Reducing dose calculation time for accurate iterative IMRT planningJeffrey V. Siebers, Marc Lauterbach, Shidong Tong, Qiuwen Wu, and Radhe Mohan

Citation: Medical Physics 29, 231 (2002); doi: 10.1118/1.1446112 View online: http://dx.doi.org/10.1118/1.1446112 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/29/2?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Reduced order constrained optimization (ROCO): Clinical application to lung IMRT Med. Phys. 38, 2731 (2011); 10.1118/1.3575416 The use of modified single pencil beam dose kernels to improve IMRT dose calculation accuracy Med. Phys. 31, 3279 (2004); 10.1118/1.1812851 Penalized likelihood fluence optimization with evolutionary components for intensity modulated radiation therapytreatment planning Med. Phys. 31, 2335 (2004); 10.1118/1.1773631 Multiple local minima in IMRT optimization based on dose–volume criteria Med. Phys. 29, 1514 (2002); 10.1118/1.1485059 Acceleration of intensity-modulated radiotherapy dose calculation by importance sampling of the calculationmatrices Med. Phys. 29, 676 (2002); 10.1118/1.1469633

Reducing dose calculation time for accurate iterative IMRT planningJeffrey V. Siebers,a) Marc Lauterbach, Shidong Tong, Qiuwen Wu, and Radhe MohanDepartment of Radiation Oncology, Medical College of Virginia Hospitals, Virginia CommonwealthUniversity, Richmond, Virginia 23298

~Received 20 June 2001; accepted for publication 21 November 2001; published 25 January 2002!

A time-consuming component of IMRT optimization is the dose computation required in eachiteration for the evaluation of the objective function. Accurate superposition/convolution~SC! andMonte Carlo ~MC! dose calculations are currently considered too time-consuming for iterativeIMRT dose calculation. Thus, fast, but less accurate algorithms such as pencil beam~PB! algo-rithms are typically used in most current IMRT systems. This paper describes two hybrid methodsthat utilize the speed of fast PB algorithms yet achieve the accuracy of optimizing based upon SCalgorithms via the application of dose correction matrices. In one method, the ratio method, aninfrequently computed voxel-by-voxel dose ratio matrix (R5DSC/DPB) is applied for each beam tothe dose distributions calculated with the PB method during the optimization. That is,DPB3R isused for the dose calculation during the optimization. The optimization proceeds until both theIMRT beam intensities and the dose correction ratio matrix converge. In the second method, thecorrection method, a periodically computed voxel-by-voxel correction matrix for each beam, de-fined to be the difference between the SC and PB dose computations, is used to correct PB dosedistributions. To validate the methods, IMRT treatment plans developed with the hybrid methodsare compared with those obtained when the SC algorithm is used for all optimization iterations andwith those obtained when PB-based optimization is followed by SC-based optimization. In the 12patient cases studied, no clinically significant differences exist in the final treatment plans devel-oped with each of the dose computation methodologies. However, the number of time-consumingSC iterations is reduced from 6-32 for pure SC optimization to four or less for the ratio matrixmethod and five or less for the correction method. Because the PB algorithm is faster at computingdose, this reduces the inverse planning optimization time for our implementation by a factor of 2 to8 compared with pure SC optimization, without compromising the quality or accuracy of the finaltreatment plan. ©2002 American Association of Physicists in Medicine.@DOI: 10.1118/1.1446112#

Key words: IMRT, dose calculations, dose accuracy

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I. INTRODUCTION

Iterative dose calculation used for IMRT optimization prsents a dilemma between the accuracy and the time requto complete the tasks. On one hand, IMRT requires accudose distributions to accurately evaluate the patient plan,on the other hand, it requires fast dose calculations sothe iterative optimization can be completed in a reasonatime frame. These issues were discussed in a recent pa1

that presented one method for reducing IMRT dose calction time. This method was a sequential approach to dcalculation, and entailed performing initial optimization docalculations with a fast pencil beam~PB! algorithm, and,following convergence, continuing the optimization with aaccurate superposition/convolution~SC! algorithm. It wasdetermined that this method resulted in IMRT beam intenand dose distributions that were clinically equivalent to thoobtained when the SC algorithm was used throughoutoptimization. The multistage method resulted in a two-fourfold time savings. In this paper, two alternative methoto reduce IMRT dose calculation time are developed. Bcause these methods entail combining or mixing dose ca

231 Med. Phys. 29 „2…, February 2002 0094-2405 Õ2002Õ2

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lation algorithms, they are termed hybrid dose calculatmethods. The aim of this work is to demonstrate thatresults obtained with these hybrid methods are clinicaequivalent to those obtained by using the accurate SC arithm throughout the optimization process, but in a fractiof the time.

