The effect of statistical uncertainty on inverse treatment planning based on Monte Carlo dose calculation

Development and comprehensive clinical validation of a deep neural network for radiation dose modelling to enhance magnetic resonance imaging guided radiotherapy

Background and purpose

Online adaptive magnetic resonance imaging (MRI)-guided radiotherapy requires fast dose calculation algorithms to reduce intra-fraction motion uncertainties and improve workflow efficiency. While Monte-Carlo simulations are precise but computationally intensive, neural networks promise fast and accurate dose modelling in strong magnetic fields. This study aimed to train and evaluate a deep neural network for dose modelling in MRI-guided radiotherapy using a comprehensive clinical dataset.

Materials and methods

A dataset of 6595 clinical irradiation segments from 125 1.5 T MRI-Linac radiotherapy plans for various tumors sites was used. A 3D U-Net was trained with 3961 segments using 3D imaging data and field parameters as input, Root Mean Squared Error and a custom loss function, with full Monte-Carlo simulations as ground truth. For 2656 segments from 50 patients, gamma pass rates (γ-PR) for 3 mm/3%, 2 mm/2%, and 1 mm/1% criteria were calculated to assess dose modelling accuracy. Performance was also tested in a standardized water phantom to evaluate basic radiation physics properties.

Results

The neural network accurately modeled dose distributions in both patient and water phantom settings. Median (range) γ-PR of 97.7% (87.5-100.0%), 89.1% (69.7-99.4%), and 60.8% (38.5-82.1%) were observed for treatment plans, and 97.1% (55.5-100.0%), 88.8% (38.8-99.7%), and 61.7% (17.9-94.4%) for individual segments, across the three criteria.

Conclusion

High median γ-PR and accurate modelling in both water phantom and clinical data demonstrate the high potential of neural networks for dose modelling. However, instances of lower γ-PR highlight the need for comprehensive test data, improved robustness and future built-in uncertainty estimation.

Efficiency enhancements of a Monte Carlo beamlet based treatment planning process: implementation and parameter study

Objective.The computational effort to perform beamlet calculation, plan optimization and final dose calculation of a treatment planning process (TPP) generating intensity modulated treatment plans is enormous, especially if Monte Carlo (MC) simulations are used for dose calculation. The goal of this work is to improve the computational efficiency of a fully MC based TPP for static and dynamic photon, electron and mixed photon-electron treatment techniques by implementing multiple methods and studying the influence of their parameters.Approach.A framework is implemented calculating MC beamlets efficiently in parallel on each available CPU core. The user can specify the desired statistical uncertainty of the beamlets, a fractional sparse dose threshold to save beamlets in a sparse format and minimal distances to the PTV surface from which 2 × 2 × 2 = 8 (medium) or even 4 × 4 × 4 = 64 (large) voxels are merged. The compromise between final plan quality and computational efficiency of beamlet calculation and optimization is studied for several parameter values to find a reasonable trade-off. For this purpose, four clinical and one academic case are considered with different treatment techniques.Main results.Setting the statistical uncertainty to 5% (photon beamlets) and 15% (electron beamlets), the fractional sparse dose threshold relative to the maximal beamlet dose to 0.1% and minimal distances for medium and large voxels to the PTV to 1 cm and 2 cm, respectively, does not lead to substantial degradation in final plan quality compared to using 2.5% (photon beamlets) and 5% (electron beamlets) statistical uncertainty and no sparse format nor voxel merging. Only OAR sparing is slightly degraded. Furthermore, computation times are reduced by about 58% (photon beamlets), 88% (electron beamlets) and 96% (optimization).Significance.Several methods are implemented improving computational efficiency of beamlet calculation and plan optimization of a fully MC based TPP without substantial degradation in final plan quality.

Comparative study of the collapsed cone convolution and Monte Carlo algorithms for radiation therapy planning of canine sinonasal tumors reveals significant dosimetric differences

Computer-based radiation therapy requires high targeting and dosimetric precision. Analytical dosimetric algorithms typically are fast and clinically viable but can have increasing errors near air-bone interfaces. These are commonly found within dogs undergoing radiation planning for sinonasal cancer. This retrospective methods comparison study is designed to compare the dosimetry of both tumor volumes and organs at risk and quantify the differences between collapsed cone convolution (CCC) and Monte Carlo (MC) algorithms. Canine sinonasal tumor plans were optimized with CCC and then recalculated by MC with identical control points and monitor units. Planning target volume (PTV)_air , PTV_{soft tissue} , and PTV_bone were created to analyze the dose discrepancy within the PTV. Thirty imaging sets of dogs were included. Monte Carlo served as the gold standard calculation for the dosimetric comparison. Collapsed cone convolution overestimated the mean dose (D_mean ) to PTV and PTV_{soft tissue} by 0.9% and 0.5%, respectively (both P < 0.001). Collapsed cone convolution overestimated D_mean to PTV_bone by 3% (P < 0.001). Collapsed cone convolution underestimated the near-maximum dose (D₂ ) to PTV_air by 1.1% (P < 0.001), and underestimated conformity index and homogeneity index in PTV (both P < 0.001). Mean doses of contralateral and ipsilateral eyes were overestimated by CCC by 1.6% and 1.7%, respectively (both P < 0.001). Near-maximum doses of skin and brain were overestimated by CCC by 2.2% and 0.7%, respectively (both P < 0.001). As clinical accessibility of Monte Carlo becomes more widespread, dose constraints may need to be re-evaluated with appropriate plan evaluation and follow-up.

TriB-RT: Simultaneous optimization of photon, electron and proton beams

PURPOSE

To develop a novel treatment planning process (TPP) with simultaneous optimization of modulated photon, electron and proton beams for improved treatment plan quality in radiotherapy.

METHODS

A framework for fluence map optimization of Monte Carlo (MC) calculated beamlet dose distributions is developed to generate treatment plans consisting of photon, electron and spot scanning proton fields. Initially, in-house intensity modulated proton therapy (IMPT) plans are compared to proton plans created by a commercial treatment planning system (TPS). A triple beam radiotherapy (TriB-RT) plan is generated for an exemplary academic case and the dose contributions of the three particle types are investigated. To investigate the dosimetric potential, a TriB-RT plan is compared to an in-house IMPT plan for two clinically motivated cases. Benefits of TriB-RT for a fixed proton beam line with a single proton field are investigated.

