, and gantry at
0 degrees. Couch and gantry angles refer to the amount of clockwise rotation as shown
in the figure.








Gantry 30


Couch 55


Gantry 130


Figure 3-5: Linac couch (rotated clockwise) at 55 degrees, and gantry arcing between 30
and 130 degrees.


Gantry 330


s Couch
305


Figure 3-6: Linac couch at 305 degrees, and gantry arcing between 230 and 330 degrees.



































Figure 3-7: Standard nine-arc set delivered with 18mm collimator, and isodose
distribution in axial, sagittal, and coronal planes. The 80%, 40%, and 16% isodose lines
are shown in each plane. The inset at lower left shows an AP view of a patient's head,
with an overlay of the linac couch angles corresponding to each arc.







The standard nine arc set is well suited for conforming the high dose region to the

target, if the target is spherically shaped. However, in the case of an ellipsoidal shaped

target, or of an adjacent critical (radiosensitive) structure, it may be necessary to alter the

shape and gradient of the dose-distribution to improve dose conformity and gradient. The

University of Florida dose-planning algorithm (Figure 3-1) guides the selection of

appropriate isocenter arc parameters to manipulate to obtain optimal dose conformity and

gradient. The nine arcs in the standard set may be manipulated to change the shape of the

high (80%) isodose shell from a spherical shape to an ellipsoidal shape with the major

axis inclined in the sagittal or coronal planes.

The "arc elimination" tool or technique may be used to steepen the dose gradient

in a lateral or axial (along the cranial-caudal axis) direction. This is accomplished by

eliminating arcs that are aligned in the direction along which a steeper dose gradient is

needed. Figure 3-8 shows how elimination of the lateral arcs changes the overall dose

distribution, causing a steeper dose gradient laterally from the isocenter, and making the

dose gradient less steep in the inferior/superior direction. This technique is appropriate to

protect a radiosensitive structure that lies medial or lateral to the target at isocenter.

Figure 3-9 shows an application of this technique to steepen the dose gradient in an

oblique direction. Elimination of the most superior arcs would likewise steepen the

superior-inferior dose gradient, at the expense of a less steep lateral dose gradient. The

arc elimination tool allows the planner to selectively steepen the dose gradient in the

coronal plane.

The dose gradient may be altered in the sagittal plane by altering the start and stop

angles of each arc, and/or by altering the span of each nominal 100 degree arc. Figure 3-







10 shows the effect on the sagittal isodose distribution of shortening each arc by

removing the posterior 40-degree portion of each arc, which shortens each arc from 100

degrees to 60 degrees. The overall dose distribution tends to follow the directional

alignment of most of the beams in each arc. Use of this planning tool allows the dose

gradient to be steepened to protect critical structures lying anterior or posterior to the

target.

In addition to protecting radiosensitive structures near the target, the arc

elimination and arc start/stop angle tools allow changing the shape of the high dose

region from a sphere to an ellipsoidal shape, which can improve the conformity of the

high dose region to the target if the target is an ellipsoid with the major axis in the sagittal

or coronal planes. However, if the target is an ellipsoid with the major axis aligned in the

transaxial plane, or if the target is irregularly shaped, multiple isocenters may be required

to achieve a dose distribution that conforms to the shape of the target.
























290


310


270


Figure 3-8: Steepening the dose gradient in the lateral direction by elimination of the
most lateral four arcs from a standard nine-arc set. The 80%, 40%, and 16% isodose
lines are shown in each plane.
























270


Figure 3-9: Rotating the distribution and steepening the dose gradient in an oblique
direction by elimination of four arcs entering from the patient's right side. The 80%,
40%, and 16% isodose lines are shown in each plane.








80%-40%-16% isodoses


Standard arcs: Zach arc 60 degrees
Zach arc 100 degr esI


Figure 3-10: Tilting the dose gradient in the sagittal plane by shortening each standard
100-degree arc (left side) to 60 degrees (right side).


lane views:







Multiple Isocenter Radiosurgery Planning Tools
Multiple spherical dose distributions may be placed adjacent to one another to

build up a composite dose distribution which conforms to the shape of an irregular target.

as was shown for the "F" shaped target in Chapter 2. When using multiple isocenters,

typically five arcs (Figures 3-11, 3-12) rather than nine arcs (Figures 3-3, 3-7) are used

with each isocenter, since the dose distribution from five arcs is very similar to that from

nine arcs, and less time is required to deliver five arcs than nine arcs. Couch and gantry

angles for the standard five arcs used in multiple isocenter planning at the University of

Florida are listed in Table 3-2, and are depicted in Figures 3-11 and 3-12. Figure 3-11

shows the resultant dose distribution from a standard five-arc set, which is very similar to

the standard nine arc dose distribution shown in Figure 3-7.

























270


340


Figure 3-11: Standard five-arc set delivered with 18mm collimator, and isodose
distribution in axial, sagittal, and coronal planes. The 80%, 40%, and 16% isodose lines
are shown in each plane. The 70%, 35%, and 14% lines (not shown) are very close to the
80%, 40%, and 16% isodose lines.


























Figure 3-12: AP superior-oblique view of the standard five arc set generally used for each
isocenter in multiple isocenter plans.








Table 3-2: Couch and gantry angles for standard University of Florida five arc set.
Couch Start Stop


20
55
340
305
270


130
130
230
230
230


30
30
330
330
330


Three factors strongly affect the dose distribution when using multiple isocenters:

1) collimator size, 2) inter-isocenter spacing, and 3) isocenter weighting. Collimator size

is chosen to match the region of the target which is being covered, and affects the

diameter of the spherical high dose region that is produced by each isocenter. Proper

selection of collimator size and isocenter location is a complex topic, which is addressed







in the next section, while the issues of isocenter spacing and weighting are discussed

here.

The effects of isocenter spacing on the overall dose distribution may be seen in

Figure 3-13, which shows 50% and 70% isodose curves in an axial plane for two equally-

weighted isocenters at several inter-isocenter spacings, each with a standard five arc set

delivered with a 30mm collimator. For this discussion, it is helpful to consider each

isocenter as a solid, 30 mm sphere, corresponding approximately to the 70% isodose

surface of a five arc set. As a first approximation, one would expect a sphere separation

of about 30mm (the sum of the radii of each sphere) to be correct. As will be shown, this

is approximately correct, but slightly more separation is optimal.

The 70% volume in the dose distributions shown in Figure 3-13 correspond

approximately to the geometrical coverage of a 30 mm diameter sphere placed at each

isocenter. At an isocenter spacing of 40 mm, the 70% volume is slightly greater than the

sum of two 30 mm spheres, and the 50% volume (outer isodose line) is slightly larger.

The "waist" between the 70% isodose lines is so pronounced that the 70% isodose shells

are actually separated from one another. As the isocenters are moved closer together, the

70% isodose shell more strongly resembles two 30 mm diameter spheres. At about 32-33

mm inter-isocenter spacing, the isodose distributions are about ideal. As the isocenters

are moved closer to one another for distances less than about 32 mm, the 70% isodose

volume contracts dramatically. This is because each dose distribution is renormalized to

1000 o at the point of maximum dose, so that as the hotspot where the two spheres overlap

one another becomes more intense, the volume covered by 700o of this increasing

maximum dose becomes smaller and smaller. This can be seen by the rapid decrease in







size of the middle 70% isodose region, from 59 mm across with a spacing of 33mm,

down to a region only 17 mm across when the inter-isocenter spacing is reduced to 24

mm. The 70% isodose region shrinks to less than a third of its initial size, while the 509 o

isodose region shrinks much-more gradually from 66 mm to 53 mm (a 20% decrease).

For this example of two 30mm isocenters, the 70% isodose shell may be approximated

as two 30mm spheres, if an inter-isocenter spacing of at least 32mm is maintained.

To assist the human radiosurgery planner in maintaining this appropriate spacing

between isocenters, a table of empirically determined optimal inter-isocenter distances is

incorporated into the University of Florida radiosurgery treatment planning system (Foote

1999). The planner enters the table with the collimator sizes for two adjacent isocenters,

and the table returns the optimal inter-isocenter distance for these two collimator sizes.

This planning tool merely serves as an aid to provide recommended isocenter spacing,

and does not directly alter any treatment plan parameters. According to this isocenter

spacing table, the optimal spacing distance for two 30mm isocenters is 31mm. Inspection

of the isodose distributions for a variety of collimator sizes and spacings, as was done in

Figure 3-9 for two 30mm collimators, shows that for two isocenters with collimator

diameters of dl and d2, an approximate spacing of 0.52(dl + d2) to 0.60(dl + d2) will

yield an overall dose distribution similar in shape to two spheres of diameters dl and d2.

Isocenter weighting is another important aspect of multiple isocenter

treatment planning. When planning radiosurgery treatments with multiple isocenters and

when the isodose distribution is normalized to maximum dose, care must be taken to

consider the additive dose from all isocenters. Examples of this are shown in Figure 3-

14(a), 3-14(b), and 3-14(c). Figure 3-14(a) shows a dose profile (cross plot) through four







optimally spaced isocenters (each separated from the others by 13.8 mm), each with an

equally weighted five arc set and a 14 mm collimator (the relative dose weight of each

isocenter is 1:1:1:1). The individual dose profile for each isocenter is shown, along with

the total dose distribution along the crossplot from all four isocenters. The central

regions of the distribution near the two isocenters in the middle of the distribution receive

140o more dose than do the two isocenters at the edges. This is because each of the

middle isocenters receives the dose from its own five arcs, and also receives a substantial

contribution from each of its neighboring isocenters as well. The desired situation is to

have equal doses at each isocenter, rather than equal weighting of the arcs associated with

each isocenter. In order to compensate for the increased dose to the middle of the total

distribution, it is necessary to decrease the weight of the two isocenters in the middle.

Figure 3-14(b) shows the individual and total dose distribution after the isocenter dose

weighting has been adjusted to 1.17 : 0.94 : 0.94 : 1.17. Making this adjustment causes a

uniform dose to be received by each of the four isocenters. Although the total dose

distribution is still somewhat heterogeneous, it is actually more homogeneous than the

total dose distribution in Figure 3-14(a). This is shown in Figure 3-14(c), which shows

the total dose distribution for both situations. The overall dose distribution after adjusting

the weights is more homogeneous, in that the volume of the 70% isodose surface has

been increased, and the "hot" volume (hotspot) receiving more than 90% of maximum

dose has been reduced. Also, note that the prescription to half-prescription isodose

gradient is steeper for the adjusted weights distribution. This can be seen in Figure 3-15,

which shows the axial isodose distribution for both the equally weighted and the adjusted

weights plans. The 35% isodose shell is almost identical between the two plans, but







since the 70% isodose shell is larger for the adjusted weights plan, it is closer to the 35%

isodose shell, and offers a steeper dose fall off. In most radiosurgery planning situations,

the same advantage holds for adjusting the isocenter weights in order to improve the dose

homogeneity, and gradient, around the target volume. An automatic weighting tool to

perform this task has been implemented in the University of Florida treatment planning

system which iteratively adjusts the arc weights associated with each isocenter to achieve

a uniform dose to each isocenter (Foote 1999).











40 mm spacing






35 mm spacing



33 mm spacing




32 mm spacing



31 mm spacing



29 mm spacing


26 mm spacing




24 mm spacing


Figure 3-13: Effects of isocenter spacing on the multiple isocenter dose distribution. The
70% and 50% isodose lines are shown in a transaxial plane for two equally weighted
30mm isocenters, each with a five arc set.





78



Four 14mm isocenters spaced at 14mm, all weights equal
1.8.

1.6 ------- --------. ----- ------ --- --- -------
1. Total dose
1.4 ---------------------- --- ---------------------

1.2 --------- -------- ---------------- -------- --------

M 1 ......... ........ .... ....- -... .......... ...

0.1 --------- --------
0.4 ------------ ---------- --
O H i I ,
I H I i I






0.2 ------------- ----- .--------------


0 25 50 75 100 125 150
Lateral distance (mm)



Figure 3-14(a): Dose profile through four optimally spaced 14mm isocenters,
each with an equally weighted five arc set. The dose profile for each
isocenter and the total combined dose profile are shown.




Four 14mm isocenters spaced at 14mm. isoc. weights adjusted 1.17 : 0.94 : 0.94 1.17
1.8

1.4 .--------- -------- .--. ------ ------- -------- ---------

1.4 --------- ---------- ------ -- -------- --------
0 -'-



1.2 -- --.. ---.--- +---

4 1 -

08 --------- --- -- ---------- ----- ------------ ---
Figure 3-14(b): Dose profile through four optimally spaced 14mm
0 ------------ -i-- ------- ----- ---- -------- -----------




0. ............. -- -........ .. ...........


0 25 50 75 100 125 150
Lateral distance (mm)

Figure 3-14(b): Dose profile through four optimally spaced 14mm


isocenters. The dose profile for each isocenter and the total combined
dose profile are shown.
i ----;--- .... -- ,






0.2 ......... ---- --- I -- I ...............










dose profile are shown.







Four 14mm isocenters spaced at 14mm, total normalized dose,adj(solid),unadj(dashed)
1 r I /-


If.'


Adjusted weights


0.9
0.8
0.7
0.6
CD
(0


cr 0.4
0.3
0.2
0.1


25 50 75 100
Lateral distance (mm)


Figure 3-14(c): Total
3-9(b).


dose from four isocenters for the plans shown in Figures 3-9(a) and


Figure 3-15: Axial plane dose distribution (70%, 35%, and 14% isodose lines shown) for
four 14 mm isocenters. (A) all weights equal, (B) weights adjusted to obtain equal
isocenter doses.


44.7 mm \ Unadjusted (equal)
44.7mm V weights




I
- I




/I \








Multiple Isocenter Radiosurgery Planning via Sphere Packing
In a simple manner, multiple isocenter radiosurgery planning may be considered

as the problem of determining the positions and sizes of the multiple spherical high dose

regions or isocenters which will be used to fill up the target volume, or put another way,

of determining the sphere-packing arrangement with which to fill the target volume.

Conventional radiosurgery optimization schema are generally iteratively based,

dosimetrically driven algorithms. They require many computations in order to compute a

radiosurgical plan dose distribution, and then to evaluate the quality of the dose

distribution. Geometrically based radiosurgery optimization has been suggested as a

possible alternative means of optimizing radiosurgery treatment planning, since

geometrical solutions are generally much less computationally expensive than the large

iterative set of dosimetric calculations required for most other optimization strategies

(Wu 1996; Bourland 1997; Wu 1999). For instance, a high isodose region around a

single isocenter may be approximated by a sphere of a diameter approxirrately equal to

that of the circular collimator used. Given such a sphere's location and diameter in

stereotactic space, it is much easier to describe this sphere's spatial relationship to the

target volume than it is to compute a three dimensional dose distribution, and to then find

the relationship of this dose distribution to the target's volume.

Wu et al (Wu 1996; Wu 1999) proposed a geometrically-based sphere packing

optimization method for automated gamma unit radiosurgery, in which the shot

(isocenter) locations and sizes are selected according only to the target's three

dimensional shape. Grandjean (Grandjean 1997) et al report on their implementation of a

similar volume packing process for linac radiosurgery, but one in which ellipsoids as well







as spheres are graphically placed by a human user in a three dimensional representation

of the target. Both of these methods are similar, in that isocenter or shot placement is

based simply on obtaining the best geometrical agreement between the target's shape and

the shape of the high dose region characteristic of the treatment unit (i.e. a sphere or

ellipsoid). Due to non-geometric constraints imposed by the physics of radiation

dosimetry (e.g. due to dose interactions and contributions between neighboring

isocenters), multiple isocenter radiosurgery planning is not exactly a sphere-packing

problem. However, in many cases, a sphere-packing arrangement will translate into a

satisfactory radiosurgery plan, particularly if simple dosimetric adjustments are made to

the automatically generated plan (i.e. use of the isocenter weighting tool discussed in

the previous section).

An alternative sphere packing method is presented in this section that shows

potential to significantly aid the planning of complex, multiple isocenter cases. Based on

tests with irregularly shaped phantom targets and with a representative sampling of

clinical example cases, the method demonstrates the ability to generate radiosurgery

plans comparable to or of better quality than multiple isocenter linac radiosurgery plans

found in the literature.

The major steps of the sphere packing process are diagrammed in Figure 3-16. A

7.6 cm3 phantom target, similar in shape to a large acoustic neuroma, is shown in Figures

3-17 and 3-18 with its sphere packing arrangement, and will be used to illustrate the

process.

Step 1: Read in target volume contours. Target volume information is obtained by

manually contouring the target on successive transaxial image slices in the University of







Florida radiosurgery treatment planning system. Code written in the MATLAB

language (Matlab v5.1, The Mathworks Inc., Natick, MA) processes the target contours

data, and computes the sphere packing arrangements.

Step 2: Map target points into 3D array. Each point identified from the target

contour data file is mapped into a three dimensional integer valued array. Each voxel, or

array element, corresponding to a target point is set to a value of 1. After mapping each

given target point into an array element, the program closes any gaps between "1" voxel

elements in the array, ensuring that the contour in each plane is a closed, continuous

curve.

Step 3: Build solid voxelized model. A fill routine assigns the voxels inside each

contour with values of 1, resulting in a solid, connected array of one-valued voxels

corresponding to the target volume, and zero-valued voxels outside the target (Figure 3-

17a). A default voxel size of 1 x 1 x 1 mm3 was used for this study, although this process

is general and may be applied to any voxel size.










START



T .


Build 30 voxel
model of target


Grassfire
-* procedure
(shelling)


Evaluate score for
-- maximum valued
voxels


Select voxel with
-- maximum score as
seed voxel


Locate max. score
in neighborhood of
seed voxel


Reset non-covered
target voxels to "1"
values

A


Place sphere


-No- STOP


Figure 3-16: Block diagram of sphere packing process








a) b)






c) d) e) /






f) g) h)

/




Figure 3-17: Major steps of the grassfire and sphere packing process for a phantom target
(phantom target number three), shown in a coronal plane. a) Voxelized model of the
target, constructed from axial contours, b) Solid model after application of the grassfire
process in 3D. Voxel intensity (color) is a function of each voxel's value after the
grassfire process. c) First isocenter, 22 mm diameter, placed at best-scoring voxel, d)
The voxels inside the sphere are effectively removed for purposes of the grassfire
process. Note the change in the voxel values (color) near the target borders, at the arrow.
e) The situation after application of grassfire process. The deepest voxels are now
identified as candidate isocenter locations for the second isocenter. f) Placement of the
second isocenter. g) Voxels inside the second sphere are effectively removed. h)
Applying the grassfire process after the situation in g). Arrows indicate locations where
voxel values have changed.







Step 4: Grassfire. The outermost layer of voxels in the target model is then

identified and removed, and the process repeated until the deepest lying voxels have been

identified. This peeling and layering, or shelling, by a grassfiree" algorithm, is so called

due to the analogy of burning-off one outer layer of the target at a time, as in a fire (Blum

1973). This edge detection process identifies the outermost layer of voxels in the 3D

model, and adds the integer 1 to each outer layer voxel's value, converting all outer layer

voxels from 1 values to 2. Voxels lying one layer deeper inside the target are easily

identified as the set of "" valued voxels which are adjacent to "2" valued voxels. These

voxels one layer deeper than 2 are assigned a value of 2 + 1 = 3, with the algorithm

continuing application of this process until all 1-valued voxels have been assigned a layer

value, with the deepest lying voxels having the largest values (Figure 3-17b). Ideally, the

deepest lying voxel in the entire target volume would thus be quickly identified as the

best location for an isocenter. Such a maximum-valued voxel's value should also indicate

the size of the sphere to be placed there as well, since (layer number minus 1 ) should

indicate approximately the depth from the surface (in units of voxel size). For example, a

maximum-valued voxel with a value of 7 should lie (7-1) = 6 voxels from the surface of

the target, which suggests that a sphere 12 voxels in diameter would be required to cover

this volume.









a) b) c)

5mm

L.




d) e) f)







Figure 3-18: Three-dimensional depiction of the example phantom target and spheres
placed by the sphere packing algorithm, a) Target volume b) Sphere packing
arrangement for five-isocenter plan c) Target volume superimposed on sphere packing
arrangement d) Prescription isodose surface (64% of maximum dose) superimposed on
sphere packing arrangement e) Prescription isodose surface superimposed over target
volume. The prescription isodose surface covers the target with the exception of isolated
'clipped" edge voxels (see arrow), f) Superposition of target volume, sphere packing
arrangement, and prescription isodose surface.






Step 5: Identify the optimal isocenter size and position (location). Ideally, a

shelling process would easily identify the deepest-lying region of the target volume as a

single voxel. However, the process described determines only an approximation to the

various layers of the target from the outside in, with each cubical voxel representing a

differential radial volume element. For the small intracranial target sizes and the 1 x 1 x

1 mm3 voxel sizes used, the discretization of the 3D target model generally does not

result in a unique identification of the deepest lying voxel. Hence, often more than one

voxel is identified as belonging to the deepest layer. In the example case we have been

following, the first application of grassfire process identifies 7 voxels with the maximum

value of 8, some of which are shown in Figure 3-17b. Interpreting the distribution of

these maximum valued voxels may be difficult, as these voxels do not always lie together

in one group. Even when the maximum valued voxels form a simple connected group,

simply taking the centroid of all such voxels will not necessarily yield the optimum

sphere location. This occurrence of multiple maximum valued voxels is especially a

problem after one or more spheres have been placed in the target volume, and many

target voxels lie at or near the surface of the target or another sphere. Using smaller

voxels does not necessarily result in unique identification of the deepest voxels, either,

but does result in much longer computation times by increasing the number of voxels

which must be processed. To resolve the ambiguity of multiple voxels apparently lying

in the same depth, a score function was used to further distinguish the maximum valued

voxels from one another.

An additional benefit of using a score function to rank candidate isocenter

locations was realized, in that a score function easily allows other factors to be







considered other than depth from the target's surface. For instance, it is often possible

and preferable to use a larger diameter sphere to cover a greater volume of target, at the

expense of covering a small volume of non-target tissue. This is particularly true of the

first isocenter, if multiple isorenters are to be used to conform the dose distribution to the

target. Renormalizing a multiple isocenter dose distribution to maximum dose causes

isodose constriction as the magnitude of the maximum dose is changed by the addition of

subsequent isocenters. The use of a score function allows the algorithm to take this factor

into consideration when attempting to optimize sphere placement. Other factors may be

considered as well, such as inter-isocenter distances.

The score function is computed at each maximum valued voxel location, for each

possible circular collimator (sphere) size, and the best-scoring (numerically largest score)

voxel from the list presented to the user. The score function is the product of several

independent factors: fl, fractional target coverage; f2, a penalty factor which is a function

of the volume of non-target tissue covered; and a third factor, f3, a function of all inter-

isocenter distances. In equation form, for a sphere k at a particular position, these

relations are



(3-2) Score = fi x f2 x f3,

with

Target volume covered by sphere
(3-3) f -= w, *
total target volume

volume of normal tissue covered by sphere
(3-4) f2 = e total target volume








(3-5) f; = f[dist(i,k)],
i=1
Itk

where

0, if dist(i,k) < 0.9dop,
(10
(3-6) f[dist(i,k) i k] =- -- dist(i,k) 9, if 0.9dop < dist(i,k) < d ,
dopt
1.0, if dist(i,k) > dopt

and dist(i,k) is the distance between isocenters i and k.

Factor fi is the fraction of target coverage for a sphere of a specified size at the

voxel under consideration, which varies from 0.0 to 1.0. Factor f2 is a normal tissue

penalty function, so that f2 = 1.0 if no normal tissue volume is covered, and f2 0.0 as

increasing volumes of normal tissue are covered. Factor f3 is a function of the distance of

each isocenter to all other isocenters. Factor f3 serves to prevent placing spheres

(isocenters) too closely to one another, which results in excessive target dose

heterogeneity (Meeks 1998c). This isocenter to isocenter distance function is zero for

isocenter-isocenter distances less than 0.9dopt (dopt = empirically determined optimal

isocenter-isocenter distance for the two spheres under consideration, implemented in the

form of a look-up table accessible to the code (Foote 1999)), is unity for isocenter-

isocenter distances greater than or equal to the optimal distance, and varies linearly

between zero and unity for distances between 0.9 dopt and dopt. Terms w1 and w2 are

relative weighting factors, with which the user may control the behavior of the algorithm.

For example, an "aggressive" setting (relatively small penalty for normal tissue over-

coverage) can be chosen by decreasing the relative weight of w:. A conventional sphere

packing (the target volume is filled with non-intersecting spheres which do not extend

outside of the target volume) results when w2 -4 c, so that f2 = 0 if any normal tissue







voxels are covered by spheres, and f3 0 if any of the spheres are too close to each

other. For all of our work, wl =1 by default, with w2 being the only adjustable variable in

the score function. Although it could also be considered a variable, the inter-isocenter

distance factor f3 was left unchanged as it is accounted for in equations (3-5) and (3-6).

The optimal maximum-valued voxel is thus identified as the voxel with the

maximum score function value. However. this voxel is not necessarily the optimal

location at which to place a sphere. For this reason, an optimization loop is used to

search the neighborhood around the best scoring voxel found so far in the process. The

best scoring maximum valued voxel is input as a seed voxel, the score calculated (for all

14 circular collimator sizes) at that voxel and all 26 of its neighboring cubic I x xl mm3

voxels, and the largest score value of all these recorded. If the seed voxel is the best

scoring of all these 27 voxels, the optimization routine has converged, and the voxel is

used as the recommended isocenter (sphere center) location, with the collimator size

corresponding to the best score. If one of the 26 neighboring voxels yields a better

(higher) score, then it is made the seed voxel, and the process repeated for the new seed

voxel and its neighbors until no further improvement in score function is found. In our

example case, a best scoring voxel was soon located within one voxel of the best scoring

maximum valued voxel, and a 22 voxel (mm) diameter sphere was placed there, as shown

in Figure 3-17c.

Step 6: Place sphere corresponding to isocenter size and location. Spheres are

placed by setting voxels lying inside the sphere to a unique numerical value, such as the

maximum voxel value plus two. For instance, if the grassfire process identified the

deepest layer of voxels as those with a value of eight, voxels inside any placed spheres







would be set to a value of ten, which easily allows one to distinguish voxels inside a

sphere from other voxels.

If the user desires to place another sphere after the first sphere has been placed, all

target voxels not covered by-the first sphere are reset to values of 1, and the entire

grassfire process repeated (Figures 3-17d and 3-17e, steps 4-6). Note that target voxels

inside the sphere which was placed have been effectively removed for purposes of the

grassfire algorithm, causing the sphere's surface to be treated as an outer surface of the

target (see arrows in Figures 3-17d and 3-17e). Figures 3-17f through 3-17h similarly

depict selection of the second 14mm isocenter location after the first isocenter has been

placed. The algorithm continues to place three more isocenters, all 5mm in diameter,

before halting. Figure 3-14 depicts three-dimensional views of the sphere packing

arrangement, the target, and the prescription isodose cloud surrounding the target. Figure

3-19 shows this final dose distribution in three orthogonal planes through the center of

the target.




Full Text
47
The UFIc converts PITV into a numerical score expressing the degree of conformity of a
dose distribution to the target volume. UFIg score increases as the dose gradient
improves, and the UFIc score increases as dose conformity improves. Perfect conformity
(assuming the target is adequately covered) of the prescription isodose volume to the
target is indicated by a PITV = 1.00 and a UFIc = 100.
As both dose gradient and dose conformity are both important parameters in
judging a stereotactic radiosurgery or radiotherapy plan, an overall figure of merit for
judging radiosurgery plans should incorporate both of these characteristics. Since clinical
data to indicate the relative importance of conformity versus gradient is currently lacking,
an index, the UF Index (UFI) is proposed which assigns equal importance to both of these
factors. The overall UF Index score, or UFI, for a radiosurgery or radiotherapy plan is
the average of the UFIc and UFIg scores (Bova 1999).
Dose homogeneity is considered by some to be an important factor in evaluating
treatment plans. A homogeneous dose distribution throughout the target volume (target
dose within +7% and -5% of the prescribed dose to the targets periphery) is desirable for
conventional, fractionated radiotherapy (Landberg 1993). In radiosurgery, however, the
importance of a homogeneous target dose distribution is less clear. Several studies have
associated large radiosurgical dose heterogeneity (maximum dose to peripheral dose
ratio, or MDPD, > 2.0) with an increased risk of complications (Nedzi 1991; Shaw
1996). However, some radiosurgeons have hypothesized that the statistically significant
correlation between large dose inhomogeneities and complication risk may be associated
with the relatively non-conformal multiple isocenter dose distributions with which some


169
Figure 4-25: Axial and sagittal isodoses for isotropic nine beam plan. The 71, 35, and
14% isodose are shown.
Figure 4-26: Axial and sagittal isodoses for 13-isocenter automatic sphere packing plan.
The 66, 33, and 13% isodoses are shown.
Dynamic Arcs with MLC
Dynamic arc technique for radiosurgery refers to delivering a radiation treatment
by moving the treatment machine gantry through an arc, while simultaneously changing


207
Figure 6-lf: Target DVHs for case S-l treatment plans. The prescription dose is 12.5
Gy.
Figure 6-lg: Nontarget volume DVHs for case S-l treatment plans. The prescription
dose is 12.5 Gy.


264
Figure 6-12a: VC-7 clinical 21 isocenter plan, 70-35-14% isodoses.
Figure 6-12b: VC-7 sphere packing autopian 18 isocenter plan, 69-35-14% isodoses.


296
a superior dose distribution, followed in order by IMRT, static beams, and dynamic
arcing plans, automatic treatment planning tools have been developed for each of these
methods which allow the clinician to quickly create a set of optimized treatment plans for
each new patient in the clinical setting. These tools allow the clinical choice of treatment
delivery to be made based on patient-specific optimized treatment plans, rather than
merely on general guidelines.


Rotation of Beam Bouquets 127
Generation of Beams Eye Views (BEVs) 129
Field Shaping with Multileaf Collimators 134
Shaped Field Dosimetry 139
Optimization of Isotropic Beam Bouquet Orientation 140
Limits on Adjusting Beam Positions from the Initial Isotropic Beam Bouquet 147
Appropriate Number of Beams for Use in Shaped Beam SRS Planning 157
Application of Isotropic Beam Bouquets Nine Beam Plan for Meningioma 162
Dynamic Arcs with MLC 169
Conclusion 172
5 INTENSITY MODULATED SRS WITH FIXED BEAMS 174
Introduction 174
Intensity Modulated Radiotherapy (IMRT) 175
IMRT Treatment Planning with CadPlan/Helios 182
Example Nine Beam and Nine Intensity-Modulated Beams for Meningioma 187
Multiple Isocenters as a Special Case of IMRT 196
6 SRS METHODS COMPARISON 199
Introduction 199
Clinical Example Case Data 202
Comparison of Alternative SRS Treatment Delivery Methods to Multiple Isocenter
SRS with Circular Collimators 268
Strengths and Weaknesses of Multiple Isocenters and IMRT 277
Applying the Results of this Research to New SRS Cases 287
Conclusions 289
7 CONCLUSION 291
LIST OF REFERENCES 297
BIOGRAPHICAL SKETCH 305
Vll


24
Figure 2-4: Output factor as a function of circular radiosurgery collimator diameter for a
6MV linear accelerator at the University of Florida.
The above measured dosimetric data may be used to compute the dose to a point
in the water phantom of Figure 2-5, as given in Eq. (2-1):
(2-1)
Dose(P) = k -MU TPR{coll, depth(P))- OAR(P) £
f
dist s-p
vdist s-cp J
In this equation, k is the treatment machines calibration constant, normally 0.01 Gy/MU,
MU is the number of monitor units delivered by the treatment machine, dists-cp is the
source to calibration point distance (nominally 100 cm for an isocentric machine
calibration), dists-p is the distance from the source to point P, TPR(coll, depth(P)) is the
TPR for the circular collimator being used at the depth of point P, Sc,p-coii is the total
scatter factor, or output factor, for the circular collimator being used, and OAR(P) is an
off-axis ratio representing the variation of dose away from the fields central axis (Khan
1994; Surgical Navigation Technologies 1996; Duggan 1998). Equation (2-1) provides


55
Table 2-3: NTCP model data for intracranial sites
TD50(1)
n
m
(Gy)
Brain (a)--_
0.25
0.15
60
Brainstem\a)
0.16
0.14
65
Brainstem (b)
0.04
0.15
65
Lens(a)
0.3
0.27
18
Optic nerve (a)
0.25
0.14
65
Source:(a) (Burman 1991), (b) (Meeks 2000)
Although these models and data represent a commonly accepted method for
modeling the biological response of tissues to irradiation, the data used to fit the model
parameters remain sparse and somewhat uncertain (Zaider 1999). For the intracranial
anatomical sites listed in Table 2-3, the brain is the organ with the greatest amount of
clinical data, a total of six data points. The lens and optic nerve models are fitted for only
two data points corresponding to 5% and 50% complication probabilities for irradiation
of each entire organ. Thus, computing NTCP values with the four-parameter model is
possible, but even under the whole organ irradiation conditions under which the model
was created, significant interpolation between clinically observed data points is
necessary. For conditions of partial organ irradiation, calculation of NTCP values would
involve significant extrapolation beyond observed data (Burman 1991). For these
reasons, complication probabilities calculated by this means are intended to serve only as
a guide for evaluating rival treatment plans, and not for use as absolute probabilities of
complication (Kutcher 1996). A previous study of such simple biological models has


TABLE OF CONTENTS
ACKNOWLEDGMENTS iv
ABSTRACT viii
CHAPTERS
1 INTRODUCTION 1
Megavoltage Photon Radiotherapy And Radiosurgery 1
Technical Evolution and Improvements Stereotactic Radiotherapy 5
Linear Accelerator Radiosurgery and Radiotherapy Treatment Techniques 6
Technical Evolution and Improvements Linear Accelerator Radiation Delivery 9
Research Problem: Comparison of SRS Treatment Methods 13
2 EVALUATION OF TREATMENT PLANS 17
Dose Calculation 18
Isodoses and Dose-volume Histograms 30
Physical Dose-volume Figures of Merit 37
Biological Models 49
3 OPTIMIZED RADIOSURGERY TREATMENT PLANNING WITH CIRCULAR
COLLIMATORS 57
Circular Collimator SRS Dosimetry 58
Single Isocenter Treatment Planning 60
Multiple Isocenter Radiosurgery Planning Tools 70
Multiple Isocenter Radiosurgery Planning via Sphere Packing 80
Converting Sphere-Packing Arrangements to Radiosurgery Plans 94
Application to Phantom and Clinical Targets 95
Results Phantom Targets 97
Results Clinical Targets 98
Sphere Packing as a Mulitple-Isocenter Radiosurgery Planning Tool 103
Sphere Packing Algorithm: Potential Developments 105
Conclusion 108
4 SHAPED BEAM SRS 109
Introduction 109
Generation of Isotropic Beam Bouquets 111
vi


92
Axial Sagittal Coronal
Figure 3-19: Phantom 3: Dose distribution in orthogonal planes through the center of
phantom target 3 for a five isocenter sphere packing plan. The prescription isodose is
64%, half prescription dose is 32%, and 20% of prescription dose is 13%. The phantom
target volume is 7.7 cc, and the PITV for this five isocenter plan is 1.18, exposing 1.4
cm3 of non-target volume to the prescription isodose.
One might question whether the grassfire process is necessary, given that a score
function optimization routine is used to identify the isocenter location. However, the
grassfire algorithm serves two important purposes. First, the grassfire algorithm reduces
the volume of solution space (candidate isocenter locations and sizes) which would
otherwise need to be searched. The grassfire algorithm identifies anywhere from one up
to several dozen voxels, which are approximately the points that an expert human planner
might try to identify in a manual planning process. By rapidly identifying these deepest-
lying voxels for use as a search starting point, the size of the solution space to be
searched is reduced by several orders of magnitude.
A second related purpose served by the grassfire algorithm is the
assistance it provides in avoiding multiple local maxima of the score function, which


7
Betti chair, which moved the patient in a side to side arc motion under a stationary
linac beam, and which produced a set of para-coronal arcs. With modem, computer
controlled linear accelerators, more complex motions other than these simple arcs are
possible. The Montreal technique, which involves synchronized motion of the patient
couch and the gantry while the radiation beam is on, is an example of this, producing a
baseball seam type of beam path (Wasserman 1996). The rationale of using arcs with
circular collimators is to concentrate radiation dose upon the target, while spreading the
beam entrance and exit doses over a larger volume of non-target tissue, theoretically
reducing the overall dose and toxicity to non-target tissue.
Figure 1-3: Patient positioned under the linear accelerator with biteblock optically guided
system. A system of stereo cameras out of the pictures field of view senses the position
of the reflective spheres attached to the biteblock in the patients mouth. This system
allows precise and repeatable patient positioning without the need for an invasive
stereotactic headring (shown attached to the patient in Figure 1-2). The white mask is an
immobilization aid to assist the patient in remaining motionless during the treatment.


191
Figure 5-7: Beams eye view (left side) for first of nine beams. The right side (magnified
view of the left side beams eye view) shows the IMRT fluence map that defines the non-
uniform intensity delivered across the radiation field. The fluence map is cooler (less
intense) in the center and on the left side, due to the slight overlap of the target with the
brainstem.


157
Appropriate Number of Beams for Use in Shaped Beam SRS Planning
In general, the larger the number of beams used in a treatment plan, the better will
be the overall conformity and gradient of the dose distribution, provided that all beams
are reasonably separated in space. Additionally, using a larger number of beams will
dilute the entrance and exit doses of all beams over a larger volume outside the target,
resulting in a generally smaller volume of non-target tissue receiving large doses. This
dose-volume effect is shown in Figure 4-20, which contains non-target dose-volume
histograms for 3, 5, 7, 9, and 15 beam treatment plans for a clinical example lesion. The
DVH curves in Figure 4-20 show that as more beams are used in a treatment plan to
cover the target, the volume of non-target tissue exposed to potentially significant dose
levels (above about 20% of maximum dose) is reduced by using more beams. Thus, on
the basis of sparing non-target tissue from high dose levels, the largest number of beams
feasible should be used spread out the total beam entrance and exit doses over the largest
possible volume.
To illustrate the effects of improved dose conformity and dose gradient
with increased numbers of beams, Figures 4-21(a) and 4-21 (b) show plots of UF Index
conformal and gradient, UFIc and UFIg, respectively, versus number of isotropic beams
for a series of irregularly shaped clinical example targets. Table 4-9 lists the diagnosis
and target volume for each case shown in Figures 4-21(a) and 4-21(b). Figure 4-21(a)
shows how conformity (higher UFIc scores indicate a more conformal dose distribution)
generally improves slowly but steadily as the number of beams increases towards fifteen
beams. Similarly, Figure 4-21(b) shows that the dose gradient (higher UFIg scores


219
O
O
E
D
O
>
0)
O)
c
o
Dose (Gy)
Figure 6-3f: Nontarget volume DVHs for case C-l treatment plans. The prescription
dose is 12.5 Gy.
Prescription dose (Gy)
Figure 6-3g: Nontarget brain NTCPs as a function of prescription dose for case C-l
treatment plans.


Nontarget brain NTCP
243
Prescription dose (Gy)
Figure 6-7h: Nontarget volume NTCP as a function of prescription dose for case VC-2.
Table 6-15: NTCPs and probability of no complication for case VC-2
Plan
Nontarget
NTCP
Brainstem
NTCP
P(NC)
clinical
3.54E-09
3.41E-07
0.9999997
spack
3.14E-09
8.26E-07
0.9999992
15 beams
3.28E-09
3.11E-07
0.9999997
9 beam IMRT
3.38E-09
1.08E-07
0.9999999
5dyn arcs
4.04E-09
5.36E-07
0.9999995


140
profile with the beam aperture shape, projected along fanlines to a number of planes
perpendicular to the beam axis (Storchi 1995; Storchi 1996).
Optimization of Isotropic Beam Bouquet Orientation
The isotropic beam bouquets presented in Webbs work and in the previous
section are not a complete solution to radiosurgery and radiotherapy treatment plan
optimization because they do not account for critical structure avoidance or beam
deliverability. An optimization scheme combining isotropic beam bouquets with beams
eye view volumetries is used to adapt an idealized, isotropic beam bouquet to avoid
patient-specific radiosensitive structures while maintaining a feasible set of beams (e.g.-
preventing beam directions from which would not be possible to deliver the beam).
Chen (Chen 1992) and Myrianthopoulos (Myrianthopoulos 1992)
discussed using geometry to compute the 3D volume of organs/structures irradiated by
conformally-shaped beams. This volume information was shown to be a helpful tool in
the selection of beam orientations, particularly for the selection of multiple non-coplanar
beams. This tool was used by Chen as an aide in the interactive development of treatment
plans. McShan (McShan 1995) extended several of the concepts (especially radiation
map) to semi-automatically design plans based on high level beam constructs (arcs and
multiple beams & segments). A radiation map is a plot of the volume of each structure of
interest that is intersected by a radiation beam. Generally, some variation of polar
coordinates is used to express beam position in relation to the patient. Such a plot is
useful in helping a human planner visualize trends in the involvement of critical
structures with a radiation beam as a function of beam position around the patient.


172
machine collimator rotation angle must be fixed at one value during the arc, since the
collimator remains stationary during the dynamic arc (Varian 1999).
Table 4-15: Couch and gantry angles for standard University of Florida five arc set.
Couch
Gantry
Start
Gantry
Stop
20
120
30
55
120
30
340
240
330
305
240
330
270
240
330
305
270
55
Figure 4-28: AP view of four arc set used for dynamic conformal MLC arc planning.
Conclusion
An automatic method of consistently generating conformal beam radiosurgery
plans has been presented, based on adapting maximally separated beam arrangements.
The optimized beam arrangements of N = 3-15, N odd, beams potentially offer similar


69
Standard arcs:
Each are 100 dgras
Each arc 60 dagras
Figure 3-10: Tilting the dose gradient in the sagittal plane by shortening each standard
100-degree arc (left side) to 60 degrees (right side).


