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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 INAIR OUTPUT FACTORS IN IRREGULAR FIELDS .........................................58 Introduction ........................................................................... ................................. 58 Formalism of Inair 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 Inair Output Factor of Open Fields Defined by Tertiary Collimator.................... 80 Inair Output Factor of Varian Type Wedge (External Wedge) Fields .................84 Inair Output Factor of Irregular Shaped Fields.................... ..................... 87 D iscu ssio n ................................................................................... ...........................87 C o n clu sio n ............................................................................... ..............................90 6 TWOEFFECTIVESOURCE 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 inair 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 inair output factor that occurs with field shaping. It has been reported that the conventional method of calculating an inair output factor cannot be used for MLC shaped fields accurately. Therefore, it is necessary to develop algorithms that allow accurate calculation of the inair output factor. A generalized solution for an inair output factor calculation was developed. Three major contributors of scatter to the inair outputflattening filter, wedge, and tertiary collimatorwere 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 inair 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 inair output to within 1% accuracy. A twoeffectivesource algorithm was developed to account for the effect of source to detector distance on inair 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 inair 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 xrays and radioactivity was promptly followed by its therapeutic application in the treatment of benign and malignant diseases. The first therapeutic use of xrays is reported to have taken place on January 29, 1896, when a patient with carcinoma of the breast was treated with xrays. 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 xray 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 xrays. 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 stateofthe 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 threedimensional 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 computercontrolled 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 setup time while reducing the probability of setup 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 Motordriven MLC systems have been in use since the midfifties (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 Cseries, and Philips SLseries) 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 ydirection. 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 xray 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 overcenter 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 leafsettings 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 addon 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 downtime 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 fanbeam which is dynamically modulated by shortstroke 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 "doublefocused", that is, leaves form a cone of irregular crosssection 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 cutoff 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 fieldsize 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 inair output factor changes according to the collimator opening. The MLC, as a collimator system, also affects the characteristics of the inair output factor. The conventional method of inair 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 inair 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 inair 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 stateoftheart 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 3D 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 machinedependent 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 addon 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 21: (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 21. 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 ydirection. 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 21. The complete source program of the module is contained within Appendix A. Figure 22 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 21. 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 21.  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 Xdir. as user input. MLCSHIFTY: This subroutine gets MLC offset in Ydir. 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 21.  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) uwrlockang b) haffblocdng c) ovwrblocking Collimator angle Contour shift lManual fit Calculation point defining  a) point eating Figure 22. 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 depthdose 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 inair 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 inair 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 collimatorset 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 areatoperimeter 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 areatoperimeter 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 scattertoprimary ratio, SPRh, as the collimatordefined field. The SPRh of any arbitrary shaped field is the integration of the differential scattertoprimary 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 scattertoprimary 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 scattertoprimary 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 scatterto 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 = bar, (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 scatterto primary ratio for scatter from the flattening filter for any field is given by SPRf= J(bar)dA (3.5) It has been reported that the contribution of backscatter into the monitor chamber has a significant influence on the dependence of inair 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 scattertoprimary 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. Inair 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+WL + In l (3.12) 12 I L+WD] 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 areatoperimeter 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 Variantype 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 miniphantom 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 inair output of (0,0) field multiplied by Sc(X, Y)/Sc(0,0) was subtracted from inair output for each field size, (X, Y). The remaining inair 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 inair output between asymmetric fields is not significant, we may use that assumption without significant error. We measured inair outputs for a pair of asymmetric wedged fields (see Figure 31). 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 inair 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 31. Description of a set of asymmetric wedged fields. The contribution of unattenuated photons to inair 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 inair output factors of an 8 MV and 18 MV photon beams of Varian 2100C are shown in Figures 32 and 33, respectively. In Figures 32 and 33, the inair 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 32. Inair 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 33. Inair 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 inair output factors between circular field and square field is within 0.2 % for both 8 MV and 18 MV beams. Measured inair 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 inair 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 34 according to the elongation ratio. In Figure 34, 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 34, 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, Rmax5 (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 34. 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 areatoperimeter 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 34 supports the fact demonstrated by Lam et al. (1996) that the formula for the areatoperimeter 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 35. Figure 35 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 36). 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 35. 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, 45Wedge 0.80 0.70 a 0.60 0.50 L 0 0.40 a 0.30 45Wedge g 0.20 0.10 0.00 0 100 200 300 400 Field Area (cm x cm) Figure 36. 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 inair outputs for a pair of asymmetric wedged fields are summarized in Table 31, where we can see that the difference is less than 1%. The contribution of unattenuated photon to inair 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 31. Comparison of inair output factors between pairs of asymmetric wedged fields for the 8 MV photon beam of a Varian 2100C. The contribution of unattenuated photon to inair output is same for both fields. However, wedge scatter contribution is different. Data are normalized to the inair output of the field of thin part. Wedge Angle Inair 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 34, 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 areatoperimeter 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 = .,LW / 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 xray 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, 'wedgehead scatter factor' for wedged field. Head (or wedgehead) 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 areatoperimeter 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 wedgehead) 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 backprojection 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 wedgehead) 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 fielddefining 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 41, 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 41. 