UFDC Home  Search all Groups  UF Institutional Repository  UF Institutional Repository  UF Theses & Dissertations  Vendor Digitized Files   Help 
Material Information
Subjects
Notes
Record Information

Full Text 
OPTIMAL DELIVERY TECHNIQUES FOR INTRACRANIAL STEREOTACTIC RADIOSURGERY USING CIRCULAR AND MULTILEAF COLLIMATORS By THOMAS H. WAGNER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2000 Copyright 2000 by Thomas H. Wagner This work is dedicated to my loving wife and friend, Nanette P. ParrattoWagner. ACKNOWLEDGMENTS I would like to express my sincere appreciation for the guidance provided me by the members of my supervisory committee. I would especially like to thank my committee chairman, Dr. Frank J. Bova, from whom I have learned much about medical physics and whose mentoring has been a key component of the successes I have enjoyed during my doctoral work. I would also like to thank and acknowledge the contributions of Dr. Sanford L. Meeks, who has always encouraged me to go beyond simply the academic requirements and to strive to publish my work, and of Dr. Beverly L. Brechner, who invested much of her personal time in teaching and coaching me through elementary topology and set theory, as well as contributing key ideas for our joint sphere packing project. I am grateful to Dr. Willaim A. Friedman and Dr. John M. Buatti for all of the valuable clinical feedback, mentoring, and support I have received from them during my doctoral work and association with the University of Florida stereotactic radiosurgery program. I also owe special thanks to Dr. Taeil Yi for contributing his ideas and for his initial computer programming efforts in our joint sphere packing project, and to Dr. Yunmei Chen, whose contributions played a key role towards the success of our joint spherepacking project. Drs. Brechner, Yi, and Chen are all from the University of Florida Department of Mathematics. I would like to give my most sincere thanks to Dr. Lionel G. Bouchet for many hours of insightful technical discussions about numerous aspects of my research, and especially for his computer programming efforts towards transferring image and anatomical structure data between the several treatment planning systems in our lab. I am grateful to Russell D. Moore for his invaluable aid in helping me navigate and use the myriad of Unix computer systems necessary to perform my research work, and to Lisa Mandell for her assistance in gathering radiosurgery patient data from the University of Florida SRSpatient database. I would like to thank Dr. Wesley E. Bolch for his support and encouragement for the entire time I have been a graduate student at the University of Florida, and to Dr. Kelly D. Foote for many hours of insightful conversations about radiosurgery and neurological surgery, and for his patient tutoring and assistance in contouring brain lesions and other intracranial structures. Finally, I am deeply indebted to my friend and wife, Nanette, without whose support and loving encouragement I would not have had the strength to begin, let alone complete, the last several years of my life in graduate school. TABLE OF CONTENTS ACKNOWLEDGMENTS ......................................................................................... iv A B STR A CT .................................................................................... ...viii CHAPTERS 1 IN TRO D U CTION ...................................................................................................... Megavoltage Photon Radiotherapy And Radiosurgery .................................... ...... 1 Technical Evolution and Improvements Stereotactic Radiotherapy.......................... 5 Linear Accelerator Radiosurgery and Radiotherapy Treatment Techniques.................. 6 Technical Evolution and Improvements Linear Accelerator Radiation Delivery ....... 9 Research Problem: Comparison of SRS Treatment Methods................................... 13 2 EVALUATION OF TREATMENT PLANS ...............................................................17 D ose C alculation...................................................................................................... 18 Isodoses and Dosevolume Histograms ................................................................... 30 Physical Dosevolume Figures of Merit .............................................................. 37 Biological M odels................................................................................................... 49 3 OPTIMIZED RADIOSURGERY TREATMENT PLANNING WITH CIRCULAR CO LLIM A TO RS .........................................................................................................57 Circular Collimator SRS Dosimetry.................................................................... 58 Single Isocenter Treatment Planning.................................................................... 60 Multiple Isocenter Radiosurgery Planning Tools .................................... ............ 70 Multiple Isocenter Radiosurgery Planning via Sphere Packing ............................... 80 Converting SpherePacking Arrangements to Radiosurgery Plans .......................... 94 Application to Phantom and Clinical Targets......................................... ........... ... 95 Results Phantom Targets ...................................................................................... 97 Results Clinical Targets ........................................................................................ 98 Sphere Packing as a MulitpleIsocenter Radiosurgery Planning Tool ..................... 103 Sphere Packing Algorithm: Potential Developments ................................................. 105 C conclusion ............................................................................................................ 108 4 SHAPED BEAM SRS ............................................................................................ 109 Introduction ...................................................................... ........................................ 109 Generation of Isotropic Beam Bouquets............................................... .......... .... 111 Rotation of Beam Bouquets ........................................................................................ 127 Generation of Beam's Eye Views (BEVs).................................................................. 129 Field Shaping with Multileaf Collimators ............................................................. 134 Shaped Field D osim etry.............................................................................................. 139 Optimization of Isotropic Beam Bouquet Orientation................................................ 140 Limits on Adjusting Beam Positions from the Initial Isotropic Beam Bouquet......... 147 Appropriate Number of Beams for Use in Shaped Beam SRS Planning ................... 157 Application of Isotropic Beam Bouquets Nine Beam Plan for Meningioma .......... 162 Dynamic Arcs with MLC...................................................................................... 169 C conclusion ............................................................................................................ 172 5 INTENSITY MODULATED SRS WITH FIXED BEAMS .....................................174 Introduction........................................................................................................... 174 Intensity Modulated Radiotherapy (IMRT).............................................................. 175 IMRT Treatment Planning with CadPlan/Helios.................................................. 182 Example Nine Beam and Nine IntensityModulated Beams for Meningioma........ 187 Multiple Isocenters as a Special Case of IMRT.......................................................... 196 6 SRS METHODS COMPARISON ....................................................................199 Introduction........................................................................................................... 199 Clinical Example Case Data....................................................................................... 202 Comparison of Alternative SRS Treatment Delivery Methods to Multiple Isocenter SRS with Circular Collimators ................................................................................... 268 Strengths and Weaknesses of Multiple Isocenters and IMRT.................................. 277 Applying the Results of this Research to New SRS Cases....................................... 287 C onclusions............................................................................................................ .. 289 7 CONCLUSION.........................................................................................................291 LIST OF REFERENCES.......................................................................................... 297 BIOGRAPHICAL SKETCH ...................................................................................... 305 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy OPTIMAL DELIVERY TECHNIQUES FOR INTRACRANIAL STEREOTACTIC RADIOSURGERY USING CIRCULAR AND MULTILEAF COLLIMATORS By Thomas H. Wagner August 2000 Chairman: Francis J. Bova Major Department: Nuclear and Radiological Engineering The University of Florida stereotactic radiosurgery (SRS) system is a well established system of single fraction, highly conformal linear accelerator based radiation therapy for intracranial lesions. As originally implemented, the system is characterized by the delivery of circular radiation beams with multiple arcs of megavoltage photon beams all impinging on the target. The introduction of multileaf collimators (MLCs) and computercontrolled treatment machinery offers the opportunity to plan and deliver more complex radiation treatments that may apply dose to the target while applying less dose to nontarget tissues. There are numerous treatment techniques that may be employed with such equipment, including multiple static fields, dynamic conformal arcing treatments, and treatment with intensity modulated radiation therapy (IMRT) fields. This expanded list of patient treatment options poses a new problem to the treatment planner: determining the optimum treatment method for a given patient. Although many centers viii report the expanding use of these and other treatment techniques, there are few, if any, reports that offer definitive comparisons of the major treatment techniques against one another. The purpose of this research was to compare radiosurgery plans using MLC static fields, dynamic conformal arcs, and IMRT, with radiosurgery plans using circular collimators and multiple isocenters, and to determine which of the MLCbased treatment methods provides the best results. Representative clinical example cases from the University of Florida radiosurgery patient database were used to examine the dosimetric performance of each type of treatment delivery. Analysis of these clinical example cases shows that circular collimators with multiple isocenters deliver dose distributions equal to or better than MLCbased techniques for every example case studied. IMRT radiosurgery treatments can yield results comparable to multiple isocenters, for cases involving larger sized targets that would require more than about fifteen isocenters, and for targets with relatively smoothsurfaced threedimensional shapes. For most target shapes, multiple isocenter dose distributions are more conformal and provide a steeper dose falloff outside of the target than the MLCbased treatment methods. The software tools developed for this research can also be employed in a clinically useful timeframe to develop patientspecific optimized treatment plans to assist in this determination. CHAPTER 1 INTRODUCTION Megavoltage Photon Radiotherapy And Radiosurgery Conventional external beam radiotherapy, or teletherapy, involves the administration of radiation absorbed dose to cure disease. The general teletherapy paradigm is to irradiate the gross lesion plus an additional volume suspected of containing microscopic disease not visible through physical examination or imaging, to a uniform dose level. External photon beams with peak photon energy in excess of 1 MeV are targeted upon the lesion site by registering external anatomy and internal radiographic anatomy to the radiation (beam) source. Due to uncertainty and errors in positioning the patient, the radiation beam, which is directed at the lesion, may need to be enlarged to ensure that errors and uncertainty in patient positioning do not cause the radiation beam to miss some or all of the target. Unfortunately, enlarging the radiation beam results in a relatively large volume of nondiseased tissue receiving a significant radiation dose in addition to the target. For instance, adding only a 2mm rim to a 24mm diameter spherical volume to ensure that the 24mm diameter target is covered even with a 2mm positional error will increase the irradiated volume from 7.2 cm3 to 11.5 cm3, an increase of 60% (Bova 1998a). It has long been known that for many cancerous diseases, a radiobiological advantage is realized by administering the total radiation dose in small doses (fractions) over an extended period of time. Bergonie and Tribondeau discovered this principle in the early twentieth century by experimenting to determine the doses of xrays to the testes required to sterilize male goats (Hall 1994a). They discovered that they could not administer a high enough dose of xrays to the testicles to cause sterilization without also causing a severe skin reaction in tissue adjacent to the testicles. However, when they administered the xray dosein small doses, given once a day over several weeks, sterilization without an adverse skin reaction was possible. They postulated that the testes were a model of tumor tissue, while the adjacent skin served as a model of dose limiting, normal tissue. Although these assumptions are now known to be false, the conclusion was valid, that in most cases, for a given level of normal tissue toxicity, better tumor control may be achieved with multiple dose fractions over an extended time. In contrast to conventional, fractionated radiotherapy, stereotactic radiosurgery (SRS) involves the administration of a relatively large, single dose of radiation (10 Gy to 20 Gy) to a small volume of disease, thereby abandoning the advantages provided by fractionation. Lars Leksell conceived of the idea of radiosurgery in 1951 (Leksell 1951). His original idea involved using many beams of orthovoltage xrays converging on an intracranial target to create a lesion. Leksell's idea, known as the Gamma Knife or gamma unit, was practically implemented in 1967 using an array of 170 Co60 sources, each of which emitted megavoltage gamma rays through radioactive decay (Leksell 1983; Colombo 1998). The decay gamma rays were collimated with holes bored in a large radiation shield to converge to a single point inside the patient's head. The use of secondary collimator helmets, each with different size holes (4, 8, 14, and 18 mm diameter), allowed for the creation of several sizes of a spherical, high dose region (Maitz 1998). Irregularly shaped lesions could be produced by "stacking" spherical regions together to build up complex shapes. The patient's skull was positioned with sub millimetric precision using a minimally invasive hearing that attached to each size of collimator helmet (Wasserman 1996). Linear