179
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
l L
1
2
3
4
1
2
3
4
1
2
3
3
1
1
1
1
Figure 5-2: Example of step and shoot IMRT delivery. The intensity modulated dose
distribution at far left, with fpur intensity levels, is the summation of four overlapping
subfields of equal intensity, shown on the right side.
The step and shoot method has the advantage of simplicity, since it is the summation of a
limited number of static fields. This simplifies the quality assurance (QA) of the step and
shoot IMRT radiation delivery process, since techniques currently used for static field
QA may be used to verify the proper delivery of each subfield. However, this technique
is generally less efficient in that a greater number of monitor units are required to deliver
a given dose with the step and shoot method than with other IMRT delivery methods.
This technique is also less efficient time-wise, since the radiation beam must be stopped
after each beam segment or subfield, to allow the MLC leaves to reposition to the next
subfield. Since one subfield is needed for intensity step level in the IMRT field, the
additional delay can be considerable when multiple intensity levels are delivered with
multiple IMRT fields. For example, using ten intensity levels with five fields could
introduce an additional 250 seconds to a five field treatment, if each subfield requires ten
seconds of beam off time to reposition the MLC leaves. Additionally, the number of
monitor units (MUs) per subfield decreases inversely as the number of intensity levels
per intensity modulated field increases. This becomes problematic when the number of
monitor units per subfield drops to a small number, such as five MU or less, such that the
subfield beam on time is on the order of the time required for beam stabilization (time


CHAPTER 3
OPTIMIZED RADIOSURGERY TREATMENT PLANNING WITH CIRCULAR
COLLIMATORS
This chapter presents the methods used in planning optimized single and multiple
isocenter radiosurgery treatments with circular collimators. Single isocenter LINAC
radiosurgery with evenly spaced arcs produces essentially spherical dose distributions at
high isodose levels (70-80%). To avoid covering excessive volumes of non-target tissue
to the prescription dose, however, the high dose region must be shaped to fit individual
targets. The high dose region near a single isocenter can be manipulated (within limits)
into a variety of ellipsoidal shapes that closely conform to a target's shape. For
irregularly shaped lesions, and those with an ellipsoidal shape in the transaxial plane,
however, multiple isocenters must be used to obtain a conformal dose distribution for
radiosurgery (Friedman 1998; Meeks 1998c).
The University of Florida radiosurgery planning algorithm, shown in Figure 3-1,
(Friedman 1998; Meeks 1998c) provides the basis for the treatment planning methods
outlined in this chapter. This algorithm organizes the tools (optimization variables)
available to the radiosurgery planner to efficiently generate conformal radiosurgery plans
that provide appropriate sparing of non-target tissues. The first step of the algorithm is to
determine whether the targeted lesion is adjacent to a radiosensitive structure. If so,
single isocenter arc parameters (presented in a later section) are adjusted to steepen the
dose gradient in the direction of the radiosensitive structure, if possible. If the lesion is
very irregular in shape or is an ellipsoid with the major axis aligned along the anterior-
57


232
of the probability of not having a complication occur in each organ or structure, is
computed as
(6-1) P(NC) = n(l NTCP,)
i=l --
where there are Ncs structures for which an NTCP has been computed, and NTCP¡ is the
probability of complication for the i-th structure. P(NC) is analogous to the quantity
probability of uncomplicated control used in radiation therapy optimization algorithms
(Meeks 1998d; Brahme 1999), with the difference in this situation being that a tumor
control probability of unity is assumed since all treatment plans under evaluation deliver
the same prescription dose to the target. Ranked in order according to the computed
probability of no complication, the sphere packing autopian and clinical multiple
isocenter plans (probabilities of no complication differing only in the sixth significant
figure) rank very slightly better than the IMRT plan, followed by the fifteen beam and
four dynamic arc plans. As shown by the probability of no complication, P(NC), curves
in Figure 6-6j, the multiple isocenter plans (clinical and sphere packing) and the IMRT
plans would theoretically allow for a higher escalation of the prescription dose level
without significantly reducing P(NC), since the multiple isocenter and IMRT plan P(NC)
curves lie to the right of the fifteen beam and four dynamic arc P(NC) curves in Figure 6-
6j-


236
din-l-o ptnerv e
spack-l-optnerve
15bm~l-optnerve
IMRT-l-oplnerve
5dyn-arcs-l-optnerve
9.0 10 0 110
12 0
Dose (Gy)
Figure 6-6h: Left optic nerve DVHs for case VC-1 treatment plans. The prescription
dose is 12.5 Gy.
Dose (Gy)
Figure 6-6i: Right optic nerve DVHs for case VC-1 treatment plans. The prescription
dose is 12.5 Gy.


59
as shown in Figure 3-2. In Eq. (3-1), k is the treatment machines calibration constant,
normally 0.01 Gy/MU, MU is the number of monitor units delivered with the beam, dists-
cp is the source to calibration point distance (nominally 100cm for an isocentric machine
calibration), dists-p is the distance from the source to point P, TPR(coll, depth(P)) is the
tissue-phantom ratio for the circular collimator being used at the depth of point P, Sc,p^0ii
is the total scatter factor, or output factor, for the circular collimator being used, and
OAR(P) is an off-axis ratio representing the variation of dose away from the fields
central axis (Khan 1994; Surgical Navigation Technologies 1996; Duggan 1998). Data
tables of measured TPR and Sc,p values for all circular collimators in use are maintained
and directly used by the treatment planning system for dose calculation at each point.
Dose distributions can be determined by a) computing the dose to each point (from each
beam) in a grid of points in the viewing planes selected by the user, or b) to a grid of
points in a three dimensional region. Each arc of radiation, formed by rotation of the
gantry about the patient with the radiation beam on, is accurately modeled as a series of
stationary beams spaced approximately 10 degrees apart. Thus, a 100-degree arc is
approximated by spacing eleven beams 10 degrees apart (Figure 2-6). The dose
algorithm assumes the patient to be water equivalent, and each beam to be perpendicular
to the patients surface. Determination of the patient's surface and the depths for each
central axis dose point is derived from the three-dimensional stereotactic computed
tomography (CT) image set of the patient. The dose calculation falls into the "three
dimensional imaging, one dimensional dose calculation" classification discussed in
Chapter 2. Although somewhat simple, this process is rapid and provides sufficient
accuracy for radiosurgery dose calculations (Schell 1995).


100
The "complex" sphere packing algorithm plans (patients 5-7) achieved a mean
PITV of 1.28 at an average prescription isodose level of 60%. The "very complex"
sphere packing algorithm plans (patients 8-10) achieved a mean PITV of 1.48 at an
average prescription isodoseJevel of 65%. As an example of a very complex clinical
plan, Figures 3-21 and 3-22 show DVHs and axial isodose distributions for clinical
example patient 8. Patient 8 presented with a 12.8 cm3 cavernous sinus meningioma,
which was clinically treated with a twenty isocenter radiosurgery plan delivering 12.5 Gy
to the 70% isodose shell. The twenty isocenter sphere packing plan delivers 12.5 Gy to
the 67% isodose shell. The target and the corresponding sphere packing determined by
the algorithm are shown in Figure 3-23.


66
10 shows the effect on the sagittal isodose distribution of shortening each arc by
removing the posterior 40-degree portion of each arc, which shortens each arc from 100
degrees to 60 degrees. The overall dose distribution tends to follow the directional
alignment of most of the beams in each arc. Use of this planning tool allows the dose
gradient to be steepened to protect critical structures lying anterior or posterior to the
target.
In addition to protecting radiosensitive structures near the target, the arc
elimination and arc start/stop angle tools allow changing the shape of the high dose
region from a sphere to an ellipsoidal shape, which can improve the conformity of the
high dose region to the target if the target is an ellipsoid with the major axis in the sagittal
or coronal planes. However, if the target is an ellipsoid with the major axis aligned in the
transaxial plane, or if the target is irregularly shaped, multiple isocenters may be required
to achieve a dose distribution that conforms to the shape of the target.


170
the shape of the radiation beam by changing an aperture. This technique could combine
the conformal advantages of using shaped radiation beams with the steep dose gradient
characteristic of arc treatments. This SRS treatment technique was previously evaluated
at the University of Florida and found to provide comparable tumor control probability
and non-target tissue complication probability with the single and multiple isocenter
techniques then in use (Moss 1992). Others have reported successfully using this
technique for radiosurgery treatment planning as well (Shiu 1997).
For purposes of comparing the efficacy of dynamic arcing MLC
treatments with the other methods presented so far, there are few variables to optimize
when planning such a radiosurgery treatment. After localizing and identifying the target
volume, an isocenter location is chosen, and field apertures designed for each arc
segment. Dosimetrically, each dynamic arc is simulated as a serried of shaped beams,
with beams placed at ten-degree intervals along the span of the arc (Figure 4-27). A
standard set of five ninety-degree arcs (Table 4-15, Figure 4-28) is used. Arcs of ninety
degrees (ten beams spaced at ten degree intervals) were used rather than the standard
100-degree arcs normally used at the University of Florida due to a limitation of the
CadPlan treatment planning system. The limitation is that CadPlan allows only up to ten
beams per treatment plan (Varan 1999). In order to simulate a plan with more than ten
beams, the doses from several treatment plans may be summed together. For the sake of
convenience, four plans, each simulating a single ninety degree arc of ten beams, each
were summed together to compute the dose distribution for a set of four dynamic arcs.
From an earlier investigation of dynamic conformal MLC radiosurgery treatment
planning (Moss 1992), ten degrees was found to provide a satisfactory approximation of


94
Global maximum
Figure 3-20: Crosses, indicated by arrows, show four local maxima of the score function
in the coronal plane. This picture corresponds to that shown in Figure 3-17h. A downhill
search algorithm will return one of these four locations as the solution, depending upon
the starting point of the search. Using the grassfire process to identify the deepest lying
voxels (near the center of the figure) helps ensure that the downhill search will begin
close to the global maximum of the score function.
Converting Sphere-Packing Arrangements to Radiosurgery Plans
Given a sphere packing by the means discussed earlier, the arrangement of spheres must
be converted into a multiple isocenter radiosurgery plan. A standard University of
Florida set (Table 3-2, Figures 3-11 and 3-12) of five equally weighted arcs was used to
generate the spherical dose distribution about each isocenter (Friedman 1998; Meeks
1998c). The simplest conversion of a sphere packing plan to a radiosurgery plan would
involve merely a substitution of isocenter locations and collimator sizes for the sphere
locations and sizes called for by the geometrically based algorithm, with each


23
Figure 2-3: Off-axis ratio (OAR) curve for a single circular collimator
The last measured quantity needed to calculate dose to any point inside the water
phantom is output factor, also referred to as total scatter factor, Sc,p (Khan 1994). Sc,p
accounts for changes in the dose due to changes in the radiation field size, and to changes
from the scattered dose due to changes in the volume of phantom irradiated. Sc,p is the
ratio of dose to a reference point on the central axis of the beam, to the dose to the same
point but under standard conditions. In linear accelerator radiosurgery treatments, Sc,p is
a function only of the collimator size (diameter) used, since the linear accelerator
secondary collimators are normally placed in a constant position when using the
radiosurgery circular collimators. A plot of output factor as a function of radiosurgery
collimator size for a 6 MV linear accelerator at the University of Florida is shown in
Figure 2-4.


145
desirable beam directions that enter the patients head inferiorly (beams entering from
below the plane of a BRW headring placed on the patient). After this grid of data has
been computed, the fractional volume of intersection (FVI) data and target cross-sectional
area data for any particular beam may be easily interpolated within the two-dimensional
lookup table. Figure 4-17(a-f) shows polar plots of FVI and target cross sectional area
for conformally shaped beams for the meningioma example case in the next section. In
these plots, polar angle is the elevation angle above (-¡-f) or below (-f) the xy plane of
Figure 4-9, and azimuth is the azimuthal angle clockwise from the +x axis of Figure 4-
9.
Figure 4-17a: Fractional volume of intersection (FVI) for the left eye (left) and left optic
nerve (right) as a function of beam position in polar coordinates for an meningioma
example case.


253
Figure 6-9g: Nontarget volume NTCP as a function of prescription dose for case VC-4.
Table 6-19: Nontarget volume NTCPs for case VC-4
Plan
NTCP
clinical
4.63E-08
spack
6.77E-08
15 beams
1.08E-07
9 beam IMRT
5.72E-08
5dyn arcs
1.12E-07
Patient VC-5
Patient VC-5 is a 43 year old female with a 12.6 cm3 meningioma. This patient
was treated clinically with a twenty-seven isocenter SRS plan using 87 arcs, delivering
12.5 Gy to the 70% isodose shell. The sphere packing autopian used eighteen isocenters
with 82 arcs. Orthogonal view isodose plots for all plans are shown in Figures 6-10a
through 6-10e, with dose-volume figures of merit listed in Table 6-20. Nontarget volume


290
treatment plans for that particular patient, if there is any question or issue with applying
the general guidelines presented in this research.


121
Table 4-3: Agreement between Webb's beam bouquets (Webb 95) and locally generated
code beam bouquets of four to eight beams, based on dosimetric figures of merit.
(cc) (cc)
Rx-dose V(Rx)
V(0.5Rx)
PITV
UFIc
UFIg
UFI
Webb 4bm
67.5
0.99
2.81
1.11
90
104
97
Local 4bm
67.5
0.99
2.82
1.11
90
104
97
Webb 5bm
67.5
1.01
2.85
1.13
89
104
96
Local 5bm
68.0
0.99
2.80
1.12
90
104
97
Webb 6bm
67.5
0.99
2.77
1.11
90
105
97
Local 6bm
67.5
0.98
2.74
1.10
91
105
98
Webb 7bm
67.5
0.99
2.76
1.11
90
105
97
Local 7bm
67.5
0.99
2.76
1.11
90
105
98
Webb 8bm
67.0
1.00
2.77
1.12
89
105
97
Local 8bm
67.5
0.99
2.81
1.11
90
104
97


98
Table 3-3: Phantom target sphere packing automatic planning results
Phantom
Target
Size (cc)
No. isoc
Prescription
Isodose (%)
MDPD
PITV
1
6.5
7
53
1.90
1.40
2
11.6*
13
68
1.48
1.18
3
7.7
5
64
1.56
1.18
4
8.1
8
60
1.68
1.23
5
12.4
13
62
1.63
1.14
Results Clinical Targets
Ten clinical example cases recently treated at the University of Florida were
selected, covering a range of difficulty for the human planner. Four simple cases, which
required only one or two isocenters, were selected as representative "simple" cases.
Likewise, three "complex" cases, each requiring six to ten isocenters for an expert
planner to cover the target, were selected, and finally, three "very complex" cases, each
requiring twenty or more isocenters when planned by an expert. Radiosurgery plans were
generated by the automatic sphere packing algorithm for each clinical case, and dose-
volume information tabulated as was done for the phantom targets. The dose-volume
information for the ten clinical cases is shown in Table 3-4.


267
Figure 6-12h: Nontarget volume NTCP as a function of prescription dose for case VC-7.
Prescription dose (Gy)
Figure 6-12i: Brainstem NTCP as a function of prescription dose for case VC-7. The
P(NC) curves for the clinical multiple isocenter plan and the nine beam IMRT plan lie
almost on top of one another.


205
Figure 6-la: Case S-l clinical plan orthogonal view isodoses. The 70%, 35%, and 14%
isodose lines are shown in the axial, sagittal, and coronal views.
Figure 6-lb: Case S-l sphere packing autopian (three isocenters with eleven arcs) plan
orthogonal view isodoses. The 67%, 38%, and 15% isodose lines are shown in the axial,
sagittal, and coronal views.
Figure 6-lc: Case S-l fifteen beam plan orthogonal view isodoses. The 71%. 35%, and
14% isodose lines are shown in the axial, sagittal, and coronal views.


45
Figure 2-17: Target and total volume DVHs for F-shaped target in Figure 2-15.
This methodology can be applied to the dose distribution shown in Figure 2-16.
Figure 2-17 shows the DVHs for the F-shaped target volume and for a large 352 cm''
cubic volume enclosing the region of interest. From this DVH it can be seen that >95%
of the target volume receives >70% of maximum dose, which is necessary to support
selection of 70% as a prescription isodose for this target. The volume receiving 70% of
the maximum dose is 5.2 cm3 (Retr= 10.8mm), with 22.6 cm3 17.5mm) receiving
35% of maximum dose. The effective dose gradient is therefore 17.5 mm 10.8 mm =
6.7 mm, corresponding to a UFIg = 62.
There is another key piece of dose-volume information contained in this DVH
(Figure 2-17), which bears on the practice of multiple isocenter radiosurgery. Table 2-2
shows the resulting prescription to half-prescription dose gradient resulting from using
various isodose shells as the prescription isodose. The important information in Table 2-


258
Table 6-21: Nontarget volume NTCPs for case VC-5
Plan
NTCP
clinical
1.33E-07
spack
1.28E-07
15 beams
8.19E-07
9 beam IMRT
2.07E-07
-- 5dyn arcs
7.07E-07
Patient VC-6
Patient VC-6 is a 78 year old male with two left parietal metastatic lesions which
were treated concurrently with an eleven isocenter SRS plan using 43 arcs. The large
(10.6 cm3), irregularly shaped lesion was treated with ten isocenters and 38 arcs, while
the smaller lesion was treated with a single isocenter and five arcs. The clinical multiple
isocenter plan delivered 17.5 Gy to the 70% isodose shell. Only the larger of the two
lesions is considered in this comparison. The sphere packing autopian program generated
a ten isocenter plan with 34 arcs for the large lesion only. Orthogonal view isodose plots
for all plans are shown in Figures 6-1 la through 6-1 le, with dose-volume figures of merit
listed in Table 6-22. Nontarget volume DVHs are shown in Figure 6-1 If. NTCPs for the
nontarget brain volume are listed in Table 6-23, and a plot of nontarget brain NTCP as a
function of prescription dose is shown in Figure 6-1 lg.
The multiple isocenter plans are simply superior to any of the alternative
plans, based on UFI scores (clinical plan UFI = 75, sphere packing autopian UFI = 75,
versus next highest scoring plan, IMRT UFI = 61). Both multiple isocenter plans are
more conformal and have a steeper dose gradient than any of the alternative plans. Plan
rankings by NTCPs (Table 6-23, Figure 6-1 lg) follow the ranking order by UFI scores,
from most preferable to least preferable in order: sphere packing autopian, clinical
multiple isocenter plan, IMRT, fifteen beams, and four dynamic arcs.


149
linearly with increasing effective gradient distance. A modified gradient score, UFIg2. is
used, which scores the difference between the half-prescription isodose surface and the
target volume. (This modification to UFIg prevents the worsening dose conformity in
extreme cases from artificially raising the gradient score).
(4-15) kTTg = 100 {lOO [(rEff,S0%Rx R Eff,Target) 0.3 cm]
The magnitude of the gradient UFIg2 score depends on the target size, being
worse (lower values) for larger targets, but demonstrates a worsening trend the more
closely together the beams in a bouquet are placed. A guideline of attempting to maintain
an isotropy factor of at least 0.8 when interactively optimizing beam placement should
prevent the worst of the deleterious effects on dose conformity and gradient of moving
beams too closely to one another.


75
optimally spaced isocenters (each separated from the others by 13.8 mm), each with an
equally weighted five arc set and a 14 mm collimator (the relative dose weight of each
isocenter is 1:1:1:1). The individual dose profile for each isocenter is shown, along with
the total dose distribution along the crossplot from all four isocenters. The central
regions of the distribution near the two isocenters in the middle of the distribution receive
14% more dose than do the two isocenters at the edges. This is because each of the
middle isocenters receives the dose from its own five arcs, and also receives a substantial
contribution from each of its neighboring isocenters as well. The desired situation is to
have equal doses at each isocenter, rather than equal weighting of the arcs associated with
each isocenter. In order to compensate for the increased dose to the middle of the total
distribution, it is necessary to decrease the weight of the two isocenters in the middle.
Figure 3-14(b) shows the individual and total dose distribution after the isocenter dose
weighting has been adjusted to 1.17 : 0.94 : 0.94 : 1.17. Making this adjustment causes a
uniform dose to be received by each of the four isocenters. Although the total dose
distribution is still somewhat heterogeneous, it is actually more homogeneous than the
total dose distribution in Figure 3-14(a). This is shown in Figure 3-14(c), which shows
the total dose distribution for both situations. The overall dose distribution after adjusting
the weights is more homogeneous, in that the volume of the 70% isodose surface has
been increased, and the hot volume (hotspot) receiving more than 90% of maximum
dose has been reduced. Also, note that the prescription to half-prescription isodose
gradient is steeper for the adjusted weights distribution. This can be seen in Figure 3-15,
which shows the axial isodose distribution for both the equally weighted and the adjusted
weights plans. The 35% isodose shell is almost identical between the two plans, but


Copyright 2000
by
Thomas H. Wagner


26
radiosurgery dose planning systems that utilize circular collimators. In applying equation
(2-1) to a radiosurgery treatment, one must assume that the contents of the patients head
are homogeneous, water equivalent, and that the geometry is similar to the reference
measurement geometry shown in Figure 2-5. Since linear accelerator radiosurgery
treatments with circular collimators are delivered with arcs of radiation rather than static
beams, each arc is simulated as a set of static beams, spaced along the path of the arc.
Typically, an arc of 100 degrees is simulated as eleven static beams, spaced 10 degrees
apart (Figure 2-6). The radiation dose to any point is the sum of the doses to that point
from all of the individual beams in the arc. Likewise, the dose to any point due to
multiple arcs and isocenters is the superposition (sum) of the doses of all of the arcs
associated with each isocenter. For any arrangement of radiosurgery beams or arcs, the
dose is calculated to a grid of points spaced closely together. Isodose curves
corresponding to the locus of isodose points may be constructed by interpolation amongst
the points in the viewing plane for which dose has been computed. Dose grid point
spacing should be no further apart than 2 mm, in order to properly sample the rapidly
changing dose distributions characteristic of radiosurgery dose distributions (Schell
1995).


53
Kutchers method (Kutcher 1991) is used to reduce each non-uniform dose volume
histogram to an equivalent volume DVH receiving the maximum dose level. This
method involves treatment of each small dose bin in the differential dose volume
histogram as a volume receiving-a. uniform dose D¡, which is a reasonable assumption if
the dose bin size is small enough. Small enough means practically using dose bins no
larger than about 2 Gy each (Kutcher 1991). The effective volume, Veff, receiving the
maximum dose Dm, is found by converting the volume in each differential DVH dose bin
to an effective volume V^, and summing them:
(2-10) Vtf = XVr
\DmJ
The source data cited above is applicable for NTCP calculations involving
fractionated radiotherapy under typical regimes of about 1.8-2.0 Gy per fraction on a five
day per week treatment schedule. These model parameters must be adjusted in order to
use this four parameter model to calculate NTCP for single dose radiosurgery cases. The
biologically equivalent dose formalism (BED) may be applied to make this modification
(Fowler 1989; Smith 1998), in which a BED may be calculated from any particular
fractionation scheme delivering dose D in fractions of dose d by
i
d


103
Figure 3-23: Patient 8:3D wireframe representation of target volume and target volume
with sphere packing arrangement. The sphere packing plan uses 20, 12, 10, and 5 mm
diameter spheres.
Sphere Packing as a Mulitple-Isocenter Radiosurgery Planning Tool
Over the fifteen cases examined in this study (five irregular phantom targets and
ten clinical examples), the sphere packing algorithm was able to generate a radiosurgery
plan which met the RTOG radiosurgery plan guidelines, that is, PITV < 2.0 and MDPD <
2.0. For the phantoms, the mean PITV was 1.28, with an average MDPD of 1.65,
corresponding to the 65% isodose shell. For the three "complex "clinical cases
examined, the mean PITV and MDPD were 1.28 and 1.67, respectively. The mean PITV
and MDPD for the three "very complex" clinical cases were 1.48 and 1.54, respectively.
These results demonstrate that even for highly irregular target shapes, it is possible to
create conformal radiosurgery plans using multiple isocenters.
These dosimetric results compare favorably with standard quoted radiosurgery
dosimetric figures of merit. Based on a number of recent comparisons of radiosurgery


227
Figure 6-5c: C-3 fifteen beam plan, 72-36-14% isodoses in dark.
: C-3 mne IMRT beam plan, 68-34-13% isodoses in dark.
Figure 6-5e: C-3 five dynamic arcs MLC plan, 72-36-14% isodoses in dark.


246
distribution, and is roughly equivalent or slightly better than the clinical multiple
isocenter plan (and is better than the sphere packing autopian) based on predicted NTCP.
Table 6-16: Dosimetric figures of merit for case VC-3
Plan
Rx-dose
PITV
Vover (cm3)
UFIc
UFIg
UFI
Gradient (mm)
clinical
70
1.45
6.6
69
45
57
8.5
spack
66
1.58
8.5
63
49
56
8.1
9 beams
72
2.00
14.6
50
45
47
8.5
15 beams
73
1.96
14.2
51
47
49
8.3
9 beam IMRT
86
1.29
4.3
77
33
55
9.7
5dyn arcs
73
2.05
15.4
49
44
46
8.6
Figure 6-8a: Case VC-3 clinical plan, 70-35-14%.
Figure 6-8b : VC-3 sphere packing twenty isocenter autopian, 66-33-13% isodoses
shown.


2
required to sterilize male goats (Hall 1994a). They discovered that they could not
administer a high enough dose of x-rays to the testicles to cause sterilization without also
causing a severe skin reaction in tissue adjacent to the testicles. However, when they
administered the x-ray dose-in small doses, given once a day over several weeks,
sterilization without an adverse skin reaction was possible. They postulated that the
testes were a model of tumor tissue, while the adjacent skin served as a model of dose-
limiting, normal tissue. Although these assumptions are now known to be false, the
conclusion was valid, that in most cases, for a given level of normal tissue toxicity, better
tumor control may be achieved with multiple dose fractions over an extended time.
In contrast to conventional, fractionated radiotherapy, stereotactic radiosurgery
(SRS) involves the administration of a relatively large, single dose of radiation (10 Gy to
20 Gy) to a small volume of disease, thereby abandoning the advantages provided by
fractionation. Lars Leksell conceived of the idea of radiosurgery in 1951 (Leksell 1951).
His original idea involved using many beams of orthovoltage x-rays converging on an
intra-cranial target to create a lesion. Leksells idea, known as the Gamma Knife or
gamma unit, was practically implemented in 1967 using an array of 170 Co-60 sources,
each of which emitted megavoltage gamma rays through radioactive decay (Leksell
1983; Colombo 1998). The decay gamma rays were collimated with holes bored in a
large radiation shield to converge to a single point inside the patients head. The use of
secondary collimator helmets, each with different size holes (4, 8, 14, and 18 mm
diameter), allowed for the creation of several sizes of a spherical, high dose region (Maitz
1998). Irregularly shaped lesions could be produced by stacking spherical regions
together to build up complex shapes. The patients skull was positioned with sub-


91
would be set to a value of ten, which easily allows one to distinguish voxels inside a
sphere from other voxels.
If the user desires to place another sphere after the first sphere has been placed, all
target voxels not covered by-the first sphere are reset to values of 1, and the entire
grassfire process repeated (Figures 3-17d and 3-17e, steps 4-6). Note that target voxels
inside the sphere which was placed have been effectively removed for purposes of the
grassfire algorithm, causing the sphere's surface to be treated as an outer surface of the
target (see arrows in Figures 3-17d and 3-17e). Figures 3-17f through 3-17h similarly
depict selection of the second 14mm isocenter location after the first isocenter has been
placed. The algorithm continues to place three more isocenters, all 5mm in diameter,
before halting. Figure 3-14 depicts three-dimensional views of the sphere packing
arrangement, the target, and the prescription isodose cloud surrounding the target. Figure
3-19 shows this final dose distribution in three orthogonal planes through the center of
the target.


110
specifically for the purpose of obtaining maximally-separated beams. The advantage of
using Webbs beam arrangements as opposed to manually placing beams to obtain
approximately maximally spaced beams is that Webbs beam arrangements are as
precisely isotropic (maximally spatially separated) as possible. The methodology
presented in Webbs paper describes this unique method of generating an isotropic
arrangement of (beam) vectors, but did not include other realistic factors in
determining beam direction, such as avoiding treatment unit couch/gantry collisions, or
avoiding radiosensitive anatomical structures.
A radiotherapy optimization method is developed in this chapter for
extending Webbs isotropic beam arrangements to practically-deliverable beam
arrangements. The general concept is to use an arrangement of N isotropically
converging vectors as a starting point for an optimization process which optimizes the
beam arrangement to include critical structure avoidance, treatment unit gantry/couch
collision considerations, and other geometric considerations. This approach is
conceptually attractive because it starts from a beam arrangement which is initially
optimized for maximal beam separation, and generally involves making relatively minor
adjustments to this arrangement to accommodate the planners priorities. Beginning the
optimization process from such a well-defined starting point mimics a human planners
actions, and is more likely to result in plans which accomplish the human planners
objectives.
An additional method of utilizing shaped beams for radiosurgery, dynamic
arcing with a multileaf collimator, is also presented in this chapter. This method has been
previously examined at the University of Florida (Moss 1992), and is included as a


217
Figure 6-3a: C-l nine isocenter clinical plan orthogonal view isodoses. The 70%, 35%,
and 14% isodose lines are shown in the axial, sagittal, and coronal views.
Figure 6-3b: C-l eight isocenter autopian orthogonal view isodoses. The 69%, 35%, and
14% isodose lines are shown in the axial, sagittal, and coronal views.
Figure 6-3c: C-l fifteen beam plan orthogonal view isodoses. The 74%, 37%, and 15%
isodose lines are shown in the axial, sagittal, and coronal views.


115
arrangements shown in Figure 4-8. after adjustment in this manner, are listed in Tables 4-
4 through 4-7 (IEC 1996).
Table 4-1: Vector-vector angular distribution for Webbs isotropic 4-beam arrangement
(in degrees). The angle from a vector to itself is zero degrees.
Vector
1
2
3
4
5
6
7
8
1
0
71
109
71
180
109
71
109
2
71
0
71
109
109
178
109
71
3
109
71
0
71
71
109
180
109
4
71
109
71
0
109
71
109
179
5
180
109
71
109
0
71
109
71
6
109
178
109
71
71
0
71
109
7
71
109
180
109
109
71
0
71
8
109
71
109
179
71
109
71
0
Table 4-2: Vector-vector angular distribution for locally-generated isotropic 4-beam
arrangement (in degrees). The angle from a vector to itself is zero degrees.
Vector
1
2
3
4
5
6
7
8
1
0
71
109
71
180
109
71
109
2
71
0
71
109
109
178
109
71
3
109
71
0
71
71
109
180
109
4
71
109
71
0
109
71
109
179
5
180
109
71
109
0
71
109
71
6
109
178
109
71
71
0
71
109
7
71
109
180
109
109
71
0
71
8
109
71
109
179
71
109
71
0


146
Figure 4-17b: Fractional volume of intersection (FVI) for the right eye (left) and right
optic nerve (right) as a function of beam position in polar coordinates for an meningioma
example case.
Figure4-17c: Fractional volume of intersection (FVI) for the brainstem as a function of
beam position in polar coordinates for an meningioma example case.


141
The treatment plan optimization process begins with selection by the user
of a bouquet of N beams (the bouquet is pre-calculated as described in the previous
section). N is chosen to be as small enough to produce the simplest and shortest
treatment, while being large enough so that the entrance and exit doses of each beam are
spread over a large number of beams and thereby minimized. N should also be chosen
large enough to provide sufficient conformity of the prescription dose volume to the
target. An automatic optimization algorithm, implemented in the form of a computer
program, places the beam bouquet on an isocenter defined at the center of the target, and
rotates the beam bouquet to find the best orientation of the fixed set of beams. In order to
ensure that the global minimum of the score function is attained despite the likely
presence of multiple local minima, a downhill optimization search is started from
multiple starting points, similar to the approach used by Das (Das 1997). Finally, each
beam may be independently moved (rotated about the target isocenter) within a
neighborhood around its starting position, to find the best orientation for each individual
beam. This plan optimization process for a bouquet of N beams is outlined as follows:
1) Select a starting bouquet of N beams from a precomputed beam template
(Tables 4-3 through 4-6, or use Webbs 3-8 beam arrangement (Webb 1995)).
2) Calculate BEVs using a projective transform (McLenaghan 1996), and
apply user-specified BEV margin to the target using a grassfire transform (Blum 1973;
Wagner 2000). Increasing the size of the BEV margin added to the target improves the
homogeneity of the target dose distribution, but at the expense of greater doses delivered
to the non-target volume.


165
Table 4-10: Initial nine isotropic beam bouquet data
Target area Fractional volumes of intersection (FVIs)
Beam
y
z>
Score
Initial
Current
RE
R-ON
LE
L-ON
BS
1
-0.338
0.313
0.888
2.5
1577
1577
0.00
0.00
0.00
0.00
0.15
2
-0.276
-0.543
0.792
358.6
1292
1292
0.34
0.19
0.00
0.00
0.00
3
0.370
-0.083
0.926
29.7
1627
1627
0.00
0.00
0.00
0.29
0.02
4
-0.880
-0.114
0.463
1.0
1446
1446
0.00
0.00
0.00
0.00
0.00
5
0.347
0.674
0.652
1.0
1544
1544
0.00
0.00
0.00
0.00
0.00
6
-0.355
0.882
0.310
1.0
1219
1219
0.00
0.00
0.00
0.00
0.00
7
-0.611
-0.784
0.101
1.0
1143
1143
0.00
0.00
0.00
0.00
0.00
8
0.453
-0.751
0.481
1.0
1233
1233
0.00
0.00
0.00
0.00
0.00
9
0.938
0.001
0.346
1.0
1522
1522
0.00
0.00
0.00
0.00
0.00
Average
44.08
1400
1400
0.04
0.C2
0.00
0.032
0.018
Table 4-11: Nine isotropic beam bouquet data, after optimal azimuthal rotation
Target area Fractional volumes of intersection (FVIs)
Beam
y
z>
SCORE
Initial
Current
RE
R-ON
LE
L-ON
BS
1
0.457
-0.054
0.888
9.8
1577
1659
0.00
0.00
0.00
0.09
0.01
2
-0.096
0.602
0.792
2.2
1292
1536
0.00
0.00
0.00
0.00
0.10
3
-0.348
-0.150
0.926
2.5
1627
1462
0.00
0.01
0.00
0.00
0.04
4
0.645
0.610
0.463
1.1
1446
1530
0.00
0.00
0.00
0.00
0.00
5
0.116
-0.749
0.652
2.4
1544
1166
0.00
0.00
0.00
0.00
0.00
6
0.806
-0.505
0.310
1.1
1219
1385
0.00
0.00
0.00
0.00
0.00
7
0.033
0.993
0.101
0.9
1143
974
0.00
0.00
0.00
0.00
0.00
8
-0.808
0.341
0.481
1.2
1233
1462
0.00
0.00
0.00
0.00
0.00
9
-0.758
-0.552
0.346
0.9
1522
1314
0.00
0.00
0.00
0.00
0.00
Average
2.44
1400
1387
0.00
0.00
0.00
0.010
0.016


257
DC T
'8C 4
'60
12 i
§ ioc;
1 5
2 -
75 10 125
Dose iGy)
50 T
40
o
o
* SO
I
o
0
0 2.5 5 7 5 10 12 5 15 17 5 20
Dose (Gy)
Figure 6-1 Of: Nontarget volume DVHs for case VC-5. The prescription dose is 12.5 Gy.
The plot on the right is the same DVH, but with a larger volume scale. The IMRT plan is
almost as conformal as the clinical multiple isocenter plan at the prescription dose of 12.5
Gy, but exposes considerably more volume to dose levels between half-prescription (6.25
Gy) and prescription dose (12.5 Gy) due to having a less steep dose gradient than the
clinical plan. The sphere packing autopian is not as conformal at 12.5 Gy, but exhibits a
much steeper dose falloff below 12.5 Gy.
Figure 6-10g: Nontarget volume NTCP as a function of prescription dose for case VC-5.
Both multiple isocenter plans (clinical and sphere packing autopian) have a considerably
lower predicted risk of complication as the prescription dose is hypothetically raised.


83
s
START
'v
f
Build 30 voxel
model of target
Grassfire Evaluate score for Select voxel with
procedure maximum valued maximum score as
(shelling) voxels seed voxel
£
Reset non-covered
target voxels to "I"
values
J
Locate max. score
In neighborhood of
seed voxel
T
Place sphere
Figure 3-16: Block diagram of sphere packing process


30
obtain sufficient calculation accuracy in stereotactic radiosurgery or radiotherapy
situations with many beams. A study by Ayyangar on two typical radiosurgery cases
compared a simple dose model similar to that of equation (2-1), with a Monte Carlo dose
model with and without inhomogeneity corrections. Not correcting the simple dose
model for the passage of the beam through the cranium caused the uncorrected dose
model to overestimate the dose by 1.5% to 2.5%, an acceptable amount of error.
Applying a TAR ratio method correction, similar to the Batho power-law correction,
reduced the dose calculation error further (Ayyangar 1998).
The small size of the beams typical of stereotactic radiosurgery and radiotherapy
allow the use of a relatively simple dose calculation model without sacrificing accuracy
of dose calculation. This simplicity is important in that it allows much faster dose
computations throughout the volume of interest, which is especially important given the
large typical numbers of beams for which dose must be calculated in radiosurgery.
Isodoses and Dose-volume Histograms
Isodose curves overlaid upon the patients three-dimensional image set are an
important plan evaluation tool, just as in two-dimensional planning. To evaluate a three-
dimensional dose distribution by this method, however, the planner must examine the
isodose distributions in a number of planes through the target region, which can be
cumbersome for large targets occupying many planes in an image set. It is possible to
display three-dimensional renderings of three dimensional dose distributions on a flat
computer display screen, but these are also very difficult to analyze. The problem with
evaluating a three-dimensional radiosurgery dose distribution, with its sharp dose


255
Figure 6-10a: VC-5 clinical twenty-seven isocenter plan, 70%-35%-14% isodose lines
shown.
Figure 6-10b: VC-5 eighteen isocenter sphere packing automatic plan, 66%-33%-13%
isodose lines shown.
Figure 6-10c: VC-5 fifteen beam plan, 70-35-14% isodose lines shown.


16
five to fixed beam IMRT planning. Chapter six is devoted to the actual comparisons of
each technique to an array of example cases, on which the guidelines and
recommendations for optimal employment of an MLC at the University of Florida are
based.


142
3) Compute the approximate volume of each critical structure irradiated by
the conformally shaped beam in the manner of Das (Das 1997). Rather than voxelizing
all structures, track intersection of each beam with points on the surface of each structure
to approximately get the volume intercepted.
4) Score each beam based on critical structure involvement, beam
deliverability, and target cross sectional area (to reduce integral dose). For beam i, a score
based on involvement with j=l ...#CS critical structures is computed by the equation
(4'12) score, = fM
Target-area
v ,ar6 Init-target-area
wt,
*CS
+I Wcs-yV
7=1
(CS-j)i
where w is the score function weight for target area or for each critical structure,
and fbeam is a factor which penalizes the beam for approaching or crossing into an
undeliverable area, and V(CS-j)i is the fractional volume of intersection of beam i with
critical structure j. The factor fbeam,i is given by the piece-wise continuous, linear
function
(4-13)
ft
1
WV1
vertex
V
be ami
0.349
1.0,
/
f
v
* | iq
1
-6
if 70 degrees <
2 )
if 0 degrees <(
l+[-5.73-(p-(w.nf-l)J,
if (p<0 degrees
where (j) is the elevation angle of the beam vector above (+<(>) or below (-(j)) the xy plane
of Figure 4-9, and winf and wvertex are factors which control the slope of fbeam,i in the
elevation angle regions corresponding to inferior beams ( < 0) and vertex beams (70


Separation angle (degrees)
120
200
Observation number
Figure 4-5: Vector-vector angular distribution for 8 isotropic vectors generated by
Webbs computer program(Webb95) and by a locally written computer program.


CHAPTER 6
SRS METHODS COMPARISON
Introduction
Previous chapters of this work presented the methods for evaluating radiosurgery
treatment plans, and for optimizing treatment plans with each delivery method. This
chapter addresses the purpose of this research project, which is to equitably compare
several methods of stereotactic radiosurgery treatment delivery based upon the overall
quality of treatment plan attainable with each.
The research problem is addressed by comparing treatment plans for a number of
representative clinical example cases drawn from the University of Florida radiosurgery
patient database. Clinical example cases are divided into three broad classes: simple,
complex, and very complex treatments, based upon the complexity of the clinical SRS
plan with circular collimators and single or multiple isocenters used to actually treat the
patient. Simple cases are those cases requiring three or fewer isocenters, complex
cases are those requiring four to nine isocenters, and very complex cases are those
cases requiring ten or more isocenters. Following patient treatment, a member of the
radiosurgery treatment planning team delineated the target volume using the University
of Florida in-house radiosurgery treatment planning system. Radiosensitive structure
volumes were also delineated with this treatment planning system, and the target and
radiosensitive structure volume data was then used to design multiple isocenter and static
beam (shaped beam and IMRT fixed beam) treatment plans as presented in Chapters 3-5.
199


21
Linear accelerator
(radiation source)
Radiation detector at isocenter
of the linear accelerator
Figure 2-1: Schematic of setup for measuring radiation dose as a function of depth in a
water phantom


272
Table 6-29: Treatment plans for cases VC-5 through VC-7, sorted by UF Index score and
by biological indices
Case VC-5
Plan
UFI
-- Plan
NTCP
spack
64
spack
1.28E-07
clinical
61
clinical
1.33E-07
9 beam IMRT
49
9 beam IMRT
2.07E-07
5dvn arcs
40
5dvn arcs
J
7.07E-07
15 beams
39
15 beams
8.19E-07
Case VC-6
Plan
UFI
Plan
NTCP
spack
75
clinplan
1.97E-05
clinical
73
spack
1.97E-05
9 beam IMRT
61
IMRT
6.10E-05
15 beams
59
15bms
1.15E-04
5dyn arcs
55
5dyn arcs
1.90E-04
Case VC-7
Plan
UFI
Plan
P(NC)
clinical
67
IMRT
0.849
9 beam IMRT
62
clinplan
0.848
15 beams
60
5 dvn arcs
0.727
spack
59
spack
0.501
5dyn arcs
56
15bms
0.456


4
advantage to improve the mechanical and overall system accuracy in positioning the
patient, in order to allow using treatment beams of the minimum necessary size (Meeks
1998a). By reducing the volume of non-target tissue irradiated to high levels, the
likelihood of incurring a complication (adverse reaction to the radiation treatment) may
be minimized.
The University of Florida radiosurgery system was developed in the mid-1980s as
a solution to the above mentioned problem of linear accelerator radiosurgery (Friedman
1989; Friedman 1992; Meeks 1998b). By using an isocentric system, as indicated by the
arrows in Figure 1-1, to position the patient and to provide tertiary, circular collimation of
the x-ray beam, the system allows a linear accelerator to be used to deliver radiosurgical
treatments (Figure 1-2) with mechanical accuracy comparable to a gamma unit.
Figure 1-1: University of Florida radiosurgery system : isocentric subsystem in place
under the gantry of a linear accelerator (linac).


