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Page i Page ia Acknowledgement Page ii Table of Contents Page iii Page iv Abstract Page v Page vi Chapter 1. Introduction Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Chapter 2. Review of the literature Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page 16 Page 17 Page 18 Page 19 Page 20 Page 21 Page 22 Page 23 Page 24 Page 25 Page 26 Chapter 3. University of Florida treatment planning Page 27 Page 28 Page 29 Page 30 Page 31 Page 32 Page 33 Page 34 Page 35 Page 36 Chapter 4. Inverse radiotherapy treatment planning Page 37 Page 38 Page 39 Page 40 Page 41 Page 42 Page 43 Page 44 Page 45 Page 46 Page 47 Page 48 Page 49 Page 50 Page 51 Chapter 5. Techniques for quantitative plan evaluation Page 52 Page 53 Page 54 Page 55 Page 56 Page 57 Page 58 Page 59 Page 60 Page 61 Page 62 Page 63 Page 64 Page 65 Page 66 Page 67 Page 68 Chapter 6. Clinical treatment planning studies Page 69 Page 70 Page 71 Page 72 Page 73 Page 74 Page 75 Page 76 Page 77 Page 78 Page 79 Page 80 Page 81 Page 82 Page 83 Page 84 Page 85 Page 86 Page 87 Page 88 Page 89 Page 90 Page 91 Page 92 Page 93 Page 94 Page 95 Page 96 Page 97 Page 98 Page 99 Page 100 Page 101 Page 102 Page 103 Page 104 Page 105 Page 106 Page 107 Page 108 Page 109 Page 110 Page 111 Page 112 Page 113 Page 114 Page 115 Page 116 Page 117 Page 118 Page 119 Page 120 Page 121 Page 122 Page 123 Page 124 Page 125 Page 126 Page 127 Page 128 Page 129 Chapter 7. Physical requirements of intensity modulation device Page 130 Page 131 Page 132 Page 133 Page 134 Page 135 Page 136 Page 137 Page 138 Page 139 Page 140 Page 141 Page 142 Page 143 Page 144 Page 145 Page 146 Page 147 Page 148 Page 149 Page 150 Page 151 Page 152 Page 153 Page 154 Page 155 Page 156 Page 157 Page 158 Page 159 Page 160 Page 161 Page 162 Page 163 Page 164 Page 165 Page 166 Page 167 Page 168 Page 169 Page 170 Chapter 8. Clinical efficacy of tomotherapy Page 171 Page 172 Page 173 Page 174 Page 175 Page 176 Page 177 Page 178 Page 179 Page 180 Page 181 Page 182 Page 183 Page 184 Page 185 Page 186 Page 187 Page 188 Chapter 9. The effect of random positional errors on inverse radiotherapy plans Page 189 Page 190 Page 191 Page 192 Page 193 Page 194 Page 195 Page 196 Page 197 Page 198 Chapter 10. Discussion Page 199 Page 200 Page 201 Page 202 Page 203 Page 204 Page 205 Page 206 Page 207 Page 208 Appendix A. Calculation of normal tissue complication probability Page 209 Page 210 Page 211 Page 212 Page 213 Page 214 Page 215 Page 216 Page 217 Page 218 Page 219 Page 220 Page 221 Appendix B. Calculation of tumor control probability Page 222 Page 223 Page 224 Page 225 Page 226 Page 227 Page 228 Page 229 Page 230 Page 231 Page 232 Page 233 Page 234 Page 235 Appendix C. Optimization of intensity modulation functions Page 236 Page 237 Page 238 Page 239 Page 240 Page 241 Page 242 Page 243 Page 244 Page 245 Page 246 Page 247 Page 248 Page 249 Page 250 Page 251 Page 252 Page 253 Page 254 Page 255 Page 256 Page 257 Page 258 Page 259 Page 260 Page 261 Page 262 References Page 263 Page 264 Page 265 Page 266 Page 267 Page 268 Page 269 Page 270 Page 271 Biographical sketch Page 272 Page 273 Page 274 
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CONFORMAL RADIOSURGERY AND RADIOTHERAPY PLANNING USING INTENSITY MODULATED PHOTON BEAMS By SANFORD L. MEEKS 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 1994 p 1W~ ACKNOWLEDGEMENTS I would like to express my sincere appreciation for the guidance provided by the members of my supervisory committee. Special thanks are due to my committee chairman, Dr. Frank Bova, who has taught me a great deal about medical physics, and whom I will always respect and admire. I would also like to thank the Nomos corporation for its support, and its technical staff for assisting me overcome numerous obstacles caused by computer and/or operator error. I am also grateful to Dr. John Buatti, Dr. Gerald Kutcher and Dr. Andrzej Niemerko for insightful discussions regarding the doseresponse modelling required for quantitative plan comparisons, and Dr. John Buatti, Dr. Yvonne Mack, Dr. William Mendenhall and Dr. Robert Ziotecki for assistance with delineation of target volumes. Finally, I would like to thank all of my family, friends and coworkers who have supported me emotionally and helped make this work enjoyable. In particular, I would like to thank my parents for their gentle prodding throughout my educational experience, and my wife, Allyson, for her patience and also for allowing me the greatest joy I've ever known by giving me a son, Alton. TABLE OF CONTENTS ACKNOWLEDGEMENTS ...................................... ii ABSTRACT .......................................... v CHAPTERS 1 INTRODUCTION .................................. 1 Conventional External Beam Radiotherapy ..................... 1 Stereotactic Radiosurgery .................................. 2 Conformal Radiotherapy .................................. 3 2 REVIEW OF THE LITERATURE ........................... 9 Inverse Radiotherapy Planning Algorithms ..................... 9 Clinical Treatment Planning Studies ........................ 21 3 UNIVERSITY OF FLORIDA TREATMENT PLANNING ......... 27 Conventional Treatment Planning .......................... 27 Three Dimensional Planning (Virtual Simulation) .............. 30 Stereotactic Radiosurgery Treatment Planning ................ 31 4 INVERSE RADIOTHERAPY TREATMENT PLANNING ......... 37 M IM IC .......................................... 37 Peacock PlanTM ............. 41 Peacock Plan TM .................................... 41 Verification of Dosimetry Algorithm ........................ 47 5 TECHNIQUES FOR QUANTITATIVE PLAN EVALUATION ...... 52 Dose Volume Histograms ................................. 52 Normal Tissue Complication Probability ...................... 56 Tumor Control Probability .............................. 60 Dosimetric Statistics .................................... 64 Biologically Normalized Dose Fractionation .................. 65 Score Functions ............................... Delivery Efficiency ............................. 6 CLINICAL TREATMENT PLANNING STUDIES ......... Stereotactic Radiosurgery Patients .................... Head and Neck Carcinomas ....................... Intact Breast ................................. Lung Cancer ................................. Carcinoma of the Prostate ......................... Discussion .................................... 7 PHYSICAL REQUIREMENTS OF INTENSITY MODULATION DEVICE .................................. Computer Simulation of Intensity Modulator ............. Derivation of Semiempirical Dose Model ........... Description of Computer Algorithm .............. Vane Width ............................... Step Resolution ........................... Clinical Resolution Requirements .................... . 67 . 68 . 69 . . .. 73 . . .. 93 . . .. 94 . . .. 96 ...... 98 . . .. 99 . . .. 130 130 131 136 137 145 152 8 CLINICAL EFFICACY OF TOMOTHERAPY ............... 9 THE EFFECT OF RANDOM POSITIONAL ERRORS ON INVERSE RADIOTHERAPY PLANS .................... 10 DISCUSSION ................................... APPENDICES 171 . 199 A CALCULATION OF NORMAL TISSUE COMPLICATION PROBABILITY .................................. 209 B CALCULATION OF TUMOR CONTROL PROBABILITY ....... 222 C OPTIMIZATION OF INTENSITY MODULATION FUNCTIONS ... 236 REFERENCES ....................................... 263 BIOGRAPHICAL SKETCH ................................ 272 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CONFORMAL RADIOSURGERY AND RADIOTHERAPY PLANNING USING INTENSITY MODULATED PHOTON BEAMS By Sanford L. Meeks December 1994 Chairperson: Frank J. Bova, Ph.D. Major Department: Nuclear Engineering Sciences This paper investigates the efficacy of inverse radiosurgery and radiotherapy planning in the clinical environment. Inverse radiotherapy plans were generated for patients with lesions at various anatomical sites using the Peacock treatment planning system, which determines the optimal conformal radiotherapy plan through backprojection and simulated annealing. These treatment plans were then compared to two and/or threedimensional conventional treatment plans generated for actual patient treatment. Plan comparisons were accomplished through conventional qualitative review of twodimensional dose distributions in conjunction with quantitative techniques such as dose volume histograms, dosimetric statistics, normal tissue complication probabilities, tumor control probabilities, numerical scoring and treatment delivery efficiency. The physical limitations of modulation devices based on multileaf collimators were studied through computer simulation of these devices in addition to examination of their utility in the clinical environment. Other treatment parameters which affect the clinical efficacy of conformal radiotherapy plans that were also studied include the use of noncoplanar beams versus single arc conformal therapy (tomotherapy) and uncertainty in patient positioning. CHAPTER 1 INTRODUCTION Conventional External Beam Radiotherapy Radiation therapy is a clinical specialty devoted to the treatment of patients with malignant or benign neoplasms through the use of ionizing radiation. The primary goal of radiotherapy is to deliver a therapeutic dose to the targeted lesion with minimal dose to surrounding normal tissue, resulting in uncomplicated eradication of the tumor. Unfortunately, the dose required for tumor control often leads to a finite probability of undesirable side effects in normal tissue. Nonetheless, radiation therapy is an appealing alternative to surgery in many instances where surgical resection may produce unacceptable anatomical, physiological or cosmetic results or for extensive lesions that cannot be surgically rejected. Radiotherapy also serves as a powerful adjunct to other treatment modalities such as surgery and chemotherapy. Radiotherapy is often used preoperatively to shrink the tumor prior to resection, or alternatively, postoperatively in order to eradicate microscopic disease left in the area of the gross tumor. Similarly, chemotherapy is used in conjunction with radiation therapy in order to reduce the initial number of clonogenic cells before irradiation, or to eradicate distant metastases which may not be within the irradiated volume [Per92]. Radiation was first used for cancer treatment by Grubbe in 1896, shortly after Roentgen's discovery of x rays in 1895 and the Curies' discovery of radium in 1896 2 [Wal88]. Technological advances in radiotherapy equipment have accrued steadily since that initial experience with improved xray generators followed by cyclotrons, synchocyclotrons, betatrons and linear accelerators [Per92]. Modem radiotherapy relies primarily on high energy gamma rays from 'Co beams and high energy x rays and electrons produced by linear accelerators, although other particulate and electromagnetic irradiations are frequently utilized. Stereotactic Radiosurgery Stereotactic radiosurgery is a technique in which small focused beams of radiation are utilized to treat intracranial targets. Radiosurgery is an attractive treatment modality because it can be used to treat patients who have lesions which are not suitable for conventional neurosurgical techniques, there is little risk of infection or hemorrhage, and the procedure may be performed quickly on an outpatient basis [Win88]. At the University of Florida, arteriovenous malformations are the most common lesions treated with stereotactic radiosurgery, but a variety of solid lesions exist which are suitable for treatment by radiosurgery. These include pituitary tumors, pinealomas, acoustic neuromas, small malignant neoplasms and craniopharyngiomas [Fri89]. Stereotactic radiosurgery was first described by Lars Leksell of the Karolinska Hospital in 1951. He first experimented with the use of finely collimated beams of 200 kVp x rays, but it was clear that higher energy radiation should be utilized [Lek51]. With the help of two physicists, Kurt Liden and Borje Larsson, Leksell experimented with the use of proton beams and linear accelerators, but he decided these devices were inadequate for radiosurgery. He and his coworkers then developed the Gamma KnifeTM, 3 which uses multiple 'Co sources focused at a central point [Lek83]. Using the Leksell Gamma Unit, these and other researchers have reported impressive control rates for a variety of small lesions [Lek87]. This high rate of success has been limited to small targets, however, since the maximum Gamma Knife field size has an 18 mm diameter. Since the average radiosurgery is approximately 24 mm, larger targets are treated with many small shots from the Gamma Knife. The overlap of these small circular shots can lead to an undesirable large dose inhomogeneity within the targeted region. In spite of this success, the Gamma Knife is not practical for use in most radiotherapy clinics since it is a costly dedicated unit with two hundred one 'Co sources which must be maintained and periodically reloaded. In order to construct an effective radiosurgical system that would be less expensive yet flexible, researchers investigated the use of linear accelerators. These systems utilize multiple noncoplanar arcs of radiation which intersect at the target to achieve a steep dose gradient outside of the target. This allows one to achieve a high dose within the targeted region while maintaining minimal dose to normal tissues outside of the target [Fri92]. One such system has been developed at the University of Florida by Friedman and Bova. This system has the highest proven treatment accuracy of the linac systems currently used. It has a radiation beam accuracy of 0.2 + 0.1 mm [Fri89]. Conformal Radiotherapy In order to reduce toxicity to normal tissues from radiotherapy, it is critical that the high dose region be shaped to fit the intracranial target volume in all dimensions. The contouring of the target region with the high dose region is known as conformation 4 therapy [Bra82]. Various methods have been utilized in an attempt to conform the dose distribution to the shape of the target. In conventional radiotherapy, combinations of weighted fields are used to help shape the isodose distribution. Wedged fields are sometimes used in conjunction with these weighted fields in order to produce dose gradients which help to further conform the distribution. Combination of different radiation qualities and modalities (photons and electrons) is a powerful tool often exploited in order to force dose deposition in a region of interest and maximize dose falloff outside of this region. Field shaping devices are employed to contour these radiation beams to the shape of the targeted lesion. One common method of field shaping is the use of custom low melting alloy blocks for each treatment field. These blocks may be designed using either radiographic or computer generated Beam's EyeView techniques (BEV). Radiographic techniques have historically been more common, since the physician need simply outline the shape of the block on radiographs taken through the target volume. CT scan data are often used to aid the radiotherapist in delineation of target and critical structures on the plane radiograph, but use of this data forces the physician to mentally integrate the two dimensional CT slices into a three dimensional image [She87]. The BEV technique more fully exploits the information obtained from CT scans by digitally reconstructing the data set in an arbitrary plane such that the observers eye may be hypothetically placed at the radiation source. By viewing the patient along the central axis of the radiation beam, the relative positions of anatomical structures may be easily determined and the target may be accurately delineated [Goi83]. 