accelerators linacss) were first used for radiosurgical use in the 1980s. Betti and Derichinsky reported using a linear accelerator with multiple fixed, isocentric beams in 1983 (Betti 1983). Several investigators reported using multiple converging arcs with a linac by 1985 (Colombo 1985; Hartmann 1985). By fitting an isocentric linear accelerator with circular collimators, multiple beams and/or arcs of radiation could be made to converge upon the machine's center of rotation, where the patient's tumor had been positioned. By such a means, dose distributions very similar to those of the gamma knife could be produced with megavoltage photons from a linac, rather than from the decay of radioactive sources. A significant practical difficulty of using an isocentric linear accelerator, however, lies in overcoming the mechanical inaccuracy of rotation inherent in heavy rotating equipment. A common upper limit on allowable mechanical error ("wobble") of rotational center of linear accelerator gantrys is 2mm, plus an additional 2mm error in the treatment couch rotation accuracy. Added in quadrature, the resultant total possible error between the expected and actual radiation isocenter can be as high as 2.8 mm, about an order of magnitude larger than the mechanical error associated with gamma unit treatments. If the mechanical inaccuracy of the treatment machine cannot be resolved, the radiosurgeon would need to increase the size of the radiation therapy beam in order to ensure that the target being treated is completely covered. Addition of even one or two millimeters of extra margin to a radiosurgical treatment beam has a markedly undesirable effect, however, by drastically increasing the volume treated to the target (prescription) dose. It is therefore strongly to the radiosurgeon's advantage to improve the mechanical and overall system accuracy in positioning the patient, in order to allow using treatment beams of the minimum necessary size (Meeks 1998a). By reducing the volume of nontarget tissue irradiated to high levels, the likelihood of incurring a complication (adverse reaction to the radiation treatment) may be minimized. The University of Florida radiosurgery system was developed in the mid1980s as a solution to the above mentioned problem of linear accelerator radiosurgery (Friedman 1989; Friedman 1992; Meeks 1998b). By using an isocentric system, as indicated by the arrows in Figure 11, to position the patient and to provide tertiary, circular collimation of the xray beam, the system allows a linear accelerator to be used to deliver radiosurgical treatments (Figure 12) with mechanical accuracy comparable to a gamma unit. Figure 11: University of Florida radiosurgery system : isocentric subsystem in place under the gantry of a linear accelerator linacc). Figure 12: Time lapse photograph showing arc rotation of the linac gantry about the patient during treatment. The patient's lesion has been positioned at the radiation isocenter with a stereotactic hearing and the isocentric subsystem. Technical Evolution and Improvements Stereotactic Radiotherapy Although minimally invasive, the hearings associated with gamma unit and linear accelerator radiosurgery make the administration of multiple radiation doses infeasible. Some physicians have experimented with leaving the stereotactic hearing on the patient for extended periods to allow a series of treatments over this time. Although it is possible to overcome problems with local infection and patient discomfort, these difficulties have generally caused other practitioners to avoid using this method of stereotactic radiotherapy (Schwade 1990). The application of noninvasive stereotactic localizing techniques allows easier delivery of repeated radiation treatments to a stereotacticallylocated lesion. The GilThomasCosman headframe is one example of how this may be done, relying on a headframe which locates to the patient's head by means of a dental mold (a "biteplate", or "biteblock"), occipital headrest, and a strap to tightly hold the frame to the head (Reinstein 1998). Systems such as these, which combine the functions of immobilization and positioning, tend to suffer reduced accuracy because of immobilization forces that are inevitably applied to the reference positioning system. Optically guided systems have been developed recently, however, which de couple the positioning function from the immobilization function. Such systems have been demonstrated to provide patient positioning with smaller errors than previous systems. One such optically guided system has demonstrated the ability to position the patient within about 1.1 mm error at isocenter, which while not as small a positioning error as attainable with an invasive stereotactic heading, is still significantly better than previous systems (Bova 1997; Bova 1998b). Because of such new, noninvasive stereotactic techniques, radiosurgery treatments can be administered in multiple fractions (Figure 13). Such fractionatedd radiosurgery" is generally known as stereotactic radiotherapy (SRT). Linear Accelerator Radiosurgery and Radiotherapy Treatment Techniques The major treatment techniques used to deliver linac radiosurgery treatments are circular collimators with arcs, conformally shaped beams, and intensity modulated radiotherapy (IMRT). Circular collimators can be used to create spherical regions of high dose. When used with linear accelerators, the circularly collimated beam is rotated around the target at isocenter by moving the gantry in arc mode while the patient and treatment couch are stationary, producing a parasagittal beam path around the target. Betti and Derichinsky developed their linac radiosurgery system with a special chair, the "Betti chair," which moved the patient in a side to side arc motion under a stationary linac beam, and which produced a set of paracoronal arcs. With modem, computer controlled linear accelerators, more complex motions other than these simple arcs are possible. The Montreal technique, which involves synchronized motion of the patient couch and the gantry while the radiation beam is on, is an example of this, producing a "baseball seam" type of beam path (Wasserman 1996). The rationale of using arcs with circular collimators is to concentrate radiation dose upon the target, while spreading the beam entrance and exit doses over a larger volume of nontarget tissue, theoretically reducing the overall dose and toxicity to nontarget tissue. 4 Figure 13: Patient positioned under the linear accelerator with biteblock optically guided system. A system of stereo cameras out of the picture's field of view senses the position of the reflective spheres attached to the biteblock in the patient's mouth. This system allows precise and repeatable patient positioning without the need for an invasive stereotactic hearing (shown attached to the patient in Figure 12). The white mask is an immobilization aid to assist the patient in remaining motionless during the treatment. The technique of multiple converging arcs delivered with circular collimators produces a spherical region of high dose with a steep dose gradient, or falloff. This dose distribution is adequate for treating a sphere or round target, but will treat a large volume of nontarget tissue to high dose if the sphere encompasses an irregularly shaped target. Multiple spheres of varying sizes may be "stacked" together to produce a high dose region which conforms closely to the shape of the target while still maintaining a sharp dose gradient, as shown in Figure 14 (Meeks 1998b). Figure 14: Conformal dose distribution produced by circular collimators and multiple isocenters. Several isocenters, each with a set of converging arcs, have been placed near one another to conform the composite dose distribution to the target's shape. An alternative means of delivering a linac radiosurgery treatment is to employ beams which are shaped to conform to the target's shape as seen from the direction of the beam, or "beam's eye view." Conventional radiotherapy practice is to use diagnostic x ray radiographic or flouroscopic images of the patient obtained in a simulator session to determine the beam's shape. In recent years, the three dimensional image sets from computed tomography or magnetic resonance image scans have been used to construct threedimensional models of the patient and internal structures, such as the target. These models of each patient structure may be used to determine the placement of radiation beams, and to design each beam's shape. Technical Evolution and Improvements Linear Accelerator Radiation Delivery Both the gamma unit and early linear accelerator radiosurgery systems produced similar spherelike dose distributions using either multiple static, circular beams (gamma unit) or multiple circular beams swept though several arcs (linear accelerator). However, the linear accelerator offers additional flexibility over the gamma unit in that multiple collimation devices may be used to produce noncircular beams, and beams with non uniform intensity profiles across the beam. This additional flexibility in radiation delivery potentially offers the ability to more closely tailor the dose distribution to the target volume with a linear accelerator than with a gamma unit. The beam shaping and modulation devices used with linear accelerators for these purposes include custom beam shaping blocks, wedge beam filters, custom beam compensating filters, and multileaf collimators. Also, linear accelerators typically can deliver a much larger range of radiation beam sizes, upwards to a 40 cm x 40 cm square field at 100 cm from the radiation source. The simplest beamshaping device used with linear accelerators (other than the machine's secondary collimators, which typically produce rectangular fields up to a 40 cm x 40 cm square field at the machine's isocenter) is the custom block. Such blocks are individually constructed by pouring low melting point alloy (cerrobend) into a mold, which is attached to a mounting tray. The edges of the apertures defined in the hardened metal block are designed to match the divergence of the radiation beam emanating from the treatment machine. A separate block must be manufactured for each beam that will be used to treat the patient. Although offering the best possible match between the shape of the target and the shape of the beamdefining aperture, the time and cost of manufacturing such blocks limits the number of blocks and radiation beams which can be used to treat a patient. Wedge beam filters may be used with or without the presence of beam shaping devices such as the custom blocks mentioned above. Wedge filters are placed in the path of the photon beam in order to tilt the shape of the isodose distribution. This provides a simple onedimensional intensity modulation across the treatment field, which is often advantageous to the treatment planner in obtaining a more homogeneous dose distribution in the target volume. This is desirable in certain cases, for example where the patient's anatomy changes significantly over the extent of the field. Proper placement of a wedge filter in this case can effectively compensate for missing tissue on one side of a treatment field. Wedges are also commonly used to reduce dose heterogeneity ("hotspots") in regions of beam overlap inside the target (Khan 1994, Ch. 11). The idea of using a filter to modulate the beam intensity across the treatment beam is extendable to a twodimensional intensity modulation. A typical such 2D compensating filter is generally used to adjust the beam intensity over a grid of small square regions, with the goal of obtaining a uniform dose distribution in a plane near the target. Such devices are designed for each patient, and are typically constructed by placing differing thicknesses of dense, radiation absorbing material such as brass in a checkerboard type pattern on a tray that is placed in the beam path. This can be done by hand, or by use of a computercontrolled milling machine which custom machines a single piece of radiation absorbing material into the desired shape (Purdy 1996). Although the dose distribution around the target may be made more homogenous by such devices, they share a disadvantage of custom blocks in excessive labor costs. Additionally, compensators requiring manual construction can remain a source of potential treatment errors despite quality assurance. These factors limit the usefulness and number of fields to which such beam modifying devices may used (Hall 1961; Sundbom 1964; Grijn 1965). Multileaf collimators (MLCs) are mechanical beam collimating devices that can combine some or all of the functions of beam shaping blocks, wedge filters, and custom compensating filters discussed above (Figure 14). The most common type of MLC consists of two banks of opposed leaves of radiation absorbing metal that can be moved in a plane perpendicular to the beam's direction. The MLC can be rotated with the treatment machine's collimator in order to align the leaves for the best fit to the target's projected shape. The simplest use of an MLC is simply as a functional replacement for custom made beam shaping blocks, in which the rectangular MLC edges are used to approximate a continuous target outline shape (Figure 15) (Brewster 1995). However, the MLC may be used in a more sophisticated fashion to form many different beam shapes of arbitrary size and intensity (by varying the amount of radiation applied through each beam aperture). In this manner, radiation fields with a similar dose profile as a shaped, wedged field may be delivered using only the computercontrolled MLC. MLCs can also deliver intensity modulated dose profiles similar to those achievable using custom beam compensators, but without the disadvantages of fabrication time or of needing to manually change a physically mounted beam filter between each treatment field (Stemick 1998). Thus, a.computercontrolled MLC and treatment machine offer the potential to deliver more sophisticated radiation treatments to each patient with the same time and cost resources available. Moss investigated the efficacy of performing radiosurgery treatments with a dynamically conforming MLC in arc mode, and concluded that dynamic arc MLC treatments offered target coverage and normal tissue sparing comparable to that offered by single and multiple isocenter radiosurgery (Moss 1992). Nedzi (Nedzi 1993) showed that even crude beam shaping devices offered some conformal benefit over single isocenter treatments with circular collimators. ris Figure 15: Multileaf collimator (arrows) attached to the gantry of a linear accelerator. The MLC leaves define a small square aperture in this picture. Figure 16: The narrow, rectangular MLC leaves conform the radiation field's shape to approximate an irregularly shaped target's shape (solid line), as seen in this beam's eye view (BEV). Research Problem: Comparison of SRS Treatment Methods The potential for improvement presented by some of these newer and more sophisticated treatment delivery methods has spurred interest in their evaluation relative to the more traditional linac SRS methods of multiple intersecting arcs and circular collimators. These comparisons generally show that for small to medium (up to about 20 cm3) intracranial targets, multiple static beams offer acceptable conformity and target dose homogeneity while offering a straightforward treatment planning process. Static beam IMRT techniques