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A numerical simulation of organ motion and daily setup uncertainties: Implications for radiation therapy

A numerical simulation of organ motion and daily setup uncertainties: Implications for radiation therapy
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  ELSEVIER PI1 SO360-3016(96)00477-4 l Physics Contribution A NUMERICAL SIMULATION OF ORGAN MOTION AND DAILY SETUP UNCERTAINTIES: IMPLICATIONS FOR RADIATION THERAPY J. H. KILLORAN, PH.D., H. M. KOOY, PH.D., D. J. GLADSTONE, Sc.D., F. J. WELTE, M.S. AND C. J. BEARD, M.D. Joint Center for Radiation Therapy, Department of Radiation Oncology, Harvard Medical School. Bouton. MA Purpose: n radiotherapy planning, the clinical target volume (CTV) is typically enlarged o create a planning target volume (PTV) that accounts or uncertainties due to internal organ and patient motion as well as setup error. Mar@ size clearly determines he volume of normal tissue rradiated, yet in practice it is often given a set value n accordance with a clinical precedent rom which variations are rare. The (CTV/PTV) formalism does not account for crltlcal structure dose. We present a numerical simulation o assess CTV) coverage and critical organ dose as a function of treatment margins n the presence f organ motion and physical setup errors. An application of the mode1 o the treatment of prostate cancer s presented, ut the method s applicable o any site where normal tissue olerance s a dose-limiting actor. Methods and Materials: A Monte Carlo approach was used o simulate he cumulative effect of variation in overall tumor position, for individual treatment fractions, relative to a fixed distribution of dose. Distributions of potential dose-volume istograms DVHs), for both tumor and normal tissues, re determlaed hat fully quan- tify the stochastic nature of radiotherapy delivery. We introduce the concept of Probability of Prescrlptlon Dose (PoPD) sosurfaces s a tool for treatment plan optimization. Outcomes esulting rom current treatme& phmnlng methods are compared with proposed echniques or treatment optimization. The standard phnmlng bchnlqne of relatively large uniform margins applied to the CTV, in the beam’s eye view (BEV), was compared wltb three other treatment strategies: a) reduced uniform margins, h) nonuniform margins adjusted o maximize normal tissue paring, and (c) a reduced margin plan in which nonuniform fluence profiles were ntroduced o compensate for potential areas of reduced dose. Results: Results based on 100 simulated ull course treatments ndicate that a 10 mm CTV to PTV margin, combined with an additional 5 mm dosimetric margin, provides adequate CTV coverage n the presence f known treatment uncertainties. Nonuniform margins can be employed o reduce dose delivered to normal tissues hile preserving CTV coverage. Nonuniform fluence profiles can also be used o further reduce dose elivered o normal tissues, hough this strategy does esult n higher dose evels delivered to a small volume of the CTV and normal tissues. Condnsions: Monte Carlo-based reatment simulation s an effective means of assessing he impact of organ motion and daily setup error on dose delivery via external beam adiation therapy. Probability of Prescription Dose PoPD) sosurfaces re a useful tool for the determination of nonuniform beam margins hat reduce dose delivered to critical organs while preserving CTV dose overage. Nonuniform fluence profiles can further after critical organ dose with potential therapeutic benefits. Clinical consequences f this latter approach can only be assessed ia clinical trials. Copyright 0 1997 Elsevier Science Inc. Prostate cancer, Organ motion, Setup error, Dose probability. INTRODUCTION Various factors, including setup error and organ motion as well as physical and geometric penumbra, imit the abil- ity of the radiotherapist to deliver tumorcidal dose to tu- mors while sparing normal tissue. Conventional treat- ment-planning methods, as prescribed by the International Commission on Radiation Units and Measurements, Tech- nical Report 50 (5). dictate that the clinical target volume (CTV) be enlarged by a margin to create a planning target volume (PTV). The margin is chosen to include uncer- tainties due to patient and organ motion as well as physical setup error. A treatment plan is then devised to deliver a prescribed level of dose to the PTV. The purpose of this methodology is to ensure consistent dose delivery to the CTV. The use of a PTV can guarantee tumor coverage with a high degree of certainty, provided an adequate mar- gin is used. For tumors in close proximity to critical or- -- -- Reprint requests to: Joseph H. Killoran, Ph.D., Joint Center Ackno&edgements-Assistance in preparing this document pro- for Radiation Therapy, Department of Radiation Oncology, vided by Drs. Robert Cormack, Edward Holupka. and @ran Harvard Medical School. 330 Brookline Ave., Boston, MA Svensson is gratefully acknowledged. 