162
80 -
-60
0 2 4 6 8 10 12 14 16
Number of beams
Figure 4-21(b): UF Index gradient scores (UFIc) for a series of irregularly shaped clinical
example targets versus the number of isotropically arranged shaped beams.
Application of Isotropic Beam Bouquets Nine Beam Plan for Meningioma
This process was applied to a clinical example case for illustrative purposes. This
patient is a male who presented with an irregularly shaped 7.3 cm3 meningioma. A nine-
beam plan was generated for this lesion according to the methods presented in this
chapter. Dose-volume histograms of the target and the total CT volume inside the patient
were computed and used for analysis of the nine-beam treatment plan.


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
OPTIMAL DELIVERY TECHNIQUES FOR INTRACRANIAL STEREOTACTIC
RADIOSURGERY USING CIRCULAR AND MULTILEAF COLLIMATORS
By
Thomas H. Wagner
August 2000
Chairman: Francis J. Bova
Major Department: Nuclear and Radiological Engineering
The University of Florida stereotactic radiosurgery (SRS) system is a well-
established system of single fraction, highly conformal linear accelerator based radiation
therapy for intracranial lesions. As originally implemented, the system is characterized
by the delivery of circular radiation beams with multiple arcs of megavoltage photon
beams all impinging on the target. The introduction of multileaf collimators (MLCs) and
computer-controlled treatment machinery offers the opportunity to plan and deliver more
complex radiation treatments that may apply dose to the target while applying less dose
to non-target tissues. There are numerous treatment techniques that may be employed
with such equipment, including multiple static fields, dynamic conformal arcing
treatments, and treatment with intensity modulated radiation therapy (IMRT) fields. This
expanded list of patient treatment options poses a new problem to the treatment planner:
determining the optimum treatment method for a given patient. Although many centers
Vlll


192
Figure 5-8a: Dose-volume histograms for total volume and target volume for example 5.4
cm' meningioma case. Both the 9 beam and 9 beam IMRT plans provide similar target
coverage, although the IMRT plan (small triangles) exposes less total volume to the
prescription dose of 10.0 Gy and is therefore more conformal.
Figure 5-8b: Total volume dose-volume histograms for 5.4 cm3 meningioma example
case.


203
As is shown in the next section, the comparison of alternative* (static beam,
static beam IMRT, and dynamic MLC arcs) SRS treatment delivery methods with
multiple isocenter, circular collimator SRS is relatively simple for the simple and
complex cases, due to clear differences in treatment plan quality. Distinguishing the best
treatment plan for the very complex plans is a more difficult and less straightforward
task, due to less distinct differences in the dose distributions between each plan.
Table 6-1: Clinical example case listing
Case
Diagnosis
Size (cc)
No. isocenters
No arcs
S-l
acoustic schwannoma
1.8
3
11
S-2
metastasis
2.6
1
9
C-l
meningioma
5.6
9
41
C-2
meningioma
12.3
7
27
C-3
meningioma
3.7
8
24
VC-1
meningioma
12.6
20
7
VC-2
meningioma
5.7
10
34
VC-3
sarcoma
15.3
20
88
VC-4
meningioma
8.0
13
61
VC-5
meningioma
12.6
27
87
VC-6
metastasis
13.8
11
43
VC-7
metastasis
12.1
21
85


193
30
Figure 5-8c: Brainstem DVHs for hypothetical nine beam and nine beam IMRT plans.
The nine beam IMRT plan is superior to the (conformal with no IMRT) nine beam plan
in terms of sparing the brainstem from radiation dose.


68
Figure 3-9: Rotating the distribution and steepening the dose gradient in an oblique
direction by elimination of four arcs entering from the patients right side. The 80%,
40%, and 16% isodose lines are shown in each plane.


206
Figure 6-Id: Case S-l nine beam IMRT plan orthogonal view isodoses. The 66%, 33%,
and 13% isodose lines are shown in the axial, sagittal, and coronal views.
Figure 6-le: Case S-l five dynamic MLC arc plan orthogonal view isodoses. The 73%,
36%, and 15% isodose lines are shown in the axial, sagittal, and coronal views.


129
(4-7) y* = cos(ar)y + cos
f 71 ^
+ a
V2 ;
(4-8) z* = eos
a
\ 2 )
y+ cos(or)z.
Equations (4-4a)-(4-6i) allow one to generate a rotated vector in terms
of the prerotation vector for rotations about the principle axes or about an
arbitrary axis. These relations are used for manipulations of vectors coresponding to
beam directions in this work.
Generation of Beam's Eve Views (BEVs)
The next problem to be solved is the problem of generating a beams eye
view of the target lesion and any other structures that may lie in the path of an arbitrarily-
shaped radiation therapy beam. A projective transform, frequently used in the field of
computer graphics, is used to compute beams eye views for each beam (McLenaghan
1996). A projective transform of this type transforms one set of homogeneous
coordinates of points in a scene to another set of homogeneous coordinates projected onto
a viewing plane. The projective transform may be compactly denoted by equations (4-9)
through (4-11) as
(4-9)
Xs
1
1
-*
KJ
o
rxo
0
0
X
ys
1
1-1
X
o
N
-rYoZo
rp
0
y
Zs
0
0
0
rp
z
_ 1 _
l
o
X
o
o
Q.
1
o
N
Cl
1
r:p_
_1


247
Figure 6-8c: VC-3 fifteen beam plan, 73-36-14%.
Figure 6-8d: VC-3 nine IMRT beam plan, 86-43-17%.
Figure 6-8e: VC-3 five dynamic MLC arcs plan, 73-36-14%.


64
Figure 3-7: Standard nine-arc set delivered with 18mm collimator, and isodose
distribution in axial, sagittal, and coronal planes. The 80%, 40%, and 16% isodose lines
are shown in each plane. The inset at lower left shows an AP view of a patients head,
with an overlay of the linac couch angles corresponding to each arc.


284
begin to overlap one another more frequently, as there are only a limited number of non
intersecting beam and arc orientations available. As the arcs intersect each other to a
greater extent outside of the target volume, more dose is deposited outside of the target
volume, and the dose gradient becomes less steep. This is demonstrated by a review of
824 multiple isocenter SRS cases at the University of Florida over a twelve year period
(Figure 6-14, Table 6-31). This data suggests a limitation on the attainable multiple
isocenter dose gradient which is a function of the number of isocenters used. Since a
larger and more complex target will require a greater number of isocenters to cover the
target volume, an accompanying worsening of the dose gradient is inevitable. This effect
lessens the efficacy of multiple isocenter SRS for targets requiring large numbers of
isocenters. For these types of targets, a nine beam (or more beams, when available in
Helios) IMRT treatment plan may offer a similar dose gradient, with a savings in
treatment delivery time. The data shown in Figure 6-14 suggest that sixteen or more
isocenters could be an appropriate decision point for favoring an IMRT plan over
multiple isocenters. Since the number of isocenters is unknown until a multiple isocenter
treatment plan has been generated, the automatic sphere packing program (Chapter 3)
could quickly provide an idea of the targets complexity and size by the number of
isocenters in the automatic plan, without requiring the clincian to expend the time to
manually generate a plan.


144
different starting point from the best azimuthally rotated bouquet. It was found that using
more than twenty searches occasionally resulted in a marginal improvement of bouquet
score, but the marginal improvement was generally not worth the increased computation
time cost.
6) If needed to reduce critical structure involvement, interactively and selectively
optimize the orientation of individual beams, within a solid angular interval of each
beams starting point in the isotropic, optimized bouquet. Let Q be the initial inter-vector
separation angle for the bouquet of N beams (e.g. Q = 47.6 degrees for the nine isotropic
beams listed in Table 4-3). Beam placement is performed by conducting a set of
downhill optimization searches within Q/4 of the initial starting point, with each beam
optimized independently of the other beams. Choosing a limit smaller than /2 (such as
Q/4) guarantees that parallel-opposed beams will be avoided. After the pre-optimization
step above, the user is presented with a printout of position and score information each
beam, and is prompted to select which, if any, individual beams are to be optimized.
Steps 1-5 are performed for bouquets of N = 3-15 beams, N odd, with the
results of each optimized bouquet of N isotropic beams written to an output file. The
human planner then selects which individual beams, if any, will be further individually
optimized from the optimally rotated isotropic bouquets. A radiation map is computed
prior to the steps listed above, in order to reduce the computation time required to
produce all of the BEV information required by equations (4-12) and (4-13). A BEV was
computed for all beams within 0-110 degrees of the +z axis in Figure 4-9, at polar and
azimuthal increments of 10 degrees. This polar angle range encompasses the 2tt
steriadians solid angle above the patients head in Figure 4-9, as well as some less


152
50 mm sphere target PITVs
Isotropy factor
Figure 4-18(c): Conformity (as expressed by PITV) versus isotropy for a 50 mm sphere
target and bouquets of 5, 7, 9, and 15 beams. An isotropy factor of 1.0 reflects an
isotropic (maximally separated in 4p space) beam arrangement, while lower values of
isotropy factor reflect a beam arrangement with an increasing sense of directionality.


230
Figure 6-5i: Brainstem NTCPs as a function of prescription dose for case C-3 treatment
plans.
Figure 6-5j: Clinical plan and sphere packing autopian isodoses in an axial plane several
mm inferior to the axial isodose planes shown in Figures 6-5a through 6-5e. The
prescription isodose lines for both multiple isocenter plans intersect a small volume of
brainstem, explaining the higher brainstem maximum dose for the multiple isocenter
plans as shown in the DVHs in the right side of Figure 6-5g.


10/16/00 3476
937 F8


262
Table 6-23: Nontarget volume NTCPs for case VC-6
Plan
NTCP
clinplan
1.97E-05
spack
1.97E-05
15bms
11.5E-05
IMRT
6.10E-05
5 dyn arcs
18.9E-05
Patient VC-7
Patient VC-7 is a 43 year old male with a 12.1 cm3 right temporal and
mesencephalic metastatic melanoma. This patient was treated clinically with a twenty-
one isocenter SRS plan using 85 arcs, delivering 17.5 Gy to the 70% isodose shell. The
sphere packing autopian program generated an eighteen isocenter plan with 82 arcs.
Orthogonal view isodose plots for all plans are shown in Figures 6-12a through 6-12e,
with dose-volume figures of merit listed in Table 6-24. Nontarget volume and brainstem
DVHs are shown in Figure 6-12f and 6-12g, respectively. NTCPs for the nontarget brain
and the brainstem are listed in Table 6-25, and plots of nontarget brain and brainstem
NTCP as a function of prescription dose are shown in Figures 6-12h and 6-12i,
respectively. Figure 6-12j shows a plot of the probability of no complication, P(NC),
versus prescription dose.
The clinical twenty-one isocenter plan is the highest UFI scoring plan, followed
by the IMRT plan, the fifteen beam plan, the sphere packing plan, and finally the four
dynamic arc plan (Table 6-24). The sphere packing, fifteen beam, and IMRT plans are
within three UFI points of one another and are therefore relatively close in terms of the
overall conformity and gradient of the physical dose distribution. The NTCPs and
probability of no complication, P(NC), are dominated by the brainstem NTCP, given the
relatively high dose prescribed to target this malignant lesion and the lesions close


114
merit (prescription isodose surface enclosing at least 95% of the target volume, PITV,
and UF index) are shown in Table 4-3. Typical DVHs for the four beam and eight beam
plans are shown in Figures 4-6 and 4-7. The treatment plans based upon Webbs beam
arrangements and the locally generated ones offer almost identical dose conformity,
homogeneity, and gradient to one another (Table 4-3). In all cases, the DVH curves for
Webbs and the locally generated N beam isotropic beam bouquets were
indistinguishable (Figures 4-6 and 4-7).
The close agreement between Webb's results and the locally generated beam
arrangements for N = 3 to 8 beams validates the results of the locally generated code used
to generate arrangements of N = 9 to 15 beams. Figure 4-8 depicts three-dimensional
views of isotropic bouquets of 9, 11, 13, and 15 beams (18, 22, 26, and 30 rays,
respectively, considering that each beam consists of an entrance ray and an opposed exit
ray). The first N beams in the bouquet are listed in terms of IEC couch and gantry
angles, and by beam unit vectors (each beam vectors x, y, and z components are denoted
by . The o brackets indicate a vector whose magnitude is unity, a unit vector).
Each beam has an opposed beam whose vector is given by <-x,-y,-z> and IEC
couch/gantry angles gantry(opposed) = gantry 180. Nominally, the first of N beam
vectors is arbitrarily assigned as <0,0,1>, which is a vertically oriented beam as shown in
Figure 4-9. The beam arrangements shown in Figure 4-8 were tilted 20 from vertical (Z
axis) in order to eliminate "vertex" beams, beams which when used on a patient would
enter the top of the patient's head and exit downwards through the rest of the patient's
body (Oldham 1998). Vector and IEC couch/gantry information for the beam


130
where p and r are defined as
(4-io) p=i[xl+yland
Equation (4-9) relates the scene coordinates of a point P (x,y,z) to the projective
plane, or screen coordinates (xs,ys,zs), as seen from an observer located at E = (Xo,y0,zo).
The geometry for this situation is shown in Figure 4-10. The observer at (x0,y0,z0) views
the scene containing point (x,y,z). A rectangular coordinate system is established on a
plane which is perpendicular to this line of sight, and which passes through the origin.
The coordinates (xs,ys,zs) give the intersection of the line of sight from the viewer to the
point (x,y,z) with this viewing or projective plane. Equations (4-9) through (4-11) may
be easily adapted to the more general case of an arbitrary viewpoint and an arbitrary
projective plane. In the radiotherapy and radiosurgery situation, the projective plane is
taken to be the plane passing through the isocenter as seen from the x-ray beam source,
nominally located 1000 mm up beam from the lesion (isocenter). This situation can be
accommodated by simply applying a translational shift to all points to bring the
observers point E in line with the origin in an up beam direction, before applying the
projective transform in equation (4-9).


34
Dose (% max)
Figure 2-10: Direct DVHs for a radiosensitive non-target structure in two hypothetical
treatment plans
Figure 2-11: Cumulative DVH plot of the direct DVH data shown in Figure 2-10.


107
was forced to begin filling in remainder target volume with large numbers of the smallest
sphere size available. 5mm diameter. The effect of using more and more isocenters (as a
result of a stiffer penalty for over-covering normal tissue volume) was better
conformation of the prescription isodose to the target, but generally at a cost of lower
target dose homogeneity and gradient. For several of the sphere packing radiosurgery
plans developed in this study, the last several 5mm isocenters placed by the algorithm
were ineffectual or even disadvantageous to the quality of the plan, and were thus
discarded. This was generally found to be due to the fact that the algorithm was
attempting to cover small peripheral target regions which remained after the bulk of the
target had been covered by previous isocenter spheres. If spheres are the only tool at
hand with which to deposit dose in the target, as is essentially the case for Gamma Knife
radiosurgery, then one must either accept the degradation in dose conformity from using
additional spheres to cover non-spherical peripheral areas, or one must prescribe a less
homogeneous dose (effectively, prescribe to a lower isodose shell) in order to cover the
target. When faced with such a situation at our institution, the human planner frequently
relies upon limited arc radiosurgery to cover small peripheral areas of the target with an
isocenter with one single arc (Schulder 1997). The use of this technique gives an expert
human planner an advantage over the less sophisticated sphere packing algorithm in
attempting to cover the target with a conformal, homogeneous dose distribution. Adding
this option for covering small, peripheral areas of the target could improve the
algorithm's performance by allowing it to more closely mimic an expert human planner.


124
13 beams 15 beams
Figure 4-8: Perspective views of 9, 11, 13, and 15-beam isotropic beam bouquets incident
upon a hemispherical dosimetry phantom. Vector information for these beam bouquets
(after rotating each set of beams 20 degrees away from the vertical) is listed in Tables 4-3
through 4-6.


_ACKNOWLEDGMENTS
I would like to express my sincere appreciation for the guidance provided me by
the members of my supervisory committee. I would especially like to thank my
committee chairman, Dr. Frank J. Bova, from whom I have learned much about medical
physics and whose mentoring has been a key component of the successes I have enjoyed
during my doctoral work. I would also like to thank and acknowledge the contributions
of Dr. Sanford L. Meeks, who has always encouraged me to go beyond simply the
academic requirements and to strive to publish my work, and of Dr. Beverly L. Brechner,
who invested much of her personal time in teaching and coaching me through elementary
topology and set theory, as well as contributing key ideas for our joint sphere packing
project. I am grateful to Dr. Willaim A. Friedman and Dr. John M. Buatti for all of the
valuable clinical feedback, mentoring, and support I have received from them during my
doctoral work and association with the University of Florida stereotactic radiosurgery
program. I also owe special thanks to Dr. Taeil Yi for contributing his ideas and for his
initial computer programming efforts in our joint sphere packing project, and to Dr.
Yunmei Chen, whose contributions played a key role towards the success of our joint
sphere-packing project. Drs. Brechner, Yi, and Chen are all from the University of
Florida Department of Mathematics. I would like to give my most sincere thanks to Dr.
Lionel G. Bouchet for many hours of insightful technical discussions about numerous
aspects of my research, and especially for his computer programming efforts towards
transferring image and anatomical structure data between the several treatment planning
IV


43
The UF Index (gradient) score, or UFIg, has been proposed as a metric for
quantifying dose gradient of a stereotactic treatment plan. From treatment planning
experience at the University of Florida, it has been observed that it is possible to achieve
a dose distribution which decreases from the prescription dose level to half of
prescription dose in a distance of 3 to 4 mm away from the target. Taking this as a guide,
a gradient score UFIg may be computed as
(2-3) UFIg 100 {l00 [(REff,50%Rx REff,Rx) -3cm]},
where Refreo%R.x is the effective radius of the half-prescription isodose volume, and Refm.x
is the effective radius of the prescription isodose volume. The effective radius of a
volume is the radius of a sphere of the same volume, so that Reff for a volume V is given
by
[w
(2'4) ^ = t
The volumes of the prescription isodose shell and the half prescription isodose
shell are obtained from a DVH of the total volume (or a sizeable volume which
completely encompasses the target volume and a volume which includes all of the half
prescription isodose shell) within the patient image dataset. The UFIg score is a
dimensionless number that exceeds 100 for dose gradients less than 3mm (steeper falloff
from prescription to half-prescription dose level), and which decreases below 100 as a
linear function of the effective distance between the prescription and half-prescription
isodose shells.


Figure 6-2a: Case S-2 clinical plan, 80-40-16% isodoses shown.
Figure 6-2b: Case S-2 sphere packing single isocenter plan, 78-39-15% isodoses shown.
Figure 6-2c: Case S-2 fifteen beam plan, 72-36-14% isodoses shown.


104
methods in the literature, one could roughly expect to obtain a PITV of about 1.5-2.0 and
an MDPD approaching 1.0-1.2 for various IMRT and mMLC treatment techniques with
moderate-to-large sized, irregularly shaped intracranial lesions. (Woo 1996; Shiu 1997;
Cardinale 1998; Kramer 1998; Verhey 1998). A common aspect in these comparisons is
the difficulty in creating a conformal and homogeneous radiosurgery plan for irregularly
shaped targets with circular collimators and multiple isocenters. Typically, the multiple
isocenter plans which are generated for such targets and comparisons suffer poor
conformity and homogeneity, due to the difficulty involved and the experience level
required of the planner. Typical multiple isocenter PITVs are on the order of 1.5-3.0, and
corresponding MDPDs on the order of 2.0-3.0. The sphere packing multiple isocenter
radiosurgery plan results cannot be compared directly with these others, since different
sets of targets are involved in each study. However, the "complex" and "very complex"
clinical example cases were chosen from a large radiosurgery patient database by an
experienced radiosurgery team as being representative of the more irregular and difficult
to plan clinical cases, which should serve to validate these results as a basis for
comparison with other studies. Based upon these results, the automatic sphere packing
algorithm demonstrates the potential to compete with experienced human planners in
generating conformal, homogenous radiosurgery plans for irregularly shaped targets. The
algorithm also demonstrates the ability to handle the opposite end of the difficulty
spectrum, by successfully identifying the optimal isocenter location for simple, single
isocenter plans.
From this initial experience with the automatic sphere packing radiosurgery
planning tool, the following may be concluded:


through 6-7e, with dose-volume figures of merit listed in Table 6-14. Nontarget volume
and brainstem DVHs are shown in Figure 6-7f and 6-7g, respectively. NTCPs for the
nontarget brain and the brainstem are listed in Table 6-15, and plots of nontarget brain
and brainstem NTCP as a function of prescription dose are shown in Figures 6-7h and 6-
7i, respectively. Figure 6-7j shows a plot of the probability of no complication, P(NC),
versus prescription dose.
In terms of the UF Index score, both multiple isocenter plans have the highest
numerical score and would therefore theoretically be the best plans. However, two of the
alternative plans, the fifteen beam and the nine beam IMRT plans, have UFI scores lying
within two or three points of both multiple isocenter plans, making the comparison based
solely on UFI score problematic. The clinical plan has slightly better conformity than
any of the other four plans, multiple isocenter or otherwise, and also has a slightly steeper
dose gradient than any of the alternative (non multiple isocenter) plans. The clinical plan
compares favorably with any of the other plans with respect to dose delivered to the
adjacent, radiosensitive brainstem (Figure 6-1 f). Thus, the clinical multiple isocenter
plan could be considered the best plan of all the plans considered, although it is not
significantly better and could even be considered roughly equivalent to most of the other
plans in terms of conformity and gradient.
The use of biological indices allows the plans to be ranked slightly more
specifically, although there are still some subtle differences between plans which are not
greatly resolved by an NTCP analysis. Table 6-15 lists nontarget brain volume and
brainstem NTCPs, as well as the probability of no complication (P(NC)) for each
treatment plan. Plots of nontarget volume and brainstem NTCP versus prescription dose


report the expanding use of these and other treatment techniques, there are few, if any,
reports that offer definitive comparisons of the major treatment techniques against one
another.
The purpose of this research was to compare radiosurgery plans using MLC static
fields, dynamic conformal arcs, and IMRT, with radiosurgery plans using circular
collimators and multiple isocenters, and to determine which of the MLC-based treatment
methods provides the best results. Representative clinical example cases from the
University of Florida radiosurgery patient database were used to examine the dosimetric
performance of each type of treatment delivery. Analysis of these clinical example cases
shows that circular collimators with multiple isocenters deliver dose distributions equal to
or better than MLC-based techniques for every example case studied. IMRT
radiosurgery treatments can yield results comparable to multiple isocenters, for cases
involving larger sized targets that would require more than about fifteen isocenters, and
for targets with relatively smooth-surfaced three-dimensional shapes. For most target
shapes, multiple isocenter dose distributions are more conformal and provide a steeper
dose falloff outside of the target than the MLC-based treatment methods. The software
tools developed for this research can also be employed in a clinically useful timeframe to
develop patient-specific optimized treatment plans to assist in this determination.
IX


252
Figure 6-9d: VC-4 nine IMRT beam plan orthogonal view isodoses.
16% isodose lines are shown in the axial, sagittal, and coronal views.
and
Figure 6-9e: VC-4 five dynamic MLC arcs plan orthogonal view isodoses. The 71%,
35%, and 14% isodose lines are shown in the axial, sagittal, and coronal views.
50
45 4
40
o 35
o :
g 30
1 25
O
2 20

£ 15
10
5
0 2.5 5 7.5 10 12.5 15 17.5 20
Dose (Gy)
din-nontarget
spack-nontarget
15bm-nontarg8t
IMRT-nontarget
5dyn-arcs-nontarget
Figure 6-9f: Nontarget volume DVHs for case VC-4. The prescription dose is 12.5 Gy.


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Colombo, F., Benedetti, A., Pozza, F., Avanzo, R. C., Marchetti, C., Chierego, G. and
Zanardo, A. (1985). External stereotactic irradiation by linear accelerator.
Neurosurgery 16(2): 154-60.
Colombo, F. and Francescon, P. (1998). Introduction and overview of stereotactic
radiosurgery. Textbook of Stereotactic and Functional Neurosurgery. Gildenberg, P.
L. and Tasker, R. R. New York, McGraw Hill: 641-648.
Das, S. K. and Marks, L. B. (1997). Selection of coplanar or noncoplanar beams using
three-dimensional optimization based on maximum beam separation and minimized
nontarget irradiation. Int J Radiat Oncol Biol Phys 38(3): 643-55.
Dirkx, M. L., Heijmen, B. J. and van Santvoort, J. P. (1998). Leaf trajectory calculation
for dynamic multileaf coilimation to realize optimized fluence profiles. Phys Vied
Biol 43(5): 1171-84.
Drzymala, R. E., Mohan, R., Brewster, L., Chu, J., Goitein, M., Harms, W. and Urie, VI.
(1991). Dose-volume histograms. Int J Radiat Oncol Biol Phys 21(1): 71-8.
Duggan, D. M. and Coffey, C. W., 2nd (1998). Small photon field dosimetry for
stereotactic radiosurgery. Med Dosim 23(3): 153-9.
Emami, B., Lyman, J., Brown, A., Coia, L., Goitein, VI., Munzenrider, J. E., Shank, B.,
Solin, L. J. and Wesson, M. (1991). Tolerance of normal tissue to therapeutic
irradiation. Int J Radiat Oncol Biol Phys 21(1): 109-22.
Flickenger, J. C., Kondziolka, D. and Lunsford, L. D. (1997). What is the effect of dose
inhomogeneity in radiosurgery? International Stereotactic Radiosurgery Society,
3rd VIeeting. Kondziolka, D. Madrid, Karger. 2: 206-213.
298


78
Four 14mm isocenters spaced at 14mm, all weights equal
Figure 3- 14(a): Dose profile through four optimally spaced 14mm isocenters,
each with an equally weighted five arc set. The dose profile for each
isocenter and the total combined dose profile are shown.
Four 14mm isocenters spaced at 14mm, isoc weights adjusted 1.17 : 0.94 0.94 1.17
0 25 50 75 100 125 150
Lateral distance (mm)
Figure 3-14(b): Dose profile through four optimally spaced 14mm
isocenters, each weighted to achieve equal total doses at each of the four
isocenters. The dose profile for each isocenter and the total combined
dose profile are shown.


5
Figure 1-2: Time lapse photograph showing arc rotation of the linac gantry about the
patient during treatment. The patient's lesion has been positioned at the radiation
isocenter with a stereotactic headring and the isocentric subsystem.
Technical Evolution and Improvements Stereotactic Radiotherapy
Although minimally invasive, the headrings associated with gamma unit and
linear accelerator radiosurgery make the administration of multiple radiation doses
infeasible. Some physicians have experimented with leaving the stereotactic headring on
the patient for extended periods to allow a series of treatments over this time. Although it
is possible to overcome problems with local infection and patient discomfort, these
difficulties have generally caused other practitioners to avoid using this method of
stereotactic radiotherapy (Schwade 1990). The application of non-invasive stereotactic
localizing techniques allows easier delivery of repeated radiation treatments to a
stereotactically-located lesion. The Gil-Thomas-Cosman headframe is one example of


Nontarget brain NTCP
261
Dose (Gy)
Figure 6-1 If: Nontarget volume DVHs for case VC-6. The prescription dose is 17.5 Gy.
Prescription dose (Gy)
Figure 6-1 lg: Nontarget volume NTCP as a function of prescription dose for case VC-6.


Table 6-12: Dosimetric figures of merit for case VC-1
Plan
Rx-dose
PITV
Vover(cm3)
UFIc
UFIg
UFI
Gradient (mm)
clinical
70
1.05
0.7
95
50
72
8.0
spack
67
1.31
3.9
77
53
65
7.7
9 beams
75
1 r55
6.9
65
46
56
8.4
15 beams
69
1.99
12.5
50
50
50
8.0
9 beam IMRT
74
1.39
4.9
72
47
59
8.3
5dyn arcs
J
67
2.10
13.9
48
43
45
8.7
Figure 6-6a: VC-1 twenty-isocenter clinical plan, 70-35-14% isodoses shown.
Figure 6-6b: VC-1 seventeen-isocenter autopian, 66-33-13% isodoses shown.


260
Figure 6-1 le: VC-6 fifteen beam plan, 68-34-14% isodoses shown.
Figure 6-1 Id: VC-6 nine IMRT beam plan, 77-39-15% isodoses shown.


200
Single and multiple isocenter dose distributions for plans using circular collimators were
computed on a 1 mm resolution dose point grid, using the University of Florida treatment
planning system. Beam apertures for shaped beam plans (static beams and dynamic arc
MLC plans) were shaped with an MLC with 5 mm leaf width projected at isocenter,
using zero added beams eye view margin to the target, leaves outside MLC leaf
justification, and automatically optimized collimator rotation angle. Beams were shaped
with zero added BEV margin to obtain the best combination of dose conformity and
gradient (Cardinale 1999). Dose distributions for shaped beam and IMRT plans were
computed on a three-dimensional grid of points within the patients anatomy, with a
dose-grid point spacing of 1.25 mm, the highest spatial resolution dose-grid spacing
available with CadPlan 6.15E (Varian 1999). The patient image sets and contours for
each volume were processed and converted into a format readable by the CadPlan
treatment planning system, and this system was used to compute dose distributions for
static beam, static beam IMRT, and dynamic arc MLC treatment plans. This conversion
process ensures the most accurate reproduction of the target volumes from the University
of Florida treatment planning system to the CadPlan system. For each treatment plan for
each patient, dose volume histograms were calculated for the target and non-target
volumes, as well as for any proximal radiosensitive structures. Each treatment plan was
analyzed primarily on the basis of the physical dose distribution, i.e. conformity and dose
gradient. For purposes of data presentation, dose-volume histograms of targets and other
relatively small structures are normalized to the volume of the structure as indicated by
the treatment planning system, in the manner of Verhey in a similar comparison of
several SRS treatment modalities (Verhey 1998). This introduces small normalization


62
IHG FEDCBA
Figure 3-3: AP (left side) and superior view (right side) of the standard nine arc set used
as a starting point for single isocenter radiosurgery plans. Each equally weighted arc
spans 100 degrees of gantry rotation at one of nine couch angles.
Gantry 0 degrees
Gantry
rotation
Figure 3-4: Schematic depiction of couch and linac gantry angles. The linear accelerator
couch and gantry are positioned in the home position, couch at 0 degrees, and gantry at
0 degrees. Couch and gantry angles refer to the amount of clockwise rotation as shown
in the figure.


256
Figure 6-10d: VC-5 nine IMRT beam plan, 83-41-16% isodose lines shown.
Figure 6-10e: VC-5 five dynamic MLC arcs plan, 703514% isodose lines shown.


9
determine the beams shape. In recent years, the three dimensional image sets from
computed tomography or magnetic resonance image scans have been used to construct
three-dimensional models of the patient and internal structures, such as the target. These
models of each patient structure may be used to determine the placement of radiation
beams, and to design each beams shape.
Technical Evolution and Improvements Linear Accelerator Radiation Delivery
Both the gamma unit and early linear accelerator radiosurgery systems produced
similar sphere-like dose distributions using either multiple static, circular beams (gamma
unit) or multiple circular beams swept though several arcs (linear accelerator). However,
the linear accelerator offers additional flexibility over the gamma unit in that multiple
collimation devices may be used to produce non-circular beams, and beams with non-
uniform intensity profiles across the beam. This additional flexibility in radiation
delivery potentially offers the ability to more closely tailor the dose distribution to the
target volume with a linear accelerator than with a gamma unit. The beam shaping and
modulation devices used with linear accelerators for these purposes include custom beam
shaping blocks, wedge beam filters, custom beam compensating filters, and multi-leaf
collimators. Also, linear accelerators typically can deliver a much larger range of
radiation beam sizes, upwards to a 40 cm x 40 cm square field at 100 cm from the
radiation source.
The simplest beam-shaping device used with linear accelerators (other than the
machines secondary collimators, which typically produce rectangular fields up to a 40
cm x 40 cm square field at the machines isocenter) is the custom block. Such blocks are


271
Table 6-28: Treatment plans for cases VC-1 through VC-4, sorted by UF Index score and
by biological indices
Case VC-1
Plan
UFI
Plan
P(NC)
clinical
72
spack
0.99998
spack
65
clinical
0.99998
9 beam IMRT
59
9 beam IMRT
0.99991
15 beams
50
5dyn arcs
0.99929
5dvn arcs
J
45
15 beams
0.99904
Case VC-2
Plan
UFI
Plan
P(NC)
clinical
68
9 beam IMRT
0.9999999
spack
67
15 beams
0.9999997
9 beam IMRT
66
clinical
0.9999997
15 beams
65
5dvn arcs
0.999999
5dyn arcs
62
spack
0.9999992
Case VC-3
Plan
UFI
Plan
NTCP
clinical
57
9 beam IMRT
5.59E-06
spack
56
clinical
6.46E-06
9 beam IMRT
55
spack
1.05E-05
15 beams
49
15 beams
2.00E-05
5dyn arcs
46
5dyn arcs
2.66E-05
Case VC-4
Plan
UFI
Plan
NTCP
clinical
66
clinical
4.63E-08
spack
61
9 beam IMRT
5.72E-08
9 beam IMRT
59
spack
6.77E-08
15 beams
55
15 beams
1.08E-07
5dyn arcs
53
5dyn arcs
1.12E-07


237
Table 6-13: NTCPs and probability of no complication for case VC-1
Plan
Nontarget
Brainstem
R-ON
L-ON
P(NC)
clinical
5.76E-08
1.99E-05
6.55E-09
2.09E-07
0.999980
spack
9.87E-08
1.69E-05
1.09E-08
8.28E-07
0.999982
15 beams
4.74E-07
9.61E-04
7.86E-09
3.28E-06
0.999035
9 beam IMRT
3.08E-07~
8.54E-05
9.49E-13
1.03E-07
0.999914
5dvn arcs
6.08E-07
6.87E-04
9.98E-08
2.36E-05
0.999290
Figure 6-6j: Probability of no complication. P(NC), as a function of prescription dose for
case VC-1.
Patient VC-2
Patient VC-2 is an 80 year old male with a 5.7 cnr meningioma. This patient was
treated clinically with a ten isocenter SRS plan using 34 arcs, delivering 10.0 Gy to the
70% isodose shell. The sphere packing autopian program generated a thirteen isocenter
plan using 54 arcs. Orthogonal view isodose plots for all plans are shown in Figures 6-7a


61
arcs (specific parameters listed in Table 3-1, in terms of International Electrotechnical
Commission (IEC) couch and gantry angles (IEC 1996)), is shown in a perspective view
in Figure 3-2, and is generally used as a basis for generating single isocenter dose
distributions. Couch and gantry angles are illustrated in Figures 3-3 through 3-6. An AP
view of a standard nine-arc set, delivered to an approximately spherical target with an
eighteen-millimeter collimator, is shown in Figure 3-7 along with the resultant isodose
distribution. Each arc is weighted equally with respect to dose to isocenter. The couch
angles are chosen to approximate an even and symmetrical beam distribution over the 2ti
steradian solid angle above the patients head, while avoiding parallel opposed beams
which would adversely affect the dose gradient (Meeks 1998a; Meeks 1998b; Meeks
1998c).
Table 3-1: Couch and gantry angles for standard University of Florida nine arc set.
(Angles are in accordance with IEC standards).
Couch
Gantry
Start
Gantry
Stop
10
130
30
30
130
30
50
130
30
70
130
30
350
230
330
330
230
330
310
230
330
290
230
330
270
230
330


188
to generate an IMRT treatment plan as described in this chapter. Dose-volume
histograms of the target and the total CT volume inside the patient were computed and
used for analysis of the nine-beam treatment plan. The optimized nine beam orientations
are shown in Figure 5-5.
Figure 5-5: Nine isotropic beam orientations for IMRT example case.
Dose-volume constraints for nearby critical structures (brainstem and optic nerves) are
entered into the Helios planning system prior to the calculation of beam intensity profiles.
The maximum dose and several dose volume constraints for the brainstem are shown in
the middle and upper portion of Figure 5-6. The target minimum dose was set to 10.0
Gy, the same as the prescribed dose for the clinical ten isocenter plan. The maximum
allowed critical structure doses were 10.0 Gy for the brainstem, and 8.0 Gy for the optic
nerves. Additionally, several intermediate dose-volume limits were set for the optic
nerves and brainstem, as shown by the triangles in the middle portion of Figure 5-6 for
the brainstem. Dose distributions and DVHs were calculated for the nine beam and the
nine beam IMRT plans. Total volume and target DVHs for both plans are shown in
Figures 5-8a and 5-8b. Brainstem DVHs are shown in Figure 5-8c. For each


CHAPTER 2
EVALUATION OF TREATMENT PLANS
Evaluating the suitability of a stereotactic radiosurgery or radiotherapy treatment
plan requires the human planner to assimilate and analyze a vast quantity of three
dimensional dose information. Given the distribution of radiation dose in three
dimensions in the vicinity of the target, the planner must assess how well the prospective
plan accomplishes the treatment goals of uniformly irradiating the target to a high dose
level while sparing nearby radiosensitive structures from the effects of a large radiation
dose. This chapter presents currently accepted methods and tools for analyzing
stereotactic radiosurgery and radiotherapy dose distributions.
In two dimensional radiotherapy planning, doses are calculated on a two
dimensional slice in a single plane through the target, assuming that the slice chosen is
representative of the entire target region, and that the slice is semi-infinite in extent
(extends infinitely in both directions perpendicular to the plane of interest). Dose
distributions are generally displayed as isodose curves superimposed upon either the
patient contour or a single CT image slice though the region of interest. Plan evaluation
is based upon inspection of the isodose curves overlaid upon this single slice or image.
In three dimensional radiation therapy planning, evaluation of the three dimensional dose
distribution involves the processing of considerably greater amounts of information.
The calculation of radiation absorbed dose is fundamental to radiation therapy, in
order to predict and control the radiation dose delivered to the lesion, and to non-target
17


182
Figure 5-3: Sliding window delivery of a non-uniform fluence map. The fluence map is
lighter colored in areas receiving a higher dose. Frames 1-9 show the MLC leaves in
various stages of movement while the beam is on, starting at frame 1 and ending with
frame 9. The black areas at the left are the open apertures defined by the MLC leaves.
The MLC leaves are completely closed before frame 1 and after frame 9, when the beam
is turned off. Note that the leaf motion for both the left and the right leaf pairs is
unidirectional, from right to left, as the aperture is progressively scanned from right to
left as it changes shape.
IMRT Treatment Planning with CadPlanTielios
The Helios module of the CadPlan radiotherapy treatment planning system
(CadPlan 6.15E with Helios, Varan Medical Systems, Palo Alto, CA) is an inverse
planning system, that is, the user provides a set of treatment plan goals and constraints,
which drives the inverse planning system to generate an intensity modulated radiotherapy


99
Table 3-4: Clinical examples: Dose-volume data for radiosurgery plans used for patient
treatment
Expen Human Planner Sphere Packing Autopian
Patient
iagnosis
Size (cc)
Isoc.
Isodose
(%)
MDPD
PITV
Isoc.
Isodose
(%)
MDPD
PITV
1
etastasis
2 7
1
80
1.25
1.02
1
78
1.28
1.09
Simple
2
emngioma
8.3
1
70
1.43
1.01
1
71
1.41
1.01
3
coustic neuroma
0.8
1
70
1.43
1.16
1
67
1.49
1.26
4
coustic neuroma
1.3
2
70
1.43
1.58
2
59
1.69
1.80
5
emangiopericytoma
7.6
6
70
1.43
1.09
7
64
1.56
1.13
Complex
6
eningioma
3.8
8
70
1.43
1.09
4
57
1.75
1.43
7
hemodectoma
12.4
10
70
1.43
1.17
15
60
1.67
1.27
Very
8
eningioma
12.8
20
70
1.43
1.05
20
67
1.49
1.27
Complex
9
arcoma
15.3
20
70
1.43
1.33
27
63
1.59
1.78
10
etastasis
13.6
21
70
1.43
1.10
28
64
1.56
1.40
The simple clinical targets (patients 1-4) were treated with single or double
isocenters, as indicated in Table 3-4. The autopian algorithm was able to closely
reproduce the expert human planner's single isocenter plan for the three single isocenter
cases (patients 1-3), resulting in very conformal and homogeneous dose coverage of the
targets. For these single isocenter cases, the algorithm placed the same size isocenter at
the same location as the isocenter placed by the human planner, within the spacing limit
of the voxel grid used to describe the 3D target (lxlxl mm3 voxel size). The large PITV
for the two isocenter case autopian (patient 4, acoustic neuroma) is due to the small target
volume (1.3 cc); the autopian two isocenter plan covered only 1.1 cm3 of non-target
tissue volume, which is more significant than the magnitude of the PITY in this case. For
the single isocenter cases, the sphere packing autopian algorithm plans achieved a mean
PITV of 1.12 at an average prescription isodose level of 72%.


178
Linear accelerators may be used to produce intensity modulated beams in a
number of different ways, but these delivery methods can generally be classified into one
of two methods: variable and binary modulation (Stemick 1998). Variable modulation
involves the placement of variable thicknesses of attenuating material across the length
and width of the radiation beam to selectively attenuate the beam. Physical compensator
devices are an example of this type of beam intensity modulation, although more
sophisticated variations of this technique have been applied to inverse IMRT treatment
planning (Harmon 1994; Harmon 1998). Binary modulation involves building up a
desired intensity profile across a larger radiation field by selectively exposing small sub-
areas of the field to differing amounts of radiation from the beam. Multi-leaf collimators
can be used to deliver binary modulation of the linear accelerator beam by several
different methods. These methods include 1) step and shoot, 2) sweeping gap, dynamic
delivery, and 3) arc mode with dynamic delivery'.
The step and shoot (also referred to as segmental IMRT) delivery method
involves the delivery of multiple static, overlapping subfields to build up a desired
intensity profile (Bortfeld 1994; Boyer 1994; Gustafsson 1995). The MLC leaves remain
stationary during the time that the beam is on, and are moved to their new positions after
the subfield has been delivered and the beam stopped. One subfield is needed for each
intensity level that will be used. Figure 5-2 illustrates the delivery of an intensity
modulated field by this method.