generally performed comparably to or better than static beam plans. A common conclusion by many of these investigators is that the use of multiple isocenters with circular collimators results in a poor quality treatment plan, as evidenced by the performance of the multiple isocenter plans they used to compare with the static beam and IMRT plans. Even in reports more favorable to multiple isocenter linac SRS, the investigators frequently note difficulty in achieving conformal and homogeneous plans, and also note needing a large amount of time to plan and deliver these treatments. Based on a number of recent comparisons of radiosurgery methods in the literature, one could roughly expect to obtain a reasonably conformal (exposing up to about the same volume of nontarget brain tissue as target tissue to the target dose level) and homogeneous (maximum dose not more than about twice the minimum target dose) dose distribution for various IMRT and mMLC treatment techniques, and moderatetolarge sized, irregularly shaped intracranial lesions. Typical multiple isocenter plans presented fare considerably worse, though, in terms of dose conformity, homogeneity, and in treatment planning and delivery times (Laing 1993; Hamilton 1995; Woo 1996; Shiu 1997; Cardinale 1998; Kramer 1998; Verhey 1998). A potential problem with these comparison studies is that they do not equitably compare the full potential of multiple isocenter radiosurgery with circular collimators. A qualitative inspection of the multiple isocenter dosimetric results shown in these comparisons leads one to suspect that in many cases, suboptimal multiple isocenter plans are being compared with reasonably optimized static beam and dynamic MLC arcs/IMRT plans. Although the multiple isocenter treatment plans in these comparisons in the literature may represent a level of plan quality achievable by an average or unfamiliar user, they do not represent the average level of plan quality in the University of Florida experience. Unlike other evaluations readily available in the literature, an evaluation of the best employment of an MLC in radiosurgery treatments at the University of Florida must consider the typical quality of treatment plan that is readily achievable in the University of Florida clinical experience. The research problem posed is to evaluate the major SRS treatment delivery methods that could be implemented clinically at the University of Florida, and other institutions using the University of Florida radiosurgery system. Many claims are being circulated about some of the newer methods mentioned earlier of employing teletherapy beams for SRS treatment. The University of Florida radiosurgery system has demonstrated the ability to plan and deliver tightly conformal dose distributions to irregularly shaped targets near radiosensitive structures, while maintaining a sharp dose gradient away from the target towards radiosensitive structures (Meeks 1998a; Meeks 1998b; Meeks 1998c; Foote 1999; Wagner 2000). While it may be attractive to contemplate the replacement of the current circular collimator system with more advanced and elaborate treatment delivery methods, such a decision should be based on a reliable study. The purpose of this research is to investigate the optimal implementation of a multileaf collimator (MLC) system for SRS at the University of Florida. An MLC could be employed in several different ways: 1) dynamic conformal arc treatments with templated arc sets, 2) multiple fixed, conformal beams, and 3) multiple fixed, intensity modulated beams. These treatment delivery options are to be compared against multiple isocenters with circular collimators. In order to ensure a proper comparison, a reasonable optimization strategy is employed for each treatment delivery technique to guard against inadvertently biasing the comparison against one or the other treatment methods. To this end, automatic planning and optimization tools were developed for multiple isocenter SRS and for multiple static beam SRS. Due to the fewer number of variables involved, treatment planning for dynamic MLC arc treatments will be based primarily on standard arc templates or sets. Chapter two provides a discussion of treatment plan evaluation techniques and tools. Chapter three is devoted to optimal treatment planning methods with circular collimators, chapter four to shaped beam radiosurgery planning, and chapter 16 five to fixed beam IMRT planning. Chapter six is devoted to the actual comparisons of each technique to an array of example cases, on which the guidelines and recommendations for optimal employment of an MLC at the University of Florida are based. CHAPTER 2 EVALUATION OF TREATMENT PLANS Evaluating the suitability of a stereotactic radiosurgery or radiotherapy treatment plan requires the human planner to assimilate and analyze a vast quantity of three dimensional dose information. Given the distribution of radiation dose in three dimensions in the vicinity of the target, the planner must assess how well the prospective plan accomplishes the treatment goals of uniformly irradiating the target to a high dose level while sparing nearby radiosensitive structures from the effects of a large radiation dose. This chapter presents currently accepted methods and tools for analyzing stereotactic radiosurgery and radiotherapy dose distributions. In two dimensional radiotherapy planning, doses are calculated on a two dimensional slice in a single plane through the target, assuming that the slice chosen is representative of the entire target region, and that the slice is semiinfinite in extent (extends infinitely in both directions perpendicular to the plane of interest). Dose distributions are generally displayed as isodose curves superimposed upon either the patient contour or a single CT image slice though the region of interest. Plan evaluation is based upon inspection of the isodose curves overlaid upon this single slice or image. In three dimensional radiation therapy planning, evaluation of the three dimensional dose distribution involves the processing of considerably greater amounts of information. The calculation of radiation absorbed dose is fundamental to radiation therapy, in order to predict and control the radiation dose delivered to the lesion, and to nontarget regions inside the patient. This section provides a discussion of general methods of dose calculation for radiotherapy and radiosurgery situations, followed by a presentation of methods to evaluate the efficacy of a radiation dose distribution. The general aims of radiotherapy and radiosurgery are simple: to deliver a high, uniform dose to the target while minimizing the radiation dose to nontarget structures. There are several tools available to the human treatment planner to quantify the degree to which these goals are accomplished: 1) isodose curves and distributions, 2) dosevolume histograms, 3) physical dosevolume figures of merit, and 4) biological models of tissue response to radiation. The following sections explain the use of each of these tools in radiation therapy and radiosurgery treatment planning, after a discussion of methods for calculating radiation dose distributions. Dose Calculation The purpose of dose calculation in radiotherapy is to be able to accurately determine the dose to target and nontarget structures inside the patient. An ideal calculation of absorbed dose to matter in all regions of interest in megavoltage external beam radiotherapy would correctly account for all of the interactions between the megavoltage photons in the therapy beam and the matter in the patient. The most accurate current methods of computing the spatial distribution of the deposition of radiation dose involve probabilistically simulating the transport of many individual radiation beam particles from their point of emission in the radiation source, using random number processes (hence the name "Monte Carlo" to describe this calculation method). Enough particles must be simulated to provide a statistically significant tally of radiation particle interactions in each region of interest, often requiring lengthy computing times to simulate the radiation transport of many (millions of) particles. This dose calculation method is attractive because it is based on first principles of radiation physics, and can therefore correctly account for any specific patient situation. However, the amount of computation time generally required by present day computers limits its usefulness in clinical situations. Because of these difficulties in calculating absorbed dose distributions from first principles of physics, the most common approach taken in radiation therapy has been to use simpler models relying on direct measurements of dose. Typically, these models involve using various radiation detectors to directly measure the dose distribution in a water phantom, and applying corrections to the measured dose distributions to account for differences between the water phantom and each actual patient situation. The dose calculations in this report rely on such models of dose distributions. A brief discussion of the dose calculation procedure for a rectangular solid water phantom follows, in order to facilitate the explanation of the dose calculation process for clinical radiosurgery situations. The dose profile as a function of depth in a water phantom (setup shown in Figure 21) from a normally incident radiation beam is shown in Figure 22. This plot shows the absorbed dose measured in water with a stationary radiation detector placed at the isocenter of the linear accelerator. As the detector's depth to the water surface is increased by adding water to the water phantom (which is a tank of water), there is a greater thickness of water interposed between the radiation source and the detector, so that the water absorbs more of the radiation beam. The curve is approximately exponential in shape, but is not a pure exponential due to the nonlinear variation in scattered radiation dose to the detector with changes in water depth, and due to beam hardening effects at greater depths. The radiation absorbed dose data measured in this manner is commonly referred toas "Tissue phantom ratio" (TPR) when the dose is normalized to the dose at a particular depth (Khan 1994). TPR data is measured for each circular radiosurgery collimator (Duggan 1998), or may be interpolated for a given collimator from data tables of several collimators spanning a range of sizes (Surgical Navigation Technologies 1996). Linear accelerator (radiation source) \ Colli photos Source to axis distance (SAD) Water surface Central axis of beam Radiation detector at isocenter of the linear accelerator Figure 21: Schematic of setup for measuring radiation dose as a function of depth in a water phantom depth 1.000 S0.800 E 0.600 E S0.400 S0.200 0.000 0 5 10 15 20 25 30 Depth to water phantom surface (cm) Figure 22: Tissuephantom ratio (TPR) curve in water phantom for a 6 MV photon beam shaped with a 30 mm diameter circular collimator. The dose profile in a plane perpendicular to the central axis (along the "cross beam direction" in Figure 21) varies with distance from the central axis, and is thus measured with a radiation detector as well in order to allow calculation of the radiation dose at offaxis points. A plot of the radiation field intensity as a function of offaxis distance, in a plane 100 cm from the radiation source, is shown in Figure 23 for a 30 mm diameter circular radiosurgery collimator. This offaxis dose data is frequently normalized to either its maximum value, or to the dose at the central axis, and is also known as "offaxis ratio", or OAR. Like TPR data, OAR data may either be measured for each individual radiosurgery collimator, or may be interpolated from a table of measured OAR values for selected collimators. Due to changes in the relative dose profile with depth (due to changes in scattered dose and beam hardening effects), OAR profiles are usually measured at several depths in order to provide measured data under conditions close to those for which dose is being computed. 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 Off axis distance (cm) Figure 23: Offaxis ratio (OAR) curve for a single circular collimator The last measured quantity needed to calculate dose to any point inside the water phantom is output factor, also referred to as total scatter factor, Sc,p (Khan 1994). Sc,p accounts for changes in the dose due to changes in the radiation field size, and to changes from the scattered dose due to changes in the volume of phantom irradiated. Sc,p is the ratio of dose to a reference point on the central axis of the beam, to the dose to the same point but under standard conditions. In linear accelerator radiosurgery treatments, Sc,p is a function only of the collimator size (diameter) used, since the linear accelerator secondary collimators are normally placed in a constant position when using the radiosurgery circular collimators. A plot of output factor as a function of radiosurgery collimator size for a 6 MV linear accelerator at the University of Florida is shown in Figure 24. a a ao M! p 1.00 a 0.95 0.90 4 / ^ 0.85 o 0.80 0.75 5 10 15 20 25 30 35 Collimator diameter (mm) Figure 24: Output factor as a function of circular radiosurgery collimator diameter for a 6MV linear accelerator at the University of Florida. The above measured dosimetric data may be used to compute the dose to a point in the water phantom of Figure 25, as given in Eq. (21): r is (21) Dose(P) = k MU TPR(coll, depth(P)) OAR(P) Sc,co distsP Kdistscp) In this equation, k is the treatment machine's calibration constant, normally 0.01 Gy/MU, MU is the number of monitor units delivered by the treatment machine, distscp is the source to calibration point distance (nominally 100 cm for an isocentric machine calibration), dists.p is the distance from the source to point P, TPR(coll, depth(P)) is the TPR for the circular collimator being used at the depth of point P, Sc,pcoll is the total scatter factor, or output factor, for the circular collimator being used, and OAR(P) is an offaxis ratio representing the variation of dose away from the field's central axis (Khan 1994; Surgical Navigation Technologies 1996; Duggan 1998). Equation (21) provides corrections to the measured dose data (TPR, OAR, and Scp) to account for changes in the dose at point P from the dose to the reference point at the linear accelerator's isocenter. If point P is moved away from the isocenter in any direction, these corrections are needed due to changes in 1) the distanceof the dose point P from the source, 2) the distance of dose point P from the central axis of the beam, 3) of changing collimator sizes, and 4) of the changing water depth (attenuation) above point P. This dose model is simple and accurate under conditions similar to the conditions under which TPR, OAR, and Sc,p were measured, i.e. a flat surfaced, homogeneous mass of water. Radiation IIOURC 1 I1" I i Collimated / I beam ! Surface I dist4S~P) dit(SCP) Figure 25: Parameters for calculation of dose to point P in a water phantom from a single radiation beam. OAD is the offaxis distance. The simple dose model of equation (21) is used as the dose engine of the University of Florida radiosurgery treatment planning system, and of most other I depthP) I OAD(P) 1 \  Isooenter / Isooenter I radiosurgery dose planning systems that utilize circular collimators. In applying equation (21) to a