In the proposed methods, the majority of the dose coputations are performed using a fast dose algorithm whresults are modified by a periodically updated dose corrtion matrix. Two different correction matrices are studied.one, the matrix is defined to be the ratio of SC and PB ddistributions at a given iteration. In the other, the correctmatrix is an additive error correction term. The rationalethese methods is that the speed advantages of the fascalculations are obtained for most iterations, yet the accurof the SC should be obtained in the final result. The aimthe work reported in this paper was to develop and impment the so-called hybrid dose calculation methodsIMRT; investigate if the converged optimization results otained with these methods method agree with those obtawhen SC is used throughout optimization; and evaluatetime reduction for optimization convergence.

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232 Siebers et al. : Reducing dose calculation time 232

II. METHODS AND MATERIALS

A. IMRT optimization system

The Medical College of Virginia~MCV! IMRT optimiza-tion system, developed in-house for research and clinpurposes, was used in this study.2 This system employs agradient-based search algorithm to adjust the intensityeach ray~beamlet! in the intensity matrix based on the door dose-volume constraints on points along the ray. Tchange in scatter contribution to neighboring points isglected during the intensity update; however, it is accounfor at the completion of each iteration by recalculating tdose distribution. The IMRT system is interfaced directlythe ADAC Pinnacle3 ~ADAC Laboratories, Milpitas, CA!treatment planning system. Pinnacle3 is used for patient contouring, dose-volume analysis, and other treatment planntasks.

Dose-volume-based objective functions were used totimize all of the IMRT plans presented. The dose-volumbased optimization algorithm and other details of the MCIMRT optimization system are described in detelsewhere.2 Briefly, in each iteration, the dose distribution fothe current intensity modulation is evaluated, and the optization system computes the current plan score, i.e., the vof the objective function. This is evaluated for convergenWhen convergence is not indicated, the optimizer adjuindividual beamlet intensities using a gradient search arithm to reduce the plan score and initiates a new iteratConvergence is indicated when the the relative differencconsecutive plan scores drops below a user-specified throld, termed the convergence criteria. The hybrid dose calation strategies described below were wrapped aroundoptimization loop of the MCV IMRT system.

B. Dose calculation algorithms

Two dose calculation algorithms were utilized to demostrate the feasibility and to evaluate the performance ofhybrid dose calculation methods for iterative IMRT plannina fast measurement-based algorithm and a slow, yet accumodel-based algorithm. For the fast algorithm, the penbeam ~PB! algorithm developed by Mohanet al.3–5 wasused, while a superposition/convolution~SC! algorithm de-veloped by Mackieet al.6 and implemented in Pinnacle3 wasused for the accurate dose calculation algorithm. Thealgorithm uses fast Fourier transforms to convolve MoCarlo-generated pencil beam dose distributions to accofor the nonuniform intensities across an IMRT field. It corects for surface irregularities and internal inhomogeneiusing the radiological path-length method, and thus, caninaccurate in inhomogeneous media. The PB algorithminterfaced to the IMRT and the Pinnacle3 systems.

The SC algorithm uses pre-stored Monte Carlo-generapoint spread kernels to integrate the contribution of radiatscattered from the entire 3D patient volume to each poThis method accounts for the nonuniform intensities acran IMRT field, and its correction for surface irregularitieand inhomogeneities is considered to be the most accura

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the non-Monte Carlo dose calculation methods. The specSC algorithm used for evaluating the hybrid dose calculatalgorithms was the adaptive convolve algorithm in Pinnac3.This algorithm performs the SC calculation on every foupoint in the dose grid. If the dose in a region is flat, dosesintermediate points are interpolated. Otherwise, theycomputed using the SC algorithm.

