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
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Abstract of Dissertation Presented to the Graduate
School of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy
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 nonconformal
stereotactic radiosurgery with several nonintersecting
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, carotidcavernous 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 largefield 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 largefield 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 xrays of
the potential treatment area are analyzed. The physician
draws the outline of the target on the xray 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, threedimensional 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
xrays, 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 noninvasive 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 threeaxis 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 fourleaf 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 twoleaf 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 threedimensions 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 threedimensional reconstruction of
implant dosimetry using stereoradiography. Metz and Fencil
[Met89] developed a method of showing threedimensional
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 threedimensional 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), offaxis
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 offaxis 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
offaxis 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
xray 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
xray 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 precalibration 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 reanalyzed in
light of new data as opposed to the "oneshot" 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 BrownRobertsWellsm
(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 31). Setup of the system modifications takes 10 to
15 minutes.
Figure 31: 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 twobearing 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 threeaxis 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 radioopaque 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]. Radioopaque 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 31: 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 31. 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 xray 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 41. 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 41: 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 sumofangles gives:
x' = dcosa cosp dsina sinp
y'= dsina cosp + dcosa sin
and by substituting the original formulas 41 and 42:
P(x', y')
d
P(x, y)
13 ,.xy)
...I
(41)
(42)
(43)
(44)
(45)
(46)
x'= xcosp ysinp (47)
y' =xsinp + ycosp (48)
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 (49)
y' =xsinO +ycos6 (410)
z'=z (411)
Rotation in the xz plane about the y axis:
x'= xcosO + zsinO (412)
y/=y (413)
z = xsinO + zcos
(414)
Rotation in the yz plane about the x axis:
X = X
(415)
y' =ycosQ zsinO
z = ysinO + zcos
(416)
(417)
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
(418)
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
(419)
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
(420)
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 42 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 42: 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 noncommutative 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 noncoplanar 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 418 and
419 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 (421)
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 (422)
UB UBI
which may be orthogonalized as:
AB = ABcosOtcosg GTsinOtcos4g +UBsinOg (423)
GT' = ABsin4 + GTcost (424)
UB = ABcos~tsinOg+GTsin(tsinOg+UBcosOg (425)
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 43 through 48
(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 43: 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 43  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 44: 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 44  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 45: 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 45  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 46: 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 46  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 47: 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 47  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 48: 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 48  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 onehalf 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 49.
Target
Margin
Locate Direction
Figure 49: 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 410
through 421 for both four jaw and two jaw multileaf colli
mators. The targets are the same as in figures 43 through
48 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 410: 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
Leaes: L
Margin: t
Target: T
Exit: ESC
m7 B
(d)
Figure 410  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 411: 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 411  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 412: 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 412  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 413: 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 413  continued
(c) Gantry 2950; (d) Gantry 3250
(a)
Figure 414: 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 414  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 415: 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 415  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 416: 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 416  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 417: 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: ii*
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 417  continued
(c) Gantry 2950; (d) Gantry 3250
Figure 418: 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 418  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 419: 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 419  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 420: 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 420  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 421: 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 421  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 offaxis
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, (51)
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 (52)
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(xa,yb,d) dadb (53)
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 53 can be rewritten in terms of Fourier
transforms as:
FiDc (x, y, d) }= FIO (x, y) } F{K(x, y, d) (54)
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 sourcetotray
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 threedimensional dose matrices. The ratios
of the corresponding elements of the matrices give a three
dimensional matrix of Cm values which are used in equation
51, 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 51. The results were extrapolated to
find times for realistic matrix sizes in table 52.
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 51: Experimental 2D FFT Times
Square Points Time (sec)
16 512 0.22
32 2048 0.88
64 8192 4.32
Table 52: 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
scatterair 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 noncoplanar 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
offit 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 threedimensional dose amplitude plots on the
axial and sagittal planes, and also by dose volume histo
grams and the integrated logistic formula.
Comparing figures 51, 52, and 53 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 54. 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 55, 56, and 57, 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 58, 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 59, 510, and 511, 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 512, 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 513, 514, 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 516 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, 518, and 519. 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
multiisocenter plans reduce coverage to the 70% line. This
reduction is common for any multiisodose plan. Homogeneity
of coverage is graphically illustrated in figures 520, 5
84
21, and 522 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 523, 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 51: 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 52: 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 53: 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
010 10I0 0 0 340 400 O0 ~0 m 0 a0 o100
Doue%
SPHERECT Normal Volume Dose
Differential DVH
S4JwCortrml
2 Jw3lU0
DO~~
(C)
Figure 54: Dose volume histograms, sphere
(a) Total volume; (b) Target volume; (c) Normal volume
S
a .
0 
3.
a
3o
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 55: 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 56: 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 57: 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 *eoo 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 58: 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
LW()
(c)
Figure 59: 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 510: 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 511: One center circular collimation, axial ovoid
80, 40, 16, 8% lines normalized to plane maximum
(a) Axial plane, (b) Sagittal plane, (c) Coronal plane