5 Obviously, these custom blocks can only be used for static radiotherapy treatments which utilize a limited number of fields. Multileaf collimators may be utilized to increase the number of static fields since the projections of the leaves into the field approximate the smooth contour of custom shielding blocks. Dynamic multileaf collimation has been proposed in order to combine the benefits of arc therapy with BEV conformal techniques [Mos92]. Using the BEV, the leaves of these collimators may be adjusted to conform to the projected area of the target as the gantry and/or treatment couch are moving. Similar conformation methods are employed in stereotactic radiosurgery. Various sizes of circular collimators are available which adequately conform the radiation beam to the shape of spherical lesions. Beam weighting and arc manipulations allow the spherical distribution to be elongated and rotated to better conform the high dose region to oblong target shapes. For highly irregularly shaped targets, more complicated techniques such as the use of multiple isocenters may be required. The use of multiple isocenters does often yield a conformal plan, but also leads to a large dose inhomogeneity (e.g., hot spots where the spherical distributions overlap) within the target volume. This appears to be undesirable since a retrospective study performed by Nedzi et al. indicates that dose inhomogeneity is associated with an increased risk of complications for the radiosurgery patient [Ned91]. McGinley et al. have designed an adjustable collimator to tailor the shape of the high dose region to the shape of irregular target volumes. This device consists of a circular collimator which was modified to allow the manual insertion of lead blocks in order to alter the beam shape and cause an elongation of the dose 6 distributions [McG92]. The dose distribution can be elongated along the rotation axis or perpendicular to this axis. Elongation along other axes is not possible, which limits the clinical usefulness of this collimating device. Dynamic field shaping is also under investigation for use in conformal radiosurgery. A retrospective study by Bova and Leavitt of over forty patients treated with radiosurgical techniques concluded that "over 2/3 of the patients would have received a reduced radiation dose to the normal brain through use of conformational field shaping techniques, had these capabilities been available" [Lea91,pg. 1249]. Conceptual studies have been performed by Moss [Mos92] and Nedzi et al. [Ned92]. Moss investigated the viability of dynamic multileaf collimation. Using computer simulations, he compared the dose distributions that would result from the use of two and four jaw multileaf collimating systems to shape the fields for treatment of a variety of target shapes. He determined that either one of these systems would provide better conformal therapy than a rotating collimation system [Lea91] or the circular collimating system currently employed. Nedzi et al. performed a computer modeling study which compared the use of five different field shaping devices. They determined the dose distributions that would result from utilizing these devices for the treatment of 43 tumors that had been previously treated at the Joint Center for Radiation Therapy of Harvard Medical School. They concluded that although an ideal multileaf collimator yields the best conformal plan, even simple field shaping devices offer an advantage over the circular collimating devices that are currently used. This improvement was most noticeable with irregularly shaped 7 targets that previously required multiple isocenters, where simple field shaping devices can provide homogeneous dose distributions and adequate field shaping [Ned92]. One of these simple collimating devices is a rotating jaw collimator. A prototype rotating jaw collimator has been designed and constructed by Leavitt et al. [Lea91]. This device has two sets of rectangular collimators upstream from the existing circular collimator. The rectangular collimators are mounted on rotating tables such that both rotation and translation of the jaws are possible. Thus, this collimating system may define a polygonal field shape having up to four straight and four curved edges. Obviously, this device can not be used to effectively treat concave field shapes of lesions that are extremely irregular. It is very simple mechanically, however, and has been shown by Moss, Nedzi and Leavitt to be useful for many situations. Although these techniques provide an attempt at conformal therapy, it is impossible to design a collimation system which can exactly tailor the shape of the dose distribution to the projected area of the target at every point on the target. These collimation schemes also fail to conform to the shape of treatment volumes that contain concave regions [Bor90]. A new conformation technique known as inverse radiotherapy planning has been proposed which theoretically alleviates some of the problems associated with current conventional techniques. Standard techniques in conformal therapy set up the beams desired for treatment and then compute a dose distribution based on these beams. If the distribution is not satisfactory, the beam set up is altered in an iterative fashion until the distribution is satisfactory. In contrast, inverse radiotherapy techniques begin with the desired dose distribution and calculate the fluences necessary to produce this 8 distribution [Bor90]. This treatment technique is analogous to the filtered backprojection technique used for reconstruction of images in computed tomography (CT). In CT, the twodimensional density distribution of tissue within the patient is projected onto onedimensional lines. These projections may be filtered and then backprojected resulting in a set of twodimensional slice images. Analogously, inverse radiotherapy planning starts with a set of prescribed twodimensional dose distributions which are projected onto lines. These projections may be mathematically filtered to obtain an intensity modulation function (IMF), and irradiation of the patient ("backprojection" of the IMF) results in the desired dose distribution. As with CT imaging, other methods have been attempted to solve this problem, and results of these research efforts will be discussed further. In radiotherapy and radiosurgery, once the high dose region has been defined by the physician's outline of the target volume, the application of inverse planning has two primary components: 1) determine the beam fluences necessary to produce the desired dose distribution and 2) design a method of physically modulating the intensity of the radiation beam in order to produce these intensities. Once adequate solutions are obtained for these two components, inverse radiotherapy can theoretically produce a dose distribution which is not only BEV conformal, but conformal to the target shape in all dimensions. This research will investigate the efficacy of this conformal planning technique for achieving the aforementioned goal of radiation therapy. CHAPTER 2 REVIEW OF THE LITERATURE Inverse Radiotherapy Planning Algorithms As mentioned previously, inverse radiotherapy planning offers a unique approach to conformal therapy in which the beam fluences necessary to create the desired dose distribution within a patient can be calculated from this very dose distribution. This technique was first examined by Brahme et al. in 1982 [Bra82]. The aim of this investigation was to determine the onedimensional lateral dose profile required for an incident beam to produce a desired radial dose distribution after one complete rotation about the axis of symmetry of a cylindrical phantom. To further simplify the problem, a plane parallel beam was assumed and depth dose was approximated by a simple exponential characterized by a practical attenuation coefficient, Ax. Buildup near the surface of the phantom was also disregarded. These simplifying assumptions allow the desired dose distribution following one complete rotation to be computed as D(r) = d(x)exp( pz)  r7 where d(x) describes the lateral dose distribution (dose variation along the xaxis), z is the distance from the center of the cylinder along the beam axis (perpendicular to the x axis) and r is the radial distance from the center of the cylinder to any point within the cylinder. Through use of a transformation to polar coordinates, this integral may be rewritten as r n 0 1 0 (r2x2)2 which is the well known Abel integral equation. In order to obtain a solution for the lateral dose distribution, d(x), of the incident beam the Abel equation can be transformed into a convolution equation through another change of variables. The Laplace transform was applied to this convolution equation, and after a return to the original variables the explicit solution to the equation is X1 d(x) = df cO'. D(r)rdr. dx3 1 ro (x2r2)2 Thus, if the dose distribution, D(r) is known to be a continuously differentiable function, the lateral dose distribution of the incident beam may be calculated. This simplified statement of the inverse problem allowed Brahme et al. to draw several important conclusions. First, they realized that the solution to this problem is nearly identical to the problem of filtered backprojection in CT scanning. Thus, algorithms already in use may be adapted to fit the inverse problem. The use of these algorithms can present problems, however, since they can lead to the need for physically unrealistic negative fluences when used for the inverse problem. Negative beam fluences are a recurring obstacle when one attempts to determine the beam fluences required to produce an ideal dose distribution (eg., a high dose region surrounded by a zero dose 11 region). Obviously, it is physically impossible to have a high dose region surrounded by a zero dose region because the radiation beam deposits some finite dose as it traverses the region surrounding the target. Purely mathematical solutions to the inverse problem thus yield negative beam fluences which essentially subtract dose from the regions surrounding the target in order to produce the ideal dose distribution. Brahme et al. suggest that this problem can be avoided in practice with the use of higher energy beams. The lower attenuation coefficients associated with such beams lessens the need for negative beam fluences. Cormack [Cor87a] attempted to extend the work of Brahme for use with dose distributions which are not circularly symmetric. Cormack utilized virtually the same simplifying assumptions as were used in the previous work. Buildup near the surface was ignored, as was scattering. These assumptions allow the dose to be directly proportional to the beam intensity. Beam divergence was also ignored, which is a reasonable approximation if the source is a large distance from the surface. This work further simplified the problem into what was termed the zeroth approximation. This approximation assumed that cosh(14x)= 1, where 4 is the attenuation coefficient and x is the distance from the lesion to the surface. This assumption leads to a small error when used with higher energy beams (> 10 MeV), but can cause a rather large error with lower energies. Mathematically, the zeroth order attempt was formulated as follows. The dose, D, delivered during a complete rotation at a point, P, with polar coordinates (p,SO) is D(p,p)= f Apcos(Qy),Q]d0, '4' nt/2 12 where f denotes the fluence delivered along a single line during the rotation, as depicted in Figure 21. Figure 21: Geometric representation of Cormack's formalism. An intensity distribution f produces a constant dose along the line through P. The line OS makes an angle 7/2  0 with the xaxis. Reproduced with permission from Elsevier Science Ltd., UK [Cor87a, pg. 625, Figure 2]. Thus, this problem takes the form of a Radon transform, which is simply the problem of determining a function from its integrals along straight lines. Radon transforms have a well established mathematical form which can be extended for use with the inverse problem. The desired result can be obtained by expanding D in orthogonal functions, and directly deriving the expansions of fl. The resulting equation is (l+n)!P(li+n+2m+2) ,3, frm (l +n+r)!f(l+n+m+3/2) s2 where s is the distance from the center of the patient to the intensity distribution, r is the 13 distance from the intensity distribution to the xaxis, G is a shifted Jacobi polynomial, and 1, m, n, and X are integers. Cormack also noted the requirement for negative beam intensities which is imposed by the mathematical formalism. To deal with this problem, the beam intensity was set equal to zero where negative intensity was required by the theory. Although this approach fails to yield the ideal dose distribution, it is "perhaps no worse than the trial and error method presently used in treatment planning" [Cor87a, pg. 630]. Cormack and Cormack [Cor87b] proceeded to a solution for what was termed the firstorder approximation. The first order approximation used the same formalism and utilized many of the same assumptions (e.g., ignored scatter, buildup, and divergence) as were used in the zeroth approximation. The first order approximation was extended to include use with larger attenuation coefficients, and thus be useful with lower energy beams. Thus the form of the equation required to solve for the integral dose after one complete rotation is very similar to the one previously seen: D(p,q)= f lpcos(Oq_),O]exp[_.(R2r2) 2]cosh[lpsin(O9)]dO. 7n 'I It was determined that the first order approximation was in the form of an attenuated circular Radon transform. The problem was then solved for several specific dose distributions with an axis of symmetry, but a general solution was not obtained due to the mathematical difficulty encountered in solving this problem. 14 In 1988, Brahme attempted to apply the inverse approach in order to obtain optimal dose distributions for dynamic therapy. The desired dose distribution was modeled as a density of point irradiations, and the fluences required by at each gantry position were obtained by backprojection of these densities on the position of the radiation source. The optimal dose distribution was subdivided into basic optimal distribution densities for point targets. The desired dose distribution could then be computed as the convolution of these point dose densities with the point irradiation intensities, D() =f ff (F)d( I F,l \)d3r v V where d is the point dose density, phi is the point irradiation intensity, r is the distance from the center of the phantom to the point of dose calculation, and r0 is the center coordinate for each point irradiation. This convolution was performed in Fourier space, which eased the inversion of the equation since we now have a simple product of two Fourier transforms F{D(r} =F{ p(j I}Fd( IrF I)} Inversion of this equation yields the irradiation intensities in Fourier space. Taking the inverse Fourier transform yields the point intensities, but also results in zeros which cause large oscillations in the intensity function. Analogous to CT filtered backprojection, introduction of a low pass filter, Z(s,X) in Fourier space smooths the intensity function resulting in the following form for solution of the point irradiation intensities: (r3 =F=F{Z(9,).) DOsI These point irradiation densities may then be decomposed into thin pencil beams and These point irradiation densities may then be decomposed into thin pencil beams and 15 convolved back with the point dose distributions taking into account the true patient geometry. This allowed the production of isodose lines, which were simply the reverse of the procedure just completed multiplied by a correction for beam absorption during backprojection. A comparison of the results from use of this technique with conventional radiotherapy techniques can be seen in Figure 22. As seen in the figure, only complex conventional treatments can provide adequate conformation in cases involving concave targets. If the dose rate is varied along with the field size, however, Brahme theorized that even simple treatments such as two or three field techniques are sufficient. CONVENTIONAL UNIFORM BEAM RADIOTHERAPY : i I f *) * ... ' : "b7T 'i f p i t I ..". ,  / ,. ia / v ../ parallel oppsd beam therapy arc therapy four field box therapy conformation therapy NON UNIFORM BEAM RADIOTHERAPY {r: ( .  ',  three field / minimal mean dose specified marximum dose minimal dos technique outside target volume, to org at risk to organ at rtek Figure 22: Schematic comparison of inverse radiotherapy planning with conventional radiotherapy techniques. Modulation of beam fluence allows dose conformation () to targets (shaded) as well as minimization of dose to critical organs. Reproduced with permission from Elsevier Science Ltd., UK [Bra88, pg. 138, Figure 7]. 16 Barth [Bar90] extended this work to the case of ideal dose distributions for convex phantoms of arbitrary shape. The general approach was to represent arbitrary dose distributions as numerous small radially symmetric dose distributions (see Figure 23). The problem was then broken down into a summation of attenuated Radon transforms, so the mathematical formalism was very similar to that used by Cormack and Cormack [Cor87]. The inversion of these transforms lead to the required beam fluences. Scatter, buildup and divergence were again ignored in order to simplify the problem. The difficulty of negative beam fluences was again encountered, and these were simply set to zero as usual. N Figure 23: A convex phantom of arbitrary shape with an arbitrarily shaped dose distribution comprised of N small radially symmetric dose distributions. Reprinted with permission from Elsevier Science Ltd., UK [Bar90, pg. 429, Figure 4]. Barth felt that these explicit methods of fluence calculation can not be used to determine the final treatment plan due to the numerous simplifying assumptions which 17 must be employed in order to perform the calculations. Instead, he felt that this technique would be useful as a starting point for traditional forward iterative methods of plan optimization. Consequently, several methods have developed which exploit the use of both analytical and iterative techniques. For example, Bortfeld et al. [Bor90] applied image reconstruction techniques to the inverse problem. The required beam fluences, or intensity modulation functions (IMF), were calculated utilizing two well established CT algorithms: filtered backprojection and the iterative reconstruction technique (IRT). Scattering, buildup, divergence and inhomogeneities were ignored. To perform backprojection, the prescribed dose distributions were first projected onto lines, which is basically a simple summation of dose densities along ray lines. A twodimensional Fourier transform of these lines was performed, and a high pass filter was applied. Backprojection was then performed to obtain the IMF, and negative values of the IMF were set to zero. It was determined that this procedure did not significantly effect the isodose lines. This explicit approach does not force the isodose lines to exactly fit the target. To further optimize the dose distribution, IRT was applied using the filtered backprojection solution as its initial guess. The following criteria were deemed important for the optimization process. 1) Target dose should be close to prescribed dose. 2) Target dose should be homogeneous. 3) Dose to sensitive organs should be below their tolerance level. 4) Dose to normal tissues surrounding the target should be low. 18 An objective function was formulated to mathematically incorporate the first two criteria. The third requirement was stated as a constraint and the fourth is already required by the conformal technique. The mathematical formulation of the objective function was as follows: FI =E (dip)2=minimum eT where d, is the calculated dose and p is the prescribed dose. The summation was taken over all target points, and the function was minimized to obtain the best dose conformation. Seven iterative steps with the objective function lead to adequate conformation for complex targets, including convex shapes such as a horseshoe targets. The authors felt that extremely complex targets, however, might require additional iterative steps. Holmes et al. have devised an iterative filtered backprojection algorithm based on the analogy between SPECT image reconstruction and rotational radiotherapy [Hol94]. The initial beam profile is obtained through inversion of the ideal dose distribution. This inversion is essentially a filtered fourier deconvolution of the dose distribution and a monte carlo generated energy deposition kernel, which results in the incident energy fluence. All negative fluence values are initialized to zero, and the forward dose is calculated using a filtered Fourier convolution of this inversely obtained incident energy fluence with the energy deposition kernel. The dose distribution thus obtained is then compared against dose constraints for regions of interest, and if all points in the distribution are within the constraints, the calculation is accepted. If the calculation is 19 deemed unacceptable, the residual dose in the regions of interest is utilized to determine a new fluence profile. Dose is recalculated using this new energy fluence, and this process continues iteratively until an acceptable solution is obtained. Harmon also explored a compromise between analytic and iterative techniques by combining deconvolution and optimization [Har94]. This approach offers more flexibility than some others since it can calculate beam fluences for either rotational therapy or multiple static beams. In order to determine a twodimensional fluence profile for each beam portal chosen by the user, deconvolution of a monte carlo generated single voxel energy deposition kernel from the desired dose distribution is performed. This results in a TERMA (total energy released to matter) profile for each beam, which can be used to calculate the physical characteristics of the intensity modulator by ray tracing back toward the radiation source. This ray trace includes inverse square, attenuation in phantom and an effective attenuation through the modulation device. With this TERMA profile in hand, forward dose calculation proceeds via convolution of the TERMA with the aforementioned kernel. If multiple beam portals are designated, relative beam weighting for each portal is determined by an optimization routine which varies all weightings until the best fit to the desired dose distribution is obtained. Purely iterative techniques have also been explored for solution of the inverse radiotherapy planning problem, as exemplified by Webb's use of simulated annealing to optimize the required beam configurations [Web89, Web91a, Web91b, Web92]. This method "mimics the way a thermalized system . achieves its ground state as the temperature slowly decreases" [Web89, pg. 1352]. Webb's initial approach begins with 20 a twodimensional dose prescription and assuming that the treatment volume is axially uniform, the dose in each small elemental beam is projected along one dimensional lines. Scatter and buildup are ignored, and the dose is then calculated as the product of beam weighting and exponential attenuation. The beam weighting is allowed to start at zero, and weighting is slowly added iteratively until the desired weighting for each elemental beam is determined. Later papers in the series extended Webb's initial work by including scatter in the twodimensional technique [Web91a] and determining optimal elemental beam weightings for threedimensional conformal treatment planning [Web91lb, Web92]. Scatter is never included in Webb's threedimensional technique. Interestingly, this iterative technique represents a purely forward approach to solution of an inverse radiation transport problem. Inverse radiotherapy planning based on this technique has been commercialized by the Nomos Corporation [Nom94]. Nomos models the elemental beams as lxl cm2 measured finite size pencil beams and calculates dose for each of these pencil beams using a simple model based on tissuemaximum ratios and offaxis ratios. Optimal beam weightings for these pencil beams are determined using a twodimensional simulated annealing algorithm. These twodimensional optimized slices are then summed in order to determine a threedimensional dose calculation. Although twodimensional optimization does not guarantee an optimal threedimensional treatment plan, time required for execution of the threedimensional optimization using computer hardware currently available renders it impractical for this approach. 21 Clinical Treatment Planning Studies Historically, treatment plans were designed utilizing a relatively limited number of radiation field arrangements and the dose delivered from these fields was then superimposed on only one or at most a select few transaxial images of the patient. Comparison of rival treatment plans was thus relatively straightforward and based primarily on the physician's experience and basic dosimetric endpoints such as target dose uniformity and maximum critical organ dose as represented on this limited number of axial slices [Kut92]. The advent of three dimensional and conformal treatment planning systems and the complexity inherent in plans generated using such systems has sparked interest in more sophisticated methods of plan evaluation. The principal complicating factor in evaluation of such treatment plans rests in the large volume of data generated by such systems. As opposed to the single slice evaluation required for conventional treatment plans, three dimensional treatment planning systems often superimpose the dose distribution on fifty or more contiguous axial CT slices. Although displays are developing with tools which aid in the graphical comparison of rival treatment plans, it remains extremely tedious and time consuming to correlate and analyze the dose distributions on multiple axial slices of the patient [Mun91]. Conformal treatment planning systems have further complicated plan evaluation by presenting the clinician with dose distributions which deviate substantially from those typically utilized for patient treatment. Various numerical evaluation techniques have developed, but have historically been associated primarily with computerized optimization routines [Nie93, Kal92, 22 Moh92, Web92]. These algorithms, some of which were discussed in the preceding section, attempt to quantify the relative merit of plans through the use of dosimetric and or biological parameters which are formulated into objective functions. The various computerized algorithms then attempt to minimize or maximize the objective function, which should result in the ideal plan. Niemierko et al., for example, optimized the beam weightings for portals chosen by the user utilizing objective function based on normal tissue complication probability (NTCP) and tumor control probability (TCP) [Nie93]. Reportedly, these researchers have studied over forty clinical treatment plans and found that on average their optimization routine could quickly determine a better plan than one constructed by an experienced treatment planner. Similarly, Mohan et al. designed an algorithm based on simulated annealing that varies beam weightings in order optimize an objective function based on NTCP and TCP [Moh92]. Demonstrating their algorithm using a case of prostate cancer, the researchers found that their algorithm could design a plan with higher TCP and lower NTCP than the plan used to treat the patient. Webb [Web92] and Kallman [Kal92] both experimented with the use of dose response functions in their respective optimizations and both presented clinical examples. Neither compared these results to treatment plans designed by an experienced treatment planner and were used simply to demonstrate the use of their respective algorithms. The first widescale attempt at quantitative evaluation of clinical treatment plans was undertaken by the Collaborative Working Group on the Evaluation of Treatment Planning for External Beam Radiotherapy (CWG) and reported on in the International Journal of Radiation Oncology Biology Physics. In their study of three dimensional 23 treatment planning systems, the CWG developed and or improved treatment plan evaluation tools such as dose volume histograms (DVIHI) [Drz91], NTCP [Kut91a], TCP and a subjective numerical scoring system [Mun91a]. In addition, the CWG reviewed twodimensional dose distributions superimposed on reconstructed axial, sagittal and coronal planes within the patient. These tools were then used for the evaluation of three dimensional treatment plans generated for eight separate treatment sites: nasopharynx [Kut91b], larynx [Coi91], intact breast [Sol91], Hodgkin's disease [Bro91], lung [Ema91b], paraaortic node [Mun91b], prostate [Sim91] and postoperative rectum [Sha91b]. Comparison of the threedimensional plans with conventional plans used for treatment of these lesions proved 3D planning a useful tool which ensured proper delineation of the target in all dimensions as opposed to one axial plane, and also allowed clinicians to better avoid critical organs near the treatment volume. Conformal radiotherapy planning has not enjoyed the benefit of thorough investigation by a collaborative working group, although several researchers have studied the efficacy of this approach. Due to the high incidence of acute and chronic toxicities associated with conventional radiotherapy of the prostate, many researchers have studied this disease site for conformal radiotherapy. In these studies, conformal is defined as treatment in which fields are designed using a beam's eye view display (BEV). Several use only a standard four field box technique with blocks designed using the BEV utility [Vij93, Sha91a, Sof92], while others add oblique fields to this standard technique in order to attain better distributions [San91]. These studies showed that dose to nearby critical structures such as the bladder and rectum could be reduced by up to 31% and 24 25%, respectively, when compared to clinical controls [Sof92]. In addition, clinical trials have proven that incidence of acute toxicity is reduced using BEV conformal techniques for radiotherapy of prostate carcinoma. Based on these results, several researches are initiating dose escalation studies in hopes of increasing local tumor control without increasing normal tissue toxicity above acceptable levels. Similarly, a group at Memorial Sloan Kettering Cancer Center has investigated the use of threedimensional conformal radiotherapy for prostate, nasopharynx and lung lesions [Lei91, Arm93]. These studies also defined conformal therapy as treatment using field shaping blocks designed with aid of the BEV utility. Rather than a clinical trial, however, the investigators used the quantitative evaluation tools developed by the CWG in order to compare their conformal and conventional therapy results. Similar to the prostate clinical trials, these