Fast, accurate and versatile Monte Carlo method for computing system matrix

This study focuses on Monte-Carlo (MC) based techniques to calculate the system matrix (SM) for iterative image reconstruction of small animal PET data. Our goal is to determine in advance if some simplifications can be done to accelerate the MC simulation without jeopardizing the accuracy of the system model. For most PET scanners, the calculation of the SM would imply extremely long simulation times, even when considering symmetries. Our small animal scanner prototype consists of a continuous LSO crystal (42 times 42 times 10 mm3 ) attached to a flat panel position sensitive photomultiplier tube which was simulated using GATE. To compute the SM elements, we investigated three different radioactivity distribution models: (a) homogeneous distribution within the voxel, (b) one unique emission point at the center of the voxel and (c) eight point sources distributed within the voxel. Each of these models was simulated for five representative voxel positions inside the field of view (FOV), two of these voxels in the inner region of the FOV and the other three voxels were in the peripheral region of the FOV. The storage and discretization of the SM elements was performed by means of: (i) tube-of-response (TOR) histograms and (ii) sinograms. By comparing the SM's elements generated for each distribution model at each voxel's position, the accuracy of the models was studied. The results show that in the inner region of the FOV, model C distribution yields the best trade-off between simulation time and SM accuracy. Whereas, for the peripheral region of the FOV, model B yields the best compromise. These results are independent of the discretization process considered. Since the scanner is capable to yield depth-of-interaction (DOI) information, the study was performed taking DOI into account

Thermal-pulse method is a powerful tool for measuring space charge distributions in polymer films. The data analysis for thermal-pulse method involves the Fredholm integral equation of the first kind, which requires an appropriate numerical procedure to obtain a solution. Various numerical techniques, including scale transformation and regulation method, are proposed. Of those numerical methods, the scale transformation (ST) is the simplest and the most widely used method. However, it presents a high spatial resolution only near the sample surface. Monte Carlo (MC) method is one of the recently proposed ways to solve the equation numerically and has been successfully applied to the analysis of laser intensity modulation method data, which also involves the Fredholm integral equation of the first kind. In this paper we attempt to analyze thermal-pulse data in frequency domain with the MC method and discuss its effectiveness based on some numerical simulations. The simulation results indicate that the electric field profiles can be effectively extracted by the MC method. The computed profiles by the MC method consist well with the supposed distributions in the entire thickness of the sample, while the profiles reconstructed by the ST method fit very well to the supposed one at the vicinity of the target surface and distort sharply along the direction of the thermal pulse propagation in the sample bulk. On the other hand, the oscillations in the computed results by the MC method could deteriorate its accuracy in this study. The influence of noise level on the analysis based on the MC method is also tested by the use of the simulated data. The results show that the computed profiles would become more fluctuant as the noise level increases. This problem can be solved by selecting a larger value of tolerance during the singular value decomposition procedure. Thus, the value of tolerance is considered to be one of the key parameters in this algorithm, which is actually hard to determine. Additionally, the experimental data obtained from a polypropylene film under applied electric field are analyzed to illustrate the feasibility of MC method to be applied to the thermal-pulse experimental data. The results also show that the spatial accuracy by the MC method in the entire sample thickness is higher than by the ST method, which verifies that the MC method is more suitable for detecting the electric field distribution in the deep bulk of the sample. Owing to noise and error, the accuracy of MC calculation depends on the chosen tolerance value, which is now considered to be an obstacle in applying this method to the practical thermal-pulse measurement.

Objective.To develop and evaluate an analytical method for calculating the system matrix of a dynamic cardiac single photon emission computed tomography (DC-SPECT) system, eliminating the need for computationally intensive Monte Carlo (MC) simulations.Approach.An analytical model was proposed for system matrix generation, incorporating solid angle calculations adapted for square-shaped pinhole collimators. The resulting sensitivity maps were validated against MC simulation results. Image reconstructions using the proposed analytical model were compared to those using an MC-simulated system matrix. Additionally, the overall system performance, including sensitivity and spatial resolution, was assessed using MC simulations.Main results.The analytical sensitivity map showed good agreement with MC-based results. Reconstructed images using the analytical model preserved key features but showed reduced performance compared to MC-based reconstructions. MC simulations of DC-SPECT demonstrated a spatial resolution of 5.5 mm for hot regions and 6.0 mm for cold regions, with an overall system sensitivity of 0.07% over a 15 cm diameter spherical field of view.Significance.The proposed analytical method offers a fast and practical alternative to MC-based system matrix generation, enabling efficient system design and prototyping. While its use in clinical image reconstruction requires further evaluation, the model provides a promising tool for accelerating the development of next-generation DC-SPECT systems.

