A Monte Carlo-Based Fiber Tracking Algorithm using Diffusion Tensor MRI

Diffusion tensor magnetic resonance imaging, which measures directional information of water diffusion in the brain, has emerged as a powerful tool for human brain studies. In this paper, we introduce a new Monte Carlo-based fiber tracking approach to estimate brain connectivity. One of the main characteristics of this approach is that all parameters of the algorithm are automatically determined at each point using the entropy of the eigenvalues of the diffusion tensor. Experimental results show the good performance of the proposed approach

A sparse parallel hybrid Monte Carlo algorithm for matrix computations

In this paper we introduce a new algorithm, based on the successful work of Fathi and Alexandrov, on hybrid Monte Carlo algorithms for matrix inversion and solving systems of linear algebraic equations. This algorithm consists of two parts, approximate inversion by Monte Carlo and iterative refinement using a deterministic method. Here we present a parallel hybrid Monte Carlo algorithm, which uses Monte Carlo to generate an approximate inverse and that improves the accuracy of the inverse with an iterative refinement. The new algorithm is applied efficiently to sparse non-singular matrices. When we are solving a system of linear algebraic equations, Bx = b, the inverse matrix is used to compute the solution vector x = B(-1)b. We present results that show the efficiency of the parallel hybrid Monte Carlo algorithm in the case of sparse matrices.

A new algorithm for Reverse Monte Carlo simulations

We present a new algorithm for Reverse Monte Carlo (RMC) simulations of liquids. During the simulations, we calculate energy, excess chemical potentials, bond-angle distributions and three-body correlations. This allows us to test the quality and physical meaning of RMC-generated results and its limitations. It also indicates the possibility to explore orientational correlations from simple scattering experiments. The new technique has been applied to bulk hard-sphere and Lennard-Jones systems and compared to standard Metropolis Monte Carlo results. (C) 1998 American Institute of Physics.

Application of a new reverse Monte Carlo algorithm to polyatomic molecular systems. I. Liquid water

Using a new reverse Monte Carlo algorithm, we present simulations that reproduce very well several structural and thermodynamic properties of liquid water. Both Monte Carlo, molecular dynamics simulations and experimental radial distribution functions used as input are accurately reproduced using a small number of molecules and no external constraints. Ad hoc energy and hydrogen bond analysis show the physical consistency and limitations of the generated RMC configurations. (C) 2001 American Institute of Physics.

Collapsed cone convolution and analytical anisotropic algorithm dose calculations compared to VMC++ Monte Carlo simulations in clinical cases

The purpose of this work was to study and quantify the differences in dose distributions computed with some of the newest dose calculation algorithms available in commercial planning systems. The study was done for clinical cases originally calculated with pencil beam convolution (PBC) where large density inhomogeneities were present. Three other dose algorithms were used: a pencil beam like algorithm, the anisotropic analytic algorithm (AAA), a convolution superposition algorithm, collapsed cone convolution (CCC), and a Monte Carlo program, voxel Monte Carlo (VMC++). The dose calculation algorithms were compared under static field irradiations at 6 MV and 15 MV using multileaf collimators and hard wedges where necessary. Five clinical cases were studied: three lung and two breast cases. We found that, in terms of accuracy, the CCC algorithm performed better overall than AAA compared to VMC++, but AAA remains an attractive option for routine use in the clinic due to its short computation times. Dose differences between the different algorithms and VMC++ for the median value of the planning target volume (PTV) were typically 0.4% (range: 0.0 to 1.4%) in the lung and -1.3% (range: -2.1 to -0.6%) in the breast for the few cases we analysed. As expected, PTV coverage and dose homogeneity turned out to be more critical in the lung than in the breast cases with respect to the accuracy of the dose calculation. This was observed in the dose volume histograms obtained from the Monte Carlo simulations.

Feasibility assessment of the interactive use of a Monte Carlo algorithm in treatment planning for intraoperative electron radiation therapy