RESULTS

In-house optimized IMPT are of at least equal or better quality than TPS-generated proton plans, and MC-based optimization shows dosimetric advantages for inhomogeneous situations. Concerning TriB-RT, for the academic case, the resulting plan shows substantial contribution of all particle types. For the clinically motivated case, improved sparing of organs at risk close to the target volume is achieved compared to IMPT (e.g. myelon and brainstem [Formula: see text] -37%) at cost of an increased low dose bath (healthy tissue V _10% +22%). In the scenario of a fixed proton beam line, TriB-RT plans are able to compensate the loss in degrees of freedom to substantially improve plan quality compared to a single field proton plan.

CONCLUSION

A novel TPP which simultaneously optimizes photon, electron and proton beams was successfully developed. TriB-RT shows the potential for improved treatment plan quality and is especially promising for cost-effective single-room proton solutions with a fixed beamline in combination with a conventional linac delivering photon and electron fields.

Recommended dose voxel size and statistical uncertainty parameters for precision of Monte Carlo dose calculation in stereotactic radiotherapy

Monte Carlo (MC)‐based treatment planning requires a choice of dose voxel size (DVS) and statistical uncertainty (SU). These parameters effect both the precision of displayed dose distribution and time taken to complete a calculation. For efficient, accurate, and precise treatment planning in a clinical setting, optimal values should be selected. In this investigation, 30 volumetric modulated arc therapy (VMAT) stereotactic radiotherapy (SRT) treatment plans, 10 brain, 10 lung, and 10 spine were calculated in the Monaco 5.11.02 treatment planning system (TPS). Each plan was calculated with a DVS of 0.1 and 0.2 cm using SU values of 0.50%, 0.75%, 1.00%, 1.50%, and 2.00%, along with a ground truth calculation using a DVS of 0.1 cm and SU of 0.15%. The variance at each relative dose level was calculated for all SU settings to assess their relationship. The variation from the ground truth calculation for each DVS and SU combination was determined for a range of DVH metrics and plan quality indices along with the time taken to complete the calculations. Finally, the effect of defining the maximum dose using a volume of 0.035 cc was compared to 0.100 cc when considering DVS and SU settings. Changes in the DVS produced greater variations from the ground truth calculation than changes in SU across the values tested. Plan quality metrics and mean dose values showed less sensitivity to changes in SU than DVH metrics. From this study, it was concluded that while maintaining an average calculation time of <10 min, 75% of plans could be calculated with variations of <2.0% from their ground truth values when using an SU setting of 1.50% and a DVS of 0.1 cm in the case of brain or spine plans, and a 0.2 cm DVS in the case of lung plans.

Clinical implementations of 4D pencil beam scanned particle therapy: Report on the 4D treatment planning workshop 2016 and 2017

In 2016 and 2017, the 8th and 9th 4D treatment planning workshop took place in Groningen (the Netherlands) and Vienna (Austria), respectively. This annual workshop brings together international experts to discuss research, advances in clinical implementation as well as problems and challenges in 4D treatment planning, mainly in spot scanned proton therapy. In the last two years several aspects like treatment planning, beam delivery, Monte Carlo simulations, motion modeling and monitoring, QA phantoms as well as 4D imaging were thoroughly discussed. This report provides an overview of discussed topics, recent findings and literature review from the last two years. Its main focus is to highlight translation of 4D research into clinical practice and to discuss remaining challenges and pitfalls that still need to be addressed and to be overcome.

Performance of a hybrid Monte Carlo-Pencil Beam dose algorithm for proton therapy inverse planning

PURPOSE

Analytical algorithms have a limited accuracy when modeling very heterogeneous tumor sites. This work addresses the performance of a hybrid dose optimizer that combines both Monte Carlo (MC) and pencil beam (PB) dose engines to get the best trade-off between speed and accuracy for proton therapy plans.

METHODS

The hybrid algorithm calculates the optimal spot weights (w) by means of an iterative optimization process where the dose at each iteration is computed by using a precomputed dose influence matrix based on the conventional PB plus a correction term c obtained from a MC simulation. Updates of c can be triggered as often as necessary by calling the MC dose engine with the last corrected values of w as input. In order to analyze the performance of the hybrid algorithm against dose calculation errors, it was applied to a simplistic water phantom for which several test cases with different errors were simulated, including proton range uncertainties. Afterwards, the algorithm was used in three clinical cases (prostate, lung, and brain) and benchmarked against full MC-based optimization. The influence of different stopping criteria in the final results was also investigated.

RESULTS

The hybrid algorithm achieved excellent results provided that the estimated range in a homogeneous material is the same for the two dose engines involved, i.e., PB and MC. For the three patient cases, the hybrid plans were clinically equivalent to those obtained with full MC-based optimization. Only a single update of c was needed in the hybrid algorithm to fulfill the clinical dose constraints, which represents an extra computation time to obtain c that ranged from 1 (brain) to 4 min (lung) with respect to the conventional PB-based optimization, and an estimated average gain factor of 14 with respect to full MC-based optimization.

CONCLUSION

The hybrid algorithm provides an improved trade-off between accuracy and speed. This algorithm can be immediately considered as an option for improving dose calculation accuracy of commercial analytical treatment planning systems, without a significant increase in the computation time (≪5 min) with respect to current PB-based optimization.