Clinical Application of In-Room Positron Emission Tomography for In Vivo Treatment Monitoring in Proton Radiation Therapy

Positron emission tomography (PET) is a promising tool for monitoring the three-dimensional dose distribution in charged particle radiotherapy. PET imaging during or shortly after proton treatment is based on the detection of annihilation photons following the ß+-decay of radionuclides resulting from nuclear reactions in the irradiated tissue. Therapy monitoring is achieved by comparing the measured spatial distribution of irradiation-induced ß+-activity with the predicted distribution based on the treatment plan. The accuracy of the calculated distribution depends on the correctness of the computational models, implemented in the employed Monte Carlo (MC) codes that describe the interactions of the charged particle beam with matter and the production of radionuclides and secondary particles. However, no well-established theoretical models exist for predicting the nuclear interactions and so phenomenological models are typically used based on parameters derived from experimental data. Unfortunately, the experimental data presently available are insufficient to validate such phenomenological hadronic interaction models. Hence, a comparison among the models used by the different MC packages is desirable. In this work, starting from a common geometry, we compare the performances of MCNPX, GATE and PHITS MC codes in predicting the amount and spatial distribution of proton-induced activity, at therapeutic energies, to the already experimentally validated PET modelling based on the FLUKA MC code. In particular, we show how the amount of ß+-emitters produced in tissue-like media depends on the physics model and cross-sectional data used to describe the proton nuclear interactions, thus calling for future experimental campaigns aiming at supporting improvements of MC modelling for clinical application of PET monitoring.

Background Small megavoltage photon fields are increasingly used in modern radiotherapy techniques such as stereotactic radiotherapy. Therefore, it is important to study the reliability of dosimetry in the small-field conditions. The IBA Razor Nano Chamber (Nano chamber) ionization chamber is particularly intended for small-field measurements. In this work, properties of the Nano chamber were studied with both measurements and Monte Carlo (MC) simulations. Material and methods The measurements and MC simulations were performed with 6 MV, 6 MV FFF and 10 MV FFF photon beams from the Varian TrueBeam linear accelerator. The source-to-surface distance was fixed at 100 cm. The measurements and MC simulations included profiles, percentage depth doses (PDD), and output factors (OF) in square jaw-collimated fields. The MC simulations were performed with the EGSnrc software system in a large water phantom. Results The measured profiles and PDDs obtained with the Nano chamber were compared against IBA Razor Diode, PTW microDiamond and the PTW Semiflex ionization chamber. These results indicate that the Nano chamber is a high-resolution detector and thus suitable for small field profile measurements down to field sizes 2 × 2 cm2 and appropriate for the PDD measurements. The field output correction factors and field OFs were determined according to TRS-483 protocol In the 6 MV FF and FFF beams, the determined correction factors were within 1.2% for the field sizes of 1 × 1 cm2–3 × 3 cm2 and the experimental and MC defined field output factors showed good agreement. Conclusion The Nano chamber with its small cavity volume is a potential detector for the small-field dosimetry. In this study, the properties of this detector were characterized with measurements and MC simulations. The determined correction factors are novel results for the NC in the TrueBeam fields.