88
considered other than depth from the targets surface. For instance, it is often possible
and preferable to use a larger diameter sphere to cover a greater volume of target, at the
expense of covering a small volume of non-target tissue. This is particularly true of the
first isocenter, if multiple isocenters are to be used to conform the dose distribution to the
target. Renormalizing a multiple isocenter dose distribution to maximum dose causes
isodose constriction as the magnitude of the maximum dose is changed by the addition of
subsequent isocenters. The use of a score function allows the algorithm to take this factor
into consideration when attempting to optimize sphere placement. Other factors may be
considered as well, such as inter-isocenter distances.
The score function is computed at each maximum valued voxel location, for each
possible circular collimator (sphere) size, and the best-scoring (numerically largest score)
voxel from the list presented to the user. The score function is the product of several
independent factors: fi, fractional target coverage; fn, a penalty factor which is a function
of the volume of non-target tissue covered; and a third factor, 3, a function of all inter
isocenter distances. In equation form, for a sphere k at a particular position, these
relations are
(3-2) Score = fi x f2 x f3,
with
_ target volume covered by sphere
(3-3) /, = w, ,
total target volume
volume of normal tissue covered by sphere
(3-4) f2 = ewr
total target volume


87
Step 5: Identify the optimal isocenter size and position (location). Ideally, a
shelling process would easily identify the deepest-lying region of the target volume as a
single voxel. However, the process described determines only an approximation to the
various layers of the target from the outside in, with each cubical voxel representing a
differential radial volume element. For the small intracranial target sizes and the 1 x 1 x
1 mnr' voxel sizes used, the discretization of the 3D target model generally does not
result in a unique identification of the deepest lying voxel. Hence, often more than one
voxel is identified as belonging to the deepest layer. In the example case we have been
following, the first application of grassfire process identifies 7 voxels with the maximum
value of 8, some of which are shown in Figure 3-17b. Interpreting the distribution of
these maximum valued voxels may be difficult, as these voxels do not always lie together
in one group. Even when the maximum valued voxels form a simple connected group,
simply taking the centroid of all such voxels will not necessarily yield the optimum
sphere location. This occurrence of multiple maximum valued voxels is especially a
problem after one or more spheres have been placed in the target volume, and many
target voxels lie at or near the surface of the target or another sphere. Using smaller
voxels does not necessarily result in unique identification of the deepest voxels, either,
but dees result in much longer computation times by increasing the number of voxels
which must be processed. To resolve the ambiguity of multiple voxels apparently lying
in the same depth, a score function was used to further distinguish the maximum valued
voxels from one another.
An additional benefit of using a score function to rank candidate isocenter
locations was realized, in that a score function easily allows other factors to be


185
No. Nome
T 7 Target
? 2 brainstem
* 8 cs avoid
Organs
i li
Organ Constraints
Dose [Gy] Vol [X] Priority
Min 0 ,100 0
Max 13 4
10
f
100.0
5.6 60.1 50.0
6.6 45.3 50.0
11 4 1 9 50.0
Loan *
. '.'-
is* Cs^yia
11.4
Add
1.9
50.0
Delete
Optimization Function
^ OH
v 1
v 2
v 3
v 4
v 5
v 6
v 7
Field Ftuence
1 Fieldl
2 Field2
3 FieldO
4 Field4
5 Fields
6 Field6
7 Field7
Fluence Map
r* A ?n : y v-
f i* - f .W
t'N,sk*£ "H /i
; Vi* /
atinns
Figure 5-4: Helios inverse planning constraint window. The dose-volume constraints on
a critical structure (cs avoid) are shown in the middle third of the window. The vertical
line represents a maximum dose constraint, while the triangle symbols represent other
dose-volume limits. The lower left window shows a plot of the score function value
versus iterations, once optimization has begun. The Fluence Map window at lower right
displays the current fluence map, if one of the fields is selected for display.


73
in the next section, while the issues of isocenter spacing and weighting are discussed
here.
The effects of isocenter spacing on the overall dose distribution may be seen in
Figure 3-13, which shows 50% and 70% isodose curves in an axial plane for two equally-
weighted isocenters at several inter-isocenter spacings, each with a standard five arc set
delivered with a 30mm collimator. For this discussion, it is helpful to consider each
isocenter as a solid, 30 mm sphere, corresponding approximately to the 70% isodose
surface of a five arc set. As a first approximation, one would expect a sphere separation
of about 30mm (the sum of the radii of each sphere) to be correct. As will be shown, this
is approximately correct, but slightly more separation is optimal.
The 70% volume in the dose distributions shown in Figure 3-13 correspond
approximately to the geometrical coverage of a 30 mm diameter sphere placed at each
isocenter. At an isocenter spacing of 40 mm, the 70% volume is slightly greater than the
sum of two 30 mm spheres, and the 50% volume (outer isodose line) is slightly larger.
The waist between the 70% isodose lines is so pronounced that the 70% isodose shells
are actually separated from one another. As the isocenters are moved closer together, the
70% isodose shell more strongly resembles two 30 mm diameter spheres. At about 32-33
mm inter-isocenter spacing, the isodose distributions are about ideal. As the isocenters
are moved closer to one another for distances less than about 32 mm, the 70% isodose
volume contracts dramatically. This is because each dose distribution is renormalized to
100% at the point of maximum dose, so that as the hotspot where the two spheres overlap
one another becomes more intense, the volume covered by 70% of this increasing
maximum dose becomes smaller and smaller. This can be seen by the rapid decrease in


292
comparison of multiple isocenter treatments with the alternative methods was needed that
would include multiple isocenter treatment plans reflecting the University of Florida
experience in producing highly conformal and homogeneous dose distributions.
To fairly compare all of these methods against one another, optimization
algorithms were implemented to produce optimized multiple isocenter, static beam, and
intensity modulated treatment plans. Using automatically optimized treatment plans for
each method avoids inadvertently biasing the comparison against one of the alternative
treatment plans, and helps to ensure that the inter-plan comparison is performed on a
consistent basis. Since radiosurgery dose distributions are characterized by many small
beams effectively focusing dose upon the target volume, a strategy of using the geometry
of beam intersections was used in lieu of explicit dosimetry to optimize the treatment
plans of each type. Multiple isocenter plan optimization was approached via a sphere
packing optimization approach. The sphere packing algorithm determines the placement
of variably-sized spheres with which the target volume is filled. The spheres indicate the
isocenter locations, collimator sizes, and number of isocenters required to generate a
multiple isocenter radiosurgery plan for an arbitrary target. Static beam plan
optimization was also performed from a geometric perspective, utilizing maximally
spaced, isotropic beam arrangements. Each isotropic beam arrangement was optimized
using a geometrically-drive beams eye view volumetric approach. The same beam
arrangements were then entered into a commercially available IMRT planning system
(CadPlan Helios, Varan Medical Systems, Palo Alto, CA) and a conjugate gradient
optimization algorithm used to generate an optimized IMRT plan. Multiple isocenter
SRS plan dose distributions were calculated using the in-house SRS planning system


117
Figure 4-2: Vector-vector angular distribution for 5 isotropic vectors generated by
Webbs computer program(Webb95) and by a locally written computer program.


197
Target axjal contours Isocenter locations and
collimator sizes
#4: 10mm
#5: 103
Figure 5-11: Multiple isocenter example case. Axial target contours are shown on the left
side, the clinical plan isocenter locations and collimator sizes are shown in the center, and
the isocenters with relative weights are shown on the right.
Figure 5-12: Isodose distribution for the eight isocenter plan in an axial plane through
the first isocenter. The 70%, 35%, and 14% isodose lines are shown, with + signs
indicating the approximate locations of isocenters 1, 2, and 4.


76
since the 70% isodose shell is larger for the adjusted weights plan, it is closer to the 35%
isodose shell, and offers a steeper dose fall off. In most radiosurgery planning situations,
the same advantage holds for adjusting the isocenter weights in order to improve the dose
homogeneity, and gradient, around the target volume. An automatic weighting tool to
perform this task has been implemented in the University of Florida treatment planning
system which iteratively adjusts the arc weights associated with each isocenter to achieve
a uniform dose to each isocenter (Foote 1999).


HMBs
102
Figure 3-22: "Very complex" clinical example patient 8, a 12.8 cm3 meningioma. The
clinical plan used for patient treatment is on the left, while a hypothetical plan generated
by the sphere packing algorithm is on the right. The clinical plan uses 20 isocenters and
68 arcs, delivered with 20, 12, and 10 mm diameter collimators. The 70, 35, and 14 % of
maximum dose isodose lines, corresponding to prescription dose, half-prescription dose,
and 20% of prescription dose, are shown in an axial plane through the center of the target
(left side figure). The PITV for the clinical plan is 1.05. The hypothetical plan uses 20
isocenters, each with a 5 arc set, delivered with 20, 12, 10, and 5 mm diameter
collimators. The 67, 38, and 13 % (of maximum dose) isodose lines are shown on the
right side figure. The PITV for the hypothetical plan is 1.27.


19
radiation particle interactions in each region of interest, often requiring lengthy
computing times to simulate the radiation transport of many (millions of) particles. This
dose calculation method is attractive because it is based on first principles of radiation
physics, and can therefore correctly account for any specific patient situation. However,
the amount of computation time generally required by present day computers limits its
usefulness in clinical situations.
Because of these difficulties in calculating absorbed dose distributions from first
principles of physics, the most common approach taken in radiation therapy has been to
use simpler models relying on direct measurements of dose. Typically, these models
involve using various radiation detectors to directly measure the dose distribution in a
water phantom, and applying corrections to the measured dose distributions to account
for differences between the water phantom and each actual patient situation. The dose
calculations in this report rely on such models of dose distributions. A brief discussion of
the dose calculation procedure for a rectangular solid water phantom follows, in order to
facilitate the explanation of the dose calculation process for clinical radiosurgery
situations.
The dose profile as a function of depth in a water phantom (setup shown in Figure
2-1) from a normally incident radiation beam is shown in Figure 2-2. This plot shows the
absorbed dose measured in water with a stationary radiation detector placed at the
isocenter of the linear accelerator. As the detectors depth to the water surface is
increased by adding water to the water phantom (which is a tank of water), there is a
greater thickness of water interposed between the radiation source and the detector, so
that the water absorbs more of the radiation beam. The curve is approximately


96
scan. The target contour information was written to an ASCII text file, which was read
by the sphere packing computer program. The sphere packing code was run with score
function weights of W| = 1.0, W2 = 1.0 to 20. The algorithm was terminated
automatically when its search-routine, described earlier, could find no voxels with a score
greater than zero. The resultant sphere packings were converted into radiosurgery
treatment plans, with a standard five arc set placed at each sphere's center with the
appropriate size collimator, and all dose distributions normalized to maximum dose. The
dose distribution for each sphere packing plan was evaluated with isocenter weights
adjusted to obtain equal isocenter doses using the isocenter weighting tool (Foote 1999).
In several cases, a "point of diminishing returns" was reached dosimetrically before the
automatic termination of the algorithm, that is, adding additional spheres (isocenters and
arc sets) as indicated by the algorithm did not provide an improvement in the dosimetric
conformity or homogeneity of the plan. In these instances, usually occurring when the
algorithm attempted to "fill in" small target areas with large numbers of 5 mm diameter
isocenters, the plan used was taken with the number of isocenters up to the point of
diminishing returns. Cumulative dose-volume histograms (DVHs) were computed for
the target volume and for all CT data set voxels for each treatment plan. An isodose
surface covering at least 95% of the target volume (as determined by target volume
DVH) was selected as the prescription isodose. Ideally, the prescription dose represents
the minimum dose to the target. However, choosing a dose based on 100% target
coverage by DVH usually results in a rather low dose level. Choosing a slightly higher
dose will cause the prescription isodose surface to slightly clip the target volume. Upon
review, this seems a reasonable approach, because the clipped, or underdosed, regions of


164
pixels. The less significant reduction in brainstem FVI and target cross sectional area are
due to the relatively low score function importance assigned to the brainstem and target
area relative to the optic nerves and eye orbits.
Dosimetric performance of the nine-beam plan is inferior to the sphere packing
multiple isocenter plan, as shown in Table 4-14, and by DVHs in Figures 4-23 and 4-24.
The nine shaped beam plan is less conformal than the multiple isocenter plan (UFIc = 65
for the multiple isocenter plan, UFIc = 54 for the nine beam plan), with a slightly less
steep dose gradient (UFIg = 56 for the multiple isocenter plan, UFIg = 52 for the nine
beam plan). Using the overall UF index, UFI, as a measure of plan quality (averaging
UFIc and UFIg), the nine beam plan, with a UFI = 53, is inferior to the multiple isocenter
plan, which has a UFI score of 61. The multiple isocenter plan covers > 95% of the
target at the 66% isodose level, while the nine-beam plan covers > 95% of the target at
the 71% isodose level. Axial and sagittal isodose plots are shown for the nine-beam plan
and the sphere-packing plan in Figures 4-25 and 4-26, respectively.
The 13 isocenter sphere packing plan would take about two and half to three
hours to treat, at the approximate rate of one isocenter with five arcs in about fifteen
minutes (Meeks 1998c). The nine field plan would be much faster to deliver with a
multileaf collimator, and would probably take no more than about 35 minutes. The time
required to plan the multiple isocenter and static beam plans is comparable. Once the
target volume was contoured and input to the sphere packing computer program, the 13
isocenter multiple isocenter plan was generated within about 45 minutes. A similar time
was required to create the nine beam plan.


158
signify a steeper dose gradient) generally improves as the number of beams is increased
from five beams or above. Thus, on the basis of dose conformity and dose gradient also,
the treatment planner should use the largest number of beams feasible.
For the purposes of this study, the maximum feasible number of beams
useful for radiosurgery with a multileaf collimator was assumed to be fifteen beams.
This limit is based upon the expectation of delivering a complete radiosurgery treatment
in about forty-five minutes to an hour. Assuming that each conformally shaped field can
be delivered in about the same amount of time as a single arc with the current circular
collimator system in use at the University of Florida, about fifteen fields could be
delivered in a forty-five minute period at a nominal rate of one isocenter with five fields
or arcs in fifteen minutes (Meeks 1998b; Meeks 1998c). Thus, unless other technical
reasons require it, fifteen isotropic beams shall be used as the maximum feasible number
of fixed beams for radiosurgery treatment planning.


183
plan that accomplishes the users goals as closely as possible while obeying the
constraints. The planning path is as follows:
1) The user selects the number of treatment beams ( CadPlan/Helios is limited to a
maximum of ten intensity modulated beams per plan) and the orientations of the beams.
2) The user enters the dose-volume goals and constraints into the system, after contouring
the target volume and all structures of interest.
3) Helios uses an interative conjugate gradient optimization algorithm based upon a
method developed by Spirou and Chui (Spirou 1998) to adjust the intensities of all of the
beamlets available to it (all beamlets which lie within a pre-defined aperture). Each
beamlet is 5 mm x 2.5 mm, which is the smallest beam element deliverable with a Varan
Millenium MLC-120 leaf MLC. Beamlet weight adjustment and optimization continues
until the algorithm converges (score function change less than a preset tolerance between
iterations) or until a specified number of iterations have been performed.
4) Each fields intensity pattern is converted into a set of dynamic MLC leaf positions
versus monitor units delivered, and saved to file for later treatment delivery (Dirkx 1998).
5) CadPlan computes the dose distribution for each intensity modulated field, using the
MLC leaf motion file for each field to determine the total fluence incident upon each
dose point.
6) Dose distributions may be displayed in the form of isodose surfaces overlaid upon the
patients image set. CadPlan will also compute dose-volume histograms of all structures
that the user has contoured to aid in treatment plan evaluation.
The process begins with the user selecting a number of beams to use, and their
orientations. The methodology of Chapter 4 was used to optimize the number and the


85
Step 4: Grassfire. The outermost layer of voxels in the target model is then
identified and removed, and the process repeated until the deepest lying voxels have been
identified. This peeling and layering, or shelling, by a "grassfire" algorithm, is so called
due to the analogy of buming-off one outer layer of the target at a time, as in a fire (Blum
1973). This edge detection process identifies the outermost layer of voxels in the 3D
model, and adds the integer 1 to each outer layer voxels value, converting all outer layer
voxels from 1 values to 2. Voxels lying one layer deeper inside the target are easily
identified as the set of 1 valued voxels which are adjacent to 2 valued voxels. These
voxels one layer deeper than 2 are assigned a value of 2 + 1 =3, with the algorithm
continuing application of this process until all 1 -valued voxels have been assigned a layer
value, with the deepest lying voxels having the largest values (Figure 3-17b). Ideally, the
deepest lying voxel in the entire target volume wrould thus be quickly identified as the
best location for an isocenter. Such a maximum-valued voxel's value should also indicate
the size of the sphere to be placed there as well, since (layer number minus 1 ) should
indicate approximately the depth from the surface (in units of voxel size). For example, a
maximum-valued voxel with a value of 7 should lie (7-1) = 6 voxels from the surface of
the target, which suggests that a sphere 12 voxels in diameter would be required to cover
this volume.


18
regions inside the patient. This section provides a discussion of general methods of dose
calculation for radiotherapy and radiosurgery situations, followed by a presentation of
methods to evaluate the efficacy of a radiation dose distribution. The general aims of
radiotherapy and radiosurgery are simple: to deliver a high, uniform dose to the target
while minimizing the radiation dose to non-target structures. There are several tools
available to the human treatment planner to quantify the degree to which these goals are
accomplished: 1) isodose curves and distributions, 2) dose-volume histograms, 3)
physical dose-volume figures of merit, and 4) biological models of tissue response to
radiation. The following sections explain the use of each of these tools in radiation
therapy and radiosurgery treatment planning, after a discussion of methods for calculating
radiation dose distributions.
Dose Calculation
The purpose of dose calculation in radiotherapy is to be able to accurately
determine the dose to target and non-target structures inside the patient. An ideal
calculation of absorbed dose to matter in all regions of interest in megavoltage external
beam radiotherapy would correctly account for all of the interactions between the
megavoltage photons in the therapy beam and the matter in the patient. The most
accurate current methods of computing the spatial distribution of the deposition of
radiation dose involve probabilistically simulating the transport of many individual
radiation beam particles from their point of emission in the radiation source, using
random number processes (hence the name Monte Carlo to describe this calculation
method). Enough particles must be simulated to provide a statistically significant tally of


25
corrections to the measured dose data (TPR, OAR, and Scp) to account for changes in the
dose at point P from the dose to the reference point at the linear accelerators isocenter.
If point P is moved away from the isocenter in any direction, these corrections are needed
due to changes in 1) the distance-of the dose point P from the source, 2) the distance of
dose point P from the central axis of the beam, 3) of changing collimator sizes, and 4) of
the changing water depth (attenuation) above point P. This dose model is simple and
accurate under conditions similar to the conditions under which TPR, OAR, and Sc,p were
measured, i.e.- a flat surfaced, homogeneous mass of water.
Radiation
source
Figure 2-5: Parameters for calculation of dose to point P in a water phantom from a single
radiation beam. OAD is the off-axis distance.
The simple dose model of equation (2-1) is used as the dose engine of the
University of Florida radiosurgery treatment planning system, and of most other


CHAPTER 7
CONCLUSION
This work presented in this report addressed the problem of prospectively
determining the best radiosurgery treatment delivery method for each new patient who is
a candidate for stereotactic radiosurgery (SRS) at the University of Florida. Currently all
radiosurgery treatments at the University of Florida are delivered with single or multiple
isocenters and multiple converging arcs with circular collimators. The introduction of the
multileaf collimator (MLC) to radiosurgery makes several new types of treatment
delivery possible, including multiple static fields, dynamic arcing technique, and intensity
modulation radiotherapy (IMRT). The purpose of this work was to provide the clinician
with guidance concerning the optimum use of each treatment delivery technique.
Previous reports in the literature addressing this problem typically favor
the alternative treatment methods such as static beams or IMRT over multiple isocenter
treatment planning. These investigations generally report that it is difficult to obtain a
conformal and homogeneous dose distribution using multiple isocenters. In the
University of Florida experience, multiple isocenter treatment planning has been used
with success to create highly conformal dose distributions while maintaining a steep dose
gradient outside of the target. Multiple isocenter treatment planning can be very
demanding and difficult, and the dosimetric results (conformity and gradient of the final
treatment plan) are highly user dependent. Poorly optimized multiple isocenter plans will
indeed be inhomogeneous and will poorly conform to the targets shape. To determine
the best treatment delivery method at the University of Florida and other institutions, a
291


273
As stated at the beginning of this chapter, the primary basis of comparison between
treatment plans is the physical dose distribution, that is, conformity and gradient.
Analysis of the simple and complex treatment plans is relatively simple based upon UF
Index scores, as multiple isocenter treatment plans (either the clinical plan used for
patient treatment or a hypothetical sphere packing autopian) rank at the top of each such
simple and complex plan comparison. Not only are multiple isocenter plans at the top of
the rankings for the simple (S) and complex (C) targtets, but the best multiple
isocenter plan generally outscores the alternative methods plans by a significant amount.
For the very complex cases, one of the multiple isocenter plans is the numerically best
(by UFI score) plan in all seven VC cases. In six of the seven VC cases, the two multiple
isocenter plans are the top two UFI scoring plans of the five considered. Of the
alternative treatment methods considered, IMRT, fifteen static beams, and four dynamic
arcs, the IMRT plans approached within two UFI points of the best plan for two of the
seven VC cases. The fifteen beam and four dynamic arc plans are consistently at the
bottom of plan rankings by UF Index score for all twelve example plans, simple,
complex, and very complex.
Plan rankings by biological indices generally follow' the treatment plan ranking by
UF Index. Multiple isocenter plans and the IMRT plans are generally ranked with low'er
NTCPs (or higher probability of no complication) than dynamic arc plans or fifteen beam
plans. Ranking the simple and complex cases by biological indices, multiple isocenter
treatment planning (or single isocenter with arcs and circular collimators for case S-2) is
generally equal or better than the alternative treatment plans. For the very complex plans,
multiple isocenter plans ranked highest by biological indices in four of the seven VC


285
HH
B
120
110
100
90
80
70
60
50
40
30
20
10
0
123456789 10-15 16-27
Number of isocenters
Figure 6-14: UF Index gradient score data for 824 SRS cases at ihe University of Florida
from 1988 to 2000. For each number of isocenters in a plan the boxplot shows the
average UFIg score plus or minus one standard deviation, along with the minimum and
maximum UFIg scores.
Table 6-31: UF Index gradient score data for 824 SRS cases at the University of Florida
from 1988 to 2000.
No. isocs.
n
UFIg-ave
std. dev.
max
min
1
470
88
10
108
61
2
135
83
12
111
58
3
74
75
14
100
32
4
47
72
14
91
38
5
20
71
11
87
44
6
18
71
10
87
49
7
10
65
10
80
44
8
12
65
11
89
42
9
14
65
11
80
43
10-15
20
59
8
70
38
16-27
9
45
3
50
41


173
dose conformity to multiple isocenter radiosurgery plans, although the dose gradient is
generally somewhat poorer for the static beam plans.


131
P(x,y,z)
(xs,ys,zs) Pnqedl^ plane
Observer point (xo,yo,zb)
Figure 4-10: Projective transform geometry
After computing the projective plane coordinates for the points belonging
to all structures of interest (Figure 4-11), a pixilated image of the beams eye view is
created by mapping each point in the field of view around the isocenter to a discrete pixel
coordinate (Figure 4-12). For simplicity, a separate pixilated image is created for the
target and for each critical structure of interest. Maintaining a separate pixilated image of
the target also facilitates the addition of beams eye view margin to the target to allow' for
setup uncertainties and beam penumbra. A grassfire algorithm adds a user-specified
margin to the targets image projected to isocenter (Blum 1973; Wagner 2000). After
the target (with added margin) pixel image is formed, a tally is conducted to check for
coincidence of on pixels in the target image with any critical structure images. A
critical structure all of whose points map outside of the field of view around the target


Harmon, J. F., Jr., Bova, F. and Meeks, S. (1998). Inverse radiosurgery treatment
planning through deconvolution and constrained optimization. Med Phvs 25(10):
1850-7.
Hartmann, G. H., Schlegel, W., Sturm, V., Kober, B., Pastyr, O. and Lorenz, W. J.
(1985). Cerebral radiation surgery using moving field irradiation at a linear
accelerator facility. Int J Radiat Oncol Biol Phys 11(6): 1185-92.
IEC (1996). International Electrotechnical Commission Report 1217: Radiotherapy
equipment-Coordinates, movements and scales.
Khan, F. M. (1994). The Physics of Radiation Therapy. Baltimore, MD, Williams and
Wilkins.
Kramer, B. A., Wazer, D. E., Engler, M. J., Tsai, J. S. and Ling, M. N. (1998).
Dosimetric comparison of stereotactic radiosurgery to intensity modulated
radiotherapy. Radiat Oncol Investig 6(1): 18-25.
Kreyszig, E. (1983). Transformation of coordinate systems and vector components.
Advanced Engineering Mathematics. New York, J. Wiley and Sons: 393-397.
Kutcher, G. J. (1996). Quantitative plan evaluation: TCP/NTCP models. Front Radiat
Ther Oncol 29: 67-80.
Kutcher, G. J., Burman, C., Brewster, L., Goitein, M. and Mohan, R. (1991). Histogram
reduction method for calculating complication probabilities for three-dimensional
treatment planning evaluations. Int J Radiat Oncol Biol Phys 21(1): 137-46.
Kutcher, G. J. and Jackson, A. (1998). Treatment plan evaluation. Treatment Planning in
Radiation Oncology. Khan, F. M. and Potish, R. A. Baltimore, Williams and
Wilkins: 281-294.
Laing, R. W., Bentley, R. E., Nahum, A. E., Warrington, A. P. and Brada, M. (1993).
Stereotactic radiotherapy of irregular targets: a comparison between static
conformal beams and non-coplanar arcs. Radiother Oncol 28(3): 241-6.
Landberg, T., Chavaudra, J., Dobbs, J., Handks, G., Johanson, K. A., Moller. T. and
Purdy, J. (1993). Prescribing, recording, and reporting photon beam therapy, ICRU
Report 50. Bethesda, MD, International Commission on Radiation Units and
Measurements.
Lawrence, T. S., Kessler, M. L. and Ten Haken, R. K. (1996). Clinical interpretation of
dose-volume histograms: the basis for normal tissue preservation and tumor dose
escalation. Front Radiat Ther Oncol 29: 57-66.
Leavitt, D. D. (1998). Beam shaping for SRT/SRS Med Dosim 23(3): 229-36.
300


Table 6-11: Maximum brainstem doses, NTCPs, and nontarget volume NTCPs for case
C-3.
Plan
Max. brainstem
dose CGy)
Nontarget
NTCP
brainstem
NTCP
clinical
15:8
8.69E-09
0.834E-06
spack
14.8
1.49E-08
0.834E-06
15 beams
13.5
1.80E-08
2.02E-06
9 beam IMRT
13.2
1.98E-08
1.07E-06
5dyn arcs
13.4
2.73E-08
2.34E-06
Prescription dose (Gy)
Figure 6-5h: Nontarget brain NTCPs as a function of prescription dose for case C-3
treatment plans. The clinical and sphere packing autopian NTCP curves lie almost on top
of one another.


97
the target are usually individual voxels extending outwards from the target contour,
which is a consequence of representing an irregular surface with discrete, cubical voxels.
By increasing the prescription isodose level in this manner, the target dose
inhomogeneity is improved-without significantly affecting the probability of tumor
control (Meeks 1998d; Verhey 1998). The prescription isodose level obtained in this
manner (dose covering > 95% of the target volume) was compared to the isodose level
covering the target volume on each axial image slice through the target. Any image
pixels of the target which were "clipped" by the prescription isodose surface were
verified to receive within a few percent of the prescription isodose (in no case did any
clipped pixels receive less than 90% of the prescription dose). For ease of comparison.
10 Gy was chosen as the prescription dose level for the phantom cases. Plan evaluation
was based upon the dose-volume data from DVHs, and also upon visual inspection of
isodose contours overlaid on each image set. Figures of merit (FOMs) based on physical
dose measurements include MDPD (maximum dose to prescription dose) and PITV (ratio
of prescription isodose volume to target volume) (Shaw 1993).
Results Phantom Targets
Summary dose-volume information for the five phantom targets is presented in Table 3-
3. When used without any human planner involvement as an autoplanning system, the
system generated plans which provided target coverage at or above the 53% (of
maximum dose) isodose shell. The mean prescription isodose level was 61 5.6%
(range 53-68%), with a mean PITV 1.23 0.10 (range 1.14 1.40).


44
Table 2-1 summarizes dose-volume and gradient information for single isocenter
dose distributions delivered with five converging arcs and 10, 20, 30, and 50 mm circular
collimators. UFIg is calculated for each dose distribution using DVH information as
described above. Since the dose gradient for single isocenter arcing dose distributions
(with circular collimators) is achieved between the 80% and 40% isodose shells, the
volumes and effective radii of the 80% and 40% isodose shells are listed, as well as the
difference between these radii. The dose gradient is steepest for the smallest collimators
(about 10 mm diameter) with an effective distance between the 80% and 40% isodose
shells of 2.4 mm and a corresponding UFIg of 106. Dose gradient gradually worsens as
the field size (collimator size) increases. At a 30 mm diameter field, what many consider
to be the upper limit on radiosurgery target size, the effective dose gradient is about 4.5
mm (UFIg ~85).
Table 2-1: Single isocenter (five converging arcs) dose-volume and gradient information
for 10-50 mm circular collimators.
Coll.
(cm3)
V80%
(mm)
Reff80%
(cm3)
V 40%
(mm)
Reff40%
(mm)
Eff. Gradient
UFIg
10
0.3
4.2
1.2
6.7
2.4
106
20
3.9
9.8
9.7
13.2
3.5
95
30
13.9
14.9
30.8
19.4
4.5
85
50
67.4
25.2
111.6
29.9
4.6
84


13
Figure 1-6: The narrow, rectangular MLC leaves conform the radiation fields shape to
approximate an irregularly shaped target's shape (solid line), as seen in this beam's eye
view (BEV).
Research Problem: Comparison of SRS Treatment Methods
The potential for improvement presented by some of these newer and more
sophisticated treatment delivery methods has spurred interest in their evaluation relative
to the more traditional linac SRS methods of multiple intersecting arcs and circular
collimators. These comparisons generally show that for small to medium (up to about 20
cm3) intracranial targets, multiple static beams offer acceptable conformity and target
dose homogeneity while offering a straightforward treatment planning process. Static
beam IMRT techniques generally performed comparably to or better than static beam
plans. A common conclusion by many of these investigators is that the use of multiple
isocenters with circular collimators results in a poor quality treatment plan, as evidenced
by the performance of the multiple isocenter plans they used to compare with the static
beam and IMRT plans. Even in reports more favorable to multiple isocenter linac SRS,
the investigators frequently note difficulty in achieving conformal and homogeneous
plans, and also note needing a large amount of time to plan and deliver these treatments.
Based on a number of recent comparisons of radiosurgery methods in the literature, one


32
one must examine and remember the isodose surface which encloses the target, and
which isodose surfaces (and to which extent) intersect nearby radiosensitive structures.
This is straightforward if somewhat tedious to do on one image slice, but the difficulty is
magnified tremendously when each slice in a large region must be examined, and the
dose area information from each slice integrated with the information from all the other
image slices. A method of comparing the volumes of dose coverage that is less error-
prone is desirable.
One commonly used solution to this problem is to use dose-volume histograms
(DVHs). DVHs are a method of condensing large quantities of three dimensional dose
information into a more manageable form for analysis. The simplest type of DVH is a
direct histogram of volume versus dose (Lawrence 1996), as shown in Figure 2-8. This
is simply a histogram showing the number of occurrences of each dose value within a
three dimensional volume. Unfortunately, the spatial information of which specific
volumes are exposed to each dose level is lost in the process of constructing a DVH. For
this reason, DVHs are generally used clinically in conjunction with the evaluation of
multiple isodose plots as mentioned earlier.
The ideal treatment planning situation is one in which the target volume receives
a uniform dose equal to the maximum dose, and the non-target volume receives zero
dose. This would be represented in a direct DVH by having a target histogram with only
one non-zero bin at 100% dose (normalized to maximum dose), and to have a direct DVH
of the non-target volume with all dose bins receiving zero dose. Plots of ideal direct
DVHs for target and non-target volumes are shown in Figure 2-8. Figure 2-9 shows
direct DVHs for target and non-target volumes for a more typical (non-ideal)


60
Radii to n
o urce
Collimated
beam ¡
v dit|S-P)
dit(S-CP)
Surface I
/ p
: %
or
depth|P) ^
I OAD(P)
-j
Isocenter 1
Figure 3-2: Radiosurgery beam dose calculation for dose at point P.
Single Isocenter Treatment Planning
A single isocenter with multiple converging arcs may be used to create a spherical
dose distribution close in size to the diameter of the circular collimator. This type of
treatment produces a conformal dose distribution for spherical or near-spherically shaped
targets. The standard set of fourteen circular collimators used at the University of Florida
covers a range of sizes from 5mm to 40mm (5, 10, 12, 14, 30, 35, and 40 mm )
diameter, projected at 100cm from the radiation source, allowing the planner to closely
match the diameter of the dose distribution to the target. As discussed in Chapter 2,
because the steepest dose gradient for single isocenter dose distributions lies between the
80% and 40% isodose shells, a collimator size should be chosen which covers the target
with the 80% isodose shell. This will ensure the steepest possible dose gradient between
the prescription and half-prescription isodose shells. A standard set of nine convergent


118
Figure 4-3: Vector-vector angular distribution for 6 isotropic vectors generated by
Webb's computer program(Webb95) and by a locally written computer program.


286
A final factor affecting multiple isocenter treatment plans with the Helios IMRT
treatment plans is the nature of the treatment planning. Multiple isocenter treatment
planning is an iterative process in which the human planner makes an adjustment to the
plan, reviews the result of the adjustment on the plan, and continues to make changes to
eventually achieve the desired result. Such forward planning has the advantage of
feedback, so that as arcs and isocenters are added to the plan to cover the target, sub-
optimal placement of an arc or isocenter will be immediately detected by its adverse
affect on the dose distribution, and corrective action taken. This is in contrast with the
inverse planning process, in which the treatment planner specifies the target volume and
any constraints such as radiosensitive structures and their dose tolerances, and allows the
automatic planning system to produce a treatment plan, generally by following some type
of iterative algorithm. The sphere packing automatic plan program discussed in Chapter
3, the static beam bouquet optimization program discussed in Chapter 4, and the Helios
IMRT planning system discussed in Chapter 5 are all examples of inverse planning
systems. Inverse planning has advantages over forward planning in that it can free a
human user from the tedious tasks associated with iteratively optimizing a treatment plan,
and that an automated system can perform tasks which are much too complicated for a
human to attempt unaided, such as optimizing the weights of many thousands of beamlet
intensities in an IMRT plan. Automated inverse planning systems, if given a consistent
set of constraints, will also tend to achieve a level of consistency in optimizing treatment
plans. However, inverse planning has at least one drawback, which is a lack of feedback
during the optimization process. For instance, when using the static beam optimization
program from Chapter 5, the user is presented with a set of optimized beam orientations


50
An example of this occurrence is shown in Figures 2-18(a) and 2-18(b), which
depict DVHs for the total intracranial volume (cubic) and several radiosensitive
structures for two hypothetical radiosurgery plans. An analysis of both sets of target
DVHs (not shown) and total volume DVHs would indicate that both plans cover the
target with similar dose homogeneity (at least 95% of the target receives >69% of
maximum dose for the first plan, and >72% of maximum dose for the second plan) with
very similar dose conformity (PITVs of 1.42 and 1.40) and gradient (UFIg of 76 and 82).
However, the two plans are not equivalent, due to the doses received by the radiosensitive
structures (e.g.-brainstem, and left and right optic nerves). One can see qualitatively that
plan 2 improves (reduces) the overall dose received by these radiosensitive structures,
since the DVH curves for the left and right optic nerve are shifted downward and to the
left in Figure 2-18(b) relative to Figure 2-18(a). However, a quantitative measure of this
effect is desirable. Normal tissue complication probability (NTCP) models have been
proposed as one such quantitative measure.


52
A four-parameter model has been suggested by Lyman (Lyman 1985; Kutcher
1991) as the basis of such an NTCP figure of merit for evaluating subtle differences in
rival SRS/SRT plans. The basic four-parameter model is
(2-6)
NTCP =
2\
y
where
(2.7) ,.D-m.w,
m'TDso(v)
(2-8) v = and
Vref
(2-9) TD(1) = TD(v) v".
Here, NTCP represents the probablity of complication for an organ of volume Vref
resulting from uniform irradiation of partial volume to homogeneous dose D. TD50 is
the tolerance dose for whole organ irradiation at which 50% of the patients receiving this
dose encounter a 50% risk of radiation induced complication within five years after
treatment. The tolerance dose for partial organ volume, v, and the entire organ volume is
given by Eq. (2-9) (Schultheiss 1983). The quantities n and m are fitting parameters
which govern the volume and dose dependence of the NTCP model. Quantity t is a
parameterization of the number of standard deviations separating the partial volume v at
dose D from TD50. TD50, m, and n model parameters used for comparisons were taken
from curve-fits (Burman 1991) to dose-volume tolerance data in the literature (Emami
1991). Since dose distributions in SRS/SRT are almost never perfectly homogeneous in
the region of interest, the four-parameter model cannot be used directly as presented.


14
could roughly expect to obtain a reasonably conformal (exposing up to about the same
volume of non-target brain tissue as target tissue to the target dose level) and
homogeneous (maximum dose not more than about twice the minimum target dose) dose
distribution for various IMRT and mMLC treatment techniques, and moderate-to-large
sized, irregularly shaped intracranial lesions. Typical multiple isocenter plans presented
fare considerably worse, though, in terms of dose conformity, homogeneity, and in
treatment planning and delivery times (Laing 1993; Hamilton 1995; Woo 1996; Shiu
1997; Cardinale 1998; Kramer 1998; Verhey 1998).
A potential problem with these comparison studies is that they do not equitably
compare the full potential of mutiple isocenter radiosurgery with circular collimators. A
qualitative inspection of the multiple isocenter dosimetric results shown in these
comparisons leads one to suspect that in many cases, sub-optimal multiple isocenter plans
are being compared with reasonably optimized static beam and dynamic MLC arcs/IMRT
plans. Although the multiple isocenter treatment plans in these comparisons in the
literature may represent a level of plan quality achievable by an average or unfamiliar
user, they do not represent the average level of plan quality in the University of Florida
experience. Unlike other evaluations readily available in the literature, an evaluation of
the best employment of an MLC in radiosurgery treatments at the University of Florida
must consider the typical quality of treatment plan that is readily achievable in the
University of Florida clinical experience.
The research problem posed is to evaluate the major SRS treatment delivery
methods that could be implemented clinically at the University of Florida, and other
institutions using the University of Florida radiosurgery system. Many claims are being


242
20
15
10
5
Dose (Gy)
Figure 6-7f: Nontarget volume DVHs for case VC-2. The prescription dose is 10.0 Gy.
1 o
0.8
E
O
>
(0
c
o
o
CO
Ll_
06
04
02
Dose (Gy)
Figure 6-7g: Brainstem DVFls for case VC-2. The prescription dose is 10.0 Gy.


287
which are used to generate a treatment plan. After the dose distribution is calculated, the
user identifies the isodose shell which satisfactorily covers the target, and sets the
prescription dose on this basis. If the dose distribution results in poor coverage of the
target, there is little the user ean do to improve the target coverage, other than perhaps to
adjust the relative beam weighting of the beam bouquet, or to choose a less homogeneous
(and less conformal) isodose surface which does satisfactorily cover the target. When
inadequate target coverage is encountered in a multiple isocenter radiosurgery plan,
however, the user may continue the forward planning process by adding arcs and
isocenters to effectively add dose only to the volumes where it is needed, until
satisfactory target coverage is attained. This ability to adapt and improve the existing
treatment plan after evaluating the plans dose distribution is a key advantage of forward
planning over inverse planning, and contributes to the effectiveness of (forward planned)
multiple isocenter treatment planning over the conformal beam and IMRT methods
presented here.
Applying the Results of this Research to New SRS Cases
The previous sections of this chapter present the dosimetric results of applying
optimized treatment planning to twelve clinical cases from the University of Florida SRS
patient database. From these cases, general conclusions were drawn about the suitability
of multiple isocenter, IMRT, static conformal beams, and dynamic arc SRS treatment
delivery. In general, multiple isocenter SRS will provide the most conformal dose
distribution with the steepest dose gradient, although in some cases IMRT and fifteen
static beams will approach the conformity and gradient attainable with multiple
isocenters. Larger targets, and targets lacking detailed shapes, are likely treatable with a


167
Sup-Inf view
AP view
Figure 4-22: AP and Superior-Inferior views of the nine isotropic beam arrangement
Dose (% max)
Figure 4-23: Target and total volume (fractional volume) DVHs for an optimized, nine
isotropic beam plan, and for a multiple isocenter (13 isocenters) plan.


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INGEST IEID E69G4P02N_GPGS4M INGEST_TIME 2013-02-14T17:42:12Z PACKAGE AA00013528_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
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39
Figure 2-14: Transaxial, sagittal, and coronal isodose distributions for five arcs of 100
degrees each delivered with a 30 mm collimator. Isodose lines in each plane increase
from 10% to 90% in 10% increments, as indicated. The ;socenter is marked with
crosshairs.
Figure 2-15: Dose crossplots through the isocenter, corresponding to the
distributions shown in Figure 2-14. The sharpest dose fall-off, from dose D to half-dose
0.5D, occurs between dose D of 80% to 0.5D = 40%, which occurs in a distance of 4.6
mm. The D to 0.5D fall-off distance is larger for 90-45% (5.1mm) and for 70-35%
(4.9mm) doses.