02115. Accepted for publication I9 September I Wt> 213  214 I. J. Radiation Oncology 0 Biology 0 Physics Volume 37, Number 1, 1997 gans, the selection of margin size is difficult, particularly because the methodology does not ensure that dose deliv- ered to surrounding critical organs is kept at an acceptable level. Thus, for tumors bordering critical organs, the se- lection of margin size involves a trade-off between tumor control and radiation-induced complications. We present a new method to quantitatively assess umor coverage and normal organ dose via numerical simulation. This method uses a Monte Carlo type approach to directly model the effects of organ motion and setup error during fractionated radiotherapy. Beginning with a distribution of dose calculated using treatment-planning software, a series of random displacements are applied, one for each simulated treatment fraction, relative to the patient anat- omy. The applied displacements are fully three dimen- sional. The dosimetric effect of each fraction is summed, resulting in a calculation of actual delivered dose for a full course of therapy. Due to the stochastic nature of treat- ment uncertainties, each delivered dose distribution cal- culated by the simulation represents a single possible out- come out of a range of possibilities. Simulation is performed multiple times to quantify the range of possible delivered dose distributions. We introduce the concept of Probability of Prescription Dose (PoPD), the probability that a given segment of the anatomy will receive full pre- scription dose or higher. Isosurfaces of PoPD have been used as a tool for treatment optimization and can be viewed as an extension to the CTV/PTV formalism pro- posed by ICRU 50. distribution. While a convolved distribution may reason- ably predict the average dosimetric outcome, our method provides an average as well as a range of possible out- comes. Additionally, it is unclear how a convolution method could simulate the systematic component of treat- ment uncertainty, and rotational effects would be very dif- ficult to model. Our Monte Carlo approach models both these effects explicitly. Our simulation method has been used to model frac- tionated conformal radiotherapy for prostate cancer. Spe- cifically, the effect of margin size and beam fluence profile on actual delivered dose has been examined. We compare the standard JCRT technique with alternative dose deliv- ery strategies designed to reduce dose delivered to normal tissues. Using PoPD isosurfaces, we have employed an iterative approach to obtain optimized margins in three dimensions. We have also combined this approach with the use of nonuniform fluence profiles as an avenue for further treatment optimization. METHODS AND MATERIALS CT-based treatment planning for conformal radiotherapy of prostate cancer The Monte Carlo technique used for this simulation could be considered a somewhat brute force approach, lacking the elegance and efficiency of error simulation methods based on convolution (3,lO). Compared to a con- volution based approach, our method is numerically in- tensive. For each treatment fraction, a volume grid of 125,000 dose values is translated and rotated, then resam- pled to the original coordinate space. A 100 treatment course simulation typically requires ~2 h computation time on a modem workstation. ’ A convolution-based method would involve convolving a static dose distribution with an integral kernel, most likely a Gaussian function of an appropriate width, re- sulting in a blurred dose distribution representative of the actual delivered dose. In principal, a method of this type would require substantially less computational resources, but the results would be more of an approximation to ac- tual treatment delivery. In particular, the blurred dose dis- tribution is strictly what would result from a treatment consisting of an infinite number of small fractions. All stochastic effects are, thus, averaged out to the maximum extent possible. Our results show a noticeable and some- times significant variation in possible outcomes for treat- ments consisting of 36 fractions, indicating that this num- ber of total fractions does not truly represent a statistical At our institution, patients who will undergo conformal radiotherapy for early stage prostate cancer have a CT scan in the treatment position with a leg immobilization device in place. An identical device is used during daily treatments. Patients are instructed to empty their bladder prior to both the CT scan and therapy. The prostate and seminal vesicles are delineated using the CT data via in- teractive contouring by a clinician. For the first course, the CTV is the combined volume of the prostate and seminal vesicles. For the second course “Cone Down” the CTV is the prostate alone. For both courses a PTV is determined by uniformly enlarging the CTV by a 10 mm margin. Beam shaping is accomplished in the BEV using a 5 mm uniform distance between the edge of the PTV and the edge of the