Modeling of a multileaf collimator

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Modeling of a multileaf collimator
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Thesis (Ph. D.)--University of Florida, 1997.
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Includes bibliographical references (leaves 203-207).
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by Siyong Kim.
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Typescript.
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Vita.

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MODELING OF A MULTILEAF COLLIMATOR


By

SIYONG KIM














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

























This dissertation is dedicated to
my loving wife, Gyejin,
and darling daughters, Minkyung and Minna,
for everything we have shared.














ACKNOWLEDGMENTS


I am very pleased to acknowledge the helpful guidance of my research advisor,

Dr. Jatinder R. Palta, who has been truly supportive in every way not only as an academic

teacher but also as a person.

I extend my gratitude to my committee member, Dr. Timothy C. Zhu, for

providing specialized guidance on the theoretical and experimental aspects of my study.

Thanks are extended to the rest of my committee members: Dr. Wesley E. Bolch,

representing the Department of Nuclear and Radiological Engineering; Dr. James K.

Walker, representing the Department of Physics; Dr. William Mendenhall, representing

the Department of Radiation Oncology at the University of Florida.

A special debt is acknowledged to Dr. Chihray Liu for his willingness to share his

precious time with me to discuss many problems and to lead me in the right direction,

especially for the development of the multileaf collimator module.

I would also like to thank Patsy McCarty and Anne Covell for their editorial

advice. The gracious assistance of John Jerico is acknowledged; he helped me to fabricate

the custom blocks for experiments. Phil Bassett and John Preisler kindly helped me to

solve several mechanical problems that occurred during operation of the linear

accelerator. My thanks are extended to them.








Finally, I would be remiss if I did not acknowledge all the time that I spent

together with every member of the physics group in the Department of Radiation

Oncology.















TABLE OF CONTENTS





A CKN O W LED G M EN TS .................................................... ....................................... iii

A B ST R A C T ................................................................................. .............................. viii

CHAPTERS

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

G general Introduction ................................................................... .............................
Significance of The Multileaf Collimator System............................. .......... 2
Overview of M LC Systems. ..................................................... ...................4
The A im of This Thesis ............................................................ ......................... 9

2 DEVELOPMENT OF AN MLC MODULE FOR A TREATMENT
PLANNING SYSTEM .................................. ..........................10

Introduction .................................. .................................................................... 10
M methods and M aterials............................... ......................... ........................11
Geometric Optimization of MLC Conformation............................ ........... 11
User Interface M odule ....................................................................13
R esu lts............................................. ................................................. .....................14
C on clu sion ................................................................................ ............................. 15

3 A STUDY OF THE EQUIVALENT FIELD CONCEPT FOR THE HEAD
SCATTER FA CTOR ............................................ ...........................................19

Introduction ......................................................................... ................................... 19
Methods and Materials........................ .. ... ....................................22
Equivalent Field for Head Scatter Factor...............................................................22
Equivalent Field for Wedge and Tertiary Collimator Scatter Factor...................27
R e su lts ............................................................................... ................................ ....2 9
Equivalent Field for Head Scatter Factor...........................................................29
Equivalent Field for Wedge and Tertiary Collimator Scatter Factor.....................34
D discussion ................................................................................. .............................3 7
C conclusion ................................................................................ .............................39








4 AN EQUIVALENT SQUARE FIELD FORMULA FOR DETERMINING
HEAD SCATTER FACTORS OF RECTANGULAR FIELDS ...............................40

Introduction ......................................................................... ...................................40
T theory ..........................................................................................................................42
Methods and Materials............................................................... ......................45
R esults............................................................................... .....................................46
D iscu ssio n ................................................................................. .............................5 3
C conclusion .................................................. ..................................................... 56

5 A GENERALIZED SOLUTION FOR THE CALCULATION OF IN-AIR
OUTPUT FACTORS IN IRREGULAR FIELDS .........................................58

Introduction ........................................................................... ................................. 58
Formalism of In-air Output Factor.........................................................61
Head Scatter Factor and Monitor Back Scatter Factor ........................................61
Presence of A Beam Modifier in The Field ...........................................64
A Shaped Field with A Tertiary Collimator .......................... ....................66
Calculation Algorithm .............................................................. .......................67
O pen F field ...................................................................... .................................. 67
W edged Field ........................................................ .................................. ......73
Methods and Materials............................................................. ........................76
R esults............................................................................... .....................................80
Tertiary Collimator Scatter Factor ......................................................................80
In-air Output Factor of Open Fields Defined by Tertiary Collimator.................... 80
In-air Output Factor of Varian Type Wedge (External Wedge) Fields .................84
In-air Output Factor of Irregular Shaped Fields.................... ..................... 87
D iscu ssio n ................................................................................... ...........................87
C o n clu sio n ............................................................................... ..............................90

6 TWO-EFFECTIVE-SOURCE METHOD FOR THE CALCULATION OF IN-
AIR OUTPUT FACTOR AT VARIOUS SDDs IN WEDGED FIELDS ...................92

Introduction ......................................................................... .......................... ......92
T theory ..................... ..................................................................................................94
Methods and Materials.............................................................. .....................100
R e su lts ....................................................................................... ........................... 10 1
D iscu ssio n ................................................................................... .........................110
C on clu sion ............................................................................. ............................. 11 1

7 CONCLUSIONS..................................................... .......................... ............113

General Discussion ........................................ ............ ...................... 113
C onclusions........................................................ .................................................. 1 8



vi








APPENDICES

A SOURCE PROGRAM OF THE MLC MODULE .........................................124

REFERENCES ................ ........................................203

BIOGRAPHICAL SKETCH ................... ...... ............ ........... 208















































vii














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

MODELING OF A MULTILEAF COLLIMATOR

By

Siyong Kim

August 1997


Chairman: Jatinder R. Palta
Major Department: Nuclear and Radiological Engineering

A comprehensive physics model of a multileaf collimator (MLC) field for

treatment planning was developed. Specifically, an MLC user interface module that

includes a geometric optimization tool and a general method of in-air output factor

calculation were developed.

An automatic tool for optimization of MLC conformation is needed to realize the

potential benefits of MLC. It is also necessary that a radiation therapy treatment planning

(RTTP) system is capable of modeling MLC completely. An MLC geometric

optimization and user interface module was developed. The planning time has been

reduced significantly by incorporating the MLC module into the main RTTP system,

Radiation Oncology Computer System (ROCS).








The dosimetric parameter that has the most profound effect on the accuracy of the

dose delivered with an MLC is the change in the in-air output factor that occurs with field

shaping. It has been reported that the conventional method of calculating an in-air output

factor cannot be used for MLC shaped fields accurately. Therefore, it is necessary to

develop algorithms that allow accurate calculation of the in-air output factor. A

generalized solution for an in-air output factor calculation was developed. Three major

contributors of scatter to the in-air output--flattening filter, wedge, and tertiary

collimator--were considered separately. By virtue of a field mapping method, in which a

source plane field determined by detector's eye view is mapped into a detector plane

field, no additional dosimetric data acquisition other than the standard data set for a range

of square fields is required for the calculation of head scatter. Comparisons of in-air

output factors between calculated and measured values show a good agreement for both

open and wedge fields. For rectangular fields, a simple equivalent square formula was

derived based on the configuration of a linear accelerator treatment head. This method

predicts in-air output to within 1% accuracy. A two-effective-source algorithm was

developed to account for the effect of source to detector distance on in-air output for

wedge fields. Two effective sources, one for head scatter and the other for wedge scatter,

were dealt with independently. Calculations provided less than 1% difference of in-air

output factors from measurements. This approach offers the best comprehensive accuracy

in radiation delivery with field shapes defined using MLC. This generalized model works

equally well with fields shaped by any type of tertiary collimator and have the necessary

framework to extend its application to intensity modulated radiation therapy.














CHAPTER 1
INTRODUCTION

General Introduction


The discovery of x-rays and radioactivity was promptly followed by its

therapeutic application in the treatment of benign and malignant diseases. The first

therapeutic use of x-rays is reported to have taken place on January 29, 1896, when a

patient with carcinoma of the breast was treated with x-rays. By 1899, the first cancer, a

basal cell epithelioma, had been cured by radiation. Nowadays, radiation therapy is used

in approximately half of cancer patients either in a stand alone therapy or in combination

with chemotherapy or surgery. Better cure rates with radiation therapy, preservation of

organ and its function, and cosmesis can be easily attributed to technological gains in

radiation physics and better insights into radiation biology and pathophysiology. The

primary goal of radiation therapy is to produce the highest probability of local and

regional tumor control with the lowest possible side effects. Most cancer cells, like other

highly proliferating cells, are more sensitive to ionizing radiation than normal cells. This

is the fundamental premise in radiation therapy. The difference, however, is not always

large enough to guarantee successful treatment all the time. Therefore, significant effort

has been expected in radiation therapy in developing means to conform the dose to the

tumor cells while minimizing the dose to the normal cells, and to deliver the dose as

accurately and safely as possible. Since the advent of radiation therapy, photon beams








have been used the most commonly. In the early days of radiation therapy, photon beams

from x-ray tubes were the only sources of radiation available at that time. Most

treatments were limited to diseases at shallow depths due to the lower penetrability of

these x-rays. With the development of the cobalt machine with the use of sealed, high-

activity 60Co source in 1951 (Johns et al. 1952, Green & Errington 1952), radiation

therapy techniques took a quantum leap. Although cobalt unit is still an important

machine today, linear accelerators have become the most commonly used treatment

machine in radiation therapy clinics. The developments of diagnostic modalities, such as

CT (computed tomography) and MRI (magnetic resonance imaging) have dramatically

increased the precision in localization of the tumor extensions and critical healthy tissues

in three dimensions. A greater precision in localization of the tumor volume has been

augmented by the computer controlled radiation therapy machines, equipped with

multileaf collimator (MLC) that enable precise customized beam shaping (Brahme 1987).



Significance of The Multileaf Collimator System

The computer controlled MLC system is regarded as the state-of-the art method

for generating arbitrary (and generally irregularly) shaped fields for radiation therapy.

Progress in imaging modalities such as CT and MRI dramatically enhance the ability to

differentiate and delineate the target volume and normal structures in three dimensions.

Better information about tumor shapes is leading to a greater need for achieving

conformal treatments. An MLC system is considered as the most versatile tool that is

available for delivery of three-dimensional conformal treatment. An MLC system for








conformal therapy is still a research tool with its use limited to only a few academic

centers. The MLC systems have also been used for shaping neutron beams. (Eenmaa et

al. 1985, Chu & Bloch 1987, Brahme 1988, Wambersie 1990). An MLC system offers a

number of other important advantages over conventional field shaping devices (Mohan

1992). First, an MLC can be used to implement computer-controlled dynamic or multi-

segmented conformal treatments in which the field aperture for each segment or direction

is automatically adjusted to conform to the shape of the target volume or to a desired

shape. Second, an MLC can be used to modulate intensity across the two dimensional

profile of a field. Third, an MLC eliminates the effort and cost of fabricating custom

blocks such as used in conventional treatments within static fields. It also eliminates the

need for storage space for blocks and blocking trays, and the effort required in lifting and

mounting heavy blocks. The use of the MLC system for static fields provides savings in

set-up time while reducing the probability of set-up mistakes.

There are some concerns in the field conformation with an MLC. An MLC can

provide only a 'zigzag' approximation to the shape of the target volume because of the

finite leaf edge dimension. This inevitable drawback of the MLC requires some change in

the concept of beam collimation. It is important to realize that an MLC does not provide

exact conformation to the target contour drawn by a physician. The degree of

nonconformality depends on the direction of the leaf placement along the contour edge.

Therefore, it is essential that there are methodologies available which allow optimized

positioning of the leaves automatically around the target contour. More importantly this

step should be completely incorporated within the treatment planning process.








Overview of MLC Systems

Motor-driven MLC systems have been in use since the mid-fifties (Mohan 1992,

Webb 1993). These devices have become very popular within the past several years and

many commercial MLCs (e.g., Siemens, Scanditronix MM50, Varian C-series, and

Philips SL-series) are now readily available. The MLC systems provided by different

venders are different in design and thus have different dosimetric characteristics. There

are two fundamentally different design concepts of MLC configuration. The first one

incorporates the MLC as an integral part of the secondary collimator system, thus

replacing either the upper or lower secondary collimator jaws. In the second design, the

MLC is attached below the secondary collimator system as a tertiary collimator system.

The advantage of the latter design is that repair of the MLC is relatively easier than an

integral MLC, thus allowing the machine to be operated in a conventional mode even

when the MLC is down. The disadvantage is that an enlarged treatment head reduces the

collision free zone for certain clinical setups.

The Philips Medical System offers an MLC system that is an integral part of the

secondary collimator system. In the Philips MLC, the MLC replaces the upper secondary

collimator jaws. The travel of MLC leaves is parallel to the axis of rotation of the gantry,

that is, in the y-direction. The MLC is augmented by a backup collimator which is located

below the leaves and above the lower jaws. The purpose of backup collimator is to

decrease the intensity of transmitted radiation through the MLC. Backup diaphragms are

designed to move automatically to the edge position of the outermost withdrawn leaf.

