Macro Monte Carlo for dose calculation of proton beams

Although the Monte Carlo (MC) method allows accurate dose calculation for proton radiotherapy, its usage is limited due to long computing time. In order to gain efficiency, a new macro MC (MMC) technique for proton dose calculations has been developed. The basic principle of the MMC transport is a local to global MC approach. The local simulations using GEANT4 consist of mono-energetic proton pencil beams impinging perpendicularly on slabs of different thicknesses and different materials (water, air, lung, adipose, muscle, spongiosa, cortical bone). During the local simulation multiple scattering, ionization as well as elastic and inelastic interactions have been taken into account and the physical characteristics such as lateral displacement, direction distributions and energy loss have been scored for primary and secondary particles. The scored data from appropriate slabs is then used for the stepwise transport of the protons in the MMC simulation while calculating the energy loss along the path between entrance and exit position. Additionally, based on local simulations the radiation transport of neutrons and the generated ions are included into the MMC simulations for the dose calculations. In order to validate the MMC transport, calculated dose distributions using the MMC transport and GEANT4 have been compared for different mono-energetic proton pencil beams impinging on different phantoms including homogeneous and inhomogeneous situations as well as on a patient CT scan. The agreement of calculated integral depth dose curves is better than 1% or 1 mm for all pencil beams and phantoms considered. For the dose profiles the agreement is within 1% or 1 mm in all phantoms for all energies and depths. The comparison of the dose distribution calculated using either GEANT4 or MMC in the patient also shows an agreement of within 1% or 1 mm. The efficiency of MMC is up to 200 times higher than for GEANT4. The very good level of agreement in the dose comparisons demonstrate that the newly developed MMC transport results in very accurate and efficient dose calculations for proton beams.

Fixed-Width Output Analysis for Markov Chain Monte Carlo

Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a complicated target distribution via simple ergodic averages. A fundamental question in MCMC applications is when should the sampling stop? That is, when are the ergodic averages good estimates of the desired quantities? We consider a method that stops the MCMC sampling the first time the width of a confidence interval based on the ergodic averages is less than a user-specified value. Hence calculating Monte Carlo standard errors is a critical step in assessing the output of the simulation. In particular, we consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution. We describe sufficient conditions for the strong consistency and asymptotic normality of both methods and investigate their finite sample properties in a variety of examples.

COVARIATE-ADJUSTED NONPARAMETRIC ANALYSIS OF MAGNETIC RESONANCE IMAGES USING MARKOV CHAIN MONTE CARLO

Permutation tests are useful for drawing inferences from imaging data because of their flexibility and ability to capture features of the brain that are difficult to capture parametrically. However, most implementations of permutation tests ignore important confounding covariates. To employ covariate control in a nonparametric setting we have developed a Markov chain Monte Carlo (MCMC) algorithm for conditional permutation testing using propensity scores. We present the first use of this methodology for imaging data. Our MCMC algorithm is an extension of algorithms developed to approximate exact conditional probabilities in contingency tables, logit, and log-linear models. An application of our non-parametric method to remove potential bias due to the observed covariates is presented.

Monte Carlo simulation of a dynamic MLC: implementation and applications

PURPOSE: Study of behavior and influence of a multileaf collimator (MLC) on dose calculation, verification, and portal energy spectra in the case of intensity-modulated fields obtained with a step-and-shoot or a dynamic technique. METHODS: The 80-leaf MLC for the Varian Clinac 2300 C/D was implemented in a previously developed Monte Carlo (MC) based multiple source model (MSM) for a 6 MV photon beam. Using this model and the MC program GEANT, dose distributions, energy fluence maps and energy spectra at different portal planes were calculated for three different MLC applications. RESULTS: The comparison of MC-calculated dose distributions in the phantom and portal plane, with those measured with films showed an agreement within 3% and 1.5 mm for all cases studied. The deviations mainly occur in the extremes of the intensity modulation. The MC method allows to investigate, among other aspects, dose components, energy fluence maps, tongue-and-groove effects and energy spectra at portal planes. CONCLUSION: The MSM together with the implementation of the MLC is appropriate for a number of investigations in intensity-modulated radiation therapy (IMRT).