In these days, Monte Carlo (MC) simulation is a method that can calculate the radiation dose that occurs in an environment in the most accurate way. The correct measurement of the dose occurring on the patient’s surface is of great importance to estimate the reactions that may occur on the patient’s skin. This importance encouraged us to do this study. The aim of this study is to determine buildup region and surface doses using MC simulation and to compare them with results of the parallel plane ion chamber and Treatment Planning System (TPS) measurements for 6-MV photon beams. Surface doses normalized to the maximum dose for the parallel plane ion chamber, MC simulation, fast photon (FP) algorithm, and collapsed cone convolution superposition (CC) algorithm are 13.6%, 30.28%, 0%, and 27.33%, respectively. The CC algorithm and parallel plane ion chamber measurements are compatible with MC simulation but the FP algorithm has calculated the dose less to a depth of 0.8 cm. Measuring the surface dose and the doses in the buildup region is of great importance in terms of accurately predicting the complications that may occur in the patient’s skin and taking precautions early. Using some methods and correction factors, the surface dose and the doses that may occur in the buildup region can be accurately calculated. It is recommended not to use the FP algorithm for stereotactic body radiation therapy and intensity-modulated radiation therapy treatments, as it cannot calculate doses correctly in the buildup region and surface.

Purpose: To create a Monte Carlo (MC) model of an ocular proton therapy device, or ocular nozzle, that can predict relative doses to within 3% or 0.5 mm, D/MU values, and be used to develop and commission an analytical algorithm to predict doses and D/MU values to within similar criteria. Methods and Materials: Depth dose profiles and D/MU values were measured in eight ocular proton therapy fields including four unmodulated and four modulated beams using a parallel‐plane ionization chamber in water. Crossfield profiles were measured at three or more depths for each of the modulated beams using film. A MC model of the ocular nozzle was constructed using the MCNPX radiation transport code. After benchmark tests against the measurements, the MC model was used to provide dosimetric data needed to develop a broad‐beam algorithm capable of predicting relative and absolute doses and to test the algorithm's predictions more comprehensively than could be afforded with measured data. Specifically, MC and analytical predictions were calculated and compared in two‐dimensions in a water phantom and in an anthropomorphic model of the eye. Results: Relative depth dose profiles between MC and measurements agreed to within 3% or 0.5 mm. MC predicted D/MU values agreed to within 1% of the measured values. Similarly, the analytical algorithm accurately predicted dose distributions where the predictions were generally within 3% or 0.5 mm of measured and simulated values at water depth > 6 mm. At shallower depths, the analytical model underestimated the dose by approximately 3% to 6%, which MC simulations revealed was due to edge‐scattered protons from the nozzle's collimators. Conclusion: The MC model accurately predicted dose distributions and D/MU values in ocular proton therapy beams. Furthermore, the present work demonstrates the value of the MC method for developing and testing contemporary analytical dose algorithms.