250
dose gradient of all five plans considered with a UFIg score of 44. The fifteen beam and
four dynamic arc plans scored at the bottom of the comparison by UFI score.
The inter-plan comparison based on NTCPs yields a similar ranking. As shown
by the NTCPs in Table 6-19-and the plot of NTCP versus hypothetical prescription dose
in Figure 6-9g, the clinical plan is superior in terms of predicted complication risk to the
nontarget brain, followed closely in order by the IMRT plan and the sphere packing
autopian. Again, the fifteen beam and four dynamic arcs plans rank at the bottom of the
comparison by NTCPs. The comparisons based on physical dose distribution and NTCPs
yields the same ranking of plans, that the clinical multiple isocenter plan is the best plan,
but that the sphere packing autopian and IMRT plans are both similar in dosimetric
quality to the clinical plan. Given the similarity in plan dosimetry, the IMRT plan
becomes a more attractive candidate when the treatment delivery aspect is considered: the
thirteen isocenter, 61 arc clinical plan required about three hours to deliver, while a nine
beam IMRT treatment of roughly the same dosimetric quality would require only about
an hour to deliver.
Table 6-18: Dosimetric figures of merit for case VC-4
Plan
Rx-dose
PITV
Vo ver (cm3)
UFIc
UFIg
UFI
Gradient (mm)
clinical
70
1.17
1.4
85
47
66
8.3
spack
66
1.53
4.3
65
56
61
7.4
9 beams
71
1.86
6.3
54
52
53
7.8
15 beams
71
1.78
6.3
56
54
55
7.6
9 beam IMRT
80
1.34
2.8
74
44
59
8.6
5dyn arcs
71
1.78
6.2
56
50
53
8.0


276
computed NTCP (on the order of 10") for the IMRT plan should not constitute an undue
risk. There is an intangible benefit in choosing the IMRT plan over the clinical thirteen
isocenter plan: an anticipated savings of about two hours in treatment delivery.
Case VC-7 is similar to VC-4 in that a multiple isocenter plan (the clinical
plan) is superior to the next highest alternative plan, the IMRT plan, but the IMRT plan
(UFI = 62) is superior to the sphere packing plan (UFI =59). The clinical multiple
isocenter plan (UFI = 67) outscores the IMRT plan by a significant amount, but ranks
slightly below the IMRT plan in terms of biological indices (probability of no
complication). The IMRT plan is very slightly superior to or equivalent to the clinical
multiple isocenter plan in terms of brainstem dose and complication risk, which is the
limiting organ in the P(NC) calculation. Thus, even though the physical dose distribution
for the IMRT plan does not have quite as good a blend of conformity and gradient, the
IMRT plan is probably a good clinical choice because it protects the brainstem (the
limiting structure) to about the same extent as the clinical plan, and also would require a
much shorter time to deliver (about an hour versus three and a half hours or more for the
clinical plan).
Based on these twelve example cases, we may conclude the following:
1. Multiple isocenter SRS treatment plans are capable of creating superior physical dose
distributions over shaped beams and static beam IMRT treatment plans for targets less
than about 15 cm3 in volume.
2. IMRT (Helios) treatment plans can approach the overall conformity and gradient (UF
Index score) of multiple isocenter plans under some conditions. For targets at least 6 cm3
in volume that do not have a great deal of fine structure, IMRT plans will compare the


181
feasibly delivered with the step and shoot technique. This is possible because the dose to
each area element of a sliding window IMRT field is proportional to the length of time
that each area element is uncovered, or exposed to the radiation source. Since this
quantity may be varied continuously, much finer control of the intensity level is possible.
The default number of intensity levels supported with CadPlan 6.15 with Helios is 320, a
figure which may be appreciated when the alternative of delivering 320 intensity levels
(subfields) with the step and shoot method is considered. Figure 5-3 shows an example
of a sliding window delivery of an IMRT field.


212
Patient S-2
Patient S-2 is a 77 vear old male with a 2.6 cm recurrent metastasis in the
j
right temporal lobe. This patient was treated clinically with a single isocenter SRS plan
using 9 arcs, delivering 17.5-Gy to the 80% isodose shell. The sphere packing autopian
program generated a single isocenter plan using an 18 mm collimator, with an isocenter
located within one image pixel (0.67 mm pixel size in the axial plane) of the isocenter
location used in the clinical plan. Orthogonal view isodose plots for all plans are shown
in Figures 6-2a through 6-e, with dose-volume figures of merit listed in Table 6-4.
Nontarget volume DVHs are shown in Figure 6-2f. For plan evaluation with biological
indices, NTCPs are listed in Table 6-5, and a plot of NTCP versus prescription dose is
shown in Figure 6-2h. For this lesion, a single isocenter SRS plan with nine arcs and a
circular collimator is markedly superior to any alternative plan, based on conformity,
gradient, and biological indices.
Table 6-4: Dosimetric figures of merit for case S-2
Plan
Rx-dose
PITV
Vover (cm3)
UFIc
UFIg
UFI
Gradient (mm)
clinical
80
1.02
<0.1
98
98
98
3.2
spack
80
1.01
<0.1
99
97
98
3.3
15 beams
72
1.32
0.8
76
74
75
5.6
9bm IMRT
81
1.37
1.0
73
71
72
5.9
5dyn arcs
72
1.42
1.1
76
72
74
5.8


15
circulated about some of the newer methods mentioned earlier of employing teletherapy
beams for SRS treatment. The University of Florida radiosurgery system has
demonstrated the ability to plan and deliver tightly conformal dose distributions to
irregularly shaped targets near radiosensitive structures, while maintaining a sharp dose
gradient away from the target towards radiosensitive structures (Meeks 1998a; Meeks
1998b; Meeks 1998c; Foote 1999; Wagner 2000). While it may be attractive to
contemplate the replacement of the current circular collimator system with more
advanced and elaborate treatment delivery methods, such a decision should be based on a
reliable study.
The purpose of this research is to investigate the optimal implementation
of a multileaf collimator (MLC) system for SRS at the University of Florida. An MLC
could be employed in several different ways: 1) dynamic conformal arc treatments with
templated arc sets, 2) multiple fixed, conformal beams, and 3) multiple fixed, intensity
modulated beams. These treatment delivery options are to be compared against multiple
isocenters with circular collimators. In order to ensure a proper comparison, a reasonable
optimization strategy is employed for each treatment delivery technique to guard against
inadvertently biasing the comparison against one or the other treatment methods. To this
end, automatic planning and optimization tools were developed for multiple isocenter
SRS and for multiple static beam SRS. Due to the fewer number of variables involved,
treatment planning for dynamic MLC arc treatments will be based primarily on standard
arc templates or sets. Chapter two provides a discussion of treatment plan evaluation
techniques and tools. Chapter three is devoted to optimal treatment planning methods
with circular collimators, chapter four to shaped beam radiosurgery planning, and chapter


277
most favorably with multiple isocenter plans based on overall conformity and gradient.
Fine structure refers to the target having small, detailed features which protrude the
main body of the target, such as seen in an axial plane with the target in case VC-1. The
degree of target shape irregularity (departure from being like a sphere) is not as important
as the degree of fine structure detail, which IMRT lacks the spatial resolution to cover in
a conformal manner.
3. A nine beam IMRT (Helios) plan will provide at worst an equivalent UF Index score
(within at least two UFI points) compared to a fifteen beam plan UFI score, and will
almost always score significantly higher in terms of UF Index than a fifteen beam plan.
4. Five dynamic MLC arcs will almost never provide dose conformity and gradient as
well as multiple isocenters, shaped beams, or IMRT. In only two of twelve cases (S-2
and VC-5) was the dynamic arc plans UFI score greater than the fifteen beam plan UFI
score, and then only by small margins.
Strengths and Weaknesses of Multiple Isocenters and IMRT
The results presented with these twelve example cases are useful in drawing
general conclusions as to the potential efficacy of IMRT (as planned with the Helios
inverse planning system), static beams, and dynamic arcing. As discussed above,
multiple isocenters generally provide a superior physical dose distribution, but there are
clinical situations in which a slightly less conformal dose distribution, or a dose
distribution with a less steep dose gradient, may be acceptable. Several factors influence
the conformity and gradient of a multiple isocenter or IMRT (Helios) dose distribution:
1) number of beams available, 2) effective spatial resolution of the intensity modulation,


95
radiosurgery isocenter being weighted equally (with respect to dose at its isocenter).
However, when attempting to obtain a homogeneous dose distribution throughout a
region containing several isocenters, it is beneficial to consider the dose contribution to
an isocenter from neighboring isocenters when selecting an isocenters weight (intensity
of dose). Hence, the weights of the isocenters placed were adjusted by the isocenter
weighting tool discussed in the previous section (Foote 1999), which iteratively adjusts
the isocenter weights in order to minimize the differences in dose delivered to each
isocenter.
Application to Phantom and Clinical Targets
The sphere packing radiosurgery planning algorithm was tested on a set of five
phantom targets, and on ten clinical cases recently treated with radiosurgery at the
University of Florida. The phantom targets were constructed of silicone molding
compound, attached to a foam support rest, and placed in a phantom head made of glass.
A BRW headring was firmly attached to the glass phantom head, using suction cups
instead of the normal pins, and a stereotactic CT scan of the glass head and target
obtained for each of the five phantoms. Transaxial CT slice thickness and spacing were
both 1mm through the region of interest in the neighborhood of the target, with a 512 x
512 in-plane pixel size of 0.67 mm.
Transaxial target contours at 1mm slice spacing were traced using the University
of Florida radiosurgery treatment planning system. Phantom targets were manually
contoured from each phantom's stereotactic CT image set. Clinical patient lesions were
manually contoured on each patient's MR image set which was fused to a stereotactic CT


215
Dose (Gy)
Figure 6-2f: Nontarget volume DVHs for case S-2 treatment plans. The prescription dose
is 17.5 Gy.
Prescription dose (Gy)
Figure 6-2g: Nontarget brain NTCPs as a function of prescription dose for case S-2
treatment plans.


OPTIMAL DELIVERY TECHNIQUES FOR INTRACRANIAL STEREOTACTIC
RADIOSURGERY USING CIRCULAR AND MULTILEAF COLLIMATORS
By
THOMAS H. WAGNER
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
2000


40
For illustrative purposes, a typical radiosurgical dose distribution, delivered with
five converging arcs and a 30 mm collimator to a hemispherical water phantom, is
depicted in Figures 2-14 and 2-15. The isodose surfaces in Figure 2-14 are normalized to
the point of maximum dose, such that 100% corresponds to the maximum dose. The
close proximity of the higher (50-90%) isodose lines to one another is a qualitative
measure of the steep dose gradient. A quantitative measure of gradient is obtained from
examining the dose profiles along orthogonal directions in the principal anatomical
planes (transaxial, sagittal, and coronal), as shown by cross-plots in Figure 2-15. This
figure shows the gradient between several dose levels, D, and half of D, in several
directions. The data show that for this single isocenter dose distribution, the steepest
dose gradient (distance between isodose shells of dose D to and 50% of D) occurs
between the 80% and 40% isodose shells, and is 4.6 mm for the 30 mm collimator and
five arcs. The steepest dose gradient is generally achieved between the 80% and 40%
isodose levels, and for this reason single isocenter dose distributions are prescribed to the
80% isodose shell (Meeks 1998c). The dose gradient is relatively independent of
direction (AP, Lateral, and Axial) between about the 90% and 40% isodose shells, since
the dose distribution is almost spherically symmetric between these isodose shells. Table
2-1 lists dose gradient information between the 80% and 40% isodose shells for single
isocenter dose distributions with 10 to 50 mm diameter collimators.
In general, however, radiosurgery dose distributions are not spherically
symmetric, and are tailored to fit the targets shape through manipulation of arc
parameters (Meeks 1998c), multiple isocenters, beam shaping, or intensity-modulation.
Additionally, dose distributions are often manipulated to steepen the dose gradient in the


11
placing differing thicknesses of dense, radiation absorbing material such as brass in a
checkerboard type pattern on a tray that is placed in the beam path. This can be done by
hand, or by use of a computer-controlled milling machine which custom machines a
single piece of radiation absorbing material into the desired shape (Purdy 1996).
Although the dose distribution around the target may be made more homogenous by such
devices, they share a disadvantage of custom blocks in excessive labor costs.
Additionally, compensators requiring manual construction can remain a source of
potential treatment errors despite quality assurance. These factors limit the usefulness
and number of fields to which such beam modifying devices may used (Hall 1961;
Sundbom 1964; Grijn 1965).
Multileaf collimators (MLCs) are mechanical beam collimating devices that can
combine some or all of the functions of beam shaping blocks, wedge filters, and custom
compensating filters discussed above (Figure 1-4). The most common type of MLC
consists of two banks of opposed leaves of radiation absorbing metal that can be moved
in a plane perpendicular to the beams direction. The MLC can be rotated with the
treatment machines collimator in order to align the leaves for the best fit to the targets
projected shape. The simplest use of an MLC is simply as a functional replacement for
custom made beam shaping blocks, in which the rectangular MLC edges are used to
approximate a continuous target outline shape (Figure 1-5) (Brewster 1995). However,
the MLC may be used in a more sophisticated fashion to form many different beam
shapes of arbitrary size and intensity (by varying the amount of radiation applied through
each beam aperture). In this manner, radiation fields with a similar dose profile as a
shaped, wedged field may be delivered using only the computer-controlled MLC. MLCs


201
differences (less than 1 cm3 or much less than 1 cm3) that do not significantly affect the
nontarget volume calculation.
Additionally, normal tissue complication probabilities (NTCPs) were computed
for the nontarget volume and-for any involved radiosensitive structures, e.g. brainstem
and optic nerves. The purpose of using biological indices is only to complement the
physical dose-volume figures of merit already discussed, and to provide additional
information to further distinguish treatment plans from one another when the plans are
numerically closely matched in terms of the physical dose distribution. The nontarget
brain NTCP calculation conservatively assumes that all volumes receiving dose outside
of the target are normal brain tissue. This conservative assumption can lead to an
overestimation of the NTCP when some of the volume receiving significant doses is bone
or other tissue with a much lower complication risk than normal brain tissue. Since the
primary focus in this investigation is to determine the treatment planning and delivery
methods that will best concentrate dose on the target while minimizing the doses to
adjacent tissue, this assumption should not introduce undue error. The NTCP
computation methodology shown in Chapter 2 was used to calculate radiosurgery NTCP
values, that is, the DVH histogram reduction method of Kutcher (Kutcher 1991) was used
to compute an equivalent organ volume for use with Lymans four-parameter NTCP
model (Lyman 1985). NTCP model parameters for all organs (except the brainstem for
case S-l) were taken from Burmans fitted parameters (Burman 1991) to Emanis organ
tolerance data (Emami 1991). Brainstem NTCP parameter data for case S-l was taken
from a more recent study recently completed on 150 acoustic neuroma patients at the
University of Florida (Meeks 2000). Each (single fraction) SRS DVH was transformed


122
Figure 4-6: Agreement between Webbs four beam bouquet (Webb 95) and locally
generated code four beam bouquet, based on total CT volume dose volume histograms.
The maximum volume disagreement between the two curves is 0.45 cm3 for doses above
5% of maximum dose.


228
15 o
o o
0.0 2.5 5 0
Dose (Gy)
clin-nontarg
spack-nontarg
IMRT-nontarg
15bm-nontarg
5dynarcs-nontarg
10.0
15 0
17.5
20 0
22.5
Figure 6-5f: Nontarget volume DVHs for case C-3 treatment plans. The prescription
dose is 12.5 Gy.
Dose (Gy) Dose (Gy)
Figure 6-5g: Brainstem DVHs for case C-3 treatment plans. The prescription dose is 12.5
Gy. The plot on the right is zoomed in to the high-dose, small volume portion of the
DVHs. Both multi-isocenter plans (clinical and spack autopian) have higher peak
brainstem doses than the other plans.


295
guidelines developed in this work. To perform such a comparison would require only
that the target volume and any radiosensitive structures be delineated on the patients CT
or MR image set and saved to file. The computer optimization algorithms for multiple
isocenter and static beam optimization (the static beam optimization output is also used to
optimize the beam directions for the IMRT treatment plans) can automatically perform
the remainder of the planning optimization process within several hours. It is also
possible to perform this process on non-stereotactic MR images the day before a patients
radiosurgery treatment, and to use the image fusion process to transform the optimized
plans to stereotactic coordinates on the day of treatment. If desired, only the sphere
packing computer program can be executed in order to gain an idea of the targets
complexity by the number of isocenters used by the automatic planning system in its
plan. This abbreviated process would require even less time than generating the
additional static beam and IMRT treatment plans as mentioned above. Thus, this work
addresses the research question in a general manner, based on the clinical examples
presented in this report, and in a patient-specific manner by providing tools for
radiosurgery treatment plan optimization on a case-by-case basis.
In conclusion, this work demonstrates the ability of multiple isocenter
SRS to produce a highly conformal dose distribution to an arbitrary target, while
maintaining a steep dose gradient outside of the target volume. Because of the lengthy
treatment delivery times and the degraded dose gradient suffered by multiple isocenter
radiosurgery treatment plans, IMRT treatments become competitive with multiple
isocenter treatments for large and/or very irregularly shaped lesions which would require
many isocenters to cover the target. Although in general multiple isocenters will produce


116
Observation number
Figure 4-1: Vector-vector angular distribution for 4 isotropic vectors generated by
Webbs computer program(Webb95) and by a locally written computer program. The
plot is a graph of all of the cells (the angle value on each cell counts as one observation)
in Tables 4-la and 4-lb, sorted by magnitude.


248
u
o
0)
E
3
O
>
ro
o
Dose (Gy)
Figure 6-8f: Nontarget volume DVHs for case VC-3. The prescription dose is 15 Gy.
Prescription dose (Gy)
Figure 6-8g: Nontarget volume NTCP as a function of prescription dose for case VC-3.


This work is dedicated to my loving wife and friend, Nanette P. Parratto-Wagner.


249
Table 6-17: Nontarget volume NTCPs for case VC-3
Plan
NTCP
clinical
6.46E-06
spack
1.05E-05
15 beams
2.00E-05
9 beam IMRT
5.59E-06
5dvn arcs
j
2.66E-05
Patient VC-4
Patient VC-4 is a 59 year old male with an 8.0 cm3 parasagittal meningioma in the
right vertex area. This patient was treated clinically with a thirteen isocenter SRS plan
using 61 arcs, delivering 12.5 Gy to the 70% isodose shell. The sphere packing autopian
used sixteen isocenters with 72 arcs. Orthogonal view isodose plots for all plans are
shown in Figures 6-9a through 6-9e, with dose-volume figures of merit listed in Table 6-
18. Nontarget volume DVHs are shown in Figure 6-9f. NTCPs for the nontarget brain
volume are listed in Table 6-19, and a plot of nontarget brain NTCP as a function of
prescription dose is shown in Figure 6-9g.
This case is somewhat similar to case VC-3, in that on the basis of UF Index
score, both the clinical and sphere packing multiple isocenter plans are numerically
superior to the nine beam IMRT plan (and the other alternative plans, as well), but the
nine beam IMRT plan (UFI = 59) is within two index points of the sphere packing
autopian (UFI = 61) and is therefore roughly comparable to the sphere packin plan on this
basis. The clinical multiple isocenter plan is the most conformal of all the plans, with a
UFIc score of 85, although the sphere packing autopian has the steepest dose gradient
with a UFIg score of 56. As with case VC-3, the nine beam IMRT plan has the poorest


218
Figure 6-3d: C-l nine IMRT beam plan orthogonal view isodoses. The 83%, 41%, and
17% isodose lines are shown in the axial, sagittal, and coronal views.
Figure 6-3e: C-l five dynamic MLC arcs plan orthogonal view isodoses. The 74%, 37%,
and 15% isodose lines are shown in the axial, sagittal, and coronal views.
Table 6-7: Nontarget brain NTCP values for case C-l
Plan
NTCP
clinical
1.48E-08
spack
1.63E-08
15 beams
3.39E-08
9 beam IMRT
3.23E-08
5dyn arcs
3.96E-08


282
which depicts the three dimensional dose clouds for multiple isocenter, IMRT, and
dynamic arc treatment plans for case VC-1.
Perspective view of patient Cut-planes showing Close-up of sphere
sphere packing 17 packing 17 isocenter
isocenter autopian dose cloud (67%).
dose cloud PITV=1.31
9 beam IMRT
prescription isodose
cloud
PITV = 1.39
5 dynamic MLC arcs
prescription iso dose
cloud
PITV = 2.10
Figure 6-13: Three-dimensional representations of the prescription isodose surfaces for
example case VC-1.
The target volume for case VC-1 is a very irregularly shaped cavernous sinus
meningioma, with several narrow projections emanating from the main part of the target.
The leftmost three panes in Figure 6-13 show the targets location inside the patient, and
the middle pane shows the sphere packing dose distribution. Note that the dose
distribution closely matches the intricacies of the irregular target surface. The IMRT plan
dose cloud also covers the target, but since the spatial resolution of the IMRT dose cloud
is more limited than that of the multiple isocenter dose distribution, some of the
concavities near the target are also covered, resulting in a less conformal dose
distribution. The four dynamic arc plan dose cloud is shown at far right, which is even
less well able to conform to the shape of the target. The dynamic arc dose cloud is over
twice the volume of the target. This figure is a graphical representation of how multiple
isocenters (manually-planned IMRT as presented in Chapter 5) are able to cover even
very small target features in a conformal manner. This ability, combined with a typically
steep dose gradient, makes it very difficult to surpass the overall conformity and gradient


245
Patient VC-3
Patient VC-3 is a 19 year old male with a 15.3 cm3 dural Ewings sarcoma. This
patient was treated clinically with a twenty isocenter SRS plan using 88 arcs, delivering
15 Gy to the 70% isodose shell. The sphere packing autopian used twenty isocenters
with 84 arcs. Orthogonal view isodose plots for all plans are shown in Figures 6-8a
through 6-8e, with dose-volume figures of merit listed in Table 6-16. Nontarget volume
DVHs are shown in Figure 6-8f. NTCPs for the nontarget brain volume are listed in
Table 6-17, and a plot of nontarget brain NTCP as a function of prescription dose is
shown in Figure 6-7g.
The top three scoring plans based on dose conformity and gradient (UFI index) in
order are the clinical multiple isocenter plan, the sphere packing autopian, and the nine
beam IMRT plan. All three of these plans are numerically close (57, 56, and 55 UF
Index points, respectively). The IMRT plan is the most conformal of these three plans
(Table 6-16, Figure 6-8f), but has the poorest dose gradient of all five plans which greatly
reduces its UFI score. All NTCPs for each treatment plan are in the range of 10'6 to 10'5
at the prescription dose level of 15 Gy. When ranked from the lowest to highest (best to
worst) in terms of NTCP, the order is the IMRT plan, clinical twenty isocenter plan,
sphere packing twenty isocenter autopian, four dynamic arcs, and fifteen beams. As
shown by the NTCP values in Table 6-17 and the plot of NTCP versus hypothetical
prescription dose in Figure 6-8g, the IMRT and clinical multiple isocenter plans are close
to one another in terms of their predicted NTCP, so that both plans are roughly equivalent
on this basis. Thus, for case VC-3, the IMRT plan is approximately even with both
multiple isocenter plans (clinical and sphere packing autopian) based on the physical dose


186
The dosimetric situation for a set of beams and associated beamlets is represented
by a set of matrices and vectors. Consider a single volume irradiated by j beamlets (each
intensity modulated beam is composed of many small beamlets). For this single
structure, the dose the i-th point or voxel from the j-th beamlet may be written in vector
form as d¡,
(5->> d=arx'
(5-2) a={aij},
and
where d, is the dose to the i-th point, Xj is the intensity of the j-th ray, and a¡j is the dose
deposited to the i-th point for a unit intensity of the j-th ray. The dose-deposition
coefficients ay are functions of the geometry between beamlet j and point i (Spirou
1998).
The score function that the conjugate gradient optimization algorithm seeks to
minimize, F0bj, is
where p is the prescribed dose, Wj is the constraint weight, and ^ is a constraint flag,
which is 1.0 if the constraint is violated, and 0.0 if the constraint is not violated. The first
term in equation (5-4) is a summation of the square of the difference between the dose to
all Nt target points and the prescribed dose to the target p. The second term is a
summation over all of the critical structure points, Nc, each weighted according to the


29
Figure 2-7: Tissue deficit due to an irregularity (inhomogeneity) in patient surface.
The assumption that the interior of the patient is a homogeneous, water equivalent
material can also lead to errors between the calculated (equation (2-1)) and actual dose to
a point in some cases. For instance, the dose model in equation (2-1) does not account
for the changes in beam attenuation due to differences in electron density from that of
water, such as those encountered near air cavities (e.g.- sinuses) and bone. Although
methods such as the Batho power-law correction (Khan 1994; Ahnesjo 1999) exist to
correct calculated doses for these effects, such corrections are generally not needed to


65
The standard nine arc set is well suited for conforming the high dose region to the
target, if the target is spherically shaped. However, in the case of an ellipsoidal shaped
target, or of an adjacent critical (radiosensitive) structure, it may be necessary to alter the
shape and gradient of the dose distribution to improve dose conformity and gradient. The
University of Florida dose-planning algorithm (Figure 3-1) guides the selection of
appropriate isocenter arc parameters to manipulate to obtain optimal dose conformity and
gradient. The nine arcs in the standard set may be manipulated to change the shape of the
high (80%) isodose shell from a spherical shape to an ellipsoidal shape with the major
axis inclined in the sagittal or coronal planes.
The arc elimination tool or technique may be used to steepen the dose gradient
in a lateral or axial (along the cranial-caudal axis) direction. This is accomplished by
eliminating arcs that are aligned in the direction along which a steeper dose gradient is
needed. Figure 3-8 shows how elimination of the lateral arcs changes the overall dose
distribution, causing a steeper dose gradient laterally from the isocenter, and making the
dose gradient less steep in the inferior/superior direction. This technique is appropriate to
protect a radiosensitive structure that lies medial or lateral to the target at isocenter.
Figure 3-9 shows an application of this technique to steepen the dose gradient in an
oblique direction. Elimination of the most superior arcs would likewise steepen the
superior-inferior dose gradient, at the expense of a less steep lateral dose gradient. The
arc elimination tool allows the planner to selectively steepen the dose gradient in the
coronal plane.
The dose gradient may be altered in the sagittal plane by altering the start and stop
angles of each arc, and/or by altering the span of each nominal 100 degree arc. Figure 3-


37
evaluate the treatment plans. The next section discusses physical dose volume metrics
for treatment plan comparison.
^ 30.0
CA
c 25.0
> 20.0
1 15.0
i-
V 10.0
£
3 5.0
o
> 0.0
0 10 20 30 40 50
Dose (relative units)
Figure 2-13: Crossing cumulative DVH curves
Physical Dose-volume Figures of Merit
The three properties of radiosurgery and radiotherapy dose distributions which
have been correlated with clinical outcome are dose conformity, dose gradient, and dose
homogeneity (Meeks 1998a). The conformity of the dose distribution to the target
volume may be simply expressed as the ratio of the prescription isodose volume to the
target volume, frequently referred to as the PITY ratio (Shaw 1993):
(2-2) PITY = Prescription isodose volume / target volume.
Perfect conformity of a dose distribution to the target, i.e. PITY = 1.00, implies that the
prescription isodose volume exactly covers the target volume while covering no non-


28
since point 2 is not as deep as point 1 (point 2 has a numerically larger TPR than point 1).
For a typical adult patient with a cranial radius of curvature of about 7.5 cm, the tissue
deficit from the center of a 10x10 cm square field is about 1.5 cm, which corresponds to
a dose error of about 6% (for 6 MV photons attenuated at about 4% per cm of depth) at
point 2, if the TPR for central axis point 1 is used instead. The magnitude of the tissue
deficit increases as the field size increases, and decreases for smaller field sizes. For a 40
mm diameter circular field, the tissue deficit for the same radius of curvature is only
about 2.6 mm, corresponding to slightly less than a 1% dose error. The tissue deficit and
dose error for a 20 mm diameter field are only 0.6mm and 0.2%, respectively. Thus, for
small (< 40 mm diameter) radiosurgery fields, the effect of surface irregularity
(inhomogeneity) can be neglected without introducing undue error (several percent) into
the dose calculation (Ahnesjo 1999).


241
Figure 6-7c: VC-2 fifteen beam plan orthogonal view isodoses. The 72%, 36%, and 14%
isodose lines are shown in the axial, sagittal, and coronal views.
Figure 6-7d: VC-2 nine IMRT beam plan orthogonal view isodoses. The 77%, 38%, and
15% isodose lines are shown in the axial, sagittal, and coronal views.
Figure 6-7e: VC-2 five dynamic arcs plan orthogonal view isodoses. The 75%, 38%, and
15% isodose lines are shown in the axial, sagittal, and coronal views.


187
critical structure weighting set by the human user. The optimization process
systematically changes the beamlet intensities, x, to find the combination of beamlet
intensities which minimizes F0bj in equation (5-4). At each iteration k, the conjugate
gradient optimization algorithm determines its next directional move (the next x vector),
(At 4-1) b
L by examining the variation in score function with changes in x. The
multidimensional direction in which X will be moved is
F*Vv f*<*>
(5-5) r"-'Fmnt-vr1
Fobi(x
obj
(x
where VF0bj is the gradient of the score function.
The next iterations beamlet intensities, x are found by
/C £\ (*+0 (*) 7 (* + 0
(5-6) x =x +t h
where t is the iteration step size. Step size t is calculated at each iteration to move x to
the anticipated minimum of F0bj.
Example Nine Beam and Nine Intensity-Modulated Beams for Meningioma
A clinical example is used here to demonstrate how an optimized IMRT plan is
developed using the methods presented in this chapter and the previous chapter. This
patient has a 5.4 cm3 meningioma located near the brainstem, and was treated at the
University of Florida with a ten-isocenter radiosurgery plan delivering 10.0 Gy to the
70% isodose shell. A hypothetical treatment plans using nine conformal, equally
weighted, and isotropically arranged beams was developed for comparison purposes,
using the methodology discussed in Chapter 4. The same nine beam directions were used


112
where 9¡j is the plane angle between vectors i and j, and is computed from the
vector dot product of each vector by
0 = cos
(4-3)
An arrangement of N beams is represented as 2N vectors, since each beam has
one vector (ray) representing the beam's entrance vector, and one vector representing the
beam's exit vector. The optimization process proceeds through three stages of iteration.
The first stage (performed for ml iterations) consists of generating sets of randomly
oriented vectors, and keeping the arrangement which maximizes the score function in Eq.
(4-1). In the second optimization stage (performed for m2 iterations), each vector in the
best arrangement found from the first stage, is randomly and systematically adjusted by a
fixed amount, such as five or ten degrees. As in the first stage, the current best
(maximum score function value in eq.(4-l)) arrangement is saved and updated with each
iteration. In the third and final stage (performed for m3 iterations), successively smaller
and smaller random adjustments are made to the current best beam arrangement, until m3
iterations have been made and the size of the adjustment has fallen to zero. Webb
reported using ml = 200k, m2 = 300k, and m3 = 500k. When optimizing arrangements
of more than eight beams, it is necessary to use larger numbers of iterations, however, to
allow the optimization algorithm sufficient opportunity to maximize the score function.
Using ml = 4.0 x lO3 to 8.0 x lO3, m2 = 6.0 x 10' to 1.2 x 106, and m3 = 8.0 x 10'" to 1.6 x
10b provided satisfactory results which were equivalent to the beam arrangements
obtained from using even larger numbers of ml, m2, and m3 iterations.
f
V,V;


222
Figure 6-4d: C-2 nine IMRT beam plan orthogonal view 76%-38%-15% isodoses.
Figure 6-4e: C-2 five dynamic MLC arcs plan orthogonal view 72%-36%-14% isodoses.


using multileaf collimator field shaping over custom blocks, since multiple fields can be
treated remotely (radiation therapist is not required to enter the room to change each field
block) in principle with a multileaf collimator and a computer controlled linear
accelerator. Therefore, beam- aperture shaping in this report will be performed with an
available miniature multileaf collimator (Meeks 1999). Miniature multileaf
collimators, or mMLCs, are generally regarded as those MLCs with leaf widths of 1.6 -
5.0 mm at isocenter, compared to a more typical 10mm leaf width projected to isocenter
for multileaf collimators used in general radiotherapy (Leavitt 1998; Meeks 1999). One
mMLC (Welhofer Dosimetrie, Schwarzenbruck, Germany) anticipated for use at the
University of Florida is shown in Figure 1-4. The unit has 20 pairs of tungsten leaves
which project to 4.5mm wide at isocenter, with a maximum achievable field size of 9x9
cm2. Each leaf may travel 2.0 cm across the beams central axis (Meeks 1999). This
mMLC is mounted on the linear accelerator as a tertiary collimator, downstream of the
accelerators secondary collimators.
Unlike a custom made block, which defines a continuous beam aperture, a
multileaf collimator approximates the beam aperture shape with rectangular leaf shapes.
Figure 4-13 shows an example beams eye view (BEV) of an irregularly shaped target
and an ideally-shaped beam aperture defined by a custom block. The target (gross tumor
plus suspected microscopic disease, referred to as the Clinical Target Volume, CTV, in
ICRU Report 50 (Landberg 1993)) is shown in light gray in the expanded view on the
right side, while the aperture defined by the block lies inside the crosshatched area. The
beam aperture defines a radiation field that covers the target plus an additional margin to
account for errors in target localization, patient setup, and for decreased target dose due


211
Prescription dose (Gy)
Figure 6-1 j: Plot of brainstem NTCP versus prescription dose (Gy) for case S-l. The
clinical plan and the sphere packing autopian curves lie to the right of the alternative plan
NTCP curves.


3
millimetric precision using a minimally invasive headring that attached to each size of
collimator helmet (Wasserman 1996).
Linear accelerators (linacs) were first used for radiosurgical use in the 1980s.
Betti and Derichinsky reported using a linear accelerator with multiple fixed, isocentric
beams in 1983 (Betti 1983). Several investigators reported using multiple converging
arcs with a linac by 1985 (Colombo 1985; Hartmann 1985). By fitting an isocentric
linear accelerator with circular collimators, multiple beams and/or arcs of radiation could
be made to converge upon the machines center of rotation, where the patients tumor had
been positioned. By such a means, dose distributions very similar to those of the gamma
knife could be produced with megavoltage photons from a linac, rather than from the
decay of radioactive sources. A significant practical difficulty of using an isocentric
linear accelerator, however, lies in overcoming the mechanical inaccuracy of rotation
inherent in heavy rotating equipment. A common upper limit on allowable mechanical
error (wobble) of rotational center of linear accelerator gantrys is 2mm, plus an
additional 2mm error in the treatment couch rotation accuracy. Added in quadrature, the
resultant total possible error between the expected and actual radiation isocenter can be as
high as 2.8 mm, about an order of magnitude larger than the mechanical error associated
with gamma unit treatments. If the mechanical inaccuracy of the treatment machine
cannot be resolved, the radiosurgeon would need to increase the size of the radiation
therapy beam in order to ensure that the target being treated is completely covered.
Addition of even one or two millimeters of extra margin to a radiosurgical treatment
beam has a markedly undesirable effect, however, by drastically increasing the volume
treated to the target (prescription) dose. It is therefore strongly to the radiosurgeons


79
Four 14mm isocenters spaced at 14mm, total normalized dose,adj(solid),unadj(dashed)
1
09
0.0
0.7
a> 0.6
CO
5 0.5
a. 0 4
0.3
0.2
0.1
0
k / v \
i V V \
51 6 mm
Adjusted weights
44 7 mm
Unadjusted (equal)
\ weights
/
V
\
25 50 75 100
Lateral distance (mm)
125
150
Figure 3-14(c): Total dose from four isocenters for the plans shown in Figures 3-9(a) and
3-9(b).
Figure 3-15: Axial plane dose distribution (70%, 35%, and 14% isodose lines shown) for
four 14 mm isocenters. (A) all weights equal, (B) weights adjusted to obtain equal
isocenter doses.


49
inhomogeneity in linear accelerator radiosurgery dose planning (Meeks 1998c; Meeks
1998).
Biological Models
In planning stereotactic radiosurgery (SRS) or stereotactic radiotherapy (SRT)
treatments, the object is to minimize the dose to radiosensitive non-target structures while
covering the target with a conformal and homogenous dose distribution. In multiple
isocenter SRS planning, non-target structures are protected primarily by the steep dose
gradient inherent in stereotactic irradiation. In single isocenter SRS plans, several
techniques (arc start and stop angles, couch angles, and differential collimators) are
generally used to enhance dose conformity and to steepen the dose gradient in the
direction of especially radiosensitive structures, such as the brainstem (Meeks 1998a;
Meeks 1998; Foote 1999). Such treatment plans can be evaluated on the basis of dose
gradient and conformity, which can be determined from dose-volume histograms of the
target and surrounding volumes (Shaw 1993; Bova 1999). When multiple critical
structures are to be spared as part of the optimization process, such as in the problem of
deciding beam orientations in conformal beam SRS and SRT, the treatment plan
evaluation problem can shift awray from determining obvious differences in the
conformity and gradient of competing plans. In such cases, biological indices, such as
the normal tissue complication probability (NTCP), may be used to evaluate rival
treatment plans, each of which demonstrates comparable dose gradient and conformity to
the target.


204
Patient S-l
Patient S-l is a 74 year old female with a 1.8 cmJ acoustic schwannoma. This
patient was treated clinically with a three isocenter SRS plan with 11 arcs, delivering 12.5
Gy to the 70% isodose shelL The sphere packing autopian program generated a three
isocenter plan using 11 arcs, with a single arc isocenter being used in lieu of a full arc set
on the third isocenter. Table 6-2 lists physical dose-volume figures of merit for the
multiple isocenter SRS and alternative treatment plans. Table 6-3 lists NTCP values for
each treatment plan. Figures 6-la through 6-le show orthogonal view isodose plots of
prescription dose, half-prescription dose, and twenty percent of prescription dose for each
plan. DVHs for each plan (target fractional volume, nontarget volume, and brainstem
fractional volume) are shown in Figures 6-If, 6-lg, and 6-lh, respectively.
Table 6-2: Dosimetric figures of merit for case S-l
Plan
Rx-dose
PITV
Vover (cc)
UFIc
UFIg
UFI
Gradient (mm)
clinical
70
1.13
0.2
89
91
90
3.8
spack
67
1.29
0.5
77
91
84
3.9
9beams
72
1.42
0.8
70
64
67
6.6
15 beams
71
1.54
1.0
65
70
68
6.0
9 beam IMRT
66
1.44
0.8
70
73
71
5.7
5dyn arcs
73
1.46
0.8
68
66
67
6.4


268
Prescription dose (Gy)
Figure 6-12j: Probability of no complication, P(NC), as a function of prescription dose
for case VC-7. The P(NC) curves for the clinical multiple isocenter plan and the nine
beam IMRT plan lie almost on top of one another.
Table 6-25: NTCPs and probability of no complication, P(NC), for case VC-7 at the
clinical prescription dose of 17.5 Gy
Nontarget Brainstem
Plan
NTCP
NTCP
P(NC)
clinical
3.08E-05
0.152
0.848
spack
7.81E-05
0.499
0.501
15bms
2.36E-04
0.544
0.456
IMRT
5.05E-05
0.151
0.849
5 dyn arcs
7.57E-05
0.273
0.727
Comparison of Alternative SRS Treatment Delivery Methods to Multiple Isocenter SP-S
with Circular Collimators
Quantitative UF Index and biological index (NTCP and probability of no
complication) results from comparing rival treatment plans for the twelve example cases
are reproduced in Tables 6-26, 6-27, and 6-28 and 6-29. In each of these tables, each


Foote, K. D., Friedman, W. A.. Meeks, S. A., Wagner. T. H., Buatti, J. M. and Bova. F. J.
(1999). Radiosurgical software and dose planning. LINAC and Gamma Knife
Radiosurgery. Germano, I. M. Park Ridge, IL, American Association of
Neurological Surgeons: 31-56.
Fowler, J. F. (1989). The linear-quadratic formula and progress in fractionated
radiotherapy. Br J Radiol &2(740): 679-94.
Friedman, W. A. and Bova, F. J. (1989). The University of Florida radiosurgery
system. Surg Neurol 32(5): 334-42.
Friedman, W. A., Bova, F. J., Buatti, J. M. and Mendenhall, W. M. (1998). Linac
radiosurgery : a practical guide. New York, Springer.
Friedman, W. A., Bova, F. J. and Spiegelmann. R. (1992). Linear accelerator
radiosurgery at the University of Florida. Neurosurg Clin N Am 3(1): 141-66.
Grandjean, P., Lefkopoulos, D., Platoni, K., Meriene, L., Viellevigne, L., Touboul, E.,
Schlienger, M. (1997). A conformal stereotactic radiosurgical procedure based on a
direct dosimetric optimizer. International Stereotactic Radiosurgery Society, 3rd
Meeting. Kondziolka, D. Madrid, Karger. 2: 214-227.
Grijn, J. v. d. (1965). The construction of individualised intensity modifying filters in
cobalt 60 teletherapy. Br J Radiol 38(455): 865-70.
Gustafsson, A., Lind, B. K., Svensson, R. and Brahme, A. (1995). Simultaneous
optimization of dynamic multileaf collimation and scanning patterns or
compensation filters using a generalized pencil beam algorithm. Med Phys 22(7):
1141-56.
Hall, E. J. (1994a). Time, dose, and fractionation in radiotherapy. Radiobiology for the
Radiologist. Philadelphia, PA, J.B. Lipponcott: 211-229.
Hall, E. J. (1994b). Dose-response relationships for normal tissues. Radiobiology for the
Radiologist. Philadelphia, PA, J.B. Lipponcott: 45-73.
Hall, E. J. and Oliver, R. (1961). The use of standard isodose distributions with high
energy radiation beams the accuracy of a compensator technique in correcting for
body contours. Br J Radiol 34: 43.
Hamilton, R. J., Kuchnir, F. T., Sweeney, P., Rubin, S. J., Dujovny, M., Pelizzari, C. A.
and Chen, G. T. (1995). Comparison of static conformal field with multiple
noncoplanar arc techniques for stereotactic radiosurgery' or stereotactic
radiotherapy. Int J Radiat Oncol Biol Phys 33(5): 1221-8.
Harmon, J. F. (1994). Inverse radiosurgery treatment planning through deconvolution
and constrained optimization, PhD dissertation, Nuclear Engineering Sciences,
University of Florida,Gainesville, FL.
299


I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor
Professor of Nuclear and Radiological
Engineering
Francis J. Bova, Chairman
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Wesley E. Bench, Co-chairman
Associate Professor of
Nuclear and Radiological Engineering
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
IX. Meeks
Assistant Professor of
Nuclear and Radiological Engineering
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
M. Buatti
'Associate Professor of Radiation
Oncology
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
f (feuJL
Beverly L. Brechner
Professor of Mathematics


58
posterior direction, multiple isocenters are used to conform the dose distribution to the
shape of the lesion. Due to the difficulty of standardizing this multiple isocenter planning
process, the major emphasis in this chapter is on a geometrically based and automated
method (sphere packing, developed in a joint project with the University of Florida
Department of Mathematics) which attempts to generate conformal multiple isocenter
dose distributions.
University of Florida
Treatment Planning Algorithm for Optimization
Is target acjacent to very radiosensitive neural structure9
Vos NO
Maximize dose gradient
1 Crtical structure interior, superior, medial :.r
ateral to 'arget use arc elimination tool
2 Critical structure anterior or posterior to target
use arc start and stop angle
Maximize conformant1/
.vitnout degrading optimized dose
gradient
Maximize :onformaltt>
Lesion snaoe >s
*
Spncric.il
equallv spaced arcs
Nor-ellj£SP_.aa! ^regular.
Use mullioie socenters
Eilipsoicta!
/principal axis in me
t Coronal plane use arc
.veigntmq .elimination tool or
ditterentiai collimator sizes1
2 Sagittal plane use arc star*
and stop angie too;
j Axiai piane use multiple
socenlers
Dose selection
Figure 3-1: University of Florida radiosurgery planning algorithm
Circular Collimator SRS Dosimetry
The dose at any point P due to a single, stationary beam that is shaped with a
circular collimator of diameter coll is computed at any point in the stereotactic space by
f V
(3-1) Dose(P) = k MU TPR(coll, depth(P)) OAR{P) £
\dist s-cp J


275
requires multiple isocenters to treat successfully with circular collimators, as presented in
the University of Florida dose planning algorithm for circular collimators in Chapter 3.
This target had no significant concavities in its shape, and was therefore covered with a
very conformal dose distribution by the shaped beam and IMRT treatment plans. The
primary purpose served by intensity modulation in this case was to limit dose to the
radiosensitive brainstem. Case VC-2 could probably have been equally well treated with
a nine beam IMRT plan, a fifteen beam plan, or four dynamic arcs, as with the clinical
multiple isocenter plan.
The target for case VC-3 is a large, flat, irregular shape without any
adjacent radiosensitive structures. The clinical multiple isocenter plan, a nine beam
IMRT plan, and the sphere packing autopian were all approximately equivalent (within
two UFI points) based on the physical dose distribution. The clinical plan was only very
slightly better than the IMRT plan based on computed NTCP. The sphere packing
autopian ranked slightly below the clinical and IMRT plans in NTCP. Case VC-3 would
also probably be equally well treated with IMRT as with multiple isocenters, irrespective
of treatment delivery duration considerations.
Case VC-4s target is an oblong shape with the major axis aligned in a
sagittal plane, with numerous, irregular extensions protruding from its sides. The IMRT
plan (UFI = 59) is almost equivalent to the sphere packing plan (UFI = 61), but is still
significantly below the clinical multiple isocenter plan in terms of UFI. The IMRT plan
ranks slightly above the sphere packing plan based on NTCP, but still ranks below the
clinical plan on this basis. Since the prescribed dose for this benign tumor (meningioma)
is relatively low and there are no adjacent radiosensitive structures, the slightly higher


63
Gantry 30
Figure 3-5: Linac couch (rotated clockwise) at 55 degrees, and gantry arcing between 30
and 130 degrees.
Gantry 330
Figure 3-6: Linac couch at 305 degrees, and gantry arcing between 230 and 330 degrees.