Stability analysis of a deterministic dose calculation for MRI-guided radiotherapy

Modern effort in radiotherapy to address the challenges of tumor localization and motion has led to the development of MRI guided radiotherapy technologies. Accurate dose calculations must properly account for the effects of the MRI magnetic fields. Previous work has investigated the accuracy of a deterministic linear Boltzmann transport equation (LBTE) solver that includes magnetic field, but not the stability of the iterative solution method. In this work, we perform a stability analysis of this deterministic algorithm including an investigation of the convergence rate dependencies on the magnetic field, material density, energy, and anisotropy expansion. The iterative convergence rate of the continuous and discretized LBTE including magnetic fields is determined by analyzing the spectral radius using Fourier analysis for the stationary source iteration (SI) scheme. The spectral radius is calculated when the magnetic field is included (1) as a part of the iteration source, and (2) inside the streaming-collision operator. The non-stationary Krylov subspace solver GMRES is also investigated as a potential method to accelerate the iterative convergence, and an angular parallel computing methodology is investigated as a method to enhance the efficiency of the calculation. SI is found to be unstable when the magnetic field is part of the iteration source, but unconditionally stable when the magnetic field is included in the streaming-collision operator. The discretized LBTE with magnetic fields using a space-angle upwind stabilized discontinuous finite element method (DFEM) was also found to be unconditionally stable, but the spectral radius rapidly reaches unity for very low-density media and increasing magnetic field strengths indicating arbitrarily slow convergence rates. However, GMRES is shown to significantly accelerate the DFEM convergence rate showing only a weak dependence on the magnetic field. In addition, the use of an angular parallel computing strategy is shown to potentially increase the efficiency of the dose calculation.

Concurrent Monte Carlo transport and fluence optimization with fluence adjusting scalable transport Monte Carlo

PURPOSE

The future of radiation therapy will require advanced inverse planning solutions to support single-arc, multiple-arc, and "4π" delivery modes, which present unique challenges in finding an optimal treatment plan over a vast search space, while still preserving dosimetric accuracy. The successful clinical implementation of such methods would benefit from Monte Carlo (MC) based dose calculation methods, which can offer improvements in dosimetric accuracy when compared to deterministic methods. The standard method for MC based treatment planning optimization leverages the accuracy of the MC dose calculation and efficiency of well-developed optimization methods, by precalculating the fluence to dose relationship within a patient with MC methods and subsequently optimizing the fluence weights. However, the sequential nature of this implementation is computationally time consuming and memory intensive. Methods to reduce the overhead of the MC precalculation have been explored in the past, demonstrating promising reductions of computational time overhead, but with limited impact on the memory overhead due to the sequential nature of the dose calculation and fluence optimization. The authors propose an entirely new form of "concurrent" Monte Carlo treat plan optimization: a platform which optimizes the fluence during the dose calculation, reduces wasted computation time being spent on beamlets that weakly contribute to the final dose distribution, and requires only a low memory footprint to function. In this initial investigation, the authors explore the key theoretical and practical considerations of optimizing fluence in such a manner.

METHODS

The authors present a novel derivation and implementation of a gradient descent algorithm that allows for optimization during MC particle transport, based on highly stochastic information generated through particle transport of very few histories. A gradient rescaling and renormalization algorithm, and the concept of momentum from stochastic gradient descent were used to address obstacles unique to performing gradient descent fluence optimization during MC particle transport. The authors have applied their method to two simple geometrical phantoms, and one clinical patient geometry to examine the capability of this platform to generate conformal plans as well as assess its computational scaling and efficiency, respectively.

RESULTS

The authors obtain a reduction of at least 50% in total histories transported in their investigation compared to a theoretical unweighted beamlet calculation and subsequent fluence optimization method, and observe a roughly fixed optimization time overhead consisting of ∼10% of the total computation time in all cases. Finally, the authors demonstrate a negligible increase in memory overhead of ∼7-8 MB to allow for optimization of a clinical patient geometry surrounded by 36 beams using their platform.

CONCLUSIONS

This study demonstrates a fluence optimization approach, which could significantly improve the development of next generation radiation therapy solutions while incurring minimal additional computational overhead.

Assessing the Dosimetric Accuracy of Magnetic Resonance-Generated Synthetic CT Images for Focal Brain VMAT Radiation Therapy

PURPOSE

The purpose of this study was to assess the dosimetric accuracy of synthetic CT (MRCT) volumes generated from magnetic resonance imaging (MRI) data for focal brain radiation therapy.

METHODS AND MATERIALS

A study was conducted in 12 patients with gliomas who underwent both MR and CT imaging as part of their simulation for external beam treatment planning. MRCT volumes were generated from MR images. Patients' clinical treatment planning directives were used to create 12 individual volumetric modulated arc therapy (VMAT) plans, which were then optimized 10 times on each of their respective CT and MRCT-derived electron density maps. Dose metrics derived from optimization criteria, as well as monitor units and gamma analyses, were evaluated to quantify differences between the imaging modalities.

RESULTS

Mean differences between planning target volume (PTV) doses on MRCT and CT plans across all patients were 0.0% (range: -0.1 to 0.2%) for D(95%); 0.0% (-0.7 to 0.6%) for D(5%); and -0.2% (-1.0 to 0.2%) for D(max). MRCT plans showed no significant changes in monitor units (-0.4%) compared to CT plans. Organs at risk (OARs) had average D(max) differences of 0.0 Gy (-2.2 to 1.9 Gy) over 85 structures across all 12 patients, with no significant differences when calculated doses approached planning constraints.

CONCLUSIONS

Focal brain VMAT plans optimized on MRCT images show excellent dosimetric agreement with standard CT-optimized plans. PTVs show equivalent coverage, and OARs do not show any overdose. These results indicate that MRI-derived synthetic CT volumes can be used to support treatment planning of most patients treated for intracranial lesions.

Technical guidelines for head and neck cancer IMRT on behalf of the Italian association of radiation oncology - head and neck working group

Performing intensity-modulated radiotherapy (IMRT) on head and neck cancer patients (HNCPs) requires robust training and experience. Thus, in 2011, the Head and Neck Cancer Working Group (HNCWG) of the Italian Association of Radiation Oncology (AIRO) organized a study group with the aim to run a literature review to outline clinical practice recommendations, to suggest technical solutions and to advise target volumes and doses selection for head and neck cancer IMRT. The main purpose was therefore to standardize the technical approach of radiation oncologists in this context. The following paper describes the results of this working group. Volumes, techniques/strategies and dosage were summarized for each head-and-neck site and subsite according to international guidelines or after reaching a consensus in case of weak literature evidence.