To evaluate the relative speed of the alternative doseculation algorithms, one set of calculations was performby using the three SC algorithms in Pinnacle3—fast convolve~FC!, adaptive convolve~SC!, and collapsed cone convolution ~CCC!—and by using two implementations of the penbeam algorithm. In the standard PB implementation, allquired quantities are calculated for each PB iteration andresulting dose distributions are loaded into Pinnacle3. TheMCV-IMRT system then reads the dose distributions froPinnacle3. In the integrated PB method~IPB!, values that donot change from one iteration to the next~TMRs, radiologi-cal path-lengths, etc.! are precomputed and stored, and tinterprocess communication with Pinnacle3 is avoided, thusminimizing the PB dose calculation time.

C. Dose calculation methods

1. SC-based optimization

The simplest dose calculation strategy to use during omization is to use the same dose computation algorithmall iterations throughout. To ensure accuracy in the resobtained, the accurate SC dose calculation algorithmused. This becomes the reference data set to which odose calculation methods are compared.

2. The sequential dose calculation method

As a reference for comparison with other dose acceletion methods, each plan was also optimized using thequential dose calculation method. This method was descrin detail in an earlier paper1 and is briefly described here focompleteness. In this method, initial optimization is peformed using the PB algorithm for dose calculations. Folloing convergence, the dose calculation algorithm is chanto the SC algorithm, and optimization continues usingintensities from the PB-based optimization as a startpoint. The first stage of this method produces a good iniguess to the second, accurate stage of this optimization arithm. Thus, it reduces the number of iterations required wthe slower SC algorithm.

3. The ratio matrix method

The modus operandi of the ratio matrix method is olined in Fig. 1. There are two loops in the optimization algrithm. One, the inner loop, which is embedded within tintensity optimization stage~box 2!, is described in Sec. II A,but is not shown explicitly in Fig. 1. The outer loop is eplicitly shown. The dose correction ratio matrix,R, is avoxel-by-voxel dose correction term for each beam. Initiaeach element ofR is set to unity for each voxel for eacbeam~box 1!. This means that in the first pass through t

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233 Siebers et al. : Reducing dose calculation time 233

optimization stage~box 2! of the outer loop, the modifieddose distributionDR is the same asDPB, that is, initial op-timization is performed with the PB dose distribution. Tintensity distribution of each beam is adjusted iterativelythe inner loop usingDR until convergence is achieved. Thstep produces optimized intensity (I R,O) and dose distribu-tions (DR,O) ~box 3!. Using I R,O, the dose distribution isrecalculated using the SC method~box 4!. Convergence ofthe dose distributions~box 5! is checked by comparing thDR,O andDSC plan scores. In the first pass through the ouloop, the score of the IMRT plan calculated withDSC isgenerally higher than theDR,O score. The difference betweethe two diminishes with each pass through the outer loWhen DR,O and DSC differ by more than the convergenccriteria, the dose correction ratio matrixR5DSC/DPB,O isrecalculated for each beam~box 6!, and the optimization~box 2! proceeds starting with intensitiesI R,O from the pre-vious iteration. Note that the initial dose distribution for thnext pass through the optimization loop isDPB,O3R5DSC,the convolution dose result. Convergence is obtained wtheDR,O andDSC plan scores differ by less than the convegence criteria. For these studies, the same convergenceteria were used for the inner optimization loop~box 2! andouter hybrid loop. In general, these convergence critecould be different.

4. The additive correction matrix method

The correction matrix method, depicted in Fig. 2, is simlar to the ratio matrix method. The difference between thmethods is that the correction matrix is an additive voxel-voxel correction term for each beam. During the optimiztion, ~box 2!, the DC5DPB1C is used to evaluate the plaobjective function.

FIG. 1. Flow diagram of the ratio hybrid method.R represents a voxel-by-voxel dose correction matrix for each beam that is used to correct the eof the PB dose algorithm. Final convergence occurs when both the opzation and the correction matrixR have converged. At that point, the dospredicted by the ratio method equals that predicted by convolution.

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The additive correction matrix method was inspiredand is similar to the ‘‘delta-pixel beam’’ method implemented in Pinnacle3 version 6,7 however, it differs in thatPinnacle3 does not iterate using the outer-loop, but insteonly performs a single SC computation following a prscribed number of iterations. Furthermore, the Pinnaimplementation uses prestored truncated pencil beamseach beam element while our implementation uses thepencil beam and computes the full dose distribution in eiteration.