radiosurgery treatment, one must assume that the contents of the patient's head are homogeneous, water equivalent, and that the geometry is similar to the reference measurement geometry shown in Figure 25. Since linear accelerator radiosurgery treatments with circular collimators are delivered with arcs of radiation rather than static beams, each arc is simulated as a set of static beams, spaced along the path of the arc. Typically, an arc of 100 degrees is simulated as eleven static beams, spaced 10 degrees apart (Figure 26). The radiation dose to any point is the sum of the doses to that point from all of the individual beams in the arc. Likewise, the dose to any point due to multiple arcs and isocenters is the superposition (sum) of the doses of all of the arcs associated with each isocenter. For any arrangement of radiosurgery beams or arcs, the dose is calculated to a grid of points spaced closely together. Isodose curves corresponding to the locus of isodose points may be constructed by interpolation amongst the points in the viewing plane for which dose has been computed. Dose grid point spacing should be no further apart than 2 mm, in order to properly sample the rapidly changing dose distributions characteristic of radiosurgery dose distributions (Schell 1995). / *Jy Figure 26: A 100 degree arc of radiation produced by a continuously moving beam, approximated by 11 beams spaced 10 degrees apart. Crosshairs indicate the center of rotation (isocenter). There are several departures from the idealized geometries shown in Figures 21 and 25 that can occur in clinical patient treatment situations, and which can potentially lead to errors between the actual dose to a point and the dose calculated with the dose model in equation (21). Inhomogeneities inside the patient or at the patient's surface can cause significant dose errors under certain circumstances, such as for large field sizes. An irregular (not flat) patient surface is one such example of inhomogeneity, shown in Figure 27. The curvature of the patient surface causes points 1 and 2 in Figure 27 to lie at different depths from the surface with respect to the beam. The resulting tissue deficit shown will cause the photon beam to undergo less attenuation from the source to point 2 than from the source to point 1. If the TPR for central axis point 1 is used to calculate the dose at points 1 and 2, then the dose to point 2 will be underestimated by equation (21), since point 2 is not as deep as point 1 (point 2 has a numerically larger TPR than point 1). For a typical adult patient with a cranial radius of curvature of about 7.5 cm, the tissue deficit from the center of a 10x10 cm2 square field is about 1.5 cm, which corresponds to a dose error of about 6% (for 6 MV photons attenuated at about 4% per cm of depth) at point 2, if the TPR for central axis point 1 is used instead. The magnitude of the tissue deficit increases as the field size increases, and decreases for smaller field sizes. For a 40 mm diameter circular field, the tissue deficit for the same radius of curvature is only about 2.6 mm, corresponding to slightly less than a 1% dose error. The tissue deficit and dose error for a 20 mm diameter field are only 0.6mm and 0.2%, respectively. Thus, for small (< 40 mm diameter) radiosurgery fields, the effect of surface irregularity (inhomogeneity) can be neglected without introducing undue error (several percent) into the dose calculation (Ahnesjo 1999). I ' I i I 1 ii Assumed flat surface for dose model Tissue deficit due to surface irregularity Figure 27: Tissue deficit due to an irregularity (inhomogeneity) in patient surface. The assumption that the interior of the patient is a homogeneous, water equivalent material can also lead to errors between the calculated (equation (21)) and actual dose to a point in some cases. For instance, the dose model in equation (21) does not account for the changes in beam attenuation due to differences in electron density from that of water, such as those encountered near air cavities (e.g. sinuses) and bone. Although methods such as the Batho powerlaw correction (Khan 1994; Ahnesjo 1999) exist to correct calculated doses for these effects, such corrections are generally not needed to obtain sufficient calculation accuracy in stereotactic radiosurgery or radiotherapy situations with many beams. A study by Ayyangar on two typical radiosurgery cases compared a simple dose model similar to that of equation (21), with a Monte Carlo dose model with and without inhomogeneity corrections. Not correcting the simple dose model for the passage of the beam through the cranium caused the uncorrected dose model to overestimate the dose by 1.5% to 2.5%, an acceptable amount of error. Applying a TAR ratio method correction, similar to the Batho powerlaw correction, reduced the dose calculation error further (Ayyangar 1998). The small size of the beams typical of stereotactic radiosurgery and radiotherapy allow the use of a relatively simple dose calculation model without sacrificing accuracy of dose calculation. This simplicity is important in that it allows much faster dose computations throughout the volume of interest, which is especially important given the large typical numbers of beams for which dose must be calculated in radiosurgery. Isodoses and Dosevolume Histograms Isodose curves overlaid upon the patient's threedimensional image set are an important plan evaluation tool, just as in twodimensional planning. To evaluate a three dimensional dose distribution by this method, however, the planner must examine the isodose distributions in a number of planes through the target region, which can be cumbersome for large targets occupying many planes in an image set. It is possible to display threedimensional renderings of three dimensional dose distributions on a flat computer display screen, but these are also very difficult to analyze. The problem with evaluating a threedimensional radiosurgery dose distribution, with it's sharp dose gradients, lies in discerning the dose received by many possibly overlapping structures around the target. Although a number of commercially available treatment planning systems can render threedimensional views of arbitrary isodose volumes in various shades of translucency, along with any structures that the user has identified, it is very difficult to determine precise (submillimetric) spatial relations between the target volume, particular isodose volumes, and radiosensitive structures. For this reason, it is usually necessary to evaluate a large number of two dimensional isodose plots through the region of interest to determine plan suitability. In a single two dimensional isodose plot, one may readily determine whether a particular isodose surface coincides with the intersection of any particular volume with the image plane, to an accuracy of within one image pixel in the plane of interest. Even this level (within an image pixel) of visual inspection precision can still lead to significant errors in assessing the volume of dose coverage for small intracranial targets. Consider a 20 mm diameter spherical radiosurgery target, for which we wish to evaluate dose coverage by inspection of an isodose line overlaid on the image set. A 10% volume error results if the isodose line is shifted half of one image pixel (one image pixel is 0.67 mm x 0.67 mm in a transaxial plane for a 512 x 512 CT image acquired with a 35 cm diameter field of view) inward or outward, which is the spatial resolution limit of our ability to discern positional shifts in the image set. The 20 mm sphere, 4.2 cm3 volume, would apparently be equally well covered by an isodose surface ranging in volume from 3.8 cm3 to 4.6 cm3. The volume error problem worsens as target size decreases, and results in a 20% volume error for a 10 mm diameter target. One can imagine then the difficulty in evaluating a large number of these isodose plots to within submillimetric image pixel resolution: on each image slice, one must examine and remember the isodose surface which encloses the target, and which isodose surfaces (and to which extent) intersect nearby radiosensitive structures. This is straightforward if somewhat tedious to do on one image slice, but the difficulty is magnified tremendously when each slice in a large region must be examined, and the dose area information from each slice integrated with the information from all the other image slices. A method of comparing the volumes of dose coverage that is less error prone is desirable. One commonly used solution to this problem is to use dosevolume histograms (DVHs). DVHs are a method of condensing large quantities of three dimensional dose information into a more manageable form for analysis. The simplest type of DVH is a "direct" histogram of volume versus dose (Lawrence 1996), as shown in Figure 28. This is simply a histogram showing the number of occurrences of each dose value within a three dimensional volume. Unfortunately, the spatial information of which specific volumes are exposed to each dose level is lost in the process of constructing a DVH. For this reason, DVHs are generally used clinically in conjunction with the evaluation of multiple isodose plots as mentioned earlier. The ideal treatment planning situation is one in which the target volume receives a uniform dose equal to the maximum dose, and the nontarget volume receives zero dose. This would be represented in a direct DVH by having a target histogram with only one nonzero bin at 100% dose (normalized to maximum dose), and to have a direct DVH of the nontarget volume with all dose bins receiving zero dose. Plots of ideal direct DVHs for target and nontarget volumes are shown in Figure 28. Figure 29 shows direct DVHs for target and nontarget volumes for a more typical (nonideal) radiosurgery dose distribution. Figure 210 shows direct DVHs from two hypothetical radiosurgery plans for a radiosensitive structure. 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 02 013 00 10 20 30 40 50 60 70 80 90 100 Relative dose 10 20 30 40 50 Relative dose Figure 28: Ideal target (A) and nontarget volume (B) direct DVHs. Note that in the ideal direct DVH of the nontarget volume (right side), the plot is empty, since there is no nontarget volume receiving any dose in the ideal case. 0.070 0.060 0.050 0.040 0.030 0.020 0.010 0.000 0 10 20 30 40 50 60 70 80 90 100 Dose (% of max) FIB 0.120 0.100 0.080 0.060 a S 0.040 0.020 0.000 0 10 20 30 40 50 60 70 80 90 100 Dose (% of max) Figure 29: Typical (nonideal) radiosurgery direct DVHs for target volume (A) and non target volume (B). A 1.0 0.8 1 0.6 o 0.4 S0.2 0.0 60 70 80 90 100  n 2.5 S2.0 1.5 S1.0  0.5 > 0.0 10.0 20.0 30.0 40.0 50.0 Dose (% max) Figure 210: Direct DVHs for a radiosensitive nontarget structure in two hypothetical treatment plans 10 20 30 40 50 Dose (% max) Figure 211: Cumulative DVH plot of the direct DVH data shown in Figure 210. Ideal cumulative target and nontarget DVHs 1.2 1.0 < .0 4 0 E 2 0.8  0 S4Target volume S0.6 Nontarget volume  0 It 0 .4   UM U. 0.2    0.0 0.0 20.0 40.0 60.0 80.0 100 Dose (percent of maximum) .0 120.0 Figure 212: Ideal cumulative DVH curve for target and nontarget volumes. The purpose of plotting two DVHs on a single set of axes is to allow a direct comparison between two or more dose distributions. In the example of Figure 210, "Plan 1" and "Plan 2" are being compared with respect to the radiation dose distribution delivered to the radiosensitive structure. As can be seen in the figure, it can difficult to evaluate competing plans using such direct histograms (Drzymala 1991). Above about 40 units of dose, both plans appear to be identical, but the two plans expose differing volumes of brainstem at doses less than about 40 units. It is difficult to determine whether one plan is better than the other from Figure 210. Plotting the dosevolume information in the form of a cumulative DVH makes it simpler to evaluate two similar DVHs against one another. A cumulative DVH is a plot of the same dose volume information as before, but with the modification that the y value displayed for each bin x is the volume receiving > dose x. Peaks in a direct DVH correspond to inflection points on a cumulative DVH curve. A cumulative DVH plot of the data in Figure 210 is shown in Figure 211. i ? r ~___; Cumulative DVHs will be used throughout the remainder of this report, unless otherwise noted. The information in DVHs can be used to compare rival treatment plans in many situations. Optimal DVH curvesfor target structures will be as far towards the upper right hand corner of the plot as possible, while the optimal DVH curves for nontarget structures will be as close as possible to the lower left hand comer of the plot axes as possible, as shown in Figure 212. Thus, one may readily evaluate two rival treatment plans based upon their DVHs, if the DVH curves for each plan do not intersect, since the more desirable curve will lie either above and to the right of the other (if it is a DVH curve of a target volume) or below and to the left if it is a nontarget volume DVH curve. With these rules for evaluating cumulative DVHs, we can use Figure 211 to evaluate Plan 1 and Plan 2 for the radiosensitive structure. Since the curve for Plan 1 always lies below and to the left of the Plan 2 curve, and the brainstem is a nontarget tissue, we can conclude that Plan 1 is the preferred plan in order to minimize the radiation effects to the brainstem. The relative ease of this comparison underscores the general utility of cumulative DVHs (Figure 211) over direct DVHs (Figure 210) (Lawrence 1996; Kutcher 1998). Unfortunately, it is rare for the cumulative DVH curves of rival treatment plans to separate themselves from one another so cleanly. A more general and common occurrence in comparing treatment plans is shown in Figure 213, in which the DVH curves cross one another, perhaps more than once. The general rules above for evaluating DVHs cannot resolve this situation, in which case we must use other means to evaluate the treatment plans. The next section discusses physical dose volume metrics for treatment plan comparison. 