Treatment planning aspects and Monte Carlo methods in proton therapy

Over the last years, the interest in proton radiotherapy is rapidly increasing. Protons provide superior physical properties compared with conventional radiotherapy using photons. These properties result in depth dose curves with a large dose peak at the end of the proton track and the finite proton range allows sparing the distally located healthy tissue. These properties offer an increased flexibility in proton radiotherapy, but also increase the demand in accurate dose estimations. To carry out accurate dose calculations, first an accurate and detailed characterization of the physical proton beam exiting the treatment head is necessary for both currently available delivery techniques: scattered and scanned proton beams. Since Monte Carlo (MC) methods follow the particle track simulating the interactions from first principles, this technique is perfectly suited to accurately model the treatment head. Nevertheless, careful validation of these MC models is necessary. While for the dose estimation pencil beam algorithms provide the advantage of fast computations, they are limited in accuracy. In contrast, MC dose calculation algorithms overcome these limitations and due to recent improvements in efficiency, these algorithms are expected to improve the accuracy of the calculated dose distributions and to be introduced in clinical routine in the near future.

Recent Advances in Adaptive Sampling and Reconstruction for Monte Carlo Rendering

Monte Carlo integration is firmly established as the basis for most practical realistic image synthesis algorithms because of its flexibility and generality. However, the visual quality of rendered images often suffers from estimator variance, which appears as visually distracting noise. Adaptive sampling and reconstruction algorithms reduce variance by controlling the sampling density and aggregating samples in a reconstruction step, possibly over large image regions. In this paper we survey recent advances in this area. We distinguish between “a priori” methods that analyze the light transport equations and derive sampling rates and reconstruction filters from this analysis, and “a posteriori” methods that apply statistical techniques to sets of samples to drive the adaptive sampling and reconstruction process. They typically estimate the errors of several reconstruction filters, and select the best filter locally to minimize error. We discuss advantages and disadvantages of recent state-of-the-art techniques, and provide visual and quantitative comparisons. Some of these techniques are proving useful in real-world applications, and we aim to provide an overview for practitioners and researchers to assess these approaches. In addition, we discuss directions for potential further improvements.

Denoising Your Monte Carlo Renders: Recent Advances in Image Space-Adaptive Sampling and Reconstruction

With the ongoing shift in the computer graphics industry toward Monte Carlo rendering, there is a need for effective, practical noise-reduction techniques that are applicable to a wide range of rendering effects and easily integrated into existing production pipelines. This course surveys recent advances in image-space adaptive sampling and reconstruction algorithms for noise reduction, which have proven very effective at reducing the computational cost of Monte Carlo techniques in practice. These approaches leverage advanced image-filtering techniques with statistical methods for error estimation. They are attractive because they can be integrated easily into conventional Monte Carlo rendering frameworks, they are applicable to most rendering effects, and their computational overhead is modest.

Monte Carlo and analytical dose calculations for ocular proton therapy

Uveal melanoma is a rare but life-threatening form of ocular cancer. Contemporary treatment techniques include proton therapy, which enables conservation of the eye and its useful vision. Dose to the proximal structures is widely believed to play a role in treatment side effects, therefore, reliable dose estimates are required for properly evaluating the therapeutic value and complication risk of treatment plans. Unfortunately, current simplistic dose calculation algorithms can result in errors of up to 30% in the proximal region. In addition, they lack predictive methods for absolute dose per monitor unit (D/MU) values. ^ To facilitate more accurate dose predictions, a Monte Carlo model of an ocular proton nozzle was created and benchmarked against measured dose profiles to within ±3% or ±0.5 mm and D/MU values to within ±3%. The benchmarked Monte Carlo model was used to develop and validate a new broad beam dose algorithm that included the influence of edgescattered protons on the cross-field intensity profile, the effect of energy straggling in the distal portion of poly-energetic beams, and the proton fluence loss as a function of residual range. Generally, the analytical algorithm predicted relative dose distributions that were within ±3% or ±0.5 mm and absolute D/MU values that were within ±3% of Monte Carlo calculations. Slightly larger dose differences were observed at depths less than 7 mm, an effect attributed to the dose contributions of edge-scattered protons. Additional comparisons of Monte Carlo and broad beam dose predictions were made in a detailed eye model developed in this work, with generally similar findings. ^ Monte Carlo was shown to be an excellent predictor of the measured dose profiles and D/MU values and a valuable tool for developing and validating a broad beam dose algorithm for ocular proton therapy. The more detailed physics modeling by the Monte Carlo and broad beam dose algorithms represent an improvement in the accuracy of relative dose predictions over current techniques, and they provide absolute dose predictions. It is anticipated these improvements can be used to develop treatment strategies that reduce the incidence or severity of treatment complications by sparing normal tissue. ^

MMonCa: An Object Kinetic Monte Carlo simulator for damage irradiation evolution and defect diffusion

In this work, we introduce the Object Kinetic Monte Carlo (OKMC) simulator MMonCa and simulate the defect evolution in three different materials. We start by explaining the theory of OKMC and showing some details of how such theory is implemented by creating generic structures and algorithms in the objects that we want to simulate. Then we successfully reproduce simulated results for defect evolution in iron, silicon and tungsten using our simulator and compare with available experimental data and similar simulations. The comparisons validate MMonCa showing that it is powerful and flexible enough to be customized and used to study the damage evolution of defects in a wide range of solid materials.

