• TABLE OF CONTENTS
HIDE
 Title Page
 Table of Contents
 Abstract
 Introduction
 Review of the literature
 The stereotactic procedure at the...
 Target definitions
 Investigational dosimetry
 The modified negative field...
 Dosimetry verification
 Collimator specification
 Clinical examples
 Conclusion
 Appendix
 Reference
 Biographical sketch
 Copyright














Title: Conformal stereotactic radiosurgery with multileaf collimation
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Title: Conformal stereotactic radiosurgery with multileaf collimation
Series Title: Conformal stereotactic radiosurgery with multileaf collimation
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Table of Contents
    Title Page
        Page i
    Table of Contents
        Page ii
        Page iii
    Abstract
        Page iv
        Page v
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
    Review of the literature
        Page 6
        Page 7
        Page 8
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        Page 10
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    The stereotactic procedure at the university of florida
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        Page 23
        Page 24
    Target definitions
        Page 25
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    Investigational dosimetry
        Page 73
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    The modified negative field method
        Page 108
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    Dosimetry verification
        Page 133
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    Collimator specification
        Page 155
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        Page 225
    Clinical examples
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    Conclusion
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    Appendix
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    Reference
        Page 345
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        Page 348
        Page 349
        Page 350
    Biographical sketch
        Page 351
        Page 352
        Page 353
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    Copyright
        Copyright
Full Text











CONFORMAL STEREOTACTIC RADIOSURGERY
WITH MULTILEAF COLLIMATION














BY

DALE C. MOSS


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


1992

















TABLE OF CONTENTS


Page


ABSTRACT . . . . . . . .


CHAPTERS


1 INTRODUCTION . . . . . .

Stereotactic Radiosurgery . .
Field Shaping . . . .
Dynamic Conformal Collimation .

2 REVIEW OF THE LITERATURE . . .

Stereotactic Radiosurgery Systems
Conformal Collimation . . .
Target Localization . . . .
Photon Dosimetry . . . . .
Verification . . . . . .


3 THE STEREOTACTIC PROCEDURE AT THE UNIVERSITY
FLORIDA . . . . . . . . .


OF
* .


Equipment . . . . . . . . .
Patient Preparation . . . . . . .
Target Localization . . . . . . .
Treatment Planning . . . . . . .
Patient Treatment . . . . . . .

4 TARGET DEFINITION . . . . . . .

The Rotation Operation . . . . . .
Stereotactic and Beam's Eye View Coordinates
Coordinate Transformation and Target Rotation
Target Localization . . . . . . .

5 INVESTIGATIONAL DOSIMETRY . . . . .

The Convolution Method . . . . . .
The Negative Field Method . . . . .
Conclusion . . . . . . . . .


.... 1


S . . 6


.....

....


......
.....

...
.....









6 THE MODIFIED NEGATIVE FIELD METHOD . . .

Output Factor . . . . . . .
Tissue Maximum Ratio . . . . . . .
Primary Off Center Ratio . . . . . .
Boundary Factor . . . . . . . .
The Dosimetry Calculation Process . . .
Dosimetry Results . . . . . . .

7 DOSIMETRY VERIFICATION . . . . . .

Irregular Field Block Construction . . .
Computerized Film Dosimetry . . . . .
Irregular Small Field Dose Model Verification
Analysis Results . . . . . . . .


8 COLLIMATOR SPECIFICATION .

Leaf Shape . . . . .
Leaf Width . . . . .
Arc Compression . . .
Gantry Incrementation . .
Localization Margin . .
Conclusion . . . . .

9 CLINICAL EXAMPLES . . .

Case 1 . . . . . .
Case 2 . . . . . .
Case 3 . . . . . .
Case 4 . . . . . .
Conclusion . . . . .

10 CONCLUSION . . . . .

APPENDICES

A TREATMENT PLANNING . . .

B TARGET LOCALIZATION PROGRAM

C DOSE MODEL PROGRAM (PLANE)

D DOSE MODEL PROGRAM (VOLUME)

E INTEGRATED LOGISTIC FUNCTION

REFERENCES . . . . . .

BIOGRAPHICAL SKETCH . . . .


S . . . . 155

S . . . . 155
S . . . . 156
S . . . . 158
S. . . . ... 158
. . . . 159
S . . . . 160

S . . . . 226

S. . . ... 227
S. . . .. 228
S . . . . 229
S. . ... 230
S . . . . 232

. . . . 258



S. . . . ... 261

S . . . . . 269

S . . . . . 296

S. . . . ... 319

PROGRAM ...... 337

S. . . . ... 345

S . . . . . 351


iii


108

110
111
113
117
120
124

133

133
135
137
141















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

CONFORMAL STEREOTACTIC RADIOSURGERY
WITH MULTILEAF COLLIMATION

by

Dale C. Moss

August, 1992

Chairman: Frank J. Bova, Ph.D.
Major Department: Nuclear Engineering Sciences


This paper outlines and implements a method of produc-

ing dose distributions that conform to any arbitrary, irreg-

ularly shaped target by means of dynamic conformal collima-

tion using a multileaf collimator. The method may be summa-

rized in three steps: production of the treatment plan;

localization of the target; and the calculation of three

dimensional dosimetry. Provision is made for volumetric

evaluation of dosimetry with dose volume histograms and

complication probability functions.

Treatment plans follow the standard of non-conformal

stereotactic radiosurgery with several non-intersecting

parasagittal arcs. A 2n geometry with at least five arcs of

1000 each has been determined to be optimal.

Target localization begins with identification and

contouring of target axial dimensions using diagnostic CT

iv








scans. A system for processing these target contours has

been produced using the Beam's Eye View technique. Pro-

jected target cross sectional areas at each gantry/table

position are found, after appropriate translation/rotation,

by graphical search and each leaf of the collimator is set

to position. Optimal localization parameters have been

determined.

The localization results are then sent to dosimetry

calculation for the production of isodose plots on the three

principal planes, individual field cross plots, dose volume

histograms, and complication probability functions. The

three dimensional dosimetry technique developed here is

termed the modified negative field method, as individual

fields with the dimension of each leaf are subtracted from

an open field defined by the combined dimensions of all of

the leaves.

Dosimetry from cases previously treated using the

University of Florida Stereotactic Radiosurgery System are

compared with the developed method and also with a rotating

collimator system that has been described in the literature.

It is shown that the method developed herein provides better

conformation and homogeneity in dose throughout the target

volume than those techniques used at present.














CHAPTER 1
INTRODUCTION


Stereotactic Radiosurgery

At its inception, stereotactic radiosurgery was consid-

ered to be a tool to remove a lesion from the treatment area

by delivering a radiation dose sufficient to cause tissue

necrosis. Hartmann observed: "If the dose gradient is very

steep . a single dose that is sufficient to cause necro-

sis of the tissue volume selected can be administered."

[Har85, pg. 1185]. For this dose, ". . the most important

factor . is the physically determined concentration of

the radiation on the target, in contrast to fractionated

radiotherapy, which is based on differences in radiosensi-

tivity between tumor cells and cells of the adjacent healthy

tissue." [Har85, pg. 1185]. Further, ". . the side ef-

fects of a single high dose irradiation can only be avoided

or minimized if the area of tissue chosen for irradiation is

precisely anatomically defined and adjusted . ." [Har85,

pg. 1186].

More recently, particularly in the case of vascular

lesions, it has been acknowledged that tissue necrosis does

not take place in the irradiated tissue (although some

tumors may become necrotic after treatment). After treat-








2

ment of a vascular lesion, through an incompletely under-

stood process, the nidus of the lesion thromboses, after

which the lesion disappears over a period of approximately

two years. Satisfactory results appear best achieved by

producing a homogeneous dose distribution throughout the

lesion [Lea91]. To this end, a successful stereotactic

radiosurgery system must incorporate hardware and software

to determine the size and location of the lesion, to plan

the treatment, and to deliver the radiation in accordance

with the plan [Win88].

Radiosurgery is used on patients who are not good

candidates for conventional neurosurgery for whatever rea-

son. Many radiosurgery treatments have been for the oblit-

eration of arteriovenous malformations (Steiner reports that

85% of such lesions treated are undetectable by angiography

two years later [Win88]). Other lesions reported treated

include acoustic neurinomas, anaplastic astrocytomas, low

grade astrocytomas, carotid-cavernous fistulas, cavernous

angiomas, choroid plexus papillomas, craniopharyngiomas,

ependymomas, germinomas, glioblastomas, lymphomas, medullo-

blastomas, meningiomas, metastases, oligodendrogliomas,

pineoblastomas, pineocytomas, pituitary tumors, and venous

angiomas [Lar90].

The auxiliary collimator used in linear accelerator

based stereotactic radiosurgery is seen by most as an impor-

tant component, as it both precisely shapes the radiation








3

beam, difficult with the main collimators alone, and reduces

beam penumbra by being physically closer to the target. The

circular auxiliary collimators generally used produce a

spherical dose distribution at isocenter. Rectangular

collimators produce a cylindrical dose distribution [Suh90]

which may be of use in certain cases. In either case, the

dose distribution produced may or may not correspond to the

shape of the target.

Field Shaping

The aim of optimizing dose distributions by conforming

the distributions to the shape of the target is summarized

in four requirements for conventional large-field telethera-

py [Bor90] which may be equally well applied to stereotactic

radiosurgery:

a. The dose applied to the target should be very

close to the prescribed dose.

b. The dose should be homogeneously distributed

across the target.

c. The dose to the organs at risk should be less

than the tolerated maximum dose.

d. In the tissue surrounding the target, the dose

should be low.

Various standard and nonstandard schemes of combining

open fields exist in practice to conform the dose to the

target. In standard large-field teletherapy, parallel

opposed open fields are weighted to move the combined field








4

isodose distribution in the direction of the more heavily

weighted field. Angled opposed fields are used to form a

triangular distribution with the apex bisecting the angle

between the beams (with equal beam weighting) or any arbi-

trary resecting angle (with unequal weighting).

Custom collimators have been employed effectively in

large field teletherapy as additions to the main (secondary)

system collimators. These beam blocks are manufactured to

the physician's specification after exploratory x-rays of

the potential treatment area are analyzed. The physician

draws the outline of the target on the x-ray and blocks

(usually of Lipowitz' metal) are made to match the outline,

taking into account any magnification and divergence.

Dynamic Conformal Collimation

In stereotactic radiosurgery, the normal open circular

beams may also be weighted to shift the distribution. The

standard arc orientations may be shifted to the same end.

Attempts at better conformal collimation may be undertaken

by using multiple isocenters and/or differing collimator

sizes in different arcs [Suh90]. This latter method is

effective and is used in practice, but is costly in both

planning and treatment time and complexity. It also results

in hot spots in the lesion in volumes where the dose distri-

butions from each isocenter overlap.

Multileaf collimators are used to shape the beam pro-

file to the target projected area either statically or








5

dynamically. Static multileaf collimation simply replaces

custom made beam blocks in normal teletherapy. Dynamic

multileaf collimation is much more challenging. In this

mode, the collimator is adjusted to conform to the projected

area of the target as the patient is moved on the table

and/or the gantry is rotated around the patient.