Because the vertical location of the MLC is close to the source, the range of motion of the








leaves is smaller in this configuration than compared to others. Consequently, it is

possible to make a more compact treatment head. On the other hand, the leaf width is

somewhat smaller and the tolerances on the dimensions of the leaves as well as the leaf

travel are tighter than those for other configurations. Another concern from an

engineering point of view is that gaps are inevitable between two adjacent leaves (to

reduce friction) and opposite leaves (to prevent collision). If the mechanical gap distance

is fixed, the irradiated area over the leakage radiation through the gap is larger when the

position of the gap is closer to the source. Therefore, a more integrated leakage is

expected for this configuration.

The configuration of the Scanditronix (Racetrack Microtron, MM50), Siemens,

and General Electric (GE) MLC systems is very similar to the previous configuration

except that the lower jaws are replaced with the MLC. In both the Scanditronix and the

Siemens design, the leaf ends are straight and are focused on the x-ray source. The leaf

sides are also matched to the beam divergence and that makes these leaves "double

focused". The Scanditronix MLC is positioned at 31 cm from the isocenter with a

maximum field size of 32 x 40 cm2 and a maximum over-center position of 5 cm. The

width of the individual leaves at isocenter is 1.25 cm. The Siemens MLC consists of 29

opposed leaf pairs. While the two outer leaves of each leaf bank project to a width of 6.5

cm, the inner 27 leaf pairs project to a width of 1.0 cm at the isocenter plane. Each leaf is

independently controlled and moves with the maximum velocity of 1.5 cm/sec. The

projected field edge of each leaf can be withdrawn up to 20 cm away from the isocenter

and can travel up to 10 cm across the isocenter. The leaves may be manually positioned








with an MLC hand control and these leaf-settings can be uploaded to an information

management record and verification system. The GE configuration uses curved leaf ends

and contains a secondary 'trimmer' similar to the Philips backup diaphragm. However,

this trimmer is located above the upper jaws in the GE design.

In the Varian design, MLC is an add-on device that mounts to the existing clinical

accelerator head thereby making it field retrofitable. The advantage of this design is that

it is possible to avoid down-time in the event of a system malfunction. In this

configuration, the leaves can be manually moved out of the field when a system failure

occurs. Treatment can continue with replacement Cerrobend blocks. A total of 26 pairs of

leaves can produce the maximum MLC field size of 26 x 40 cm2 at the isocenter plane.

The newer model of the Varian MLC has 40 pairs of leaves which gives a maximum field

size of 40 x 40 cm2. Each leaf can travel up to 16 cm beyond the isocenter with the

maximum leaf speed of 1.5 cm/sec (5 cm/sec in new design). Since the MLC is located

far from the source, the travel length of the leaves required to produce the same field size

is longer than in other configurations, thus it enlarges the diameter of the treatment head.

Clearance (from the bottom of the MLC to the isocenter) is 42.4 cm. Clearance can

potentially be a minor problem in some clinical cases.

Another tertiary system is the Mimic device provided by NOMOS Corporation.

This is designed to mount on the blocking tray of a linear accelerator. It collimates the x-

ray field to a fan-beam which is dynamically modulated by short-stroke leaves as the

gantry of the accelerator is rotated. The modulated fan beam irradiates a transverse plane








of the patient that is 2 cm thick. The leaves are either fully inserted into the beam or fully

retracted, providing either full attenuation or no attenuation at a given gantry angle.



In general, the following attributes of an MLC system affect its dosimetric

characteristics:



1) Leaf shape: Ideally one would like the leaves to be "double-focused", that is,

leaves form a cone of irregular cross-section diverging from an apex located at the

radiation source. The leaves travel on a spherical shell centered at the source.

This type of MLC produces a sharp cut-off at the edge and is used by at least two

of the manufacturers (Scanditronix and Siemens). However, double focusing is

difficult to achieve from the engineering point of view. Therefore some

manufacturers (Varian and Philips) use rounded leaf edges. The edge of each leaf

is a section of a cylinder and the leaves travel in a plane perpendicular to the

central ray. The purpose of rounded edges is to keep the transmission through the

leaf constant regardless of its position with respect to the central ray. There are

some potential problems with such designs: first, the light field may not coincide

with the 50% width of the radiation field; secondly, the radiation field may shift

as much as 5 mm when the leaves move from 0 to 20 cm.



2) Integral MLC vs. optional attachment: The integral MLC (such as those by

Scanditronix and Philips) replaces one pair ofjaws. In most instances, however,








the MLC is offered as an optional attachment (e.g., Varian). In an integral MLC,

the leaves are at the same distance from the flattening filter and the source as the

jaws they replace. Therefore, they affect the output in the same manner as the

jaws. On the other hand, an MLC offered as optional attachment is farther away

from the flattening filter and it affects the output in a manner similar to

conventional blocks.



Many authors have studied general dosimetric characteristics of MLC systems,

such as field-size dependence of output factors (Jordan & Williams 1994, Palta et al.

1996, Boyer et al. 1992), depth doses (Boyer et al. 1992, Huq et al. 1995, Palta et al.

1996), isodose distribution (Boyer et al. 1992, Zhu et al. 1992), penumbra (Galvin et al.

1992 and 1993, Boyer et al. 1992, LoSasso et al. 1993, Jordan & Williams 1994, Huq et

al. 1995, Palta et al. 1996, Powlis et al. 1993), and leaf transmission data (Jordan &

Williams 1994, Palta et al. 1996, Boyer et al. 1992, Huq et al. 1995, Galvin et al. 1993,

Klein et al. 1995). The dosimetric parameter that has the most profound effect on the

accuracy of dose delivered with an MLC is the change in output factor, especially the in-

air output factor that occurs with field shaping.

In linear accelerators, the in-air output factor changes according to the collimator

opening. The MLC, as a collimator system, also affects the characteristics of the in-air

output factor. The conventional method of in-air output factor calculation can often have

a significant discrepancy between the predicted and measured values when it is applied to








MLC systems. Therefore it is necessary to develop an accurate method of in-air output

factor calculation that can be applied to MLC shaped fields.



The Aim of This Thesis



The aim of this work is to develop a physics model for treatment planning which

describes the high energy photon beam collimated by an MLC system.

The above objective is divided into three goals which are essential in clinically

supporting MLC systems:



1. To develop and implement an algorithm for the geometric optimization of MLC

conformation based on an arbitrary contour shape (Chapter 2).



2. To develop and implement a user interface module of the MLC into a radiation

therapy treatment planning (RTTP) system based on a beam's eye view (BEV)

display (Chapter 2).



3. To develop an algorithm to determine the change of in-air output factor for

shaped fields (Chapters 3 6).













CHAPTER 2
DEVELOPMENT OF AN MLC MODULE FOR
A TREATMENT PLANNING SYSTEM

Introduction


An MLC system offers a state-of-the-art method for field shaping in radiation

therapy. The advantage of using an MLC is that since the field shaping is performed

using leaves, the fabrication of custom blocks is no longer needed. This increases the

treatment delivery efficiency because multiple fields can be treated in a short time

without reentering the treatment room. It also eliminates all problems associated with

heavy blocks, alterations, remodeling and remounting. The most important advantage of

this technology lies in its potential for use in the delivery of 3-D conformal therapy and

intensity modulated radiation therapy.

An issue that discourages some clinicians from accepting MLCs more readily is

the 'zigzag' approximation to the shape of the target volume with an MLC system

because of the finite leaf edge dimension compared with the smooth conformation using

shaped blocks. This inherent drawback of MLCs introduces some change in the concept

of beam collimation; that is, an MLC does not necessarily coincide with the target

contour prescribed by a physician. Given the geometrical constraints of the setup, it is

only possible to achieve an 'optimal' field fit with the MLC system. The optimization

criteria must be incorporated into the planning process as efficiently as possible. Manual

placement of all leaves (52 or 80 leaves maximum) that define an MLC portal can be








unacceptably time consuming. Therefore, a facility that automatically derives optimized

MLC leaf positions from a prescribed target contour and uses this information for a

subsequent treatment plan is necessary.



Methods and Materials



Geometric Optimization of MLC Conformation

The MLC system should be completely integrated in the planning process to

realize its full potential clinical benefits. The problem that must be solved is to determine

the best MLC leaf positions for the optimal target volume conformation. The use of

conventional Cerrobend blocks to get tertiary field margins has provided radiation

oncologists a means of smoothly matching the edge of collimation with the projection of

the irradiation volume. However, when an MLC is used, the collimation occurs in

discrete steps. Therefore, it is important to determine optimal placement of each leaf with

respect to the field edge. Several treatment machine-dependent characteristics must be

made known to determine leaf settings automatically with a computer algorithm, such as

the number of leaves, their widths, travel limits, source to MLC distance, and relative leaf

travel direction.

In this study, an optimization program was designed to fit a Varian MLC system.

Nevertheless, it is flexible in nature and can be adapted to any MLC systems. In the

Varian design, the MLC is an add-on device that mounts to the existing clinical

accelerator head. A total of 26 pairs of leaves can produce the maximum MLC field size








of 26 x 40 cm2 at the isocenter plane. Each leaf can travel up to 16 cm beyond the

isocenter with the maximum leaf speed of 1.5 cm/sec.

In the design of the optimization program, three automatic leaf coverage strategies

were provided as illustrated in Figure 2-1:



(a) 1/2 Overblocking : Each leaf end intersects with the prescribed field edge at its

midpoint. This is a simple algorithm that sets equal amounts of overblocking and

underblocking with regard to each leaf (LoSasso et al. 1993).

(b) Full overblocking (or zero underblocking): Leaf positions are always inside the field

to minimize the irradiation of normal tissue.

(b) 1/3 Overblocking: Each leaf end intersects with the prescribed field edge at one of the

'one third point' of the leaf end. In this strategy, about 1/3 of the leaf end is inside the

field. This strategy is a simplified algorithm of'variable insertion' done by Zhu et al.

(1992) that results in the 50% isodose line always outside the desired field edge.


Figure 2-1. Three automatic leaf conformation strategies.








Depending on the shape of the contour, it is often necessary to rotate the

collimator or to shift the contour with respect to the beam to get a better fit of leaves with

the target contour (e.g., 90 rotation for the diamond shape of contour). Strategies of

collimator rotation and contour shift are also provided. In the contour shift option, a

contour can be shifted in both the x- and y-direction.

Regardless of the automatic technique used, the MLC aperture shape may not be

logical when evaluated by the treatment planner. Sometimes, it is necessary to adjust

individual leaves to ensure target coverage in a critical region or to avoid small critical

structures, e.g., the optic chiasm, which may be close to a target volume. Therefore, a

manual leaf adjustment facility is provided in the BEV. In this option, each leaf can be

manually positioned, around a target volume or a critical structure.



User Interface Module

It is desirable to have MLC field shaping algorithm which is incorporated into the

RTTP system. A stand alone software package is more error prone and time consuming.

Therefore, it is necessary to develop and implement an user interface module of the MLC

model within an existing RTTP system.

There are many commercially available RTTP systems. Although the functional

characteristics of RTTP systems are very similar to each other, each RTTP system is

different from others in the structure of its programming; thus, an user interface module

of the MLC must be compatible with the RTTP system used at each hospital. One of the

more popular commercial RTTP systems is the Radiation Oncology Computer Systems








(ROCS) RTTP system (ROCS 1994) which was installed in the University of Florida's

Department of Radiation Oncology in 1994 and has been used as its main RTTP system.

In this study, an MLC user interface module which is adaptable to the ROCS RTTP

system was developed.

The source program for the user interface module is written in BASIC. Because

most modules of the ROCS RTTP system are written in BASIC, this was the

programming language of first choice. The following key points were adhered to during

the development of this MLC software module:

a) minimal change of the present source program,

b) minimal change of the present program structure,

c) minimal change of the present data library and their format, and

d) easy adaptation of the new module to the present RTTP system.



Results



A total of 38 subroutines were newly created and 8 present subroutines were

revised to develop an MLC optimization and user interface module for the ROCS main

RTTP system. The description of each newly generated subroutine is summarized in

Table 2-1. The complete source program of the module is contained within Appendix A.

Figure 2-2 shows a flow chart of the module. In the ROCS main module, users

enter into the irregular field module. Using the 'field editor' module, users can create

irregular fields. Once irregular fields are provided, the 'MLC field editor' module can be








used. In the 'MLC field editor' module, users can create MLC fields using the 'edit field'

tool. To perform leaf conformation, MLC geometric optimization strategies are used in

the 'edit field' tool. For geometric optimization, 'automatic fit', collimatorr angle

selection', 'contour shift', and 'manual fit' strategies are used. Calculation points can be

defined after the MLC field is provided using the 'point editing' tool. Once an MLC field

is created, users can make the opposite field simply by selecting the 'opposite field'

option in the 'MLC field editor' module. The 'export field' option creates an ASCII file

for file transfer to the MLC controller computer on the treatment machine.



Conclusion



An MLC geometric optimization and user interface module was developed as part

of this research. The module was implemented to the main RTTP system, ROCS (version

5.1.1) and is currently in clinical use. The planning time was significantly reduced by

incorporating the MLC module into the main RTTP system.








Table 2-1. Description of subroutines.