D. Patients and plans

The goals of this study were~1! to demonstrate that theplans obtained with the hybrid dose calculation methodsclinically equivalent to those developed when the accurdose computation is used throughout, and~2! to determinethe time savings possible by using the dose correction mods as compared with using an accurate dose computathroughout the optimization process. The methods wtested by applying them to several IMRT patients withverse locations, shapes and sizes of tumors. Patient treatsites and descriptions are summarized in Table I. Five ofcases studied were head and neck cases. The anatocomplexities and the presence of low-density internal inmogeneities make this an ideal site for evaluating they pposed methods. The head and neck patients were part oIMRT dose escalation and parotid sparing study for sqmous cell carcinomas. Other cases~brain, gyn, prostate,spine, and lung! were included in the study to demonstrathe applicability of the methods to additional sites.

For each patient, IMRT plans were initially developed uing the SC dose calculation algorithm for each iteration

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FIG. 2. Flow diagram of the correction hybrid method.C represents a voxel-by-voxel dose correction matrix for each beam that is used to correcterrors of the PB dose algorithm. Final convergence occurs when bothoptimization and the correction matrixC have converged. At that point, thedose predicted by the correction method equals that predicted by convtion.

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234 Siebers et al. : Reducing dose calculation time 234

the optimization. The dose-volume parameters of the obtive function were adjusted to obtain the desired optimIMRT dose distributions. Results obtained using this methare designated SCopt and were used as a benchmark to assother methods. The same dose-volume parameters wereused to perform optimization using each of the other meods tested. The convergence criteria used for each caseset to be the same as when the case was clinically planand are indicated Table I.

Optimized plans obtained were compared using isoddose distributions and dose-volume histograms~DVHs! be-cause these are typically used to judge the clinical accability of a plan. Furthermore, the optimization system’s pquality score is compared because this is the value thatoptimizer is attempting to minimize.

FIG. 3. Isodose contours through a transverse slice of head and necPatient I. In~a!, optimization was performed using SC for all dose calcutions in the optimization. In~b!, initial optimization used the PB algorithmand final optimization used the SC algorithm. In~c!, the ratio method wasused for dose evaluation, and in~d!, the correction method was used.

TABLE I. Summary of patients, beam and the optimization convergenceteria used in this study.

Patient SiteNumber of

beamsConvergence

criteria

I Head/Neck 9 1.0%II Head/Neck 9 1.0%III Head/Neck 9 1.0%IV Head/Neck 9 1.0%V Head/Neck 9 0.5%VI Brain 9 1%VII Gyn 4 0.5%VIII Prostate 7 1%IX Prostate 7 0.5%X Spine 7 0.5%XI Lung 7 0.5XII Lung 5 0.5%

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III. RESULTS AND DISCUSSION

Detailed results for the various methods are shownone patient~Patient I! and are summarized for the otherPatient I was prescribed to receive a dose of 68 Gy to 98%the gross disease~PTV-I!, 60 Gy to a;1 cm margin formicroscopic extension~PTV-II!, and 54 Gy to electively

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FIG. 4. Dose-volume histograms for each dose calculation method uduring optimization for Patient I. In~a!, the PTV-1, representing gross disease, is plotted. In~b!, the dose to the parotids (right1 left) is displayed, andin ~c!, the dose to the cord is displayed.

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235 Siebers et al. : Reducing dose calculation time 235

treated nodal volumes~PTV-III !. Additionally, 50% of theparotid volume was to be below 30 Gy and the maximdose to the cord and brainstem were to be below 40 Gy.plan was delivered in 30 fractions using the simultaneintegrated boost method8 utilizing 9 equispaced coplanarMV beams@0° ~AP!, 40,..., 320#. The plan was optimizedusing dose-volume criteria. Figure 3 compares isodosetributions on a single transverse slice for plans optimizusing SCopt, the sequential dose calculation method, andtwo hybrid dose calculation methods. The isodose linessimilar for each dose calculation method. Figure 4 compadose-volume histograms for the PTV-1~gross disease!, pa-rotid and the cord for this patient. The SCopt method deliversa slightly higher dose~;0.3 Gy! to the PTV-1 for volumesabove ;70 Gy ~,;90% PTV-1 volume!, resulting in aslightly higher plan score~see below!. Recall that the pre-scription was to have 98% of this structure receive 68 GFor other structures, the DVHs are virtually identical. Nsignificant difference in these dose distributions is observOther patients demonstrate similar results, indicating thatfour dose computation methods produce similar plans.