Leavitt et al. [Lea91, pg. 1249] cite Nedze et al.

having ". . shown that tumor dose inhomogeneity introduced

through the use of multiple isocenters is the strongest

variable predicting complication, and have emphasized the

need for development of alternative treatment techniques for

lesions otherwise requiring multiple isocenter techniques."

The goal of this work then is to develop a stereotactic

radiosurgical technique to shape the dose distribution to

the target volume in such a manner that the dose distribu-

tion throughout that volume is homogeneous, the target

volume is enclosed in the prescribed isodose volume, and the

dose drops off rapidly outside of the defined treatment

volume. In support of this goal, research has been conduct-

ed in target localization, multileaf collimator vane speci-

fication, three-dimensional irregular field photon dosimetry

(both plane dosimetry and dose volume histogram), and guide-

lines for optimization through treatment plan variation.

The end product should be useful clinically.














CHAPTER 2
REVIEW OF THE LITERATURE


To recapitulate the elements necessary for a function-

ing radiosurgery system we recall the strictures set forth

in Chapter 1 [Bor90]:

a. The dose applied to the target should be very

close to the prescribed dose.

b. The dose should be homogeneously distributed

across the target.

c. The dose to the organs at risk should be less

than the tolerated maximum dose.

d. In the tissue surrounding the target, the dose

should be low.

With these guidelines in mind, the literature was

reviewed to gain insights in five categories in support of

this research. Stereotactic radiosurgery systems that have

been described were assimilated for historical background

and differing technique. Conformal collimation methods in

both large and small field radiotherapy were investigated,

the large field methods being generally applicable, while

the small field methods were specifically oriented to ste-

reotactic radiosurgery. Target localization procedures were

assessed as a necessary adjunct to conformal collimation








7

since computed rotational dosimetry uses superposition of

discrete beam locations to simulate the integration of a

moving radiation beam, and therefore the target must be able

to be visualized at any possible gantry/table position

combination. Historical and contemporary photon dosimetry

algorithms were analyzed as an important aspect, as the con-

cept of "virtual target" is fully realized in this treatment

modality. Finally, verification strategies were looked at

as support for any dosimetry system adopted.

Stereotactic Radiosurgery Systems

Stereotactic radiosurgery was first suggested by

Leksell in 1951 [Lek51]. He initially used 200 to 300 kVp

x-rays, then charged particles. He finally settled on

collimated 60Co beams, first 179 and later 201, the number

used in the present Leksell Gamma Knifem. This device was

conceived as a non-invasive method for performing functional

neurosurgery, a course which was later abandoned for various

considerations [Gil90]. Research then began on the treat-

ment of intracranial lesions. The Gamma Knife is in clini-

cal use today in many centers.

Other teams began experimenting with charged particle

beams in the late 1950's at sites in Sweden, Berkeley, and

Boston (studies which continue to the present). These beams

of proton or helium ions are produced by synchrocyclotrons,

and take advantage of the Bragg peak of the particles to

focus the beams at depth [Pik87].








8
While these methods are undeniably effective, they also

require the use of very expensive, dedicated equipment found

only in a few large medical and research centers. Betti and

his coworkers appear to be the first to develop a linear

accelerator as a treatment machine, reported in 1984, used

in Buenos Aires since 1982, with circular brass auxiliary

collimators [Bet84]. Colombo and associates reported in

1985 on a linear accelerator based system in use in Vicenza,

Italy, since 1982, with only the linear accelerator collima-

tor jaws used to define the treatment area [Fri90].

The treatment accuracy of a linac radiosurgery system

is dependent on the linac mechanical accuracy (how well the

central axis of the rotating beam continuously coincides

with the rotation isocenter), and on the target localization

accuracy (how accurately the target is located with combi-

nations of biplanar angiography, computed tomography, and

magnetic resonance imaging). Hartmann, in Heidelberg,

reported on his use of a linear accelerator as a treatment

machine in 1985 [Har85]. He used an auxiliary collimator

coupled directly to the head of the linear accelerator, with

the consequence that gantry sag limited the accuracy of the

delivered dose (the treatment accuracy) to approximately

2.0 mm. Lutz et al. [Lut88] also used this type of auxil-

iary collimator, with variously sized inserts, and reported

a treatment accuracy of 2.4 mm in any direction at the 95%

confidence level. Souhami et al. [Sou90] used simultaneous








9
rotation of the linac gantry and couch with lead auxiliary

collimators without reporting accuracy.

Friedman and Bova [Fri89b] developed a three-axis slid-

ing bearing system to couple the auxiliary collimator to the

linear accelerator head, thus avoiding the effects of gantry

sag and improving the dose delivery of the University of

Florida Stereotactic Radiosurgery System to an average

mechanical accuracy of 0.2 mm. To date, this is the most

precise and accurate system of those that have been des-

cribed in the literature, and is commercially available as

the Philips SRS 200 Stereotactic Radiosurgery System.

Conformal Collimation

A simple translational four-leaf collimator system was

described by Chin [Chi81]. In his system, the beam is swept

superior to inferior over the treatment volume by motion of

the table under the beam. The two-leaf set parallel to the

axial plane is narrowed to a slit, and the perpendicular set

of leaves are adjusted to coincide with the projected target

edges. This produces distributions which conform well to

the target and can be specifically set to avoid sensitive

structures.

Spelbring et al. [Spe87] performed a computer simula-

tion of large field teletherapy multivane collimator systems

that showed an advantage for these systems on a case specif-

ic basis. Leavitt et al. also investigated the use of

dynamic multivane collimators in electron arc therapy com-








10

putationally for the purposes of optimization [Lea87], and

by hardware realization [Lea89]. Both computation and

measurement found conformal collimation to be effective in

improving homogeneity in target dose while restricting high

dose areas to the target, computationally by an average of

11% for areas covered by the 100% dose line to 15% for areas

covered by the 90% line, confirmed by measurements using the

prototype multivane collimator.

Flickinger et al. [Fli90c] have studied conformal

collimation as applied to the Leksell Gamma Knife. By

blocking various patterns of the 201 60Co beams dose volume

shapes may be altered from the normal spherical distribu-

tions. Examples of calculational dosimetry are given. Left

and right lateral ports may be plugged to produce distribu-

tions that are extended in the axial direction (cepha-

lad/caudad). An AP strip in the sagittal plane may be

plugged to produce distributions that are extended lateral-

ly. A lateral strip in the coronal plane may be plugged to

extend distributions anterior to posterior. All these are

used to shape distributions to extended ellipsoid targets.

An example of film dosimetry shows good fit to calculated

high isodose lines.

It has been suggested that rectangular collimators,

employed with rotation to follow major target axes, be used

to improve distributions in stereotactic radiosurgery

[Suh90]. A rectangular target was followed with the Beam's









11

Eye View technique to define the direction of the target's

major axis and projected target dimensions at each gan-

try/table position. A standard four arc plan (equally

spaced arcs) was generated using a cylindrical dose model.

This plan was compared, using a dose volume histogram, to a

plan employing two isocenters to cover the same target

volume. The histogram showed a slight improvement of dosim-

etry with the Beam's Eye View technique, although dose

homogeneity was not addressed.

A simple four blade rotating conformal collimator was

constructed and described by Leavitt et al. [Lea91]. The

collimator was a double layer design with two leaves in each

layer. The layers and the leaves in the layers could be

rotated to best fit the target projected area. The Beam's

Eye View technique was used to follow the target through all

gantry/table angles and to automatically adjust the leaf

positions at each increment of angle. An irregular field

dosimetry system was developed and was evaluated against

measured distributions with both film and diode. Isodose

plots were then compared between the standard circular

collimator, the conformal vane collimator, and the dual

isocenter techniques. This showed a 24% improvement in the

amount of normal brain covered by the 80% isodose line in

favor of the conformal technique when compared to the circu-

lar, and a 1% improvement in the same volume in favor of the

conformal technique when compared to the dual isocenter. It








12
was noted that concave shapes could not be effectively fit

using this technique.

There is no multileaf collimator system described in

the literature for the case of small field linac based

stereotactic radiosurgery. The system, here proposed, would

be capable of fitting concave or other irregularly shaped

targets limited only by the size of the leaf and by the

treatment margin desired.

Target Localization

Prior to a stereotactic treatment of any kind it is

necessary to precisely locate the target. This is done with

angiography, computerized tomography, and magnetic resonance

imaging, alone or in any combination [Fri89a]. At present,

localization consists of obtaining two orthogonal views in

planes which best describe the target and using these views

to determine the target isocenter.

Stereotactic localization of targets has been the

object of many presentations. Siddon and Barth [Sid87]

reported on the use of the BRW frame to obtain isocenter and

orthogonal view data. Their method reports the ability to

localize a target pointer to within 0.3 mm using a modified

localizer box. In two papers, Saw et al. [Saw87a; Saw87b]

gave a system of calculations using a standard BRW frame for

the purpose of stereotactic neurosurgical implants, although

accuracy of placement is not shown. Lulu [Lul87] published

a description of a system, also using the standard BRW








13
localizer, for transforming CT coordinates to BRW coordi-

nates for localization. This system uses basic geometrical

transformations made possible by the unique positioning

information imparted by axial slices of the localizer.

Localization errors are reported to be between 0.5 and 1 CT

pixel width.

Visualization of the target after localization is

necessary to observe dosimetry presentations, usually in the

form of isodose lines. The target and dosimetry information

must be viewed from any angle in three-dimensions to ensure

coverage of the target and sparing of critical organs that

may be in close proximity. Fitzgerald and Mauderli [Fit75]

analyzed the errors in three-dimensional reconstruction of

implant dosimetry using stereo-radiography. Metz and Fencil

[Met89] developed a method of showing three-dimensional

structure based on two different but arbitrarily oriented

radiographs. Boesecke et al. [Boe90] and Toennies et al.

[Toe90] used prominent bony landmarks to register and

visualize their targets when rotated.

The Beam's Eye View (BEV) technique is useful in target

visualization under dynamic conditions. This technique is

based on the acquisition of target data such that the target

may be viewed along the radiation path through the collima-

tor as the gantry and table rotate about the target, located

at the rotation isocenter of the system. Mohan et al.

[Moh88] have incorporated the BEV technique as an integral








14

part of a complete three-dimensional treatment planning

system. Myrianthopoulos et al. [Myr88] and Low et al.

[Low90] both presented BEV rotational methods coupled with

volume analysis to determine adequacy of target coverage in

dynamic radiotherapy.

Dynamic localization is necessary for dynamic conformal

collimation. There is no method described in the literature

for localizing a rotating target such that its projected

area may be defined by a multileaf collimator.

Photon Dosimetry

Photon beam dose models are many and widespread. Most

of these models incorporate primary dose (from primary

photons), secondary dose (from scattered photons), off-axis

ratios (for points off of the central axis of the incident

beam), percent depth dose or tissue maximum ratio (to ac-

count for exponential falloff of the beam intensity in

tissue), and relative output factors (to correct for field

sizes other than that calibrated).