As energy demand increases and global warming progresses, expectations for fuel cells, which generate electricity through chemical reactions between hydrogen and oxygen, are rising. There are various types of fuel cells, which are classified according to the electrolyte. Polymer electrolyte fuel cells (PEFCs) are expected to be used in stationary power sources for home use and fuel cell vehicles because of their low operating temperature, short start-up time, and ease of miniaturization. The cost has been an issue in the widespread use of fuel cells. The amount of platinum used in the catalyst layer (CL) must be reduced to reduce costs. However, it increases the current density per unit area of platinum. There are three factors that contribute to voltage drop: ohmic polarization, activation polarization, and diffusion polarization. At high current densities, the voltage drop due to diffusion polarization is dominant. The main cause of diffusion polarization is the transport resistance of oxygen molecules in the CL, and improving the oxygen transport properties in the CL will lead to lower cost PEFCs. In this study, we analyzed the transport properties of oxygen molecules in the CLs of PEFCs using the Monte Carlo (MC) method. The effect of oxygen scattering on the overall oxygen transport properties was investigated by considering the behavior on the surface of the ionomer film (surface diffusion) into the MC method, which simulates the overall transport in the PEFC CL. The objective of this study is to reproduce accurate oxygen transport by comparing the results of MC and molecular dynamics (MD) methods. First, we used the MC method to analyze oxygen scattering phenomena. In this study, we used the 3D structure data of CL in the MC simulations. The three-dimensional structure of the sample was reconstructed from sequential slice images. Molecules were assumed to reflect specularly on the boundaries of the simulation domain. Oxygen molecules were randomly placed in the simulation system. The time step was set at 5 ps and the simulation time was set at 4 μs. In order to examine the effect of surface diffusion on the transport properties of oxygen molecules, the simulation was performed using various conditions of surface diffusion. We calculated the effective diffusion coefficient of oxygen in the CL as the transport property of oxygen molecules in the MC method. As the surface diffusion coefficient increases, the effective diffusion coefficient of oxygen increases. When the surface diffusion coefficient is small, the effective diffusion coefficient of oxygen increases due to a decrease in the time constant, which determines the probability distribution of the surface residence time. However, when the surface diffusion coefficient is large, a different trend emerges. As the time constant increases, the effective diffusion coefficient has a peak value and then decreases. Next, to verify the model of surface diffusion in the MC method, we analyzed the scattering phenomenon of oxygen molecules in a simulation system that simulates the pores in the CL using the MD method. We modeled the nano pores in the CL as a slit between the ionomer walls in the MD method. Nafion with the equivalent weight (EW) of 1146 was used as polymer model. The number of Nafion chains is set at 4, and the water content λ is set at 7. Three-dimensional periodic boundary conditions were applied to the simulation domain. After the system was equilibrated, 1 ns of NVT simulation was performed for production. The temperature was set at 297 K. The behavior of oxygen molecules impacting on the ionomer wall was analyzed. We analyzed the behavior of oxygen molecules colliding with the ionomer membrane using the MD method. The average residence time of surface diffusion on the ionomer thin film was of the order of 10-10s. When the calculation results were compared with the MC results, it was found that the average residence time obtained by the MD method was the value where the surface diffusion coefficient affects much on the effective diffusion coefficient. Comparing the results of the MD method with the surface diffusion model used in the MC method, there are some discrepancies between the results and the model. For example, the MC method used a model in which oxygen molecules reflect diffusively on the ionomer surface. However, in the MD method, it was found that oxygen molecules tend to reflect in the direction of travel (Fig. 1). Therefore, a more accurate model of the MC method needs to be developed in the future. Figure 1

Objective.Carbon ion therapy could benefit from range verification due to its sensitivity to range uncertainties. Positron emission tomography (PET) aids in this and comparing PET signals to a predicted positron emitter distribution (PED) is one viable approach. Monte Carlo (MC) simulations are one way to predict PED but are computationally intensive and time-consuming. To address this, an analytical approach was previously suggested to predict 1D PED from depth dose profiles. Here we aim to develop a computational framework for 3D PED prediction in carbon ion therapy, building on the 1D approach to provide a faster method than MC simulations, with potential for integration into treatment planning systems (TPS).Approach.The 1D approach was revised by considering more PEs channels and introducing new modeling functions. A mapping process for handling longitudinal heterogeneity effects in projectile PED was developed. Then, a dedicated framework for 3D PED generation based on a pencil beam algorithm (PBA) and the updated 1D method was proposed. Validation was performed throughin-silicostudies against MC calculations for several phantoms as well as realistic computed tomography scans from patient data.Main results.For range assessment, the differences between distal fall-off positions of predicted and simulated 1D PED profiles were calculated to be below 0.8 mm for all validation cases. The comparison of predicted 3D PED with simulated results was performed by global gamma index analysis using the 2%/2 mm and 1%/1 mm criteria. For patient cases, the passing rates for 1%/1 mm criteria were above 95%.Significance.These results demonstrated the capability of our approach to predict 3D PED with good accuracy in terms of range and magnitude, paving the way to future implementation in a TPS, which commonly relies on PBA for12C ions. Moreover, a significant speed-up compared to MC simulations was achieved, with future speed-optimized implementations.