analyses suggest that threedimensional conformal radiotherapy may provide a clinical advantage over conventional techniques. For example, a study of nine lung patients showed both an increase in the minimum target dose and a significant decrease in the calculated NTCPs when conformal treatment planning was used [Arm93]. Conformal stereotactic radiosurgery techniques have also been studied to determine their efficacy for clinical treatments. Moss studied the use of multileaf collimators, both real and hypothetical, for small intracranial lesions [Mos92]. Using dose distributions, DVHs and the integrated logistic function, which is a doseeffect model based on NTCP theory, he concluded that clinically useful conformal therapy for small targets could only be achieved through the construction of multileaf collimators with 5 mm wide leaves 25 (size projected to isocenter) as opposed to the 1 cm wide leaves currently manufactured. Nedzi et al. used fortythree patient data sets to study treatment plans designed using five dynamic field shaping devices for stereotactic radiosurgery: fixed circular collimators, two independent jaw collimator, four independent jaw collimator, four independent rotatable jaw collimator and an ideal multileaf collimator [Ned92]. Comparison of rival plans was accomplished via DVHs and a construct they termed the treatment volume ratio, TVR. The TVR is defined as the target volume divided by the volume receiving at least the minimum target dose. As expected, the ideal multileaf collimator provides the best field shaping, but even simple BEV field shaping devices provide a clinical advantage over fixed circular collimators. Clearly, the literature indicates that the initial step towards acceptance of novel treatment methods is to establish that they are clinically superior to the status quo. Interestingly, however, this has not yet occurred with inverse radiotherapy planning. Physicists have repeatedly demonstrated the utility of inverse radiotherapy planning for fitting arbitrary desired dose distributions. Various conic sections [Woo93, Har94] and concave targets [Hol94, Har94] are the most often matched by inverse planning investigators. A few investigators have attempted clinical examples, but have not compared these examples to conventional treatment plans [Har94]. The following investigation will attempt to bridge the gap left between laboratory novelty and clinical viability. In so doing, it is also hoped that this work will contribute to the growing body of knowledge that has been made possible by the advent of threedimensional treatment 26 planning systems which adequately model dose deposition. Since accurate dose volume data is only available through the use of such systems, radiotherapy treatment planning has historically been based primarily on the training and experience of the physician. Through this and other similar studies, more detailed dosevolume data can be obtained for both the current state of the art in radiotherapy, and for potential future improvements on the state of the art. Armed with these facts rather than dogma, hopefully the art of radiotherapy treatment planning can some day be transformed into a true science. CHAPTER 3 UNIVERSITY OF FLORIDA RADIOTHERAPY TREATMENT PLANNING Traditionally, the term radiotherapy treatment planning has been used to describe computation of the dose distribution for one or a few transaxial sections within the patient. Recent advances have improved the way in which treatments are planned, however. Improved imaging modalities such as computed tomography (CT) and magnetic resonance imaging (MRI) coupled with improved computer assisted planning techniques permit threedimensional treatment planning based upon realistic representation of the patient's anatomy [Goi88]. Recognizing the effect of these advances on treatment planning, the term now generally includes target localization and delineation in addition to field design and dose calculation. This chapter will briefly discuss treatment planning for the three primary teletherapy planning methods used at the University of Florida's Shands Cancer Center: conventional planning, threedimensional beam's eye view planning (virtual simulation) and radiosurgery treatment planning. Conventional Treatment Planning Numerous imaging modalities, most notably CT and MRI, are utilized to determine the extent of disease and its position relative to normal structures. Definitive treatment field design is accomplished, however, via use of a treatment simulator, which incorporates a diagnostic xray tube into an apparatus that duplicates the geometrical and mechanical properties of the treatment unit. Although information obtained from CT and 28 MRI studies can be used as an aid for target delineation, conventional treatment planning cannot fully exploit this threedimensional data base due mainly to the fact that the geometrical relationship between the patient's anatomy and the radiation beam cannot be duplicated using a standard diagnostic xray unit [Kha84]. The simulator has fluoroscopic capabilities which allow dynamic visualization of the patient's anatomy and ensure proper positioning of the treatment fields. After the fields have been positioned, plane radiographs are taken and the irregular fields which encompass the target are designed on these films and digitized into the treatment planning computer system (Theraplan, Version 5, produced by Theratronics International Limited). Dose calculation requires not only information regarding the irregular field shapes, but also the patient's external contour. This information is obtained via placement of solder wire around the patient and passing through the central axes of the treatment fields. Since the wire is quite malleable it easily conforms to the contour of the patient. This contour information may then be digitized into the treatment planning computer to generate a central axis slice of the patient (generally transaxial). After input of these treatment data, Theraplan calculates dose from photon fields using a twodimensional semiempirical model which separates dose deposition into its primary and scattered components. The primary dose may simply be modeled as [The90] D,, = f(d,x,y) DA (d) TAR(d,O) where f(d,x,y) = a function which describes the beam intensity profile in air at depth d, DA = the dose in free space at depth d and TAR(d,0) = the zero area tissue air ratio, which describes attenuation of the primary beam by a thickness, d, of tissue. 29 The scatter dose contribution, which is deposited by photons which undergo at least one interaction before depositing dose, is calculated using a Clarkson integration technique [Joh83]. Since this scatter component is dependent both on field size and shape, the field is divided into n equal sectors with an angle, 0, between each. The scatter components from all n sectors are then summed as follows 6 n .= E .SAR(dr) 27t i where SAR(d,r)= scatter air ratio for circular field size r at depth d = TAR(d,r)  TAR(d,0). After performing these two calculations, the scatter and primary contributions are reassembled in order to determine the total dose calculation. Electron dose calculation is performed in Theraplan by first dividing each electron beam into square pencil beams measuring 0.5 cm on each side. Using a modification of a semiempirical method derived from the age diffusion equation [Kaw75], the dose contribution, D, from each pencil at a point (x,y,z) is calculated as [The90] y. = [ ,.(z)x Xo(z)+ .1 Y(e, Y (z)y) D(xyz,.) = A e rf( )+ erf( + )j rf )+ erf( ) 2 rKr 2xr 2L 2v/icr 2^ Jiv SZ2 Z 2 1exp( )2( SSD )2 *cos(GI + G2 + G)exp( VX0 R2 RRF SSD+z where X0(z) = half the pencil width at depth z Y0(z) = half the pencil length at depth z x = distance from pencil center to calculation point in direction of field width y = distance from pencil center to calculation point in direction of field length z = depth in tissue Rp = practical range for electrons = intersection of depth dose curve with bremsstrahlung background KT = (C/RP + 0.051") SSD = distance form source to surface of patient 30 GI, G2, G3, C, N, and A = parameters which Theraplan varies in order to obtain the best fit to measured data. After calculation of the dose contribution from each pencil beam, each pencil is weighted depending on its position relative to the field edge. The weighted doses from all the pencil beams are then summed to determine the total dose given to the point (x,y,z). Threedimensional Treatment Planning (Virtual Simulation) Although CT scanners provide detailed information about the anatomy of a patient, it is not in a practical form for radiotherapy treatment planning. When utilizing these scans as an aid to treatment planning, the radiotherapist must "mentally integrate a set of 2D shapes into a 3D structure, visualize the intersection of his prescribed treatment beams with that structure, visualize the resulting film, correlate that imagined film with the actual simulation film, and determine what if any adjustments need to be made." [She87, pg 433]. Virtual simulation more adequately integrates the CT scanner into the treatment planning process and thus allows the radiation oncologist to better exploit the 3D data set by reconstructing a virtual patient from the CT data transferred to Theraplan. In order to ensure accurate coordinate transfer between the CT scanner, treatment planning computer and treatment machine, CT scans must be performed with the patient immobilized in the treatment position. Position information is registered in an imagesinfo file that is stored along with the image data. These CT simulation scans are transferred to the treatment planning computer, where delineation of target and critical structures can be performed. Although Theraplan allows the user to now digitize the fields into the system from simulation films, the strength of virtual simulation is that it allows the user to design radiation portals utilizing a beam's eye view display. 31 Theraplan's BEV utility places the user's eye at the radiation source, and permits interactive portal design while the user looks along the central axis of the beam. From this vantage point, the radiotherapist can view the full 3D anatomy at once and examine the relative positions of anatomical structures as seen by the primary beam [Goi88]. This option provides a superior display from which to vary field size and also to design field shaping blocks to match the patient's anatomy. Unfortunately, the time investment required for collaboration of physician and dosimetrist to perform virtual simulation prohibits its use except for cases in which portal design is especially difficult. Dose calculation in Theraplan is performed the same for virtual simulations as it is for conventional treatment planning situations. Although the system performs all calculations in 2D, it can perform a pseudo 3D calculation. This option calculates the 2D dose distribution on all of the transaxial slices within the data set and presents a 3D dose distribution. Using this tool, the radiotherapist may calculate the 3D dose distribution from portals he has designed, and then interactively alter these portals if this distribution is deemed unacceptable. Stereotactic Radiosurgery Treatment Planning Stereotactic radiosurgery was the first clinical application of virtual simulation since treatment plans are designed exclusively using a virtual patient recreated from imaging studies of the actual patient. In order to accurately localize the lesion, a frame of reference known as the BrownRobertsWellsTM (BRW) ring must be attached to the patient's head. This device is a metal ring which attaches to the patient's head via four aluminum pins [Fri89]. Once this frame is attached, it becomes the reference point for 32 all localization and enables accurate coordinate transfer between imaging devices, treatment planning system and linear accelerator. To obtain CT images, the BRW ring is affixed to the CT couch and a localizer is then attached to the BRW ring via three tooling balls. The CT localizer consists of nine rods; three pairs which are aligned with the patient and angled rods between each pair [Saw87]. After a scout image has been obtained, transverse slices are obtained in the region of the lesion. The localizer rods also appear in each image slice. Since the spacing of the rods is known, the position of any object within the CT localizer can be determined [Saw87]. Certain types of lesions require other diagnostic localization techniques. For example, arteriovenous malformations often require the use of contrast angiography in addition to CT. A special angiographic localizer cage is required for radiographic localization. This localizer has four lucite plates which each contain fiducial marks. These fiducial marks act as the reference points for localization [Sid87]. After the BRW ring is attached to an immobilization mount and the localizer, a standard angiogram is performed. After numerous biplane images are obtained, the anteroposterior (AP) and lateral images where the nidus is best defined are selected. Another special localization technique is the use of magnetic resonance imaging (MRI). This technique is most often utilized for the localization of acoustic neuromas or tumors which are near a bone that could cause an artifact in CT localization. Since high magnetic fields are used in MRI, a special BRW head ring made of aluminum is attached to the patient's head with nonmagnetic pins. Once again, a special localizer 33 cage is required. Geometrically, this cage is exactly the same as the CT localizer cage. Due to the magnetic fields, however, the cage is composed of plastic. The localizer rods on the MRI localizer are filled with a contrast material, propandiol, so that they may be seen on the scan. To improve the signaltonoise ratio of the scan, a special head coil was designed for use in stereotactic localization. Once the BRW ring is attached to the localizer cage and a special bracket on the head coil, the MRI scan proceeds as a normal head scan. A threedimensional treatment planning system is utilized which runs on a SUN SPARCstation. CT images are transferred to the SUN system via a network connection. The nine localization rods must be identified in the first slice, and each pixel is mapped into stereotactic space. The computer program automatically locates the position of the rods in subsequent slices. The neurosurgeon then uses a mouse to outline the target in the axial, coronal and sagittal planes. A treatment plan is designed which will focus noncoplanar arcs of radiation such that they intersect at the center of the target, which is known as the treatment isocenter. Figure 31 illustrates the location of arcs relative to the patient's external contour. The intersection of these arcs at the isocenter concentrates the dose in the targeted region while spreading low dose throughout the normal tissue, thus creating a very steep dose gradient outside of the target. Typically the first step in treatment design is selection of a standard treatment plan which contains default values for the number of arcs, table angle, gantry start and stop angles and weighting for each arc. These treatment variables are then altered such that the dose distribution best conforms to the projected area of the target in three 34 dimensions. For example, the collimator size is chosen such that it will produce a circular beam which best fits the size of the target. Arcs and/or table angles may be altered or deleted which changes the shape of the distribution. For nonspherical lesions multiple isocenters are sometimes employed, although as stated earlier, the dose inhomogeneity introduced by this technique may be undesirable. This iterative technique is repeated until the dose distribution fits the shape of the lesion with minimal dose to normal tissues. The 80% isodose line is generally chosen as the portion of the dose distribution which should best conform to the shape of the lesion. The fit may be examined by starting at the first CT slice and having the computer step through the subsequent slices in 1 mm increments. The system computes and displays the isodose lines for each slice as it steps through the images. 