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 areatoperimeter 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 acceleratordependent. Methods and Materials Head (or wedgehead) 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 42. Figure 43 shows the measured wedgehead 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 areatoperimeter relationship (Sterling et al. 1964). The same data are plotted in Figures 44 and 45 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 41 and 42. 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 46 and Figure 47, respectively, according to the side of the equivalent square field obtained by Sterling's areatoperimeter 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. . FixX(30) 0.96 FixY(30) 0.96 0.95 0 5 10 15 20 25 30 Side of Eq. Square (cm) Figure 42. 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 areatoperimeter relation. 0 5 10 15 Side of Eq. Square Field (cm) Figure 43. Wedgehead 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 FixX(30) SFixY(30) 0.96 0.95 0 5 10 15 20 25 30 Side of Eq. Square Field (cm) Figure 44. 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, 45wedge, k=1.5 1.06 1.04 I 1.02 LL I 1.00 o 0.98 0.96  Square FixX(20) 0.94 FixY(20) 0.92 0 5 10 15 20 Side of Eq. Square Field (cm) Figure 45. Wedgehead 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 / FixX(30) SA FixY(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 46. 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, 60wedge, k=1 1.07 1.07 1.05 S 1.03 ,, A . 1.01 g 0.99 0.97 S0.95  Square 0.93 FixX(30) SFixX(30) 0.93 1 / FixY(30) 0.91 0.89 0 5 10 15 20 25 30 Side of Eq. Square Field (cm) Figure 47. Wedgehead 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 48 and 49, 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 fielddetermining 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 FixX(30) 0.95 FixY(30) 0.94 0.93 0 5 10 15 20 25 30 Side of Eq. Square Field (cm) Figure 48. 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, 60wedge, k=1.85 1.09 a _ 1.07 1.05 I 1.03 1.01 S0.99 0.97 Square S0.95 FixX(30) 0.93 FixY(30) 0.91 0.89 0 5 10 15 20 25 30 Side of Eq. Square Field (cm) Figure 49. Wedgehead 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 wedgehead 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 wedgehead scatter in Figure 45 show that Eq. (4.9) gives an accurate calculation of output even for a Variantype 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 INAIR 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 tissueairratio (TAR) or tissuemaximum ratio (TMR), are calculated based on the actual field shape created by a custom Cerrobend block, but the inair 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 inair 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 inair output can be significantly different from the one obtained with conventional methods. Many authors have studied the physical origin of inair 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 fielddefining 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 modelbased 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 inair output calculation formalism was set up and a simple algorithm for calculation of inair 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 contributorsflattening filter, wedge, and tertiary collimatorare 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 nonlinearity of inair 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 inair 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 inair 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 Inair 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 inair 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 51. In Figure 51, 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 detectortosource 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 51. 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 ith 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, inair 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 inair 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 52 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 52. 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, inair 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 inair 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 Inair output factors of tertiary collimator shaped 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. A shonka plastic 0.1 cc ionization chamber was inserted in the miniphantom 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 miniphantom 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, inair output factors of two irregular fields were also measured. One shape was made with Cerrobend material and the other was made with MLC. Figures 53 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, inair 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 53. 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 54. 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 55. 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 55 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. Inair Output Factor of Open Fields Defined by Tertiary Collimator Inair 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 56 and 57, 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 inair 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 55. 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 56. Inair 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 57. Inair 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 inair 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 56 and 57 that the conventional method of calculating inair inair 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 inair output very well but it underestimates the inair output if the tertiary collimator scatter factor is not included. Once the tertiary collimator scatter factor is included, the agreement between the calculated inair output and measured inair 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 inair 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. Inair 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 58. In the Figure 58 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), inair output factor of wedge field was calculated and compared with measured data in Figure 59. Since block can not 0 5 10 15 20 Side of Square Field (cm) Figure 58. 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, 45External 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 59. Inair 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. Inair 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 inair output factor value for all field sizes. Field mapping method through DEV field without separating S, always overestimated the inair 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. Inair Output Factor of Irregular Shaped Fields Inair output factors for irregular fields were calculated and compared with experimental data in Table 51 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 inair output factors matched well with the measurements. The maximum difference was less than 0.5 %. Inair output factors obtained by conventional method were also tabulated in Table 51 for comparison. The conventional method tends to overestimate inair 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 51. Inair 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. Inair output factors obtained by conventional method are also included for comparison. Beam's eye view irregular field shapes are shown in Figures 53 and 54. Tertiary Collimator Energy (MV) Inair 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 56, 57, and 59. A close examination of Figure 56 shows that as the field is increasingly blocked, the relative inair 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 inair output accurately. The tertiary collimator scatter from field shaping blocks must be included to achieve better accuracy. Even the calculations show lower relative inair 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 57 indicates that the amount of scatter contribution from MLC is not significant. Therefore, it may not be necessary to consider MLC scatter factor for inair 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 59. 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, inair 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 sourcetodetector (SDD) distance changes, the inverse law has been used to calculate inair 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 inair 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 inair output factor calculation algorithm based on field mapping through the detector's eye view field was developed and programmed. This method can predict inair 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 inair 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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