MLCINI: This subroutine specifies MLC dimension and set main variables.
MLCDRAW: This subroutine draws MLC leaves with leaf position data.
MLCOPT: This subroutine searches geometrically optimized MLC leaf
position.
MANOPTI: This subroutine enables manual MLC field editing.
LEAFLT: This subroutine moves leaf to left direction during manual fit.
LEAFUP: This subroutine selects upper leaf during manual fit.
LEAFRT: This subroutine moves leaf to left direction during manual fits
LEAFDN: This subroutine selects lower leaf during manual fit.
REDRAWMLC: This subroutine redraws MLC leaf changed during manual fit.
NOTELEAF: This subroutine assigns different color to selected leaf during leaf
change in same side.
NOTE2LEAF: This subroutine moves cursor and assigns different color to
selected leaf during leaf change between two different sides.
MLCSETMENU: This subroutine displays MLC field editor menu.
AUTOFIT: This subroutine carries out geometric optimization for MLC field
automatically.
MANUFIT: This subroutine carries out geometric optimization for MLC field
manually.
MLCOPTUNDER: This subroutine searches geometrically underblocked MLC leaf
position.
MLCOPTOVER: This subroutine searches geometrically overblocked MLC leaf
position.
AUTOUNDER: This subroutine carries out geometric underblocked optimization
for MLC field automatically.
AUTOOVER: This subroutine carries out geometric overblocked optimization
for MLC field automatically.








Table 2-1. -- continued.

CONVERTANG: This subroutine converts collimator angle in degree to radian
and get sine, cosine values.
MLCGETANG: This subroutine gets collimator angle in degree as user input.
MLCSHIFTX: This subroutine gets MLC offset in X-dir. as user input.
MLCSHIFTY: This subroutine gets MLC offset in Y-dir. as user input.
MFLDDATA: This subroutine gets collimator opening, field outline and
calculation point location for MLC field.
SAVEMFLD: This subroutine prompts the user to save MLC field data. If the
user chooses to save the data the MLC data file and the irregular
library file are updated.
MFLDDEF: This subroutine displays an MLC field based on user input. The
user selects an MLC field and chooses to edit, load, oppose or
export MLC fields.
GETMFLD: This subroutine gets MLC field data from the file.
IR7: This subroutine is the MLC field main editing menu. Control is
transferred to the appropriate routine based on which function key
is pressed.
ISODRW: This subroutine draws original isocenter before MLC offset
LEAFINI: This subroutine sets initial values for leaf position.
LEAFRETRIV: This subroutine sets existing MLC field.
GETIFLD2: This subroutine gets irregular field data from the file.
SAVEIFLD2: This subroutine prompts the user to save irregular field data. If the
user chooses to save the data the irregular data file and the irregular
library file are updated.
GETMFLD2: This subroutine gets MLC field data from the file.
SAVEMFLD2: This subroutine prompts the user to save MLC field data. If the
user chooses to save the data the MLC data file and the irregular
library file are updated.









Table 2-1. -- continued.

MLCOPPOSE: This subroutine creates opposed MLC field. Opposed block field is
generated at the same time.
MLCEXPORTV: This subroutine creates MLC field data file to be exported for
Varian type. Exported file can be directly used by Varian MLC
software, "SHAPER".
MLCSELECT: This subroutine prompts the user to select MLC type.
MLCIPAGE: This subroutine displays one page of beam information for MLC
field.


ROCS main module

Irregular field module
I


SLeaf conformation

Automatic fit
a) uwr-lockang
b) haff-blocdng
c) ovwr-blocking

Collimator angle

Contour shift

lManual fit


Calculation point defining -
a) point eating


Figure 2-2. Outline of MLC module.














CHAPTER 3
A STUDY OF THE EQUIVALENT FIELD CONCEPT FOR
THE HEAD SCATTER FACTOR

Introduction


In general, the equivalent field is defined as a field having the same central axis

depth-dose characteristics as the given field (Jones 1949, Day 1950). The relationship

between equivalent fields is based on integration of the phantom scatter parameter for

shaped fields. Therefore, a field is determined that produces the same ratio of phantom

scatter to primary dose on the central axis (Day & Aird 1983). It has been generally

assumed that the radiation output has two scatter components, Sc and S,; in convention, Sc

is referred to as the collimator scatter factor, which is characterized by the X and Yjaw

collimator openings, and Sp accounts for phantom scatter, which depends on the area of

the irradiated phantom. Although Sc is called the collimator scatter factor, Sc accounts for

both the monitor backscatter contribution and the head scatter contribution to the in-air

output. The monitor backscatter factor (Lam et al. 1996, Ahnesjo et al. 1992, Patterson &

Shragge 1981, Luxton & Astrahan 1988, Moyer 1978, Higgins et al. 1989, Kubo & Lo

1989, Kubo 1989, Duzenli et al. 1993) can be separated from Sc. The term, 'head scatter

factor' is limited to the contribution of head scatter in this present study. For nonstandard

fields such as rectangular and irregular fields, conventionally, S, is obtained through the

equivalent field relation, and the equivalent field relation for phantom scatter is well








established (Day & Aird 1983, Bjmrngard & Siddon 1982). The equivalent field method

has also been applied for determination of the scatter contribution to the in-air dose from

any scattering structure, such as the flattening filter. The stipulation is that the equivalent

field contributes the same amount of scatter radiation on the central axis as the

collimator-set field. The relationship between equivalent fields for head scatter is based

on integrating the head scatter parameter of the shaped field and finding the field that

produces the same ratio of head scatter to primary dose on the central axis. The head

scatter characteristics are not the same as the phantom scatter characteristics. Therefore, it

is necessary to establish the equivalent field relationship for head scatter separately from

that for phantom scatter.

When a scattering structure is located above the collimator, such as the flattening

filter or an internal wedge, the amount of scatter radiation that can reach a detector is

related to the configuration of the field at the source plane as seen from the detector, that

is, the detector's eye view (DEV) field (Lam et al. 1996, Ahnesjo 1994). When head

scatter factor is parametrized at the flattening filter (or the source) plane (Lam et al. 1996)

or the field mapping method (see Chapter 4) is used, it is imperative to assess the

equivalent field relationship at the source (or flattening filter) plane. Lam et al. (1996)

empirically showed that the formula of the area-to-perimeter ratio for the equivalent

square of a rectangular field for phantom scatter (Sterling et al. 1964, Worthley 1966) is

also valid for head scatter at the source plane and this relationship was successfully

applied to obtain a modified equivalent square formula at the detector plane through the

field mapping method. For an irregular field, conventionally, the head scatter factor is








approximated by that of the rectangular field determined by the secondary collimators.

Although the conventional method gives a good approximation in most clinical cases, the

difference of head scatter factor between a rectangular field and an irregular field can be

significant when the irregular field is much smaller than the rectangular field such as

mantle fields and fields in intensity modulation therapy. Furthermore, when an irregular

field is created by Philips type MLCs, which replace the upper set of secondary

collimators, the conventional method can not be used (Palta et al. 1996). In these cases,

Clarkson integration (Clarkson 1941) can be applied for a better estimation of head

scatter factor for irregular fields (Boyer 1996). To use Clarkson integration, it is required

to evaluate the equivalent field relationship between a circular field and a square field.

The use of Clarkson integration can also be expanded for the prediction of scatter

contribution from both the beam modifier (e.g., wedge) and the tertiary collimator (e.g.,

Cerrobend block and Varian type MLC) when it is needed to independently deal with

wedge scatter or tertiary collimator scatter. The amount of scattered radiation from a

wedge depends on the area of the wedge that intercepts the radiation coming downstream

through the treatment head. If a wedge is located above the collimator jaws like that in a

Philips machine, the detector's eye view field at the source plane can be used for both

head scatter and wedge scatter. However, when the wedge is located underneath the

secondary collimator like that in a Varian machine equipped with an MLC, the field size

for the wedge scatter contribution is different from the field size for the head scatter

contribution. Whereas the head scatter contribution is determined by the field seen by the

detector's eye view, the wedge scatter contribution depends on the field size projected at








the detector plane. Therefore, in this case, wedge scatter should be dealt with separately

from head scatter. Tertiary collimator scatter contribution may also be separately treated

when the amount of scatter is not negligible. For both wedge and tertiary collimator

scatter, the amount of scatter radiation that can reach a detector is related to the

configuration of the field projected at the detector plane. Therefore, in these cases, the

equivalent field relationship is obtained at the detector plane.

In this chapter, the equivalent field relationship of square and circular fields was

provided at the source plane for the head scatter factor. The fact that the area-to-perimeter

ratio of the equivalent square of a rectangular field for phantom scatter is also valid for

head scatter at the source plane (Lam et al. 1996) was analytically investigated. The

equivalent field relationships for wedge scatter and tertiary collimator scatter were

assessed at the detector plane.



Methods and Materials



Equivalent Field for Head Scatter Factor

The photon energy fluence equation at a detector point may be defined as




F= p(1 + (3.1)


= 'Tp(l + SPRh), (3.1)








where 4p is the energy fluence due to primary photons, ,s is the energy fluence due to

scatter photons from the head, and SPRh is the ratio of scatter fluence originating in head

to primary fluence. Assuming that dose is linearly proportional to energy fluence in

megavoltage photon beam, the equivalent field can be defined as the field that gives the

same scatter-to-primary ratio, SPRh, as the collimator-defined field. The SPRh of any

arbitrary shaped field is the integration of the differential scatter-to-primary ratio function

over the whole field,

SPR dSPRh dA (3.2)
dA

Several models have appeared in the literature that accurately describe the scatter photon

energy fluence distribution that emanates from the head such as uniform (Ahnesj et al.

1992), triangular (Ahnesjo 1994), Gaussian (Dunscombe & Nieminen 1992), a

combination of several functions (Yu & Sloboda 1993), and experimentally determined

distribution functions (Jaffray et al. 1993). Ahnesjb (1994) concentrated on scattered

photons from the flattening filter and calculated the differential scatter-to-primary ratio of

flattening filter scatter, dSPR,/dA, according to the radius from the central axis, using the

first scatter approximation. Ahnesjo's work showed that dSPRf/dA is well described by

either Gaussian or triangular function (Ahnesj6 1994). Since the dominant contributor of

head scatter is the flattening filter (Kase & Svensson 1986), we assume that the

equivalent field relationship for head scatter primarily depends on the characteristics of

scatter from the flattening filter. We can replace SPRh with SPRf, the scatter-to-primary

ratio of scatter from the flattening filter, in Eq. (3.2):








SPRf = J dSPRfA (3.3)
dA

Based on Ahnesj6's study (Ahnesj6 1994), it is assumed that the differential scatter-to-

primary ratio of flattening filter scatter, dSPR,/dA, decreases linearly according to the

radius within the physical radius of the flattening filter, that is,

dSPRf
dP = b-ar, (3.4)


where a and b are coefficients dependent on the photon beam energy and the shape and

material of the flattening filter. By substituting Eq. (3.4) into Eq. (3.3), the scatter-to-

primary ratio for scatter from the flattening filter for any field is given by

SPRf= J(b-ar)dA (3.5)

It has been reported that the contribution of backscatter into the monitor chamber

has a significant influence on the dependence of in-air output on secondary collimator

settings (Lam et al. 1996, Ahnesjo et al. 1992, Patterson & Shragge 1981, Luxton &

Astrahan 1988, Moyer 1978, Higgins et al. 1989, Kubo & Lo 1989, Kubo 1989, Duzenli

et al. 1993). However, monitor backscatter affects both primary and scatter photons in the

same way, thus, the shape of the differential scatter-to-primary ratio function, dSPR
dA
does not change. That is, the equivalent field relationship is not affected by the monitor

backscatter at the source plane if monitor backscatter factor is separated from collimator

scatter factor.

Equivalent square of a circular field. For a circular field with radius R, the result of the

integration (Eq. [3.5]) is








SPRi(cir) = bntR2 a 2 nR
3

=3.142bR2 -2.094aR3 (3.6)

For a square field with a side of s=2o the result of the integration (Eq. [3.5]) is

SPRf (sq)=4b 2 -3.061ao3 (3.7)

From Equations (3.6) and (3.7),

4ba2 -3.061ac3 =3.142bR -2.094aR3 (3.8)

By dividing both sides with b R3 and using (a/b) = (1/R, in Eq. (3.8), we can

eliminate the coefficients, a and b, that is, we get


4( )2 3.061( ),( 3 = 3.142( 2.094 1 (3.9)
Ra ) \ R R Rm '

where Rm is the maximum radius of the flattening filter. Now, multiply Eq. (3.9) by R

and rearrange to obtain

(4a2 3.142)+(2.094- 3.061a3 R R =0 (3.10)

where =(c IR). Equation (3.10) indicates that a is dependent on the radius R. For a

very small field, that is, when R -> 0, a =0.886 is obtained. Note that this is the same

result that would be obtained by simply equating the area of the circle to the area of the

square. Whereas Eq. (3.6) is valid within the maximum radius of the flattening filter, R,

, the valid range of Eq. (3.7) is given by one half the side of the largest square which can

be inscribed within the circle of radius R,,, that is, a mx =Rmiax /-2. Therefore, the safe

limit of R, which guarantees the validity of Eq. (3.10), is given by Rm,, = Rax / J2. With








R = Rim,, Eq. (3.10) gives a 0.9. Therefore, we can find the approximate range within

which the equivalent square field exists for the given circular field,

0.886R < a < 0.9R (3.11)

where R = the radius of the circle anda =one half of the side of the square. For

convenience, we may use one value of a = 0.9R. Equation (3.11) is obtained within

the dimension of flattening filter. However, it is considered that it can be used even when

a field at the flattening filter plane (or source plane) is larger than the dimension of the

flattening filter because the amount of scatter outside the flattening filter is relatively

small and slightly varies according to the radius. This fact is discussed in detail in

discussion section.