Evaluation of dose prediction error and optimization convergence error in four-dimensional inverse planning of robotic stereotactic lung radiotherapy

Inverse optimization of robotic stereotactic lung radiotherapy is typically performed using relatively simple dose calculation algorithm on a single instance of breathing geometry. Variations of patient geometry and tissue density during respiration could reduce the dose accuracy of these 3D optimized plans. To quantify the potential benefits of direct four-dimensional (4D) optimization in robotic lung radiosurgery, 4D optimizations using 1) ray-tracing algorithm with equivalent path-length heterogeneity correction (4EPL(opt)), and 2) Monte Carlo (MC) algorithm (4MC(opt)), were performed in 25 patients. The 4EPL(opt) plans were recalculated using MC algorithm (4MC(recal)) to quantify the dose prediction errors (DPEs). Optimization convergence errors (OCEs) were evaluated by comparing the 4MC(recal) and 4MC(opt) dose results. The results were analyzed by dose-volume histogram indices for selected organs. Statistical equivalence tests were performed to determine the clinical significance of the DPEs and OCEs, compared with a 3% tolerance. Statistical equivalence tests indicated that the DPE and the OCE are significant predominately in GTV D98%. The DPEs in V20 of lung, and D2% of cord, trachea, and esophagus are within 1.2%, while the OCEs are within 10.4% in lung V20 and within 3.5% in trachea D2%. The marked DPE and OCE suggest that 4D MC optimization is important to improve the dosimetric accuracy in robotic-based stereotactic body radiotherapy, despite the longer computation time.

Monte Carlo dose verification of prostate patients treated with simultaneous integrated boost intensity modulated radiation therapy

BACKGROUND

To evaluate the dosimetric differences between Superposition/Convolution (SC) and Monte Carlo (MC) calculated dose distributions for simultaneous integrated boost (SIB) prostate cancer intensity modulated radiotherapy (IMRT) compared to experimental (film) measurements and the implications for clinical treatments.

METHODS

Twenty-two prostate patients treated with an in-house SIB-IMRT protocol were selected. SC-based plans used for treatment were re-evaluated with EGS4-based MC calculations for treatment verification. Accuracy was evaluated with-respect-to film-based dosimetry. Comparisons used gamma (gamma)-index, distance-to-agreement (DTA), and superimposed dose distributions. The treatment plans were also compared based on dose-volume indices and 3-D gamma index for targets and critical structures.

RESULTS

Flat-phantom comparisons demonstrated that the MC algorithm predicted measurements better than the SC algorithm. The average PTVprostate D98 agreement between SC and MC was 1.2% +/- 1.1. For rectum, the average differences in SC and MC calculated D50 ranged from -3.6% to 3.4%. For small bowel, there were up to 30.2% +/- 40.7 (range: 0.2%, 115%) differences between SC and MC calculated average D50 index. For femurs, the differences in average D50 reached up to 8.6% +/- 3.6 (range: 1.2%, 14.5%). For PTVprostate and PTVnodes, the average gamma scores were >95.0%.

CONCLUSION

MC agrees better with film measurements than SC. Although, on average, SC-calculated doses agreed with MC calculations within the targets within 2%, there were deviations up to 5% for some patient's treatment plans. For some patients, the magnitude of such deviations might decrease the intended target dose levels that are required for the treatment protocol, placing the patients in different dose levels that do not satisfy the protocol dose requirements.

Evaluation of dose prediction errors and optimization convergence errors of deliverable-based head-and-neck IMRT plans computed with a superposition/convolution dose algorithm

The purpose of this study is to evaluate dose prediction errors (DPEs) and optimization convergence errors (OCEs) resulting from use of a superposition/convolution dose calculation algorithm in deliverable intensity-modulated radiation therapy (IMRT) optimization for head-and-neck (HN) patients. Thirteen HN IMRT patient plans were retrospectively reoptimized. The IMRT optimization was performed in three sequential steps: (1) fast optimization in which an initial nondeliverable IMRT solution was achieved and then converted to multileaf collimator (MLC) leaf sequences; (2) mixed deliverable optimization that used a Monte Carlo (MC) algorithm to account for the incident photon fluence modulation by the MLC, whereas a superposition/convolution (SC) dose calculation algorithm was utilized for the patient dose calculations; and (3) MC deliverable-based optimization in which both fluence and patient dose calculations were performed with a MC algorithm. DPEs of the mixed method were quantified by evaluating the differences between the mixed optimization SC dose result and a MC dose recalculation of the mixed optimization solution. OCEs of the mixed method were quantified by evaluating the differences between the MC recalculation of the mixed optimization solution and the final MC optimization solution. The results were analyzed through dose volume indices derived from the cumulative dose-volume histograms for selected anatomic structures. Statistical equivalence tests were used to determine the significance of the DPEs and the OCEs. Furthermore, a correlation analysis between DPEs and OCEs was performed. The evaluated DPEs were within +/- 2.8% while the OCEs were within 5.5%, indicating that OCEs can be clinically significant even when DPEs are clinically insignificant. The full MC-dose-based optimization reduced normal tissue dose by as much as 8.5% compared with the mixed-method optimization results. The DPEs and the OCEs in the targets had correlation coefficients greater than 0.71, and there was no correlation for the organs at risk. Because full MC-based optimization results in lower normal tissue doses, this method proves advantageous for HN IMRT optimization.