Small field dose models incorporate these factors to a

greater or lesser extent. Bjarngard et al. [Bja82] derived

an analytical term for the scatter component of the small

beam, which was averaged over the radius of the beam. Chui

et al. [Chu86] use off-axis ratios derived from a product of

backscatter factors. Hartmann et al. [Har85] subsume all

these factors into measured dose profiles and depth dose

curves. Pike et al. [Pik87] rely on percent depth doses,








15

off-axis ratios, and inverse square corrections and shows

measured and calculated dose distributions [Pik90]. Bova

[Bov90] uses TMR and OAR tables in the University of Florida

stereotactic radiosurgery system.

Bjarngard et al. [Bja90] observe that for small 6 MV

x-ray beams the central axis dose is significantly reduced

for fields of less than 1 cm radius due to electron disequi-

librium, that photons scattered from the collimator do not

affect dose, and that only very small beams of less than

0.07 cm radius are affected by source size induced penumbra.

Khan et al. [Kha80] allude to the idea that scatter dose is

of little effect in small beams, while Arcovito et al.

[Arc85] and Rice et al. [Ric87] specifically allow for and

calculate a scatter correction factor for small 9 and 6 MV

x-ray beams, respectively.

Perhaps the most interesting are the convolution mod-

els. Boyer and Mok [Boy85] and Iwasaki [Iwa85] use these

models to provide a fast method of completely describing an

incident photon beam energy distribution. Boyer and Mok

[Boy86] extended their method to calculate distributions in

inhomogeneous media. Mohan et al. [Moh87] and Starkschall

[Sta88] use convolutions of pencil beam profiles with irreg-

ular field shapes by Fourier transform operations to arrive

at dose distributions. These models use nothing but the

primary dose modified by simple factors derived from the

convolution operations.









16

Verification

Calibrated ion chambers are the primary measurement

tool in radiation therapy. After a beam is calibrated with

an ion chamber, the secondary methods of film and diode

dosimetry are used. The latter are secondary because they

rely on pre-calibration with known beams to derive fitting

factors that allow the calculation of unknown doses.

Ion chambers, as a standard, are accurate and precise,

and can measure unknown field quantities without recourse to

prior knowledge about the field. However, they are diffi-

cult to use with small fields, as they must be carefully

aligned so that the full chamber volume is irradiated. Rice

et al. [Ric87a] approached this problem by aligning the

central axis of the chamber parallel to and coincident with

the beam central axis, significantly reducing the required

lateral coverage.

Films have advantages over both ion chambers and diodes

in that they record a continue of data points versus a

single point for chambers and diodes, and that their data

collection is a permanent record that may be re-analyzed in

light of new data as opposed to the "one-shot" nature of the

other methods. Films are, however, sensitive to handling

and processing variables. Bjarngard et al. [Bja90] have

found that small field densitometry with film is a satisfac-

tory tool.








17

Diodes are compact, reproduce well, and may be remotely

read out in real time. They are sensitive to placement,

however, and may give inaccurate readings if not oriented

correctly in the radiation beam. They are also physically

sensitive and prone to catastrophic failure.

Each of these methods has its place and each will be

used to provide data for and to verify the dosimetry methods

developed in this work.














CHAPTER 3
THE STEREOTACTIC PROCEDURE AT THE UNIVERSITY OF FLORIDA


Equipment

A standard linear accelerator is used at the University

of Florida for stereotactic radiosurgery. It is modified by

the addition of a head stand for the Brown-Roberts-Wellsm

(BRW) stereotactic ring (a conventional piece of neuro-

surgery apparatus), a shortened couch top to clear the head

stand, and a bearing/holder system for auxiliary collimation

(figure 3-1). Setup of the system modifications takes 10 to

15 minutes.
















Figure 3-1: University of Florida Stereotactic Radiosurgery
System ([Fri90, page 993], used with author's permission)


The BRW ring is the reference point for all localiza-

tion of targets. It is a metal ring which is fixed to the









19

patient's head with stainless steel pins. The top surface

of the ring is placed inferior to the target position and

becomes the reference point for all localization and cal-

culation.

The head stand and bearing/holder system are incorpo-

rated in a single portable piece of equipment that is posi-

tioned under the gantry of the linear accelerator such that

the target can be placed accurately at the rotation iso-

center of the radiation beam. The BRW ring is rigidly and

precisely attached to the head stand. Micrometer adjust-

ments allow the positioning of the localized target center

to coincide with the system isocenter. A two-bearing system

mechanically connects the head stand to the gantry. One set

serves to rotate the BRW ring in the table plane, keeping

the target centered while the table is rotated. The second

set couples the collimator system to the head stand by a

swing arm around the axis of gantry rotation, allowing accu-

rate and precise beam positioning.

The swing arm end, directly under the linear accelera-

tor head, is the mount for the auxiliary collimators. The

purpose of auxiliary collimation is to both precisely define

the beam and diminish penumbra effects. These collimators

are 15 cm thick Lipowitz' metal (beam transmission approxi-

mately 2%) with circular apertures ranging from 0.5 to 3 cm

in diameter. The apertures are tapered to match the beam

divergence. The auxiliary collimator is loosely coupled to









20

the linear accelerator by a three-axis sliding bearing

mounted on the head. This sliding bearing system divorces

the auxiliary collimator from any gantry torque induced by

sag or gantry bearing inexactness, thus improving the accu-

racy of the dose delivery.

Patient Preparation

The stereotactic radiosurgery treatment is conducted on

an outpatient basis. The patient is initially seen in

clinic where the BRW ring is fixed to the head. This is

done under local anaesthesia (mixed lidocaine and markane

injection). The ring is pinned to the skull with stainless

steel pins at each of the four injection sites. The BRW

ring used is a standard ring rebuilt to tighter tolerances

to accommodate the demands of radiosurgery.

Target Localization

Targets are localized depending on their type. Vascu-

lar targets, such as arteriovenous malformations (AVM's),

are localized by contrast angiography and by computerized

tomography (CT). Other targets employ CT localization only.

In angiographic localization, the BRW ring is attached

to a mount placed on the table end. An angiographic local-

izer is attached to the ring. The localizer consists of

four lucite panels (anterior, posterior, left, and right)

with radio-opaque fiducial marks (four in each, eight per

AP/lateral projection) as defined reference points [Sid87].

Contrast is injected and fast biplane films are taken. The








21

neuroradiologist and neurosurgeon select the AP and lateral

films that best define the nidus of the AVM for treatment

planning.

The setup for CT localization is similar, though with a

different localizer being attached to the BRW ring. The CT

localizer is made up of three pairs of parallel rods orient-

ed on the patient's major axis, with angled rods between

them. Transverse CT slices show six fixed rod profiles with

the angled rod profiles at varying positions between the

fixed. The positions of the angled rod profiles relative to

the fixed uniquely locates that slice in BRW space. As the

spacing between the rods is known, any object circumscribed

by the localizer cage can be localized accurately and pre-

cisely [Lul87; Saw87a]. Radio-opaque contrast is injected

to define the target. All the CT data is transferred to 9

track tape for treatment planning.

Treatment Planning

At the University of Florida, treatment planning begins

by transferring localization information to the planning

system. If angiography has been performed to locate the

target, the biplane films are placed on a digitizer and the

neurosurgeon enters the position of each fiducial mark and

traces the AP and lateral nidus boundaries. The system

computes a geometrical center and a center of mass for each

nidus projection, which should closely match if the nidus

has been outlined correctly [Bov91]. The best matching








22

center pair is used as the center of the target. The CT

tape is then mounted and the axial slice images are trans-

ferred into the system. Starting at the top slice, the

position of each of the localizing rods is defined. The

system automatically steps through the remaining slices,

finds each corresponding rod position, and registers each

slice. If CT is the only localizing modality used, the

neurosurgeon traces the target boundary in each of the

axial, coronal, and sagittal planes, then selects two of the

planes in which the target centers best match, as in the

angiography case, to define the target center.


Table 3-1: Standard nine arc treatment plan

Arc Collimator Table Gantry Gantry Arc
Number Size Angle Start Stop Weight

1 10 mm 100 30 1300 1
2 10 mm 300 300 1300 1
3 10 mm 500 300 1300 1
4 10 mm 700 300 1300 1
5 10 mm 3500 2300 3300 1
6 10 mm 3300 2300 330 1
7 10 mm 3100 2300 3300 1
8 10 mm 2900 2300 3300 1
9 10 mm 2700 2300 3300 1


An initial treatment plan is entered, consisting of the

number of arcs, collimator size for each arc, arc orienta-

tion (table angle), arc start and stop angles (gantry an-

gles), and arc weighting. A standard nine arc treatment








23
plan is shown in table 3-1. Note that the table angles

describe nine equally spaced parasagittal arc positions, all

arcs are 1000 (gantry start to gantry stop angle), and all

arc weights and collimator sizes are equal.

Plan variables may be changed as necessary. Changing

the collimator size will change the diameter of the isodose

lines. Moving or deleting table angles will change the

shape of the dose distribution. For example, deleting the

lateral arcs (100, 300, 3500, and 330 table angles) will

result in an axial extension and lateral contraction of the

dose distribution. Setting different weighting on different

arcs can also shift the distribution.

Multiple isocenters may be specified for extended or

irregularly shaped targets, with each isocenter set to cover

a portion of the volume. Problems with this approach in-

volve increased treatment plan complexity, increased treat-

ment time, and often severe dose inhomogeneity within the

treatment volume. This, however, is the only current opera-

tional approach to conformal stereotactic radiosurgery at

the University of Florida.

Isodose distributions are then calculated and may be

viewed on any arbitrary slice, as well as dose profiles

across any defined line and dose volume histograms within

the treatment volume. At present, plan optimization is by

the visual, iterative method which can, and frequently does,

entail lengthy planning sessions.








24

Patient Treatment

The stereotactic radiosurgery system accessories are

attached to the linear accelerator and the isocenter posi-

tion is set on the head stand. Independently, a phantom

target is set up with an isocenter matching that set on the

head stand [Win88]. The phantom target is attached to the

head stand and x-ray images of the phantom target are taken

at various standard gantry and table positions. If the

images show the phantom target in the center of the colli-

mated beam (0.2 mm) on each exposure, the headstand set-

tings are considered correct.

The patient is then brought into the treatment room and

attached to the headstand. Treatment proceeds as defined by

the treatment plan. At the conclusion of treatment, the BRW

ring is removed and the patient is free to leave. Follow up

consultation and angiography takes place at regular inter-

vals.