Figure 5 shows the relative plan quality score as a fution of the iteration number for each method. Plan scoresgiven relative to the SCopt method for ease in comparing thvalues. The spikes in the score at constant iteration numindicate a change or update in the dose calculation algoritFor the sequential method, this indicates a change in arithm; for the ratio method, this indicates an update inratio matrix; and for the correction method, it indicates a nbasis SC computation. Note that the scores for the firstiterations, including the first spike, are identical for the squential, ratio, and correction methods since they all esstially use the PB algorithm for the first 23 iterations, and tSC algorithm for the 24th iteration. From the 25th iteration, the plan scores for these methods differ due to difences in the dose calculation algorithms.

Although the hybrid methods take many more iteratio

FIG. 5. Relative plan quality score as a function of iteration number for eof the methods for Patient I. At iteration zero, the relative plan quality scwas 17.3 for the SCopt method and 17.7 for all of the other methods. Fiterations 0–23, the sequence, ratio, and correction have identicalscores, as they are all essentially using the PB for dose calculations apoint. The spikes at constant iteration number~i.e., 23! indicate an update orchange in the dose calculation method.

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they are completed in less time, as indicated in Fig. 6, whshows the plan quality score as a function of time. The timshown include not only the dose calculation time, but athe time taken to interface to the external dose calculaalgorithms, and the time taken by the optimization algorithFor comparison purposes, Table II shows the dose calction time for one iteration for the three convolution algrithms available in Pinnacle3 for Patient I. For this case, thAC algorithm was only 25% faster than the full CCC algrithm, however, for other patients and plans this speed rcan be a factor of 2 or more. Table II also shows the dcomputation times for the standard external pencil beamculation and the integrated pencil beam. Note, the relatimes given are for the same computer hardware, howethe times are specific to the implementation of the algrithms. For our implementation, the pencil beam is 10 totimes faster than the adaptive convolve algorithm of Pnacle. The optimization time sequence using the ramethod and the IPB algorithm, which reuses precompubeam data, is also indicated in Fig. 6. From this data,time savings afforded by use of the hybrid dose methoespecially if they are integrated into the optimization systeare apparent.

Table III summarizes the number of iterations for eadose calculation algorithm and the relative final plan scofor test cases for all patients. No discernible difference

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FIG. 6. Relative plan quality score as a function of time for each ofmethods for Patient I. The data is plotted to indicate what the observedscore would be at any point in time.~Note: All times are wall clock times.!

TABLE II. Relative time required to complete just the dose calculation in oiteration of the optimization for various algorithms for Patient I. Each opmization iteration requires additional time to evaluate the objective funcand suggest improved intensities. For the PB algorithms, additional ohead time is consumed by transferring data~mainly intensities and doses! toand from the external dose calculation algorithm.

AlgorithmRelative time per

iteration

Collapsed cone convolution 1.25Adaptive convolution 1.00Fast convolve 0.54Pencil beam 0.098Integrated pencil beam 0.032

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236 Siebers et al. : Reducing dose calculation time 236

TABLE III. Number of dose calculations of each type and plan quality scores for each optimization method.NSC represents the number of SC dose calculatiowhile NPB represents the number of PB dose calculations. Initial plans were developed using the SC algorithm throughout the optimization (SCopt). The othermethods used identical optimization parameters. Plan scores are normalized to the SCopt score to facilitate comparison.

Patient

SCOpt Sequence method Ratio method Correction method

NSC Score NPB NSC Score NPB NSC Score NPB NSC Score

I ~H/N! 20 1.- 24 9 0.93 38 3 0.90 40 3 0.89II ~H/N! 19 1.- 19 6 0.91 24 2 0.91 28 3 0.87III ~H/N! 8 1.- 8 4 1.02 11 2 1.02 13 3 1.01IV ~H/N! 19 1.- 19 5 0.94 30 3 0.94 28 3 0.96V ~H/N! 26 1.- 28 11 0.95 54 4 0.87 61 5 0.83VI ~Brain! 9 1.- 10 2 1.01 13 3 1.00 12 2 1.00VII ~GYN! 13 1.- 10 6 1.00 16 3 1.00 18 3 1.00VIII ~Prostate! 15 1.- 16 6 0.98 21 2 0.98 24 3 0.96IX ~Prostate! 15 1.- 23 10 0.93 36 3 0.91 40 4 0.92X ~Spine! 32 1.- 20 7 1.03 33 3 1.01 29 3 1.02XI ~Lung! 6 1.- 5 6 1.02 11 2 1.02 15 3 1.02XII ~Lung! 8 1.- 8 5 1.00 13 2 1.01 12 2 1.01

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observed between the dose distributions, dose-volume hgrams, or other plan quality factors in the final convergresults for each plan.