lead block. This additional margin is to ac- count for beam penumbra and ensure adequate coverage of the PTV. The first course consists of 25 fractions and the second of 11. (Since this study began, the JCRT treat- ment protocol has changed. An additional fraction has been added to the second course for a total of 12.) The fraction size for both courses is 1.8 Gy delivered to the 95 isodose line (referenced to isocenter). Analysis of organ motion and setup error To be directly applicable to actual therapy, a thorough understanding of organ and patient motion for the treat- ment site is required for our simulation. The results of a detailed study of prostate motion, performed by van Herk et al. (1 l), were incorporated in our simulation. This study involved an analysis of multiple CT scans made for a ‘DEC 3000/500, Digital Inc., Maynard, MA.  A numerical simulation of organ motion and daily setup errors 0 J. H. KILLOKAN rt d. 2 I5 Table 1. Values to quantify organ motion expressed as standard deviations of determined translations and rotations along and about each axis Axis Motion type L-R A-P I-S Translation along axis (mm) 0.9 2.1 1.7 Rotattion around axis (degrees) 4.0 1.3 2.1 Additionally, a linear correlation of -0.53 was found to exist between A-P translation and L-R rotation. group of patients undergoing therapy for prostate cancer. The motion of organs was quantified by aligning pairs of CT scans, for the same patient, based on the pelvic bone. A similar matching procedure was then performed on the combined volumes of the prostate and seminal vesicles to determine the translations and rotations necessary to bring the two combined volumes into alignment. The results from this study used for our simulation are presented in Table 1. Standard deviations are given for translations and rotations relative to the left-right (L-R), anterior-posterior (A-P). and inferior-superior (I-S) axes. Additionally, translation in the (A-P) direction was found to be linearly correlated with rotation about the (L-R) axis. This indi- cates that rotation tends to occur round a point near the apex of the prostate. The accuracy of these values was reported to be OS-O.9 mm for translations and 1” for rotations. A study to assess typical setup errors present for pa- tients undergoing treatment for prostate cancer was per- formed by Gladstone et al. (2). This study was intended to assess the potential benefit of obtaining a localization image prior to treatment, via an electronic portal imaging device (EPID), to determine setup accuracy with the op- tion to reposition the patient if necessary. The results of this study are summarized in Table 2. The corrected values indicate the level of setup error present if on-line reposi- tioning is utilized. Repositioning was only performed, however, if the portal image indicated a setup error greater than 3 mm. For our simulation, the uncorrected values were used to model treatment without the benefit of on- line portal image analysis. Table 2. Values to quantify setup error, determined by Gladstone et al. (2), expressed as standard deviations along each axis Daily setup error L-R Corrected (mm) 1.6 Uncorrected (mm ) 2.4 Axis A-P 2.0 3.4 I-S 2.0 3.9 Fig. I. Generation of conformal beam apertures in the beams eye view (BEV). Shown are the projected tumor and critical organ volumes superimposed on the DRR for the anterior beam. The conformal beam aperture shown here is for a IS mm total margin. the minimum distance from the clinical target volume (CTV) to the beam edge. 30 treatment planning Dose distributions used by the treatment simulation were generated using an internal version of the Xknife’ 3D treatment-planning system. This system, which is cur- rently used exclusively for stereotactic treatment planning, runs on Hewlett Packard 9000/700 series workstations and utilizes high resolution graphics for volumetric rendering of anatomical structures and dose distributions. Investi- gational extensions to the planning system have made it possible to perform planning for nonstereotactic treat- ments. Conformal shaping of individual treatment beams is easily accomplished using Beam’s Eye View (BEV) projections of the tumor volume and critical organs. These projected volumes can be displayed over a DRR, as shown in Fig. 1. to depict organ positions relative to bony anat- omy. XKnife has the capability to generate uniform con- formal beam apertures automatically. based on a specified margin size. Beam apertures with nonuniform margins must be defined manually. Relevant anatomical structures were contoured interactively from CT images having a 1.5 X 1.5 X 5 mm voxel resolution. Volume dose distributions were calculated over a 3 x 3 X 3 mm grid by the planning system. DVHs were calculated using an algorithm ( 1) de- rived from Graphical Plan Evaluation Tool (GPET) a soft- ware package developed under NC1 contract NOI -CM- 97564. Monte Carlo treatment simulation The purpose of the treatment simulation is to quantify the range of possible dosimetric treatment outcomes, given the uncertainties of specific treatment parameters as well as the limited information available to the treatment planner. A number of assumptions are inherent to this sim- ulation. Specifically, it is assumed that: I ) organ position varies from day to day, but does not change significantly while an individual treatment fraction is delivered. 