Calibration of a portal imaging device for high-precision dosimetry: a Monte Carlo study

Today electronic portal imaging devices (EPID's) are used primarily to verify patient positioning. They have, however, also the potential as 2D-dosimeters and could be used as such for transit dosimetry or dose reconstruction. It has been proven that such devices, especially liquid filled ionization chambers, have a stable dose response relationship which can be described in terms of the physical properties of the EPID and the pulsed linac radiation. For absolute dosimetry however, an accurate method of calibration to an absolute dose is needed. In this work, we concentrate on calibration against dose in a homogeneous water phantom. Using a Monte Carlo model of the detector we calculated dose spread kernels in units of absolute dose per incident energy fluence and compared them to calculated dose spread kernels in water at different depths. The energy of the incident pencil beams varied between 0.5 and 18 MeV. At the depth of dose maximum in water for a 6 MV beam (1.5 cm) and for a 18 MV beam (3.0 cm) we observed large absolute differences between water and detector dose above an incident energy of 4 MeV but only small relative differences in the most frequent energy range of the beam energy spectra. It is shown that for a 6 MV beam the absolute reference dose measured at 1.5 cm water depth differs from the absolute detector dose by 3.8%. At depth 1.2 cm in water, however, the relative dose differences are almost constant between 2 and 6 MeV. The effects of changes in the energy spectrum of the beam on the dose responses in water and in the detector are also investigated. We show that differences larger than 2% can occur for different beam qualities of the incident photon beam behind water slabs of different thicknesses. It is therefore concluded that for high-precision dosimetry such effects have to be taken into account. Nevertheless, the precise information about the dose response of the detector provided in this Monte Carlo study forms the basis of extracting directly the basic radiometric quantities photon fluence and photon energy fluence from the detector's signal using a deconvolution algorithm. The results are therefore promising for future application in absolute transit dosimetry and absolute dose reconstruction.

BENCHMARKING AND IMPLEMENTATION OF A NEW INDEPENDENT MONTE CARLO DOSE CALCULATION QUALITY ASSURANCE AUDIT TOOL FOR CLINICAL TRIALS

Introduction Commercial treatment planning systems employ a variety of dose calculation algorithms to plan and predict the dose distributions a patient receives during external beam radiation therapy. Traditionally, the Radiological Physics Center has relied on measurements to assure that institutions participating in the National Cancer Institute sponsored clinical trials administer radiation in doses that are clinically comparable to those of other participating institutions. To complement the effort of the RPC, an independent dose calculation tool needs to be developed that will enable a generic method to determine patient dose distributions in three dimensions and to perform retrospective analysis of radiation delivered to patients who enrolled in past clinical trials. Methods A multi-source model representing output for Varian 6 MV and 10 MV photon beams was developed and evaluated. The Monte Carlo algorithm, know as the Dose Planning Method (DPM), was used to perform the dose calculations. The dose calculations were compared to measurements made in a water phantom and in anthropomorphic phantoms. Intensity modulated radiation therapy and stereotactic body radiation therapy techniques were used with the anthropomorphic phantoms. Finally, past patient treatment plans were selected and recalculated using DPM and contrasted against a commercial dose calculation algorithm. Results The multi-source model was validated for the Varian 6 MV and 10 MV photon beams. The benchmark evaluations demonstrated the ability of the model to accurately calculate dose for the Varian 6 MV and the Varian 10 MV source models. The patient calculations proved that the model was reproducible in determining dose under similar conditions described by the benchmark tests. Conclusions The dose calculation tool that relied on a multi-source model approach and used the DPM code to calculate dose was developed, validated, and benchmarked for the Varian 6 MV and 10 MV photon beams. Several patient dose distributions were contrasted against a commercial algorithm to provide a proof of principal to use as an application in monitoring clinical trial activity.