CHAPTER 4
TARGET DEFINITION


A necessary preliminary to dose planning for conformal

collimation is the setting of the leaves of the multileaf

collimator to the margins of the projected target cross-

section at each of the arc increments for all of the speci-

fied arcs. The Beam's Eye View (BEV) method, employed by

Mantel et al. [Man77] for conventional rotation teletherapy,

is used as the basis for visualizing and specifying the

target boundaries. A graphical search is used for finding

the boundaries after the target has been drawn on the com-

puter screen. Each leaf is then set to the limit found for

that leaf's sector of coverage. As background to the full

explication of the method developed here, a discussion of

graphical translation/rotation systems from a basic text

[Fol82] follows.

The Rotation Operation

Rotation of any discrete point about the origin of a

coordinate system is a mathematical process that is shown in

figure 4-1. Point P(x,y) is rotated to point P(x',y').

P(x,y) can be specified by the x and y coordinates computed

from the angle a and the distance to the origin d:




























Figure 4-1: Point rotation about the origin


x= dcosa



y= dsina



Point P(x',y') can then be seen to be simply:


x'= dcos (a+P)



y/= dsin(a+P)



Expanding by the sum-of-angles gives:


x' = dcosa cosp dsina sinp



y'= dsina cosp + dcosa sin


and by substituting the original formulas 4-1 and 4-2:


P(x', y')

d

P(x, y)
13 -,.xy)

...I


(4-1)


(4-2)






(4-3)



(4-4)






(4-5)



(4-6)











x'= xcosp -ysinp (4-7)



y' =xsinp + ycosp (4-8)


Adding the third dimension (the z axis positive perpen-

dicular to and coming out of the page), we see that any

rotation in x or y does not change the distance d from the z

axis, therefore a rotation about the z axis simply results

in all the points of rotation being multiplied by 1. This

can be generalized to any rotation axis to result in the

following sets of equations:

Rotation in the xy plane about the z axis:

x' = xcosO ysinO (4-9)



y' =xsinO +ycos6 (4-10)


z'=z (4-11)



Rotation in the xz plane about the y axis:

x'= xcosO + zsinO (4-12)



y/=y (4-13)


z = -xsinO + zcos


(4-14)










Rotation in the yz plane about the x axis:


X = X


(4-15)


y' =ycosQ zsinO



z = ysinO + zcos


(4-16)


(4-17)


It is the usual case to express these sets as matrix

operations:

Rotation in the xy plane about the z axis:


x' cos8 -sin6 0 x
y = sin6 cos8 0 y =RzP
z 0 0 1 z


(4-18)


Rotation in the xz plane about the y axis:


x' cosO 0 sinl x
y' = 0 1 0 y =RyP
z' -sinO 0 cosO z


(4-19)


Rotation in the yz plane about the x axis:


x' 1 0 0 x
y' = 0 cos -sinO y =RxP
z/ 0 sinO cosO z


(4-20)








29

where Rx/y/z is the rotation operator about the x, y, or z

axis and P is the orthogonalized representation of the point

to be rotated (expressed in x, y, and z), respectively. By

matrix multiplication, then, any combination of rotations

about any combination of axes may be realized, recalling

that matrix multiplications are not commutative (i.e. AB 0

BA).

This suffices to rotate any point or group of points

about the origin. To rotate about any arbitrary center, the

rotation center must be first translated to the origin, the

points rotated as previously described, and the origin

translated back to the original rotation center. The trans-

lation is easily accomplished by subtracting the distance

from the origin to the rotation center, properly orthogon-

alized, from all the points being translated (translation to

the origin), and by adding the distance from the origin to

the rotation center to all the points being translated

(translation from the origin).

Stereotactic and Beam's Eye View Coordinates

Figure 4-2 shows the relationship between the stereo-

tactic (BRW) and the Beam's Eye View (BEV) coordinate sys-

tems. The BRW coordinate system, with the axes axial (Ax,

commonly called the vertical axis), lateral (Lat), and

anterior/posterior (AP), has its origin centered in each of

the three BRW localizer dimensions, and is fixed to and

rotates with the table (rotation about the AP axis). This








30

system has the Cartesian coordinates xyz such that x is

positive left lateral, y is positive anterior, and z is

positive cranial [Lul87; Saw87a]. When fixed to the treat-

ment table, the BRW location of the localized target is

placed at rotation isocenter.

The BEV coordinate system has axes positive towards the

gantry (GT), positive to the collimator left (AB), and

positive towards the radiation source (UB, up beam). The

origin is at rotation isocenter, is fixed to the collimator

position, and rotates with the gantry (rotation about the GT

axis). The BEV system is a generalization of that defined

by Siddon [Sid86].






Gantry
Rotation

AP/UB Ax/GT



Isooenter


/PRoA
/ Table
Rotation

Figure 4-2: Stereotactic and beam's eye view coordinates


The target is captured in axial CT slices in the BRW

coordinate system. This system must be transferred to the








31

BEV coordinate system to allow mapping of the target pro-

jected area as the table and gantry rotate about the desig-

nated target center.

Coordinate Transformation and Target Rotation

Recalling the non-commutative nature of matrix multi-

plications, care is necessary in the order of rotation, i.e.

the order of axes about which the target is rotated, as the

combined effect of rotating about several axes effectively

results in a matrix multiplication process. In dealing with

the many non-coplanar arcs of stereotactic radiosurgery as

performed with the University of Florida system, two rota-

tion axes are apparent; as the table rotates the target is

rotated about the AP/UB axis, and as the gantry rotates the

target is rotated about the Ax/GT axis, in this order.

One must be able to visualize rotation operations in

three dimensions to arrive at this order of rotation.

Consider the inverse, gantry rotation followed by table

rotation. As the gantry rotates, in the BEV coordinate

system the target counter rotates about the GT axis. If

then followed by table rotation, still in the BEV coordinate

system, the target must rotate about the UB and AB axes

simultaneously, leading to complications in the mathematical

treatment.

Consider, then, the stated order of rotation. As the

table rotates, the target rotates about the UB axis. Then

as the gantry rotates, the transformed target counter ro-








32

states about the GT axis. Each of the operations is a previ-

ously defined rotation about a single axis. As a series of

rotation operations results in a matrix multiplication, this

combined operation may be expressed using equations 4-18 and

4-19 as Rtable*Rgantry*P = RSRS.P with Rtable Rgantry now de-

fined as RSRS, the SRS operator. Formally:

cos4tcose -sin4tcosOg sinO9
Rs = sin14 cost 0 (4-21)
-cos~tsinOg sin4tsinOg cosog



where 4, is table rotation, and 8g is gantry rotation.

The SRS rotation process is then:

AB' AB
GT' = RsS G (4-22)
UB UBI


which may be orthogonalized as:

AB = ABcosOtcosg GTsinOtcos4g +UBsinOg (4-23)



GT' = ABsin4 + GTcost (4-24)


UB = -ABcos~tsinOg+GTsin(tsinOg+UBcosOg (4-25)


Given a target positioned at rotation isocenter that is

described in an axial series of CT slices, the operation of

rotating the target to a series of BEV positions for local-

ization follows this algorithm:








33

1) Map the BRW axes onto the BEV axes:

BEV AB axis = BRW Lateral axis

BEV GT axis = BRW Vertical axis

BEV UB axis = BRW AP axis

2) Convert data points defining the target in the BRW

system and convert to BEV coordinates by:

BEV AB point = BRW Lateral point

BEV GT point = BRW Vertical point

BEV UB point = BRW AP point

3) For each gantry position in each arc:

a) Translate the BRW isocenter to the rotation

isocenter.

b) Rotate the target points with the SRS operator.

This process has been coded in the program LFLOC.C

(appendix B) and is illustrated by figures 4-3 through 4-8

(from the program LFDEMO.C, a version of LFLOC.C, that re-

moves hidden lines). The targets are, respectively, a

sphere, an AP oriented ovoid, an axially oriented ovoid, a

laterally oriented ovoid, an oblique ovoid, and a double

oblique ovoid. All the targets are located at the center of

the 20 cm diameter spherical head phantom. The sphere is 2

cm in diameter. The ovoids are 2 cm on the major axis, 1 cm

on the minor axes. The AP, axial, and lateral ovoids have

their major axis in the direction referenced. The oblique

ovoid has its major axis in the sagittal plane, oriented 450

to the AP, resulting in an ovoid oriented from anterior
























































(a)


SPHERE.CT: 6 leaves 0.50 Cn
Oantry: 265.00 dag


G ntrw:
Table:
Angles:
Find:
Jaws:
Leaves:
Margin:
Target:
Exit:


guide per Jawu 0.250 cn margin, 4 Jaus
Table: 270.00 deg
0


Figure 4-3: Sphere target rotation

(a) Gantry 2350; (b) Gantry 2650


SPHERE.CT: 6 leaves 0.50 cn guide oer Jaw. 0.250 cn margin, 4 Jaus
Oantry: 235.00 dag Table: 270.00 deo
Oantr : 4 4
Table: <--.
Angles: A
Find: F
Jaws: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A B





















































(c)

SPHERE.CT: 6 leaves 0.50 c, uide per Jau. 0.250 Ce margin, 4 Jaux
Gantru: 325.00 deg Table: 270.00 deg
a
Gantry: 4
Table: <--
Angles: A
Find: F
Jaus: J
Laeaus: L
Margin: M
Target: T
Exit: ESC





A B














T


(d)



Figure 4-3 -- continued
(c) Gantry 2950; (d) Gantry 3250


SPHERE.CT: 6 leaves 0.50 ea uide per jau. 0.250 ctn argin. 4 Jaus
Oantry: 295.00 deg Table: 270.00 deg
Oantru: 4
Table: --.
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A B























































(a)

APOUD.CT: 6 leagues 0.50 cn uide per jaw. 0.250 cn margin. 4 Jaus
Gantry: 265.00 deg Table: 270.00 deg
Gantru: 1+
Table: <--
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A B















T


(b)


Figure 4-4: AP ovoid target rotation

(a) Gantry 2350; (b) Gantry 2650


APOUO.CT: 6 leagues 0.50 ,e uide per Jau. 0.250 c margin. 4 Jaus
Gantry: 235.00 dag Table: 270.00 deg
aGntru: +
Table: i--
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: K
Target: T
Exit: ESC





A B






















































(c)

APOULI.CT: 6 leaves 0.50 en uide per Jau, 0.250 e, Margin. 4 Jaus
OantrV: 325.00 deg Table: 270.00 deg
Oantrw: 4 4
Table: c--
Angles: A
Find: F
Jaws: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A B















T


(d)



Figure 4-4 -- continued
(c) Gantry 295; (d) Gantry 3250


APOUD.CT: 6 lea~s 0.50 en uide per jau. 0.250 en Margin. 4 jaus
Oantru: 295.00 dag Table: 270.00 deg
Oantru: 4
Table: --.
Angles: A
Find: F
Jaws: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A B























































(a)


AXQUD.CT: 6 lauaes 0.50 en
Oantru: 265.00 deg
Gantry: 4
Table: .--
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: M
Target: T
Exit: ESC


guide per Jau, 0.250 cH Margin, 4 jaus
Table: 270.00 deg
0


(b)