2) Variation of the parameters that quantify daily prostate organ position can be approximated by a Gaussian distri- ‘RSA. Inc. Burlington. MA. -_.- .- _--- ,_.. --.  216 I. J. Radiation Oncology l Biology l Physics Dose Volume 37, Number 1, 1997 Repeat for Each Fraction - Systematic Daily Error wOrgan Motion w Apply Offset Offset Setup Error Sum Dose I I Anatomy Repeat N * Times N Simulations Treatment Course Calculate DVHs ate U VHs complete omplete Record Voxels ord Voxels Receiving 2 RX Dose ing 2 RX Dose 1 Beam Margin Optimization Complete I-1 I + VH Distribution Fig. 2. A schematic of the 3D treatment simulation. Starting with anatomical and dosimetric information, a systematic offset is determined that is held constant over the simulated treatment course. For each simulated fraction, a displacement is determined resulting from both organ motion and setup error. Results are quantified as distributions of dose volume histograms (DVHs) for relevant organs and volumetric probability of prescription dose (PoPD) distributions. The latter can be utilized to optimize beam margins, resulting in a new distribution of dose. bution. 3) The shape of the prostate organ remains con- stant, as does the shape and relative position of surround- ing organs. 4) Positional setup errors displace the anatomy with respect to the planned dose distribution, but do not change the overall shape of the dose distribution. The assumption of a constant organ shape was inherent to the method of Chamfer matching used to quantify the motion of the prostate and seminal vesicles. A change in organ shape may result in a reported difference in orien- tation as well as a possible failure of the matching algo- rithm to determine a unique fit. As observed by van Herk (1 l), variations in organ shape were sufficiently small for consistent results to be obtained. Variation in the shape and orientation of surrounding organs during treatment is also of concern, particularly in light of a recent study of Lebesque et al. (7), in which substantial variations were observed in rectal and bladder volume in patients under- going prostate radiotherapy. The ultimate purpose of de- lineating these organs, however, is to compare various treatment strategies with regard to critical structure dose. While variation in position and shape will alter the dose these organs receive during treatment, it is highly unlikely that these variations would alter the relative ranking of one treatment strategy with respect to another. A schematic representation of the treatment simulation is shown in Fig. 2. The simulation requires two volumetric data sets, both specific to an individual patient, which quantify the patient’s anatomy as well as the distribution of dose that would result from a specific treatment beam configuration. Anatomical information is derived from contours drawn interactively on individual CT slices by a clinician. The dose distribution, later referred to as the static dose distribution, is calculated in the coordinate frame of the CT data. In the ideal treatment scenario, in which no organ motion, setup errors, or other dosimetric uncertainties were present, the static dose distribution is also the dose delivered to the patient. Our simulation at- tempts to model the effects of organ motion and setup error based on currently available estimates of these quantities. The simulation operates by sampling displacements for organ motion and setup error using a random number gen- erator. The Box-Muller method (9) is used to sample val- ues for translations and rotations from Gaussian distribu- tions, so that the degree of organ motion observed by the study of van Herk et al. (11) is duplicated. Rotations are performed around the center of mass of the CTV. This position also represents a single sampling of all possible  A numerical simulation of organ motion and daily setup errors 0 J. H. KILLORAN rt d 217 organ positions. The practice of treatment planning based on a single CT scan thus introduces a systematic deviation between the organ position observed on the CT scan and the true mean organ position. While it is not possible to determine the mean organ position, it is possible to predict the probability of a given magnitude deviation. From the perspective of the treatment planner, the deviation be- tween the organ position on CT and the true mean position can be treated as a random variable. A separate displace- ment of the organ, sampled in the same manner as the daily organ displacements, is used to represent this devi- ation. This displacement is added as a constant offset to