The effect of Monte Carlo statistical uncertainties on the evaluation of dose distributions in radiation treatment planning

This paper discusses the effect of statistical uncertainties present in Monte Carlo (MC) calculated dose distributions on the evaluation of a 'cost function' that expresses the suitability of a treatment plan for the intended treatment. The mathematical derivations given are valid for any 'well-behaved' cost function. The validity of the general expressions is demonstrated using numerical examples. It is shown that random dose uncertainties lead to statistical and systematic uncertainties on the cost function. The balance between the two types of uncertainty and the desired accuracy on the cost function presents a clear criterion for the maximum acceptable MC dose uncertainties. It is demonstrated that it is possible to remove the systematic cost function uncertainty. Finally, it is shown that when the dose distribution is close to a true optimum, MC calculations of the cost function converge to the true result as one over the number of particles simulated, i.e. much faster than the individual dose uncertainties.     

EUD-based radiotherapy treatment plan evaluation: incorporating physical and Monte Carlo statistical dose uncertainties

The purpose of this work is to quantify the impact of dose uncertainty on radiobiologically based treatment plan evaluation. Dose uncertainties are divided into two categories: physical and statistical. Physical dose uncertainty is associated with the systematic and/or random errors incurred during treatment planning and/or delivery. The dose uncertainty associated with Monte Carlo calculated dose distributions is deemed statistical and noted as artificial with respect to the actual delivered dose. We will refer to all dose uncertainties that arise from either calculation or delivery as stochastic. Both physical and statistical dose uncertainties are considered at the intra- and inter-voxel levels. To account for voxel dose uncertainty, we calculate the mean survival fraction (SF) for the random dose deposition. Mathematically, the expression for the mean survival fraction is identical to that used by Niemierko (1997 Med. Phys. 24 103-10) in defining equivalent uniform dose (EUD). To distinguish between spatial and probabilistic dose variations, we define equivalent stochastic dose (ESD) as a voxel dose that gives the mean expected survival fraction for the randomly deposited dose. For a probability density function f(D), that represents the probabilistic voxel dose, SF(ESD) can be calculated by convolving SF(D) with f(D). In the case where the probability density function follows a Gaussian distribution, an analytic expression is derived for SF(ESD). The derived expression is verified using the Monte Carlo method and ESD values calculated with varied radiosensitivities for cases of 60 and 70 Gy at 2 Gy per fraction. The analytic expression is also extended to account for a multi-voxel dose distribution that incorporates a spatial dose heterogeneity. The results show that survival fraction increases with an increased dose uncertainty. This reduction depends on radiobiological parameters attributed to tissue and tumour. For tissue, ESD drops to 55% of the mean physical dose when the dose has a 10% intra- and inter-voxel dose uncertainty and inhomogeneity.     

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

The effect of the statistical uncertainty, or noise, in inverse treatment planning for intensity modulated radiotherapy (IMRT) based on Monte Carlo dose calculation was studied. Sets of Monte Carlo beamlets were calculated to give uncertainties at Dmax ranging from 0.2% to 4% for a lung tumour plan. The weights of these beamlets were optimized using a previously described procedure based on a simulated annealing optimization algorithm. Several different objective functions were used. It was determined that the use of Monte Carlo dose calculation in inverse treatment planning introduces two errors in the calculated plan. In addition to the statistical error due to the statistical uncertainty of the Monte Carlo calculation, a noise convergence error also appears. For the statistical error it was determined that apparently successfully optimized plans with a noisy dose calculation (3% 1sigma at Dmax), which satisfied the required uniformity of the dose within the tumour, showed as much as 7% underdose when recalculated with a noise-free dose calculation. The statistical error is larger towards the tumour and is only weakly dependent on the choice of objective function. The noise convergence error appears because the optimum weights are determined using a noisy calculation, which is different from the optimum weights determined for a noise-free calculation. Unlike the statistical error, the noise convergence error is generally larger outside the tumour, is case dependent and strongly depends on the required objectives.     