Commissioning a fast Monte Carlo dose calculation algorithm for lung cancer treatment planning

A commercial Monte Carlo simulation package, NXEGS 1.12 (NumeriX LLC, New York, NY), was commissioned for photon‐beam dose calculations. The same sets of measured data from 6‐MV and 18‐MV beams were used to commission NXEGS and Pinnacle 6.2b (Philips Medical Systems, Andover, MA). Accuracy and efficiency were compared against the collapsed cone convolution algorithm implemented in Pinnacle 6.2b, together with BEAM simulation (BEAMnrc 2001: National Research Council of Canada, Ottawa, ON). We investigated a number of options in NXEGS: the accuracy of fast Monte Carlo, the re‐implementation of EGS4, post‐processing technique (dose de‐noising algorithm), and dose calculation time. Dose distributions were calculated with NXEGS, Pinnacle, and BEAM in water, lung‐slab, and air‐cylinder phantoms and in a lung patient plan. We compared the dose distributions calculated by NXEGS, Pinnacle, and BEAM. In a selected region of interest (7725 voxels) in the lung phantom, all but 1 voxel had a γ (3% and 3 mm thresholds) of 1 or less for the dose difference between the NXEGS re‐implementation of EGS4 and BEAM, and 99% of the voxels had a γ of 1 or less for the dose difference between NXEGS fast Monte Carlo and BEAM. Fast Monte Carlo with post‐processing was up to 100 times faster than the NXEGS re‐implementation of EGS4, while maintaining ±2% statistical uncertainty. With air inhomogeneities larger than 1 cm, post‐processing preserves the dose perturbations from the air cylinder. When 3 or more beams were used, fast Monte Carlo with post‐processing was comparable to or faster than Pinnacle 6.2b collapsed cone convolution.

PACS numbers: 87.18.Bb, 87.53.Wz

The effect of statistical noise on IMRT plan quality and convergence for MC-based and MC-correction-based optimized treatment plans

Monte Carlo (MC) is rarely used for IMRT plan optimization outside of research centres due to the extensive computational resources or long computation times required to complete the process. Time can be reduced by degrading the statistical precision of the MC dose calculation used within the optimization loop. However, this eventually introduces optimization convergence errors (OCEs). This study determines the statistical noise levels tolerated during MC-IMRT optimization under the condition that the optimized plan has OCEs <100 cGy (1.5% of the prescription dose) for MC-optimized IMRT treatment plans.Seven-field prostate IMRT treatment plans for 10 prostate patients are used in this study. Pre-optimization is performed for deliverable beams with a pencil-beam (PB) dose algorithm. Further deliverable-based optimization proceeds using: (1) MC-based optimization, where dose is recomputed with MC after each intensity update or (2) a once-corrected (OC) MC-hybrid optimization, where a MC dose computation defines beam-by-beam dose correction matrices that are used during a PB-based optimization. Optimizations are performed with nominal per beam MC statistical precisions of 2, 5, 8, 10, 15, and 20%. Following optimizer convergence, beams are re-computed with MC using 2% per beam nominal statistical precision and the 2 PTV and 10 OAR dose indices used in the optimization objective function are tallied. For both the MC-optimization and OC-optimization methods, statistical equivalence tests found that OCEs are less than 1.5% of the prescription dose for plans optimized with nominal statistical uncertainties of up to 10% per beam. The achieved statistical uncertainty in the patient for the 10% per beam simulations from the combination of the 7 beams is ~3% with respect to maximum dose for voxels with D>0.5D(max). The MC dose computation time for the OC-optimization is only 6.2 minutes on a single 3 Ghz processor with results clinically equivalent to high precision MC computations.

Evaluation of uncertainty-based stopping criteria for monte carlo calculations of intensity-modulated radiotherapy and arc therapy patient dose distributions

PURPOSE

To formulate uncertainty-based stopping criteria for Monte Carlo (MC) calculations of intensity-modulated radiotherapy and intensity-modulated arc therapy patient dose distributions and evaluate their influence on MC simulation times and dose characteristics.

METHODS AND MATERIALS

For each structure of interest, stopping criteria were formulated as follows: sigma(rel) <or=sigma(rel,tol) or Dsigma(rel) <or=D(lim)sigma(rel,tol) within >or=95% of the voxels, where sigma(rel) represents the relative statistical uncertainty on the estimated dose, D. The tolerated uncertainty (sigma(rel,tol)) was 2%. The dose limit (D(lim)) equaled the planning target volume (PTV) prescription dose or a dose value related to the organ at risk (OAR) planning constraints. An intensity-modulated radiotherapy-lung, intensity-modulated radiotherapy-ethmoid sinus, and intensity-modulated arc therapy-rectum patient case were studied. The PTV-stopping criteria-based calculations were compared with the PTV+OAR-stopping criteria-based calculations.

RESULTS

The MC dose distributions complied with the PTV-stopping criteria after 14% (lung), 21% (ethmoid), and 12% (rectum) of the simulation times of a 100 million histories reference calculation, and increased to 29%, 44%, and 51%, respectively, by the addition of the OAR-stopping criteria. Dose-volume histograms corresponding to the PTV-stopping criteria, PTV+OAR-stopping criteria, and reference dose calculations were indiscernible. The median local dose differences between the PTV-stopping criteria and the reference calculations amounted to 1.4% (lung), 2.1% (ethmoid), and 2.5% (rectum).

CONCLUSIONS

For the patient cases studied, the MC calculations using PTV-stopping criteria only allowed accurate treatment plan evaluation. The proposed stopping criteria provided a flexible tool to assist MC patient dose calculations. The structures of interest and appropriate values of sigma(rel,tol) and D(lim) should be selected for each patient individually according to the clinical treatment planning goals.

Performance of a hybrid MC dose algorithm for IMRT optimization dose evaluation

This paper presents a hybrid intensity modulated radiation therapy (IMRT) optimization strategy which combines the speed of pencil beam (PB) and the accuracy of Monte Carlo (MC) dose calculations. After an initial deliverable-based optimization using a PB algorithm, doses are recomputed using the VMC++ MC code to determine dose correction factors, which are then utilized during further PB-based optimization. The hybrid method is benchmarked with respect to full MC deliverable-based optimization for ten prostate and ten head-and-neck IMRT plans. Final optimized plans are compared in terms of dose-volume indices used for the plan optimization. Dose prediction errors (DPEs) and optimization convergence errors (OCEs) at intermediate steps of the hybrid sequence are evaluated. The hybrid method is found to produce optimized plans that are clinically equivalent to full MC-based optimization, yet requires only 40% of the number of MC dose calculations. With the hybrid strategy presented here, MC-based optimization results are achieved in 35 min or less on a modest computing cluster. While the initial PB-deliverable-based optimization is found to have DPEs and OCEs of up to 3 Gy relative to the 65-73 Gy prescription doses, application of the first MC correction reduces the average DPEs to less than 0.3 Gy for the prostate plans and less than 0.06 Gy for the head and neck plans. The maximum observed DPE or OCE is 0.7 Gy after 1 MC dose correction, indicating that a single MC dose calculation correction might be sufficient for IMRT optimization.