Figure 4-5: Axial ovoid target
(a) Gantry 2350; (b) Gantry 2650


AXOUD.CT: 6 league 0.50 e M uide per Jaw, 0.250 c Margin. 4 jaus
Gantrw: 235.00 deg Table: 270.00 dge
Oantru: +
Table: <--
Angles: A
Find: F
Jauws: J
Leaus: L
Margin: H
Target: T
Exit: ESC





A B






















































AXOUD.CT: 6 leaves 0.50 en ulde per Jau. 0.250 C margin. 4 Jaus
Oantru: 325.00 deg Table: 270.00 deg
Gantru:
Table: 4,
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A8


(d)


Figure 4-5 -- continued
(c) Gantry 2950; (d) Gantry 3250













40


LATOUD.CT: S leaves 0.50 en uide per Jau, 0.250 c" nargin. 4 Jaus
Gantry: 235.00 deg Table: 270.00 dag
G
Gantru: 1
Table: <--
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A B















T



(a)

LATOUD.CT: 6 leaves 0.50 me uide per Jau, 0.250 ca margin, 4 Jaus
Gantry: 265.00 dag Table: 270.00 deg
0
Oantrw: +
Table: i--
Angles: A
Find: F
Jaeus: J
Leaves: L
Margin: M
Target: T
Exit: ESC





















T



(b)


Figure 4-6: Lateral ovoid target
(a) Gantry 2350; (b) Gantry 2650







































(c)


LATOUD.CT: 6 leaves 0.50 en guide per Jau, 0.250 en margin, 4 Jaus
Gantry: 325.00 deg Table: 270.00 deg
0
Oantrw: t 4
Table: *--
Angles: A
Find: F
Jaus: J
Leave.: L
Margin: M
Target: T
Exit: ESC



A (U


(d)

Figure 4-6 -- continued
(c) Gantry 2950; (d) Gantry 3250













42


OBLOUD.CT: 6 leagues 0.50 c uide oer Jau. 0.250 oe margin. 4 Jaus
Gantry: 235.00 dog Table: 270.00 deg
G
Gantry: t
Table: i--
Angles: A
Find: F
Jaus: J
Leaues: L
Margin: M
Target: T
Exit: ESC





AB















T


(a)

OBLOUD.CT: 6 leagues 0.50 ci guide per jau, 0.250 Cn margin. 4 Jaus
Oantru: 265.00 dog Table: 270.00 deg
0
Oantry: I
Table:! --
angles: A
Find: F
Jaus: J
Leaues: L
Margin: n
Target: T
Exit: ESC





A















T


(b)


Figure 4-7: Oblique ovoid target

(a) Gantry 2350; (b) Gantry 2650























































(c)

OBLOUD.OT: 6 leaves 0.50 en uide per Jau. 0.250 M margin, 4 Jaus
Gantrw: 325.00 deg Table: 270.00 deg
Oantru: f 4
Table: --*
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A B















T


(d)


Figure 4-7 -- continued
(c) Gantry 2950; (d) Gantry 3250


OBLOUD.OT: 6 leaves 0.50 cr guide per jau, 0.250 C margin. 4 Jaus
OantrM: 295.00 deg Table: 270.00 deg
Oantru : +
Table: <--
Angles: A
Find: F
Jaws: J
Leawes: L
Margin: M
Target: T
Exit: ESC





A B





44


DOBLOUD.OT: 6 leaves 0.50 c wide per jawu 0.250 en margin, 4 Jaus
Gantru: 235.00 deg Table: 270.00 deg
0
Oantru: f +
Table: --
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A B















T


(a)

DOBLOUO.CT: 6 leagues 0.50 CH wide per Jau, 0.250 e margin, 4 Jaus
Gantry: 265.00 deg Table: 270.00 deg
G
Gantry: t
Table!: --
Angles: A
Find: F
Jaus: J
Leaues: L
Margin: M
Target: T
Exit: ESC





A















T


(b)



Figure 4-8: Doubly oblique ovoid target
(a) Gantry 2350; (b) Gantry 2650

















































(c)

DOBLOUD.CT: 6 leaves 0.50 ca guide per Jau, 0.250 en Margin, 4 jaus
Oantru: 325.00 deg Table: 270.00 deg
Oantru: +
Table: *--
Angles: A
Find: F
Jaus: J
Leagues: L
Margin: M
Target: T
Exit: ESC




A













T


(d)


Figure 4-8 -- continued
(c) Gantry 295; (d) Gantry 3250


DOBLOUD.CT: 6 leagues 0.50 ci guide per Jaw, 0.250 ien argin. 4 jaus
GantrU: 295.00 deg Table: 270.00 deg
0
Oantru: f +
Table: --.
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: M
Target: T
Exit: ESC




A (








46

superior to posterior inferior. The doubly oblique ovoid is

similar, but with its major axis oriented from left anterior

superior to right inferior posterior. The figures show a

series of rotated beam's eye views of the target at a table

angle of 2700 with gantry angles of 2350, 2650, 2950, and

3250 (covering a standard 1000 arc in four steps). The

axial CT points have been tiled to a surface by extending

the points to plus and minus one-half of the slice thickness

and connecting the related points to form a series of

stacked right prisms. The resulting structure is then

submitted to the rotation algorithm. The final rotated

images at each gantry position show the appropriately scaled

(rotation center at 100 cm, view screen at 70 cm) projected

area of the target. Determination of the boundary of this

projected area is then necessary to correctly position the

leaves of the multileaf collimator.

Target Localization

The target is localized by a stepwise graphical search

method. Consider the individual elements (pixels) of each

graphics vector in the target representation to be in a set

state. Those elements that are set on the periphery define

the projected cross section of the target, suitably scaled

to viewing distance. As these peripheral elements are the

sole elements of interest, hidden line removal in the repre-

sentation of the target in the localization program is

unnecessary.









47

The leading, or field, edge of each leaf, in turn

clockwise from the upper left in the BEV coordinate system

(the gantry leaf on the A side), is advanced by one element.

Each element on the leading edge of the leaf is then sequen-

tially scanned to determine if coincidence with a set ele-

ment has occurred. If no set elements are found, the sides

of the leaf are checked by rotating about each apex at the

margin radius, as illustrated in figure 4-9.



Target




Margin







Locate Direction



Figure 4-9: Target search and localization


If a set element is not encountered to the sides, the

leaf edge is again advanced one element and scanned. This

process continues until a set element is encountered (either

the target periphery, the edge of an opposing leaf where

applicable, or the limit of the view window which defines

the limit of the collimator open aperture). Leaf movement

is stopped, the leaf position is translated from screen









48

coordinates to world coordinates, and the position is re-

corded. After all leaf positions have been resolved, the

settings are sent to a data file for processing by the

dosimetry program.

The result of the localization is shown in figures 4-10

through 4-21 for both four jaw and two jaw multileaf colli-

mators. The targets are the same as in figures 4-3 through

4-8 respectively, as are the table and gantry positions. As

many of the multileaf collimators described in the litera-

ture are of the two jaw type, a comparison of coverage was

deemed appropriate.





49


SPHERE.CT! 6 leaves 0.50 ag uide per Jau. 0.250 en margin. 4 Jaus
Oantre: 235.00 dag Table: 270.00 deg
a
Oantru : +
Table: a--.
Angles: A
Find: F
Jaus: J
Levela : L
Margin: M
Target: T
Exit: ESC



















T


(a)

SPHERE.OT: 6 leauvs 0.50 c uida per Jau. 0.250 luargin. 4 Jaus
Oantry: 265.00 dog Table: 270.00 deg
Oantrs T :
Table: -- ]
Angles: A
Find: F
Jeas: J
Leaves: L
Margin: N
Target: T
Exit: ESC



















T


(b)


Figure 4-10: Sphere, 4 jaw localized
(a) Gantry 2350; (b) Gantry 2650














































(c)
SPHERE.CT: 6 league 0.50 em guide per Jau, 0.250 cn Margin, 4 Jaus
Oantru: 325.00 deg Table: 270.00 deg
0
Gantry: +
Table: --+
Angles: A
Find: F
Jaus: J
Le-aes: L
Margin: t
Target: T
Exit: ESC




m7 B


(d)


Figure 4-10 -- continued
(c) Gantry 2950; (d) Gantry 3250


SPHERE.CT: 6 league 0.50 cn wide per Jau. 0.250 em Margin, 4 Jaus
Gantru: 295.00 dag Table: 270.00 dag
Gantru: f 4
Table: --
Anglas: A
Find: F
Jaus: J
Lgaes: L
Margin: M
Target: T
Exit: ESC




A B




















































(a)

SPHERE.CT: 6 leaves 0.50 eM uide per Jau. 0.250 ex margin. 2 Jaus
Oantry: 265.00 deg Table: 270.00 deg
nantru: I
Table: <--
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: n
Target: T
Exit: ESC


(b)



Figure 4-11: Sphere, 2 jaw localized
(a) Gantry 2350; (b) Gantry 2650


SPHERE.CT: 6 leaves 0.50 Ce uide per Jau. 0.250 en Margin. 2 Jaus
Oantrw: 235.00 deg Table: 270.00 deg
Oantru: *4
Table: .--
Angles: A
Find: F
.aus: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A






















































(C)

SPHERE.OT: 6 leaves 0.50 en wide per jau. 0.250 cn margin, 2 Jaus
Gantry: 325.00 deg Table: 270.00 deg
Gantrw: 4
Table: -.- _.
Angles: A
Find: F
Jaws: J
Leaves: L
Margin: M
Target: T
Exit: ESC


(d)


Figure 4-11 -- continued
(c) Gantry 2950; (d) Gantry 3250


SPHERE.CT: 6 leaves 0.50 en uide oer jaw, 0.250 en Margin, 2 Jaus
Gantry: 295.00 deg Table: 270.00 deg
0
Gentrw: 4
Table: ,-
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A



















































(a)

APOUD.CT: 6 leaves 0.50 a~ guide per jawu 0.250 cin argin. 4 Jaus
Oantry: 265.00 deg Table: 270.00 deg
0
Oantry: + 4
Table: *--
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: M
Target: T
Exit: ESC





Ai B


(b)


Figure 4-12: AP ovoid, 4 jaw localized
(a) Gantry 2350; (b) Gantry 2650


APOUD.CT: 6 leaves 0.50 en wide Per Jau. 0.250 en margin. 4 jaus
Gantry: 235.00 deg Table: 270.00 deg
0
gantru: t +
Table: <--
Angles: A
Find: F
Jaus: J
Leaues: L
Margin: M
Target : T
Exit: ESC





Armmrmr 1 1 1 t ) mmrrrmr























































(c)

APOUD.CT: 6 leaves 0.50 on uide per Jau. 0.250 an Margin. 4 Jaus
(antry: 325.00 deg Table: 270.00 deg
0
Gantri;: #
Table: ,--
Angles: A
Find: F
Jaus: J
Leav : L
Margin: n
Target: T
Exit: ESC





B


















(d)