270 290 70 310 500 3500\ / .1 100 Figure 31: Location of nine standard table angles relative to patient's head. Typically, arcs are 100 degrees in length at each table angle. Figure redrawn from [Spi92]. 35 The dose algorithm uses tissuephantom ratios (TPR), off axis ratios (OAR), and the inverse square law to compute the dose anywhere along the beam [Bov90]. TPR gives the relationship of the dose along the central axis of the beam, OAR is used to determine the relative intensity along the cross section of the beam, and the inverse square law gives the variation of the intensity of the beam with distance from the source. Thus, the dose at any point, p, in a circular field may be computed from [Suh90]: D,(c,STD,d,r) = D,,f.ROF(c) TMR(wd) OAR(c,STDdw) (SAD)2 STD where c = field size at SAD STD = sourcetotarget distance d = depth of point p r = off axis distance w = field size at point p D, = reference dose and ROF = relative output factor. Similar treatment planning techniques are employed with MRI and angiographic localization. MRI images are transferred via the network system and treatment planning proceeds as it does with the CT localization. Since the images obtained through use of MRI can have spatial inaccuracies, planning is also performed using the stereotactic CT images, and the end plans are correlated to ensure accuracy. The procedure is slightly different when angiographic localization is used. Since the angiographic images are not stored digitally, the AP and lateral plane films chosen during localization are utilized for treatment planning. The films are placed on a digitizer and the positions of the fiducial marks are entered. The digitizer is then used to outline the nidus in both projections. Using this data, the computer can calculate the 36 geometric center and the center of mass of the target. Angiography presents several problems that make it inadequate for localization by itself. These problems include errors in determining target size and shape [Bov91]. For example, there is a risk of underestimating the true maximum target diameter by as much as 41% [Bov91]. Thus, when angiographic localization is utilized, it must be used in conjunction with CT localization in order to avoid significant errors which can lead the unnecessary treatment of a large amount of normal tissue [Bov92]. Since the stereotactic CT scans are always utilized, the planning system allows the user to plan and evaluate the plan in three dimensions using interpolated reformatted CT scans. Through the use of this technique, the full set of anatomic data is available to the user. The system allows the user to contour lesions and anatomical structures, but these tools are not commonly utilized since they are very time consuming and unnecessary for evaluation of a given treatment plan. Without these contours, however, it is impossible to obtain dose volume histograms for the structures of interest. For purposes of comparison within this project, these data were obtained for several stereotactic radiosurgery patients. CHAPTER 4 INVERSE RADIOTHERAPY TREATMENT PLANNING Inverse radiotherapy treatment planning may be performed using the Peacock Plan' system developed by the Nomos corporation. This treatment planning system is part of an integrated 3D conformal planning/multivane intensity modulating system. Treatment plans produced using Peacock Plan generate a set of beam weights which allow the multivane intensity modulating compensator (MIMIC) to deliver a conformal treatment [Nom93]. MIMIC The operation of the treatment planning system is best understood if one first has some understanding of the device which is simulated by Peacock Plan. The MIMIC consists of twenty independent vanes which each project a lx1 cm block at the machine isocenter. It attaches directly to a linear accelerator and modulates the intensity of a slit collimated radiation beam. Intensity modulated slit irradiation, in conjunction with the rotation of the gantry about the patient, allows for a slice of the patient to be treated with a radiation dose that conforms to the shape of the target volume within the slice. After this slice has been treated, the table is indexed and the next slice is treated. This procedure may then be repeated until all slices within the target volume have been treated. Obviously, this treatment modality is analogous to the method in which CT scanners image in a slice by slice fashion. In order to shorten the required treatment time, the MIMIC is capable of modulating two one centimeter thick slices per gantry rotation. Figure 41: Beam's Eye View (BEV) of MIMIC, which contains two sets of twenty 1 cm wide independent tungsten vanes. 39 The MIMIC shapes the intensity of the beam through temporal modulation. Each of the singly focused vanes may be independently addressed and translated into the path of the radiation beam via use of pneumatic pistons. Since the eight cm tall tungsten vanes allow minimal transmission of the primary beam (approximately 2% for 10 MV x rays), the intensity of the beam underneath a vane will be proportional to the amount of time that the vane is open during irradiation. The Peacock PlanT allows for eleven different dwell times, which leads to effective transmittance values ranging from 0 (actually 2) to 100 percent in ten percent increments. For computer simulation purposes this number of transmittances may be varied, and if found to significantly effect the treatment plans it could easily be modified for the MIMIC. This all or nothing approach to dynamic beam compensation has two primary advantages. First, beam transmission is determined by the dwell time of full height tungsten vanes, so beam hardening effects need not be considered as they must be with conventional compensation techniques and collimators which spatially modulate the beam. Secondly, unlike spatial modulating collimators, accurate distance encoding is not necessary for the vanes since the vanes have only two positions (in or out) [Mac94]. As with any onedimensional multivane dynamic modulator, the MIMIC has several limitations. These problems are due primarily to the inefficiency of dose delivery through these devices. Modulation of the beam intensity requires blockage of a majority of the beam for the patient treatment. Thus, to deliver the same dose, the beam on time is much more than with conventional treatments. Since there is a small transmission through the vanes, a small background dose will be present within the patient. Further, 40 since the beam on time is lengthened, there will be an increase leakage dose from the linear accelerator which may necessitate increased shielding thickness of the secondary barriers in the treatment vault or increase in linac head shielding. These are engineering details which can be examined if intensity modulated treatments prove beneficial. In fact, with clever design, some of the current disadvantages of intensity modulation could possibly become advantages. For example, utilizing a twodimensional modulator can potentially increase the efficiency of treatment under certain situations such as with stereotactically treated brain lesions which require multiple isocenters [Har94]. I \ Xray Beam Compensator I I Leaves Open Open Closed Figure 42: Illustration of MIMIC operation. Reproduced with author's permission [Mac94, pg. 1711, Figure 3]. 41 Peacock Plan' The general concept of inverse radiotherapy planning allows the user to specify the desired result, and then the treatment planning system automatically computes a plan that satisfactorily produces this distribution. In order to specify this desired result, Peacock Plan' has various tools which allow the user to delineate the contour of the target tissue and any critical structures that appear on CT data which have been transferred to the system. It is imperative that this image overlay data contain all structures pertinent to the planning process, since the inverse planning process relies on information about the sensitivity of critical structures near the treatment volume and their importance (weighting) relative to the target. Peacock also requires input of dose prescribed to target (cGy), desired treatment complexity and safety margins which take into account setup inaccuracies and the possibility of microscopic disease surrounding the target. Once these data are input, the planning process is performed automatically by the computer. The isocenter is determined as the geometric center of the defining rectangle of the target. Peacock Plan' then simulates the MIMIC by subdividing each beam portal into 20 one by one centimeter pencil beams. An initial guess for the weight of each of these pencil beams is obtained through a backprojection technique Beam Weight = Volume get (41) TMR[dwg] where Volume,, is the volume of the target that is intercepted along the ray line of the pencil beam and d,., is the depth at which the target is first intercepted along the ray line of the pencil beam. Although this backprojection technique yields only a crude 42 approximation to the required beam weightings, accuracy is not that important at this juncture since these weightings will serve as input to an optimization routine that will determine the best plan. Optimization is performed using simulated annealing, a method which mathematically models the annealing process of metals in which the many final crystalline configurations are possible depending on the rate of cooling [Boh86]. According to the general principles of statistical mechanics, any system that is cooled sufficiently slowly will seek its state of minimum energy. Assuming that the cooling rate is chosen correctly, simulated annealing will avoid local traps and minimize the objective function for a given situation. The annealing process is mathematically modelled as a biased random walk that samples the objective function. The first sampling is performed using the objective function calculated using the beam weights obtained from the initial backprojection. A random pencil beam is then chosen, and a step of ten percent transmission (a beam "grain") is taken in a random direction. The objective function is then recalculated. This new step is always accepted if the new objective function is smaller than the first. If the new objective function is not smaller, however, there is still a finite probability of acceptance given by p = ( (42) where po is the objective function and 3 is inversely proportional to the temperature of the system. This probability of accepting a detrimental step follows directly from the statistical mechanics of annealing, in which the probability that the system will transit 43 from a state of lower energy to one of higher energy is  (43) p = e where k is Boltzmann's constant (8.62 x 10 ev/K) and T is the absolute temperature of the system. Conditional acceptance is unique to simulated annealing, and is the feature which makes it so powerful. Unlike purely downhill optimization methods which greedily accept local minima, the probability of accepting a bad move allows the system to step back out of a local minimum. As the temperature is decreased, the probability of accepting an uphill step is also decreased and the steps should become confined to the global minimum of the function. This is extremely important in radiotherapy optimization, since the solution space can be extremely complex and many local minima may exist near the global optimum solution. An example of this complexity can be seen in the fact that a single arc optimized by Peacock may have as many as 200 dimensions to randomly vary while it attempts to minimize the following average square deviation objective function V (D. Dj?2 2 qp = < wweighttrge. + D;.,( (44) 2 E (2 'weightar e zztructurelimitj where n. = number of targets or critical structures, 44 weight = user defined weight for each target or structure (0.0 < weight < 2.0) and D. = maximum target dose or dose goal for target i or structure j The brackets (< >) denote an average over all i target voxels or j structure voxels. Obviously this function, in its attempt to achieve high consistent target dose and low critical structure dose, can contain a large number of local minima. Figure 43: Downhill methods (dotted arrows) seek nearest well and are easily trapped in local minima. Conditional acceptance of bad steps allows simulated annealing (solid arrows) to escape these traps and find the best global solution. Peacock Plan's optimization has some limitations, however. Although simulated annealing is widely accepted as a reliable optimization method, there are situations in which it can get trapped in local minima. The problem generally lies in the definition 45 of an annealing schedule that cools the system sufficiently slowly. Success is often determined by the choice of annealing schedule, and the choice is quite often problem dependent [Pre91]. Given an infinite amount of time and iterations, simulated annealing can find the global optimum for any problem. For example, logarithmic cooling schedules have been proven to always approach the absolute minimum, but these schedules are far too slow for routine clinical use [Pre91]. In an effort to speed the optimization, Peacock Plan' uses a simple inverse cooling schedule which results in an algorithm known as the Fast Simulated Annealing optimization method. At each iteration, the temperature is determined by 10 T = kTo0' (45) 'iterations where kT0 is set to 0.1 and ni...g is the number of iterations completed before this iteration. Using fast simulated annealing the plan may be computed in a reasonable amount of time, but there is also a possibility that the final result will actually be a local minimum rather than the global optimum solution. Another limitation within the system is that Peacock Plan' develops its 3D plan as a series of twodimensional slices that overlap the target volume. Since optimization is such a slow process and computational time increases rapidly with the number of dimensions in an optimization, the optimization is performed on a slice by slice basis. After the beam weighting has been optimized for each slice, the dose is computed using a threedimensional dose model. The inherent assumption is that the sum of optimized slice plans yields an optimized plan. This assumption, however, has not been proven. 