Application of an inverse kernel concept to Monte Carlo based IMRT

Inverse treatment planning by means of pencil beam algorithms can lead to errors in the calculation of dose in areas without secondary electron equilibrium. Monte Carlo (MC) simulations give accurate results in such areas but result in increased computation times. We present a new, so-called inverse kernel concept that offers MC precision in inverse treatment planning with acceptable computation times and memory consumption. Inverse kernels are matrices that describe the dose contribution from all bixels of a beam to a distinct voxel of the patient phantom. The concept is similar to other generalized pencil-beam concepts, except that inverse kernel elements are precalculated using a single MC simulation and stored as binary trees. In this procedure a modified MC code (XVMC) is applied to trace the photon history for each dose deposition. Iterative optimization is then applied in a second step. The inverse process is separated into (i) a slower MC simulation and (ii) a faster iterative optimization, followed by (iii) the segmentation procedure, and (iv) a final MC dose calculation step including a segment weight reoptimization. Inverse kernel optimization, or IKO, with segmentation and reoptimization steps is demonstrated by means of a lung cancer case. To demonstrate the superiority of an inverse MC system over pencil-beam or collapsed-cone based systems, the final result of the IKO is compared to plans where all segments have been calculated by pencil beam or collapsed cone, respectively. Dose-volume histograms and dose-difference histograms show remarkable differences, which can be attributed to systematic errors in both algorithms. IKO is a precise, nonhybrid, inverse MC treatment planning system which suits current clinical needs, as several optimization steps can follow one single MC-simulation step for a distinct beam setup.

Improving IMRT dose accuracy via deliverable Monte Carlo optimization for the treatment of head and neck cancer patients

The purpose of this work is to investigate the effect of dose-calculation accuracy on head and neck (H&N) intensity modulated radiation therapy (IMRT) plans by determining the systematic dose-prediction and optimization-convergence errors (DPEs and OCEs), using a superposition/convolution (SC) algorithm. Ten patients with locally advanced H&N squamous cell carcinoma who were treated with simultaneous integrated boost IMRT were selected for this study. The targets consisted of gross target volume (GTV), clinical target volume (CTV), and nodal target volumes (CTV nodes). The critical structures included spinal cord, parotid glands, and brainstem. For all patients, three IMRT plans were created: A: an SC optimized plan (SCopt), B: an SCopt plan recalculated with Monte Carlo [MC(SCopt)], and C: an MC optimized plan (MCopt). For each structure, DPEs and OCEs were estimated as DPE(SC)=D(B)-D(A) and OCE(SC)=D(C)-D(B) where A, B, and C stand for the three different optimized plans as defined above. Deliverable optimization was used for all plans, that is, a leaf-sequencing step was incorporated into the optimization loop at each iteration. The range of DPE(SC) in the GTV D98 varied from -1.9% to -4.9%, while the OCE(SC) ranged from 0.9% to 7.0%. The DPE(SC) in the contralateral parotid D50 reached 8.2%, while the OCE(SC) in the contralateral parotid D50 varied from 0.91% to 6.99%. The DPE(SC) in cord D2 reached -3.0%, while the OCE(SC) reached to -7.0%. The magnitude of the DPE(SC) and OCE(SC) differences demonstrate the importance of using the most accurate available algorithm in the deliverable IMRT optimization process, especially for the estimation of normal structure doses.

Clinical comparison of head and neck and prostate IMRT plans using absorbed dose to medium and absorbed dose to water

Conventional photon radiation therapy dose-calculation algorithms typically compute and report the absorbed dose to water (D(w)). Monte Carlo (MC) dose-calculation algorithms, however, generally compute and report the absorbed dose to the material (D(m)). As MC-calculation algorithms are being introduced into routine clinical usage, the question as to whether there is a clinically significant difference between D(w) and D(m) remains. The goal of the current study is to assess the differences between dose-volume indices for D(m) and D(w) MC-calculated IMRT plans. Ten head-and-neck (H&N) and ten prostate cancer patients were selected for this study. MC calculations were performed using an EGS4-based system. Converting D(m) to D(w) for MC-based calculations was accomplished as a post-MC calculation process. D(w) and D(m) results for target and critical structures were evaluated using the dose-volume-based indices. For H&N IMRT plans, systematic differences between dose-volume indices computed with D(w) and D(m) were up to 2.9% for the PTV prescription dose (D(98)), up to 5.8% for maximum (D(2)) dose to the PTV and up to 2.7% for the critical structure dose indices. For prostate IMRT plans, the systematic differences between D(w)- and D(m)-based computed indices were up to 3.5% for the prescription dose (D(98)) to the PTVs, up to 2.0% for the maximum (D(2)) dose to the PTVs and up to 8% for the femoral heads due to their higher water/bone mass stopping power ratio. This study showed that converting D(m) to D(w) in MC-calculated IMRT treatment plans introduces a systematic error in target and critical structure DVHs. In some cases, this systematic error may reach up to 5.8% for H&N and 8.0% for prostate cases when the hard-bone-containing structures such as femoral heads are present. Ignoring differences between D(m) and D(w) will result in systematic dose errors ranging from 0% to 8%.

Reporting and analyzing statistical uncertainties in Monte Carlo-based treatment planning

PURPOSE

To investigate methods of reporting and analyzing statistical uncertainties in doses to targets and normal tissues in Monte Carlo (MC)-based treatment planning.