Towards the elimination of Monte Carlo statistical fluctuation from dose volume histograms for radiotherapy treatment planning

The Monte Carlo calculation of dose for radiotherapy treatment planning purposes introduces unavoidable statistical noise into the prediction of dose in a given volume element (voxel). When the doses in these voxels are summed to produce dose volume histograms (DVHs), this noise translates into a broadening of differential DVHs and correspondingly flatter DVHs. A brute force approach would entail calculating dose for long periods of time--enough to ensure that the DVHs had converged. In this paper we introduce an approach for deconvolving the statistical noise from DVHs, thereby obtaining estimates for converged DVHs obtained about 100 times faster than the brute force approach described above. There are two important implications of this work: (a) decisions based upon DVHs may be made much more economically using the new approach and (b) inverse treatment planning or optimization methods may employ Monte Carlo dose calculations at all stages of the iterative procedure since the prohibitive cost of Monte Carlo calculations at the intermediate calculation steps can be practically eliminated.     

An efficient framework for photon Monte Carlo treatment planning

Currently photon Monte Carlo treatment planning (MCTP) for a patient stored in the patient database of a treatment planning system (TPS) can usually only be performed using a cumbersome multi-step procedure where many user interactions are needed. This means automation is needed for usage in clinical routine. In addition, because of the long computing time in MCTP, optimization of the MC calculations is essential. For these purposes a new graphical user interface (GUI)-based photon MC environment has been developed resulting in a very flexible framework. By this means appropriate MC transport methods are assigned to different geometric regions by still benefiting from the features included in the TPS. In order to provide a flexible MC environment, the MC particle transport has been divided into different parts: the source, beam modifiers and the patient. The source part includes the phase-space source, source models and full MC transport through the treatment head. The beam modifier part consists of one module for each beam modifier. To simulate the radiation transport through each individual beam modifier, one out of three full MC transport codes can be selected independently. Additionally, for each beam modifier a simple or an exact geometry can be chosen. Thereby, different complexity levels of radiation transport are applied during the simulation. For the patient dose calculation, two different MC codes are available. A special plug-in in Eclipse providing all necessary information by means of Dicom streams was used to start the developed MC GUI. The implementation of this framework separates the MC transport from the geometry and the modules pass the particles in memory; hence, no files are used as the interface. The implementation is realized for 6 and 15 MV beams of a Varian Clinac 2300 C/D. Several applications demonstrate the usefulness of the framework. Apart from applications dealing with the beam modifiers, two patient cases are shown. Thereby, comparisons are performed between MC calculated dose distributions and those calculated by a pencil beam or the AAA algorithm. Interfacing this flexible and efficient MC environment with Eclipse allows a widespread use for all kinds of investigations from timing and benchmarking studies to clinical patient studies. Additionally, it is possible to add modules keeping the system highly flexible and efficient.     

Clinical implementation of a Monte Carlo treatment planning system.

The purpose of this study was to implement the Monte Carlo method for clinical radiotherapy dose calculations. We used the EGS4/BEAM code to obtain the phase-space data for 6-20 MeV electron beams and 4, 6, and 15 MV photon beams for Varian Clinac 1800, 2100C, and 2300CD accelerators. A multiple-source model was used to reconstruct the phase-space data for both electron and photon beams, which retained the accuracy of the Monte Carlo beam data. The multiple-source model reduced the phase-space data storage requirement by a factor of 1000 and the accelerator simulation time by a factor of 10 or more. Agreement within 2% was achieved between the Monte Carlo calculations and measurements of the dose distributions in homogeneous and heterogeneous phantoms for various field sizes, source-surface distances, and beam modulations. The Monte Carlo calculated electron output factors were within 2% of the measured values for various treatment fields while the heterogeneity correction factors for various lung and bone phantoms were within 1% for photon beams and within 2% for electron beams. The EGS4/DOSXYZ Monte Carlo code was used for phantom and patient dose calculations. The results were compared to the dose distributions produced by a conventional treatment planning system and an intensity-modulated radiotherapy inverse-planning system. Significant differences (>5% in dose and >5 mm shift in isodose lines) were found between Monte Carlo calculations and the analytical calculations implemented in the commercial systems. Treatment sites showing the largest dose differences were for head and neck, lung, and breast cases.     