Figure 4-12 -- continued

(c) Gantry 2950; (d) Gantry 3250


APOUD.CT! 6 league 0.50 on ulde per Jau. 0.250 c Margin. 4 Jaus
Gantry: 293.00 deg Table: 270.00 deg
0
Oantru: 9
Table: <--
Angles: A
Find: F
Jaus: J
Leauv : L
Margin: M
Target: T
Exit: ESC





A B






















































(a)

APOUD.CT: 6 leaves 0.50 en uide per Jaw. 0.250 en margin, 2 Jaus
Gantry: 265.00 deg Table: 270.00 des
0
Gantru : +~
Table: --
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A B















T


(b)



Figure 4-13: AP ovoid, 2 jaw localized

(a) Gantry 2350; (b) Gantry 2650


APOUD.CT: 6 leaves 0.50 cm guide per Jau, 0.250 cn margin, 2 Jaw
Gantru: 235.00 deg Table: 270.00 deg
0
Gantry: t*
Table: --
Aglies: A
Find: F
Jaws: J
L_..a : L
Margin: n
Target: T
Exit: ESC





AB B






















































POUD.CT: 6 leaIes 0.50 cn guide ner Jaw. 0.250 en Margin. 2 Jaus
Gantry: 325.00 deg Table: 270.00 deg
Gantri: -
Table: _--
Angles: 0
Find: F
Jaws: J
L.ea.s : L
Margin: M
Target: T
Exit: ESC





AB














T


(d)


Figure 4-13 -- continued
(c) Gantry 2950; (d) Gantry 3250















































(a)


Figure 4-14: Axial ovoid,
(a) Gantry 2350; (b)


4 jaw localized
Gantry 2650


AXOUD.CT: 6 leaves 0.50 cn uide par Jau. 0.250 cn margin. 4 Jaus
Gantru: 235.00 deg Table: 270.00 deg
G
Oantry: 9 4
Table: --,
fngles: t
Find: F
Jaus: J
Leaves: L
Margin: M
Target : T
Exit: ESC





















































(c)

AXOUD.CT: 6 leagues 0.50 cn wide per Jau, 0.250 eon argin, 4 Jaus
Oantr': 325.00 deg Table: 270.00 deg
Oantrw: f
Table: *--
Angles: A
Find: F
Jaus: J
Leam s: L
Margin: M
Target: T
Exit: ESC


(d)


Figure 4-14 -- continued
(c) Gantry 2950; (d) Gantry 3250


AXUOD.CT: G leauas 0.50 en guide per Jaw. 0.250 eH margin. 4 jaws
Gantrw: 295.00 deg Tablr: 270.00 deg
0
Oantru: +
Table: --
Angles: A
Find: F
Jaus: J
Leuavs: L
Margin: M
Target: T
Exit: ESC





A a





















































(a)

AXOUD.CT: 6 leaves 0.50 rc guide per Jau, 0.250 en margin. 2 jaus
Gantry: 265.00 deg Table: 270.00 deg
Gantry: + 4
Table: --
Angles: A
Find: F
Jaws: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A B














T


(b)



Figure 4-15: Axial ovoid, 2 jaw localized
(a) Gantry 2350; (b) Gantry 2650


OAOUD.CT: G leagues 0.50 en uide per Jaw. 0.250 en Margin. 2 jaus
Gantry: 235.00 deg Table: 270.00 deg
Gantry: t
Table: --
Angles: A
Find: F
Jaus: J
Leaue.: L
Margin: M
Target: T
Exit: ESC





A





60


AXOUD.CT: 6 leaves 0.50 cm uide per Jau. 0.250 rn margin. 2 Jaus
OGntrw: 295.00 dog Table: 270.00 dag
Q
Oantru: t -
Table: --
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A B














T



(c)

AXOUD.CT: 6 leaves 0.50 cn uide per Jau, 0.250 ce margin. 2 Jaus
Oantrw: 325.00 deg Table: 270.00 deg
Gantruw -
Table: --.
Angles: A
Find: F
Jaws: J
Loavs: L
Margin: MI
Target : T
Exit: ESO





A B














T


(d)


Figure 4-15 -- continued
(c) Gantry 2950; (d) Gantry 3250





61


LATOUD.CT: 6 leaves 0.50 an uide per Jau, 0.250 c" margin. 4 Jaus
Gantry: 235.00 deg Table: 270.00 dog
Gentrg: 4 4
Table: .--
Angles: A
Find: F
Jaus: J
Leaves: L
Hargin: M
Target: T
Exit: ESC





B














T


(a)

LATOUD.CT! 6 leaves 0.50 c" uide per Jaw. 0.250 ngargin, 4 Jaus
Oantru: 265.00 deg Table: 270.00 deg
0
oantru: 4
Table: <--o
angles: A
Find: F
Jaus: J
Leavem: L
Margin: M
Target: T
Exit: ESC





AB














T


(b)


Figure 4-16: Lateral ovoid, 4 jaw localized
(a) Gantry 2350; (b) Gantry 2650













62


LATOUD.CT: 6 leaves 0.50 cn guide per Jau, 0.250 an Margin. 4 Jaws
Gantru: 295.00 deg Table: 270.00 deg
0
Oantr;: 4
Table: +--
angles: A
Find: F
Jaws: 3
Lea.es: L
Margin: M
Target: T
Exit: ESC




















T



(C)

LATOUD.CT: 6 leaves 0.50 en wide per Ja,. 0.250 en margin, 4 Jaws
Gantru: 325.00 deg Table: 270.00 deg
Gantry: +
Table: s--
Angles: A
Find: F
Jaus: J
Leave : L
Margin: M
Target: T
Exit: ESC





A B


















(d)


Figure 4-16 -- continued
(c) Gantry 2950; (d) Gantry 3250













63


LATOUD.CT: 6 leaues 0.50 en uide per jau, 0.250 en Margin, 2 Jaus
Oantru: 235.00 deg Table: 270.00 deg
Gantru: +
Table: --.
Angles: A
Find: F
Jaus: J a
Leew : L
Margin: M
Target: T
Exit: ESC





















T


(a)

LATOUD.OT: 6 leaues 0.50 nc uide per Jaw, 0.250 en Margin. 2 Jaus
Oantrw: 265.00 deg Table: 270.00 deg
0
Gantru: *
Table:
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: M
Target: T
Exit: ESC




















T


(b)


Figure 4-17: Lateral ovoid, 2 jaw localized
(a) Gantry 2350; (b) Gantry 2650





64


LATOUD.CT: 6 leaves 0.50 cn guide per Jaw, 0.250 C Margin. 2 Jaus
Gantry: 295.00 deg Table: 270.00 deg
Gantre: +
Table: i--i*
Angles: A
Find: F
Jaus: J
Laues.: L
Margin: M
Target: T
Exit: ESC




















T


(c)

LATOUD.CT: leagues 0.50 cm guide per jau, 0.250 en margin, 2 Jaws
Gantry: 325.00 deg Table: 270.00 deg
Gantry: +
Table: --
Angles: A
Find: F
Jaus: J
Leaves : L
Margin: M
Target: T
Exit: ESC





A B














T


(d)


Figure 4-17 -- continued
(c) Gantry 2950; (d) Gantry 3250





















































Figure 4-18: Oblique ovoid, 4 jaw localized
(a) Gantry 2350; (b) Gantry 2650





66


OBLOUD.CT: 6 leaves 0.50 cm uide per Jau, 0.250 eM margin, 4 Jaus
Oantru: 290.00 deg Table: 270.00 deg
0
Oantru: t +
Table: --*
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: N
Target: T
Exit: ESC





7B














T



(c)

OBLOUD.CT: 6 leaves 0.50 cM guide per JaM. 0.250 c margin. 4 Jaus
Oantrt: 325.00 deg Table: 270.00 des
Oantru: 9 +
Table: --
Angles: A
Find: F
Jaws: J
Leaves: L
Margin: M
Target: T
Exit: ESO























(d)


Figure 4-18 -- continued
(c) Gantry 2950; (d) Gantry 3250













67


OBLOUD.CT: 6 leaves 0.50 Cn wide per jaw. 0.250 e margin, 2 jaus
Gantry: 235.00 deg Table: 270.00 deg
G
Gantry: +
Table: --
Angles: A
Find: F
Jaus: J
Leaves: L
Margin: M
Targt : T
Exit: ESC





A















T


(a)

OBLOUD.CT: 6 leaves 0.50 cm guide per jau. 0.250 en Margin. 2 jaus
Gantry: 265.00 deg Table: 270.00 deg
0
Gantrw: 9
Table: --
Angles: A
Find: F
Jaws: J
Leaves: L
Margin: MI
Target: T
Exit: ESC





















T


(b)


Figure 4-19: Oblique ovoid, 2 jaw localized

(a) Gantry 2350; (b) Gantry 2650
















OBLOUD.CT: 6 leaves 0.50 en wide per jaw, 0.250 Cn margin, 2 jaws
Oantrw: 295.00 deg Table: 270.00 deg
0
Gantrw: *
Table: --
Angles: A
Find: F
Jaws: J
LIves: L
Margin: M
Target: T
Exit: ESC





A 0B















T



(c)

OBLOUD.CT: 6 leaves 0.50 eu wide per jau, 0.250 en Margin, 2 Jaws
Oantrw: 325.00 deg Table: 270.00 deg
0
Gantry: 4 *
Table: --
Angles: A
Find: F
Jaws : J
Leaves: L
Margin: M
Target: T
Exit: ESC





A B















T


(d)


Figure 4-19 -- continued
(c) Gantry 2950; (d) Gantry 3250












69


DOBLOUD.CT: 6 leaves 0.50 en guide per Jau. 0.250 en Margin. 4 Jaus
Gantry: 235.00 deg Table: 270.00 deg
Gantry: 4 +
Table: i--
Angles: A
Find: F
Jaus: J
Laves: L
Margin: M
Target: T
Exit: ESC




















T


(a)

DOBLOUD.CT: 6 leaves 0.50 cn uide per Jawu 0.250 en margin, 4 Jaus
Gantry: 265.00 deg Table: 270.00 deg
0
Dantrss: # +
Table: --s.
Angles: A
Find: F
Jaws: J
Leaves: L
Margin: M
Target: T
Exit: ESC




















T


(b)


Figure 4-20: Double oblique ovoid, 4 jaw localized
(a) Gantry 2350; (b) Gantry 2650























































(c)

DOBLOUD.CT: 6 leaves 0.50 Ce wide per jaw, 0.250 ci margin, 4 jaws
Qantrw: 325.00 deg Table: 270.00 deg
0
Oantru: +T
Table: i--
Angles: A
Find: F
Jaws: J
Leaves : L
Margin: M
Target: T
Exit: ESC


(d)



Figure 4-20 -- continued
(c) Gantry 2950; (d) Gantry 3250


DOBLOUD.CT: 6 leaves 0.50 ec wide per Jawu 0.250 en Margin, 4 Jaws
Gantru: 295.00 deg Table: 270.00 deg
Gantry: f 4
Table: <--
Angles: A
Find: F
Jaws: J
Leaves: L
Margin: M
Target: T
Exit: ESC