We combine molecular dynamics (MD) and Monte Carlo (MC) simulations to study the properties of gas molecules confined between two hard walls of a microchannel or nanochannel. The coupling between MD and MC simulations is introduced by performing MD near the boundaries for accuracy and MC in the bulk because of the low computational cost. We characterize the influence of different densities and molecule sizes on the equilibrium properties of the gas in the microchannel. The effect of the particle size on the simulation results is very small in the case of a dilute gas and increases with the density. The hybrid MD-MC simulation method is validated by comparing the results for density and temperature profiles with those of pure MD and pure MC simulations. These results compare well for pure MD and pure MC, as well as hybrid MD-MC, both in the bulk and near the boundaries, when hard-sphere interactions are used. When Lennard-Jones potentials are used to accurately model the interactions between the gas and wall molecules instead, the results of pure MD simulations differ significantly from the pure MC simulations near the boundaries, but the results of the hybrid method compare well with the pure MD results near the wall, and with the pure MC and pure MD results in the middle of the channel. The hybrid method also very accurately simulates the interface between the MD and MC simulation domains. Comparisons between MD, MC, and hybrid MD-MC computational costs are outlined. The speedup when using 50% of the domain for MD simulations and 50% for MC simulations is very small compared to pure MD simulations times, but this speedup increases drastically for more realistic situations where the region near the wall is small compared to the bulk region.

Purpose: For microdosimetric calculation event-by-event Monte Carlo (MC) simulation is considered the most accurate, but it is very time-consuming. In this work we present an event-by-event MC simulation of low energy electron and proton for accelerated microdosimetric MC simulations on a graphic processing unit (GPU). Methods: The MC simulation of particle was implemented in C and executed on a multi-core CPU, and a commercially available general purpose GPU using the compute unified device architecture (CUDA). Additionally, a hybrid implementation scheme was realized by employing OpenMP and CUDA so that both GPU and multi-core CPU were utilized simultaneously. The two implementation schemes have been tested and compared with the sequential single threaded MC simulation on the CPU. A calculation time comparison was established on the speed-up for a set of benchmarking cases of electron and proton. Results: Dosimetric results were obtained with both the parallel and serial MC codes. A GPU over CPU speed-up of 67.2 and 19.2 times was achieved for 300 eV and 2 keV electron tracks respectively. For proton tracks, the GPU-based code was approximately 5 times faster than the CPU-single-thread code. By incorporating a multi-core CPU and running the MC code simultaneously on the GPU and CPU, an increase of 2%-7% and 20% in the speedup was noticed for electrons and protons tracks respectively. A good dosimetric agreement between the CPU- and GPU-based MC methods was observed for both electrons and proton. Conclusions: A GPU-based MC method for microdosimetric calculations of low energy electron and proton has been presented. The results indicate the capability of our GPU-based implementation for accelerated MC simulations of both electron and proton without loss of accuracy. Lastly, the potential of a hybrid approach by utilizing simultaneously a GPU and a multi-core CPU for further acceleration of MC microdosimetric calculations has been demonstrated.

Objective. Monte Carlo (MC) simulations are the benchmark for accurate radiotherapy dose calculations, notably in patient-specific high dose rate brachytherapy (HDR BT), in cases where considering tissue heterogeneities is critical. However, the lengthy computational time limits the practical application of MC simulations. Prior research used deep learning (DL) for dose prediction as an alternative to MC simulations. While accurate dose predictions akin to MC were attained, graphics processing unit limitations constrained these predictions to large voxels of 3 mm × 3 mm × 3 mm. This study aimed to enable dose predictions as accurate as MC simulations in 1 mm × 1 mm × 1 mm voxels within a clinically acceptable timeframe. Approach. Computed tomography scans of 98 breast cancer patients treated with Iridium-192-based HDR BT were used: 70 for training, 14 for validation, and 14 for testing. A new cropping strategy based on the distance to the seed was devised to reduce the volume size, enabling efficient training of 3D DL models using 1 mm × 1 mm × 1 mm dose grids. Additionally, novel DL architecture with layer-level fusion were proposed to predict MC simulated dose to medium-in-medium (D m,m ). These architectures fuse information from TG-43 dose to water-in-water (D w,w ) with patient tissue composition at the layer-level. Different inputs describing patient body composition were investigated. Main results. The proposed approach demonstrated state-of-the-art performance, on par with the MC D m,m maps, but 300 times faster. The mean absolute percent error for dosimetric indices between the MC and DL-predicted complete treatment plans was 0.17% ± 0.15% for the planning target volume V 100, 0.30% ± 0.32% for the skin D 2cc , 0.82% ± 0.79% for the lung D 2cc , 0.34% ± 0.29% for the chest wall D 2cc and 1.08% ± 0.98% for the heart D 2cc . Significance. Unlike the time-consuming MC simulations, the proposed novel strategy efficiently converts TG-43 D w,w maps into precise D m,m maps at high resolution, enabling clinical integration.