More than just Good Luck. How to Explain the Success of Monte Carlo Simulations

Monte Carlo simulation is a powerful method in many natural and social sciences. But what sort of method is it? And where does its power come from? Are Monte Carlo simulations experiments, theories or something else? The aim of this talk is to answer these questions and to explain the power of Monte Carlo simulations. I provide a classification of Monte Carlo techniques and defend the claim that Monte Carlo simulation is a sort of inference.

Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators

This article proposes computing sensitivities of upper tail probabilities of random sums by the saddlepoint approximation. The considered sensitivity is the derivative of the upper tail probability with respect to the parameter of the summation index distribution. Random sums with Poisson or Geometric distributed summation indices and Gamma or Weibull distributed summands are considered. The score method with importance sampling is considered as an alternative approximation. Numerical studies show that the saddlepoint approximation and the method of score with importance sampling are very accurate. But the saddlepoint approximation is substantially faster than the score method with importance sampling. Thus, the suggested saddlepoint approximation can be conveniently used in various scientific problems.

Forward treatment planning for modulated electron radiotherapy (MERT) employing Monte Carlo methods

PURPOSE This paper describes the development of a forward planning process for modulated electron radiotherapy (MERT). The approach is based on a previously developed electron beam model used to calculate dose distributions of electron beams shaped by a photon multi leaf collimator (pMLC). METHODS As the electron beam model has already been implemented into the Swiss Monte Carlo Plan environment, the Eclipse treatment planning system (Varian Medical Systems, Palo Alto, CA) can be included in the planning process for MERT. In a first step, CT data are imported into Eclipse and a pMLC shaped electron beam is set up. This initial electron beam is then divided into segments, with the electron energy in each segment chosen according to the distal depth of the planning target volume (PTV) in beam direction. In order to improve the homogeneity of the dose distribution in the PTV, a feathering process (Gaussian edge feathering) is launched, which results in a number of feathered segments. For each of these segments a dose calculation is performed employing the in-house developed electron beam model along with the macro Monte Carlo dose calculation algorithm. Finally, an automated weight optimization of all segments is carried out and the total dose distribution is read back into Eclipse for display and evaluation. One academic and two clinical situations are investigated for possible benefits of MERT treatment compared to standard treatments performed in our clinics and treatment with a bolus electron conformal (BolusECT) method. RESULTS The MERT treatment plan of the academic case was superior to the standard single segment electron treatment plan in terms of organs at risk (OAR) sparing. Further, a comparison between an unfeathered and a feathered MERT plan showed better PTV coverage and homogeneity for the feathered plan, with V95% increased from 90% to 96% and V107% decreased from 8% to nearly 0%. For a clinical breast boost irradiation, the MERT plan led to a similar homogeneity in the PTV compared to the standard treatment plan while the mean body dose was lower for the MERT plan. Regarding the second clinical case, a whole breast treatment, MERT resulted in a reduction of the lung volume receiving more than 45% of the prescribed dose when compared to the standard plan. On the other hand, the MERT plan leads to a larger low-dose lung volume and a degraded dose homogeneity in the PTV. For the clinical cases evaluated in this work, treatment plans using the BolusECT technique resulted in a more homogenous PTV and CTV coverage but higher doses to the OARs than the MERT plans. CONCLUSIONS MERT treatments were successfully planned for phantom and clinical cases, applying a newly developed intuitive and efficient forward planning strategy that employs a MC based electron beam model for pMLC shaped electron beams. It is shown that MERT can lead to a dose reduction in OARs compared to other methods. The process of feathering MERT segments results in an improvement of the dose homogeneity in the PTV.