A 1B




















































DOBLOUD.CT: 6 leaves 0.50 en wide per jaw, 0.250 en margin, 2 jaws
Gantry: 265.00 deg Table: 270.00 deg
Gantrj: 4 +
Table: --.
Angles: A
Find: F
Jaws: J
Leaves: L
Margin: M
Target: T
Exit: ESC


(b)


Figure 4-21: Double oblique ovoid, 2 jaw localized
(a) Gantry 2350; (b) Gantry 2650



















































(c)

DOBLOUD.CT: 6 leaves 0.50 en wide per Jau. 0.250 n Mnargin, 2 Jaus
Gantry: 325.00 deg Table: 270.00 deg
G
Oantrn: _
Table: --
Angles: A
Find: F
Jaws: J
Leaves: L
Margin: M
Target: T
Exit: ESC



















T


(d)


Figure 4-21 -- continued
(c) Gantry 2950; (d) Gantry 3250


DOBLOUD.CT: 6 leaves 0.50 eC wide per Jaw, 0.250 c margin. 2 Jaus
Gantry: 295.00 deg Table: 270.00 deg
0
Gantru:
Table: --
Angles: A
Find: F
Jaws:
Lau--: L
Margin: MH
Target: T
Exit: ESC



Af B














CHAPTER 5
INVESTIGATIONAL DOSIMETRY


The current dose model used in the University of Flori-

da stereotactic radiosurgery planning system is the TMR/OAR

model [Bov90]. This model calculates dose along the central

axis of the beam at the required depth and modifies the

central axis dose by multiplying with a measured off-axis

ratio. This is acceptable in small beams, as their nearly

parallel pencil kernels produce little or no scatter compo-

nent. This model has been implemented for microcomputers by

Suh [Suh90] for both circular and rectangular fields. As

presently used, however, this model only calculates the

effects of radiation beams produced by circular apertures

and cannot model the effects of dynamic conformal collima-

tion with changing, irregular fields.

Two dosimetry methods to predict such effects have been

proposed for this work, the convolution method and the

negative field method. Each is investigated in turn to

determine if its application is appropriate for conformal

stereotactic radiosurgery. Also covered in the initial

investigation of dosimetry are the effects of two jaw versus

four jaw localization, as illustrated in the previous chap-

ter.








74

The Convolution Method

The first dosimetry method investigated is that of

convolutions using Fourier transforms, based on work by

Mohan et al. [Moh87], and Starkschall [Sta88]. The basis of

this method is the fact that convolutions are easily com-

puted by taking the Fourier transforms of the functions to

be convolved (a complex function of integration). The

transformed functions are point multiplied and the product

is inverse transformed to arrive at the convolution of the

original two functions. This is analogous to adding the

logarithms of two numbers one wishes to multiply and taking

the antilogarithm of the sum to arrive at the product.

The following discussion of calculating three dimen-

sional dose distributions is taken from Mohan et al.

[Moh87]. The basic dose equation is:


D(pt) =DoCm*C, (5-1)

where D(pt) is the dose in the patient, Do is the dose at

the same point in a flat, homogeneous, tissue equivalent

phantom for an open field of the same size and incident

normally on the phantom (obtained from table lookup and

interpolation), Cm is the correction due to beam modifiers,

and Ci is the correction for inhomogeneity and surface

irregularities (unity for small beam stereotactic radiosur-

gery).










Cm may be calculated by:


CDoc (5-2)


where Dm,c and DO,c are found at the given depth by con-

volving the relative primary fluence distribution with the

profile of the pencil beam distribution at the same depth.

The dose for open or modified fields may then be writ-

ten as:


Dc(x,y,d) =ff (a,b) K(x-a,y-b,d) dadb (5-3)


where Dc is either Dm,c (modified field) or DOc (open

field), x,y,a,b are the lateral distances from the central

axis (cm), # is the relative fluence distribution for the

open or modified field, and K is the two dimensional cross-

section profile of the pencil beam at depth d (the convolu-

tion kernel).

Equation 5-3 can be re-written in terms of Fourier

transforms as:

FiDc (x, y, d) }= FIO (x, y) } F{K(x, y, d) (5-4)

where F signifies taking the two dimensional Fourier trans-

forms of the quantities in braces.

The initial point source fluence can be approximated by

a relative fluence of unity at all points inside the open

beam and by the collimator transmission at points outside of

the open beam. A second point source fluence matrix is








76
created in which all values of the first have been exponen-

tially attenuated according to the path length of the rays

originating from the point source through the beam shaping

blocks (approximated by the narrow beam transmission factors

of the blocks). To be noted here is the observation that,

for a multileaf collimator model, this second matrix results

in a quantized representation of leaf position, i.e. each

leaf in the model can have a positioning accuracy no smaller

than the real space matrix point separation. This fact will

dictate the matrix calculation time, which is a function of

both matrix size, corresponding to the desired area of

spacial coverage, and point spacing, corresponding to the

desired accuracy of leaf positioning.

The source size must be included in the model to ac-

count for penumbra effects. This is accomplished by assum-

ing a circular disk for the source and determining how much

of the source is visible to each point of computation by

calculating the area of the source disk inside the projec-

tion of the open part of the beam aperture on the plane of

the source using the point of computation as the focal

point. At isocenter, a source of radius r has a radius r' =

ar (a = (SAD STD) / STD where STD is the source-to-tray

distance, i.e. the location of the block). The source

kernel matrix elements in a circular region of r' at the

center of the matrix are set to a constant value represent-

ing the source strength or to unity to normalize, and to








77

zero elsewhere. The source kernel matrix is then convolved

with the point source fluence matrices (open and blocked).

For the small source size of a linear accelerator, convolu-

tion is unnecessary if the source occupies only one source

kernel matrix point.

Mohan arrives at the pencil beam kernel by Monte Carlo

calculations, however the same endpoint is possible by

taking broad beam profiles at several selected depths and

deconvolving the x and y beam profiles to develop the kernel

[Chu88b]. The pencil beam kernel is convolved with both the

open and blocked beam matrices at each selected depth re-

sulting in two three-dimensional dose matrices. The ratios

of the corresponding elements of the matrices give a three

dimensional matrix of Cm values which are used in equation

5-1, with interpolation to find doses between selected

points.

For initial investigation of this model, a two dimen-

sional fast Fourier transform (FFT) routine by Press et al.

[Pre88] was coupled to a driver/timer program. An arbitrary

input function was prepared, the timer was started, a for-

ward and reverse transform pair was performed on 16, 32, and

64 square matrices, and the timer was stopped. Test results

are shown in table 5-1. The results were extrapolated to

find times for realistic matrix sizes in table 5-2.

Using sixteen planes of computation per gantry/table

position (4 cm squares spaced at 2.5 cm), and a 512 square









78

FFT pair (a 5.12 cm square with 0.1 mm spacing, necessary

for good resolution of leaf positioning, recalling that in

the convolution model the area of spacial coverage is deter-

mined by the matrix size and the projected leaf position

accuracy is determined by the point spacing), the extrap-

olated 540 seconds for a single transform pair, i.e. a

single gantry/table position and a single arbitrary plane,

results in a computation time of 240 hours, excluding inter-

polations, for a modest 5 arc plan with 100 degree arcs at a

5 degree calculation increment (100 gantry/table positions).


Table 5-1: Experimental 2D FFT Times

Square Points Time (sec)

16 512 0.22
32 2048 0.88
64 8192 4.32


Table 5-2: Extrapolated 2D FFT Times

Square Points Time (sec)

128 32768 21.6
256 131072 108.0
512 524288 540.0


The FFT matrix size for the completion of a dose volume

histogram in a reasonable time of approximately two hours is

the 64 square, however this allows leaf positioning to be

set to accuracy limits of only 0.625 mm on a 4 cm square








79
grid, which is more than three times the system average

mechanical accuracy.

Further, using the more realistic measure for a rotat-

ing model, in which the FFT planes must cover the volume of

interest on any projected area, the 4 cm square grid needs a

minimum coverage of 6.9 cm on a side. This gives a resolu-

tion of 1.08 mm per point for a 64 square FFT matrix, and

the same resolution for the leaf settings. This is in

contrast to the 0.2 mm average mechanical accuracy of the

system, and is even greater than the 0.6 mm pixel resolution

of the CT images used for planning [Fri89b] and which would

be used for localization.

This analysis shows that the 2D FFT convolution dose

model is an inappropriate method for small field rotational

dosimetry and work on this model was not continued.

The Negative Field Method

The second approach uses the negative field method

[Kha70, Kha84] and has the advantage of being a simple

modification to a known, verified model. Preliminary inves-

tigation of the utility of collimating the beam to the

target with this technique was completed using the circular

beam model as the standard and modifying the rectangular

beam model to calculate blocked irregular fields (both

models from Suh [Suh90]). Collimator rotation was not used.

The negative field model derives its name from the

calculation technique employed. In this case, a basic








80

square open field is first calculated with full rotation

arcs. Next, each rectangular leaf is treated as if it were

an open field (dosimetry is performed over an open field of

the dimension each leaf), and the contributions from each

are summed over the same arcs. Finally, the sum of the leaf

fields is subtracted from the base open field, i.e. the leaf

fields act as a "negative" field. This technique includes

scatter-air ratios which are part of the measured data at

the edges of the leaves, and thus is effectively equivalent

to the SAR method and Clarkson integration.

A spherical head phantom of 20 cm in diameter was used

with the target at the center. This phantom size and shape

is considered appropriate for the head as Pike uses an 18 cm

diameter spherical phantom for verification work [Pik90],

and the ICRP standard man phantom head is modeled by a 20 x

24 cm right circular cylinder topped by a hemisphere

[Ker80]. Four target shapes were modelled: one by a 2 cm

diameter sphere at the center of the head phantom; the other

three by an ellipsoid (2 cm on the major axis, 1 cm on the

minor axes) at the center of the head phantom. The first

had the major axis in the AP orientation and the minor axes

in the coronal plane, the second had the major axis in the

superior/inferior orientation and the minor axes in the

axial plane, and the third had the major axis oriented

obliquely from anterior/superior to posterior/inferior.








81

A treatment plan, the same for each target for compari-

son purposes, was prepared using five non-coplanar para-

sagittal 1000 arcs with 50 incrementation at arbitrary table

angles of 500, 70, 90, 2900, and 3100. Minimum margins

for each were set at 5 mm. The targets were localized for

the conformal cases using 2.5 mm leaves and the plan was run

for four jaw conformal collimation, two jaw conformal colli-

mation (with localization in the AB collimator dimension),

and for conventional, single isocenter collimation.

Axial, sagittal, and coronal dose distributions through

isocenter were computed to visually evaluate the goodness-

of-fit of distribution to target. Differential dose volume

histograms were computed to quantitatively evaluate the

plans. The histograms were further evaluated using the

integrated logistic function [Fli89; Fli90b], modified for

qualitative comparison (see appendix E).