In three cases~Patients III, X, and XI!, the hybrid planscores were more than 1% higher than the SCopt plan scores.For Patient III, the plan score change in the iteration previto convergence was 2%, and the plan score change initeration at convergence was just less than the 1% congence criteria. One additional hybrid iteration results inplan score within 1% of the SCopt result. For Patient X, forthe last few iterations of the SCopt case, the score changremained just above the 0.5% convergence criteria, whilethe sequence method, the slope dipped just below 0.5%convergence. Further optimization~beyond convergence!was performed using the sequence method to ascertainshape of the solution space near the convergence point.enteen additional iterations were required to get frompoint of convergence at 1.03 times the SCopt score to theSCopt score. The rate of change of the plan score in tregion was very low. For cases where the hybrid resultresulted in a higher plan score, additional iterations aconvergence resulted in a plan quality score that is neequal to the SCopt score. This points out a weakness in dfining convergence in terms of the rate of change of the pscore. In broad, low-gradient regions, early convergemight be indicated. It indicates that for our optimization sytem, final plan scores obtained with different dose calcution algorithms within a few times the convergence critecan not be discerned and should be considered identica

Similarly, for 5 of the 12 patients, the hybrid method plscores were more than 5% less than that for the Sopt

method. The fact that the hybrid optimization results inlower score was due to the fact that they utilize more toiterations. The absolute minimum was not achieved bySCopt because near the minimum, the plan quality scchanges very gradually. The main function of the additioiterations in the hybrid methods was to adjust intensitiesovercome PB dose calculation error. However, in regiowhere the PB algorithm was sufficiently accurate, the ad

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tional iterations continue to update the intensities to mimize the score. Thus, by the time the PB dose calculaerror was eliminated, other areas were further refined, resing in a lower total final score. Note that even though tfinal plan scores may have differed between the SCopt andhybrid dose calculation methods, for all cases studied,difference in the resultant plans~dose distributions and dosevolume histograms! were minimal.

For every hybrid method case in which only one iteratiwas performed in the inner loop, the outer loop convergedthe next SC computation~that is, there was no discernibldifference between theDSC and DR for the ratio matrixmethod!. This occurred in one-quarter of the cases overallthe optimization was stopped when only 1 iteration occurin the inner loop, then the number of SC iterations decreaby one for these cases. For Patient VI~brain!, this reducedthe number of SC calculations required to one, essentiindicating that for this patient, the PB algorithm was sufciently accurate. This is not surprising given that the brainnearly homogeneous.

An alternative to the hybrid methods proposed abowould be to truncate the computation so that at most twocomputations are performed, one after initial PB convgence and one following the first convergence with thebrid method~ratio method or correction method!. Table IVshows results for the 12 patients if this approach is takenshows the plan score and the number of PB dose calctions, as well as the apparent plan quality score, which isscore predicted by the PB algorithm~with the ratio matrix orcorrection matrix applied for those methods!. The differencebetween the apparent and actual plan scores indicatesresidual dose error in the method. The truncated hybmethods reduce this error, compared with using just theduring optimization~the PBopt method!, yet, they do noteliminate it. The full hybrid methods eliminate this error.

IV. SUMMARY

Two hybrid dose calculation methods, the ratio methand the correction method, have been developed and te

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237 Siebers et al. : Reducing dose calculation time 237

TABLE IV. Number of dose calculations with the pencil beam and the relative plan quality scores when optimization is stopped at the completion of tbeam optimization (PBopt) and following one pass through the outer loop for the hybrid methods. The scores listed in the shaded box represent tpredicted by the PB or hybrid method in the final iteration. The corresponding actual scores determined with the SC algorithm are listed in the unshbox.The difference between these scores is due to the systematic error of the PB or hybrid dose calculation method.