3D Direct Simulation Monte Carlo Modelling of the Inner Gas Coma of Comet 67P/Churyumov-Gerasimenko: A Parameter Study

Direct Simulation Monte Carlo (DSMC) is a powerful numerical method to study rarefied gas flows such as cometary comae and has been used by several authors over the past decade to study cometary outflow. However, the investigation of the parameter space in simulations can be time consuming since 3D DSMC is computationally highly intensive. For the target of ESA's Rosetta mission, comet 67P/Churyumov-Gerasimenko, we have identified to what extent modification of several parameters influence the 3D flow and gas temperature fields and have attempted to establish the reliability of inferences about the initial conditions from in situ and remote sensing measurements. A large number of DSMC runs have been completed with varying input parameters. In this work, we present the simulation results and conclude on the sensitivity of solutions to certain inputs. It is found that among cases of water outgassing, the surface production rate distribution is the most influential variable to the flow field.

Propagation of nuclear data uncertainties in fuel cycle calculations using MONTE-CARLO Technique

The uncertainty propagation in fuel cycle calculations due to Nuclear Data (ND) is a important important issue for : issue for : • Present fuel cycles (e.g. high burnup fuel programme) • New fuel cycles designs (e.g. fast breeder reactors and ADS) Different error propagation techniques can be used: • Sensitivity analysis • Response Response Surface Method Surface Method • Monte Carlo technique Then, p p , , in this paper, it is assessed the imp y pact of ND uncertainties on the decay heat and radiotoxicity in two applications: • Fission Pulse Decay ( y Heat calculation (FPDH) • Conceptual design of European Facility for Industrial Transmutation (EFIT)

Monte-Carlo dosimetry on a realistic cell monolayer geometry exposed to alpha particles

The energy and specific energy absorbed in the main cell compartments (nucleus and cytoplasm) in typical radiobiology experiments are usually estimated by calculations as they are not accessible for a direct measurement. In most of the work, the cell geometry is modelled using the combination of simple mathematical volumes. We propose a method based on high resolution confocal imaging and ion beam analysis (IBA) in order to import realistic cell nuclei geometries in Monte-Carlo simulations and thus take into account the variety of different geometries encountered in a typical cell population. Seventy-six cell nuclei have been imaged using confocal microscopy and their chemical composition has been measured using IBA. A cellular phantom was created from these data using the ImageJ image analysis software and imported in the Geant4 Monte-Carlo simulation toolkit. Total energy and specific energy distributions in the 76 cell nuclei have been calculated for two types of irradiation protocols: a 3 MeV alpha particle microbeam used for targeted irradiation and a 239Pu alpha source used for large angle random irradiation. Qualitative images of the energy deposited along the particle tracks have been produced and show good agreement with images of DNA double strand break signalling proteins obtained experimentally. The methodology presented in this paper provides microdosimetric quantities calculated from realistic cellular volumes. It is based on open-source oriented software that is publicly available.

FocusDET, a new toolbox for SISCOM analysis. Evaluation of the registration accuracy using monte carlo simulation

Subtraction of Ictal SPECT Co-registered to MRI (SISCOM) is an imaging technique used to localize the epileptogenic focus in patients with intractable partial epilepsy. The aim of this study was to determine the accuracy of registration algorithms involved in SISCOM analysis using FocusDET, a new user-friendly application. To this end, Monte Carlo simulation was employed to generate realistic SPECT studies. Simulated sinograms were reconstructed by using the Filtered BackProjection (FBP) algorithm and an Ordered Subsets Expectation Maximization (OSEM) reconstruction method that included compensation for all degradations. Registration errors in SPECT-SPECT and SPECT-MRI registration were evaluated by comparing the theoretical and actual transforms. Patient studies with well-localized epilepsy were also included in the registration assessment. Global registration errors including SPECT-SPECT and SPECT-MRI registration errors were less than 1.2 mm on average, exceeding the voxel size (3.32 mm) of SPECT studies in no case. Although images reconstructed using OSEM led to lower registration errors than images reconstructed with FBP, differences after using OSEM or FBP in reconstruction were less than 0.2 mm on average. This indicates that correction for degradations does not play a major role in the SISCOM process, thereby facilitating the application of the methodology in centers where OSEM is not implemented with correction of all degradations. These findings together with those obtained by clinicians from patients via MRI, interictal and ictal SPECT and video-EEG, show that FocusDET is a robust application for performing SISCOM analysis in clinical practice.