30.0 25.0 20.0 15.0 10.0 5.0 0.0 10 20 30 40 Dose (relative units) Figure 213: Crossing cumulative DVH curves Physical Dosevolume Figures of Merit The three properties of radiosurgery and radiotherapy dose distributions which have been correlated with clinical outcome are dose conformity, dose gradient, and dose homogeneity (Meeks 1998a). The conformity of the dose distribution to the target volume may be simply expressed as the ratio of the prescription isodose volume to the target volume, frequently referred to as the PITV ratio (Shaw 1993): (22) PITV = Prescription isodose volume / target volume. Perfect conformity of a dose distribution to the target, i.e. PITV = 1.00, implies that the prescription isodose volume exactly covers the target volume while covering no non target tissues. Typically, perfect conformity of the prescription isodose surface to the target volume is not achievable, and some volume of nontarget tissue must be irradiated to the same dose level as the target, resulting in PITV ratios greater than unity. The most conformal treatment plans are those with the lowest PITVs, if all of the plans under comparison provide equivalent target coverage. This stipulation is necessary because the definition of PITV does not specify how the prescription isodose is determined. It is possible (but undesirable) to lower, and thus improve, the PITV by selecting an isodose level which incompletely covers the target as the prescription isodose, and therefore reduces the numerator of Eq. (22). Unless otherwise stated, prescription isodose levels in the remainder of this report are selected to ensure that > 95% of the target volume receives the prescription isodose. This ensures a more consistent basis of comparisons for all treatment plans. A sharp dose gradient (fall off in dose with respect to distance away from the target volume) is an important characteristic of radiosurgery and stereotactic radiotherapy dose distributions. Dose gradient may be characterized by the distance required for the dose to decrease from a therapeutic (prescription) dose level to one at which no ill effects are expected (half prescription dose). Figure 214: Transaxial, sagittal, and coronal isodose distributions for five arcs of 100 degrees each delivered with a 30 mm collimator. Isodose lines in each plane increase from 10% to 90% in 10% increments, as indicated. The :socenter is marked with crosshairs. '*  ~_   Figure 215: Dose crossplots through the isocenter, corresponding to the isodose distributions shown in Figure 214. The sharpest dose falloff, from dose D to halfdose 0.5D, occurs between dose D of 80% to 0.5D = 40%, which occurs in a distance of 4.6 mm. The D to 0.5D falloff distance is larger for 9045% (5.1mm) and for 7035% (4.9mm) doses. For illustrative purposes, a typical radiosurgical dose distribution, delivered with five converging arcs and a 30 mm collimator to a hemispherical water phantom, is depicted in Figures 214 and 215. The isodose surfaces in Figure 214 are normalized to the point of maximum dose, such that 100% corresponds to the maximum dose. The close proximity of the higher (5090%) isodose lines to one another is a qualitative measure of the steep dose gradient. A quantitative measure of gradient is obtained from examining the dose profiles along orthogonal directions in the principal anatomical planes (transaxial, sagittal, and coronal), as shown by crossplots in Figure 215. This figure shows the gradient between several dose levels, D, and half of D, in several directions. The data show that for this single isocenter dose distribution, the steepest dose gradient (distance between isodose shells of dose D to and 50% of D) occurs between the 80% and 40% isodose shells, and is 4.6 mm for the 30 mm collimator and five arcs. The steepest dose gradient is generally achieved between the 80% and 40% isodose levels, and for this reason single isocenter dose distributions are prescribed to the 80% isodose shell (Meeks 1998c). The dose gradient is relatively independent of direction (AP, Lateral, and Axial) between about the 90% and 40% isodose shells, since the dose distribution is almost spherically symmetric between these isodose shells. Table 21 lists dose gradient information between the 80% and 40% isodose shells for single isocenter dose distributions with 10 to 50 mm diameter collimators. In general, however, radiosurgery dose distributions are not spherically symmetric, and are tailored to fit the target's shape through manipulation of arc parameters (Meeks 1998c), multiple isocenters, beam shaping, or intensitymodulation. Additionally, dose distributions are often manipulated to steepen the dose gradient in the direction of adjacent radiosensitive structures. This additional complexity makes it necessary to complement the dose crossplot with other methods to evaluate the dose gradient. Figure 216 illustrates this point with a hypothetical radiosurgery target shaped like a threedimensional letter "F", which is covered by a multiple isocenter dose distribution using 10 mm collimators and five converging arcs at each of eight isocenters. The 70% isodose shell, which covers the hypothetical target, represents the prescription isodose and is shown along with the half of prescription isodose (35%), and twenty percent of prescription isodose (14% = 0.2 x 70%). Unlike the single isocenter, spherically symmetric dose distribution of Figures 214 and 215, the multiple isocenter dose distribution is asymmetric, and the prescription isodose to halfprescription isodose gradient therefore has a directional and spatial dependence. Depending on where the dose crossplot is centered and the direction, the distance between the prescription (70%) and halfprescription (35%) isodose shells varies from 2 to 7 mm. In order to obtain a representative sample average gradient distance, it would be necessary to take a large number of gradient measurements at many points at the target's edge. However, a method has been proposed which uses easily obtainable DVH information to generate a numerical measure of the overall dose gradient, and which may be used with arbitrary dose distributions. 42 ~1 * 11 Wireframe representation of 3D target 4' *4'   4 4 7^ 0,* Figure 216: Irregular "F" shaped target and multiple isocenter dose distribution in hemispherical water phantom. The LF Index (gradient) score, or UFIg, has been proposed as a metric for quantifying dose gradient of a stereotactic treatment plan. From treatment planning experience at the University of Florida, it has been observed that it is possible to achieve a dose distribution which decreases from the prescription dose level to half of prescription dose in a distance of 3 to 4 mm away from the target. Taking this as a guide, a gradient score UFIg may be computed as (23) UFIg = 100 00 [(REff,50%Rx REff,Rx) 0.3cm]} where Refso%Rx is the effective radius of the halfprescription isodose volume, and RefRx is the effective radius of the prescription isodose volume. The "effective radius" of a volume is the radius of a sphere of the same volume, so that Reff for a volume V is given by _3V (24) R., The volumes of the prescription isodose shell and the half prescription isodose shell are obtained from a DVH of the total volume (or a sizeable volume which completely encompasses the target volume and a volume which includes all of the half prescription isodose shell) within the patient image dataset. The UFIg score is a dimensionless number that exceeds 100 for dose gradients less than 3mm (steeper falloff from prescription to halfprescription dose level), and which decreases below 100 as a linear function of the effective distance between the prescription and halfprescription isodose shells. Table 21 summarizes dosevolume and gradient information for single isocenter dose distributions delivered with five converging arcs and 10, 20, 30, and 50 mm circular collimators. UFIg is calculated for each dose distribution using DVH information as described above. Since the dosegradient for single isocenter arcing dose distributions (with circular collimators) is achieved between the 80% and 40% isodose shells, the volumes and effective radii of the 80% and 40% isodose shells are listed, as well as the difference between these radii. The dose gradient is steepest for the smallest collimators (about 10 mm diameter) with an effective distance between the 80% and 40% isodose shells of 2.4 mm and a corresponding UFIg of 106. Dose gradient gradually worsens as the field size collimatorr size) increases. At a 30 mm diameter field, what many consider to be the upper limit on radiosurgery target size, the effective dose gradient is about 4.5 mm (UFIg 85). Table 21: Single isocenter (five converging arcs) dosevolume and gradient information for 1050 mm circular collimators. (cm3) (mm) (cm3) (mm) (mm) Coll. Vsoo. Reff8o% V40% Reff40% Eff. Gradient UFIg 10 0.3 4.2 1.2 6.7 2.4 106 20 3.9 9.8 9.7 13.2 3.5 95 30 13.9 14.9 30.8 19.4 4.5 85 50 67.4 25.2 111.6 29.9 4.6 84 1.000 0.900 g 0.800  j 0.700 c 0.600 z" 0.500  c 0.400  0.300  0.200 0.100 0.000  Target  Total volume ~ _~ : 10 20 30 40 50 60 70 80 90 1C Dose (% of maximum) Figure 217: Target and total volume DVHs for Fshaped target in Figure 215. This methodology can be applied to the dose distribution shown in Figure 216. Figure 217 shows the DVHs for the Fshaped target volume and for a large 352 cm3 cubic volume enclosing the region of interest. From this DVH it can be seen that >95% of the target volume receives >70% of maximum dose, which is necessary to support selection of 70% as a prescription isodose for this target. The volume receiving 709 o of the maximum dose is 5.2 cm3 (Rff = 10.8mm), with 22.6 cm3 (R ff= 17.5mm) receiving 35% of maximum dose. The effective dose gradient is therefore 17.5 mm 10.8 mm= 6.7 mm, corresponding to a UFIg = 62. There is another key piece of dosevolume information contained in this DVH (Figure 217), which bears on the practice of multiple isocenter radiosurgery. Table 22 shows the resulting prescription to halfprescription dose gradient resulting from using various isodose shells as the prescription isodose. The important information in Table 2 F 10 2 is that the steepest dose gradient for most (properly planned) multiple isocenter dose distributions lies between the 70% and 35% isodose shells, with an effective distance between the prescription and halfprescription isodose shells of 6.8 mm, corresponding to a UFIg score of 62. Therefore, in multiple isocenter radiosurgery planning, the planner should attempt to fit the 70% isodose shell to the target (as opposed to the 80%, 60%, or other isodose shells) in order to maximize the dose gradient and nontarget tissue sparing (Meeks 1998c). Table 22: Dose gradient variation with selection of prescription isodose shell for multiple isocenter "F"shaped dose distribution Rx isodose Gradient (mm) UFIg 90 8.6 44 80 7.1 59 70 6.8 62 60 7.3 57 50 8.3 47 40 9.7 33 30 10.7 23 20 9.3 37 Dose conformity is another important characteristic of a radiosurgery treatment plan which should be considered in plan evaluation. A means of con erting dose conformity in terms of PITV into a conformal index score on a common scale with UFIg has been proposed, the UFIc score. The UF Index conformall), or UFIc, is defined as (25) UFIc =IO0( Target volume = (PITV) l00. Prescription isodose volume The UFIc converts PITV into a numerical score expressing the degree of conformity of a dose distribution to the target volume. UFIg score increases as the dose gradient improves, and the UFIc score increases as dose conformity improves. Perfect conformity (assuming the target is adequately covered) of the prescription isodose volume to the target is indicated by a PITV = 1.00 and a UFIc = 100. As both dose gradient and dose conformity are both important parameters in judging a stereotactic radiosurgery or radiotherapy plan, an overall figure of merit for judging radiosurgery plans should incorporate both of these characteristics. Since clinical data to indicate the relative importance of conformity versus gradient is currently lacking. an index, the UF Index (UFI) is proposed which assigns equal importance to both of these factors. The overall UF Index score, or UFI, for a radiosurgery or radiotherapy plan is the average of the UFIc and UFIg scores (Bova 1999). Dose homogeneity is considered by some to be an important factor in evaluating treatment plans. A homogeneous dose distribution throughout the target volume (target dose within +7% and 5% of the prescribed dose to the target's periphery) is desirable for conventional, fractionated radiotherapy (Landberg 1993). In radiosurgery, however, the importance of a homogeneous target dose distribution is less clear. Several studies have associated large radiosurgical dose heterogeneity (maximum dose to peripheral dose ratio, or MDPD, > 2.0) with an increased risk of complications (Nedzi 1991; Shaw 1996). However, some radiosurgeons have hypothesized that the statistically significant correlation between large dose inhomogeneities and complication risk may be associated with the relatively nonconformal multiple isocenter dose distributions with which some patients in these studies were treated, and not with dose inhomogeneity alone. One theory is that the extreme "hot spots" associated with large dose heterogenities may be acceptable, if the dose distribution is very conformal to the target volume and the hot spot is contained within the target volume. Nonconformal dose distributions could easily cause the hot spots to occur outside of the target, greatly increasing the risk of a treatment complication. The extensive successful experience of gamma unit treatments administered worldwide (almost all treatments with MDPD > 2.0) lends support to this hypothesis (Flickenger 1997). Therefore, as a general principle, one strives for a homogeoneous radiosurgery dose distribution, but this is likely not as important a factor as conformity of the high dose region to the target volume, or the dose gradient outside of the target. As was shown in Tables 21 and 22, in order to maintain as steep a dose gradient as possible, the 70% (of maximum dose ) isodose shell is generally used for planning multiple isocenter treatments, while the 80% isodose shell is used for single isocenter treatments. An additional benefit of selecting the 70% to 80% isodose shell, rather than the 50% isodose shell commonly used in gamma unit radiosurgery, as the prescription isodose is an improvement in treatment efficiency, in terms of the total number of monitor units which must be delivered. Setting the 50% isodose shell as the prescription isodose surface rather than 70% would require 1.4 times as many monitor units to be given to deliver the prescription dose to the target. Also, this would impart a larger integral dose to the patient in order to deliver the same peripheral target dose. Although the 70% and 80% prescription isodose levels were chosen based primarily on maintaining the steepest possible dose gradient, they represent a guideline for acceptable dose inhomogeneity in linear accelerator radiosurgery dose planning (Meeks 1998c; Meeks 1998). Biological Models In planning stereotactic radiosurgery (SRS) or stereotactic radiotherapy (SRT) treatments, the object is to minimize the dose to radiosensitive nontarget structures while covering the target with a conformal and homogenous dose distribution. In multiple isocenter SRS planning, nontarget structures are protected primarily by the steep dose gradient inherent in stereotactic irradiation. In single isocenter SRS plans, several techniques (arc start and stop angles, couch angles, and differential collimators) are generally used to enhance dose conformity and to steepen the dose gradient in the direction of especially radiosensitive structures, such as the brainstem (Meeks 1998a; Meeks 1998; Foote 1999). Such treatment plans can be evaluated on the basis of dose gradient and conformity, which can be determined from dosevolume histograms of the target and surrounding volumes (Shaw 1993; Bova 1999). When multiple critical structures are to be spared as part of the optimization process, such as in the problem of deciding beam orientations in conformal beam SRS and SRT, the treatment plan evaluation problem can shift away from determining obvious differences in the conformity and gradient of competing plans. In such cases, biological indices, such as the normal tissue complication probability (NTCP), may be used to evaluate rival treatment plans, each of which demonstrates comparable dose gradient and conformity to the target. An example of this occurrence is shown in Figures 218(a) and 218(b), which depict DVHs for the total intracranial volume ("cubic") and several radiosensitive structures for two hypothetical radiosurgery plans. An analysis of both sets of target DVHs (not shown) and total volume DVHs would indicate that both plans cover the target with similar dose homogeneity (at least 95% of the target receives >69% of maximum dose for the first plan, and >72% of maximum dose for the second plan) with very similar dose conformity (PITVs of 1.42 and 1.40) and gradient (UFIg of 76 and 82). However, the two plans are not equivalent, due to the doses received by the radiosensitive structures (e.g.brainstem, and left and right optic nerves). One can see qualitatively that plan 2 improves (reduces) the overall dose received by these radiosensitive structures, since the DVH curves for the left and right optic nerve are shifted downward and to the left in Figure 218(b) relative to Figure 218(a). However, a quantitative measure of this effect is desirable. Normal tissue complication probability (NTCP) models have been proposed as one such quantitative measure.  