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.

Efficient Monte Carlo methods for multi-dimensional learning with classifier chains

Multi-dimensional classification (MDC) is the supervised learning problem where an instance is associated with multiple classes, rather than with a single class, as in traditional classification problems. Since these classes are often strongly correlated, modeling the dependencies between them allows MDC methods to improve their performance – at the expense of an increased computational cost. In this paper we focus on the classifier chains (CC) approach for modeling dependencies, one of the most popular and highest-performing methods for multi-label classification (MLC), a particular case of MDC which involves only binary classes (i.e., labels). The original CC algorithm makes a greedy approximation, and is fast but tends to propagate errors along the chain. Here we present novel Monte Carlo schemes, both for finding a good chain sequence and performing efficient inference. Our algorithms remain tractable for high-dimensional data sets and obtain the best predictive performance across several real data sets.

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

We review the main results from extensive Monte Carlo (MC) simulations on athermal polymer packings in the bulk and under confinement. By employing the simplest possible model of excluded volume, macromolecules are represented as freely-jointed chains of hard spheres of uniform size. Simulations are carried out in a wide concentration range: from very dilute up to very high volume fractions, reaching the maximally random jammed (MRJ) state. We study how factors like chain length, volume fraction and flexibility of bond lengths affect the structure, shape and size of polymers, their packing efficiency and their phase behaviour (disorder–order transition). In addition, we observe how these properties are affected by confinement realized by flat, impenetrable walls in one dimension. Finally, by mapping the parent polymer chains to primitive paths through direct geometrical algorithms, we analyse the characteristics of the entanglement network as a function of packing density.

A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Dynamic weighting in Monte Carlo and optimization

Dynamic importance weighting is proposed as a Monte Carlo method that has the capability to sample relevant parts of the configuration space even in the presence of many steep energy minima. The method relies on an additional dynamic variable (the importance weight) to help the system overcome steep barriers. A non-Metropolis theory is developed for the construction of such weighted samplers. Algorithms based on this method are designed for simulation and global optimization tasks arising from multimodal sampling, neural network training, and the traveling salesman problem. Numerical tests on these problems confirm the effectiveness of the method.

Searching for convergence in phylogenetic Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a methodology that is gaining widespread use in the phylogenetics community and is central to phylogenetic software packages such as MrBayes. An important issue for users of MCMC methods is how to select appropriate values for adjustable parameters such as the length of the Markov chain or chains, the sampling density, the proposal mechanism, and, if Metropolis-coupled MCMC is being used, the number of heated chains and their temperatures. Although some parameter settings have been examined in detail in the literature, others are frequently chosen with more regard to computational time or personal experience with other data sets. Such choices may lead to inadequate sampling of tree space or an inefficient use of computational resources. We performed a detailed study of convergence and mixing for 70 randomly selected, putatively orthologous protein sets with different sizes and taxonomic compositions. Replicated runs from multiple random starting points permit a more rigorous assessment of convergence, and we developed two novel statistics, delta and epsilon, for this purpose. Although likelihood values invariably stabilized quickly, adequate sampling of the posterior distribution of tree topologies took considerably longer. Our results suggest that multimodality is common for data sets with 30 or more taxa and that this results in slow convergence and mixing. However, we also found that the pragmatic approach of combining data from several short, replicated runs into a metachain to estimate bipartition posterior probabilities provided good approximations, and that such estimates were no worse in approximating a reference posterior distribution than those obtained using a single long run of the same length as the metachain. Precision appears to be best when heated Markov chains have low temperatures, whereas chains with high temperatures appear to sample trees with high posterior probabilities only rarely. [Bayesian phylogenetic inference; heating parameter; Markov chain Monte Carlo; replicated chains.]

Guiding Monte Carlo tree searches with neural networks in the game of go

A dissertation submitted in fulfillment of the requirements to the degree of Master in Computer Science and Computer Engineering

Monte Carlo modeling of the patient and treatment delivery complexities for high dose rate brachytherapy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Monte Carlo Simulation Of The Response Functions Of Cdte Detectors To Be Applied In X-ray Spectroscopy.

In this work, the energy response functions of a CdTe detector were obtained by Monte Carlo (MC) simulation in the energy range from 5 to 160keV, using the PENELOPE code. In the response calculations the carrier transport features and the detector resolution were included. The computed energy response function was validated through comparison with experimental results obtained with (241)Am and (152)Eu sources. In order to investigate the influence of the correction by the detector response at diagnostic energy range, x-ray spectra were measured using a CdTe detector (model XR-100T, Amptek), and then corrected by the energy response of the detector using the stripping procedure. Results showed that the CdTe exhibits good energy response at low energies (below 40keV), showing only small distortions on the measured spectra. For energies below about 80keV, the contribution of the escape of Cd- and Te-K x-rays produce significant distortions on the measured x-ray spectra. For higher energies, the most important correction is the detector efficiency and the carrier trapping effects. The results showed that, after correction by the energy response, the measured spectra are in good agreement with those provided by a theoretical model of the literature. Finally, our results showed that the detailed knowledge of the response function and a proper correction procedure are fundamental for achieving more accurate spectra from which quality parameters (i.e., half-value layer and homogeneity coefficient) can be determined.