The accuracy of the system model in an iterative reconstruction algorithm greatly affects the quality of reconstructed positron emission tomography (PET) images. For efficient computation in reconstruction, the system model in PET can be factored into a product of a geometric projection matrix and sinogram blurring matrix, where the former is often computed based on analytical calculation, and the latter is estimated using Monte Carlo simulations. Direct measurement of a sinogram blurring matrix is difficult in practice because of the requirement of a collimated source. In this work, we propose a method to estimate the 2D blurring kernels from uncollimated point source measurements. Since the resulting sinogram blurring matrix stems from actual measurements, it can take into account the physical effects in the photon detection process that are difficult or impossible to model in a Monte Carlo (MC) simulation, and hence provide a more accurate system model. Another advantage of the proposed method over MC simulation is that it can easily be applied to data that have undergone a transformation to reduce the data size (e.g., Fourier rebinning). Point source measurements were acquired with high count statistics in a relatively fine grid inside the microPET II scanner using a high-precision 2D motion stage. A monotonically convergent iterative algorithm has been derived to estimate the detector blurring matrix from the point source measurements. The algorithm takes advantage of the rotational symmetry of the PET scanner and explicitly models the detector block structure. The resulting sinogram blurring matrix is incorporated into a maximum a posteriori (MAP) image reconstruction algorithm. The proposed method has been validated using a 3 × 3 line phantom, an ultra-micro resolution phantom and a 22Na point source superimposed on a warm background. The results of the proposed method show improvements in both resolution and contrast ratio when compared with the MAP reconstruction with a MC-based sinogram blurring matrix, and one without a detector response model. The reconstruction time is unaffected by the new method since the blurring component takes a relatively small part of the overall reconstruction time. The proposed method can be applied to other PET scanners for human and animal imaging.

Purpose: To investigate dose distributions in the prostate and surrounding tissues for I–125 brachytherapy using Monte Carlo (MC) calculations with patient‐specific phantoms derived from CT images. We explore the effectiveness of different techniques to mitigate streaking artifacts due to brachytherapy sources in post‐implant CT images. Methods: Nine patients (45–87 sources) are considered. Streaking artifacts in post‐implant CT images are mitigated using various metallic artifact reduction (MAR) techniques: raw sinogram, fan beam virtual sinogram and 3D median filter. Segmented structures (CTV, rectum and bladder) guide the assignment of tissues (air, muscle, prostate, calcification, average tissue and bone) to develop patient‐specific MC phantoms. The EGSnrc user‐code Brachydose and GEANT4 user‐code ALGEBRA are employed for MC dose calculations using patient‐specific phantoms derived from CT images. Dose distributions generated with patient models derived using different MAR techniques and different calculation methods (MC, TG‐43) are compared directly, and using recommended dose metrics. Results: Application of each MAR technique to patient CT data results in comparable mitigation of streaking artifacts within the treatment volume in CT images. MC calculations based on uncorrected CT data Result in high dose spikes (>200%) in the treatment volume and lower doses (40–70%) in surrounding tissues compared to MC calculations with corrected phantoms. Dose distributions within the prostate from MC simulations using phantoms generated with different MAR techniques are comparable to each other but differ from TG‐43 calculations with significant (10%+) local differences. Conclusion: Mitigation of streaking artifacts in CT images is necessary for patient‐specific MC dose calculations; however, dose distributions and clinical metrics in the target and OAR are insensitive to the particular MAR technique applied. Differences between MC and TG‐43 dose distributions within the target volume and surrounding organs for I‐125 prostate brachytherapy underline the importance of patient‐specific model‐based dose calculations for treatment planning and evaluation. NSERC, CCSRI, The Canada Research Chairs Program