46 The forward dose calculation algorithm uses measured finite size pencil beam data (MFSPB) and is based loosely on a model developed by Luxton for stereotactic radiosurgery [Lux91]. The actual calculation is ISAD 2] D(d,rdL) = TMR(d)OAR(r) [ j (46) This model assumes that the MIMIC is composed of separate lxW cm pencil beams, each having the same off axis ratios (OAR) across the pencil. Tissuemaximum ratios (TMR), however, are assumed to vary for each pencil due to spectral changes across the beam axis, and separate TMRs must be measured for each pencil beam. SAD is the distance from source to isocenter distance, STD is the distance along the beam central axis and r' is the off axis distance of the calculation point from the central ray at depth d., (assuming that OARs are measured at dcLand is equal to r/ = r (SAD +d) (47) STD) where r is the actual off axis distance of the calculation point. Noticeably absent from the calculation is an output factor to account for field size dependence as multiple vanes are open during irradiation. This factor is implicitly included in the calculation since the offaxis ratio data are acquired in the penumbral region outside of the one centimeter width of the pencil beam in order to account for side scatter from each pencil beam. The doses from pencil beams are then summed and the penumbral overlap found in this summation accounts for the output factor (see Fig 44). Figure 44: Overlap of measured finite size pencil beams yields effective output factor (field size dependence) when their profiles are summed. Dose is calculated separately for each pencil beam using equation 46, and these doses are all summed. As with conventional treatment planning systems, the dose is then normalized to the maximum value within the calculation grid and two dimensional dose distributions may be superimposed on the reconstructed CT images in the axial, coronal and sagittal planes. Verification of Dosimetry Algorithm Peacock Plan' currently models beam data for the MIMIC attached to a 10 MV linear accelerator at Methodist Hospital in Houston, Texas. Experimental verification of the system was performed at Methodist Hospital [Gra94], and required production and 48 execution of several different treatment planning scenarios. A cubic film phantom containing Kodak XV2 film was placed in the beam during execution of the treatment plan, and film dosimetry was performed utilizing a HeliumNeon laser scanning densitometer. Two example plan verifications are illustrated in Figures 45 and 46: a small spherical treatment and a U shaped distribution, respectively. Isodose distributions on three planes are represented for each test to allow qualitative evaluation. The first shown is the central axis slice, while the other two plots represent planes that are + 6 mm off of the central axis. Recent quality assurance documents have recommended acceptable criteria for the uncertainty of treatment planning algorithms dependent upon the dose in the region of interest and the dose gradient within this region [Van93]. The primary criteria of concern are that the uncertainty not exceed + 4% in a low dose gradient, high dose region and that positional uncertainty of isodose contours within a high dose gradient remain less than 4 mm [Van93]. VanDyk et al. define high dose as > 7% of the normalization (prescribed) dose, while a high dose gradient is defined as > 30%/cm. Data from the two cases presented are tabulated in Table 41. As seen in the table, data on the central axis slice is very good, while off axis the uncertainty increases. Also, it is suspected that the one very bad data point may be the result of positional errors during film readout. P I ( iml '. j ) pxel 1 (2 mm/pixel) (b) Pixel $ (2 m=/pixel) (c) Figure 45: Isodose plots for a planned circluar distribution on (a) the central axis, (b) +6 mm off axis, and (c) 6 mm off axis. Dashed lines represent the planned distribution, while the solid lines were measured from XV2 film. P 1e (2 a) /pixel) (a) 7  Pixel / (2 w//pixel) (b) Figure 46: Isodose plots for planned Ushaped distribution on (a) the central axis, (b) +6 mm off axis, and (c) 6 mm off axis. Dashed lines represent the planned distribution, while the solid lines were measured from XV2 film. 51 Table 41: Average uncertainties in Peacock Plan dosimetry for circle and U on the central axis (CA), 6 mm off the central axis and 6 mm off of the central axis for the treatment plan [Gra94]. ______ Circle Circle Circle U U U CA 6 mm 6 mm CA 6 mm 6 mm High dose, 1.86% 0.85% 12% 2.5% 4.5% 4.3% low gradient ____ ____ High gradient 3.8mm 2.7mm 3.0mm 2.8mm 4.4mm 3.8mm Total Volume 1.9% 0.8% 12.2% 2.2% 4.2% 3.6% CHAPTER 5 TECHNIQUES FOR QUANTITATIVE PLAN EVALUATION As conformal therapy techniques have developed, their ability to produce arbitrary dose distributions has been thoroughly investigated [Har94, Car93, Mos92, Hol94]. The true test of the utility of inverse radiotherapy planning will be in its ability to produce clinical treatment plans which are superior to those produced through conventional treatment planning. The comparison of such plans is quite difficult, however, due to the large amount of data which must be reviewed for a full threedimensional evaluation [Kut91a]. Historically, treatment plan evaluation has been achieved through the graphical display of the twodimensional dose distributions superimposed on the patient contour. In addition to these dose distributions, tools for quantitative plan evaluation have been developed. Some of these tools will be discussed in the following sections. Dose Volume Histograms Dose volume histograms effectively condense the dose distribution data by graphically displaying the volume of tissue irradiated through execution of a given treatment plan. There are two common forms for dose volume histograms which may be found in the literature: differential and cumulative. Differential dose volume histograms are plotted as histograms according to the mathematical definition, with dose binned along the abscissa and the height of each bin proportional to the volume of the organ which receives a dose within that range (see Figure 51). Alternatively, 53 cumulative dose volume histograms are frequency distributions which represent the fractional volume of an organ receiving a dose greater than or equal to a specified dose as a function of dose (see Figure 52). Since differential dose volume histograms represent the volume in each dose bin directly, they can facilitate comparison of dose intervals between rival plans. Also, the finer structure provided by true histograms offers more detail for quantitative analysis than that given by cumulative frequency distributions. The appearance of differential histograms can become confusing, however, when one attempts to use them for comparison of rival plans [Drz91]. Cumulative dose volume histograms can alleviate this problem when presented as smooth line graphs. Thus, cumulative dose volume histograms will be used as the graphic display for visual comparison of rival plans, while quantitative analysis of plans will require the finer structure provided by differential dose volume histograms. In order to remain consistent with the literature, the term dose volume histogram (DVH) will be applied to the cumulative frequency distribution [Kut92]. DVHs are generally computed for the target volume and each organ within the irradiated volume. Ideal DVHs for target and critical structure are shown in Figures 5 3a and 53b. Thus, DVHs for rival plans may be compared simply by plotting them on the same graph and noting how closely each approximates the ideal graph. This comparison can become muddled, however, if the DVHs cross each other as in Figure 54 so that it is not clear which histogram is better [Kut92]. The presence of multiple critical organs within the irradiated volume also increases the complexity of treatment 0.2 0.18 0.16 0.14 0 ci ,0.12 o '" 0.1 30.08 "5 0.06 0.04 0.02 0 0.0 01 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Normafized Dose Figure 51: Example differential dose volume histogram for target volume. 1 0.9 0.8 0.7 5 0.6 a L S0.5 S0.4 o 0.1 0.2 0.5 0.4 0.5 0.6 Normrized Dose 0.7 0.8 0.9 1.0 Figure 52: Cumulative DVH corresponding to Fig 51. 0 01 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Normalized Dose U. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Normalized Dose (b) Figure 53: Ideal DVH for (a) target volume and (b) normal tissue volume. 56 plan comparison via DVHs. A further limitation of DVHs exists in their inability to provide spatial information regarding the location of hot and cold spots within the irradiated volume [Drz91]. Thus, if hot or cold spots are detected using a DVH, their position must be obtained through the use of spatial dose distributions. Nevertheless, dose volume histograms are a powerful tool for evaluation of many treatment planning situations due to their ability to condense a vast amount of information into a limited number of distributions. 1 0.9 0.8 0.7 0.6 0.5 S0.4 D.3 0.2 0.1 0 0.0 01 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Normalized Dose Figure 54: Crossing dose volume histograms for normal tissue volume. Normal Tissue Complication Probability Although DVHs provide very accurate information about the dosimetric properties of treatment plans, it may be difficult to infer the clinical significance from differences in rival DVHs [Kut92]. Therefore, a means of quantifying the clinical importance of 57 rival plans is desirable. One method of quantifying the biological implications of a given treatment plan is to estimate the radiation toxicity to normal tissues through the calculation of normal tissue complication probabilities (NTCPs). Ideally, this calculation could then be balanced with the tumor control probability to provide an absolute numerical value which represents the validity of a given treatment plan [Moh92]. Unfortunately, these calculations are still under development and may provide probabilities which are highly uncertain. However, these calculations represent an attempt to model the clinical relevance of a given treatment plan and have proven worthwhile in the comparison of rival treatment plans [Kut92]. New models under development start from basic biological principles and should prove more accurate than current models [Jac93]. The most promising new model assumes that organs are comprised of functional subunits (FSUs), for example the kidney is comprised of nephrons, and the radiosensitivity of the organ depends on the radiosensitivity of the FSUs as well as their organization. FSU organization may be classified broadly as serial or parallel. Organs with a serial architecture have a chance of complication when a very small volume is irradiated since their function is disrupted if a single FSU is destroyed. Parallel organs have a threshold volume which must be irradiated before a complication arises since a certain number of FSUs must be destroyed before organ function is disrupted. Since many organs fall somewhere in between, their behavior is described using a parameter related to their relative seriality. Since this model is still under development and many of the requisite parameters are unknown for specific tissues, NTCP may be calculated utilizing a four parameter 58 model suggested by Lyman [Lym85] and used by the collaborative working group in their study [Kut91a]. This model estimates the complication probability arising from uniform irradiation of a partial organ by fitting a general sigmoidal function to the available clinical data for dose volume relationships. Although this model does not explicitly contain the radiological parameters of other models, all relevant radiobiological aspects are implicitly taken into account within the NTCP calculation [Lym85]. Two general sigmoidal functions have been investigated for analytic representation of the response of an organ to irradiation: a logistic function and the integrated standard normal distribution. It has been shown that these two functions differ by less than 0.9% over their entire range, however, so the choice is essentially irrelevant [Sch85]. Following the model originally proposed by Lyman, the integrated standard normal distribution may be used to determine the NTCP for an organ of volume Vrf, with partial volume V irradiated to a homogeneous dose D as I NTCP 1 fe 5t 1'2dt (51) v'2T  where t, the normal deviate, represents the number of standard deviations D is away from the tolerance dose and may be determined from [D TD5o(v)] (52) t = (52) TD()where  where v (53) V 'ref 59 and TD5o is the tolerance dose at which 50% of patients can expect a radiation related complication within five years after treatment. The partial and whole volume tolerance doses are related by a power law relationship [Sch83] TD(v) = TD(V) v  (54) Two fitting parameters, n and m, which govern the volume and dose dependence of NTCP, respectively, may be found in a report by Burman et al. [Bur91]. Tolerance doses for a variety of organs were compiled by Emami et al. based on data available in the literature [Ema91]. The fourth parameter required by the model, Vref can be obtained from the CT data if the entire organ is included in the scan, or alternatively, a standard value may be utilized. Data used for these calculations are shown in table 51. In order to utilize this model for clinically realistic situations in which the organ is inhomogeneously irradiated, it is necessary to convert the nonuniform dose distribution into a uniform distribution. The effective volume histogram reduction method proposed by Kutcher et al. transforms a nonuniform differential DVH into a one step histogram with an effective volume V, and dose equal to the maximum dose of the histogram, DM [Kut91]. Assuming that each volume element, Vi with dose Di, of the differential DVH independently obeys the same dose volume relationship as the whole organ, each interval may be transformed into an effective volume with dose DM through the power law relationship V = Vi(DJDM (55) This procedure is repeated for each interval of the dose volume histogram, and the total 60 effective volume may be found from the sum of equation 55 Y= V (D DM) =Ev i e i (56) The effective volume, Vff, found using this method may then be substituted for V in equations (52) through (54) in order to calculate the NTCP for inhomogeneous partial organ irradiation. Table 51: Normal tissue endpoints and tolerance parameters [Bur91]. Organ V"f n m TD50 End Point Bladder Whole organ 0.5 0.11 80 Symptomatic contracture Brain Whole organ 0.25 0.15 60 Necrosis Brain Whole 0.16 0.14 65 Necrosis Stem organ Femur Whole organ 0.25 0.12 65 Necrosis Heart Whole organ 0.35 0.10 48 Pericarditis Lens Whole organ 0.30 0.27 18 Cataract Lung Whole organ 0.87 0.18 24.5 Pneumonitis Optic Nerve Whole organ 0.25 0.14 65 Blindness Rectum Whole organ 0.12 0.15 80 Proctitis/necrosis Retina Whole organ 0.20 0.19 65 1Blindness Skin 100 cm2 0.10 0.12 70 Necrosis/ulceration Spinal Cord 20 cm 0.05 0.17 66.5 Myelitis/necrosis Tumor Control Probability While minimizing normal tissue toxicity is an important goal of conformal therapy, it is also important to determine the probability of tumor sterilization using rival 61 treatment plans. As with NTCP, currently there is no model which can provide an accurate assessment of the absolute tumor control probability (TCP). Models do exist, however, which should be useful in comparison of rival treatment plans that are similar in nature. The model used is based on that developed by Goitein [Goi94,Goi83] and Niemierko [Nie94] which assumes that the tumor consists of noninteracting clonogens which all must be killed in order to control the tumor. The probability of killing a clonogen after a single treatment fraction is estimated by determining the surviving fraction using the following variation of the linear quadratic formula d rg/p4 +d] dF rf+dI (57) SFd SF2[~~2 where d is the dose per fraction to the clonogen, SF2 is the probability that the clonogen will survive a dose of 2 Gy and ca/ is the ratio of linear quadratic parameters which determine the curvature of the dose survival curve for a cell population. The clonogen's survival probability after undergoing n fractions may