A Monte Carlo dose calculation tool for radiotherapy treatment planning

A Monte Carlo user code, MCDOSE, has been developed for radiotherapy treatment planning (RTP) dose calculations. MCDOSE is designed as a dose calculation module suitable for adaptation to host RTP systems. MCDOSE can be used for both conventional photon/electron beam calculation and intensity modulated radiotherapy (IMRT) treatment planning. MCDOSE uses a multiple-source model to reconstruct the treatment beam phase space. Based on Monte Carlo simulated or measured beam data acquired during commissioning, source-model parameters are adjusted through an automated procedure. Beam modifiers such as jaws, physical and dynamic wedges, compensators, blocks, electron cut-outs and bolus are simulated by MCDOSE together with a 3D rectilinear patient geometry model built from CT data. Dose distributions calculated using MCDOSE agreed well with those calculated by the EGS4/DOSXYZ code using different beam set-ups and beam modifiers. Heterogeneity correction factors for layered-lung or layered-bone phantoms as calculated by both codes were consistent with measured data to within 1%. The effect of energy cut-offs for particle transport was investigated. Variance reduction techniques were implemented in MCDOSE to achieve a speedup factor of 10-30 compared to DOSXYZ.     

Photon beam characterization and modelling for Monte Carlo treatment planning

Photon beams of 4, 6 and 15 MV from Varian Clinac 2100C and 2300C/D accelerators were simulated using the EGS4/BEAM code system. The accelerators were modelled as a combination of component modules (CMs) consisting of a target, primary collimator, exit window, flattening filter, monitor chamber, secondary collimator, ring collimator, photon jaws and protection window. A full phase space file was scored directly above the upper photon jaws and analysed using beam data processing software, BEAMDP, to derive the beam characteristics, such as planar fluence, angular distribution, energy spectrum and the fractional contributions of each individual CM. A multiple-source model has been further developed to reconstruct the original phase space. Separate sources were created with accurate source intensity, energy, fluence and angular distributions for the target, primary collimator and flattening filter. Good agreement (within 2%) between the Monte Carlo calculations with the source model and those with the original phase space was achieved in the dose distributions for field sizes of 4 cm x 4 cm to 40 cm x 40 cm at source surface distances (SSDs) of 80-120 cm. The dose distributions in lung and bone heterogeneous phantoms have also been found to be in good agreement (within 2%) for 4, 6 and 15 MV photon beams for various field sizes between the Monte Carlo calculations with the source model and those with the original phase space.     

Electron beam modeling and commissioning for Monte Carlo treatment planning

A hybrid approach for commissioning electron beam Monte Carlo treatment planning systems has been studied. The approach is based on the assumption that accelerators of the same type have very similar electron beam characteristics and the major difference comes from the on-site tuning of the electron incident energy at the exit window. For one type of accelerator, a reference machine can be selected and simulated with the Monte Carlo method. A multiple source model can be built on the full Monte Carlo simulation of the reference beam. When commissioning electron beams from other accelerators of the same type, the energy spectra in the source model are tuned to match the measured dose distributions. A Varian Clinac 2100C accelerator was chosen as the reference machine and a four-source beam model was established based on the Monte Carlo simulations. This simplified beam model can be used to generate Monte Carlo dose distributions accurately (within 2%/2 mm compared to those calculated with full phase space data) for electron beams from the reference machine with various nominal energies, applicator sizes, and SSDs. Three electron beams were commissioned by adjusting the energy spectra in the source model. The dose distributions calculated with the adjusted source model were compared with the dose distributions calculated using the phase space data for these beams. The agreement is within 1% in most of cases and 2% in all situations. This preliminary study has shown the capability of the commissioning approach for handling large variation in the electron incident energy. The possibility of making the approach more versatile is also discussed.     