In-air output factors of circular fields and square fields were measured with a

cylindrical acrylic miniphantom as described by van Gasteren et al. (1991). The

cylindrical phantom is 3.8 cm in diameter and 15 cm long. Measurements were taken on a

Varian 2100C with 8 MV and 18 MV photon beams. A shonka plastic 0.1 cc ionization

chamber was inserted in the miniphantom with its center located at 5 cm for 8 MV or 10

cm for 20 MV from the front surface and 100 cm from the source. Both circular fields

(radius, r = 2.2, 3.3, 5.6, 7.8, and 10 cm at the source plane) and square fields (side, s = 4,

6, 10, 14, and 18 cm at the source plane) were created by an MLC. Each square field

corresponds to the equivalent square field of each circular field. During the

measurements, secondary collimators were set as 40 x 40 to eliminate the relative effect

of monitor backscatter.








Equivalent square of a rectangular field. For a rectangular field of dimensions L x W, the

integration (Eq. [3.5]) gives


SPRf(rec) = bLW a I2 2LWD+ L3ntan4 +_ +W3 ntan( _i-
I4 2 \2 2


= bLW -a 12LWD+L In D+W-L + In l (3.12)
12 I L+W-D] L W 11

where D is the length of the diagonal of the rectangle and < = tan-' W I L. In Equations

(3.7) and (3.12), it is not easy to obtain a simple equivalent square correlation for a

rectangular field.

Lam et al. (1996) obtained good agreements between the head scatter factors of

square fields and those of rectangular fields by using the area-to-perimeter ratio formula

as an equivalent square formula at the flattening filter plane for 6 MV and 15 MV photon

beams of Varian 2100C. We have calculated 1 +SPRyvalues, using Eq. (3.12) for different

L x Wrectangular fields and Eq. (3.7) for square fields of s = 2LW / (L + W) and

compared each other.



Equivalent Field for Wedge and Tertiary Collimator Scatter Factor

For both wedge and tertiary collimator such as a conventional Cerrobend block

and Varian-type MLC, we can assume

dSPR
-d =a (3.13)
dA

With Eq. (3.13), it is trivial to calculate an equivalent square field,








o = 0.886R, for a circular field with radius R, (3.14a)

and

s = 2a = -LW, for a rectangularfieldof Lx W. (3.14b)

For convenience, we can use a = 0.9 R for a circular field without significant error.

To evaluate the validity of the assumption, Eq. (3.13), scatter contribution from

tertiary collimator (Cerrobend block and Varian MLC) was measured according to the

irradiated area with the same mini-phantom as described in the section Equivalent square

of a circularfield. A set of measurements were made underneath a solid piece made out

of the same material as the tertiary collimator material (Cerrobend or MLC) with field

sizes ranging from 4 x 4 to 20 x 20 cm2 at the detector plane. The thickness of Cerrobend

block was 7.5 cm. The data were extrapolated to 0 x 0 cm2 field. The in-air output of (0,0)

field multiplied by Sc(X, Y)/Sc(0,0) was subtracted from in-air output for each field size,

(X, Y). The remaining in-air output of each field is only due to the scatter radiation from

tertiary collimator material. Scatter contribution from a 450 wedge was also measured.

When Clarkson integration is carried out on wedge scatter for an irregular field, the

assumption Eq. (3.13) is theoretically not correct, except in the case of a symmetric field,

because of the change in wedge thickness. However, if the difference in in-air output

between asymmetric fields is not significant, we may use that assumption without

significant error. We measured in-air outputs for a pair of asymmetric wedged fields (see

Figure 3-1). One field contains the most thin part and very little of the thick part of the

wedge, and the other is reverse (e.g., field sizes [X1=2.5, X2=10, Y1=10, Y2=10] and

[Xl=10, X2=2.5, YI=10, Y2=10], in which the Xaxis was parallel to the axis of slope of








the wedge). The contribution of unattenuated photons to in-air output is same for both

fields because the detector is located at the isocenter. The only difference comes from

wedge scatter contributions.


a) Field of thin part


b) Field of thick part


Figure 3-1. Description of a set of asymmetric wedged fields. The contribution of
unattenuated photons to in-air output is same for both fields. However, the wedge scatter
contribution is different.


Results



Equivalent Field for Head Scatter Factor

Equivalent square of a circular field. The measured in-air output factors of an 8 MV and

18 MV photon beams of Varian 2100C are shown in Figures 3-2 and 3-3, respectively. In

Figures 3-2 and 3-3, the in-air output is normalized to that of 10 x 10 MLC field at the

source plane. Circular fields are converted to equivalent square fields using the equivalent
















1.01
Varian 2100C, 8 MV, open, 40 x 40 fixed jaw settings
."

0
S 1.00
X




0.99

0 ..-.- Square
SCircle
0.98
0



0.97
0 5 10 15 20

Side of Equivalent Square Field at Source Plane (cm)



Figure 3-2. In-air output factor as a function of a circular field at the source plane for the
8 MV photon beam of a Varian 2100C. Fields were made by an MLC system. During the
measurements, secondary collimators were fixed at 40 x 40 cm2. Data are plotted
according to the side of the equivalent square obtained by a = 0.9R. Data for square
fields are also plotted for comparison.
















1.01
Varian 2100C, 18 MV, open, fixed 40 x 40 jaw settings

"o
1.00
x
0



S0.99


0 /.- Square
Circle
S0.98
0
.h



0.97
0 5 10 15 20

Side of Equivalent Square Field at Source Plane (cm)


Figure 3-3. In-air output factor as a function of a circular field at the source plane for the
18 MV photon beam of a Varian 2100C. Data are plotted according to the side of the
equivalent square obtained by a = 0.9 R.








field relation, a = 0.9R. The difference of in-air output factors between circular field

and square field is within 0.2 % for both 8 MV and 18 MV beams. Measured in-air output

accounts for not only head scatter but also the effect of backscatter into the monitor

chamber and forward scatter to the detector from the MLC. However, since the field

shapes of circular fields and square fields are very close, it is considered that the amounts

of scatters (both backscatter to the monitor chamber and forward scatter to the detector)

of both fields are almost the same. Therefore, the difference of in-air output factors

between two fields (circular and square fields) indicates the difference of head scatter

factors. In a Varian 2100C, the radius of flattening filter is 3.6 cm at the source plane.

That is, two fields (r = 2.2 and 3.3 cm) are smaller than the flattening filter and others are

larger. Measurements show that the equivalent field relation, r = 0.9R is also valid

even when a field is larger than the flattening filter.

Equivalent square of a rectangular field. Values of the percentage differences between

values for 1+SPRffor rectangular and square fields are plotted in Figure 3-4 according to

the elongation ratio. In Figure 3-4, the percentage difference was calculated as

100[{l+SPR/eq. square)}-{l+SPR/rectangle)}] / {1+SPR/rectangle)} (3.14)

The coefficients a and b in Eq. (3.4) are obtained from Ahnesj6's work (Ahnesjb 1994).

From Figure 3-4, it can be noted that the amount of difference is dependent on the beam

energy and the material and size of flattening filter. The most dominant factor is the

material of the flattening filter. Whereas an aluminum flattening filter shows a larger

difference (maximum -2.9 % with an elongation ratio of 10), a tungsten filter shows a

smaller difference (maximum -1.4 % with an elongation ratio of 10). We can also see that















0.50


0.00 -


-0.50


S -.00 -o *
-* !

-1.50
S* Al Filter, 24MV, Rmax=4 (a=0.0025, b=0.01)
-2.00 At Filter, 4MV, Rmax=4 (a=0.0005, b=0.002) 4
AW Filter, 24MV, Rmax=4 (a=0.0012, b=0.0048)
-2.50 W Filter, 4MV, Rmax=4 (a=0.0004, b=0.0016)
x Al Filter, 24MV, Rmax-5 (a=0.00225, b=0.0124)
3.00 W Filter, 24MV, Rmax=5 (a=0.00102, b=0.0056)
-3.00 J
0.0 2.0 4.0 6.0 8.0 10.0
Elongation Ratio



Figure 3-4. Difference (%) of I +SPRJ between a rectangular field and the equivalent
square field according to the elongation ratio. The equivalent field is determined by the
area-to-perimeter relation. The difference (%) is given by 100[{l+SPR,(eq. square)}-
{1+SPR rectanglee)] / {1+SPR/rectangle)}. Data for determination of dSPRf/dA are
obtained from Ahnesj6's work (Ahnesji 1994). The elongation ratio is given by [length
of long side] / [length of short side] of the rectangular field.








a smaller flattening filter (R,_= 4 cm) gives less difference (-1.27 % for an aluminum

filter with an elongation ratio of 7 and -0.63 % for a tungsten filter with an elongation

ratio of 7) than does a larger filter (for R,, = 5 cm, -2.38 % for an aluminum filter with

an elongation ratio of 7 and -1.10 % for a tungsten filter with an elongation ratio of 7) at

the same elongation ratio. In principle, the amount of difference is dependent on the

coefficient, a. The stiffer slope causes the larger difference. Lower Z material, higher

energy beam, and larger radius of flattening filter require a thicker flattening filter which

causes stiffer slope of scatter function. Since Rma is the physical radius of a flattening

filter at 15 cm downstream from the source, the maximum radial field size at 100 cm SSD

becomes 6.67R,, That is, for R,, = 4 cm, the radius of the field at 100 cm is 26.7 cm

(diameter d = 53.3 cm). Considering the fact that most linear accelerators allow a

maximum 40 x 40 cm2 field size and also that a high Z material is preferred as a

flattening filter, it appears Figure 3-4 supports the fact demonstrated by Lam et al. (1996)

that the formula for the area-to-perimeter ratio can also be used as the equivalent field

formula for head scatter at the source plane.



Equivalent Field for Wedge and Tertiary Collimator Scatter Factor

Measured scatter contributions from the tertiary collimator (Cerrobend block and

Varian MLC) of an 8 MV photon beam of Varian 2100C are shown in Figure 3-5. Figure

3-5 shows that the behavior of tertiary collimator scatter is very close to a linearly

increasing function according to the irradiated area. Therefore, it is considered that Eq.

(3.13) is a reasonable assumption. A similar result is obtained for a wedge (Figure 3-6).














1

0.9 Varian 2100C, 8 MV

0.8

o 0.7

iE 0.6
--Block
S0.5 MLC

g 0.4

0.3

S0.2

I 0.1

0

0 100 200 300 400
Field Area (cm x cm)



Figure 3-5. Tertiary collimator scatter contribution as a function of field area of solid
tertiary collimator material for the 8 MV photon beam of a Varian 2100C. Data are
plotted according to the irradiated area projected to the detector plane.













1.00

0.90 Varian 2100C, 8 MV, 45-Wedge

0.80

0.70

a 0.60

0.50
L-
0 0.40

a 0.30
-45-Wedge
g 0.20

0.10

0.00
0 100 200 300 400
Field Area (cm x cm)




Figure 3-6. Wedge scatter contribution as a function of field area of 450 wedge for the 8
MV photon beam of a Varian 2100C. Data are plotted according to the irradiated area
projected to the detector plane.








The measured in-air outputs for a pair of asymmetric wedged fields are summarized in

Table 3-1, where we can see that the difference is less than 1%. The contribution of

unattenuated photon to in-air output is same for both fields because the detector is located

at the isocenter. The only difference comes from the wedge scatter contribution.

Considering that most practical fields are closer to symmetric than those studied, we can

expect that the differences will become smaller in most clinical cases. Therefore, we can

use Eq. (3.13) without compromising accuracy.



Discussion



In the derivation of equivalent field relationship, SPRh is replaced with SPRfand it

is assumed SPRf is a linear function. There are two concerns with this approach. The one

is that SPRh can be described better as either a Gaussian (Dunscombe & Nieminen 1992)

or polynomial (Yu & Sloboda 1993) function. The other is that SPRfis restricted within

the physical dimensions of the flattening filter. However, the approach is very reasonable

for circular fields. For a circular field with radius of R, the equivalent square field exists

within the range of 0. 71R < a < R The circle which can inscribe the square a = R is r =

1.41R. Thus, the range we are interested in for the integration of SPR function to obtain

the equivalent square is only 0. 71R < r
SPR varies both inside 0. 71R and outside 1.41R. If SPR is close to a linear function

between r = 0. 71R and r = 1.41R, our assumption can be applied and this is the most

cases even outside the flattening filter. For rectangular fields, these concerns still remain,









Table 3-1. Comparison of in-air output factors between pairs of asymmetric wedged
fields for the 8 MV photon beam of a Varian 2100C. The contribution of unattenuated
photon to in-air output is same for both fields. However, wedge scatter contribution is
different. Data are normalized to the in-air output of the field of thin part.