unoptcubic  unoptbrainstem .. unoptroptnerve  unopt1optnerve 0 5 10 15 20 25 30 35 40 Dose (% of maximum) Figure 218(a): DVHs for hypothetical radiosurgery plan (Plan 1). 1.0 0.9 ... ...... ._  optcubic 0.8 * optbrainstem 0.7 .... optroptnerve 0.6 .. ..  optloptnerve 0.4 0.3 0.2 0.1 0.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40 0 Dose (o of maximum) Figure 218(b): DVHs for hypothetical radiosurgery plan (Plan 2). A fourparameter model has been suggested by Lyman (Lyman 1985; Kutcher 1991) as the basis of such an NTCP figure of merit for evaluating subtle differences in rival SRS/SRT plans. The basic fourparameter model is 1 t (26) NTCP = j Jexp 4t, 72=r, 2 t where (27) t= TD , mTDo0(v) V (28) v= ,and Vgf (29) TD(1) = TD(v). Vn Here, NTCP represents the probability of complication for an organ of volume Vref resulting from uniform irradiation of partial volume to homogeneous dose D. TDso is the tolerance dose for whole organ irradiation at which 50% of the patients receiving this dose encounter a 50% risk of radiation induced complication within five years after treatment. The tolerance dose for partial organ volume, v, and the entire organ volume is given by Eq. (29) (Schultheiss 1983). The quantities n and m are fitting parameters which govern the volume and dose dependence of the NTCP model. Quantity t is a parameterization of the number of standard deviations separating the partial volume v at dose D from TDso. TDso, m, and n model parameters used for comparisons were taken from curvefits (Burman 1991) to dosevolume tolerance data in the literature (Emami 1991). Since dose distributions in SRS/SRT are almost neN er perfectly homogeneous in the region of interest, the fourparameter model cannot be used directly as presented. Kutcher's method (Kutcher 1991) is used to reduce each nonuniform dose volume histogram to an equivalent volume DVH receiving the maximum dose level. This method involves treatment of each small dose bin in the differential dose volume histogram as a volume receivinga uniform dose Di, which is a reasonable assumption if the dose bin size is small enough. "Small enough" means practically using dose bins no larger than about 2 Gy each (Kutcher 1991). The effective volume, Veff, receiving the maximum dose Di, is found by converting the volume in each differential DVH dose bin to an effective volume Vefi, and summing them: (210) Ve = V,. D \ Dm The source data cited above is applicable for NTCP calculations involving fractionated radiotherapy under typical regimes of about 1.82.0 Gy per fraction on a five day per week treatment schedule. These model parameters must be adjusted in order to use this four parameter model to calculate NTCP for single dose radiosurgery cases. The biologically equivalent dose formalism (BED) may be applied to make this modification (Fowler 1989; Smith 1998), in which a BED may be calculated from any particular fractionation scheme delivering dose D in fractions of dose d by (211) BED= D. .I a P The BED represents a biologically effective dose for tissues with an a/p ratio of (o/p) when delivered in fractions of dose size d. In this relation, ct and P are the coefficients in the linearquadratic cell survival curve (Hall 1994a; Hall 1994b). To gauge the biological effect of twodifferent doses, Di and D2, given in individual fraction doses of di and d2, respectively, one would calculate and compare the BEDs calculated for Dl and dl, and for D2 and d2 using equation (211). Unit analysis of Eq. (211) shows that BED has units of Gray (Gy), although to indicate that the quantity BED is biologically effective dose rather than a physical absorbed dose, BEDs are usually subscripted with their a/P ratio, e.g. Gy2. For the purposes of comparing rival treatment plans, 2.0 is an acceptable default a/p ratio for normal brain and nervous tissue (Smith 1998). To use the NTCP models in equations (26) through (29) with single fraction SRS dose distributions, the volume element in each SRS DVH dose bin must be transformed into a biologically equivalent dose using equation (211), and each organ's tolerance dose (TDso, in units of Gy) must be transformed into a biologically equivalent single fraction BETDso. Table 23 summarizes NTCP model data taken from Burman (Burman 1991) and Emani (Emami 1991) for intracranial anatomy. The radiosurgery BED for each organ's TDso is calculated for a fractionation schedule of 2 Gy per fraction and an a/P ratio of 2.0, in units of Gy2. Table 23: NTCP model data for intracranial sites TD50(1) n m (Gy) Brain (a)_ 0.25 0.15 60 Brainstem ta) 0.16 0.14 65 Brainstem (b) 0.04 0.15 65 Lens (a) 0.3 0.27 18 Optic nerve (a) 0.25 0.14 65 Source:(a) (Burman 1991), (b) (Meeks 2000) Although these models and data represent a commonly accepted method for modeling the biological response of tissues to irradiation, the data used to fit the model parameters remain sparse and somewhat uncertain (Zaider 1999). For the intracranial anatomical sites listed in Table 23, the brain is the organ with the greatest amount of clinical data, a total of six data points. The lens and optic nerve models are fitted for only two data points corresponding to 5% and 50% complication probabilities for irradiation of each entire organ. Thus, computing NTCP values with the fourparameter model is possible, but even under the whole organ irradiation conditions under which the model was created, significant interpolation between clinically observed data points is necessary. For conditions of partial organ irradiation, calculation of NTCP values would involve significant extrapolation beyond observed data (Burman 1991). For these reasons, complication probabilities calculated by this means are intended to serve only as a guide for evaluating rival treatment plans, and not for use as absolute probabilities of complication (Kutcher 1996). A previous study of such simple biological models has 56 shown that it is possible to use them in the ranking of rival treatment plans, despite uncertainties in the model parameters (Kutcher 1991). CHAPTER 3 OPTIMIZED RADIOSURGERY TREAT MENT PLANNING WITH CIRCULAR COLLIMATORS This chapter presents the methods used in planning optimized single and multiple isocenter radiosurgery treatments with circular collimators. Single isocenter LINAC radiosurgery with evenly spaced arcs produces essentially spherical dose distributions at high isodose levels (7080%). To avoid covering excessive volumes of nontarget tissue to the prescription dose, however, the high dose region must be shaped to fit individual targets. The high dose region near a single isocenter can be manipulated (within limits) into a variety of ellipsoidal shapes that closely conform to a target's shape. For irregularly shaped lesions, and those with an ellipsoidal shape in the transaxial plane, however, multiple isocenters must be used to obtain a conformal dose distribution for radiosurgery (Friedman 1998; Meeks 1998c). The University of Florida radiosurgery planning algorithm, shown in Figure 31, (Friedman 1998; Meeks 1998c) provides the basis for the treatment planning methods outlined in this chapter. This algorithm organizes the tools (optimization variables) available to the radiosurgery planner to efficiently generate conformal radiosurgery plans that provide appropriate sparing of nontarget tissues. The first step of the algorithm is to determine whether the targeted lesion is adjacent to a radiosensitive structure. If so, single isocenter arc parameters (presented in a later section) are adjusted to steepen the dose gradient in the direction of the radiosensitive structure, if possible. If the lesion is very irregular in shape or is an ellipsoid with the major axis aligned along the anterior posterior direction, multiple isocenters are used to conform the dose distribution to the shape of the lesion. Due to the difficulty of standardizing this multiple isocenter planning process, the major emphasis in this chapter is on a geometrically based and automated method (sphere packing, developed in a joint project with the University of Florida Department of Mathematics) which attempts to generate conformal multiple isocenter dose distributions. University of Florida Treatment Planning Algorithm for Optimizaeton IThe d' t a p cenP to a single, stationar ea tat is saed it ura / , circular collimator of diameter "coll" is computed at any point in the stereotactic space by, \C3 l:cii i 3rucgture nrtte Cr sci nr^,r m^ i, ..*.:.l ^R3CC * (31) Dose(P) = k MU TPR(coll,depth(P)) OAR(P) Sc.pcol distsP ilie"3: r; 'L1'A 5. lirfb' ?nLI Ir '! ' / . S,1 3 ':*"C r i :C<; j A;xi: C:i e t *' i"..:So OosO S ieC', ion Figure 31: University of Florida radiosurgery planning algorithm Circular Collimator SRS Dosimetry The dose at any point P due to a single, stationary beam that is shaped with a circular collimator of diameter "coll" is computed at any point in the stereotactic space by (31) Dose(P) = k MU. TPR(coll, depth(P)). OAR(P). S .p_*on. distsp C distscp,) as sho\%n in Figure 32. In Eq. (31), k is the treatment machine's calibration constant, normally 0.01 Gy MU, MU is the number of monitor units delivered with the beam, dists cp is the source to calibration point distance (nominally 100cm for an isocentric machine calibration), dists.p is the distance from the source to point P, TPR(coll, depth(P)) is the tissuephantom ratio for the circular collimator being used at the depth of point P, S,pco1l is the total scatter factor, or output factor, for the circular collimator being used, and OAR(P) is an offaxis ratio representing the variation of dose away from the field's central axis (Khan 1994; Surgical Navigation Technologies 1996; Duggan 1998). Data tables of measured TPR and Sc, values for all circular collimators in use are maintained and directly used by the treatment planning system for dose calculation at each point. Dose distributions can be determined by a) computing the dose to each point (from each beam) in a grid of points in the viewing planes selected by the user, or b) to a grid of points in a three dimensional region. Each arc of radiation, formed by rotation of the gantry about the patient with the radiation beam on, is accurately modeled as a series of stationary beams spaced approximately 10 degrees apart. Thus, a 100degree arc is approximated by spacing eleven beams 10 degrees apart (Figure 26). The dose algorithm assumes the patient to be water equivalent, and each beam to be perpendicular to the patient's surface. Determination of the patient's surface and the depths for each central axis dose point is derived from the threedimensional stereotactic computed tomography (CT) image set of the patient. The dose calculation falls into the "three dimensional imaging, one dimensional dose calculation" classification discussed in Chapter 2. Although somewhat simple, this process is rapid and provides sufficient accuracy for radiosurgery dose calculations (Schell 1995). 60 Radiation Surface t \ P depth(P) OAD(P) S Single Isocenter Treatment Planning A single isocenter with multiple converging arcs may be used to create a spherical dose distribution close in size to the diameter of the circular collimator. This type of treatment produces a conformal dose distribution for spherical or nearspherically shaped targets. The standard set of fourteen circular collimators used at the University of Florida covers a range of sizes from 5mm to 40mm (5, 10, 12, 14, ..., 30, 35, and 40 mm ) diameter, projected at 100cm from the radiation source, allowing the planner to closely match the diameter of the dose distribution to the target. As discussed in Chapter 2, because the steepest dose gradient for single isocenter dose distributions lies between the 80% and 40% isodose shells, a collimator size should be chosen which covers the target with the 80% isodose shell. This will ensure the steepest possible dose gradient between the prescription and halfprescription isodose shells. A standard set of nine convenrent t \ Surface / \ __ __OAP .... Figure 32: Radiosurgery beam dose calculation for dose at point P. Single Isocenter Treatment Planning A single isocenter with multiple converging arcs may be used to create a spherical dose distribution close in size to the diameter of the circular collimator. This type of treatment produces a conformal dose distribution for spherical or nearspherically shaped targets. The standard set of fourteen circular collimators used at the University of Florida covers a range of sizes from 5mm to 40mm (5, 10, 12, 14, ..., 30, 35, and 40 mm ) diameter, projected at 100cm from the radiation source, allowing the planner to closely match the diameter of the dose distribution to the target. As discussed in Chapter 2, because the steepest dose gradient for single isocenter dose distributions lies between the 80% and 40% isodose shells, a collimator size should be chosen which covers the target with the 80% isodose shell. This will ensure the steepest possible dose gradient between the prescription and halfprescription isodose shells. A standard set of nine convergent arcs (specific parameters listed in Table 31, in terms of International Electrotechnical Commission (IEC) couch and gantry angles (IEC 1996)), is shown in a perspective view in Figure 32, and is generally used as a basis for generating single isocenter dose distributions. Couch and gantry angles are illustrated in Figures 33 through 36. An AP xiew of a standard ninearc set, delivered to an approximately spherical target with an eighteenmillimeter collimator, is shown in Figure 37 along with the resultant isodose distribution. Each arc is weighted equally with respect to dose to isocenter. The couch angles are chosen to approximate an even and symmetrical beam distribution over the 2x steradian solid angle above the patients head, while avoiding parallel opposed beams which would adversely affect the dose gradient (Meeks 1998a; Meeks 1998b; Meeks 1998c). Table 31: Couch and gantry angles for standard University of Florida nine arc set. (Angles are in accordance with IEC standards). Gantry Gantry Couch Start Stop 10 130 30 30 130 30 50 130 30 70 130 30 350 230 330 330 230 330 310 230 330 290 230 330 270 230 330 as a starting point for single isocenter radiosurgery plans. Each equally weighted arc 4 .4.. spans 100 degrees of gantry rotation at one of nine couch angles. Gantry 0 degrees Gantry rotation Couch rotation Couch 0 degrees Figure 34: Schematic depiction of couch and linac gantry angles. The linear accelerator