A vectorized Monte Carlo code for radiotherapy treatment planning dose calculation

How to speed up Monte Carlo (MC) simulation in dose calculation without losing its intrinsic accuracy is one of the key issues of making a clinical MC dose engine. In this study we intensively investigated a special parallel computation technique, the vectorization technique, to boost simulation efficiency on a personal computer (PC) without extra hardware investment. A MC code, dose planning method (DPM), was extensively modified into a vectorized code, V-DPM, using the streaming single-instruction-multiple-data extension (SSE) parallel computation model. Comparative simulations were conducted for typical simulation cases in both DPM and V-DPM codes. We found that in every case the V-DPM code runs 1.5 times faster than the DPM code with variance of 0.6%.     

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.     

An integrated Monte Carlo dosimetric verification system for radiotherapy treatment planning

An integrated Monte Carlo (MC) dose calculation system, MCRTV (Monte Carlo for radiotherapy treatment plan verification), has been developed for clinical treatment plan verification, especially for routine quality assurance (QA) of intensity-modulated radiotherapy (IMRT) plans. The MCRTV system consists of the EGS4/PRESTA MC codes originally written for particle transport through the accelerator, the multileaf collimator (MLC), and the patient/phantom, which run on a 28-CPU Linux cluster, and the associated software developed for the clinical implementation. MCRTV has an interface with a commercial treatment planning system (TPS) (Eclipse, Varian Medical Systems, Palo Alto, CA, USA) and reads the information needed for MC computation transferred in DICOM-RT format. The key features of MCRTV have been presented in detail in this paper. The phase-space data of our 15 MV photon beam from a Varian Clinac 2300C/D have been developed and several benchmarks have been performed under homogeneous and several inhomogeneous conditions (including water, aluminium, lung and bone media). The MC results agreed with the ionization chamber measurements to within 1% and 2% for homogeneous and inhomogeneous conditions, respectively. The MC calculation for a clinical prostate IMRT treatment plan validated the implementation of the beams and the patient/phantom configuration in MCRTV.     

Sensitivity study for CT image use in Monte Carlo treatment planning

An important step in Monte Carlo treatment planning (MCTP), which is commonly performed uncritically, is segmentation of the patient CT data into a voxel phantom for dose calculation. In addition to assigning mass densities to voxels, as is done in conventional TP, this entails assigning media. Mis-assignment of media can potentially lead to significant dose errors in MCTP. In this work, a test phantom with exact-known composition was used to study CT segmentation errors and to quantify subsequent MCTP inaccuracies. For our test cases, we observed dose errors in some regions of up to 10% for 6 and 15 MV photons, more than 30% for an 18 MeV electron beam and more than 40% for 250 kVp photons. It is concluded that a careful CT calibration with a suitable phantom is essential. Generic calibrations and the use of commercial CT phantoms have to be critically assessed.     

Use of Monte Carlo computation in benchmarking radiotherapy treatment planning system algorithms

Radiotherapy treatments are becoming more complex, often requiring the dose to be calculated in three dimensions and sometimes involving the application of non-coplanar beams. The ability of treatment planning systems to accurately calculate dose under a range of these and other irradiation conditions requires evaluation. Practical assessment of such arrangements can be problematical, especially when a heterogeneous medium is used. This work describes the use of Monte Carlo computation as a benchmarking tool to assess the dose distribution of external photon beam plans obtained in a simple heterogeneous phantom by several commercially available 3D and 2D treatment planning system algorithms. For comparison, practical measurements were undertaken using film dosimetry. The dose distributions were calculated for a variety of irradiation conditions designed to show the effects of surface obliquity, inhomogeneities and missing tissue above tangential beams. The results show maximum dose differences of 47% between some planning algorithms and film at a point 1 mm below a tangentially irradiated surface. Overall, the dose distribution obtained from film was most faithfully reproduced by the Monte Carlo N-Particle results illustrating the potential of Monte Carlo computation in evaluating treatment planning system algorithms.     