each daily displacement for the duration of the simulated course of therapy. The random nature of this offset means that each full course treatment must be simulated multiple times using a new sampled value to represent the mean position. Displacements due to setup error are also sampled from Gaussian distributions. These displacements are assumed to consist of translations only (no rotations). The study of Gladstone et al. (2) did not quantify rotational setup errors, and the results of van Herk et al. (11) indicate such effects are small compared to rotations of the prostate organ. Fur- thermore, setup error was observed to be purely random. The total displacement resulting from the combined ef- fects of setup error and organ motion is applied as a shift of the anatomy relative to the static dose distribution. The dose delivered to the anatomy is then tabulated on a per- voxel basis. This process is repeated for each treatment fraction until all fractions comprising a complete treat- ment course have been delivered. The final result is quan- tified as a dose-volume histogram (DVH) for each of the relevant organs, as well as a volumetric data set, which tabulates which voxels received prescription level dose or higher. This volumetric data set is the basis for the Prob- ability of Prescription Dose (PoPD) distribution. The results of simulating a multifraction course of ther- apy represent one outcome out of a possible distribution of outcomes. To quantify the range of possibilities, each complete course of therapy was simulated multiple times (typically 100). For a large number of simulated treat- ments it is possible to estimate the PoPD, the probability that a given voxel will receive full prescription dose or higher. Isosurfaces of PoPD can be viewed graphically, in the same manner as an isodose surface, and provide ad- ditional information for plan optimization. Treatment strategies compared Figure 3 illustrates qualitatively in one dimension three dose profiles representative of the basic dose delivery strategies evaluated using our simulation. A hypothetical tumor volume is shown (CTV), which is directly adjacent to a critical organ. The solid vertical line indicates the nominal boundary between the two, which varies in po- sition due to organ motion and setup error. The dotted vertical lines indicate a range within which the boundary is expected to fall with a reasonable level of certainty. In Fig. 3. This simple 1D arrangement of organs illustrates three basic dose delivery strategies assessed ia numerical simulation. The solid vertical line denotes the nominal boundary between the clinical target volume (CTV) and an adjacent critical organ. The position of the boundary is uncertain but is expected to fall within the dashed vertical lines with a reasonable degree of’ certainty. The heavy dashed line indicates the standard approach that guarantees tumor coverage by using a large margin. This strategy irradiates a large volume of adjacent tissue. The lighter dashed line shows an improved strategy in which the dose profile is more optimally conformed to the expected level of uncertainty. The solid line is a strategy for further margin reduction with preserved tumor coverage. Dose levels are raised slightly at the border to compensate for potentially underdosed regions of the CTV. the terms of ICRU 50, the dotted vertical line on the right could be said to denote the boundary of the PTV. In actual practice, the level of uncertainty is often unclear and may vary at different portions of the CTV/critical organ bound- ary. Three dose profiles are shown, representing three dif- ferent treatment approaches. The heavy dashed line shows the standard approach of a large margin used to insure complete tumor coverage. The lighter dashed line shows a dose profile more closely matched to the level of uncer- tainty in CTV position. One application of our numerical treatment simulation is a more thorough understanding of the expected uncertainties, thereby allowing for a careful optimization of treatment margins. The solid line in Fig. 3 represents a strategy, proposed previously by Lind et al. (8), for further margin reduction while preserving tumor coverage. Dose levels at the field edges are moderately increased to compensate for poten- tial areas of reduced dose. Again, our numerical simula- tion is necessary to design and assess the benefits of a treatment strategy using this approach. Table 3 summarizes four treatment strategies examined via treatment simulation. All strategies compared were based on the four-field box technique. Strategy I is the traditional benchmark, consisting of a 10 mm uniform margin, applied to the CTV to create a PTV. As well as an additional 5 mm uniform dosimetric margin from the edge of the PTV to the edge of the lead block. Specifically, these margins are applied to the projection of the CTV in the BEV, as shown in Fig. I. Strategy II uses a similar
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