Wedge Angle In-air Output Factor (normalized to field of thin part)
XI = 10, X2 = 2.5, Thin Part XI = 2.5, X2 = 10, Thick Part
Y=5 Y=20 Y=5 Y=20


15 1.000 1.000 1.002 1.005
30 1.000 1.000 1.002 1.007
45 1.000 1.000 1.002 1.007


XI = 7.5, X2 = 2.5, Thin Part Xl = 2.5, X2 = 7.5, Thick Part


60 1.000 1.000 1.001 1.004


especially for highly elongated fields. Therefore, Eq. (3.12) and the analysis results,

Figure 3-4, are restricted within the physical dimensions of the flattening filter (e.g., D=

3.55 cm at the source plane for Varian 2100C).

In an irregular field, scatter contribution from a tertiary collimator depends not

only on the irradiated area perpendicular to the axis, but also on the irradiated area of side

wall on the field edge. However, the scatter contribution from side wall is not included in

the derivation of Eq. (3.14). This effect should be independently treated because it is

dependent of contour shape.








Conclusion



Equivalent field relationships for the head scatter factor at the source plane were

analyzed. A relationship of a /R 0.9 was obtained for a circular field, where a is one

half the side length of the equivalent square and R is the radius of the circular field. The

fact that the formula for the area-to-perimeter ratio of the equivalent square of a

rectangular field for phantom scatter is also valid for head scatter at the source plane in

most clinical linear accelerators was analytically investigated. The equivalent field

relationships for wedge and tertiary collimator scatter were also studied. The relationships

of a = 0.886 R (or 0.9 for convenience) for a circular field and a = .,L-W / 2 for a

rectangular field were obtained. These relationships can be used in the calculation of in-

air output factors for irregular fields in clinical applications.














CHAPTER 4
AN EQUIVALENT SQUARE FIELD FORMULA FOR
DETERMINING HEAD SCATTER FACTORS OF RECTANGULAR FIELDS

Introduction


The head scatter factor (or collimator scatter factor) accounts for the change in

scattered radiation with collimator setting that reaches the point of measurement on the

central axis in high energy x-ray beams. Conventionally, the head scatter factor is

expressed as

H(XT, Y) = D(X YO)/D(X,=10,Y=10) (4.1)

where D(XD Y0) is the dose in air on the central axis at the reference plane (which we call

the detector plane hereafter), which is usually the isocenter, and XD, YD are the field sizes

determined by the lower and upper collimator jaws, respectively, at the detector plane.

The collimator setting for the reference field size is 10 cm for both x and y sets of jaws.

For a wedged field, the change in scattered radiation with collimator setting depends not

only on the head scatter but also on the wedge scatter. Thus, we will use a different

terminology, 'wedge-head scatter factor' for wedged field.

Head (or wedge-head) scatter factor, H is often measured as a function of square

field size at the isocenter. To account for Hofa rectangular field, usually the well

established equivalent square relations are used, either in the form of table (Day & Aird

1983) or the area-to-perimeter ratio formula (Sterling et al. 1964). These formulae give an








estimate of the effect of field elongation only. An inherent assumption is that the head (or

wedge-head) scatter factors for two different rectangular fields, L x W(i.e., Xo=L, Y=W)

and W x L (i.e., XD=W, Y,=L), are the same. In reality, H(XD, Yo) is different from

H(Y,XD) by 2 3% for open fields (Moyer 1978, Kase & Svensson 1986, Tatcher &

Bjamgard 1993) and 3 ~ 4% for wedged fields (Tatcher & Bjmrngard 1993) between two

different rectangular fields, L x W and W x L. This collimator exchange effect has been

discussed extensively in the literature (Vadash & Bjarngard 1993, Moyer 1978, Kase &

Svensson 1986, Tatcher & Bjarngard 1993, Lam et al. 1996). Vadash and Bjmrngard

(1993) obtained an empirical formula to account for this exchange effect for a Philips

machine. Yu et al. (1995) obtained the same empirical formula for a Varian machine.

Lam et al. (1996) suggested parametrization with the equivalent square at the flattening

filter to account for this effect. Ahnesja (1994) modeled the energy fluence of scattered

photons from the flattening filter by approximating the fluence to be proportional to the

solid angle of the filter seen from the isocenter. All of these recent publications provide

methods to calculate change in head scatter as a function of the field size; these methods

explicitly account for the upper and lower collimator settings.

Another simple equivalent square formula that accounts for the collimator

exchange effect was provided. The formula was derived by a method that will henceforth

be called thefield mapping method. In the field mapping method, a field that is defined in

the source plane by back-projection from the point of measurement (i.e., the detector's

eye view) is mapped back into the detector plane by an equivalent field relationship.

Therefore, this method retains parametrization at the detector plane (measurement point).








No new data are required to implement the method clinically. The field size dependence

of head (or wedge-head) scatter that is measured for a range of square field sizes is

sufficient to implement this method.



Theory



The head scatter factor primarily depends on scattered radiation called extrafocal

radiation (Jaffray et al. 1993) above the field-defining collimators (e.g., the flattening

filter). Therefore, head scatter accounts for not only the primary but also the scattered

radiation. The magnitude of the scattered radiation from extrafocal sources is accurately

determined by the projected area in the source plane from the detector's eye view rather

than the conventional field area at the detector plane (Lam et al. 1996, Ahnesjb 1994).

Because of the different positions of the lower and upper collimatorjaws, projected field

sizes at the source plane as determined by the detector's eye view are different for L x W

and W x L rectangular fields. The projected field in the source plane as defined by the

detector's eye view is illustrated in Figure 4-1, where X, YD are the field sizes

determined by the lower (or X) and upper (or Y) collimator jaws, respectively, at the

detector plane; Xs, Ys are the field sizes determined by the X and Y collimator jaws at the

source plane through the detector's eye view; l1, ly are the distances from the source

plane to the top of the X and Y collimators, respectively; and 12, 12, are the distances

from the detector plane to the top of the X and Y collimators. Based on simple divergent













Ys/2 Xs/2


- - -


Source Plane


----------------.Q----------- xr------------ -------------.
SDetector Plane
Detector's Eye

Yn/2 XD/2


Figure 4-1. Schematic diagram showing the geometric relationship between the detector
and the collimator jaws. Also shown are field sizes projected in the source plane and
detector plane.








geometry, we can define the field conversion factors from detector to source plane, kx for

Xand k for Yside, as

kx = /12x, (4.2)

k = lIl2y (4.3)

Note that for most medical linear accelerators, k, and k are less than one. The field size at

the source plane, Xs and Ys. becomes

Xs = kXo, (4.4)

Ys = kYD (4.5)

Using the area-to-perimeter ratio formula of the equivalent square at the source plane

(Lam et al. 1996), we can obtain the equivalent square at the source plane, Seq :

Ss = 2XsY/(X + Y). (4.6)

Since most dosimetric data are obtained for square fields at the detector plane, it is

necessary to find an equivalent square at the detector plane, Sq, that gives the same head

scatter factor as Ssq. If we convert the square field, SDeq, to the source plane, it becomes a

rectangular field, kSDeq x kSoD'. If we let SS' be the equivalent square at the source

plane for this field, then

SSq' = 2kSDeqkgDeq/(kSDe + Seq) (4.7)

Since S"' should match Ss9, we obtain

Soq = {(k + k/2kky^}S (4.8)

From Eq. (4.8) and Eq. (4.6), we obtain a modified equivalent square formula,

SDo" = (1 + k)XDY/(kXD + YD) (4.9)

where k is a geometrical weighting factor, defined as:








k = kky = (71jl12)2,/1 ). (4.10)

Equation (4.9) provides an equivalent square, which is based on a rectangular field, XD x

YD, projected in the detector plane, and the geometric weighting factor, which is

accelerator-dependent.



Methods and Materials



Head (or wedge-head) scatter factors of rectangular fields were measured with a

cylindrical acrylic miniphantom as described by van Gasteren et al. (1991). The

cylindrical phantom is 3.8 cm in diameter and 15 cm long. Measurements were taken on a

Varian 2100C with an 8 MV photon beam and a Philips SL25 with a 20 MV photon

beam for both open and wedged fields. A shonka plastic 0.1 cc ionization chamber was

inserted in the miniphantom with its center located at 5 cm for 8 MV or 10 cm for 20 MV

from the front surface and 100 cm from the source. Two independent sets of data were

taken. The first set of measurements was taken with the X (lower) collimator jaws fixed

while the Y (upper) jaws were varied. In the second set of measurements, the Y

collimators were fixed and the X collimators were varied. Collimators were varied from

30 x 4 to 30 x 30 cm2 for the open fields. For wedged fields, collimators were varied

from 20 x 4 to 20 x 20 cm2 with a 450 wedge (external wedge) for an 8 MV (Varian

2100C) and from 30 x 4 to 30 x 30 cm2 with a 600 wedge (internal wedge) for a 20 MV

(Philips SL25) photon beam. The wedge gradient was always orthogonal to the long axis

of the chamber. The data also were measured for a range of square field sizes projected at








the isocenter. Special attention was paid to the position of the chamber on the central axis

for measurements with a wedge. Reversing the wedge did not change the measured

readings by more than 0.4%.



Results



The measured head scatter factors of an 8 MV photon beam of Varian 2100C

normalized to a 10 x 10 cm2 field size are shown in Figure 4-2. Figure 4-3 shows the

measured wedge-head scatter factors of 450 wedged fields for 8 MV photon beam of

Varian 2100C. The rectangular fields are plotted according to the side of the equivalent

square field obtained by Sterling's area-to-perimeter relationship (Sterling et al. 1964).

The same data are plotted in Figures 4-4 and 4-5 for open and wedged fields but

according to the side of the square field obtained by the modified equivalent square

formalism presented in Equation (4.9) with the calculated geometric weighting factor, k =

1.5, for a Varian 2100C. The collimator exchange effects are obvious in Figures 4-1 and

4-2. The magnitude of the difference in output caused by this effect ranges from 0.2% to

2.5% for both open and wedged fields. The maximum difference is for the most elongated

fields. The modified equivalent square formalism provides output with a difference of

less than 1% for open fields and less than 0.5% for wedged fields.

Similar results were obtained with the 20 MV photon beam. Head and wedge-

head scatter factors are shown in Figure 4-6 and Figure 4-7, respectively, according to the

side of the equivalent square field obtained by Sterling's area-to-perimeter relationship
















1.04
Varian 2100C, 8 MV, open, k=1

1.03

1.01
LL.
S1.00

g 0.99

/ 0.98 -.- Square

S0.97. -. Fix-X(30)
0.96 Fix-Y(30)
0.96

0.95
0 5 10 15 20 25 30
Side of Eq. Square (cm)




Figure 4-2. Head scatter factor as a function of a rectangular open field for the 8 MV
photon beam of a Varian 2100C. During these measurements, one set of collimator jaws
was fixed and the other set of collimator jaws was changed symmetrically. The field size
varied from 30 x 4 to 30 x 30 cm2. Data are plotted according to the side of the
equivalent square obtained by the conventional area-to-perimeter relation.



































0 5 10 15
Side of Eq. Square Field (cm)


Figure 4-3. Wedge-head scatter factor as a function of a rectangular 450 wedged field for
the 8 MV photon beam of a Varian 2100C.

















1.04
Varian 2100C, 8 MV, open, k=1.5
1.03

1.02

S1.01

1.00
0/
8 0.99

S0.98 Square

0.97 / a Fix-X(30)
SFix-Y(30)
0.96

0.95
0 5 10 15 20 25 30
Side of Eq. Square Field (cm)




Figure 4-4. Head scatter factor as a function of a rectangular open field for the 8 MV
photon beam of a Varian 2100C. Data are plotted according to the side of the equivalent
square obtained by Eq. (4.9) with k = 1.5.
















1.08
Varian 2100C, 8 MV, 45-wedge, k=1.5
1.06

1.04

I 1.02
LL
I 1.00

o 0.98

0.96 -- Square
Fix-X(20)
0.94 Fix-Y(20)

0.92
0 5 10 15 20
Side of Eq. Square Field (cm)




Figure 4-5. Wedge-head scatter factor as a function of a rectangular 450 wedged field for
the 8 MV photon beam of a Varian 2100C. Data are plotted according to the side of the
equivalent square obtained by Eq. (4.9) with k = 1.5.
















1.04
1.03 Philips SL25, 20 MV, open, k=1
1.02
1.01
3 1.00
S0.99 -Square
S0.98 / Fix-X(30)
SA Fix-Y(30)
0.97
I 0.96
0.95
0.94
0.93
0 5 10 15 20 25 30
Side of Eq. Square Field (cm)


Figure 4-6. Head scatter factor as a function of a rectangular open field for the 20 MV
photon beam of a Philips SL25.
















1.11
1.09 Philips SL25, 20 MV, 60-wedge, k=1

1.07
1.07
1.05
S 1.03
,, A .
1.01
g 0.99
0.97
S0.95 -- Square
0.93 Fix-X(30)
SFix-X(30)
0.93
1 / Fix-Y(30)
0.91
0.89
0 5 10 15 20 25 30
Side of Eq. Square Field (cm)


Figure 4-7. Wedge-head scatter factor as a function of a rectangular 600 wedged field for
the 20 MV photon beam of a Philips SL25.