couch and gantry are positioned in the "home" position, couch at 0 degrees, and gantry at 0 degrees. Couch and gantry angles refer to the amount of clockwise rotation as shown in the figure. Gantry 30 Couch 55 Gantry 130 Figure 35: Linac couch (rotated clockwise) at 55 degrees, and gantry arcing between 30 and 130 degrees. Gantry 330 s Couch 305 Figure 36: Linac couch at 305 degrees, and gantry arcing between 230 and 330 degrees. Figure 37: Standard ninearc set delivered with 18mm collimator, and isodose distribution in axial, sagittal, and coronal planes. The 80%, 40%, and 16% isodose lines are shown in each plane. The inset at lower left shows an AP view of a patient's head, with an overlay of the linac couch angles corresponding to each arc. The standard nine arc set is well suited for conforming the high dose region to the target, if the target is spherically shaped. However, in the case of an ellipsoidal shaped target, or of an adjacent critical (radiosensitive) structure, it may be necessary to alter the shape and gradient of the dosedistribution to improve dose conformity and gradient. The University of Florida doseplanning algorithm (Figure 31) guides the selection of appropriate isocenter arc parameters to manipulate to obtain optimal dose conformity and gradient. The nine arcs in the standard set may be manipulated to change the shape of the high (80%) isodose shell from a spherical shape to an ellipsoidal shape with the major axis inclined in the sagittal or coronal planes. The "arc elimination" tool or technique may be used to steepen the dose gradient in a lateral or axial (along the cranialcaudal axis) direction. This is accomplished by eliminating arcs that are aligned in the direction along which a steeper dose gradient is needed. Figure 38 shows how elimination of the lateral arcs changes the overall dose distribution, causing a steeper dose gradient laterally from the isocenter, and making the dose gradient less steep in the inferior/superior direction. This technique is appropriate to protect a radiosensitive structure that lies medial or lateral to the target at isocenter. Figure 39 shows an application of this technique to steepen the dose gradient in an oblique direction. Elimination of the most superior arcs would likewise steepen the superiorinferior dose gradient, at the expense of a less steep lateral dose gradient. The arc elimination tool allows the planner to selectively steepen the dose gradient in the coronal plane. The dose gradient may be altered in the sagittal plane by altering the start and stop angles of each arc, and/or by altering the span of each nominal 100 degree arc. Figure 3 10 shows the effect on the sagittal isodose distribution of shortening each arc by removing the posterior 40degree portion of each arc, which shortens each arc from 100 degrees to 60 degrees. The overall dose distribution tends to follow the directional alignment of most of the beams in each arc. Use of this planning tool allows the dose gradient to be steepened to protect critical structures lying anterior or posterior to the target. In addition to protecting radiosensitive structures near the target, the arc elimination and arc start/stop angle tools allow changing the shape of the high dose region from a sphere to an ellipsoidal shape, which can improve the conformity of the high dose region to the target if the target is an ellipsoid with the major axis in the sagittal or coronal planes. However, if the target is an ellipsoid with the major axis aligned in the transaxial plane, or if the target is irregularly shaped, multiple isocenters may be required to achieve a dose distribution that conforms to the shape of the target. 290 310 270 Figure 38: Steepening the dose gradient in the lateral direction by elimination of the most lateral four arcs from a standard ninearc set. The 80%, 40%, and 16% isodose lines are shown in each plane. 270 Figure 39: Rotating the distribution and steepening the dose gradient in an oblique direction by elimination of four arcs entering from the patient's right side. The 80%, 40%, and 16% isodose lines are shown in each plane. 80%40%16% isodoses Standard arcs: Zach arc 60 degrees Zach arc 100 degr esI Figure 310: Tilting the dose gradient in the sagittal plane by shortening each standard 100degree arc (left side) to 60 degrees (right side). lane views: Multiple Isocenter Radiosurgery Planning Tools Multiple spherical dose distributions may be placed adjacent to one another to build up a composite dose distribution which conforms to the shape of an irregular target. as was shown for the "F" shaped target in Chapter 2. When using multiple isocenters, typically five arcs (Figures 311, 312) rather than nine arcs (Figures 33, 37) are used with each isocenter, since the dose distribution from five arcs is very similar to that from nine arcs, and less time is required to deliver five arcs than nine arcs. Couch and gantry angles for the standard five arcs used in multiple isocenter planning at the University of Florida are listed in Table 32, and are depicted in Figures 311 and 312. Figure 311 shows the resultant dose distribution from a standard fivearc set, which is very similar to the standard nine arc dose distribution shown in Figure 37. 270 340 Figure 311: Standard fivearc set delivered with 18mm collimator, and isodose distribution in axial, sagittal, and coronal planes. The 80%, 40%, and 16% isodose lines are shown in each plane. The 70%, 35%, and 14% lines (not shown) are very close to the 80%, 40%, and 16% isodose lines. Figure 312: AP superioroblique view of the standard five arc set generally used for each isocenter in multiple isocenter plans. Table 32: Couch and gantry angles for standard University of Florida five arc set. Couch Start Stop 20 55 340 305 270 130 130 230 230 230 30 30 330 330 330 Three factors strongly affect the dose distribution when using multiple isocenters: 1) collimator size, 2) interisocenter spacing, and 3) isocenter weighting. Collimator size is chosen to match the region of the target which is being covered, and affects the diameter of the spherical high dose region that is produced by each isocenter. Proper selection of collimator size and isocenter location is a complex topic, which is addressed in the next section, while the issues of isocenter spacing and weighting are discussed here. The effects of isocenter spacing on the overall dose distribution may be seen in Figure 313, which shows 50% and 70% isodose curves in an axial plane for two equally weighted isocenters at several interisocenter spacings, each with a standard five arc set delivered with a 30mm collimator. For this discussion, it is helpful to consider each isocenter as a solid, 30 mm sphere, corresponding approximately to the 70% isodose surface of a five arc set. As a first approximation, one would expect a sphere separation of about 30mm (the sum of the radii of each sphere) to be correct. As will be shown, this is approximately correct, but slightly more separation is optimal. The 70% volume in the dose distributions shown in Figure 313 correspond approximately to the geometrical coverage of a 30 mm diameter sphere placed at each isocenter. At an isocenter spacing of 40 mm, the 70% volume is slightly greater than the sum of two 30 mm spheres, and the 50% volume (outer isodose line) is slightly larger. The "waist" between the 70% isodose lines is so pronounced that the 70% isodose shells are actually separated from one another. As the isocenters are moved closer together, the 70% isodose shell more strongly resembles two 30 mm diameter spheres. At about 3233 mm interisocenter spacing, the isodose distributions are about ideal. As the isocenters are moved closer to one another for distances less than about 32 mm, the 70% isodose volume contracts dramatically. This is because each dose distribution is renormalized to 1000 o at the point of maximum dose, so that as the hotspot where the two spheres overlap one another becomes more intense, the volume covered by 700o of this increasing maximum dose becomes smaller and smaller. This can be seen by the rapid decrease in size of the middle 70% isodose region, from 59 mm across with a spacing of 33mm, down to a region only 17 mm across when the interisocenter spacing is reduced to 24 mm. The 70% isodose region shrinks to less than a third of its initial size, while the 509 o isodose region shrinks muchmore gradually from 66 mm to 53 mm (a 20% decrease). For this example of two 30mm isocenters, the 70% isodose shell may be approximated as two 30mm spheres, if an interisocenter spacing of at least 32mm is maintained. To assist the human radiosurgery planner in maintaining this appropriate spacing between isocenters, a table of empirically determined optimal interisocenter distances is incorporated into the University of Florida radiosurgery treatment planning system (Foote 1999). The planner enters the table with the collimator sizes for two adjacent isocenters, and the table returns the optimal interisocenter distance for these two collimator sizes. This planning tool merely serves as an aid to provide recommended isocenter spacing, and does not directly alter any treatment plan parameters. According to this isocenter spacing table, the optimal spacing distance for two 30mm isocenters is 31mm. Inspection of the isodose distributions for a variety of collimator sizes and spacings, as was done in Figure 39 for two 30mm collimators, shows that for two isocenters with collimator diameters of dl and d2, an approximate spacing of 0.52(dl + d2) to 0.60(dl + d2) will yield an overall dose distribution similar in shape to two spheres of diameters dl and d2. Isocenter weighting is another important aspect of multiple isocenter treatment planning. When planning radiosurgery treatments with multiple isocenters and when the isodose distribution is normalized to maximum dose, care must be taken to consider the additive dose from all isocenters. Examples of this are shown in Figure 3 14(a), 314(b), and 314(c). Figure 314(a) shows a dose profile (cross plot) through four optimally spaced isocenters (each separated from the others by 13.8 mm), each with an equally weighted five arc set and a 14 mm collimator (the relative dose weight of each isocenter is 1:1:1:1). The individual dose profile for each isocenter is shown, along with the total dose distribution along the crossplot from all four isocenters. The central regions of the distribution near the two isocenters in the middle of the distribution receive 140o more dose than do the two isocenters at the edges. This is because each of the middle isocenters receives the dose from its own five arcs, and also receives a substantial contribution from each of its neighboring isocenters as well. The desired situation is to have equal doses at each isocenter, rather than equal weighting of the arcs associated with each isocenter. In order to compensate for the increased dose to the middle of the total distribution, it is necessary to decrease the weight of the two isocenters in the middle. Figure 314(b) shows the individual and total dose distribution after the isocenter dose weighting has been adjusted to 1.17 : 0.94 : 0.94 : 1.17. Making this adjustment causes a uniform dose to be received by each of the four isocenters. Although the total dose distribution is still somewhat heterogeneous, it is actually more homogeneous than the total dose distribution in Figure 314(a). This is shown in Figure 314(c), which shows the total dose distribution for both situations. The overall dose distribution after adjusting the weights is more homogeneous, in that the volume of the 70% isodose surface has been increased, and the "hot" volume (hotspot) receiving more than 90% of maximum dose has been reduced. Also, note that the prescription to halfprescription isodose gradient is steeper for the adjusted weights distribution. This can be seen in Figure 315, which shows the axial isodose distribution for both the equally weighted and the adjusted weights plans. The 35% isodose shell is almost identical between the two plans, but since the 70% isodose shell is larger for the adjusted weights plan, it is closer to the 35% isodose shell, and offers a steeper dose fall off. In most radiosurgery planning situations, the same advantage holds for adjusting the isocenter weights in order to improve the dose homogeneity, and gradient, around the target volume. An automatic weighting tool to perform this task has been implemented in the University of Florida treatment planning system which iteratively adjusts the arc weights associated with each isocenter to achieve a uniform dose to each isocenter (Foote 1999). 40 mm spacing 35 mm spacing 33 mm spacing 32 mm spacing 31 mm spacing 29 mm spacing 26 mm spacing 24 mm spacing Figure 313: Effects of isocenter spacing on the multiple isocenter dose distribution. The 70% and 50% isodose lines are shown in a transaxial plane for two equally weighted 30mm isocenters, each with a five arc set. 78 Four 14mm isocenters spaced at 14mm, all weights equal 1.8. 1.6  .      1. Total dose 1.4    1.2      M 1 ......... ........ .... .... ... .......... ... 0.1   0.4    O H i I , I H I i I 0.2   . 0 25 50 75 100 125 150 Lateral distance (mm) Figure 314(a): Dose profile through four optimally spaced 14mm isocenters, each with an equally weighted five arc set. The dose profile for each isocenter and the total combined dose profile are shown. Four 14mm isocenters spaced at 14mm. isoc. weights adjusted 1.17 : 0.94 : 0.94 1.17 1.8 1.4 .  ..     1.4       0 ' 1.2  .. . + 4 1  08        Figure 314(b): Dose profile through four optimally spaced 14mm 0  i      0. .............  ........ .. ........... 0 25 50 75 100 125 150 Lateral distance (mm) Figure 314(b): Dose profile through four optimally spaced 14mm isocenters. The dose profile for each isocenter and the total combined dose profile are shown. i ; ....  , 0.2 .........   I  I ............... dose profile are shown. Four 14mm isocenters spaced at 14mm, total normalized dose,adj(solid),unadj(dashed) 1 r I / If.' Adjusted weights 0.9 0.8 0.7 0.6 CD (0 cr 0.4 0.3 0.2 0.1 25 50 75 100 Lateral distance (mm) Figure 314(c): Total 39(b). dose from four isocenters for the plans shown in Figures 39(a) and Figure 315: Axial plane dose distribution (70%, 35%, and 14% isodose lines shown) for four 14 mm isocenters. (A) all weights equal, (B) weights adjusted to obtain equal isocenter doses. 