278
3) the score function driving the optimization, 4) the number of isocenters that will be
required to cover the target if multiple isocenters are used, as the dose gradient degrades
as more isocenters are used, and 5) whether the planning occurs in a forward, iterative
fashion, or is purely inverse planning.
The number of beams used in the treatment plan affects the dose gradient, with
more beams providing a steeper dose gradient as discussed in Chapter 4. Single isocenter
SRS represents a limiting case of this principle, where a set of nine convergent arcs
effectively places almost one hundred beams dispersed uniformly over a 2;t steriadian
solid angle onto the target, providing a very steep dose gradient. Although static, shaped
beam treatment plans in CadPlan can be constructed with more than ten beams per plan,
CadPlan and Helios limit IMRT plans to a maximum of ten beams (nine IMRT beams
were used in all of the IMRT plans presented). As shown in the dose-volume figure of
merit tables for cases VC-1 through VC-7, adding intensity modulation to an existing set
of conformally shaped beams improves the overall conformity and gradient of the dose
distribution over that of just the conformally shaped beams, by an average of 5.8 UFI
points (minimum 4, maximum 9). Assuming that a similar benefit in overall conformity'
and gradient would be realized from adding intensity modulation to a fifteen beam
conformal plan, the improvement in overall plan performance (based on UF Index
scoring) would make fifteen beam IMRT plans more competitive with multiple isocenter
planning than are the nine beam IMRT plans. If the Helios IMRT planning system were
modified to permit IMRT planning with more beams, for example fifteen IMRT beams, it
is possible that the improvement in overall plan performance (effectively adding an
average of 5.8 UFI points to the fifteen beam UFI score) would make fifteen beam IMRT


198
Table 5-2: Example multiple isocenter treatment plan data for case C-3.
Isoc.
No. arcs
Collimator (mm)
Weight
1
5
16
77
2
5
12
79
3
5
10
57
4
"-5
10
89
5
- 1
10
103
6
1
10
153
7
1
10
94
8
1
10
39
In this example, a total of 24 arcs of varying beam diameters and beam intensities
(as indicated in the right hand side of Figure 5-11 and in Table 5-2) are brought to bear
upon the target from a variety of directions to produce the relatively uniform dose
distribution partially shown in Figure 5-12. If the arc weights (intensities) are not
adjusted to be non-uniform, i.e. if all arc weights are left at the same uniform value,
then a less homogeneous dose distribution results. As discussed in Chapter 3, uniform
arc and isocenter weighting generally results in non-uniform dose distributions, while
appropriately non-uniformly weighting each isocenter results in a uniform dose
distribution. In this fashion, then, multiple isocenter SRS with circular collimators is
effectively manually-planned IMRT.


269
example case is presented in two smaller tables. The first table lists the ranking of
treatment methods (plans) in descending order of UF Index score, with the best scoring
plan at the top of each list. The second table is a ranked listing of the rival treatment
plans according to biological-index, either ascending order of NTCP, if nontarget brain is
the only radiosensitive structure in the plan, or by descending order of P(NC) if there are
additional radiosensitive structures involved. As with the first table, the best (lowest
NTCP or highest P(NC)) plan is listed at the top of each table.
Table 6-26: Treatment plans for cases S-l and S-2, sorted by UF Index score and by
biological indices
Case S-l
Plan
UFI
Plan
P(NC)
clinical
90
clinical
0.999
spack
84
9 beam IMRT
0.999
9 bm IMRT
77
5dyn arcs
0.997
15 beams
68
spack
0.997
5dyn arcs
67
15 beams
0.996
Case S-2
Plan
UFI
Plan
NTCP
spack
98
spack
1.31E-07
clinical
98
clinical
1.48E-07
15 beams
75
15 beams
8.30E-07
5dyn arcs
74
5dyn arcs
9.52E-07
9bm IMRT
72
9bm IMRT
1.05E-06


82
Florida radiosurgery treatment planning system. Code written in the MATLAB
language (Matlab v5.1, The Mathworks Inc., Natick, MA) processes the target contours
data, and computes the sphere packing arrangements.
Step 2: Map target points into 3D array. Each point identified from the target
contour data file is mapped into a three dimensional integer valued array. Each voxel, or
array element, corresponding to a target point is set to a value of 1. After mapping each
given target point into an array element, the program closes any gaps between 1 voxel
elements in the array, ensuring that the contour in each plane is a closed, continuous
curve.
Step 3: Build solid voxelized model. A fill routine assigns the voxels inside each
contour with values of 1, resulting in a solid, connected array of one-valued voxels
corresponding to the target volume, and zero-valued voxels outside the target (Figure 3-
17a). A default voxel size of 1 x 1 x 1 mm3 was used for this study, although this process
is general and may be applied to any voxel size.


90
voxels are covered by spheres, and -> 0 if any of the spheres are too close to each
other. For all of our work, wi =1 by default, with W2 being the only adjustable variable in
the score function. Although it could also be considered a variable, the inter-isocenter
distance factor f? was left unchanged as it is accounted for in equations (3-5) and (3-6).
The optimal maximum-valued voxel is thus identified as the voxel with the
maximum score function value. However, this voxel is not necessarily the optimal
location at which to place a sphere. For this reason, an optimization loop is used to
search the neighborhood around the best scoring voxel found so far in the process. The
best scoring maximum valued voxel is input as a seed voxel, the score calculated (for all
14 circular collimator sizes) at that voxel and all 26 of its neighboring cubic lxlxl mm '
voxels, and the largest score value of all these recorded. If the seed voxel is the best
scoring of all these 27 voxels, the optimization routine has converged, and the voxel is
used as the recommended isocenter (sphere center) location, with the collimator size
corresponding to the best score. If one of the 26 neighboring voxels yields a better
(higher) score, then it is made the seed voxel, and the process repeated for the new seed
voxel and its neighbors until no further improvement in score function is found. In our
example case, a best scoring voxel was soon located within one voxel of the best scoring
maximum valued voxel, and a 22 voxel (mm) diameter sphere was placed there, as shown
in Figure 3-17c.
Step 6: Place sphere corresponding to isocenter size and location. Spheres are
placed by setting voxels lying inside the sphere to a unique numerical value, such as the
maximum voxel value plus two. For instance, if the grassfire process identified the
deepest layer of voxels as those with a value of eight, voxels inside any placed spheres


8
The technique of multiple converging arcs delivered with circular collimators
produces a spherical region of high dose with a steep dose gradient, or falloff. This dose
distribution is adequate for treating a sphere or round target, but will treat a large volume
of non-target tissue to high dose if the sphere encompasses an irregularly shaped target.
Multiple spheres of varying sizes may be stacked together to produce a high dose
region which conforms closely to the shape of the target while still maintaining a sharp
dose gradient, as shown in Figure 1-4 (Meeks 1998b).
Figure 1-4: Conformal dose distribution produced by circular collimators and multiple
isocenters. Several isocenters, each with a set of converging arcs, have been placed near
one another to conform the composite dose distribution to the target's shape.
An alternative means of delivering a linac radiosurgery treatment is to employ
beams which are shaped to conform to the targets shape as seen from the direction of the
beam, or beams eye view. Conventional radiotherapy practice is to use diagnostic x-
ray radiographic or flouroscopic images of the patient obtained in a simulator session to


71
270
305
340
Figure 3-11: Standard five-arc set delivered with 18mm collimator, and isodose
distribution in axial, sagittal, and coronal planes. The 80%, 40%, and 16% isodose lines
are shown in each plane. The 70%, 35%, and 14% lines (not shown) are very close to the
80%, 40%, and 16% isodose lines.


151
30 mm sphere target PITVs
Isotropy factor
Figure 4-18(b): Conformity (as expressed by PITV) versus isotropy for a 30 mm sphere
target and bouquets of 5, 7, 9, and 15 beams. An isotropy factor of 1.0 reflects an
isotropic (maximally separated in 4p space) beam arrangement, while lower values of
isotropy factor reflect a beam arrangement with an increasing sense of directionality.


150
10 mm sphere target PITVs
Isotropy factor
Figure 4-18(a): Conformity (as expressed by PITV) versus isotropy for a 10 mm sphere
target and bouquets of 5, 7, 9, and 15 beams. An isotropy factor of 1.0 reflects an
isotropic (maximally separated in 4p space) beam arrangement, while lower values of
isotropy factor reflect a beam arrangement with an increasing sense of directionality.


72
Figure 3-12: AP superior-oblique view of the standard five arc set generally used for each
isocenter in multiple isocenter plans.
Table 3-2: Couch and gantry angles for standard University of Florida five arc set.
Couch
Start
Stop
20
130
30
55
130
30
340
230
330
305
230
330
270
230
330
Three factors strongly affect the dose distribution when using multiple isocenters:
1) collimator size, 2) inter-isocenter spacing, and 3) isocenter weighting. Collimator size
is chosen to match the region of the target which is being covered, and affects the
diameter of the spherical high dose region that is produced by each isocenter. Proper
selection of collimator size and isocenter location is a complex topic, which is addressed


153
Dose gradient as scored by UFIg2
for 10 mm diameter sphere target
100
Isotropy factor
Figure 4-19(a): Dose gradient (as expressed by UFIg2) versus isotropy for 10 mm sphere
target and bouquets of 5, 7, 9, and 15 beams. As expected intuitively, dose gradient
(effective distance between target volume and the half-prescription isodose shell)
worsens as each beam bouquet becomes less isotropic. Absolute value of the gradient is
a function of target size (steeper dose gradient for smaller targets) but the trend is the
same for all size targets and for all numbers of beams tested.


281
As can be seen in Table 6-30, hypothetical fifteen beam IMRT scores change the
comparison somewhat. For case VC-2, hypothetical fifteen beam IMRT (UFI = 72)
would be clearly better than multiple isocenters, while fifteen beam IMRT would be
equivalent to multiple isocenters for case VC-3, and would rank in-between the clinical
and sphere packing multiple isocenter plans for cases VC-4 and VC-7.
The achievable spatial resolution of the dose distribution is another important
factor in comparing multiple isocenters with IMRT. With respect to dose conformity, the
primary advantage of multiple isocenters over the Helios implementation of IMRT
planning is the ability to tightly conform areas of high dose to the target with high spatial
resolution. As discussed in chapter 3, a set of five one hundred degree arcs with a 10 mm
diameter collimator produces a nominal 10 mm diameter spherical shaped region of high
dose, with a steep dose falloff outside of this volume. In the Helios implementation of
IMRT. the intensities of small, 2.5 mm x 5 mm beam elements are modulated to attempt
to satisfy the dose-volume constraints entered into the system (Chapter 5). However, due
to the limited number of beam directions available (ten, nine IMRT beams were used for
the plans presented in this chapter) in Helios/CadPlan, the dose gradient outside of a
region of beamlet overlap is not as steep as that attainable with the circular collimators
and arcs. Additionally, a smoothing algorithm applied to the beamlet weight
optimization process artificially prevents high-spatial frequency modulation of the
beamlet weights, further preventing a set of IMRT beamlets in the Helios implementation
from achieving the same focused dose distribution as with circular collimators.
Because of these effects, the spatial resolution of IMRT dose distributions
currently available with the Helios system is limited. This effect is shown in Figure 6-13,


194
Figure 5-9: Orthogonal view isodoses for nine beam conformal plan. The 75%, 38%,
and 15% isodoses are shown.
Figure 5-10: Orthogonal view isodoses for nine IMRT beam conformal plan. The 77%,
38%, and 15% isodoses are shown.


IP
IT2D
IPX)
. WI35"
UNIVERSITY OF FLORIDA


139
Figure 4-15: Effect of changing collimator angle (rotation) on goodness of fit of the
MLC-defined beam aperture with the ideal, continuous beam aperture. (A) Collimator at
0 degrees, note the relatively poor fit of the leaves to the target shape, resulting in
overexposure of adjacent non-target tissue. (B) Collimator rotated to 60 degrees,
resulting in a better fit. (C) Collimator rotation optimized at 284 degrees, resulting in the
best fit of the MLC leaves to the ideal aperture shape.
Shaped Field Dosimetry
Dose distributions for conformally shaped radiosurgery and radiotherapy
treatment plans were computed using a commercially available treatment planning
system(CadPlan 6.08, Varian Oncology Systems, Palo Alto, CA). For radiation fields
shaped with custom blocks or MLC, CadPlan computes the three-dimensional dose
distribution with a double pencil beam (DPB) photon dose model. The DPB model
computes depth dose and off-axis ratios by the convolution of two dose kernels with the
radiation beam aperture shape. Depth dose is determined by a pencil beam kernel
computed from depth dose measurements and output factor measurements of square
fields in the users beam. Off-axis ratio is determined by a convolution of a boundary


159
500
400
'y 300
o>
rj
H
Jji
200
100
0
0 20 40 60 80 100
Dose (% max)
Figure 4-20: Non-target volume DVHs for isotropic static, conformally shaped beam
treatment plans for example case S-l in Table 4-8. As more beams are used to cover the
target, lower volumes of non-target tissue are exposed to dose levels above about 20% of
maximum dose.


221
Figure 6-4a: C-2 seven isocenter clinical plan orthogonal view 70%-35%-14% orthogonal
view isodoses.
Figure 6-4b: C-2 eighteen isocenter autopian orthogonal view 60%-30%-12% orthogonal
view isodoses.
Figure 6-4c: C-2 fifteen beam plan orthogonal view 69%-35%-14% isodoses.


166
Table 4-12: Nine isotropic beam bouquet data, following first downhill optimization
search
Target area Fractional volumes of intersection (FVIs)
Beam
y
z>
SCORE
Initial
Current
RE
R-ON
LE
L-ON
BS
1
0.486
-0.071
0.872
3.1
1577
1668
0.00
0.00
0.00
0.02
0.00
2
-0.047
0.604
0.795 '
2.2
1292
1532
0.00
0.00
0.00
0.00
0.10
3
-0.321
-0.139
0.938'
3.5
1627
1471
0.00
0.02
0.00
0.00
0.04
4
0.682
0.586
0.440
1.1
1446
1527
0.00
0.00
0.00
0.00
0.00
5
0.112
-0.754
0.648
1.9
1544
1159
0.00
0.00
0.00
0.00
0.00
6
0.798
-0.533
0.282
1.1
1219
1362
0.00
0.00
0.00
0.00
0.00
7
0.072
0.992
0.100
0.9
1143
976
0.00
0.00
0.00
0.00
0.00
8
-0.778
0.368
0.509
1.2
1233
1467
0.00
0.00
0.00
0.00
0.00
9
-0.764
-0.526
0.372
0.9
1522
1326
0.00
0.00
0.00
0.00
0.00
Average
1.74
1400
1388
0.00
0.00
0.00
0.002
0.017
Table 4-13: Beam bouquet data for final, fully optimized nine isotropic beam bouquet
Target area Fractional volumes of intersection (FVIs)
Beam
y
z>
SCORE
Initial
Current
RE
R-ON
LE
L-ON
BS
1
-0.876
-0.301
0.377
0.9
1577
1415
0.00
0.00
0.00
0.00
0.00
2
-0.808
0.543
0.215
1.1
1292
1361
0.00
0.00
0.00
0.00
0.00
3
0.926
-0.004
0.374
0.9
1627
1534
0.00
0.00
0.00
0.00
0.00
4
-0.467
0.204
0.865
1.1
1446
1513
0.00
0.00
0.00
0.00
0.00
5
0.628
0.734
0.265
0.9
1544
1361
0.00
0.00
0.00
0.00
0.00
6
-0.281
-0.842
0.457
0.8
1219
1000
0.00
0.00
0.00
0.00
0.00
7
-0.127
0.848
0.518
1.2
1143
1331
0.00
0.00
0.00
0.00
0.00
8
0.503
-0.671
0.536
1.1
1233
1317
0.00
0.00
0.00
0.00
0.00
9
0.344
0.128
0.933
1.6
1522
1695
0.00
0.00
0.00
0.00
0.05
Average
1.06
1400
1392
0.00
0.00
0.00
0.000
0.006


214
Figure 6-2d: Case S-2 nine IMRT beam plan, 80-40-16% isodoses shown.
Figure 6-2e: Case S-2 five dynamic MLC arcs plan, 70-35-14% isodoses shown.
Table 6-5: Nontarget brain NTCP values for case S-2
Plan
NTCP
clinical
1.48E-07
spack
1.31E-07
15 beams
8.30E-07
9bm IMRT
1.05E-06
5dyn arcs
9.52E-07


259
Table 6-22: Dosimetric figures of merit for case VC-6
Plan
Rx-dose
PITV
Vo ver (cm3)
UFIc
UHg
UFI
Gradient (mm)
clinical
70
1.18
1.9
85
61
73
6.9
spack
62
1.24
2.5
81
70
75
6.0
9 beams
67
1.75
8.0
57
58
58
7.2
15 beams
68
1.69
7.3
59
59
59
7.1
9 beam IMRT
77
1.50
5.3
67
56
61
7.4
5dvn arcs
69
'1.80
8.5
56
55
55
7.5
Figure 6-1 la: VC-6 clinical ten isocenter plan, 70-35-14% isodoses shown with dark
lines.
Figure 6-1 lb: VC-6 sphere packing autopian ten isocenter plan, 62-31-12% isodoses
shown.


108
Conclusion
The University of Florida radiosurgery treatment planning algorithm organizes
the treatment planning variables available to the planner to allow efficient optimization of
radiosurgery treatments delivered with circular collimators. Several manual tools, such as
arc elimination and arc start and stop angle manipulation, allow a nominally spherical
dose distribution to be easily altered to improve the dose gradient in the direction of
critical structures and to improve conformity of the dose distribution to the target.
Irregularly shaped targets and ellipsoidal targets with the major axis inclined in the AP
direction require the use of multiple isocenters. A geometrically based method of
multiple isocenter linac radiosurgery treatment planning optimization can provide a
standard means of generating radiosurgery plans for difficult, irregularly shaped targets.
When used to complement the standard manual planning methods used in the University
of Florida radiosurgery planning algorithm, conformal and optimized radiosurgery plans
may be generated for any arbitrary target. The automatic nature of the sphere packing
optimization aids the comparison of multiple isocenter treatment planning with circular
collimators to other radiosurgery treatment methods, by removing biases which a human
planner might introduce in the comparison.


27
Figure 2-6: A 100 degree arc of radiation produced by a continuously moving beam,
approximated by 11 beams spaced 10 degrees apart. Crosshairs indicate the center of
rotation (isocenter).
There are several departures from the idealized geometries shown in Figures 2-1
and 2-5 that can occur in clinical patient treatment situations, and which can potentially
lead to errors between the actual dose to a point and the dose calculated with the dose
model in equation (2-1). Inhomogeneities inside the patient or at the patients surface can
cause significant dose errors under certain circumstances, such as for large field sizes.
An irregular (not flat) patient surface is one such example of inhomogeneity, shown in
Figure 2-7. The curvature of the patient surface causes points 1 and 2 in Figure 2-7 to lie
at different depths from the surface with respect to the beam. The resulting tissue deficit
shown will cause the photon beam to undergo less attenuation from the source to point 2
than from the source to point 1. If the TPR for central axis point 1 is used to calculate the
dose at points 1 and 2, then the dose to point 2 will be underestimated by equation (2-1),


77
40 mm spacing
35 mm spacing
33 iran spacing
32 iran spacing
31 iran spacing
29 iran spacing
26 mm spacing
24 mm spacing
Figure 3-13: Effects of isocenter spacing on the multiple isocenter dose distribution. The
70% and 50% isodose lines are shown in a transaxial plane for two equally weighted
30mm isocenters, each with a five arc set.


184
orientations of the IMRT beams. Although the optimal orientations of IMRT beams are
not necessarily the same as those of conformal beam plans (Stein 1997), using the same
beam orientations makes a comparison between conformal beam SRS and IMRT beam
SRS more direct. Next, the-user must enter the inverse planning parameters into the
system. The inverse planning constraints are entered as a set of maximum and minimum
dose-volume constraints, such as no more than X% of organ Y may receive more than
dose Z. Each constraint has its own priority weight, which determines how strongly
approaching or violating a limit on that constraint will affect the score function.


220
Patient C-2
Patient C-2 is a 74 year old female with a recurrent 11.9 cm' tentorial
meningioma. This patient was treated clinically with a seven isocenter SRS plan using
27 arcs, delivering 12.5 Gy to the 70%. The sphere packing autopian program generated
an eighteen-isocenter plan using 62 arcs. Orthogonal view isodose plots for all plans are
shown in Figures 6-4a through 6-4e, with dose-volume figures of merit listed in Table 6-
8. Nontarget volume DVHs are shown in Figure 6-4f. For plan evaluation with
biological indices, NTCPs are listed in Table 6-9, and a plot of NTCP versus prescription
dose is shown in Figure 6-4h. Multiple isocenters with circular collimators (spack
autopian) is the best plan based on conformity, gradient, and biological indices. The
clinical plan maintains a steeper dose gradient than the sphere packing eighteen isocenter
plan due to using significantly fewer isocenters and arcs. The fifteen static beam plan is
slightly better than the sphere packing plan in terms of gradient, but is significantly less
conformal than the sphere packing plan. The fifteen beam plan and the nine beam IMRT
plan are roughly comparable in terms of overall UF index. The fifteen beam, nine beam
IMRT, and four dynamic arcs plans are similar in terms of NTCPs (Figure 6-4h, Table 6-
5b).
Table 6-8: Dosimetric figures of merit for case C-2
Plan
Rx-dose
PITV
Vover (cm3)
UFIc
UFIg
UFI
Gradient (mm)
clinical
70
2.13
13.5
47
62
54
6.8
spack
60
1.45
5.6
69
53
61
7.7
15 beams
69
1.75
8.9
57
54
56
7.6
9 beam IMRT
76
1.68
8.1
60
51
55
7.9
5 dyn arcs
72
1.72
8.6
58
49
54
8.1


128
rotation beam vector may described in terms of the pre-rotation beam vector
by the system of equations (4-4a) through (4-4c):
(4-4a) x* = Cnx + Ctly + Cnz + bt
(4-4b) y* = C*x + Cny + C2,z + b,
(4-4c) z* = Cx + Cny + C}3z+b,-
If both coordinate systems have a common origin, which is the case for rotation of
a beam about a fixed isocenter, then the bl-b3 terms describing the translations are zero,
and the c¡j coefficients in equations (4-4a) through (4-4c) may be determined by equations
(4-5a) through (4-5i) (Kreyszig 1983).
(4-5a)
(4-5b)
1 **j = C\2 (4"5C)
i*,k=ci
(4-5d)
(4-5e)
i**i' = C22 (45f)
j*'k = C2,
(4-5g)
(4-5h)
k**J=C} 2 (4_5i)
In these equations, the coefficients ctJ are determined by the vector dot product
between the pre-rotation unit vectors denoted as < >, and the post-rotation unit vectors,
denoted as < >. Therefore, simple rotation operations about the principal axes (x,y, and
z) may be described with equations derived from equations (4-4a) through (4-4c) and (4-
5a) through (4-5i). For instance, a rotation of a beam vector of angle a about the
x-axis would be related to the post-rotation vector as follows:
(4-6) x* = x,


138
Y2
Figure 4-13: Beams eye view (BEV) of an irregularly shaped target and a beam aperture
defined by a custom block (expanded view on right side). The beam aperture shaped by
the block covers the target plus a margin to allow for beam penumbra and errors in target
localization.
Figure 4-14: Approximating the continuous beam aperture with a multileaf collimator.
(A) Leaves match inside of aperture (inbound), (B) middle of each leaf matches aperture
(crossbound), (C) leaves match outside of aperture (outbound).


6
how this may be done, relying on a headframe which locates to the patients head by
means of a dental mold (a biteplate, or biteblock), occipital headrest, and a strap to
tightly hold the frame to the head (Reinstein 1998). Systems such as these, which
combine the functions of immobilization and positioning, tend to suffer reduced accuracy
because of immobilization forces that are inevitably applied to the reference positioning
system. Optically guided systems have been developed recently, however, which de
couple the positioning function from the immobilization function. Such systems have
been demonstrated to provide patient positioning with smaller errors than previous
systems. One such optically guided system has demonstrated the ability to position the
patient within about 1.1 mm error at isocenter, which while not as small a positioning
error as attainable with an invasive stereotactic headring, is still significantly better than
previous systems (Bova 1997; Bova 1998b). Because of such new, non-invasive
stereotactic techniques, radiosurgery treatments can be administered in multiple fractions
(Figure 1-3). Such fractionated radiosurgery is generally known as stereotactic
radiotherapy (SRT).
Linear Accelerator Radiosurgery and Radiotherapy Treatment Techniques
The major treatment techniques used to deliver linac radiosurgery treatments are
circular collimators with arcs, conformally shaped beams, and intensity modulated
radiotherapy (IMRT). Circular collimators can be used to create spherical regions of high
dose. When used with linear accelerators, the circularly collimated beam is rotated
around the target at isocenter by moving the gantry in arc mode while the patient and
treatment couch are stationary, producing a para-sagittal beam path around the target.
Betti and Derichinsky developed their linac radiosurgery system with a special chair, the


81
as spheres are graphically placed by a human user in a three dimensional representation
of the target. Both of these methods are similar, in that isocenter or shot placement is
based simply on obtaining the best geometrical agreement between the targets shape and
the shape of the high dose region characteristic of the treatment unit (i.e. a sphere or
ellipsoid). Due to non-geometric constraints imposed by the physics of radiation
dosimetry (e.g. due to dose interactions and contributions between neighboring
isocenters), multiple isocenter radiosurgery planning is not exactly a sphere-packing
problem. However, in many cases, a sphere-packing arrangement will translate into a
satisfactory radiosurgery plan, particularly if simple dosimetric adjustments are made to
the automatically generated plan (i.e. use of the isocenter weighting tool discussed in
the previous section).
An alternative sphere packing method is presented in this section that shows
potential to significantly aid the planning of complex, multiple isocenter cases. Based on
tests with irregularly shaped phantom targets and with a representative sampling of
clinical example cases, the method demonstrates the ability to generate radiosurgery
plans comparable to or of better quality than multiple isocenter linac radiosurgery plans
found in the literature.
The major steps of the sphere packing process are diagrammed in Figure 3-16. A
7.6 cm3 phantom target, similar in shape to a large acoustic neuroma, is shown in Figures
3-17 and 3-18 with its sphere packing arrangement, and will be used to illustrate the
process.
Step 1: Read in target volume contours. Target volume information is obtained by
manually contouring the target on successive transaxial image slices in the University of


74
size of the middle 70% isodose region, from 59 mm across with a spacing of 33mm,
down to a region only 17 mm across when the inter-isocenter spacing is reduced to 24
mm. The 70% isodose region shrinks to less than a third of its initial size, while the 50%
isodose region shrinks much-more gradually from 66 mm to 53 mm (a 20% decrease).
For this example of two 30mm isocenters, the 70% isodose shell may be approximated
as two 30mm spheres, if an inter-isocenter spacing of at least 32mm is maintained.
To assist the human radiosurgery planner in maintaining this appropriate spacing
between isocenters, a table of empirically determined optimal inter-isocenter distances is
incorporated into the University of Florida radiosurgery treatment planning system (Foote
1999). The planner enters the table with the collimator sizes for two adjacent isocenters,
and the table returns the optimal inter-isocenter distance for these two collimator sizes.
This planning tool merely serves as an aid to provide recommended isocenter spacing,
and does not directly alter any treatment plan parameters. According to this isocenter
spacing table, the optimal spacing distance for two 30mm isocenters is 31mm. Inspection
of the isodose distributions for a variety of collimator sizes and spacings, as was done in
Figure 3-9 for two 30mm collimators, shows that for two isocenters with collimator
diameters of dl and d2, an approximate spacing of 0.52(dl + d2) to 0.60(dl + d2) will
yield an overall dose distribution similar in shape to two spheres of diameters dl and d2.
Isocenter weighting is another important aspect of multiple isocenter
treatment planning. When planning radiosurgery treatments with multiple isocenters and
when the isodose distribution is normalized to maximum dose, care must be taken to
consider the additive dose from all isocenters. Examples of this are shown in Figure 3-
14(a), 3-14(b), and 3-14(c). Figure 3-14(a) shows a dose profile (cross plot) through four


67
Figure 3-8: Steepening the dose gradient in the lateral direction by elimination of the
most lateral four arcs from a standard nine-arc set. The 80%, 40%, and 16% isodose
lines are shown in each plane.


160
Table 4-9: Diagnosis and lesion size for irregularly shaped clinical example targets
Designation
Diagnosis
Lesion size (cc)
SI
acoustic neuroma
2.4
Cl
meningioma
6.1
C2
meningioma
15.1
C3
meningioma
3.8
VC1
meningioma
12.8
VC2
meningioma
6.0
VC3
sarcoma
15.3
VC4
meningioma
7.5
VC5
meningioma
17.8
VC6
metastasis
13.7
VC7
metastasis
13.6


189
hypothetical plan, the prescription isodose shell was chosen as the isodose level covering
at least 95% of the target volume. Treatment plan figures of merit (prescription isodose
level, PITV, UF Index, gradient) were computed and are shown in Table 5-1. Orthogonal
view isodose plots are for the nine beam conformal and nine beam IMRT plans are
shown in Figures 5-9 and 5-10, respectively.
Table 5-1: Dosimetric figures of merit for hypothetical 9 beam and 9 beam IMRT SRS
treatment plans for 5.4 cm3 meningioma example case.
Plan
Rx-dose
PITV
Vover(cc)
UFIc
UFIg
UFI
Gradient (mm)
9 beams
75
1.35
2.0
74
61
67
6.9
9 beam IMRT
77
1.25
1.5
80
61
71
6.9


270
Table 6-27: Treatment plans for cases C-l through C-3, sorted by UF Index score and by
biological indices
Case C-l
Plan
UFI
Plan
NTCP
clinical
81
clinical
1.48E-08
spack
79
spack
1.63E-08
9 beam IMRT
66
9 beam IMRT
3.23E-08
15 beams
65
15 beams
3.39E-08
5dyn arcs
64
5dyn arcs
3.96E-08
Case C-2
Plan
UFI
Plan
NTCP
spack
61
spack
1.30E-07
15 beams
56
9 beam IMRT
1.97E-07
9 beam IMRT
55
15 beams
2.23E-07
clinical
54
5dyn arcs
2.27E-07
5dyn arcs
54
clinical
4.40E-07
Case C-
Plan
3
UFI
Plan
P(NC)
clinical
82
clinical
0.999999
spack
73
spack
0.999999
9 beam IMRT
67
9 beam IMRT
0.999999
15 beams
67
15 beams
0.999998
5dyn arcs
60
5dvn arcs
J
0.999997


208
clin-bs
spack-bs
15bm-bs
5dynarcs-bs
imrt-bs
Dose (Gy)
Figure 6-lh: Brainstem volume DVHs for case S-l treatment plans. The prescription
dose is 12.5 Gy.
Table 6-3: NTCPs for case S-l treatment plans
Plan
Nontarget
NTCP
Brainstem
NTCP
clinical
3.03E-09
6.29E-04
spack
3.74E-09
3.42E-03
15 beams
1.46E-08
4.28E-03
9 beam IMRT
1.23E-08
1.35E-03
5dvn arcs
1.54E-08
2.75E-03
Based on dose conformity and gradient, the multiple isocenter plans (clinical and
spack) are clearly superior to any of the other treatment plans. Each multiple isocenter


224
Table 6-9: Nontarget brain NTCP values for case C-2
Plan
NTCP
clinical
4.40E-07
spack
1.30E-07
15 beams
2.23E-07
9 beam IMRT
1.97E-07
- 5dyn arcs
2.27E-07
Patient C-3
Patient C-3 is a 61 year old female with a 5.6 cm3 cavernous sinus meningioma.
This patient was treated clinically with an eight isocenter SRS plan using 24 arcs,
delivering 12.5 Gy to the 70% isodose shell. The sphere packing autopian program
generated a nine isocenter plan using 30 arcs. Orthogonal view isodose plots for all plans
are shown in Figures 6-5a through 6-5e, with dose-volume figures of merit listed in Table
6-10. Nontarget volume DVHs are shown in Figure 6-5f, and brainstem DVHs are
shown in Figure 6-5g. For plan evaluation with biological indices, NTCPs and maximum
brainstem doses are listed in Table 6-11. Nontarget volume NTCPs versus prescription
dose are plotted in Figure 6-5h, while similar plots for brainstem NTCPs are shown in
Figure 6-5i.
Based upon conformity and gradient of the dose distribution (UF Index score),
both multiple isocenter plans are better than any alternative plans. The most conformal
alternative plan (15 beams) to multiple isocenters approaches the sphere packing autopian
in terms of conformity (UFIc of 73 versus 76), but has a significantly less steep dose
gradient than the sphere packing plan. The superiority of the multiple isocenter plans is
shown by the nontarget volume DVH curves (Figure 6-5f), in which the multiple
isocenter DVH curves lie below and to the left of the DVH curves for the other plans.


41
direction of adjacent radiosensitive structures. This additional complexity makes it
necessary to complement the dose cross-plot with other methods to evaluate the dose
gradient.
Figure 2-16 illustrates this point with a hypothetical radiosurgery target
shaped like a three-dimensional letter F, which is covered by a multiple isocenter dose
distribution using 10 mm collimators and five converging arcs at each of eight isocenters.
The 70% isodose shell, which covers the hypothetical target, represents the prescription
isodose and is shown along with the half of prescription isodose (35%), and twenty
percent of prescription isodose (14% = 0.2 x 70%). Unlike the single isocenter,
spherically symmetric dose distribution of Figures 2-14 and 2-15, the multiple isocenter
dose distribution is asymmetric, and the prescription isodose to half-prescription isodose
gradient therefore has a directional and spatial dependence. Depending on where the
dose cross-plot is centered and the direction, the distance between the prescription (70%)
and half-prescription (35%) isodose shells varies from 2 to 7 mm. In order to obtain a
representative sample average gradient distance, it would be necessary to take a large
number of gradient measurements at many points at the targets edge. However, a
method has been proposed which uses easily obtainable DVH information to generate a
numerical measure of the overall dose gradient, and which may be used with arbitrary
dose distributions.


280
Table 6-30: Very complex (VC) case UF Index scores for cases VC-1 through
VC-7, including hypothetical fifteen beam IMRT UF Index scores.
Case VC-1
Case VC-5
Plan
UFI
Plan
UFI
clinical
72
spack
64
spack
65
clinical
61
9 beam IMRT
59
9 beam IMRT
49
9 beams
56
hyp. 15 beam IMRT
48
hyp. 15 beam IMRT
54
9 beams
40
15 beams
50
5dyn arcs
40
5dyn arcs
45
15 beams
39
Case VC-2
Case VC-6
Plan
UFI
Plan
UFI
hyp. 15 beam IMRT
72
spack
75
clinical
68
clinical
73
spack
67
hyp. 15 beam IMRT
63
9 beam IMRT
66
9 beam IMRT
61
15 beams
65
15 beams
59
5dvn arcs
62
9 beams
58
9 beams
59
5dvn arcs
j
55
Case VC-3
Case VC-7
Plan
UFI
Plan
UFI
clinical
57
clinical
67
hyp. 15 beam IMRT
57
hyp. 15 beam IMRT
64
spack
56
9 beam IMRT
62
9 beam IMRT
55
15 beams
60
15 beams
49
spack
59
9 beams
47
9 beams
58
5dvn arcs
J
46
5dyn arcs
56
Case VC-4
Plan
UFI
clinical
66
hyp. 15 beam IMRT
62
spack
61
9 beam IMRT
59
15 beams
55
9 beams
53
5dyn arcs
53


223
Figure 6-4f: Nontarget volume DVHs for case C-2 treatment plans. The prescription
dose is 12.5 Gy.
Prescription dose (Gy)
Figure 6-4g: Nontarget brain NTCPs as a function of prescription dose for case C-2
treatment plans.


133
test-bev2bx2.m,R-EYE = blue, L-EYE = cyan, BRAINSTEM = green
Beam vector = <0.001,0.001,1,000>.
Figure 4-11: Beams eye view of a target, brainstem, optic nerves, and eye orbits. The
beam vector is <0,0,1> in the coordinate system of Figure 4-9, corresponding to a
vertex beam entering the patients cranium from the +Z axis and exiting through the
patients body. This BEV is generated by plotting the projective transform coordinates of
each point belonging to each structure for the <0,0,1> beam. The outermost extent of the
target has been enhanced for viewability. The heavy dashed lines indicate the field of
view for the pixilated beams eye view shown in Figure 4-12.