Patient

PBOpt

Truncated ratiomethod

Truncated correctionmethod

NPB

Apparentscore Score NPB

Apparentscore Score NPB

Apparentscore Score

I ~H/N! 24 0.87 1.26 37 0.85 0.90 36 0.86 0.91II ~H/N! 19 0.89 1.07 24 0.91 0.91 25 0.89 0.91III ~H/N! 8 0.91 1.24 11 1.03 1.03 11 1.01 1.03IV ~H/N! 19 1.02 1.14 26 0.95 0.97 27 0.95 0.96V ~H/N! 27 0.82 1.30 45 0.86 0.94 46 0.86 0.94VI ~Brain! 10 0.86 1.02 11 1.01 1.01 12 1.00 1.00VII ~GYN! 10 1.01 1.36 15 1.01 1.02 15 1.01 1.02VIII ~Prostate! 16 0.76 1.27 21 0.97 0.98 22 0.96 0.98IX ~Prostate! 24 0.61 1.27 33 0.88 0.93 32 0.87 0.94X ~Spine! 20 0.95 1.13 30 1.00 1.01 25 1.03 1.04XI ~Lung! 5 1.02 1.23 11 1.02 1.02 11 1.02 1.04XII ~Lung! 8 0.87 1.19 13 1.01 1.01 12 1.01 1.01

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for reducing the dose computation time for iterative IMRinverse planning. Both methods are based on correctingPB dose computations by a periodically updated SC dcomputation. The methods produce results that are equlent to those obtained when the SC algorithm is usthroughout the optimization and substantially reducestime required for dose calculation. The two hybrid methoare nearly equivalent in the number of iterations requiwith each algorithm. For our implementation, use of the hbrid methods reduces the dose calculation time by a facto2 to 4. If truncated versions of the hybrid methods are usfurther time savings can be achieved. For the 12 patient cstudied here, the truncated hybrid methods resulted in pscores that were comparable~13% to 210%! to the opti-mized plan score obtained with SC calculations throughoHowever, full implementation of the hybrid methods resuin a further improvement in the plan quality scores and guantees that the results will agree with the SC results becthe convergence criteria require that the hybrid and SC dresults agree.

The methods developed in this paper should be applicto other implementations of PB and SC dose computaalgorithms, and for other dose computation algorithms agether, for example, Monte Carlo. For other algorithms,number of iterations required for the hybrid methods to cverge may differ, but convergence should occur for reasably accurate dose computation algorithms.

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ACKNOWLEDGMENTS

This work is supported by the grants CA74043 aCA74158 from the National Cancer Institute.

a!Author to whom correspondence should be addressed. Electronic mjsiebers@vcu.edu1J. V. Siebers, S. Tong, M. Lauterbach, Q. Wu, and R. Mohan, ‘‘Acceletion of dose calculations for intensity-modulated radiotherapy,’’ MePhys.28, 903–910~2001!.

2Q. Wu and R. Mohan, ‘‘Algorithms and functionality of an intensitmodulated radiotherapy optimization system,’’ Med. Phys.27, 701–711~2000!.

3R. Mohan and C. S. Chui, ‘‘Use of fast Fourier transforms in calculatdose distributions for irregularly shaped fields for three-dimensiotreatment planning,’’ Med. Phys.14, 70–77~1987!.

4R. Mohan, ‘‘Dose calculations for radiation treatment planning,’’Monte Carlo Transport of Electrons and Photons, edited by T. M. Jen-kins, W. R. Nelson, and A. Rindi~Plenum, New York, 1988!, pp. 549–572.

5R. Mohan, ‘‘Dose computations for three-dimensional radiation treatmplanning,’’ Australas. Phys. Eng. Sci. Med.12, 241–251~1989!.

6T. R. Mackie, J. W. Scrimger, and J. J. Battista, ‘‘A convolution methof calculating dose for 15-MV x-rays,’’ Med. Phys.12, 188–196~1985!.

7ADAC, ‘‘P3IMRT User Guide,’’ P/N 9201-5070A-ENG Ref. A~Version6.0!, ADAC Laboratories, 2001.

8R. Mohan, Q. Wu, M. Manning, and R. Schmidt-Ullrich, ‘‘Radiobiologcal analysis of fractionation strategies for intensity-modulated radiatreatments of head and neck cancers,’’ Int. J. Radiat. Oncol., Biol., P46, 619–630~2000!.