This work analysed the feasibility of using a fast, customized Monte Carlo (MC) method to perform accurate computation of dose distributions during pre- and intraplanning of intraoperative electron radiation therapy (IOERT) procedures. The MC method that was implemented, which has been integrated into a specific innovative simulation and planning tool, is able to simulate the fate of thousands of particles per second, and it was the aim of this work to determine the level of interactivity that could be achieved. The planning workflow enabled calibration of the imaging and treatment equipment, as well as manipulation of the surgical frame and insertion of the protection shields around the organs at risk and other beam modifiers. In this way, the multidisciplinary team involved in IOERT has all the tools necessary to perform complex MC dosage simulations adapted to their equipment in an efficient and transparent way. To assess the accuracy and reliability of this MC technique, dose distributions for a monoenergetic source were compared with those obtained using a general-purpose software package used widely in medical physics applications. Once accuracy of the underlying simulator was confirmed, a clinical accelerator was modelled and experimental measurements in water were conducted. A comparison was made with the output from the simulator to identify the conditions under which accurate dose estimations could be obtained in less than 3 min, which is the threshold imposed to allow for interactive use of the tool in treatment planning. Finally, a clinically relevant scenario, namely early-stage breast cancer treatment, was simulated with pre- and intraoperative volumes to verify that it was feasible to use the MC tool intraoperatively and to adjust dose delivery based on the simulation output, without compromising accuracy. The workflow provided a satisfactory model of the treatment head and the imaging system, enabling proper configuration of the treatment planning system and providing good accuracy in the dosage simulation.

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.

A New Algorithm for Monte Carlo for American Options

2000 Mathematics Subject Classification: 91B28, 65C05.

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

Hybrid Monte Carlo algorithm for the double exchange model

The Hybrid Monte Carlo algorithm is adapted to the simulation of a system of classical degrees of freedom coupled to non self-interacting lattices fermions. The diagonalization of the Hamiltonian matrix is avoided by introducing a path-integral formulation of the problem, in d + 1 Euclidean space–time. A perfect action formulation allows to work on the continuum Euclidean time, without need for a Trotter–Suzuki extrapolation. To demonstrate the feasibility of the method we study the Double Exchange Model in three dimensions. The complexity of the algorithm grows only as the system volume, allowing to simulate in lattices as large as 163 on a personal computer. We conclude that the second order paramagnetic–ferromagnetic phase transition of Double Exchange Materials close to half-filling belongs to the Universality Class of the three-dimensional classical Heisenberg model.

Examination of pencil beam predictions of small-field dose using dosimetry film and Monte Carlo simulations

The iPlan treatment planning sys-tem uses a pencil beam algorithm, with density cor-rections, to predict the doses delivered by very small (stereotactic) radiotherapy fields. This study tests the accuracy of dose predictions made by iPlan, for small-field treatments delivered to a planar solid wa-ter phantom and to heterogeneous human tissue using the BrainLAB m3 micro-multileaf collimator.

Investigation of stereotactic radiotherapy dose using dosimetry film and Monte Carlo simulations

This study uses dosimetry film measurements and Monte Carlo simulations to investigate the accuracy of type-a (pencil-beam) dose calculations for predicting the radiation doses delivered during stereotactic radiotherapy treatments of the brain. It is shown that when evaluating doses in a water phantom, the type-a algorithm provides dose predictions which are accurate to within clinically relevant criteria, gamma(3%,3mm), but these predictions are nonetheless subtly different from the results of evaluating doses from the same fields using radiochromic film and Monte Carlo simulations. An analysis of a clinical meningioma treatment suggests that when predicting stereotactic radiotherapy doses to the brain, the inaccuracies of the type-a algorithm can be exacerbated by inadequate evaluation of the effects of nearby bone or air, resulting in dose differences of up to 10% for individual fields. The results of this study indicate the possible advantage of using Monte Carlo calculations, as well as measurements with high-spatial resolution media, to verify type-a predictions of dose delivered in cranial treatments.

Latent degradation indicators estimation and prediction : a Monte Carlo approach

Asset health inspections can produce two types of indicators: (1) direct indicators (e.g. the thickness of a brake pad, and the crack depth on a gear) which directly relate to a failure mechanism; and (2) indirect indicators (e.g. the indicators extracted from vibration signals and oil analysis data) which can only partially reveal a failure mechanism. While direct indicators enable more precise references to asset health condition, they are often more difficult to obtain than indirect indicators. The state space model provides an efficient approach to estimating direct indicators by using indirect indicators. However, existing state space models to estimate direct indicators largely depend on assumptions such as, discrete time, discrete state, linearity, and Gaussianity. The discrete time assumption requires fixed inspection intervals. The discrete state assumption entails discretising continuous degradation indicators, which often introduces additional errors. The linear and Gaussian assumptions are not consistent with nonlinear and irreversible degradation processes in most engineering assets. This paper proposes a state space model without these assumptions. Monte Carlo-based algorithms are developed to estimate the model parameters and the remaining useful life. These algorithms are evaluated for performance using numerical simulations through MATLAB. The result shows that both the parameters and the remaining useful life are estimated accurately. Finally, the new state space model is used to process vibration and crack depth data from an accelerated test of a gearbox. During this application, the new state space model shows a better fitness result than the state space model with linear and Gaussian assumption.