(Sterling et al. 1964). In Figures 4-8 and 4-9, the same data are plotted according to the

side of the square field obtained by the modified equivalent square formalism. The

geometric weighting factor k= 1.85 is obtained for the Philips SL25. The magnitude of

the difference in output caused by the collimator exchange effect ranges from 0.3% to 3%

for open and 0.4% to 5% for wedged fields. The modified equivalent square formalism

provides output with a difference of less than about 1% for both open and wedged fields.



Discussion



The top edge of the collimator was considered to be the field-determining edge for

calculation of the geometric weighting factor k. Although the distance from the source

plane to the top of the collimator, lx, or 1,y, changes according to the field size because of

the circular movement, the amount of variation is negligible. Therefore, one value of lIx

or I,, can be used. Interestingly, our formula has the same format as the formula that was

empirically obtained by Vadash and Bjmrngard (1993). In this study, k = 1.5 for the

Varian 2100C and k = 1.85 for the Philips SL25 were obtained. Vadash and Bjamgard

(1993) empirically obtained k= 1.92 for open fields and k= 1.84 for wedged fields for

the Philips SL25 25MV photon beam, and Yu et al. (1995) obtained k = 1.7 for the

Varian 2300CD 6 MV photon beam. Equation (4.9) shows that the equivalent field size

varies slightly according to k. For example, the equivalent square field size for a 5 x 20

cm2 (or 20 x 5 cm2) field is 9.1 x 9.1 cm2 (or 7.1 x 7.1 cm2) with k= 1.5, and 9.5 x 9.5














1.04
1.03 Philips SL25, 20 MV, open, k=1.85
1.02
1.01
I 1.00
U-
S0.99
U 0.98
*o 0.97
~S Square
I 0.96
Fix-X(30)
0.95 Fix-Y(30)
0.94
0.93
0 5 10 15 20 25 30
Side of Eq. Square Field (cm)



Figure 4-8. Head scatter factor as a function of a rectangular open field for the 20 MV
photon beam of a Philips SL25. Data are plotted according to the side of the equivalent
square obtained by Eq. (4.9) with k = 1.85.














1.11
Philips SL25, 20 MV, 60-wedge, k=1.85
1.09 a _
1.07
1.05

I 1.03
1.01

S0.99

0.97
Square
S0.95-
Fix-X(30)
0.93 Fix-Y(30)
0.91
0.89
0 5 10 15 20 25 30
Side of Eq. Square Field (cm)




Figure 4-9. Wedge-head scatter factor as a function of a rectangular 600 wedged field for
the 20 MV photon beam of a Philips SL25. Data are plotted according to the side of the
equivalent square obtained by Eq. (4.9) with k = 1.85.









cm2 (or 6.9 x 6.9 cm2) with k = 1.7. And the difference of head scatter factors between

9.1 x 9.1 and 9.5 x 9.5 cm (or 7.1 x 7.1 and 6.9 x 6.9 cm2) fields is about 0.2%.

The wedge-head scatter factor of a wedged field depends on both the scatter from

scatterers in the head like the flattening filter and scatter from the wedge itself. The

scattered radiation from a wedge depends on the area of the wedge that intercepts the

radiation coming downstream through the treatment head. If the wedge is located above

the collimatorjaws like that in a Philips machine, the detector's eye view field at the

source plane can be used for both head scatter and wedge scatter. However, when the

wedge is located underneath the secondary collimator like that in a Varian machine

equipped with an MLC, the field size for the wedge scatter contribution is different from

the field size for the head scatter contribution. Whereas the head scatter contribution is

determined by the field seen by the detector's eye view, the wedge scatter contribution

depends on the field size projected at the detector plane. Therefore, in this case, the

formula shown as Eq. (4.9) may slightly overcompensate for the collimator exchange

effect. Our results for wedge-head scatter in Figure 4-5 show that Eq. (4.9) gives an

accurate calculation of output even for a Varian-type wedged field.



Conclusion



The equivalent square field formula (Eq. [4.9]) with the geometric weighting

factor (Eq. [4.10]) provides an accurate estimate of output even when there is a

significant collimator exchange effect in a linear accelerator. Since only the geometric





57

weighting factor is considered, this formula is very simple and is applicable to any

accelerator as long as the geometric data are known. Also, this formula can be used

directly with conventional dosimetric data, which are always measured for a set of square

fields at isocenter. It is not necessary to measure data for a series of rectangular fields

(except for verification) for parametrization, as has been discussed extensively in the

literature.













CHAPTER 5
A GENERALIZED SOLUTION FOR THE CALCULATION OF
IN-AIR OUTPUT FACTORS IN IRREGULAR FIELDS

Introduction


Most treatment fields used in radiation therapy are irregular in shape while the

dosimetry data is measured with square or rectangular fields. Conventionally, the in-

phantom dosimetric parameters, such as the tissue-air-ratio (TAR) or tissue-maximum-

ratio (TMR), are calculated based on the actual field shape created by a custom

Cerrobend block, but the in-air output factor calculation is based on the rectangular field

shaped by collimator jaw(secondary collimator), and is considered independent of any

tertiary blocking (Kahn 1994). This conventional method for the calculation of in-air

output of irregular field is valid when the size of irregular field is close to the size of

collimator jaw opening. However, if the irregular field is much smaller than the

collimatorjaw opening or is extremely irregular so that part of block is close to central

axis, the measured in-air output can be significantly different from the one obtained with

conventional methods. Many authors have studied the physical origin of in-air output

factors (Patterson & Shragge 1981, Kase & Svensson 1986, Mohan et al. 1985, Huang et

al. 1987, Luxton & Astrahan 1988, Chaney & Cullip 1994, Zhu & Bjarngard 1995). It is

primarily due to the amount of scattered radiation that is produced within the accelerator

head structure and the fraction that can reach the point of measurement as the position of








the collimators is varied. There are several components in the head which produce scatter

radiation. The flattening filter is considered to be the most dominant source of scattered

radiation from the head (Kase & Svensson 1986, Mohan et al. 1985, Luxton & Astrahan

1988, Chaney & Cullip 1994). When a tertiary collimator, such as a conventional

Cerrobend block or MLC installed below the field-defining secondary collimators, is

used for field shaping, scatter radiation from the tertiary collimator may not be negligible,

especially for small tertiary collimator openings with a large secondary collimator setting.

The scatter radiation from beam modifiers such as physical wedges or compensators, can

also be significant. There are several models which have appeared in the literature that

accurately describe the scatter photon energy fluence distribution emanating from the

head (Ahnesjo et al. 1992, Ahnesjo 1994, Dunscombe & Nieminen 1992, Yu & Sloboda

1993, Jaffray et al. 1993). However, these model-based approaches, which are based on

uniform (Ahnesjo et al. 1992), triangular (Ahnesjo 1994), Gaussian (Dunscombe &

Nieminen 1992), combination of several functions (Yu & Sloboda 1993), and

experimentally determined distribution functions (Jaffray et al. 1993) require

sophisticated programming and/or complex measurements. Moreover, most of these

studies have mainly concentrated on the modeling of scatter radiation from the flattening

filter. Recently, a method of parametrization with the equivalent square at the flattening

filter was studied (Lam et al. 1996) and a similar approach, in which the parametrization

was kept at the detector plane, was studied in the previous chapter (see Chapter 4). These

studies have been limited to rectangular fields only.








In this chapter, an in-air output calculation formalism was set up and a simple

algorithm for calculation of in-air output factor of irregular shaped fields was developed

for both open and wedged fields by expanding the application of field mapping method

that is based on detector's eye view field which has been successfully applied to

rectangular fields (see Chapter 4).

In the algorithm, three major scatter contributors--flattening filter, wedge, and

tertiary collimator--are considered. For the calculation of flattening filter scatter, first, the

collimatorjaw field and tertiary collimator shaped field are projected into the source

plane through the detector's eye view to get a combinational field shape. Clarkson

integration (Clarkson 1941) is carried out on the combined field using measured data at

the detector plane in conjunction with field mapping method, instead of describing a

discrete scatter source function that has been described in the literature. In the field

mapping method, a field at the source plane is segmented and each segment field is

mapped into a corresponding field at the detector plane by using equivalent field

relationships obtained in Chapter 3. The algorithm is also valid for the treatment

machines in which MLC replaces the upper or lower collimatorjaw instead of being a

tertiary collimator system. In that case only one projected field is used since there is no

additional field. For a machine in which the MLC replaces the upper collimator jaws,

Palta et al. (1996) have suggested an equivalent field method at the detector plane.

Although equivalent field method at the detector plane provides a simple methodology, it

does not explicitly account for both the collimator jaw exchange effects and non-linearity

of in-air output dependence on field size.








The change of scatter radiation from tertiary collimator was also measured and

parametrized. In the calculation of total head scatter factor, the tertiary collimator scatter

factor is added to the collimator scatter factor.

In the case of wedged fields, the in-air output is dependent not only on scatter

from flattening filter but also scatter from the wedge itself. Therefore, the relative

position of the collimators (both secondary collimator and tertiary collimator) and wedge

will determine the method of calculation of in-air output. When wedge is below the

tertiary collimator (e.g., external wedge), the field size for wedge scatter contribution is

different from the field size for head scatter contribution. The conventional collimator

scatter factor for wedged field is separated into two components: one for the change of

scatter radiation from flattening filter and the other for the change of scatter radiation

from the wedge. Each component is independently calculated using a field mapping

method with corresponding detector's eye view field sizes.



Formalism of In-air Output Factor



Head Scatter Factor and Monitor Back Scatter Factor

The total energy fluence in air on central axis produced by an external photon

beam can be divided into two components: one is due to unscattered primary photons

from the target and the other is due to scattered photons, which are generated in

scattering materials in the head (for example, primary collimator, flattening filter, and

field defining collimators).








T = Vp + I's


=Y, 1+ V (5.1)


where, Tp is the energy fluence due to primary photons, 's is the energy fluence due to

scatter photons from the scattering materials in the head. Considering the effect of

backscatter radiation to the monitor chamber (Lam et al. 1996, Ahnesj6 et al. 1992,

Patterson & Shragge 1981, Luxton & Astrahan 1988, Moyer 1978, Higgins et al. 1989,

Kubo & Lo 1989, Kubo 1989, Duzenli et al. 1993), primary energy fluence can be

expressed as

, (X, Y)= (o,oo),,(X,, Y,) (5.2)

where, (Xc, Y,) is secondary collimator setting, 'F (oom,) is unperturbed energy

fluence, and f,, is the function which accounts for the monitor backscatter effect on the

energy fluence. By both multiplying and dividing Eq. (5.2) with monitor backscatter

effect function, fb (X,, Y,) for a reference collimator setting, (X,,Y,), we can get


f. (X, Y,)

= Y,(,(Y,,)f (X,, Y,) ( )
=, (oo, oo)f,, (X,, (Xr Y

= ',(X,, Y,)Sb (Xc, Y,) (5.3a)

where, (X,, Y,) is secondary collimator setting for the reference field and S,, is monitor

backscatter factor, defined as,

f,(Xt 'Y)
S (X, YY) = ) (5.3b)
fmh(X, YD)








Now, consider head scatter contribution. For the energy fluence of any field, we can get,


4(X ,, Y)= (X,, Y,) (X Y)
Y(X,,Y,)
y(X, 'y )
= (x,, Y,) ) (5.4)
T'(X,,Y,)

By substituting Eq. (5.1) into Eq. (5.4), we have


I + T., (X, Y,)

TV,(X,,Y,) Iv,(X,,Y,)
S,((X,,Y,))

Using Eq. (5.3a), we can get,

(X, Y,) = (X,, Y, )S,, (X., Y, )S, (X, Y, ) (5.6a)

with head scatter factor, S, defined as


1+ p(X, Y,)
S,.(XI, Y)= -- (X"Y'). (5.6b)
I+- (X,, Yr)
f (X,,Y,))

From the conventional definition of collimator scatter factor, S we can get


SI(XI, e) = T(X YD
T(X,, Y,)


=S,, (X, Y,)S.,(X,,Y,) (5.7)

Equations (5.6) and (5.7) show that we can separate collimator scatter factor, S,. into two

components, monitor back scatter factor, S,,, and head scatter factor, S,. When a field is








very small, source obscuring may occur. In that case, a source obscuring factor should be

included in the Eq. (5.7) (Zhu & Bjarngard 1995).



Presence of A Beam Modifier in The Field

When photon beam passes a beam modifier (for example, a wedge), the energy

fluence changes due to both attenuation of incident photons and scatter photons produced

in the beam modifier. If we denote the energy fluence below the beam modifier as (D,

then, we can express

I=0 ,+D,



= du -,+ ) (5.8)


where D, is the unscattered energy fluence which is due to the primary head scattered

photons and (, is the energy fluence due to scatter photons by the beam modifier. With

attenuation factor of beam modifier, Abm (~u is given by

,.=Abm- (5.9)

where T is the total energy fluence incident on the beam modifier, expressed in Eq.