Validation of a Monte Carlo dose calculation tool for radiotherapy treatment planning

A new EGS4/PRESTA Monte Carlo user code, MCDOSE, has been developed as a routine dose calculation tool for radiotherapy treatment planning. It is suitable for both conventional and intensity modulated radiation therapy. Two important features of MCDOSE are the inclusion of beam modifiers in the patient simulation and the implementation of several variance reduction techniques. Before this tool can be used reliably for clinical dose calculation, it must be properly validated. The validation for beam modifiers has been performed by comparing the dose distributions calculated by MCDOSE and the well-benchmarked EGS4 user codes BEAM and DOSXYZ. Various beam modifiers were simulated. Good agreement in the dose distributions was observed. The differences in electron cutout factors between the results of MCDOSE and measurements were within 2%. The accuracy of MCDOSE with various variance reduction techniques was tested by comparing the dose distributions in different inhomogeneous phantoms with those calculated by DOSXYZ without variance reduction. The agreement was within 1.0%. Our results demonstrate that MCDOSE is accurate and efficient for routine dose calculation in radiotherapy treatment planning, with or without beam modifiers.     

Monte Carlo treatment planning for molecular targeted radiotherapy within the MINERVA system

The aim of this project is to extend accurate and patient-specific treatment planning to new treatment modalities, such as molecular targeted radiation therapy, incorporating previously crafted and proven Monte Carlo and deterministic computation methods. A flexible software environment is being created that allows planning radiation treatment for these new modalities and combining different forms of radiation treatment with consideration of biological effects. The system uses common input interfaces, medical image sets for definition of patient geometry and dose reporting protocols. Previously, the Idaho National Engineering and Environmental Laboratory (INEEL), Montana State University (MSU) and Lawrence Livermore National Laboratory (LLNL) had accrued experience in the development and application of Monte Carlo based, three-dimensional, computational dosimetry and treatment planning tools for radiotherapy in several specialized areas. In particular, INEEL and MSU have developed computational dosimetry systems for neutron radiotherapy and neutron capture therapy, while LLNL has developed the PEREGRINE computational system for external beam photon-electron therapy. Building on that experience, the INEEL and MSU are developing the MINERVA (modality inclusive environment for radiotherapeutic variable analysis) software system as a general framework for computational dosimetry and treatment planning for a variety of emerging forms of radiotherapy. In collaboration with this development, LLNL has extended its PEREGRINE code to accommodate internal sources for molecular targeted radiotherapy (MTR), and has interfaced it with the plugin architecture of MINERVA. Results from the extended PEREGRINE code have been compared to published data from other codes, and found to be in general agreement (EGS4-2%, MCNP-10%) (Descalle et al 2003 Cancer Biother. Radiopharm. 18 71-9). The code is currently being benchmarked against experimental data. The interpatient variability of the drug pharmacokinetics in MTR can only be properly accounted for by image-based, patient-specific treatment planning, as has been common in external beam radiation therapy for many years. MINERVA offers 3D Monte Carlo-based MTR treatment planning as its first integrated operational capability. The new MINERVA system will ultimately incorporate capabilities for a comprehensive list of radiation therapies. In progress are modules for external beam photon-electron therapy and boron neutron capture therapy (BNCT). Brachytherapy and proton therapy are planned. Through the open application programming interface (API), other groups can add their own modules and share them with the community.     

Clinical use of a commercial Monte Carlo treatment planning system for electron beams

In 2002 we fully implemented clinically a commercial Monte Carlo based treatment planning system for electron beams. The software, developed by MDS Nordion (presently Nucletron), is based on Kawrakow's VMC++ algorithm. The Monte Carlo module is integrated with our Theraplan Plustrade mark treatment planning system. An extensive commissioning process preceded clinical implementation of this software. Using a single virtual 'machine' for each electron beam energy, we can now calculate very accurately the dose distributions and the number of MU for any arbitrary field shape and SSD. This new treatment planning capability has significantly impacted our clinical practice. Since we are more confident of the actual dose delivered to a patient, we now calculate accurate three-dimensional (3D) dose distributions for a greater variety of techniques and anatomical sites than we have in the past. We use the Monte Carlo module to calculate dose for head and neck, breast, chest wall and abdominal treatments with electron beams applied either solo or in conjunction with photons. In some cases patient treatment decisions have been changed, as compared to how such patients would have been treated in the past. In this paper, we present the planning procedure and some clinical examples.