254
DVHs are shown in Figure 6-1 Of. NTCPs for the nontarget brain volume are listed in
Table 6-21, and a plot of nontarget brain NTCP as a function of prescription dose is
shown in Figure 6-10g.
Ranking the treatment plans on the basis of UFI score places the multiple
isocenter plans (clinical and sphere packing autopian) well ahead of the other treatment
methods. Again, the IMRT plan delivers a very conformal (and homogeneous) dose
distribution to the target, but suffers from the poorest dose gradient of any of the five
plans. The fifteen beam and four dynamic arc plans rank at the bottom of the UFI
comparison. The plan ranking by NTCPs (Table 6-21, Figure 6-10g) follows the same
order as the UFI ranking: both multiple isocenter plans are similar with respect to
predicted NTCP, followed by the IMRT plan, and then by the four dynamic arc and
fifteen beam plans.
Table 6-20: Dosimetric figures of merit for case VC-5
Plan
Rx-dose
PITV
Vover (cm3)
UFIc
UFIg
UFI
Gradient (mm)
clinical
70
1.23
2.8
82
41
61
8.9
spack
66
1.39
4.9
72
56
64
7.4
9 beams
69
2.39
17.5
42
38
40
9.2
15 beams
70
2.27
16.0
44
34
39
9.6
9 beam IMRT
83
1.30
3.8
77
21
49
10.9
5dyn arcs
70
2.19
15.0
46
35
40
9.5


106
parameters in addition to isocenter weight may be necessary to maintain a sharp enough
dose gradient in the direction of the critical structure.
It is possible in principle to incorporate some degree of critical structure
avoidance into this geometrically based algorithm. For instance, rather than simply
designate the volume in the neighborhood of the target as either "target" or "non-target"
voxels, one could also designate "critical structure" voxels. These voxels could be scored
as a separate penalty factor in the score function. This could improve the utility of the
sphere packing algorithm by geometrically forcing an isocenter away from sensitive
structures.
Another area which bears further study is the behavior of the algorithm with
respect to the score function weight parameters. As presented here, the variable
parameters in the score function are W2 (Eq.(3-4)), the non-target tissue penalty weight,
and the inter-isocenter distance penalty function factor, f3 (Eq.(3-5)). The inter-isocenter
distance score function, f3, was based on simple observations of the dose distributions
from two adjacent isocenters. It is possible that a more detailed model of the optimal
inter-isocenter distances could provide improved results.
In the non-target tissue penalty factor f2 (Eq. (3-4)), W2 controls the slope of the
penalty function which worsens (lowers) the overall score function when normal tissue is
encroached upon. In almost all of the phantom target and clinical cases presented, the
best radiosurgery plans arose from sphere packings generated with W2 set to a value of 10
to 20. The general trend observed in testing the algorithm was that as W2 increased,
thereby increasing the penalty for sphere coverage into non-target tissue, the number of
spheres (isocenters) used to fill a given target volume rose dramatically as the algorithm


systems in our lab. I am grateful to Russell D. Moore for his invaluable aid in helping me
navigate and use the myriad of Unix computer systems necessary to perform my research
work, and to Lisa Mandell for her assistance in gathering radiosurgery patient data from
the University of Florida SRS-patient database. I would like to thank Dr. Wesley E.
Bolch for his support and encouragement for the entire time I have been a graduate
student at the University of Florida, and to Dr. Kelly D. Foote for many hours of
insightful converstations about radiosurgery and neurological surgery, and for his patient
tutoring and assistance in contouring brain lesions and other intracranial structures.
Finally, I am deeply indebted to my friend and wife, Nanette, without whose support and
loving encouragement I would not have had the strength to begin, let alone complete, the
last several years of my life in graduate school.
v


274
cases, and in two of the seven cases both the clinical and sphere packing automatic plans
ranked as the two highest plans of the five plans considered for each case. For the three
VC cases in which multiple isocenter planning was not the top-ranked plan by biological
index (VC-2, VC-3, and VC-7), the IMRT plan was the highest ranking plan. With the
exception of case VC-7, the differences in biological index scores for the rival treatment
plans are minor and likely not significant.
Based on these clinical example cases, it appears that properly planned
multiple isocenter treatment planning is dosimetrically equivalent to or superior to IMRT,
and is superior to static beams and dynamic MLC arc treatment plans. There is little
doubt of this for simple and complex targets (i.e. targets which required fewer than ten
isocenters clinically to treat at the University of Florida), as the physical dose
distributions for multiple isocenter plans consistently demonstrate better conformity and
gradient than do treatment plans for the alternative treatment delivery methods
considered here. For the very complex targets, in only one out of seven VC cases (VC-2)
was the UFI score of an alternative plan within two UFI points of both multiple isocenter
plans.
For four of the seven VC cases, an IMRT plan and possibly a fifteen beam
plan achieved a UFI score within two or three UFI points of a multiple isocenter plan.
For case VC-2, the clinical, sphere packing autopian, IMRT plan, and fifteen beam plan
were all within about three UFI points of each other. At the prescription dose of 10 Gy,
all of the plans were equivalent to the third significant digit when gauged by biological
indices (probability of no complication). The target for case VC-2 was almost an
ellipsoidal shape with the major axis inclined in an oblique plane. This type of target


175
Intensity Modulated Radiotherapy (IMRT)
As was indicated in Chapter 1, the concept of improving the quality of
radiotherapy treatments by modulating the intensity profile of the treatment beam is not a
new concept. The use of wedge filters is one-dimensional modulation of the beam profile
along the toe-to-heel direction of the wedge, while compensators provide two-
dimensional modulation across the width and length of the treatment field. The goal of
these simpler methods was generally limited to improving the homogeneity of the target
dose distribution (Stemick 1998). The use of more sophisticated intensity modulation
methods developed recently allows the planner to exert even greater control of the dose
distribution, and allows the high dose region to be shaped to fit the targets shape better
than is achievable than by simply using conformally shaped beams without intensity
modulation (Stemick 1998). Figures 5-1(a) and 5-1(b) show a two-dimensional example,
whereby an intensity modulated radiation delivery is able to attain better conformity of
the dose distribution to a concave target. In this figure, the dose inside each cell is
modeled simply as the number of beams intersecting the cell. The four uniform intensity
beams cover the target uniformly, but also cover several non-target cells with 4 units of
radiation dose (light gray area). The four intensity modulated beams (Figure 5- 1(b)) are
able to conform the high dose region to the target more closely than the conformal beam
plan.


CHAPTER 1
INTRODUCTION
Megavoltage Photon Radiotherapy And Radiosurgery
Conventional external beam radiotherapy, or teletherapy, involves the
administration of radiation absorbed dose to cure disease. The general teletherapy
paradigm is to irradiate the gross lesion plus an additional volume suspected of
containing microscopic disease not visible through physical examination or imaging, to a
uniform dose level. External photon beams with peak photon energy in excess of 1 MeV
are targeted upon the lesion site by registering external anatomy and internal radiographic
anatomy to the radiation (beam) source. Due to uncertainty and errors in positioning the
patient, the radiation beam, which is directed at the lesion, may need to be enlarged to
ensure that errors and uncertainty in patient positioning do not cause the radiation beam
to miss some or all of the target. Unfortunately, enlarging the radiation beam results in a
relatively large volume of non-diseased tissue receiving a significant radiation dose in
addition to the target. For instance, adding only a 2mm rim to a 24mm diameter spherical
volume to ensure that the 24mm diameter target is covered even with a 2mm positional
error will increase the irradiated volume from 7.2 cm3 to 11.5 cm3, an increase of 60%
(Bova 1998a).
It has long been known that for many cancerous diseases, a radiobiological
advantage is realized by administering the total radiation dose in small doses (fractions)
over an extended period of time. Bergonie and Tribondeau discovered this principle in
the early twentieth century by experimenting to determine the doses of x-rays to the testes
1


148
space to a conical polar angle region about the z-axis. (The z-axis is chosen for
convenience, to establish a consistent direction to each collection of beams.) Treatment
plans with 5, 7, 9, and 15 beams for 10mm sphere, 30mm sphere, and 50mm sphere
targets are created and analyzed. A simple measure of beam bouquet anisotropy, the
isotropy factor, can be defined as the ratio of the compressed N beam bouquet average
minimum separation angle, to the average minimum isotropic N beam separation angle.
For example, consider an isotropic bouquet of 15 beams (Table 4-7). The beams in an
isotropic 15-beam bouquet are separated by 38.1 degrees. If a maximally spatially
separated beam arrangement is created while restricting the beams to a region within a
45-degree cone about the z-axis, the resultant beams are separated by only 24.1 degrees.
The isotropy factor is therefore 24.1 / 38.1 = 0.63, meaning this bouquet of beams retains
about 63% of the inter-beam separation of the initial bouquet.
The plots of PITV and UF Index versus isotropy factor shown in Figures
4-18(a) through 4-18(c) and 4-19(a) through 4-19(c) demonstrate the deleterious effects
of orienting the beams more closely together from an isotropic condition. As the isotropy
factor decreases below about 0.8, the conformity of the prescription isodose surface to the
target and the dose gradient worsen significantly. In terms of conformity (planning
isodose volume to target volume ratio, or PITV (Shaw 1993)), the effect of decreasing the
isotropy of the beam arrangement is similar for all target sizes. A gradient score similar
to the UF Index gradient score was used to evaluate dose gradient (Bova 1999). The UF
index (gradient) score, or UFIg, is a dimensionless number which equals 100 when an
optimal effective gradient distance of 3mm exists between the half-prescription and
prescription isodose shells (Chapter 2, Evaluating treatment plans). UFIg decreases


288
nine beam IMRT plan with a similar degree of conformity and gradient as with multiple
isocenters.
There is another clinically useful way of providing the clinician with
information on which treatment plan option is best for a particular patient: an optimized
treatment plan for each method can be generated and compared with the other plans. The
computer programs which implement the methods of Chapters 3, 4, and 5 to produce
optimized treatment plans can be run in a fairly short period of time (less than half a day).
This was suggested in the previous section as a method of gauging a targets complexity,
by using the automatic sphere packing program to determine the approximate number of
isocenters a given target would require to treat. It is possible at least to perform this
process on a limited number of patients on the day of SRS treatment, to produce
optimized treatment plans with multiple isocenters, static beams, and IMRT, and to let
the clinician choose the best option based on each customized plan. (Due to the
consistent relatively poor performance of dynamic arc SRS plans compared to the other
treatment methods, it is assumed that this treatment option need not be generally
explored). Generating a customized set of treatment plans for each patient would be
preferable to extrapolating from the results of the research presented here.
At the University of Florida, the majority of SRS patients receive a non
stereotactic MRI examination the day before treatment. On the day of treatment, each
patients MRI image set is fused with a stereotactic CT image set to allow treatment
planning to be performed on both image sets. It is possible to perform a preliminary
multiple isocenter treatment plan with the non-stereotactic MRI image set the day before
treatment, and to then convert this pre-plan into a stereotactic multiple isocenter plan


35
Ideal cumulative target and non-target DVHs
1.2
Figure 2-12: Ideal cumulative DVH curve for target and non-target volumes.
The purpose of plotting two DVHs on a single set of axes is to allow a direct comparison
between two or more dose distributions. In the example of Figure 2-10, Plan 1 and
Plan 2 are being compared with respect to the radiation dose distribution delivered to
the radiosensitive structure. As can be seen in the figure, it can difficult to evaluate
competing plans using such direct histograms (Drzymala 1991). Above about 40 units of
dose, both plans appear to be identical, but the two plans expose differing volumes of
brainstem at doses less than about 40 units. It is difficult to determine whether one plan
is better than the other from Figure 2-10. Plotting the dose-volume information in the
form of a cumulative DVH makes it simpler to evaluate two similar DVHs against one
another. A cumulative DVH is a plot of the same dose volume information as before, but
with the modification that the y value displayed for each bin x is the volume receiving >
dose x. Peaks in a direct DVH correspond to inflection points on a cumulative DVH
curve. A cumulative DVH plot of the data in Figure 2-10 is shown in Figure 2-11.


48
patients in these studies were treated, and not with dose inhomogeneity alone. One
theory is that the extreme hot spots associated with large dose heterogenities may be
acceptable, if the dose distribution is very conformal to the target volume and the hot spot
is contained within the target volume. Non-conformal dose distributions could easily
cause the hot spots to occur outside of the target, greatly increasing the risk of a treatment
complication. The extensive successful experience of gamma unit treatments
administered worldwide (almost all treatments with MDPD > 2.0) lends support to this
hypothesis (Flickenger 1997). Therefore, as a general principle, one strives for a
homogeoneous radiosurgery dose distribution, but this is likely not as important a factor
as conformity of the high dose region to the target volume, or the dose gradient outside of
the target.
As was shown in Tables 2-1 and 2-2, in order to maintain as steep a dose gradient
as possible, the 70% (of maximum dose ) isodose shell is generally used for planning
multiple isocenter treatments, while the 80% isodose shell is used for single isocenter
treatments. An additional benefit of selecting the 70% to 80% isodose shell, rather than
the 50% isodose shell commonly used in gamma unit radiosurgery, as the prescription
isodose is an improvement in treatment efficiency, in terms of the total number of
monitor units which must be delivered. Setting the 50% isodose shell as the prescription
isodose surface rather than 70% would require 1.4 times as many monitor units to be
given to deliver the prescription dose to the target. Also, this would impart a larger
integral dose to the patient in order to deliver the same peripheral target dose. Although
the 70% and 80% prescription isodose levels were chosen based primarily on maintaining
the steepest possible dose gradient, they represent a guideline for acceptable dose


42
Figure 2-16: Irregular "F" shaped target and multiple isocenter dose distribution in
hemispherical water phantom.



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CHAPTER 5
INTENSITY MODULATED SRS WITH FIXED BEAMS
Introduction
This chapter presents the methods used to generate static beam intensity
modulated SRS treatment plans using a commercially available treatment planning
system (CadPlan 6.15E with Helios, Varan Medical Systems, Palo Alto, CA). The
CadPlan/Helios system, given a user-specified set of beams and planning constraints,
computes non-uniform intensity profiles for each user-defined beam and converts each
intensity profile into a data file which will allow an MLC-equipped linear accelerator to
deliver the planned IMRT treatment. The CadPlan/Helios system is used in Chapter 6 of
this report to compute dose distributions for intensity modulated SRS treatments, for the
purposes of comparing the efficacy of intensity modulated SRS treatments with the other
SRS treatment delivery methods already discussed (multiple isocenter SRS and
conformal beam SRS). As discussed in Chapter 4 for shaped beam SRS, using a single
treatment planning system for computing the dosimetry (DVHs and isodose plots) for all
treatment plans not involving circular collimators should result in more consistent
dosimetry than if a separate treatment planning system were used for shaped beams,
another for dynamic arc SRS, and yet another for IMRT SRS. This should allow a better
comparison to be made between SRS planning with circular collimators (multiple
isocenters) and other SRS methods.
174


240
Table 6-14: Dosimetric figures of merit for case VC-2
Plan
Rx-dose
PITV
Vover(cm3)
UFIc
UFIg
UFI
Gradient (mm)
clinical
70
1.44
2.4
70
66
68
6.4
spack
59
1.54
3.0
65
70
67
6.0
9 beams
67
1.85
2.8
54
65
59
6.5
15 beams
72
1.49
2.8
67
64
65
6.6
9 beam IMRT
73
1.50
2.8
67
64
66
6.6
5dyn arcs
71
1.61
3.5
62
62
62
6.8
Figure 6-7a: VC-2 ten isocenter clinical plan orthogonal view isodoses. The 70%, 35%,
and 14% isodose lines are shown in the axial, sagittal, and coronal views.
Figure 6-7b: VC-2 thirteen isocenter autopian plan orthogonal view isodoses. The 59%,
30%, and 12% isodose lines are shown.


244
o.
o
t-
z
E
QJ
c
'ra
k-
m
Prescription dose (Gy)
Figure 6-7i: Brainstem NTCP as a function of prescription dose for case VC-2.
Prescription dose (Gy)
Figure 6-7j: Probability of no complication, P(NC), as a function of prescription dose for
case VC-2.


293
used at the University of Florida, while dose distributions for all other treatment methods
were calculated using the CadPlan treatment planning system. It is assumed throughout
this work that the dose distributions calculated by both systems are valid. To obtain the
most accurate and consistent comparison between the treatment methods modeled on
each planning system, a locally developed computer program was used to transfer image
data and anatomical structure information from the UF in-house planning system to
CadPlan.
A set of twelve representative clinical example cases was selected from
the University of Florida SRS patient database for comparison. The cases were classified
according to the complexity of the clinical multiple isocenter (or single isocenter in one
of the twelve cases) plan with which the patient was treated. For each example case, five
radiosurgery plans were compared: 1) the clinical multiple isocenter plan, 2) an
optimized sphere packing multiple isocenter plan, 3) a (fifteen beam) static beam plan, 4)
an IMRT plan using nine isotropic beams, and 5) a four dynamic arc plan using a
templated set of four ninety degree arcs. Dose-volume histograms (DVHs) of the target
volume, nontarget volume, and any involved radiosensitive structures were computed,
and isodose plots were generated for each plan. The DVHs were analyzed to determine
the conformity and dose gradient of the physical dose distribution, and biological indices
used to further compare plans with similar physical dose distributions.
Based on physical dose distributions, multiple isocenter treatment
planning is clearly superior to the alternative methods for the simple and complex
example cases (up to nine isocenters used in the clinical SRS plan). For the very
complex cases (ten or more isocenters in the clinical SRS plan), multiple isocenters were


physics program at the University of Florida in August 1997. During his doctoral work,
he served as a graduate teaching assistant in the Department of Nuclear and Radiological
Engineering, and also as a graduate research assistant in the Radiosurgery and
Radiobiology Laboratory at the University of Florida Brain Institute.
He is a member of the American Association of Physicists in Medicine and the
Health Physics Society. He is also a member of the Tau Beta Pi engineering honor
society, the Eta Kappa Nu electrical engineering honor society, the Delta Phi Alpha
German honor society, the Golden Key National Honor Society', the Phi Kappa Phi
graduate honor society, and the Alpha Nu Sigma nuclear sciences honor society.
306


86
Figure 3-18: Three-dimensional depiction of the example phantom target and spheres
placed by the sphere packing algorithm, a) Target volume b) Sphere packing
arrangement for five-isocenter plan c) Target volume superimposed on sphere packing
arrangement d) Prescription isodose surface (64% of maximum dose) superimposed on
sphere packing arrangement e) Prescription isodose surface superimposed over target
volume. The prescription isodose surface covers the target with the exception of isolated
'clipped" edge voxels (see arrow), f) Superposition of target volume, sphere packing
arrangement, and prescription isodose surface.


143
degrees < < 90 degrees). Typically, values of wvenex = 3 and winl- = 5 were used,
resulting in an fbeam factor as shown in Figure 4-16.
Relative score function importance weights of eye orbits = 1000, optic nerves =
100, brainstem = 10, and target area = 1 are generally chosen, to ensure that the
optimization algorithm will encourage protecting the most radiosensitive structures (eye
orbits and optic nerves) first, before accommodating the less important objective of
minimizing target cross sectional area.
35
30
25
I20
OJ

-Q
15
10
5
0
-80 -60 -40 -20 0 20 40 60 80
Phi (matlab elevation angle sph coords), degrees
Figure 4-16: Plot of fbeam.i versus elevation angle.
5) Optimize the orientation the entire bouquet of beams as a fixed set. The score
for an entire bouquet of N beams is
(414^ score = H scorer
/=!
Optimization consists of azimuthally rotating the bouquet through 360 degrees,
followed by a large number ( 20) of downhill optimization searches, each from a
fbeamZm with Wvertex = 3. Winf = 5


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Wilkins: 55-88.
Sailer, S. L., Rosenman, J. G., Symon, J. R., Cullip, T. J. and Chaney, E. L. (1994). The
tetrad and hexad: maximum beam separation as a starting point for noncoplanar 3D
treatment planning: prostate cancer as a test case. Int J Radiat Oncol Biol Phys
30(2): 439-46.
Schell, M. C., Bova, F. J., Larson, D. A., Leavitt, D. D., Lutz, W. R Podgorsak, E. B.
and Wu, A. (1995). Stereotactic Radiosurgery: Report of Task Group 42 Radiation
Therapy Committee. New York, American Association of Physicists in Medicine.
Schulder, M., Narra, V., Cathcart, C. and Halpem, J. (1997). Limited arc LIN AC
radiosurgery (abstract). International Stereotactic Radiosurgery Society (ISRS) 3rd
Congress. Madrid: 90.
302


33
radiosurgery dose distribution. Figure 2-10 shows direct DVHs from two hypothetical
radiosurgery plans for a radiosensitive structure.
10 20 30 40 50 60 70 80 90 100
B
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
10 20 30 40 50 60 70 80 90 100
Relative dose
Relative dose
Figure 2-8: Ideal target (A) and non-target volume (B) direct DVHs. Note that in the
ideal direct DVH of the non-target volume (right side), the plot is empty, since there is no
non-target volume receiving any dose in the ideal case.
0 10 20 30 40 50 60 70 80 90 100
Dose(% of max)
Dose (% of max)
Figure 2-9: Typical (non-ideal) radiosurgery direct DVHs for target volume (A) and non-
target volume (B).


210
high UF index score (conformity and gradient) with a lowered predicted risk of
complication based on biological models.
Figure 6-li: Plot of nontarget brain NTCP versus prescription dose (Gy) for case S-l.
The clinical plan and the sphere packing autopian curves lie to the right of the alternative
plan NTCP curves.


251
Figure 6-9a: VC-4 thirteen isocenter clinical plan orthogonal view isodoses. The 70%,
35%, and 14% isodose lines are shown in the axial, sagittal, and coronal views.
Figure 6-9b: VC-4 seventeen isocenter automatic plan orthogonal view isodoses. The
66%, 33%, and 12% isodose lines are shown in the axial, sagittal, and coronal views.
isodose lines are shown in the axial, sagittal, and coronal views.


54
The BED represents a biologically effective dose for tissues with an a/p ratio of
(a/p) when delivered in fractions of dose size d. In this relation, a and P are the
coefficients in the linear-quadratic cell survival curve (Hall 1994a; Hall 1994b). To
gauge the biological effect of two' different doses, Di and D2, given in individual fraction
doses of di and d2, respectively, one would calculate and compare the BEDs calculated
for DI and di, and for D2 and d2 using equation (2-11). Unit analysis of Eq. (2-11) shows
that BED has units of Gray (Gy), although to indicate that the quantity BED is
biologically effective dose rather than a physical absorbed dose, BEDs are usually
subscripted writh their a/p ratio, e.g. Gy2. For the purposes of comparing rival treatment
plans, 2.0 is an acceptable default a/p ratio for normal brain and nervous tissue (Smith
1998). To use the NTCP models in equations (2-6) through (2-9) with single fraction
SRS dose distributions, the volume element in each SRS DVH dose bin must be
transformed into a biologically equivalent dose using equation (2-11), and each organs
tolerance dose (TD50, in units of Gy) must be transformed into a biologically equivalent
single fraction BETD50. Table 2-3 summarizes NTCP model data taken from Burman
(Burman 1991) and Emani (Emami 1991) for intracranial anatomy. The radiosurgery
BED for each organs TD50 is calculated for a fractionation schedule of 2 Gy per fraction
and an a/p ratio of 2.0, in units of Gy2.


36
Cumulative DVHs will be used throughout the remainder of this report, unless otherwise
noted.
The information in DVHs can be used to compare rival treatment plans in many
situations. Optimal DVH curves- for target structures will be as far towards the upper
right hand comer of the plot as possible, while the optimal DVH curves for non-target
structures will be as close as possible to the lower left hand comer of the plot axes as
possible, as shown in Figure 2-12. Thus, one may readily evaluate two rival treatment
plans based upon their DVHs, if the DVH curves for each plan do not intersect, since the
more desirable curve will lie either above and to the right of the other (if it is a DVH
curve of a target volume) or below and to the left if it is a non-target volume DVH curve.
With these mies for evaluating cumulative DVHs, we can use Figure 2-11 to evaluate
Plan 1 and Plan 2 for the radiosensitive structure. Since the curve for Plan 1 always lies
below and to the left of the Plan 2 curve, and the brainstem is a non-target tissue, we can
conclude that Plan 1 is the preferred plan in order to minimize the radiation effects to the
brainstem. The relative ease of this comparison underscores the general utility of
cumulative DVHs (Figure 2-11) over direct DVHs (Figure 2-10) (Lawrence 1996;
Kutcher 1998).
Unfortunately, it is rare for the cumulative DVH curves of rival treatment plans to
separate themselves from one another so cleanly. A more general and common
occurrence in comparing treatment plans is shown in Figure 2-13, in which the DVH
curves cross one another, perhaps more than once. The general mies above for
evaluating DVHs cannot resolve this situation, in which case we must use other means to


12
can also deliver intensity modulated dose profiles similar to those achievable using
custom beam compensators, but without the disadvantages of fabrication time or of
needing to manually change a physically mounted beam filter between each treatment
field (Stemick 1998). Thus, a computer-controlled MLC and treatment machine offer the
potential to deliver more sophisticated radiation treatments to each patient with the same
time and cost resources available. Moss investigated the efficacy of performing
radiosurgery treatments with a dynamically conforming MLC in arc mode, and concluded
that dynamic arc MLC treatments offered target coverage and normal tissue sparing
comparable to that offered by single and multiple isocenter radiosurgery (Moss 1992).
Nedzi (Nedzi 1993) showed that even crude beam shaping devices offered some
conformal benefit over single isocenter treatments with circular collimators.
Figure 1-5: Multileaf collimator (arrows) attached to the gantry of a linear accelerator.
The MLC leaves define a small square aperture in this picture.


163
The patient was treated clinically with a 13-isocenter circular collimator
radiosurgery plan using 18, 16, and 10 mm diameter collimators, delivering a prescribed
dose of 12.5 Gy to the 70% (of maximum dose) isodose shell. The patients lesion was
manually contoured following treatment, and a sixteen isocenter sphere packing multiple
isocenter plan automatically generated (by the method presented in Chapter 3) to
compare with the nine beam plan.
Beam vector and score function data for the initial nine beam bouquet are shown
in Table 4-10. Several beams irradiate the right optic nerve and orbit, the left eye orbit,
and brainstem, as indicated by non-zero fractional volumes of intersection (FVIs). Table
4-11 shows the same data for the nine beam bouquet after it has been optimally
azimuthally rotated, and Table 4-12 shows the bouquet data after the best azimuthally
rotated bouquet has undergone one downhill optimization search. The final, fully
optimized isotropic nine beam bouquet beam directions and score function data are
shown in Table 4-13, and the optimized beam bouquet is shown in Figure 4-22. The
average score and average FVI for each critical structure decreases as the bouquet
undergoes each stage of optimization. The initial bouquet from Table 4-10 has an
average beam score of 44.08 (due mostly to beam 2 with a score of 358.6, which covers
34% of the right eye orbit volume). By the final stage of optimization, the average score
has decreased to 1.06, and all critical structures except the brainstem have been
completely avoided (all non-brainstem FVIs are zero). The brainstem average FVI
decreases from the initial, unoptimized bouquet brainstem FVI of 0.018, to a brainstem
FVI of 0.006 for the fully optimized bouquet. Average target area decreases very slightly
during the optimization process, from an initial bouquet value of 1400 pixels to 1388


234
Figure 6-6c: VC-1 fifteen beams plan, 70-35-14%.
Figure 6-6d: VC-1 nine IMRT beams plan, 75-38-15% isodoses shown.
Figure 6-6e: VC-1 five dynamic MLC arcs plan, 67-34-13%.


46
2 is that the steepest dose gradient for most (properly planned) multiple isocenter dose
distributions lies between the 70% and 35% isodose shells, with an effective distance
between the prescription and half-prescription isodose shells of 6.8 mm, corresponding to
a UFIg score of 62. Therefore, in multiple isocenter radiosurgery planning, the planner
should attempt to fit the 70% isodose shell to the target (as opposed to the 80%, 60%, or
other isodose shells) in order to maximize the dose gradient and non-target tissue sparing
(Meeks 1998c).
Table 2-2: Dose gradient variation with selection of prescription isodose shell for
multiple isocenter "F"-shaped dose distribution
Rx isodose
Gradient (mm)
UFIg
90
8.6
44
80
7.1
59
70
6.8
62
60
7.3
57
50
8.3
47
40
9.7
33
30
10.7
23
20
9.3
37
Dose conformity is another important characteristic of a radiosurgery treatment
plan which should be considered in plan evaluation. A means of converting dose
conformity in terms of PITV into a conformal index score on a common scale with UFIg
has been proposed, the UFIc score. The UF Index (conformal), or UFIc, is defined as
(2-5) UFIc = 100
Target volume
Prescription isodose volume
= (PITV)" x 100.


Beam
176
r
Beam
Resultant dose
0 *
2
2
2
2
0
0
J
0.0
0.5
0.5
0 5
0.5
0.0
1
2
4
4
"4
4
2
1
0.5
1.0
1.0
1.0
1.0
0.5
1
1
2
2

4
4
4
4
4
4
4
1
1
0 5
1 0
1 n
1 n
1 n
0.5
4
2
_l Beam
0.5
1.0
1.0
1.0
1.0
0.5
0
0
2
2
2
2
0
0.0
0.5
0.5
0 5
0.5
0.0
1111
Target
*
Beam
Figure 5-la: Simulated dose distribution from four conformal fields of equal intensity,
with an irregularly shaped target. Each beam shown schematically on the left has an
intensity of 1 where it intersects the target shape. The dose to each individual cell is
modeled as the sum of all beam intensities intersecting that cell. The total dose
distribution is shown on the right side, with the dose level completely covering the target
(4 units) normalized to a value of 1.0. The average dose to the non-target cells is 0.5.


101
Patient 8 -12.8 cc meningioma
Total CT volume dose-volume histogram
Patient 8 -12.8 cc meningioma
Target and total volume dose-volume histograms
Figure 3-21: Dose volume histograms for patient 8, a 12.8 cm3 cavernous sinus
meningioma. The clinical plan (solid line) uses 20 isocenters, prescribed dose is 12.5 Gy
to the 70% isodose shell, with a PITV of 1.05. The automatic sphere packing plan
(dashed line) uses 20 isocenters, with a prescription dose of 12.5 Gy to the 67% isodose
shell, and a PITV of 1.27. The clinical plan exposes 0.6 cm3 of non-target volume to the
prescription dose level (12.5 Gy), while the automatic sphere packing plan exposes 3.5
cm3 of non-target volume to the prescription dose level.


10
individually constructed by pouring low melting point alloy (cerrobend) into a mold,
which is attached to a mounting tray. The edges of the apertures defined in the hardened
metal block are designed to match the divergence of the radiation beam emanating from
the treatment machine. A separate block must be manufactured for each beam that will
be used to treat the patient. Although offering the best possible match between the shape
of the target and the shape of the beam-defining aperture, the time and cost of
manufacturing such blocks limits the number of blocks and radiation beams which can be
used to treat a patient.
Wedge beam filters may be used with or without the presence of beam shaping
devices such as the custom blocks mentioned above. Wedge filters are placed in the path
of the photon beam in order to tilt the shape of the isodose distribution. This provides a
simple one-dimensional intensity modulation across the treatment field, which is often
advantageous to the treatment planner in obtaining a more homogeneous dose
distribution in the target volume. This is desirable in certain cases, for example where
the patients anatomy changes significantly over the extent of the field. Proper placement
of a wedge filter in this case can effectively compensate for missing tissue on one side of
a treatment field. Wedges are also commonly used to reduce dose heterogeneity
(hotspots) in regions of beam overlap inside the target (Khan 1994, Ch. 11).
The idea of using a filter to modulate the beam intensity across the treatment
beam is extendable to a two-dimensional intensity modulation. A typical such 2D
compensating filter is generally used to adjust the beam intensity over a grid of small
square regions, with the goal of obtaining a uniform dose distribution in a plane near the
target. Such devices are designed for each patient, and are typically constructed by


119
1 21 41 61 81 101 121 141 161 181
Observation number
Figure 4-4: Vector-vector angular distribution for 7 isotropic vectors generated by
Webbs computer program(Webb95) and by a locally written computer program.


BIOGRAPHICAL SKETCH
Thomas H. Wagner was bom in September 1966 in Knoxville, TN. He attended
the University of Tennessee from 1984 to 1988, earning a Bachelor of Science in
electrical engineering (with honors) in June 1988. Following college, he entered the U.S.
Navy through the Nuclear Power Officer Candidate Program, and entered the U.S. Naval
Officer Candidate School (OCS) in Newport, RI in July of 1988. After receiving his
ensigns commission, he received nuclear power training at the Naval Nuclear Power
School in Orlando, FL, and at the S-1C submarine prototype reactor in Windsor Locks,
CT. He reported to the USS Francis Scott Key (SSBN-657)(BLUE) in Charleston, SC, in
June of 1990. He completed four SSBN deterrent patrols aboard the Key during three
years at-sea, serving as Reactor Controls Officer, Torpedo and Missile Officer, Sonar
Officer, and Assistant Strategic Weapons Officer, and also served as a shipyard
Engineering Duty Officer during the Francis Scott Keys decommissioning and reactor
defueling at Pearl Harbor Naval Shipyard in Pearl Harbor, HI. He also served as a Shift
Engineer and Staff Instructor at the Nuclear Power Training Unit, Charleston, SC from
1993 to 1995, when he left the naval service.
He entered graduate school at the University of Florida in August 1995 as a U.S.
Department of Energy Applied Health Physics Fellow, and completed a Master of
Engineering degree in medical health physics and radioactive waste management in May
1997. Following an internship at the Radiation Internal Dose Information Center at Oak
Ridge National Laboratory, he commenced fulltime work as a student in the medical
305


132
produce simply a blank image, which does not produce any overlapping pixels with the
target (Figure 4-6). For each structure in a beam's eye view, the number of points
belonging to the structure which intersect the target plus margin is noted, and is used to
calculate an approximate fractional volume of intersection (FVI) of the structure with the
beam (McShan 1995). For instance, if a structure has 1000 points distributed around the
periphery of all of its axial contours, and 500 of these points map into a region of the
BEV which overlaps the target, then the structure of has an FVI of 500/1000 = 0.50 for
this beam. A "true" computation of FVI for a structure with a beam would count the
intersection of an arbitrarily shaped beam with all of the volume elements comprising the
structure. The computation of FVI described here is not exact, since it is really a
calculation of the intersection of the beam with points distributed over the target's surface
rather than throughout it's volume. However, this approximate FVI is a close
approximation to the "true" FVI, and may be computed in a much simpler manner than
the "true" FVI. The approximate FVI calculation here is suitable for determining which
of several possible beam directions will encompass a greater volume of a critical
structure (Das 1997).


51
Dose (% of maximum)
Figure 2-18(a): DVHs for hypothetical radiosurgery plan (Plan 1).
Dose (% of maximum)
Figure 2-18(b): DVHs for hypothetical radiosurgery plan (Plan 2).


239
are shown in Figures 6-7h and 6-7i, respectively, while Figure 6-7j shows a plot of P(NC)
versus prescription dose. From Table 6-15 and Figure 6-7j, it can be seen that the
treatment plans are ranked somewhat differently based on NTCPs, or P(NC), than when
rankings are based upon UFI.- Ranking plans in descending order of the probability of no
complication, P(NC), shows the IMRT plan as the best-performing plan, followed by the
fifteen beam plan, the clinical multiple isocenter plan, the four dynamic arc plan, and the
sphere packing multiple isocenter plan. From Figure 6-7j, the IMRT plan and fifteen
beam P(NC) curves are to the right of the other curves, and appear slightly better than the
other plans based upon P(NC). The sphere packing plan appears slightly worse in terms
of P(NC), since its P(NC) curv e is to the left of all the other P(NC) curves, although it is
only about 2.5 Gy to the left of the curves for the IMRT and fifteen beam plans. The
same ranking is obtained from Table 6-15, although the differences between the rival
plans are much less pronounced, amounting to a difference only in the seventh significant
digit of P(NC) at the clinical prescription dose of 10 Gy.
Based on these comparisons, it is difficult to determine the best treatment plan
with much certainty, based only on the dose-volume and NTCP information available. It
is reasonable to conclude that at a prescription dose of 10 Gy, all of the treatment plans
except for the four dynamic arc plan are approximately dosimetrically equivalent.


84
a)
b)
Figure 3-17: Major steps of the grassfire and sphere packing process for a phantom target
(phantom target number three), shown in a coronal plane, a) Voxelized model of the
target, constructed from axial contours, b) Solid model after application of the grassfire
process in 3D. Voxel intensity (color) is a function of each voxel's value after the
grassfire process, c) First isocenter, 22 mm diameter, placed at best-scoring voxel, d)
The voxels inside the sphere are effectively removed for purposes of the grassfire
process. Note the change in the voxel values (color) near the target borders, at the arrow,
e) The situation after application of grassfire process. The deepest voxels are now
identified as candidate isocenter locations for the second isocenter, f) Placement of the
second isocenter, g) Voxels inside the second sphere are effectively removed, h)
Applying the grassfire process after the situation in g). Arrows indicate locations where
voxel values have changed.


113
Webbs algorithm was coded in ANSI C locally, and its output checked to verify
agreement with Webbs published isotropic beam arrangements of 3-8 beams. The code
was then used to generate additional arrangements of 9, 11, 13, and 15 beams. The
optimization program runs on-a DEC Alpha workstation or a SGI Onyx R10000 in about
ten to twenty minutes. An example of the agreement between the locally generated beam
vectors and Webbs is shown in Tables 4-1 and 4-2. These tables list the vector-vector
angular spacings for two four-beam (four beams and eight vectors, since each beam
entrance vector is opposed by a beam exit vector) bouquets, one generated by Webbs
program, and the other by the locally written program. Inspection shows that Tables 4-1
and 4-2 are identical, indicating that both four-beam bouquets are equivalent. Figure 4-1
shows a plot of all of the cells in Figures 4-la and 4-lb, sorted by magnitude. The inter
vector angle distribution of Webbs four-beam bouquet is identical to the locally
generated four-beam bouquet. Webbs four-beam bouquet has an average minimum
separation angle of 70.5 degrees, as does the locally generated four-beam bouquet.
Similarly, Figures 4-2, 4-3, 4-4, and 4-5 show the distribution of vector-vector angles for
Webbs and locally generated bouquets of five, size, seven, and eight beams,
respectively. In each case there is very close agreement in terms of the inter-vector
angular distribution between Webbs published bouquets and the locally generated
bouquets.
Agreement between Webbs isotropic beam arrangements and the locally
generated arrangements was further verified by generating static beam treatment plans
with 4-8 beams for a 30mm diameter spherical target in a hemispherical dosimetry
phantom, based on each set of isotropically converging beams. The dosimetric figures of


263
proximity to the brainstem. Ranking plans by P(NC) based upon computed NTCPs
(Table 6-25) results in a plan ranking from best to worst of IMRT, clinical multiple
isocenters, four dynamic arcs, sphere packing autopian multiple isocenters, and fifteen
beams. The clinical plan P(NC) at the prescription dose of 17.5 Gy is almost identical to
the IMRT plan P(NC, and the plot of P(NC) versus hypothetical prescription dose also
shows that the IMRT plan and the clinical plan are very close to one another in terms of
predicted complication risk. The IMRT plan exposes a similar volume of brainstem to
doses above about 12.5 Gy (Figure 6-12g) as the clinical plan. The IMRT plan however
exposes a lower volume of brainstem to doses below' 12.5 Gy than the clinical plan.
Based on the physical dose distribution, the clinical multiple isocenter plan is
preferable over any of the other plans, although not by a very large margin. When
biological indices are used to evaluate the nontarget brain and brainstem response to each
dose distribution, the IMRT plan and the clinical plan are equivalent. Based upon the
physical dose distribution (UFI score), the sphere packing autopian, the fifteen beam
plan, and the nine beam IMRT plan are comparable to one another, all having UFI scores
within about 3 points of each other.
Table 6-24: Dosimetric figures of merit for case VC-7
Plan
Rx-dose
PITV
Vo ver (cm3)
UFIc
UFIg
UFI
Gradient (mm)
clinical
70
1.09
1.1
92
43
67
8.7
spack
69
1.38
4.6
73
45
59
8.5
9 beams
77
1.47
5.7
68
49
58
8.1
15 beams
78
1.44
5.3
70
50
60
8.0
9 beam IMRT
85
1.25
3.0
80
45
62
8.5
5dyn arcs
78
1.47
5.7
68
44
56
8.6


294
generally superior to the other methods, and at worst multiple isocenter treatment
planning was approximately equivalent to the alternative methods. Plan rankings on the
basis of biological models generally agreed with and followed the plan rankings on the
basis of physical dose distribution. For larger targets, and for targets without detailed
features, such as small protrusions, the IMRT plans performed fairly comparably to the
multiple isocenter plans, and in several cases would probably have been an acceptable
substitute for the multiple isocenter treatment plan used for clinical treatment. Because
the time required to deliver a multiple isocenter treatment increases linearly with the
number of isocenters, and because the multiple isocenter dose gradient degrades as more
isocenters are added, IMRT could potentially effectively compete with multiple isocenter
SRS for treating large or irregularly shaped lesions without detailed features, which
would still require many (more than about sixteen) isocenters. The fifteen static beam
plans and four dynamic arc plans consistently ranked below the multiple isocenter plans
and IMRT plans based on the physical dose distribution and on ranking by biological
indices.
These general guidelines allow the clinician to apply the results of
optimized treatment planning from these twelve example cases to deciding upon the
optimal treatment method to use for prospective clinical cases in the future. Since the
computer algorithms for each type of treatment plan optimization have been developed
and can be executed in a clinically useful timeframe, the best answer to the clinicians
question of which treatment method to use for a specific patient would best be found by
generating optimized treatment plans specifically for that patient case, and making the
decision based on the set of optimized treatment plans rather than applying the general


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226
plan or the sphere packing plan) are the best treatment option in this case, owing to their
significantly improved conformity and dose gradient over the alternative plans, and lower
predicted risk of complication with non-target brain and brainstem.
Table 6-10: Dosimetric figures of merit for case C-3
Plan
Rx-dose
PITV
Vover (cm3)
UFIc
UH&
UFI
Gradient (mm)
clinical
70
1.09
0.3
92
73
82
5.7
spack
63
1.32
1.1
76
71
73
5.9
15 beams
74
1.37
1.3
73
61
67
6.9
9 beam IMRT
68
1.46
1.6
68
66
67
6.4
5dyn arcs
72
1.67
2.3
60
59
60
7.1
Figure 6-5a: C-3 clinical 8 isocenter plan, 70-35-14% isodoses.
Figure 6-5b: C-3 sphere packing code 9 isocenter plan, 63-32-13% isodoses.


265
Figure 6-12d VC-7 nine IMRT beam plan, 85-42-17% isodoses.
Figure 6-12e: VC-7 five MLC arcs plan, 78-39-16% isodoses.


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Biol Phys 33(5): 1209-19.
McLenaghan, R. and Levy, S. (1996). Projective transformations. CRC Standard
Mathematical Tables and Formulae. Zwilinger, D. Boca Raton, CRC Press: 304.
McShan, D. L., Kessler, M. L. and Fraass, B. A. (1995). Advanced interactive planning
techniques for conformal therapy: high level beam descriptions and volumetric
mapping techniques. Int J Radiat Oncol Biol Phys 33(5): 1061-72.
Meeks, S., Buatti, J., Foote, K., Friedman, W. and Bova, F. (2000). Calculation of
cranial nerve complication probability for acoustic neuroma radiosurgery. Int J
Radiat Oncol Biol Phys: (in press).
Meeks, S. L., Bova, F. J. and Friedman, W. A. (1998a). Technical aspects of radiation
physics. Textbook of Stereotactic and Functional Neurosurgery. Gildenberg, P. L.
and Tasker, R. R. New York, McGraw Hill: 649-668.
Meeks, S. L., Bova, F. J., Friedman, W. A., Buatti, J. M. and Mendenhall, W. M.
(1998b). Linac scalpel radiosurgery at the University of Florida. Med Dosim
23(3): 177-85.
Meeks, S. L., Bova, F. J., Kim, S., Tom, W. and Buatti, J. M. (1999). Dosimetric
characteristics of a double-focused miniature multileaf collimator. Med Phys
26(5): 729-733.
Meeks, S. L., Buatti, J. M., Bova, F. J., Friedman, W. A. and Mendenhall, W. M.
(1998c). Treatment planning optimization for linear accelerator radiosurgery. Int
J Radiat Oncol Biol Phys 41(1): 183-97.
Meeks, S. L., Buatti, J. M., Bova, F. J., Friedman, W. A., Mendenhall, W. M. and
Zlotecki, R. A. (1998d). Potential clinical efficacy of intensity-modulated
conformal therapy. Int J Radiat Oncol Biol Phys 40(2): 483-95.
301


289
following the fusion of the MR images with the stereotactic CT image set on the day of
treatment. In principle, this would provide up to an extra half-day or so of extra time in
which to run the computer optimization programs and to generate optimized treatment
plans of each type. Thusr- rather than extrapolating from the research SRS cases
presented here, customized multiple isocenter, static beam, and IMRT treatment plans for
each patient may be reviewed to decide on the optimal treatment delivery method for
each patient.
Conclusions
Optimized multiple isocenter, static beam, fixed beam IMRT, and dynamic arc treatment
plans were generated for twelve clinical example cases from the University of Florida
SRS patient database. The treatment plans were analyzed on the basis of physical dose
distributions and biological indices. For simple and complex cases (requiring one to nine
isocenters), multiple isocenter treatment plans provide the best physical dose distributions
and are deliverable in a reasonable amount of time. For larger, more complex targets,
multiple isocenters generally provide the best dose distribution, but IMRT plans can
approach multiple isocenter plans in terms of the physical dose distribution, and are much
less cumbersome to deliver than multiple isocenter plans with many isocenters.
General guidelines for appropriate use of multiple isocenter and IMRT treatment
delivery were presented. A process was developed which allows the clinician to generate
optimized multiple isocenter, static beam, and IMRT treatment plans in a clinically
relevant timeframe. The clincian can therefore make the decision as to the optimum
treatment method for a new SRS case based on a customized and optimized set of


279
plans more competitive with multiple isocenter planning than are the nine beam IMRT
plans. Hypothetical fifteen beam scores are shown in Table 6-30.