(5.1). For the energy fluence of any field with beam modifier, we can get,


<(Xc,Ye)=0(Xy)(
(c(X,,Y,)


= (X I Y,) (5.10)
(XBy substituting, Yinto Eq. (5.10),

By substituting Eq. (5.8) into Eq. (5.10),









o)(Xc,rY) Y((Xc,Yc)-
i(X Y, Y) = o(X, Y) (5.11)
S -,(X,,Y,) o(X,,Y,)
~, (X,,Y,)

is obtained. Using Eq. (5.9) and (5.7), we can get,

D(X, Y e) = ((X,, Y, )S,, (X,, Y,)S,, (X,, Y,)S,,, (X,, Y,), (5.12a)

with beam modifier scatter factor, S,,, defined as



Sbs (X' Y)= X,, Y,) (5.12b)
I DO,(X,,Y,)J

In the derivation of Eq. (5.12), we assumed the dependency of Abm on field size is

negligible. When wedge is used as a beam modifier, using the standard convention of

collimator scatter factor of wedged field, S, we can get

S, (X, I Y) =, (Xc, e)
,(X,, (,)


=S,,b (X,, IY )SX,, (X, I Y)S-,(X, I Y)
= S, (X,, Y)S,, (Xo,Y, ) (5.13)

where Sh,, is replaced with wedge scatter factor, S., in order to indicate wedge is the

beam modifier. Equations (5.12) and (5.13) show we can separate wedge scatter factor,

S,, from conventional collimator scatter factor of wedge field, S,.,.








A Shaped Field with A Tertiary Collimator

Tertiary collimator, such as conventional Cerrobend block and Varian type MLC,

can change the in-air output factors. There are two components. One is the change of

head scatter factor, S, due to the change of detector's eye view of head scatter area. The

other is scatter photons produced in the tertiary collimator itself which, in some cases,

may not be negligible. If we let the energy fluence below the tertiary collimator as (p,

then, we can express

(P(P ,+(P, (5.14)

where cpU is the energy fluence coming from upstream of the tertiary collimator and (p,

is the energy fluence due to scatter photons by the tertiary collimator. We define

p, (X ,Y.) as energy fluence due to scattered photons that emanate from a solid material

of same thickness and composition as tertiary collimator with X, x Y, collimator setting.

For a field with tertiary collimator, we get,


cp(Xe,,,X.,c)=cP,(Xc,Yc,X,,Yc)+cp,(Xc,Yc)- tP( Yps(X,c ,) (5.15)


where (X,c, Y,) is setting of the tertiary collimator. Without tertiary collimator,

(X Y,,)=(oo,oo) and cp is the same as F, that is,

(p,(X ,Y,,o,o)=y(Xc, Y) (5.16)

By both multiplying and dividing with 'F(X,,Y,) to Eq. (5.15), we can get








(p(X,Y,X,Y ) = V(X ,Y)


x p.(Xc, Y,,)+I,(xY r) .(Xo,Y,) (5.17)
1 ,(X,,Y,) V(X,,Y,) (X,,,Y,) (X,,Y,) (.1

Then, collimator scatter factor for a shaped field with tertiary collimator, S,,c is given

by


Sh (Xtertiary colli r scate f(X" S, ),
X(X,, Y,)



= (X,,Y,) Y(X,,Y,) T(XcYc) (X,,Y,)

=sM(xc'y,xoY)+Sc,(xc',)-. (X, )S, s(xc ^),

(5.18a)
with tertiary collimator scatter factor, Sc, defined as

S, (X,Y)- ( Y) (5.18b)
Y(X,,Y,)



Calculation Algorithm


Open Field

Head scatter factor and field definition by DEV. The head scatter factor given in Eq.

(5.6b) depends on head scattered radiation which can reach the detector. If any ray line of

head scatter to the detector is blocked by tertiary collimator such as Cerrobend block or

MLC, the head scatter factor will decrease. Therefore, S,, is dependent on the field size








determined by detector's eye view instead of the collimator field size. The field defined

by detector's eye view is illustrated in Figure 5-1. In Figure 5-1, l,, 1;, and lir are the

distances from the source plane to the top of X Y collimator jaws and tertiary collimator,

respectively. The distances from the detector plane to the top of X Ycollimators, and

tertiary collimator are noted as 12, 2y, and 12T. Now, let X, Yo and TD be the field sizes

determined by the lower (or X), upper (or Y) collimator jaws and the tertiary collimator,

respectively, at the detector plane andX, Ys and Ts be the field sizes determined by the

X, Ycollimator jaw, and tertiary collimator at the source plane through the detector's eye

view. Then, the field conversion factors from detector-to-source plane, k, ky and k are

given by

kx = l12, (5.19)

ky = 1/12y, (5.20)

kr= 117/12T- (5.21)

Then, field sizes at the source plane, X, Ys and Ts become

Xs = ko, (5.22)

Ys = YD, (5.23)

Ts = kTo. (5.24)

After the field size conversion from the detector plane to source plane, the projected

collimator jaw and tertiary collimator shaped fields are combined in the source plane.

That is, the area common to both fields is used to determine head scatter factor.

Clarkson integration and field mapping. The head scatter factor is calculated by carrying

out Clarkson integration in the combined field in the source plane. Typically,

















Field edge is determined
by Upper Collimator Jaw
Source -------.-. ........ -



Upper(Y) Collimator Jaw


Lower(X) Collimator Jaw

Tertiary Collimator
(Block or MLC)












Detector Plane Det


Field edge is determined
by Tertiary Collimator
S ----------- ----











12y









-etor's Eye ......
ector's Eye


Figure 5-1. Schematic diagram showing the geometrical relationship among detector, X
and Y collimator jaw settings, tertiary collimator settings, detector plane field size and
source plane field size.








conventional dosimetric data is available only for square fields at detector plane.

Therefore, it is convenient to project source plane field to detector plane. For any circular

field of radius, rs at source plane, we can get equivalent square field at source plane, ss'

from equivalent field relationship for head scatter,

ss"'(rs) = 1.8rs. (5.25)

It is necessary to find an equivalent square in the detector plane, seD which is equivalent

to s"'. If we project sq' to source plane, the square field changes to the rectangular field,

ko' x kyS S. Once again, by using the equivalent field relationship, we can let

sq' = [2kxk/(kx + k)]SD (5.26)

Since ss"' should match with sS', we can get an equivalent square field at detector plane,

sf'(rs) for the circular field, rs at the source plane,

s o'(rs) = [(kx + k)/2k1ky]ss'(rs)

= 0.9[(k, + k/k)k]rs. (5.27)

The head scatter factor for irregular shaped open field is obtained by


Sh(irregular) = (1/360) S r(seq(r))A (5.28)


where, Sh,(sDe(rs)) is the head scatter factor of the equivalent square field at detector

plane which corresponds to circular field with radius rs, at source plane. And A4, is i-th

interval of angle in Clarkson summation. To get conventional collimator scatter factor, S,

we must multiply Eq. (5.28) with monitor backscatter factor. Since monitor backscatter

factor is primarily dependent on secondary collimator settings, we can multiply monitor

backscatter factor of X x YD rectangular field at detector plane, that is, Sm,(XD, Yo). We

can rewrite Eq. (5.28) as,








Sl(irregular)= S,(irregular)/Smb(X ,Y


= (1/360) D [Sc(se(rs))/Smb(sD(rsl)] A,, (5.29a)

or,


S,(irregular) = Sb(XY) (1/60) [S(s (rs)) /Smb(sq(rs))] A, (5.29b)

where S,(seq'(rs)) is the collimator scatter factor of the equivalent square field at detector

plane which corresponds to circular field with radius rs, at source plane. Monitor

backscatter factor can be measured by telescopic method (Kubo 1989). Ahnesj6 et. al.

(1992) assumed that the amount of backscatter to the monitor chamber from the back

surface of a collimator jaw is proportional to the irradiated surface area. With same

assumption, Lam et. al. (1996) modeled monitor back scatter factor as a function of

collimator settings. When each segmented field is not much different from collimator

settings, we can make an approximation,


S,(irregular) = (1/360) C Sc(sD'(rsd) Ai,, (5.30a)

by assuming,

Smb(XYd) zSmb(sDe (rs)) Smb(SDeq (2)) ..... (5.30b)

In most clinical situations, this expression is a good approximation. Equation (5.29) can

be directly used with the measurement of monitor backscatter factor if a more accurate

monitor backscatter factor is required. This will probably be necessary in the case of

beam intensity modulation, in where very small shaped fields with large secondary

collimator setting may be used.








Scatter Factor of Tertiary Collimator. Since the tertiary collimator transmits more

radiation and is closer to the detector than collimator jaws, it is necessary to consider

scatter contribution from tertiary collimator itself. The amount of scatter contribution is

dependent on irradiated area of tertiary collimator. We define tertiary collimator scatter

factor, Sc,(s), as the ratio of scatter dose from a solid block material with s x s collimator

setting to the dose of reference 10 x 10 field in Eq. (5.18b). Tertiary collimator scatter

factor of an irregular shaped field with XD x Y, collimator jaw setting can be obtained as


St,(irregular) = Scs(XD,Y (1/360) [S,(XD, YoW/Sc(s(rD))] St,(so,(rD)Ai ,


(5.31)

where sDeq(rD) is the equivalent square field at detector plane which gives same tertiary

collimator scatter contribution as a circular field with radius rD, at detector plane, and is

obtained by s,"(r,) = 1.8rD. When each segmented field is not much different from

collimator settings, we can make an approximation,


S./(irregular) = S,(XDr D) (1/360) S,(sD (rD)) i, (5.32a)

by assuming,

Sc(X, Yar) S,(sD D(r) Sc(SDeq(rs2)) ... (5.32b)

Finally, in-air output factor for irregular open field, OF, becomes

OF(irregular) = S,(irregular) + Sc,(irregular) (5.33)

where Sc is obtained by Eq. (5.29b) or Eq. (5.30a) and S,c is obtained by Eq. (5.31) or Eq.

(5.32a). Note that the MLC on Varian linear accelerators, which is mounted below the X








and Y jaws, is handled the same way as a block except S,, that corresponds to the scatter

from the leaves of the MLC system.



Wedged Field

Depending on the position of wedge, the method of in-air output factor calculation

are different. On a Varian accelerator with MLC, a wedge is inserted underneath the

tertiary collimator (MLC). In this case, the field size for wedge scatter contribution is

different from the field size for head scatter contribution. It can be clearly seen from

Figure 5-2 that the head scatter contribution is determined by the detector's eye view of

the field defined by collimator jaws and the wedge scatter contribution is dependent on

irregular field shaped by the tertiary collimator in the detector plane. To account for this

fact, the collimator scatter factor for wedged field is separated into collimator scatter

factor and wedge scatter factor as given in Eq. (5.13),

S,w =S ,. (5.34)

Therefore,

S, = Sc,/Sc. (5.35)

For an irregular field, each component is calculated by,


S(irregular) = (1/360) Y Sc(s o'(rs))Ad (5.36a)


with

SD'(rs) = 0.9[(kx + /kk]rs,,

and
















Head Scatter is determined by Source Plane Field Size
through Detector's Eye View


Source --. -- --- -----------.-------



Upper Collimator Jaw

Lower Collimator Jaw

Tertiary Collimator
(Block or MLC)
Wedge

edge Scatter is determined/


Detector Plane- -


L.---


Detector's Eye


Figure 5-2. Schematic diagram showing the detector's eye view scatter area for head
scatter and wedge scatter in Varian type (external) wedged MLC field.









S,,(irregular) = (1/360) Sjs0f(ro,))Ai,, (5.36b)

with

s "(rDd = 1.8 rDi .

Finally, in-air output factor for irregular wedged field is obtained by

OF,(irregular) = Sc (irregular) S. (irregular) (5.37)

Note that the scatter contribution from the tertiary collimator is not considered since

wedge is underneath the tertiary collimator.

If the wedge is located above the collimator jaws, the field size for wedge scatter

contribution is the same as that for head scatter contribution. That is, the collimator

scatter factor of a wedge fi id.. is given by


S, (irregular) =[(1/360) Sc(sq(rs,))A, ][(1/360) S, (s (rs)s)Ai, ] (5.38)

and the in-air output factor of a wedge field, OF, is obtained by

OF(irregular) = S, (irregular) + Sb.w (irregular),

where Sb, is the block scatter factor for a wedged beam. In Eq. (38), sD'q(rsi)c is the

equivalent square field at the detector plane for head scatter contribution and is the same

as for Eq. (27). However, the equivalent square field at the detector plane for wedge

scatter contribution, sD'(rsi)ws, is not the same as sD'q(rsi). From the equivalent field

relationship,

s'q(rs) = 1.8rs (5.39)








If we project so'e (an equivalent square at detector plane) to the source plane, the square

field changes to a rectangular field, kxSDq x kSyD'. Using the equivalent field relationship

for wedge scatter, we can let

ssq' = (k)/)"2 seq. (5.40)

Because Eq. (5.39) and Eq. (5.40) should match each other, we can get the equivalent

square field at the detector plane, sD'(r,), for any circular field with a radius ofrs at the

source plane:

sfq(rs)s= 1.8 rs/(k,)1/"2. (5.41)



Methods and Materials



In-air output factors of tertiary collimator shaped fields were measured with a

cylindrical acrylic mini-phantom as described by van Gasteren et al. (1991). The

cylindrical phantom is 3.8 cm in diameter and 15 cm long. A shonka plastic 0.1 cc

ionization chamber was inserted in the mini-phantom with its center located at 5 cm from

the front surface and 100 cm from the source. Measurements were taken on a Varian

2100C with 8 MV photon for both open and wedge fields. Since wedge can not be used

with conventional block in Varian machine that is equipped with MLC, only MLC fields

were considered with wedges. The measurements were taken with the fixed X and Y

collimator jaw settings (22.5 x 22.5 cm2 for Cerrobend block field, 21.6 x 20.4 cm2 for

open MLC field, and 20 x 20 cm2 for wedged MLC field). The tertiary collimated field

sizes were varied for 4 x 4 to 20 x 20 cm2 for both open and 450 wedge field (for








systematic analysis of calculated data, only square shapes were devised with tertiary

collimator instead of irregular shape fields). Special care was taken to position the

chamber on the central axis for measurements with wedge. Reversing the wedge direction

did not change the measured readings by more than 0.4%. In the case of open field,

scatter contribution from tertiary collimator (Cerrobend block and Varian MLC) was also

measured with the same mini-phantom as described above. A set of measurements were

made underneath a solid piece made out of the same material as the tertiary collimator

material (Cerrobend or MLC) with field sizes ranging from 4 x 4 to 20 x 20 cm2. The

thickness of Cerrobend block was 7.5 cm. The data were extrapolated to 0 x 0 cm2 field.