METHODS AND MATERIALS

Methods for quantifying statistical uncertainties in dose, such as uncertainty specification to specific dose points, or to volume-based regions, were analyzed in MC-based treatment planning for 5 lung cancer patients. The effect of statistical uncertainties on target and normal tissue dose indices was evaluated. The concept of uncertainty volume histograms for targets and organs at risk was examined, along with its utility, in conjunction with dose volume histograms, in assessing the acceptability of the statistical precision in dose distributions. The uncertainty evaluation tools were extended to four-dimensional planning for application on multiple instances of the patient geometry. All calculations were performed using the Dose Planning Method MC code.

RESULTS

For targets, generalized equivalent uniform doses and mean target doses converged at 150 million simulated histories, corresponding to relative uncertainties of less than 2% in the mean target doses. For the normal lung tissue (a volume-effect organ), mean lung dose and normal tissue complication probability converged at 150 million histories despite the large range in the relative organ uncertainty volume histograms. For "serial" normal tissues such as the spinal cord, large fluctuations exist in point dose relative uncertainties.

CONCLUSIONS

The tools presented here provide useful means for evaluating statistical precision in MC-based dose distributions. Tradeoffs between uncertainties in doses to targets, volume-effect organs, and "serial" normal tissues must be considered carefully in determining acceptable levels of statistical precision in MC-computed dose distributions.

Application of the Inverse Monte Carlo Treatment Planning System IKO for an Inhomogeneous Dose Prescription in the Sense of Dose Painting* *This work was presented at the ICMP 2005 and awarded by the Siemens Prize

Biological imaging (PET SPECTJfMRI, MRS, etc.) is able to provide tri-dimensional biological information, i.e. proliferation, cell density, hypoxia or choline/citrate ratio. The implementation of this information in a treatment plan can be utilised to escalate the dose in target subvolumes. For this purpose, a treatment planning system has to be able to realise an inhomogeneous dose prescription with sufficient spatial resolution. The present study investigated to which extent the inverse Monte Carlo treatment planning system IKO (inverse kernel optimization), developed at our department, can modulate an inhomogeneous dose prescription. As a qualifier to describe this ability, we defined in analogy to imaging a modulation transfer function for treatment planning systems. In addition two clinical cases, a prostate case and a head-and-neck case, were set up with different dose prescriptions in different subtargets. The modulation transfer function revealed that IKO is able to modulate structures larger than 1.3 cm with sharp dose gradients. Also, IKO is able to modulate several subtargets inside a prostate with different escalated doses. The dose-volume histograms of the head-and-neck case showed a good dose coverage of the target volumes, as well as a good protection of the organs at risk according to the dose constraints. As a result, IKO is able to realise a heterogeneous dose prescription in the sense of "dose painting".

Incorporating model parameter uncertainty into inverse treatment planning

Radiobiological treatment planning depends not only on the accuracy of the models describing the dose-response relation of different tumors and normal tissues but also on the accuracy of tissue specific radiobiological parameters in these models. Whereas the general formalism remains the same, different sets of model parameters lead to different solutions and thus critically determine the final plan. Here we describe an inverse planning formalism with inclusion of model parameter uncertainties. This is made possible by using a statistical analysis-based frameset developed by our group. In this formalism, the uncertainties of model parameters, such as the parameter a that describes tissue-specific effect in the equivalent uniform dose (EUD) model, are expressed by probability density function and are included in the dose optimization process. We found that the final solution strongly depends on distribution functions of the model parameters. Considering that currently available models for computing biological effects of radiation are simplistic, and the clinical data used to derive the models are sparse and of questionable quality, the proposed technique provides us with an effective tool to minimize the effect caused by the uncertainties in a statistical sense. With the incorporation of the uncertainties, the technique has potential for us to maximally utilize the available radiobiology knowledge for better IMRT treatment.

Adaptive anisotropic diffusion filtering of Monte Carlo dose distributions

The Monte Carlo method is the most accurate method for radiotherapy dose calculations, if used correctly. However, any Monte Carlo dose calculation is burdened with statistical noise. In this paper, denoising of Monte Carlo dose distributions with a three-dimensional adaptive anisotropic diffusion method was investigated. The standard anisotropic diffusion method was extended by changing the filtering parameters adaptively according to the local statistical noise. Smoothing of dose distributions with different noise levels in an inhomogeneous phantom, a conventional and an IMRT treatment case is shown. The resultant dose distributions were analysed using several evaluating criteria. It is shown that the adaptive anisotropic diffusion method can reduce statistical noise significantly (two to five times, corresponding to the reduction of simulation time by a factor of up to 20), while preserving important gradients of the dose distribution well. The choice of free parameters of the method was found to be fairly robust.

Optimizer convergence and local minima errors and their clinical importance

Two of the errors common in the inverse treatment planning optimization have been investigated. The first error is the optimizer convergence error, which appears because of non-perfect convergence to the global or local solution, usually caused by a non-zero stopping criterion. The second error is the local minima error, which occurs when the objective function is not convex and/or the feasible solution space is not convex. The magnitude of the errors, their relative importance in comparison to other errors as well as their clinical significance in terms of tumour control probability (TCP) and normal tissue complication probability (NTCP) were investigated. Two inherently different optimizers, a stochastic simulated annealing and deterministic gradient method were compared on a clinical example. It was found that for typical optimization the optimizer convergence errors are rather small, especially compared to other convergence errors, e.g., convergence errors due to inaccuracy of the current dose calculation algorithms. This indicates that stopping criteria could often be relaxed leading into optimization speed-ups. The local minima errors were also found to be relatively small and typically in the range of the dose calculation convergence errors. Even for the cases where significantly higher objective function scores were obtained the local minima errors were not significantly higher. Clinical evaluation of the optimizer convergence error showed good correlation between the convergence of the clinical TCP or NTCP measures and convergence of the physical dose distribution. On the other hand, the local minima errors resulted in significantly different TCP or NTCP values (up to a factor of 2) indicating clinical importance of the local minima produced by physical optimization.