then be expressed as i 4 r" ta (58) SF = SF 't2 a  The model further assumes that clonogens within an individual's tumor may differ in their radiation sensitivities, and this variation may be expressed as a gaussian distribution of SF2,md around the tumor mean with a standard deviation ad F2.W 3F, j F_ 1 fe 2.o SFd(SF ) (59) Assuming that a tumor is composed of NC clonogens, an individual's tumor control probability may then be calculated as NB NC i,SF, (510) TCPi = e i where the sum is taken over the NB bins of the differential dose volume histogram, each with a fractional volume vi. In addition to the intratumoral variation in cell sensitivities, Goitein's model also assumes there exists an interpatient heterogeneity which may be expressed as a gaussian distribution. Inclusion of this function yields the following final version of the TCP calculation (SF,.b.,d F2,, TCP 1 fe 2"' TCP,,d(SF2, (511) In order to perform the preceding calculation, certain biological parameters must be input. The first is the slope of the dose response curve, gamma50, as defined by Brahme [Bra84] Y = TCD5 d(TCP) ID=TCD5 (512) dD where TCD50 represents the dose required to achieve TCP of fifty percent. TCD50 is not a well known parameter, while gamma50 has been tabulated for many tumors [Mun91a, Tha92]. Thus, it is often easier to reverse the calculation. For example, physicians can generally estimate the TCP for a treatment assuming that the entire tumor is homogeneously irradiated to the prescription dose. This dose is the TCDTcp, or the dose required to eradicate TCP percentage of such tumors. Assuming that the values are on 63 the linear portion of the dose response curve, the TCD50 can then be approximated from TCD5 = TCD, *yY50(513) Y +0.01 (TCP50O) In addition to the dose response, the model requires a parameter, X, which characterizes the variation of TCD50 with volume. The model also requires input of the linear quadratic parameters a and 3, which have been tabulated for many tumors. Using these input radiobiological parameters, all other parameters within the model can be easily calculated. Internal parameters calculated from these input values include the number of clonogens NC, TCD" (514) NC = /n210 " and the surviving fraction at 2 Gy, SF2 SF2 102/ (515) After utilization of such a model to determine the TCP for a malignancy, Munzendrider et al. have observed that in regions of microscopic or suspected disease TCP is underestimated [Mun91a]. This is because there is a finite probability that no tumor exists in such regions, and thus there is nonzero probability of tumor control even with zero dose delivered to the region. To compensate for this possibility, the calculated probability is modified using TCP = P. U, + (1 P, uo TCP0 (516) where Pno tumor is the probability that no tumor exists in the targeted region. 64 Dosimetric Statistics As previously mentioned, the ideal radiotherapy treatment would result in homogenous irradiation of the targeted region to the prescribed dose. In general, however, it is physically impossible to homogenously irradiate the tumor while homogeneously sparing normal tissue. Thus, treatment of the entire lesion to the prescription dose produces hot spots within the volume. These hot spots can help destroy the lesion, but they can also damage or necrose the underlying tissue stroma and increase the risk of complications. For example, Nedzi et al. have correlated stereotactic radiosurgery tumor dose inhomogeneity and the corresponding increase in maximum tumor dose with increased complication rates [Ned91]. Unfortunately, this effect is not well understood and varies widely according to the type and location of tumor. For example, primary tumors located in the breast [Lim89] and larynx [Par94] have exhibited susceptibility to radiation damage from hot spots within the irradiated volume, while locations such as the nasopharynx [Par94] and prostate [Lei94, Per94] do not seem particularly sensitive to radiation dose escalation. Further, it is difficult to determine whether increased risk is due to necrosis of the target stroma or due to increased dose to surrounding normal tissue. Due to the vagueness of this problem, radiation oncologists typically avoid the situation by limiting the allowable target dose inhomogeneity and no method has been proposed for determining the probability of damaging the connective tissue and fine vasculature that may be associated with the target volume. Since the algorithm within Peacock Plan places no constraint on the dose 65 inhomogeneity, large hot spots can result which complicate the comparison with rival conventional plans. In order to provide some idea of dose inhomogeneity for plans presented in this work, dose statistics such as minimum dose, mean dose and maximum dose will be included. To further quantify the tumor dose inhomogeneity, researchers have often simply reported dose endpoints such as the D95, which is the dose received by at least 95% of the region of interest and D5, which is the dose received by at least 5% of this volume [Kut92]. Presentation of such data provides a clear indication of tumor coverage and the magnitude of hot or cold spots within the tumor volume and critical structures, and should help clarify the information found in DVHs and previously described biologically based statistics. While these statistics do not provide an absolute score to ease plan comparison, they do provide enough information that a physician can easily discern whether or not he is comfortable with the use of a given treatment plan. Biologically Normalized Dose Fractionation Dosimetric information for NTCP and TCP calculations is entered through differential dose volume histograms as described previously. Normal tissue tolerance has only been tabulated for conventional fractionation schedules of 180200 cGy [Ema91]. In addition, the NTCP and TCP calculations are valid only if the dose per fraction is equal at each calculational point [Nie94]. In order to account for differences in fractionation schedules and the radiosensitivity of various tissues, a biologically normalized dose volume histogram (BNDVH) may be calculated from the differential dose volume histogram, and then input into the TCP calculation [Nie92]. This 66 transformation follows directly from a manipulation of the linear quadratic formula which yields the following rule of thumb for the dose response of tissue to variable fractionation schedules [Wit83]: D d +a/P3 (517) D d'+ a/P where D is the total dose given in fractions of size d. The BNDVH normalizes the differential DVH to 2 Gy per fraction by using a variant of this calculation [Nie91]: BND, = D (di + al) (518) (2Gy+a/p) where Di is the dose for bin i of the differential DVH, di is the corresponding fractionated dose and BND1 is the total dose for bin i normalized to 2 Gy per fraction. NTCP calculations for variable fractionation schedules require a modification of the TD)50 in order to normalize these tolerance data to 2 Gy/fraction. For this work, the biologically normalized tolerance dose, BNTD50, will be defined as: BNTD = TD a f/ + 2 Gy (519) using the same manipulation of the linear quadratic equation as before. The TCDs0 used for the TCP calculation in this work need not be similarly normalized, since this parameter is determined uniquely for each case subsequent to user input of pertinent data. Although normalization of these data facilitates NTCP and TCP calculations for treatment schedules other than 2 Gy/fraction, it should be noted that such normalization contributes additional error to the probability calculations. This matters little for 67 comparison of the rival plans in this study, since the fractionation schedules will remain constant for each comparison. Thus, normalization of these dosimetric parameters should enhance the realism of calculations for variable fractionation schedules, but discretion should be exercised when comparing calculated probabilities with those expected. Score Functions Although the tools discussed previously are very effective in condensing the amount of information required for treatment plan evaluation, a method of numerically scoring each plan such that a single number may quantify the merit of a given plan is desired to further reduce the amount of information. The simplest objective score function is the probability of uncomplicated tumor control [Sch85]. This function, although objective, is based on NTCP and TCP calculations, and is therefore limited in its ability to achieve an absolute probability. It is, however, a simple calculation that yields a single number with which to quantify the merit of a particular treatment plan. This score function, S, may be expressed as a product of the fractional probability of effect for each organ within the irradiated volume [Kut92]: S = I (lP) (520) where where PO = 1 TCP P,>o = NTCP (521) 68 Delivery Efficiency In addition to dose conformity, any system clinically utilized must have the ability to deliver treatments quickly and efficiently. All methods of intensity modulation of the radiation beam will result in an increase in monitor units required for a treatment, and it is important to appreciate the effect this can have in clinical situations. The delivery efficiency of a conformal treatment system can be quantified via modification of an expression suggested by Galvin et al [Gal93]: Efficiency = MUcowd'f"aI7tWP (522) MUco,of,.rdjp1 This efficiency factor reveals several features of the conformal treatment plan in relation to its conventional counterpart. First, beam on time increases linearly with an increase in monitor units, which possibly leads to a prolonged treatment session. Conformal treatment systems may, however, reduce time required for patient set up and compensate for this increased beam on time. Decreasing the delivery efficiency may have even more severe consequences on shielding requirements. A system which requires a large number of monitor units may effect linear accelerator design in terms of transmitted radiation through the primary and secondary collimators, as well as increase the leakage contribution to the room shielding requirements. CHAPTER 6 CLINICAL TREATMENT PLANNING STUDIES After consulting staff physicians at University of Florida, it was determined that several treatment sites could best demonstrate the potential benefit from conformal therapy and should be included in the clinical study; these sites and respective patient designations appear in Table 61. CT scans were obtained of the diseased region, and staff physicians delineated the regions of gross tumor and suspected disease. This volume has been designated the biological target volume (BTV) by the photon treatment planning collaborative working group [Smi91]. The physicians also designated any margin necessitated by set up uncertainties and organ motion. Including this margin around the BTV yields the mobile target volume (MTV). Table 61: Treatment sites chosen for study and the respective patient designations. Site Patient Designations Intracranial lesions SRS1, SRS2, SRS3, treated stereotactically SRS4, SRS5, SRS6 Head and Neck HN1, HN2 Intact Breast B1, B2 Lung Ll Prostate P 1, P2 Three separate treatment plans were generated for each patient with the first being the conventional treatment plan as described in Chapter 3. These conventional plans were used for actual patient treatment, and thus represent the optimum plan as designed 70 by the attending physician and dosimetrist or physicist. A 3D plan was then generated with traditional field arrangements but using the full volumetric CT information to design the fields instead of just a central axis slice. The conventional and 3D plans are the same for stereotactic radiosurgery and other virtual simulation applications, so only two plans were designed for these cases. The third and final plan is the conformal plan generated utilizing the Peacock Plan' system. Table 62: Default five table angle plan parameters for Peacock. Table angles are given using the 360 degree convention described in Figure 31. Site Table Angles (degrees) Arc Length (degrees) Head 0 290 30 & 330 245 60 & 300 215 Head and Neck 0 290 15 & 345 245 30 & 330 215 Abdomen/Thorax 0 290 15 & 345 245 30 & 330 215 All conformal plans generated using Peacock were designed using five table angles. When the user selects five table angles, Peacock starts with the default sets shown in Table 62, and determines the actual arcs used through its optimization process. Intuitively, the optimal dose gradient is obtained when the beam entrance points are evenly distributed over the entire surface of the patient. To approximate this, the treatment planning system starts with long arcs which can be altered by the system. Given a perfect optimization algorithm or alternatively a large amount of computer time, this is the best approach since beams which deleteriously effect the dose distribution will 71 be discarded. However, experience with stereotactic radiosurgery has shown that when the irradiation geometry is reduced from 4r it must be reduced to less than 2w in order to avoid parallel opposed beams which decrease the steepness of the dose falloff [Pik90]. Since Peacock currently allows these opposing fields, suboptimal plans with a poor dose gradient can result. Since this effect was most obvious for the intracranial plans, these plans were all run utilizing the three different arc sets shown in Table 63: the Peacock default arc set, the Peacock set with shortened arcs and a default five arc set used in the University of Florida stereotactic radiosurgery program. These three plans were compared and the best was chosen. For one patient (SRS3) the shortened arc sets never resulted in a plan which adequately conformed to the target and the default arc set was used. Comparing the dose gradient achieved with this plan (see Figure 66) with the dose gradient in other plans, the effect of the opposing fields becomes obvious. For all other plans, one of the shortened arc set plans was utilized. Table 63: Arc sets used for planning intracranial cases in Peacock system. Name Table Angles Arc Lengths Peacock Default 0 290 30 & 330 245 60 & 300 215 Shortened Peacock 0 160 Default 30, 60, 300 & 330 110 UF SRS Default 20, 55, 270, 305 & 340 100 Upon completion of the treatment planning process, Peacock specifies the minimum dose to the target. Although this could be chosen as the prescription isodose for the plan, the manufacturer suggests that the user slightly increase the prescription line which 72 allows the prescription dose to slightly clip the target volume. This seems reasonable since the underdosed regions are generally comprised of individual voxels protruding from the delineated target and modem tumor dose response models have found a stronger correlation between mean tumor dose and TCP than between minimum target dose and TCP [Bra87, Kut92, Nie93]. Thus, by slightly increasing the prescription line, one can decrease the normal tissue dose and magnitude of hot spots within the tumor without profoundly effecting the probability of tumor control. In order to maintain consistency, all plans were prescribed to an isodose line which underdosed no more than 1.5% of the tumor volume. As previously mentioned, threedimensional planning generates a large amount of data which can complicate plan comparison. In order to condense this information, the quantitative tools discussed in Chapter 5 will be used along with displays of two dimensional slices through the lesion for selected representative patients. All treatment plans were designed to match the MTV, while target DVH and TCP calculations were performed for the BTV only. When viewing these plans it is important to remember that the conventional and conformal treatment planning systems contain inherent inaccuracies, and the dose calculations are not exact. This study is not designed to examine these inadequacies, but rather the clinical efficacy of inverse radiotherapy planning. If this method is deemed beneficial, then it will be appropriate to allocate the necessary resources to develop more sophisticated methods of dosimetry calculation. Following are the parallel planning studies for the chosen treatment sites. 