The fluence of (0,0) field multiplied by Sc(X Y)/S(O, 0) was subtracted from total fluence

for each field size, (X, Y). The remaining fluence of each field is divided by the fluence of

10 x 10 cm2 reference open field to get tertiary collimator (block or MLC) scatter factor,

S,,,. Finally, in-air output factors of two irregular fields were also measured. One shape

was made with Cerrobend material and the other was made with MLC. Figures 5-3 and 5-

4 show beam's eye view of block and MLC shaped irregular fields projected at the

detector plane, respectively. For all these experimental measurements, in-air output

factors were calculated using the algorithm described in the previous section.






































-15 L
-1i


5


-10 -5 0 5 10 15


X (cm)




Figure 5-3. A beam's eye view irregular field shaped by Cerrobend block at detector
plane. Outer rectangle indicates collimator jaw setting at detector plane. Both 8 and 18
MV photon beams of Varian 2100C were used.
































-4



-8



-12
-12 -8 -4 0 4


8 12


X (cm)




Figure 5-4. A beam's eye view irregular field shaped by MLC at detector plane. Outer
rectangle indicates collimator jaw setting at detector plane. Both 8 and 18 MV photon
beams of Varian 2100C were used.








Results



Tertiary Collimator Scatter Factor

The measured tertiary collimator scatter factor, Sc for Cerrobend block and

Varian MLC are shown in Figure 5-5. As defined in Eq. (5.18b), S,,(20,20) for blocked

field is the ratio of energy fluence due to scattered photons from a 20 x 20 cm2 solid

Cerrobend block to energy fluence of a 10 x 10 cm2 open field at the reference point.

Therefore, for a 20 x 20 cm2 completely blocked field, energy fluence due to scattered

photons is 1.3 % of energy fluence of 10 xl0 cm2 open field. As an example, The value

of Sc for a Cerrobend block with outer dimension of 20 x 20 cm2 and inner dimension of

15 x 15 cm2 from Figure 5-5 is 0.005. This is the difference in S,,(20,20) and S,(15,15)

values. The tertiary collimator scatter factors for Cerrobend block are almost twice as

large as those for MLC. Two possible reasons for this may be that the block is closer to

the detector than MLC and that it has larger transmission than MLC.



In-air Output Factor of Open Fields Defined by Tertiary Collimator

In-air output factors for open fields were calculated using Eqs. (5.30a), (5.32a),

and (5.33). The calculated data for fields shaped with Cerrobend block and MLC are

compared with measured data in Figures 5-6 and 5-7, respectively. Note that the

secondary collimator settings were fixed for these measurements. The settings were 22.5

x 22.5 cm for Cerrobend block and 21.6 x 20.4 cm2 for MLC shaped fields. Two other

alternate methods of obtaining in-air output factors are also shown for comparison. One















0.014
3 Varian2100C, 8 MV
w 0.012

IM 0.010
U.

0.008

S0.006

0 0.004 MLC

0.002
1-
0.000
0 5 10 15 20
Side of Square Field (cm)





Figure 5-5. Tertiary collimator scatter factor for 8 MV photon beam of Varian 2100C.
Where tertiary collimator scatter factor is defined as the ratio of scatter dose from solid
tertiary collimator material(Cerrobend block or Varian type MLC) to the dose of
reference 10 x 10 cm2 open field at detector plane.















1.05
Varian2100C, 8MV, Block field

1.04


S1.03 ------
U-

& 1.02
0 -~ Measurement]

-e- Sc + Stcs
1.01

-..... Conventional

1.00
0 5 10 15 20 25
Side of Square Field (cm)



Figure 5-6. In-air output factor of open fields with Cerrobend block tertiary collimator for
8 MV photon beam of Varian 2100C. While the collimator jaw setting is fixed as 22.5 x
22.5 cm2, block shaped field is changed from 4 x 4 to 21 x 21 cm2 at detector plane.















1.04
Varian2100C, 8 MV, MLC field

1.03


1.02


., 1.01
-10- Measurement
0
/ Sc + Stcs

1.00 --Sc
......Conventional


0.99
0 5 10 15 20
Side of Square Field (cm)



Figure 5-7. In-air output factor of open field with MLC tertiary collimator for 8 MV
photon beam of Varian 2100C. While the collimator jaw setting is fixed as 21.6 x 20.4
cm2, MLC shaped field is changed from 4 x 4 to 20 x 20 cm at detector plane.








of the methods is labeled as conventional method in which it is assumed that the in-air

output depends on only Xand Y secondary collimatorjaw settings and is independent of

tertiary collimator. The other method is labeled as Sc method. This is simply a field

mapping method through detector's eye view field and it does not include tertiary

collimator scatter factor. It is obvious from Figures 5-6 and 5-7 that the conventional

method of calculating in-air in-air output factor is grossly inadequate when the tertiary

collimated field is much smaller than the secondary collimator opening. This is attributed

to the screening of head scattered photon fluence by the tertiary collimator. Field

mapping method through DEV field predicts the behavior of in-air output very well but it

underestimates the in-air output if the tertiary collimator scatter factor is not included.

Once the tertiary collimator scatter factor is included, the agreement between the

calculated in-air output and measured in-air output for all field sizes is very good (within

0.5 %). However, for fields defined with MLC, the agreement between the calculated in-

air output and measured in-air output is fairly good with field mapping method through

DEV field even if tertiary collimator scatter factor is not included. This is primarily due

to the small scatter contribution from MLC.



In-air Output Factor of Varian Type Wedge (External Wedge) Fields

Wedge scatter factor, S,,, for 450 wedge was obtained by Eq. (5.35) and is shown

in Figure 5-8. In the Figure 5-8 for field sizes 4 x 4 to 20 x 20 cm2. The data were

extrapolated to 0 x 0 field. Using the Eq. (5.36) and (5.37), in-air output factor of wedge

field was calculated and compared with measured data in Figure 5-9. Since block can not


































0 5 10 15 20
Side of Square Field (cm)





Figure 5-8. Wedge scatter factor, S, of 450 wedge field for 8 MV photon beam of Varian
2100C. Wedge scatter factor is obtained by dividing the collimator scatter factor of
wedge field, S, with collimator scatter factor of open field, S,.















1.10
Varian2100C, 8MV, 45-External Wedge, MLC field
1.08


1.06


S1.04


1.02
0

-.- Separation of Sc, Sws
0.98 -- No Separation
...... Conventional

0.96
0 5 10 15 20
Side of Square Field (cm)






Figure 5-9. In-air output factor of wedge field with MLC tertiary collimator for 8 MV
photon beam of Varian 2100C. While the collimator jaw setting is fixed as 20 x 20 cm2,
MLC shaped field is changed from 4 x 4 to 20 x 20 cm2 at detector plane.








be used with wedge in Varian 2100C, only MLC fields were considered. In-air output

factors obtained by conventional method and field mapping method with DEV field

without separating S., were also plotted for comparison. Conventional method gives one

in-air output factor value for all field sizes. Field mapping method through DEV field

without separating S, always overestimated the in-air output with the differences

reaching to about 4 %. The separation of S, and S, shows good agreement (within 0.5 %

difference) with experimental data for all field sizes.



In-air Output Factor of Irregular Shaped Fields

In-air output factors for irregular fields were calculated and compared with

experimental data in Table 5-1 for both 8 and 18 MV photon beams. The experimental

data were also measured with 18 MV photon beam available on the same Varian 2100C

and compared with the calculated data to verify the validity of algorithm for other photon

energies. Calculated in-air output factors matched well with the measurements. The

maximum difference was less than 0.5 %. In-air output factors obtained by conventional

method were also tabulated in Table 5-1 for comparison. The conventional method tends

to overestimate in-air output in the presence of wedges and underestimate for open fields.



Discussion



The importance of piecewise separation of scatter radiation component in the in-

air output from a linear accelerator obvious from the measured data are shown in Figures








Table 5-1. In-air output factors of test irregular fields for 8 and 18 MV photon beams of
Varian 2100C. Data are normalized to reference 10 x 10 cm2 field. In-air output factors
obtained by conventional method are also included for comparison. Beam's eye view
irregular field shapes are shown in Figures 5-3 and 5-4.


Tertiary Collimator Energy (MV) In-air Output


Measurement Calculation Conventional


Block(open) 8 1.034 1.031 1.026
18 1.032 1.028 1.024


MLC(open) 8 1.013 1.012 1.020
18 1.012 1.010 1.017


MLC(450 wedge) 8 1.021 1.021 1.047
18 1.020 1.018 1.041




5-6, 5-7, and 5-9. A close examination of Figure 5-6 shows that as the field is

increasingly blocked, the relative in-air output starts to increase first and then decreases

as the field blocking becomes extreme. This is attributed to increasing scatter from the

tertiary collimator and decreasing head scatter as the field is progressively blocked. A

simple geometrical back projection of the field to the source plane that accounts for the

head scatter is not sufficient to predict the in-air output accurately. The tertiary collimator

scatter from field shaping blocks must be included to achieve better accuracy. Even the

calculations show lower relative in-air output than measured data for larger tertiary

collimated fields. The reason for this small difference can be attributed to the scatter








contribution from side wall of tertiary collimator that is not included in our calculation

model. Figure 5-7 indicates that the amount of scatter contribution from MLC is not

significant. Therefore, it may not be necessary to consider MLC scatter factor for in-air

output calculation as long as head scatter is calculated accurately. But the inclusion of

scatter from MLC gives better accuracy. The importance of separating scatter component

from the head and beam modifier (wedge) is clearly demonstrated in Figure 5-9. Thicker

wedges introduce significant amount of scatter. The magnitude of scattered radiation

from an external wedge is dependent upon the surface area of the wedge seen by the

photon fluence that is incident on it.

Scatter source distribution functions described in the literature have been defined

within the physical dimension of flattening filter. In reality, in-air output may changes

even when the field size becomes larger than the flattening filter dimension. If this effect

is not considered, the calculation can result in an increasing discrepancy with

measurement. To account for this effect, Yu and Sloboda (1993) assumed a pseudo

source distribution function outside the flattening filter and it is determined by

experiment for each beam. In field mapping method, since measurement data is directly

used combined with equivalent field relationships, this effect is inherently included, thus,

no additional experiment is required.

When the source-to-detector (SDD) distance changes, the inverse law has been

used to calculate in-air output change. As the detector point changes, the field through

detector's eye view also changes. Therefore, the effective field size for inverse square law

calculation should be changed and this can be easily done with field conversion factors








specific for each detector point. This effect may not be negligible with very small field

size because the gradient of in-air output change is much steeper in smaller field sizes

than larger field sizes. However, it is not easy to separate these two effects, pure inverse

square law and DEV field size change due to SDD change. It is found the effective source

position of photon beam is not the same as physical source position in megavoltage linear

accelerators (Tatcher & Bjamgard 1992, McKenzie & Stevens 1993). The effective

source position can be easily determined by experiments (Tatcher & Bjarngard 1992).

When a effective source position is determined by experiments with fixed field size for

all SDD (Tatcher & Bjmrngard 1992), it inherently includes the effect of field size

change.

However, there are two complications for external wedge field: 1) effective source

position is dependent on field size, and 2) field sizes for head scatter and wedge scatter

are different each other when tertiary collimator is used. Therefore, it may be necessary to

separate each effective source position corresponding to each scatter source.



Conclusion



An in-air output factor calculation algorithm based on field mapping through the

detector's eye view field was developed and programmed. This method can predict in-air

output factor behavior in irregular fields with very good agreement for both open and

wedge fields. Although source plane field size is used to determine the head scatter

factor, parametrization at detector plane is kept by mapping the source plane field size





91

into the detector plane field size. That is, no additional dosimetric data acquisition is

required, which makes it is very simple to implement this method. In order to include the

scatter contribution from tertiary collimator, tertiary collimator scatter factor can be

measured and parametrized. This gives more accurate prediction of in-air output,

especially in the case of the use of Cerrobend block. By virtue of the simplicity, field

mapping method through the detector's eye view field can be easily implemented in any

clinic.




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