Guidance document on delivery, treatment planning, and clinical implementation of IMRT: report of the IMRT Subcommittee of the AAPM Radiation Therapy Committee

Intensity-modulated radiation therapy (IMRT) represents one of the most significant technical advances in radiation therapy since the advent of the medical linear accelerator. It allows the clinical implementation of highly conformal nonconvex dose distributions. This complex but promising treatment modality is rapidly proliferating in both academic and community practice settings. However, these advances do not come without a risk. IMRT is not just an add-on to the current radiation therapy process; it represents a new paradigm that requires the knowledge of multimodality imaging, setup uncertainties and internal organ motion, tumor control probabilities, normal tissue complication probabilities, three-dimensional (3-D) dose calculation and optimization, and dynamic beam delivery of nonuniform beam intensities. Therefore, the purpose of this report is to guide and assist the clinical medical physicist in developing and implementing a viable and safe IMRT program. The scope of the IMRT program is quite broad, encompassing multileaf-collimator-based IMRT delivery systems, goal-based inverse treatment planning, and clinical implementation of IMRT with patient-specific quality assurance. This report, while not prescribing specific procedures, provides the framework and guidance to allow clinical radiation oncology physicists to make judicious decisions in implementing a safe and efficient IMRT program in their clinics.

Comparison of IMRT optimization based on a pencil beam and a superposition algorithm

To investigate the role of sophisticated dose calculation methods for treatment planning, we compared conventional pencil beam optimized 6 and 15 MV intensity-modulated treatment plans with optimizations based on the superposition technique. Five lung and five head and neck IMRT cases with spatial resolutions of bixels and dose voxels usually employed in clinical practice were considered for tumor volumes between 15 and 500 cm3. We investigated the systematic error of the pencil beam algorithm and the pencil beam induced error to the optimal solution of bixel weights. For the lung cases, the pencil beam overestimated the mean dose deposited inside the planning target volume (PTV) by about 8%, for small lung tumors even up to 20.6%. In the head and neck cases only a slight overestimation in mean PTV dose of 1.5% was observed. The optimization with the superposition method substantially improved the dose coverage of the considered radiation targets. Additionally, for the head and neck cases, the brainstem was significantly spared by about 4% mean PTV dose through the use of the superposition technique. Our studies showed that, in target regions with intricate tissue inhomogeneities, superposition or Monte Carlo techniques have to be used for the optimization and the final dose calculation of intensity-modulated treatment plans.

The effect of dose calculation accuracy on inverse treatment planning

The effect of dose calculation accuracy during inverse treatment planning for intensity modulated radiotherapy (IMRT) was studied in this work. Three dose calculation methods were compared: Monte Carlo, superposition and pencil beam. These algorithms were used to calculate beamlets. which were subsequently used by a simulated annealing algorithm to determine beamlet weights which comprised the optimal solution to the objective function. Three different cases (lung, prostate and head and neck) were investigated and several different objective functions were tested for their effect on inverse treatment planning. It is shown that the use of inaccurate dose calculation introduces two errors in a treatment plan, a systematic error and a convergence error. The systematic error is present because of the inaccuracy of the dose calculation algorithm. The convergence error appears because the optimal intensity distribution for inaccurate beamlets differs from the optimal solution for the accurate beamlets. While the systematic error for superposition was found to be approximately 1% of Dmax in the tumour and slightly larger outside, the error for the pencil beam method is typically approximately 5% of Dmax and is rather insensitive to the given objectives. On the other hand, the convergence error was found to be very sensitive to the objective function, is only slightly correlated to the systematic error and should be determined for each case individually. Our results suggest that because of the large systematic and convergence errors, inverse treatment planning systems based on pencil beam algorithms alone should be upgraded either to superposition or Monte Carlo based dose calculations.

A method of simulating dynamic multileaf collimators using Monte Carlo techniques for intensity-modulated radiation therapy

A method of modelling the dynamic motion of multileaf collimators (MLCs) for intensity-modulated radiation therapy (IMRT) was developed and implemented into the Monte Carlo simulation. The simulation of the dynamic MLCs (DMLCs) was based on randomizing leaf positions during a simulation so that the number of particle histories being simulated for each possible leaf position was proportional to the monitor units delivered to that position. This approach was incorporated into an EGS4 Monte Carlo program, and was evaluated in simulating the DMLCs for Varian accelerators (Varian Medical Systems, Palo Alto. CA, USA). The MU index of each segment, which was specified in the DMLC-control data, was used to compute the cumulative probability distribution function (CPDF) for the leaf positions. This CPDF was then used to sample the leaf positions during a real-time simulation, which allowed for either the step-shoot or sweeping-leaf motion in the beam delivery. Dose intensity maps for IMRT fields were computed using the above Monte Carlo method, with its accuracy verified by film measurements. The DMLC simulation improved the operational efficiency by eliminating the need to simulate multiple segments individually. More importantly, the dynamic motion of the leaves could be simulated more faithfully by using the above leaf-position sampling technique in the Monte Carlo simulation.

Monte Carlo based treatment planning for modulated electron beam radiation therapy

A Monte Carlo based treatment planning system for modulated electron radiation therapy (MERT) is presented. This new variation of intensity modulated radiation therapy (IMRT) utilizes an electron multileaf collimator (eMLC) to deliver non-uniform intensity maps at several electron energies. In this way, conformal dose distributions are delivered to irregular targets located a few centimetres below the surface while sparing deeper-lying normal anatomy. Planning for MERT begins with Monte Carlo generation of electron beamlets. Electrons are transported with proper in-air scattering and the dose is tallied in the phantom for each beamlet. An optimized beamlet plan may be calculated using inverse-planning methods. Step-and-shoot leaf sequences are generated for the intensity maps and dose distributions recalculated using Monte Carlo simulations. Here, scatter and leakage from the leaves are properly accounted for by transporting electrons through the eMLC geometry. The weights for the segments of the plan are re-optimized with the leaf positions fixed and bremsstrahlung leakage and electron scatter doses included. This optimization gives the final optimized plan. It is shown that a significant portion of the calculation time is spent transporting particles in the leaves. However, this is necessary since optimizing segment weights based on a model in which leaf transport is ignored results in an improperly optimized plan with overdosing of target and critical structures. A method of rapidly calculating the bremsstrahlung contribution is presented and shown to be an efficient solution to this problem. A homogeneous model target and a 2D breast plan are presented. The potential use of this tool in clinical planning is discussed.