93
usually occur after one or more isocenter spheres have been placed. Figure 3-20 shows
such a situation for the phantom target depicted in Figure 3-17. The crosses in Figure 3-
17 show the location of several local maxima of the score function. In order to locate the
global maximum of the scoreJunction, either a more sophisticated optimization algorithm
is needed which can escape local extrema of the score function, or the starting point of
the downhill search must be chosen to be in the neighborhood of the global maximum
(Mohan 1996). Without prior knowledge of the solution space, the only way to locate the
global maximum with a downhill search algorithm is to perform a number of searches,
initiating each search from a different starting point (Das 1997). The grassfire algorithm
provides information about likely isocenter locations, since the deepest lying voxels
determined by grassfire are approximately the same locations corresponding to optimal
isocenter locations. The score function (Equation (3-2)) can be quickly computed for this
list of deepest voxels, which will quickly identify the best of them (highest scoring) as an
isocenter location. In Figure 3-20, one or two lighter colored voxels can be seen close to
the white crosses near the middle of the target. One of these is the starting location for
the downhill search which ends at the white cross location, nearby. Using this knowledge
of the approximate solution, obtained by the grassfire process and score function, allows
the downhill search algorithm to be started close to the global maximum of the score
function and ensuring that the global maximum will be found by the downhill search.


209
plan is more conformal than any other plan, and each has a steeper dose gradient than any
other plan. Both of these factors lead to the multiple isocenter plans exposing less
nontarget tissue to all except very low dose levels (Figure 6-lg). The steeper dose
gradient of the multiple isocenter plans relative to the alternative plans also provides for
better sparing of the brainstem from high dose levels, as shown by the brainstem DVHs
(Figure 6-lh). The superior conformity, gradient, and sparing of the radiosensitive
brainstem lead to lower predicted toxicity (NTCPs, Table 6-2b) for the multiple isocenter
plans. The decreased predicted risk of complication for the multiple isocenter plans over
the alternatives may be appreciated by plotting the predicted NTCP as a function of
prescription dose, as shown in Figure 6-i for the nontarget volume and in Figure 6-j for
the brainstem. These plots were generated by computing the NTCP for each structure
(nontarget volume, brainstem) with the prescription dose level (in Gray) set to a different
level. In theory, the least toxic plan would be that plan which allows the prescription
dose level to be escalated to the highest dose before incurring a specific risk of
complication. As shown by Figure 6-i, the superior conformity and dose gradient of the
multiple isocenter plans results in a significantly lower predicted risk of complication
within the nontarget volume for these plans over the nontarget plans. Similarly, the
superior brainstem sparing of the multiple isocenter plans allows significant theoretical
dose escalation with multiple isocenters without incurring an unacceptable predicted risk
of brainstem or cranial nerve complication, as shown by Figure 6-lj. It should be
emphasized that the purpose of this type of analysis is not to argue for actually escalating
the prescription dose. Rather, the purpose is simply to illustrate the correlation between a


168
Dose (% max.)
Figure 4-24: Total volume DVHs for an optimized, nine isotropic beam plan, and for a
multiple isocenter (13 isocenters) plan.
Table 4-14: Dose-volume data and figures of merit for sphere packing plan and for
isotropic nine beam plan
Plan
Rx-dose
Vtarg
V(Rx)
V(0.5Rx)
PITV
UFIc
UFIg
UFI
spack
66
7.3
12.9
44.1
1.53
65
56
61
9 beams
71
7.3
14.2
50.0
1.86
54
52
53


Targe t+3ramstem
Brainstem
Figure 4-12: The same BEV as in Figure 4-11, but composed of discrete lxl mm2 pixels
instead of continuously plotted points. This pixilated image is a composite image of the
target and each critical structure. For illustrative purposes, image pixels have been
assigned values as follows: 0 = pixel not in target nor in a radiosensitive structure, 1 =
pixel inside target but not inside a radiosensitive structure, 2= pixel inside target and
overlapping optic nerve, 3 = pixel inside target and overlapping brainstem.
Field Shaping with Multileaf Collimators
In three dimensional conformal radiotherapy, each beam aperture may be
shaped with custom blocks constructed of Lipowitzs metal, or with a multileaf
collimator. Using a multileaf collimator can save the cost and effort of block fabrication,
as well as reduce the likelihood of errors in the construction of each beam aperture
(Brewster 1995). Additionally, a reduction in treatment delivery time may be realized by


161
Number of beams
Figure 4-21(a): UF Index conformity scores (UFIc) for a series of irregularly shaped
clinical example targets versus the number of isotropically arranged shaped beams.


147
Figure 4-17d: Target cross-sectional area (relative units) as a function of beam position in
polar coordinates for an meningioma example case.
Limits on Adjusting Beam Positions from the Initial Isotropic Beam Bouquet
The rationale of using isotropic beam bouquets as a planning starting point is to
maximize dose gradient and to minimize the non-target volume exposed to significant
dose levels. As Webb mentioned, isotropically converging beam sets are only a starting
point for optimization, since such beam sets do not consider avoidance of critical
structures, or beam deliverability. Therefore, it will generally be necessary to adjust an
isotropic beam bouquet from its initial, maximally spaced-out state to a less isotropic
state. Guidelines are needed to establish how much perturbation from the initial isotropic
beam arrangement is acceptable.
This question may be answered by examining non-isotropic, but still
maximally spatially separated bouquets. The locally written isotropic beam bouquet code
may be used to generate arrangements of N beams, but which are restricted in allowable


20
exponential in shape, but is not a pure exponential due to the non-linear variation in
scattered radiation dose to the detector with changes in water depth, and due to beam
hardening effects at greater depths. The radiation absorbed dose data measured in this
manner is commonly referred to- as Tissue phantom ratio (TPR) when the dose is
normalized to the dose at a particular depth (Khan 1994). TPR data is measured for each
circular radiosurgery collimator (Duggan 1998), or may be interpolated for a given
collimator from data tables of several collimators spanning a range of sizes (Surgical
Navigation Technologies 1996).


171
dynamic arcing dosimetry: using smaller intervals between beams (resulting in more
beams per arc) resulted in increased dose computation time and did not provide
significantly more accurate dosimetry than the ten degree beam interval. Using a twenty-
degree beam interval, such that a 100-degree arc would be approximated by six beams
spaced at twenty degrees from one another, resulted in faster dose computation times but
did begin to degrade the quality of the overall dose calculation. Therefore, ten degrees is
an appropriate inter-beam interval for approximating each dynamic arc.
Shaped beams
Figure 4-27: Dynamic MLC arc technique. A ninety-degree dynamic arc is simulated as
ten individually shaped beams at ten-degree intervals.
Techniques used for shaping the field-defining aperture for each of the fields in a
dynamic MLC arc are similar to those described earlier for the isotropic N-beam
arrangements. Each fields aperture can be automatically generated by the treatment
planning system after the target has been defined by manually contouring it on the
patients MR or CT image dataset. One difference between setting an MLC-defined
aperture for dynamic arcing as compared with N isotropic beams is that the treatment


56
shown that it is possible to use them in the ranking of rival treatment plans, despite
uncertainties in the model parameters (Kutcher 1991).


CHAPTER 4
SHAPED BEAM SRS
Introduction
In radiotherapy treatments utilizing multiple beams (more than about 4
beams), such as stereotactic radiosurgery, the geometry of the beam arrangement
dominates the overall dose distribution. In stereotactic conformal radiotherapy (SCRT),
geometrical considerations have been used to advantage in planning the arrangement of
the therapy beams (Bourland 1994; Sailer 1994; Marks 1995; Das 1997). A general
geometrical objective of the methods described by these investigators has been to
converge conformally shaped photon beams upon a single target isocenter while
minimizing the overlapping volumes between beam entrance and exit paths. This
objective is believed to be achieved when beams are arranged with maximal spatial
separation in three-dimensional space. Such arrangements have been approximated by
placing beams manually (Bourland 1994; Marks 1995), starting with several equispaced
coplanar beams, and then rotating additional beams out of the beam plane between
existing beams. Iterative beam placement optimization algorithms have also been used
for this purpose, which incorporate a measure of beam separation with beam intersection
with non-target volumes as part of the objective function (Das 1997).
Webb proposed arrangements of isotropically convergent beams which
could be used as the starting point for a radiotherapy optimization process (Webb 1995).
Webbs arrangement of beam vectors were designed through a Monte Carlo process
109


105
1) For highly irregular targets, many isocenters may be needed with circular
collimators to achieve reasonable dose conformity and homogeneity. This can be very
difficult and time-consuming for a novice planner, especially for irregular lesion shapes
which are difficult to visualize.in 3D.
2) Although promising, the automatic sphere packing algorithm has not yet been
able to perform better than an expert human planner (based on both conformity and
homogeneity). This tool may serve to significantly reduce the effort involved in planning
irregular targets with many isocenters, however. The automatic sphere packing tool can
also serve as a useful basis for comparing multiple-isocenter radiosurgery plans to other
treatment methods, since as an automatic tool, it removes any biases that an experienced
human planner might bring to a comparison.
Sphere Packing Algorithm: Potential Developments
When the sphere packing algorithm was used as an autoplanner, reasonable
results were obtained, demonstrating the efficacy of sphere packing as a planning
methodology for multiple isocenter radiosurgery planning. However, several cautionary
distinctions should be made regarding clinical implementation of such a system. First, in
its current implementation as showm here, conformation of the high isodose region is the
only goal of the sphere packing algorithm. In cases in which the radiosurgical target is
adjacent to a critical structure, such as acoustic neuromas, which abut the brain stem, the
only sparing of the critical structure which will occur is that due to the dose gradient of
the multiple isocenter dose distribution in the direction of the structure, which may not be
satisfactory (Meeks 1998c). In such cases, manipulation of at least one isocenter's arc


70
Multiple Isocenter Radiosurgery Planning Tools
Multiple spherical dose distributions may be placed adjacent to one another to
build up a composite dose distribution which conforms to the shape of an irregular target,
as was shown for the F shaped target in Chapter 2. When using multiple isocenters,
typically five arcs (Figures 3-11, 3-12) rather than nine arcs (Figures 3-3, 3-7) are used
with each isocenter, since the dose distribution from five arcs is very similar to that from
nine arcs, and less time is required to deliver five arcs than nine arcs. Couch and gantry
angles for the standard five arcs used in multiple isocenter planning at the University of
Florida are listed in Table 3-2, and are depicted in Figures 3-11 and 3-12. Figure 3-11
shows the resultant dose distribution from a standard five-arc set, which is very similar to
the standard nine arc dose distribution shown in Figure 3-7.


........ Nontarget volume (cc)
Fractional brainstem volume 3 '
30
25 -
20 -
15 -
10
5 -
0 --
75
din-nontarg
spack-nontarg
15bm-nontarg
IMRT-nontarg
5dynarcs-nontarg
10 12 5 15 17 5 20 22 5 25
Dose (Gy)
2f: Nontarget volume DVHs for case VC-7. The prescription dose is 17.5 Gy.
1.0
03
0.6
04
02
Dose (Gy)
Figure 6-12g: Brainstem DVHs for case VC-7. The prescription dose is 17.5 Gy.


155
Dose gradient as scored by UFIg2
for 50 mm diameter sphere targe
so
Isotropy factor
Figure 4-19(c): Dose gradient (as expressed by UFIg2) versus isotropy for 50 mm sphere
target and bouquets of 5, 7, 9, and 15 beams.
The amount of angular movement (rotation) needed to attain an isotropy factor of
0.8 was determined by selectively perturbing isotropic beam arrangements. To determine
allowable angular movement limits of beams in each isotropic bouquet, a set of isotropic
beam bouquets was perturbed from its isotropic state by rotating all of the beams in the
bouquet towards a common point (in the same direction). By repeating this process for
each bouquet with different degrees of rotation, the rotation required to attain an isotropy
factor of about 0.8 was empirically determined for each bouquet. These results are
summarized in Table 4-8 for bouquets of five, seven, nine, and fifteen beams. A simple


123
Dose (% max.)
Figure 4-7: Agreement between Webbs eight beam bouquet (Webb 95) and locally
generated code eight beam bouquet, based on total CT volume dose volume histograms.
The maximum volume disagreement between the two curves is 0.2 cm3 for doses above
5% of maximum dose.


216
Patient C-l
Patient C-l is a 37 year old female with a 5.6 cm" transverse sinus meningioma.
This patient was treated clinically with a nine isocenter SRS plan using 41 arcs,
delivering 12.5 Gy to the 70% isodose shell. The sphere packing autopian program was
used to generate an eight isocenter plan using 32 arcs. Orthogonal view isodose plots for
all plans are shown in Figures 6-3a through 6-3e, with dose-volume figures of merit listed
in Table 6-6. Nontarget volume DVHs are shown in Figure 6-3f. For plan evaluation
with biological indices, NTCPs are listed in Table 6-7, and a plot of NTCP versus
prescription dose is shown in Figure 6-3h. Based on UF index (conformity and gradient)
and on biological indices (NTCP), both multiple isocenter plans (clinical and the spack
autopian) are superior to any of the alternative plans.
Table 6-6: Dosimetric figures of merit for case C-l
Plan
Rx-dose
PITV
Vover (cm3)
UFIc
UFift
UFI
Gradient (mm)
clinical
70
1.10
0.6
91
72
81
5.8
spack
69
1.22
1.2
82
77
79
5.3
15 beams
74
1.44
2.4
69
61
65
6.9
9 beam IMRT
83
1.34
1.9
74
57
66
7.3
5dyn arcs
75
1.49
2.6
67
60
64
7.0


195
The nine-beam plan provides a conformal dose distribution (PITV 1.35) with a
relatively steep dose gradient of 6.9 mm from the prescription dose of 10.0 Gy to half
prescription, 5.0 Gy. The IMRT plan provides very similar target coverage and dose
homogeneity to the nine-beam plan, but improves on the nine-beam plan in two respects,
dose conformity and dose delivered to the brainstem. The nine-beam IMRT plan has a
better PITV than the nine beam conformal plan (PITV 1.25 versus 1.35). Also, Figure 5-
8c shows the clear superiority of the IMRT plan brainstem DVH over the brainstem DVH
with the nine beam plan, as the nine beam IMRT plan brainstem DVH curve lies below
and to the left of the nine beam plan brainstem DVH curve for all dose levels above about
1 Gy. The IMRT plan is able to completely spare the brainstem of doses above the
prescription 10.0 Gy, while the nine beam conformal plan exposes a small volume of
brainstem to the prescription dose level. This example case shows the potential
improvements over conformal beam radiotherapy possible with intensity modulation,
i.e- improved conformity of the prescription isodose surface to the target without
degradation of the dose gradient outside of the target.


127
Rotation of Beam Bouquets
A beam coordinate system as shown in Figure 4-9, with the patient lying supine
on the treatment unit couch, was used to establish beam directions. Beams are described
by unit vectors in this system. Beam vectors are converted to IEC
gantry/table angles by a conversion routine using trigonometric relations between the x.y,
and z vector components to determine the spherical coordinate angles corresponding to
IEC couch/gantry angles. Users with other gantry/couch angle coordinates would require
different conversion transformations between each beam vector and its corresponding
couch and gantry angle. The discussion relating to beam orientation with respect to beam
vectors is general to any user, however.
+Y
Figure 4-9: Coordinate system for isotropic beam bouquet vectors
Rotation of a beam from one position to another is equivalent to rotating the
coordinate system through the same angle, and providing the new coordinates. The post-


38
target tissues. Typically, perfect conformity of the prescription isodose surface to the
target volume is not achievable, and some volume of non-target tissue must be irradiated
to the same dose level as the target, resulting in PITV ratios greater than unity. The most
conformal treatment plans are those with the lowest PITVs, if all of the plans under
comparison provide equivalent target coverage. This stipulation is necessary because the
definition of PITV does not specify how the prescription isodose is determined. It is
possible (but undesirable) to lower, and thus improve, the PITV by selecting an isodose
level which incompletely covers the target as the prescription isodose, and therefore
reduces the numerator of Eq. (2-2). Unless otherwise stated, prescription isodose levels
in the remainder of this report are selected to ensure that > 95% of the target volume
receives the prescription isodose. This ensures a more consistent basis of comparisons
for all treatment plans.
A sharp dose gradient (fall off in dose with respect to distance away from the
target volume) is an important characteristic of radiosurgery and stereotactic radiotherapy
dose distributions. Dose gradient may be characterized by the distance required for the
dose to decrease from a therapeutic (prescription) dose level to one at which no ill effects
are expected (half prescription dose).


31
gradients, lies in discerning the dose received by many possibly overlapping structures
around the target. Although a number of commercially available treatment planning
systems can render three-dimensional views of arbitrary isodose volumes in various
shades of translucency, along with any structures that the user has identified, it is very
difficult to determine precise (sub-millimetric) spatial relations between the target
volume, particular isodose volumes, and radiosensitive structures. For this reason, it is
usually necessary to evaluate a large number of two dimensional isodose plots through
the region of interest to determine plan suitability. In a single two dimensional isodose
plot, one may readily determine whether a particular isodose surface coincides with the
intersection of any particular volume with the image plane, to an accuracy of within one
image pixel in the plane of interest. Even this level (within an image pixel) of visual
inspection precision can still lead to significant errors in assessing the volume of dose
f A
coverage for small intracranial targets. Consider a 20 mm diameter spherical
radiosurgery target, for which we wish to evaluate dose coverage by inspection of an
isodose line overlaid on the image set. A 10% volume error results if the isodose line is
shifted half of one image pixel (one image pixel is 0.67 mm x 0.67 mm in a transaxial
plane for a 512 x 512 CT image acquired with a 35 cm diameter field of view) inward or
outward, which is the spatial resolution limit of our ability to discern positional shifts in
the image set. The 20 mm sphere, 4.2 cm3 volume, would apparently be equally well
covered by an isodose surface ranging in volume from 3.8 cm3 to 4.6 cm3. The volume
error problem worsens as target size decreases, and results in a 20% volume error for a 10
mm diameter target. One can imagine then the difficulty in evaluating a large number of
these isodose plots to within submillimetric image pixel resolution: on each image slice,


137
Collimator rotation affects the fit of the mMLC aperture to the ideal beam
aperture as well. Figure 4-15(a-c) shows the same target and mMLC aperture BEV for
several collimator rotation angles, writh leaves outside justification. The optimal
collimator rotation situation-is shown Figure 4-15(c), in which the non-target area
exposed to the beam has been minimized.
Although beam apertures defined by an MLC do not precisely match the
ideal target aperture, proper selection of leaf justification and collimator rotation can
greatly improve the closeness of fit between the MLC aperture and the ideal beam
aperture. The treatment planning system used in this study (CadPlan 6.08, Varian
Oncology Systems, Palo Alto, CA) offers the options of user-selected leaf justification,
and also of automatic collimator rotation optimization, which systematically calculates an
MLC aperture every degree of possible collimator rotation to find the best fit.


202
into an equivalent fractionated DVH using the biologically equivalent dose methodology
of Fowler (Fowler 1989). The treatment plans other than the clinical plan (the
alternative plans) used for patient treatment were designed to deliver the same
prescription dose to the target, with the prescription isodose shell chosen as that isodose
shell covering at least 95% of the target volume as indicated by the target dose-volume
histogram. As explained in Chapter 3 for the comparison of the automatic multiple
isocenter planning procedure, using this as a basis for the prescription isodose results in
small isolated pixels of the target being excluded from the prescription isodose shell, but
does not significantly impact the expected tumor control probability.
Clinical Example Case Data
Twelve clinical example cases are presented, consisting of two simple cases
(designated S-l and S-2), three complex cases (designated C-l through C-3), and seven
very complex cases (designated VC-1 through VC-7), classified as previously
described in Chapter 4, based upon the number of isocenters used in the clinical treatment
plan. In the data tables for each specific example case, the column heading Rx dose
refers to the prescription isodose surface in units of percent of maximum dose, Vover
refers to the amount of overcoverage, or the volume of non-target tissue receiving the
prescription dose or higher, UFI refers to the UF Index, and gradient refers to the
difference in effective radii between the prescription and half-prescription isodose shells
as defined by equations (2-3) and (2-4). Table 6-1 contains a summary of the size of the
lesion and diagnosis for each example case. The column titled No. of isocenters refers
to the number of isocenters used for each cases clinical SRS plan. A greater amount of
detail is shown for illustrative purposes for case S-l than is shown for the other cases.


Gradient score UFIg2
154
Dose gradient as scored by UFIg2
for 30 mm diameter sphere target
100
1 i i i
0.2 0.4 0.6 0.8 1.0
Isotropy factor
Figure 4-19(b): Dose gradient (as expressed by UFIg2) versus isotropy for 30 mm sphere
target and bouquets of 5, 7, 9, and 15 beams.


I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
V'j,;
William A. Friedman
Professor of Neurosurgery
This dissertation was submitted to the Graduate Faculty of the College of
Engineering and to the Graduate School and was accepted a^ partial fulfillment of the
requirements for the degree of Doctor of Philosoj
August 2000
J. Ohanian
Dean, College of Engineering
Winfred M. Phillips
Dean, Graduate School




89
(3-5) /3 =nf[dist(i,k)],
/=l
i*k
where
(3-6) /[dist(i,k) | / k] =
o,
10
dopt
1.0,
*dist(i,k)-9,
if dist(i,k) < 0.9doPi
if 0.9doPt < dist(i,k) < dop, ,
if dist(i,k) > dopt
and dist(i,k) is the distance between isocenters i and k.
Factor f[ is the fraction of target coverage for a sphere of a specified size at the
voxel under consideration, which varies from 0.0 to 1.0. Factor f: is a normal tissue
penalty function, so that fz = 1.0 if no normal tissue volume is covered, and f; -> 0.0 as
increasing volumes of normal tissue are covered. Factor f3 is a function of the distance of
each isocenter to all other isocenters. Factor f3 serves to prevent placing spheres
(isocenters) too closely to one another, which results in excessive target dose
heterogeneity (Meeks 1998c). This isocenter to isocenter distance function is zero for
isocenter-isocenter distances less than 0.9dopt (dopt = empirically determined optimal
isocenter-isocenter distance for the two spheres under consideration, implemented in the
form of a look-up table accessible to the code (Foote 1999)), is unity for isocenter-
isocenter distances greater than or equal to the optimal distance, and varies linearly
between zero and unity for distances between 0.9 dopt and dopt. Terms wi and W2 are
relative weighting factors, with which the user may control the behavior of the algorithm.
For example, an aggressive setting (relatively small penalty for normal tissue over
coverage) can be chosen by decreasing the relative weight of W2. A conventional sphere
packing (the target volume is filled with non-intersecting spheres which do not extend
outside of the target volume) results when W2 oc, so that fi = 0 if any normal tissue


225
Similarly, the nontarget volume NTCP vs. prescription dose curves (Figure 6-5h) lie to
the right of the NTCP curves for the alternative plans.
The clinical and sphere packing autopian multiple isocenter plans expose a very
small volume of brainstem to higher maximum doses than do the alternative plans, as
shown by the brainstem DVHs in Figure 6-5g. For doses below the prescription dose of
12.5 Gy, the multiple isocenter plan brainstem DVH curves lie below and to the left of
the brainstem DVH curves for the alternative plans. A closer examination (right side of
Figure 6-5g) shows that a very small volume of brainstem receives higher doses above
12.5 Gy with the multiple isocenter plans than with the alternative plans. This is due to
the prescription isodose line in both multiple isocenter plans intersecting a very small
amount of brainstem in an axial plan several millimeters away from the axial plane
shown in Figures 6-5a through 6-5e. This small intersection is shown in Figure 6-5j. The
maximum dose for the clinical plan and sphere packing multiple isocenter plans is 15.8
Gy and 14.8 Gy, respectively, albeit to very small volumes, with about (each 0.001 unit
along the DVH vertical axis represents 0.02 cm3 of fractional volume) 0.03 cmJ or less of
brainstem receiving the prescription dose level. These very small brainstem volumes at
high dose levels do not result in a greater calculated risk of complication (using Burmans
1991 published NTCP model parameters) for the multiple isocenter plans, as shown in
Table 6-11 and Figure 6-5i. The larger brainstem volumes receiving about 12.5 Gy and
less for the alternative plans, cause the alternative plans to have a higher predicted risk of
brainstem complication than the multiple isocenter plans.
Considering the physical conformity and gradient of each dose distribution along
with the biological index considerations discussed above, multiple isocenters (clinical


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303


180
required for the beams radiation output to stabilize after initiation of the beam, typically
1-5 MUs). For instance, consider an intensity modulated field delivered with a total of
400 MU, composed of 100 intensity levels. Each intensity level (subfield) would be
delivered with only 4 MU, barely enough (or not enough) to allow the beam to stabilize
before being turned off for the next subfield. To avoid this problem, the planner would
need to reduce the number of intensity levels used per intensity modulated field, or would
need to accept the possibility of having some subfields delivered with a not fully
stabilized beam, introducing an additional random error between calculated and actual
dose delivered. Neither of these possibilities is ideal, reducing the potential efficacy of
stop and shoot as an IMRT delivery method.
A more efficient method of delivering an IMRT field is to dynamically move the
MLC leaves to form a moving beam of radiation with the MLC leaves in motion while
the radiation beam is on. The IMRT fluence profile is divided into strips, with each strip
corresponding to the path of an opposed pair of MLC leaves. The leaves form an open
gap of variable width, which changes position and gap width while the beam is on until
each area under the pair of leaves has received the proper dose. This sliding window
technique is more efficient than the step and shoot technique in terms of the total
numbers of monitor units required to deliver the dose distribution. The sliding window
delivery techinique also avoids beam stabilization problems which can be encountered
when the beam is turned on and off again in increments of only a few monitor units, since
the beam is only turned on once at the beginning of the IMRT field and runs continuously
while the MLC leaves move. Finally, the sliding window technique offers a much wider
possible range of intensity values across each intensity modulated field than can be


190
Figure 5-6: Helios IMRT optimization window after 54 iterations. The score function
limits and weights are shown in the middle and upper part of the window, along with an
approximate DVH used by the optimization algorithm to compute the score function. As
shown, the optimization algorithm has almost converged, since the score function is no
longer decreasing. The bottom left portion of the window shows the optimization
progress as measured by the score function of equation (5-4). The bottom right side of
the window shows the current fluence map for the selected field (field 2 in this case).


283
of a multiple isocenter dose distribution. This effect can also be seen in the isodose
distributions for most of the very complex (VC) cases. In these cases, the IMRT
prescription isodose distribution is relatively conformal, but can be seen to be
smoothed with respect to the multiple isocenter plan prescription isodose lines, which
better follow the detailed surface of the target.
The score function which drives the IMRT beamlet weighting optimization
algorithm may have a bearing on the dosimetric results of an IMRT radiosurgery
treatment plan. As discussed in Chapter 5, the Helios IMRT optimization algorithm uses
a score function that includes dose-volume constraints from the target and from any
structures which the user has contoured and for which dose-volume constraints are
entered. This approach may not be well-suited for optimizing a radiosurgery beam
intensity distribution, in which dose conformity and dose gradient are the chief objectives
sought by experienced human planners. Using a score function which explicitly
considers these properties of the IMRT dose distribution could potentially result in IMRT
radiosurgery treatment plans which achieve a better blend of conformity and gradient
than achievable with the Helios IMRT planning system.
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gradient of multiple isocenter radiosurgery treatment plans. As was demonstrated for
cases S-l and S-2, multiple convergent arcs delivered with circular collimators produces
a much steeper dose gradient than that attainable with shaped or nine intensity modulated
beams. However, the multiple isocenter dose gradient worsens for larger and more
irregularly shaped targets which require large numbers of isocenters to cover a target
volume. As the number of isocenters and associated arcs increases, the beams in each arc


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304


196
Multiple Isocenters as a Special Case of IMRT
Multiple isocenter SRS with circular collimators is a form of temporally
modulated IMRT. In general, multiple isocenter SRS treatments involve the delivery of
non-uniform intensities of photons through a variety of apertures to achieve a uniform
dose distribution covering the target and a minimum of non-target tissue as a result. The
multiple isocenter treatment planning methodology presented in Chapter 3 is simply a
different means of determining the optimal photon intensity distribution than the Helios
inverse planning algorithm presented earlier.
To illustrate this point, consider a clinical example case (complex
clinical example case C-3 presented in Chapter 6). The clinical plan used to treat the
patient used eight isocenters with 24 arcs, delivering 12.5 Gy to the 70% isodose shell.
The target, isocenter locations, and associated collimator sizes (diameters) are shown in
Figure 5-11, and the numbers of arcs and relative weights of each arc set are listed in
Table 5-2. Isocenters with a single arc are depicted as 5 mm diameter spheres in Figure
5-11. Figure 5-12 shows the resultant isodose distribution, in wiiich the 70% isodose
shell covers the target volume.


Ill
related method to the isotropic beam bouquet approach. A single commercially available
3D treatment planning system (CadPlan 6.15, Varan Medical Systems, Palo Alto, CA)
was used to plan and compute the patient dosimetry for each isotropic beam and dynamic
MLC arcing treatment plan. By using a single treatment planning system for all SRS
treatment plans not involving circular collimators, difficulties with accurately and
consistently transferring patient data from one treatment planning system to another are
minimized.
Generation of Isotropic Beam Bouquets
Each bouquet of isotropic beam vectors is generated by a Monte Carlo
process described by Webb (Webb 1995) that iteratively generates maximally separated
beam vectors of N beams. Webb's algorithm systematically adjusts the orientations of
each beam in an arrangement of N beams, and attempts to find an arrangement which
maximizes the angular spacing between all beams. The optimization algorithm driving
this process scores each bouquet of N beams as a function of the angle between each
beam vector and every other beam vector. The optimization process maximizes a score
function.
(4-1)
In equation (4-1), 0p 2N vectors in the beam bouquet,
(4-2)


22
Depth to water phantom surface (cm)
Figure 2-2: Tissue-phantom ratio (TPR) curve in water phantom for a 6 MV photon beam
shaped with a 30 mm diameter circular collimator.
The dose profile in a plane perpendicular to the central axis (along the cross
beam direction in Figure 2-1) varies with distance from the central axis, and is thus
measured with a radiation detector as well in order to allow calculation of the radiation
dose at off-axis points. A plot of the radiation field intensity as a function of off-axis
distance, in a plane 100 cm from the radiation source, is shown in Figure 2-3 for a 30 mm
diameter circular radiosurgery collimator. This off-axis dose data is frequently
normalized to either its maximum value, or to the dose at the central axis, and is also
known as off-axis ratio, or OAR. Like TPR data, OAR data may either be measured
for each individual radiosurgery collimator, or may be interpolated from a table of
measured OAR values for selected collimators. Due to changes in the relative dose
profile with depth (due to changes in scattered dose and beam hardening effects), OAR
profiles are usually measured at several depths in order to provide measured data under
conditions close to those for which dose is being computed.


126
Table 4-6: Vectors and IEC gantry/couch angles for isotropic thirteen beam bouquet.
Each beam is separated from its nearest neighbor by an average of 39.8 1.3.
Ray
y.
1
-0734
0.00
2
0.38
-0.20
3
0.51
0.45
4
-0.03
-0.70
5
-0.11
0.69
6
-0.66
-0.54
7
-0.72
0.50
8
0.88
-0.05
9
0.59
-0.67
10
-0.98
-0.05
11
0.79
0.60
12
-0.28
-0.95
13
-0.34
0.93
z >
Couch
Gantry
0.94
70
90
0.90
293
259
0.73
305
296
0.71
88
134
0.71
81
46
0.52
38
123
0.48
34
60
0.47
332
267
0.45
323
228
0.20
11
93
0.14
350
307
0.14
26
162
0.12
20
21
Table 4-7: Vectors and IEC gantry/couch angles for isotropic fifteen beam bouquet. Each
beam is separated from its nearest neighbor by an average of 38.10 0.2.
Ray
< x,
y>
1
0.00
0.34
2
0.64
0.11
3
-0.01
0.86
4
-0.53
0.34
5
-0.27
-0.21
6
0.41
0.56
7
0.11
-0.61
8
-0.57
0.82
9
0.94
0.09
10
0.18
0.99
11
-0.38
-0.66
12
0.77
-0.55
13
-0.98
0.18
14
-0.78
-0.57
15
0.14
-0.87
z >
Couch
Gantry
0.94
270
290
0.76
310
276
0.51
89
31
0.78
56
70
0.94
74
102
0.72
300
304
0.79
278
232
0.02
2
35
0.34
340
275
0.01
358
350
0.64
59
132
0.34
336
237
0.01
1
80
0.27
19
124
0.47
287
209


136
to beam penumbra. In conventional radiotherapy, the beams eye view and block
aperture outline are determined through plane radiographs of the patient on a treatment
simulator, while in 3D virtual simulation the target shape and beams eye view are
determined from three-dimensional CT scan information. If custom blocks are used to
define the beam aperture, either the simulator film or the beams eye view from the
virtual simulation is used to construct a block of low melting point alloy, which will be
used to treat the patient. In the case of multileaf collimation, the user, aided by the virtual
simulation and/or treatment planning system, decides how to best approximate the ideal,
continuous beam aperture with the mMLC.
Figure 4-14 (a-c) shows several possible ways of fitting the mMLC-
defined aperture (jagged edges) to the ideal beam shape (smooth, continuous line). In
Figure 4-14(a), the mMLC leaves match inside of the ideal beam aperture, while in
Figures 4-14(b) and 4-14(c), the mMLC leaves match the middle and outside of the ideal
aperture, respectively. The inside leaf, or inbound justification method exposes the
least area (and volume) of non-target tissue to the radiation beam, but at the cost of
covering small areas (volumes) of the target with the edges of the mMLC leaves. As one
progresses from leaves inside to leaves outside mMLC leaf justification (from
inbound, to crossbound, and to outbound leaf justifications), better target coverage is
obtained, but at the expense of covering larger areas of non-target tissue with the beam.
There is currently no universally accepted correct method of leaf justification;
customization of a default MLC leaf justification may be needed depending on the
treatment site (anatomical location and size of the lesion) (Mohan 1998).


177
ts^-m
0
1
3
1
3
0
0
-2
6
2
6
0
0.0
0.2
0.6
0.2
0.6
0.0
4 '
6
10
6
10
4
2 s
0.4
0.6
1.0
0.6
1.0
0.4
8
10
14
10
14
8
4 u
0.3
1.0
1.4
1.0
1.4
0.8
4
6
10
6
10
4
2 X
0.4
0.6
1.0
0.6
1.0
0.4
0
2
6
2
6
0
ju_h
0.0
0.2
0.6
0.2
0.6
0.0
k 0 1 3 1 3 0 4
Figure 5-lb: Simulated dose distribution from four intensity modulated fields, with an
irregularly shaped target. Each beam shown schematically on the left has an intensity of
at least 1 where it intersects the target shape. The dose to each individual cell is
modeled as the sum of all beam intensities intersecting that cell. The total dose
distribution is shown on the right side, with the dose level completely covering the target
(4 units) normalized to a value of 1.0. The average dose to the non-target cells is 0.41.


80
Multiple Isocenter Radiosurgery' Planning via Sphere Packing
In a simple manner, multiple isocenter radiosurgery planning may be considered
as the problem of determining the positions and sizes of the multiple spherical high dose
regions or isocenters which will be used to fill up the target volume, or put another way,
of determining the sphere-packing arrangement with which to fill the target volume.
Conventional radiosurgery optimization schema are generally iteratively based,
dosimetrically driven algorithms. They require many computations in order to compute a
radiosurgical plan dose distribution, and then to evaluate the quality of the dose
distribution. Geometrically based radiosurgery optimization has been suggested as a
possible alternative means of optimizing radiosurgery treatment planning, since
geometrical solutions are generally much less computationally expensive than the large
iterative set of dosimetric calculations required for most other optimization strategies
(Wu 1996; Bourland 1997; Wu 1999). For instance, a high isodose region around a
single isocenter may be approximated by a sphere of a diameter approximately equal to
that of the circular collimator used. Given such a spheres location and diameter in
stereotactic space, it is much easier to describe this spheres spatial relationship to the
target volume than it is to compute a three dimensional dose distribution, and to then find
the relationship of this dose distribution to the target's volume.
Wu et al (Wu 1996; Wu 1999) proposed a geometrically-based sphere packing
optimization method for automated gamma unit radiosurgery, in which the shot
(isocenter) locations and sizes are selected according only to the targets three
dimensional shape. Grandjean (Grandjean 1997) et al report on their implementation of a
similar volume packing process for linac radiosurgery, but one in which ellipsoids as well


125
Table 4-4: Vectors and IEC gantry/couch angles for isotropic nine beam bouquet. Each
separated from
its nearest
neighbor by
an average of 47.6
if
o
o
Ray
< x,
z >
Couch
Gantry
1
-0.34
0.31
0.89
69
72
2
-0.28
-0.54
0.79
71
123
3
0.37
-0.08
0.93
292
265
4
-0.88
-0.11
0.46
28
97
5
0.35
0.67
0.65
298
312
6
-0.36
0.88
0.31
41
28
7
-0.61
-0.78
0.10
9
142
8
0.45
-0.75
0.48
313
221
9
0.94
0.00
0.35
340
270
Table 4-5: Vectors and IEC gantry/couch angles for isotropic eleven beam bouquet. Each
beam is separated from its nearest neighbor by an average of 44.3 1.0.
Ray
< x,
y,
z >
Couch
Gantry
1
-0.34
0.00
0.94
70
90
2
0.26
-0.43
0.87
287
245
3
0.56
0.25
0.79
305
284
4
-0.06
0.66
0.75
85
49
5
-0.43
-0.69
0.58
54
134
6
-0.90
-0.08
0.44
26
95
7
-0.69
0.63
0.35
27
51
8
0.92
-0.25
0.29
342
256
9
0.38
-0.88
0.28
324
208
10
0.84
0.53
0.15
350
302
11
0.23
0.96
0.13
331
345


156
rule of thumb can be derived from this table: the lowest amount of beam rotation
allowable by Table 4-8 is about 0.26 times the initial inter-beam separation angle. Thus,
if the initial inter-beam separation angle between beams in an N-beam bouquet is
designated as W, then an isotropy factor of < 0.8 is assured even if all beams are rotated
towards the same point by W/4 (=0.25 x W) or less. Observing this beam movement
limit will also prevent inadvertently placing beams into a parallel-opposed beam
arrangement.
This data is useful because it confirms that small adjustments to the
orientations of beams in an isotropic bouquet may be made without significantly
adversely affecting the conformity or gradient of the dose distribution. Such adjustments
may occasionally be desirable in order to enhance the avoidance of critical structures, for
instance, when all but one or two beams in a bouquet avoid a nearby critical structure.
Moving one or two beams several degrees will have a very small effect on the isotropy
and thereby dose conformity and gradient of the overall dose distribution.
Table 4-8: Amount of beam rotation of all beams in isotropic beam bouquets to attain an
isotropy factor of 0.8. The amount of rotation as a fraction of the initial separation angle
of the isotropic beam arrangements is shown in the right column.
No. beams
Allowable
movement
angle (deg)
Fraction of
initial sep. angle
5
16.6
0.26
7
16.6
0.30
9
13.0
0.27
15
12.6
0.31


235
1000 T
90 0
00.0 -
70.0 -
u
o
o
E
3
60 0 -
o
>
<5
S
50 0 -
40 0 .
o
z
30 0 -
20 0 -
10 0 -
0 0 -
0.0 2.5 5.0 7 5 10.0 12.5
Dose (Gy)
15.0
17.5
20.0
Figure 6-6f: Nontarget volume DVHs for case VC-1 treatment plans. The prescription
dose is 12.5 Gy.
1.0
08
02
---din-brainstem
a spack-brainstem
-o 1£bm-brainstem
IMRT-brainstem
5dyn-arcs-brainstem
0.0 2.5 5 0 7 5 10 0 12.5 15 0 17 5
Dose (Gy)
Figure 6-6g: Brainstem DVHs for case VC-1 treatment plans. The prescription dose is
12.5 Gy.


Patient VC-1
Patient VC-1 is a 58 year old female with a 12.6 cm3 petroclival meningioma.
This patient was treated clinically with a twenty isocenter SRS plan using 68 arcs,
delivering 12.5 Gy to the 7jD% isodose shell. The sphere packing autopian program
generated a seventeen isocenter plan using 69 arcs. Orthogonal view isodose plots for all
plans are shown in Figures 6-6a through 6-6e, with dose-volume figures of merit listed in
Table 6-12. For this patient case and the other very complex (VC) patient cases, the
dose-volume figures of merit for nine conformally shaped beams are shown as well, for
comparison with the nine beam IMRT plans, and to illustrate the improvement in the
overall conformity and gradient of each nine beam IMRT plan over each nine beam
conformal plan. Nontarget volume, brainstem, left optic nerve, and right optic nerve
DVHs are shown in Figure 6-6f, 6-6g, 6-h, and 6-6i, respectively. NTCPs for the
nontarget brain, the brainstem, and the right and left optic nerves are listed in Table 6-13.
Based on physical dose-volume figures of merit (i.e. UF Index overall score),
the clinical and sphere packing autopian multiple isocenter plans are superior to any of
the alternative plans (Table 6-12). The fifteen beam plan achieves the same effective
dose gradient as the clinical twenty isocenter plan (UFIg = 50), but is much less
conformal (UFIc = 50 for fifteen beams versus UFIc = 95 for the clinical plan, or UFIc =
77 for the sphere packing automatic plan). The sphere packing autopian achieves the
steepest dose gradient of any of the plans, with an effective gradient of 7.7 mm (UFIg =
53). The nine beam IMRT plan is the most conformal alternative plan, with a UFIc score
of 72.
NTCPs for the nontarget brain and radiosensitive structures are listed in Table 6-
13, along with the computed probability of no complication, P(NC). P(NC), the product