44.7 mm \ Unadjusted (equal) 44.7mm V weights I  I /I \ Multiple Isocenter Radiosurgery Planning via Sphere Packing In a simple manner, multiple isocenter radiosurgery planning may be considered as the problem of determining the positions and sizes of the multiple spherical high dose regions or isocenters which will be used to fill up the target volume, or put another way, of determining the spherepacking arrangement with which to fill the target volume. Conventional radiosurgery optimization schema are generally iteratively based, dosimetrically driven algorithms. They require many computations in order to compute a radiosurgical plan dose distribution, and then to evaluate the quality of the dose distribution. Geometrically based radiosurgery optimization has been suggested as a possible alternative means of optimizing radiosurgery treatment planning, since geometrical solutions are generally much less computationally expensive than the large iterative set of dosimetric calculations required for most other optimization strategies (Wu 1996; Bourland 1997; Wu 1999). For instance, a high isodose region around a single isocenter may be approximated by a sphere of a diameter approxirrately equal to that of the circular collimator used. Given such a sphere's location and diameter in stereotactic space, it is much easier to describe this sphere's spatial relationship to the target volume than it is to compute a three dimensional dose distribution, and to then find the relationship of this dose distribution to the target's volume. Wu et al (Wu 1996; Wu 1999) proposed a geometricallybased sphere packing optimization method for automated gamma unit radiosurgery, in which the shot (isocenter) locations and sizes are selected according only to the target's three dimensional shape. Grandjean (Grandjean 1997) et al report on their implementation of a similar volume packing process for linac radiosurgery, but one in which ellipsoids as well as spheres are graphically placed by a human user in a three dimensional representation of the target. Both of these methods are similar, in that isocenter or shot placement is based simply on obtaining the best geometrical agreement between the target's shape and the shape of the high dose region characteristic of the treatment unit (i.e. a sphere or ellipsoid). Due to nongeometric constraints imposed by the physics of radiation dosimetry (e.g. due to dose interactions and contributions between neighboring isocenters), multiple isocenter radiosurgery planning is not exactly a spherepacking problem. However, in many cases, a spherepacking arrangement will translate into a satisfactory radiosurgery plan, particularly if simple dosimetric adjustments are made to the automatically generated plan (i.e. use of the isocenter weighting tool discussed in the previous section). An alternative sphere packing method is presented in this section that shows potential to significantly aid the planning of complex, multiple isocenter cases. Based on tests with irregularly shaped phantom targets and with a representative sampling of clinical example cases, the method demonstrates the ability to generate radiosurgery plans comparable to or of better quality than multiple isocenter linac radiosurgery plans found in the literature. The major steps of the sphere packing process are diagrammed in Figure 316. A 7.6 cm3 phantom target, similar in shape to a large acoustic neuroma, is shown in Figures 317 and 318 with its sphere packing arrangement, and will be used to illustrate the process. Step 1: Read in target volume contours. Target volume information is obtained by manually contouring the target on successive transaxial image slices in the University of Florida radiosurgery treatment planning system. Code written in the MATLAB language (Matlab v5.1, The Mathworks Inc., Natick, MA) processes the target contours data, and computes the sphere packing arrangements. Step 2: Map target points into 3D array. Each point identified from the target contour data file is mapped into a three dimensional integer valued array. Each voxel, or array element, corresponding to a target point is set to a value of 1. After mapping each given target point into an array element, the program closes any gaps between "1" voxel elements in the array, ensuring that the contour in each plane is a closed, continuous curve. Step 3: Build solid voxelized model. A fill routine assigns the voxels inside each contour with values of 1, resulting in a solid, connected array of onevalued voxels corresponding to the target volume, and zerovalued voxels outside the target (Figure 3 17a). A default voxel size of 1 x 1 x 1 mm3 was used for this study, although this process is general and may be applied to any voxel size. START T . Build 30 voxel model of target Grassfire * procedure (shelling) Evaluate score for  maximum valued voxels Select voxel with  maximum score as seed voxel Locate max. score in neighborhood of seed voxel Reset noncovered target voxels to "1" values A Place sphere No STOP Figure 316: Block diagram of sphere packing process a) b) c) d) e) / f) g) h) / Figure 317: Major steps of the grassfire and sphere packing process for a phantom target (phantom target number three), shown in a coronal plane. a) Voxelized model of the target, constructed from axial contours, b) Solid model after application of the grassfire process in 3D. Voxel intensity (color) is a function of each voxel's value after the grassfire process. c) First isocenter, 22 mm diameter, placed at bestscoring voxel, d) The voxels inside the sphere are effectively removed for purposes of the grassfire process. Note the change in the voxel values (color) near the target borders, at the arrow. e) The situation after application of grassfire process. The deepest voxels are now identified as candidate isocenter locations for the second isocenter. f) Placement of the second isocenter. g) Voxels inside the second sphere are effectively removed. h) Applying the grassfire process after the situation in g). Arrows indicate locations where voxel values have changed. Step 4: Grassfire. The outermost layer of voxels in the target model is then identified and removed, and the process repeated until the deepest lying voxels have been identified. This peeling and layering, or shelling, by a grassfiree" algorithm, is so called due to the analogy of burningoff one outer layer of the target at a time, as in a fire (Blum 1973). This edge detection process identifies the outermost layer of voxels in the 3D model, and adds the integer 1 to each outer layer voxel's value, converting all outer layer voxels from 1 values to 2. Voxels lying one layer deeper inside the target are easily identified as the set of "" valued voxels which are adjacent to "2" valued voxels. These voxels one layer deeper than 2 are assigned a value of 2 + 1 = 3, with the algorithm continuing application of this process until all 1valued voxels have been assigned a layer value, with the deepest lying voxels having the largest values (Figure 317b). Ideally, the deepest lying voxel in the entire target volume would thus be quickly identified as the best location for an isocenter. Such a maximumvalued voxel's value should also indicate the size of the sphere to be placed there as well, since (layer number minus 1 ) should indicate approximately the depth from the surface (in units of voxel size). For example, a maximumvalued voxel with a value of 7 should lie (71) = 6 voxels from the surface of the target, which suggests that a sphere 12 voxels in diameter would be required to cover this volume. a) b) c) 5mm L. d) e) f) Figure 318: Threedimensional depiction of the example phantom target and spheres placed by the sphere packing algorithm, a) Target volume b) Sphere packing arrangement for fiveisocenter plan c) Target volume superimposed on sphere packing arrangement d) Prescription isodose surface (64% of maximum dose) superimposed on sphere packing arrangement e) Prescription isodose surface superimposed over target volume. The prescription isodose surface covers the target with the exception of isolated 'clipped" edge voxels (see arrow), f) Superposition of target volume, sphere packing arrangement, and prescription isodose surface. Step 5: Identify the optimal isocenter size and position (location). Ideally, a shelling process would easily identify the deepestlying region of the target volume as a single voxel. However, the process described determines only an approximation to the various layers of the target from the outside in, with each cubical voxel representing a differential radial volume element. For the small intracranial target sizes and the 1 x 1 x 1 mm3 voxel sizes used, the discretization of the 3D target model generally does not result in a unique identification of the deepest lying voxel. Hence, often more than one voxel is identified as belonging to the deepest layer. In the example case we have been following, the first application of grassfire process identifies 7 voxels with the maximum value of 8, some of which are shown in Figure 317b. Interpreting the distribution of these maximum valued voxels may be difficult, as these voxels do not always lie together in one group. Even when the maximum valued voxels form a simple connected group, simply taking the centroid of all such voxels will not necessarily yield the optimum sphere location. This occurrence of multiple maximum valued voxels is especially a problem after one or more spheres have been placed in the target volume, and many target voxels lie at or near the surface of the target or another sphere. Using smaller voxels does not necessarily result in unique identification of the deepest voxels, either, but does result in much longer computation times by increasing the number of voxels which must be processed. To resolve the ambiguity of multiple voxels apparently lying in the same depth, a score function was used to further distinguish the maximum valued voxels from one another. An additional benefit of using a score function to rank candidate isocenter locations was realized, in that a score function easily allows other factors to be considered other than depth from the target's surface. For instance, it is often possible and preferable to use a larger diameter sphere to cover a greater volume of target, at the expense of covering a small volume of nontarget tissue. This is particularly true of the first isocenter, if multiple isorenters are to be used to conform the dose distribution to the target. Renormalizing a multiple isocenter dose distribution to maximum dose causes isodose constriction as the magnitude of the maximum dose is changed by the addition of subsequent isocenters. The use of a score function allows the algorithm to take this factor into consideration when attempting to optimize sphere placement. Other factors may be considered as well, such as interisocenter distances. The score function is computed at each maximum valued voxel location, for each possible circular collimator (sphere) size, and the bestscoring (numerically largest score) voxel from the list presented to the user. The score function is the product of several independent factors: fl, fractional target coverage; f2, a penalty factor which is a function of the volume of nontarget tissue covered; and a third factor, f3, a function of all inter isocenter distances. In equation form, for a sphere k at a particular position, these relations are (32) Score = fi x f2 x f3, with Target volume covered by sphere (33) f = w, * total target volume volume of normal tissue covered by sphere (34) f2 = e total target volume (35) f; = f[dist(i,k)], i=1 Itk where 0, if dist(i,k) < 0.9dop, (10 (36) f[dist(i,k) i k] =  dist(i,k) 9, if 0.9dop < dist(i,k) < d , dopt 1.0, if dist(i,k) > dopt and dist(i,k) is the distance between isocenters i and k. Factor fi is the fraction of target coverage for a sphere of a specified size at the voxel under consideration, which varies from 0.0 to 1.0. Factor f2 is a normal tissue penalty function, so that f2 = 1.0 if no normal tissue volume is covered, and f2 0.0 as increasing volumes of normal tissue are covered. Factor f3 is a function of the distance of each isocenter to all other isocenters. Factor f3 serves to prevent placing spheres (isocenters) too closely to one another, which results in excessive target dose heterogeneity (Meeks 1998c). This isocenter to isocenter distance function is zero for isocenterisocenter distances less than 0.9dopt (dopt = empirically determined optimal isocenterisocenter distance for the two spheres under consideration, implemented in the form of a lookup table accessible to the code (Foote 1999)), is unity for isocenter isocenter distances greater than or equal to the optimal distance, and varies linearly between zero and unity for distances between 0.9 dopt and dopt. Terms w1 and w2 are relative weighting factors, with which the user may control the behavior of the algorithm. For example, an "aggressive" setting (relatively small penalty for normal tissue over coverage) can be chosen by decreasing the relative weight of w:. A conventional sphere packing (the target volume is filled with nonintersecting spheres which do not extend outside of the target volume) results when w2 4 c, so that f2 = 0 if any normal tissue voxels are covered by spheres, and f3 0 if any of the spheres are too close to each other. For all of our work, wl =1 by default, with w2 being the only adjustable variable in the score function. Although it could also be considered a variable, the interisocenter distance factor f3 was left unchanged as it is accounted for in equations (35) and (36). The optimal maximumvalued voxel is thus identified as the voxel with the maximum score function value. However. this voxel is not necessarily the optimal location at which to place a sphere. For this reason, an optimization loop is used to search the neighborhood around the best scoring voxel found so far in the process. The best scoring maximum valued voxel is input as a seed voxel, the score calculated (for all 14 circular collimator sizes) at that voxel and all 26 of its neighboring cubic I x xl mm3 voxels, and the largest score value of all these recorded. If the seed voxel is the best scoring of all these 27 voxels, the optimization routine has converged, and the voxel is used as the recommended isocenter (sphere center) location, with the collimator size corresponding to the best score. If one of the 26 neighboring voxels yields a better (higher) score, then it is made the seed voxel, and the process repeated for the new seed voxel and its neighbors until no further improvement in score function is found. In our example case, a best scoring voxel was soon located within one voxel of the best scoring maximum valued voxel, and a 22 voxel (mm) diameter sphere was placed there, as shown in Figure 317c. Step 6: Place sphere corresponding to isocenter size and location. Spheres are placed by setting voxels lying inside the sphere to a unique numerical value, such as the maximum voxel value plus two. For instance, if the grassfire process identified the deepest layer of voxels as those with a value of eight, voxels inside any placed spheres would be set to a value of ten, which easily allows one to distinguish voxels inside a sphere from other voxels. If the user desires to place another sphere after the first sphere has been placed, all target voxels not covered bythe first sphere are reset to values of 1, and the entire grassfire process repeated (Figures 317d and 317e, steps 46). Note that target voxels inside the sphere which was placed have been effectively removed for purposes of the grassfire algorithm, causing the sphere's surface to be treated as an outer surface of the target (see arrows in Figures 317d and 317e). Figures 317f through 317h similarly depict selection of the second 14mm isocenter location after the first isocenter has been placed. The algorithm continues to place three more isocenters, all 5mm in diameter, before halting. Figure 314 depicts threedimensional views of the sphere packing arrangement, the target, and the prescription isodose cloud surrounding the target. Figure 319 shows this final dose distribution in three orthogonal planes through the center of the target. 
Full Text 
xml version 1.0 encoding UTF8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd INGEST IEID E69G4P02N_GPGS4M INGEST_TIME 20130214T17:42:12Z PACKAGE AA00013528_00001 AGREEMENT_INFO ACCOUNT UF PROJECT UFDC FILES 