73 Stereotactic Radiosurgery Patients SRS1 is a 40yearold male with a centrally located posterior third ventricle area arteriovenous malformation (AVM). Conventional treatment was executed through a single isocenter plan using 9 arcs delivered through a 20 mm collimator to a total dose of 1500 cGy prescribed to the 80% isodose line. The conformal treatment plan achieved high target dose homogeneity with the prescription dose delivered to the 94% isodose line. The inferior dose gradient provided by the intensity modulation device, however resulted in a spread in the low isodose lines and a higher average critical structure dose. Although TCP calculations were not necessarily designed for AVMs, TCP was still calculated in order to provide relative scores for the rival treatment plans. For this and the other AVM examples, it is especially important to recall that TCP does not represent a true probability, but rather a quantitative evaluation of a proposed treatment plan. Table 64: Conventional treatment plan designed for SRS1. Arc Isocenter Collimator Angle Arc Start Arc Stop Weight 1 1 20 10 30 130 1 2 1 20 30 30 130 1 3 1 20 50 30 130 1 4 1 20 70 30 130 1 5 1 20 350 230 330 1 6 1 20 330 230 330 1 7 1 20 310 230 330 1 8 1 20 290 230 330 1 9 1 20 270 230 330 1 74 SRS2 is a 59yearold female with metastatic adenocarcinoma of the lung to the right frontal lobe of her brain. A dose of 1750 cGy was delivered to the 80% isodose line through a nine arc single isocenter plan which used both the 20 and 24 mm collimators. Since the lesion is fairly spherical, it may be easily treated through conventional stereotactic radiosurgery using spherical collimators. The plan designed by Peacock is also quite conformal and treats the lesion with a more homogeneous dose distribution, although the average brain dose experiences a significant increase. This increase is partially offset by a decrease in the maximum brain dose, but still represents an undesirable increase. Table 65: Conventional treatment plan for SRS2. Arc Isocenter Collimator Table Arc Start Arc Stop Weight 1 1 20 10 30 130 1 2 1 20 30 30 130 1 3 1 24 50 30 130 1 4 1 24 70 30 130 1 5 1 20 350 230 330 1 6 1 20 330 230 330 1 7 1 24 310 230 330 1 8 1 24 290 230 330 1 9 1 24 270 230 330 1 SRS3 is a 62yearold male with a left trigone AVM. Due to the highly irregular shape of the AVM nidus, the treatment plan generated utilizing the SRS software required two isocenters. The first isocenter consisted of nine arcs treated with a 24 mm collimator, while the second isocenter required 4 arcs using the 12 mm collimator. The 75 resultant distribution from the combination of the two isocenters delivered 1500 cGy normalized to the 70% isodose line. Peacock again generated a homogenous distribution, but the overlapping and opposed fields also resulted in an inferior dose gradient. Table 66: Conventional treatment plan for SRS3 Arc Isocenter Collimator Table Arc Start Arc Stop Weight 1 1 24 10 80 230 1 2 1 24 30 80 130 1 3 1 24 50 80 130 1 4 1 24 70 100 130 2 5 1 24 350 230 280 1 6 1 24 330 230 280 1 7 1 24 310 230 280 1 8 1 24 290 230 260 1 9 1 24 270 230 260 2 10 2 12 10 30 130 1.5 11 2 12 30 30 130 1.5 12 2 12 350 230 330 1.5 13 2 12 330 230 330 1.5 SRS4 is a 50yearold female with 2 metastatic brain lesions. This patient provides an interesting test of the conformal radiotherapy system, since it has the ability to treat both lesions through a single isocenter. The conventional treatment plan required two isocenters consisting of 7 arcs each. Both isocenters utilized the 10 mm collimator, since the lesions were compact, and a dose of 1500 cGy was prescribed to the 80% isodose line. Peacock designed a plan which delivered the 1500 cGy to the 79% line. As can be seen from the statistics, the dose to critical structures (brain) is again increased in the 76 Peacock plan relative to conventional SRS planning. This two target plan illustrates one distinct advantage of inverse radiotherapy planning, however; the ability to treat multiple lesions using a single isocenter. Unfortunately, the MIMIC treats in a slice by slice manner and cannot take full advantage of this ability. Two dimensional modulation devices which treat the entire volume in one arc, however, could easily treat both lesions in one arc and increase delivery efficiency [Har94]. Table 67: Conventional treatment plan for SRS4 Arc Isocenter Collimator Table Arc Start Arc Stop Weight 1 1 10 30 30 130 1 2 1 10 50 30 130 1 3 1 10 70 30 130 1 4 1 10 330 230 330 1 5 1 10 310 230 330 1 6 1 10 290 230 330 1 7 1 10 270 230 330 1 8 2 10 30 30 130 1 9 2 10 50 30 130 1 10 2 10 70 30 130 1 11 2 10 330 230 330 1 12 2 10 310 230 330 1 13 2 10 290 230 330 1 14 2 10 270 230 330 1 SRS5 is a 73yearold female with a right petroclival meningioma which presented a significant treatment planning challenge. The lesion was treated using a 3 isocenter plan with 15 total arcs and 4 separate collimators: 22, 26 and 12 mm, respectively. As 77 is characteristic of multiple isocenter plans, there was significant dose inhomogeneity within the target volume and the dose was prescribed to the 70% isodose line. Due to the target's proximity to the brain stem, a relatively low target dose of 10 Gy was prescribed. The plan designed by Peacock provided better and more homogeneous target coverage than did the conventional plan, resulting in dose prescription at the 83 % isodose level. It did, however result in a higher dose delivered to critical normal structures. Table 68: Conventional treatment plan for SRS5. Arc Isocenter Collimator Table Arc Start Arc Stop Weight 1 1 22 10 50 80 1 2 1 22 350 230 260 1 3 1 22 330 230 260 1 4 1 22 310 240 300 1 5 1 26 290 260 310 1 6 1 26 270 260 310 1 7 1 26 70 50 80 1 8 2 12 10 60 90 .75 9 2 12 30 60 90 .75 10 2 12 350 240 290 .75 11 2 12 330 240 290 .75 12 3 12 10 60 90 .75 13 3 12 30 60 90 .75 14 3 12 350 240 290 .75 15 3 12 330 240 290 .75 SRS6 is a 65yearold male with an AVM located in the right anterior portion of the corpus callosum. Since the nidus was fairly compact and regular, treatment was 78 delivered in a single isocenter with the 16 mm collimator through nine arcs. A dose of 1500 cGy was prescribed to the 80% line. Peacock designed a five arc plan which would deliver the 1500 cGy to the 89 % line, thus lowering the tumor dose inhomogeneity and maximum brain dose. Table 69: Conventional treatment plan for SRS6. Arc Isocenter Collimator Table Arc Start Arc Stop Weight 1 1 16 10 30 130 1 2 1 16 30 30 130 1 3 1 16 50 30 130 1 4 1 16 70 30 130 1 5 1 16 350 230 330 1 6 1 16 330 230 330 1 7 1 16 310 230 330 1 8 1 16 290 230 330 1 9 1 16 270 230 330 1 Since NTCP calculations for brain irradiation were formulated based on data from large field irradiation using conventional fractionation schedules, the NTCP parameters may not be suitable for stereotactic radiosurgery. Data from Kjellberg et al. are commonly used as standards for choosing treatment doses in linear accelerator radiosurgery [Kje83]. It has been shown that their 1% isoeffect line for brain necrosis from treatment with x rays and protons closely matches the 3% isoeffect line for brain necrosis from linear accelerator radiosurgery [Fli90]. Further, all patients with permanent radiation induced complications in the University of Florida series received doses above this line [Fri92]. As shown in Figure 61, NTCP calculations using the 79 model parameters found in the literature underestimate the actual complication probability. In an attempt to force the NTCP calculations to better fit the radiosurgery data in the literature, the NTCP model parameters were modified using a simulated annealing optimization algorithm. This computer program varied the parameters governing dose (m) and volume (n) dependence to provide the best fit to Kjellberg's 1% necrosis line over the range of doses and collimators of interest. As shown in Figure 1, calculations using the modified parameters provide a much better fit to the Kjellberg's curve although the slope of the predicted isoeffect line is still less than expected.Thus, NTCP calculations for stereotactic brain irradiation were performed using these modified parameters. Results of these planning studies are shown in Figures 62 through 614. 40 30 "N 20 (Jn 0  . KjIllberg's Curve  Calulated NTOP (Orgingh Parameters) eO Caloulated NTCP (Modified Parameters) 10 20 30 40 Average Diameter (mm) Figure 61: Kjellberg's isoeffect curve for 1% brain necrosis compared to 3% isoeffect curves obtained from NTCP calculations using parameters (n and m) found in the literature and modified parameters. [ .5t. ' '::'.) 'm...' " ? ,;. B^iiiv"'^^ir I r I **'' sS'lBy^ i f^. *t'^si a i^ *?' f tviI^ 7,,7fXIWl I I Is (b) Figure 62: 15, 7.5, 3 and 1.5 Gy isodose lines are superimposed on axial, sagittal and coronal slices through isocenter from (a) conventional and (b) conformal plans for SRS 1. 100 90 80 70 S60 S50 0 > 40 30 20 10 0 0 I Min D_95 Mean I D_5 Max NTCP/TCP AVM 780.4 1387.5 1739.9 1856.3 1875.0 81.5 Brain 0.0 3.2 51.6 161.2 1866.1 1.1 Score 80.5 (a) 100 90 80 70 S60 50 > 40 30 20 10 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Dose (cGy) Min D_95 Mean D_5 Max NTCP/TCP AVM 1362.9 1524.5 1566.6 1604.4 1612.9 80.8 I Bra!n I 0.0 I Ri I 15fl7 I Afl~ 7 I 1~Q~ R I 1 Q I rin00 2 1 1 0 4 57 I I a I I Score 1 79.3 I Figure 63: DVH and statistics for (a) conventional and (b) conformal plans for SRS1. 200 400 600 800 1000 1200 1400 1600 1800 2000 Dose (cGy) Max NTCP/TCP I I I is (b) Figure 64: 17.5, 8.75, 3.5 and 1.75 Gy isodose lines are superimposed on orthogonal slices through isocenter from (a) conventional and (b) conformal plans for SRS2. 100 90 80 70 " 60 S50 > 40 30 20 10 0 Dose (cGy) Min D_9 5 Mean I I Mctx I NTCP/TC~P I Target 1708.9 1950.0 2090.7 2175.0 2187.5 78.8 Brain 0.0 2.4 55.2 225.9 2121.4 2.5 Score 76.8 (a) 100 90 80 70 S60 S50 0 > 40 30 20 10 o: 0 500 1000 1500 2000 2500 Dose (cGy) Min D_95 Mean D5 Max NTCP/TCP Target 1673.1 1779.3 1843.5 1903.2 1923.1 77.1 Brain 0.0 8.0 126.2 442.3 1884.6 3.3 I Score I 74.5 Figure 65: DVH and statistics for (a) conventional and (b) conformal plans for SRS2. I A' ~ mIll I I I I ', kvu) Figure 66: 15, 7.5, 3 and 1.5 Gy isodose lines are superimposed on axial, sagittal and coronal slices through isocenter from (a) conventional and (b) conformal plans for SRS3. Brain stem Broin Dose (cOy) I Min I D_95 Mean I D_5 S Max I NTCP/TCP AVM 1362.9 1493.8 1601.8 1908.7 2130.8 81.0 Brain 0.0 3.0 77.5 320.0 2074.5 1.8 Brain Stem 19.4 29.1 193.6 514.6 853.1 0.0 Score 79.6 (a) 90 AVM 100 so 80. 70 j 60 50 S50 > 40 30 Brain 201 Brain stem 10 0 0 300 600 900 1200 1500 1800 2100 Dose (cGy) Min D_95 Mean D_5 Max NTCP/TCP AVM 1292.2 1593.8 1724.5 1795.8 1807.2 81.5 Brain 0.0 21.6 179.8 564.8 1798.2 3.2 Brain Stem 36.1 46.2 120.1 217.4 533.1 0.0 Score 78.8 (b) Figure 67: DVH and statistics for (a) conventional and (b) conformal plans for SRS3. 86 (a) , l1, 1 1 ,1 .,I 1 .4 .ki " (b) Figure 68: 15, 7.5, 3 and 1.5 Gy isodose lines are superimposed on orthogonal slices through isocenter one for (a) conventional and (b) conformal plans for SRS4. ~ ~j ~ .~hI I I I I .1 4 U. it (b) Figure 69: 15, 7.5, 3 and 1.5 Gy isodose lines are superimposed on orthogonal slices through isocenter two from (a) conventional and (b) conformal plans for SRS4. I I 100 90 80 70 0 :.,' > 40 30 20 10 0 Min D_95 Mean D_5 I Max I NTCP/TCP Target 1 1222.1 1395.0 1684.8 1824.8 1824.8 81.3 Target 2 1741.1 1753.1 1808.9 1858.3 1858.3 82.8 Brain 0.0 0.0 24.9 24.9 1832.1 0.9 Score 66.7 (a) 100  90 rTorget 1  80 70 Torgel 2 60 50 > 40 30 20 2 Brain 10 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Dose (cGy) Min D_95 Mean D5 Max NTCP/TCP Target 1 1598.3 1652.8 1726.9 1780.2 1785.7 81.9 Target 2 1410.8 1437.1 1563.9 1654.2 1660.7 79.9 Brain 0.0 5.6 71.3 254.5 1750.1 1.4 Score 64.5 (b) Figure 610: DVH and statistics for (a) conventional and (b) conformal plans for SRS4. A r i7 1 1 *:! rI i 1 1:1 (b) Figure 611: 10, 5, 2 and 1 Gy isodose lines are superimposed on axial, sagittal and coronal slices through isocenter from (a) conventional and (b) conformal plans for SRS5. 90 stem Dose (cGy) Min D_95 Mean D_5 Max NTCP/TCP Tumor 776.8 857.1 1088.3 1285.7 1372.8 92.1 Brain 0.0 7.7 50.9 174.1 1044.6 0.6 Brain Stem 46.9 43.0 304.2 565.0 957.6 0.9 Score 90.7 (a) 100 90 80 70 Target S 60 Ba in Stemrn S50 0 30 > 40 30 Brain 20 10 0 200 400 600 800 1000 1200 1400 1600 Dose (cGy) Min D_95 Mean D_5 Max NTCP/TCP Tumor 925.0 1072.1 1171.0 1236.7 1250.0 94.4 Brain 0.0 9.5 88.8 256.3 1237.5 0.9 Brain Stem 93.8 110.0 292.3 746.4 1075.0 3.7 Score 90.2 (b) Figure 612: DVH and statistics for (a) Conventional and (b) conformal plans for SRS5. A i Ik (b) Figure 613: 15, 7.5, 3 and 1.5 Gy isodose lines are superimposed on axial, sagittal and coronal slices through isocenter from (a) conventional and (b) conformal plans for SRS6. , l I,\l/ l/ l. 'J. J  I iO0 90 80 70 60 S50 23 > 40 30* 20 0 0. Dose (cGy) Min D95 Mean D5 Max NTCP/TCP AVM 1037.9 1200.9 1661.1 1858.3 1875.0 81.2 Brain 17.0 19.6 56.2 152.7 1815.2 1.2 Score 80.3 (a) 80 70 S60 S50. > 40 30 20 Min D_95 Mean D_5 Max NTCP/TCP AVM 1441.0 1555.9 1628.8 1676.6 1685.4 81.1 Brain 0.0 6.9 100.9 273.1 1677.0 1.5 Score 79.9 (b) Figure 614: DVH and statistics for (a) Conventional and (b) conformal plans for SRS6. 93 Head and Neck Carcinoma The first patient studied (HN1) is a 66yearold female diagnosed with a T4 left maxillary sinus adenoid custic carcinoma. Due to the extensive nature of her disease, she was not a viable candidate for surgery, and thus underwent a course of radiotherapy. She was treated to a dose of 7480 cGy in 68 fractions employing a twice daily fractionation schedule with 6 MV photons. A three field technique (AP and laterals) with wedges was used and the portals were reduced at 5060 cGy in order to reduce normal tissue toxicity. Through BEV planning the radiation portals can be designed to better match the target volume thus better sparing normal tissue and avoiding tumor underdosage. The Peacock plan further spares normal tissue, but results in a fairly significant tumor dose inhomogeneity with the dose prescribed to the 74 percent isodose line. Results of conventional, BEV and conformal plans are shown in Figures 615 through 620. HN2 is a 17 yearold female who suffered from T4N3B carcinoma of the nasopharynx. Using modem radiotherapy techniques, local control rates for nasopharynx carcinomas range from 8090% for T1 or T2 primaries to about 50% for more advanced tumors [Kut91b]. Although this control rate is already very good using conventional techniques, the proximity of the nasopharynx to critical structures such as brain, brain stem, spinal cord and eyes leads to a high risk of complication from radiotherapy. Thus, it is attractive to use inverse radiotherapy planning in order to conformally avoid these critical structures. The conventional treatment plan required 7200 cGy in 60 fractions to the primary disease site delivered using mixed photon (Co) and electron (10 MeV) 