Massively parallelizable list-mode reconstruction using a Monte Carlo-based elliptical Gaussian model

Purpose: A fully three-dimensional (3D) massively parallelizable list-mode ordered-subsets expectation-maximization (LM-OSEM) reconstruction algorithm has been developed for high-resolution PET cameras. System response probabilities are calculated online from a set of parameters derived from Monte Carlo simulations. The shape of a system response for a given line of response (LOR) has been shown to be asymmetrical around the LOR. This work has been focused on the development of efficient region-search techniques to sample the system response probabilities, which are suitable for asymmetric kernel models, including elliptical Gaussian models that allow for high accuracy and high parallelization efficiency. The novel region-search scheme using variable kernel models is applied in the proposed PET reconstruction algorithm. Methods: A novel region-search technique has been used to sample the probability density function in correspondence with a small dynamic subset of the field of view that constitutes the region of response (ROR). The ROR is identified around the LOR by searching for any voxel within a dynamically calculated contour. The contour condition is currently defined as a fixed threshold over the posterior probability, and arbitrary kernel models can be applied using a numerical approach. The processing of the LORs is distributed in batches among the available computing devices, then, individual LORs are processed within different processing units. In this way, both multicore and multiple many-core processing units can be efficiently exploited. Tests have been conducted with probability models that take into account the noncolinearity, positron range, and crystal penetration effects, that produced tubes of response with varying elliptical sections whose axes were a function of the crystal's thickness and angle of incidence of the given LOR. The algorithm treats the probability model as a 3D scalar field defined within a reference system aligned with the ideal LOR. Results: This new technique provides superior image quality in terms of signal-to-noise ratio as compared with the histogram-mode method based on precomputed system matrices available for a commercial small animal scanner. Reconstruction times can be kept low with the use of multicore, many-core architectures, including multiple graphic processing units. Conclusions: A highly parallelizable LM reconstruction method has been proposed based on Monte Carlo simulations and new parallelization techniques aimed at improving the reconstruction speed and the image signal-to-noise of a given OSEM algorithm. The method has been validated using simulated and real phantoms. A special advantage of the new method is the possibility of defining dynamically the cut-off threshold over the calculated probabilities thus allowing for a direct control on the trade-off between speed and quality during the reconstruction.

A new PET prototype for proton therapy: comparison of data and Monte Carlo simulations

Ion beam therapy is a valuable method for the treatment of deep-seated and radio-resistant tumors thanks to the favorable depth-dose distribution characterized by the Bragg peak. Hadrontherapy facilities take advantage of the specific ion range, resulting in a highly conformal dose in the target volume, while the dose in critical organs is reduced as compared to photon therapy. The necessity to monitor the delivery precision, i.e. the ion range, is unquestionable, thus different approaches have been investigated, such as the detection of prompt photons or annihilation photons of positron emitter nuclei created during the therapeutic treatment. Based on the measurement of the induced β+ activity, our group has developed various in-beam PET prototypes: the one under test is composed by two planar detector heads, each one consisting of four modules with a total active area of 10 × 10 cm2. A single detector module is made of a LYSO crystal matrix coupled to a position sensitive photomultiplier and is read-out by dedicated frontend electronics. A preliminary data taking was performed at the Italian National Centre for Oncological Hadron Therapy (CNAO, Pavia), using proton beams in the energy range of 93–112 MeV impinging on a plastic phantom. The measured activity profiles are presented and compared with the simulated ones based on the Monte Carlo FLUKA package.