Additionally, the AP oriented ovoid conformal plan was

compared to a two isocenter and a three isocenter plan using

the same treatment parameters as above. The plans were

compared using dose distributions on the three major planes,

by generating three-dimensional dose amplitude plots on the

axial and sagittal planes, and also by dose volume histo-

grams and the integrated logistic formula.

Comparing figures 5-1, 5-2, and 5-3 for the case of the

spherical target, we note that all the figures display

similar isodose patterns. This is confirmed by observing









82

the dose volume histograms for this case, figure 5-4. In

each histogram (total volume, target volume, normal tissue

volume) the histograms show similar dosimetry. This demon-

strates that the addition of conformal collimation does not

degrade system performance already established, and indeed

that a spherical target is best fit with a spherical dose

distribution. Additionally, the integrated logistic func-

tion results for the normal tissue in the calculated volume

are also (roughly) similar with values of 0.175 for the 4

jaw localization, 0.407 for the 2 jaw localization, and

0.299 for the circular field for prescribed doses of 1000

cGy to the 70% line for each. Note that in the integrated

logistic function comparison, lower numbers are defined as

better (although only qualitatively better) and that no

evaluation of homogeneity within the target volume is per-

formed.

Figures 5-5, 5-6, and 5-7, the AP oriented ovoid, show

great improvement for the 4 jaw conformal collimation versus

the 2 jaw or the single isocenter circular, with the dosime-

try of the 2 jaw and the circular being fairly similar.

This is confirmed by observing the dose volume histogram,

figure 5-8, and by evaluating the integrated logistic func-

tion. This evaluation gives values of <0.001 for the 4 jaw,

0.360 for the 2 jaw, and 0.391 for the circular.

Figures 5-9, 5-10, and 5-11, for the axial ovoid, show

steps of improvement, with the best fit being produced by








83

the 4 jaw collimation, followed by 2 jaw, and then by circu-

lar. This is quantitatively confirmed by the dose volume

histogram comparison, figure 5-12, and by the integrated

logistic function results: <0.001 for the 4 jaw; 0.231 for

the 2 jaw; and 0.428 for the circular.

These results are echoed by figures 5-13, 5-14, and 5-

15, for the oblique ovoid. Again, the 4 jaw collimation

produces the best results, followed by the 2 jaw, and

trailed by the circular. The dose volume histogram in

figure 5-16 also shows this. Calculating the integrated

logistic function for these volumes gives: <0.001 for the 4

jaw; 0.274 for the 2 jaw; and 0.397 for the circular.

Finally, the AP ovoid is localized with a 4 jaw colli-

mator and the resulting dosimetry is compared with two

isocenter and three isocenter treatment plans in figures 5-

17, 5-18, and 5-19. This comparison is important in that

the common method for producing conformal dosimetry at the

present time is by employing multiple isocenters. Observing

these figures shows similar conformation in the high isodose

regions, with the low isodose lines on the multiple iso-

center plots being much more spread out. Also of importance

is the observation that the conformally collimated plan has

the target enclosed in the 80% isodose line, whereas the

multi-isocenter plans reduce coverage to the 70% line. This

reduction is common for any multi-isodose plan. Homogeneity

of coverage is graphically illustrated in figures 5-20, 5-








84

21, and 5-22 for the multileaf collimator, the two iso-

center, and the three isocenter plans, respectively. The

multileaf collimator quite obviously produces a homogeneous

dose across the target. The two and three isocenter plans

show the characteristic peaks in dose where the edges of the

isodose spheres produced by the circular collimators over-

lap. The dose volume histogram, figure 5-23, also decisive-

ly shows the difference, with the target volume dose volume

histogram reflecting these peaks and valleys. The integrat-

ed logistic function computes values of <0.001 for the

conformal collimator, 0.154 for the two isocenter plan, and

0.196 for the three isocenter plan.

Conclusion

The convolution method has been shown to be inappro-

priate for use with small field stereotactic radiosurgery

because of the tradeoffs between accuracy and time. The

negative field method will form the basis of the dosimetry

to be further developed in this work. Each of the preceding

dosimetry comparisons shows the superiority of conformal

collimation, 4 jaw conformal collimation in particular, to

single or multiple isocenter treatment plans, and the feasi-

bility of such multileaf collimator planning.












Conformal Collimation, 4 Jaw
Axiol. SPHERECT


etr (em)


(a)
Conformal Collimation. 4 Jaw
Sagittal. SPHERE.CT


A-(ml


(b)
Conformal Collimation, 4 Jaw
Coronal. SPHERLCT


Lan(ln)


(c)


Figure 5-1: Four jaw conformal collimation, sphere
80, 40, 16, 8% lines normalized to plane maximum
(a) Axial plane; (b) Sagittal plane; (c) Coronal plane













Conformal Collimation. 2 Jaw
Aiodl. SPHERE.CT
2






0






-2
-2 -1 0 1 2
WtCl(-m)


(a)

Conformal Collimation. 2 Jaw
Sogttal, SPHERE.CT


-1 0


(b)

Conformal Collimation. 2 Jaw
Coronal, SPHERE.CT


-1 0
Ulteranm)


(c)


Figure 5-2: Two jaw conformal collimation, sphere
80, 40, 16, 8% lines normalized to plane maximum
(a) Axial plane; (b) Sagittal plane; (c) Coronal plane











87


Conventional Collimation. 1 Isocenter
Axial, SPHERE.CT















2


-1 0
uki to)


(a)

Conventional Collimation. 1 Isocenter
Sogittal. SPHERE.CT






-2







-2
-2 -1 0 1 2
teMl(en)


(b)

Conventional Collimation, 1 Isocenter
Coronal, SPHERECT


-2 -1 0
Loal(.l)


(c)


Figure 5-3: One center circular collimation, sphere
80, 40, 16, 8% lines normalized to plane maximum
(a) Axial plane; (b) Sagittal plane; (c) Coronal plane


1




















SPHERE.CT Total Volume Dose
Differential DVH


20MM


0 Jw,00Vwt


010 IM am0 0D oe sam sW0 m40 -IM -
Dose %




(a)


SPHERECT Target Volume Dose
Differential DVH


2jW00V
Z wwwww


0-10 10-I0 0 0 340 40-0 O0 ~0 m 0 a0 o-100
Doue%


SPHERECT Normal Volume Dose
Differential DVH


S4JwCortrml

2 Jw3lU0
DO~~


(C)


Figure 5-4: Dose volume histograms, sphere

(a) Total volume; (b) Target volume; (c) Normal volume


S-

a .
0 -
3.
a-


3-o
3-


e0-


a
6-
6sab -1
9-


10B-
100-



9o-
U-
3-


3 -


40


10-



0o


as









Ii
30-





V 0
a




0
|

13a


a











89


Conformal Collimation, 4 Jaw
Axial. APOV.CT










-1



-2
-2 -1 0 1 2



(a)

Conformal Collimation, 4 Jaw
Sogittal, APOVD.CT


Ad (-l


(b)

Conformal Collimation, 4 Jaw
Coronal, APVD.CT


-1 0
Umt"m


(c)


Figure 5-5: Four jaw conformal collimation, AP ovoid
80, 40, 16, 8% lines normalized to plane maximum
(a) Axial plane, (b) Sagittal plane, (c) Coronal plane










90


Conformal Collimation. 2 Jaw
Axial. APOVD.CT











-1
'II

-2
-2 -1 0 1 2



(a)

Conformal Collimation, 2 Jaw
Sglttal. APOVD.CT
2













-2 ---
-2 -1 0 1 2
AMhlICn


(b)

Conformal Collimation. 2 Jaw
Coronal,APOVD.CT


0
laeOm


(c)


Figure 5-6: Two jaw conformal collimation, AP ovoid
80, 40, 16, 8% lines normalized to plane maximum
(a) Axial plane, (b) Sagittal plane, (c) Coronal plane










91


Conventional Collimation. 1 Isocenter
Axial. APOVD.CT













- 2 ....... . .. ... ..............
-2
-2 -1 0 1 2



(a)

Conventional Collimation. 1 Isocenter
Sagttal. APOVD.CT


0
a
A~iUaa


(b)

Conventional Collimation, 1 Isocenter
Coronal, APOVD.CT


0
Latml (m)


(c)


Figure 5-7: One center circular collimation, AP ovoid
80, 40, 16, 8% lines normalized to plane maximum
(a) Axial plane, (b) Sagittal plane, (c) Coronal plane


















APOVD.CT Total Volume Dose
Differential DVH


4Jw ownraU
0Jmisw c
ZOMNI"


0.10 1020 -ao O40 44 eo *eo-o o040 ON0 IO.1
oose%


APOVD.CT Target Volume Dose
Differential DVH


0o1o 100 -O W 40 N40 7 70 71 ON WI00.l
Dno


APOVD.CT Normal Volume Dose
Differential DVH


S4J0a.wtamw
t w4wnws


a.1 w 040 40 040 N70 N o 4n 0 -WI





(c)


Figure 5-8: Dose volume histograms, AP ovoid

(a) Total volume; (b) Target volume; (c) Normal volume


Ir-
ist-
110-
100-
U-



-0
U-
10.


M.


10.
16-


R] 4jmv~cnl
m aceMm


U0.
n -



a.
a.
70.


U.


a-
0o-
Ua.
a.
U-
10-
0-













Conformal Collimation. 4 Jaw
Mal, AXOVD.CT
2 ......... ......... ... .......... .....








-1



-2 ..
-2 -1 0 1 2



(a)

Conformal Collimation. 4Jow
Sagittal, AXOVD.CT


(b)
Conformal Collimation. 4 Jaw
Coronal AXOVD.CT


L-W()


(c)


Figure 5-9: Four jaw conformal collimation, axial ovoid
80, 40, 16, 8% lines normalized to plane maximum
(a) Axial plane, (b) Sagittal plane, (c) Coronal plane














Conformal Collimation. 2 Jaw
Aidol,AXOVD.CT
2






0



-- -


-,


-2 -1 0
urtwOt-)


(a)

Conformal Collimation. 2 Jaw
Sagittal,AXOVD.CT


-2 -1 0
AJAt(-n)


(b)

Conformal Collimotion, 2 Jaw
Coronal, AXOVD.CT


-2 -1 0
imM0


(c)


Figure 5-10: Two jaw conformal collimation, axial ovoid
80, 40, 16, 8% lines normalized to plane maximum
(a) Axial plane, (b) Sagittal plane, (c) Coronal plane


1













Conventional Collimation. 1 Isocenter
Alal. AXOVD.CT


2 -1 0 1
Lat (em)


(a)

Conventional Collimation. 1 Isocenter
Sogitlal.AXOVD.CT


-1 0
-I


(b)

Conventional Collimation, 1 Isocenter
Coronal. AXOVD.CT


0



(c)


Figure 5-11: One center circular collimation, axial ovoid
80, 40, 16, 8% lines normalized to plane maximum
(a) Axial plane, (b) Sagittal plane, (c) Coronal plane




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