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Results for “Monte Carlo Method”

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PubMed2000

IORT apparatus design improvement through the evaluation of electron spectral distributions using Monte Carlo methods.

Clinically used IORT electron beam characteristics may vary with respect to typical external beams due to the decrease of lateral scatter equilibrium and the addition of the IORT apparatus itself. Additionally, chamber size effects may lead to inaccurate measurements of the changes in electron beam characteristics. The causal components of these beam characteristics are often difficult or impossible to measure using experimental techniques. For this reason, and for potential design improvement, the electron beams were modeled using the OMEGA/BEAM Monte Carlo software for radiation transport. The IORT electron beam characteristics of the Varian Clinac 1800 were studied for 6, 12, and 20 MeV electrons and 1-4 in. diameter flat-end applicators. The characteristics studied include electron energy spectra, percentage depth dose, and cross-plane profiles. It was found that by increasing the thickness of the aluminum base plate of the main attachment, the dose at d(max) outside the primary field could be reduced from approximately 9% to 1% of maximum.

Biophysical Phenomena↗

PubMed2004

Joint oligogenic segregation and linkage analysis using bayesian Markov chain Monte Carlo methods.

One of the most challenging areas in human genetics is the dissection of quantitative traits. In this context, the efficient use of available data is important, including, when possible, use of large pedigrees and many markers for gene mapping. In addition, methods that jointly perform linkage analysis and estimation of the trait model are appealing because they combine the advantages of a model-based analysis with the advantages of methods that do not require prespecification of model parameters for linkage analysis. Here we review a Markov chain Monte Carlo approach for such joint linkage and segregation analysis, which allows analysis of oligogenic traits in the context of multipoint linkage analysis of large pedigrees. We provide an outline for practitioners of the salient features of the method, interpretation of the results, effect of violation of assumptions, and an example analysis of a two-locus trait to illustrate the method.

Bayes Theorem↗

PubMed1998

Measuring departures from Hardy-Weinberg: a Markov chain Monte Carlo method for estimating the inbreeding coefficient.

Many well-established statistical methods in genetics were developed in a climate of severe constraints on computational power. Recent advances in simulation methodology now bring modern, flexible statistical methods within the reach of scientists having access to a desktop workstation. We illustrate the potential advantages now available by considering the problem of assessing departures from Hardy-Weinberg (HW) equilibrium. Several hypothesis tests of HW have been established, as well as a variety of point estimation methods for the parameter which measures departures from HW under the inbreeding model. We propose a computational, Bayesian method for assessing departures from HW, which has a number of important advantages over existing approaches. The method incorporates the effects-of uncertainty about the nuisance parameters--the allele frequencies--as well as the boundary constraints on f (which are functions of the nuisance parameters). Results are naturally presented visually, exploiting the graphics capabilities of modern computer environments to allow straightforward interpretation. Perhaps most importantly, the method is founded on a flexible, likelihood-based modelling framework, which can incorporate the inbreeding model if appropriate, but also allows the assumptions of the model to he investigated and, if necessary, relaxed. Under appropriate conditions, information can be shared across loci and, possibly, across populations, leading to more precise estimation. The advantages of the method are illustrated by application both to simulated data and to data analysed by alternative methods in the recent literature.

Algorithms↗

PubMed2006

Application of advanced Monte Carlo Methods in numerical dosimetry.

Many tasks in different sectors of dosimetry are very complex and highly sensitive to changes in the radiation field. Often, only the simulation of radiation transport is capable of describing the radiation field completely. Down to sub-cellular dimensions the energy deposition by cascades of secondary electrons is the main pathway for damage induction in matter. A large number of interactions take place until such electrons are slowed down to thermal energies. Also for some problems of photon transport a large number of photon histories need to be processed. Thus the efficient non-analogue Monte Carlo program, AMOS, has been developed for photon and electron transport. Various applications and benchmarks are presented showing its ability. For radiotherapy purposes the radiation field of a brachytherapy source is calculated according to the American Association of Physicists in Medicine Task Group Report 43 (AAPM/TG43). As additional examples, results for the detector efficiency of a high-purity germanium (HPGe) detector and a dose estimation for an X-ray shielding for radiation protection are shown.

Algorithms↗

PubMed2006

Robust segmentation of cerebral arterial segments by a sequential Monte Carlo method: particle filtering.

In this paper a method to extract cerebral arterial segments from CT angiography (CTA) is proposed. The segmentation of cerebral arteries in CTA is a challenging task mainly due to bone contact and vein contamination. The proposed method considers a vessel segment as an ellipse travelling in three-dimensional (3D) space and segments it out by tracking the ellipse in spatial sequence. A particle filter is employed as the main framework for tracking and is equipped with adaptive properties to both bone contact and vein contamination. The proposed tracking method is evaluated by the experiments on both synthetic and actual data. A variety of vessels were synthesized to assess the sensitivity to the axis curvature change, obscure boundaries, and noise. The experimental results showed that the proposed method is also insensitive to parameter settings and requires less user intervention than the conventional vessel tracking methods, which proves its improved robustness.

Cerebral Angiography↗

PubMed2001

Extended state-space Monte Carlo methods.

In this paper various extensions of the parallel-tempering algorithm are developed and their properties are analyzed. The algorithms are designed to alleviate quasiergodic sampling in systems which have rough energy landscapes by coupling individual Monte Carlo chains to form a composite chain. As with parallel tempering, the procedures are based upon extending the state space to include parameters to encourage sampling mobility. One of the drawbacks of the parallel-tempering method is the stochastic nature of the Monte Carlo dynamics in the auxiliary variables which extend the state space. In this work, the possibility of improving the sampling rate by designing deterministic methods of moving through the parameter space is investigated. The methods developed in this article, which are based upon a statistical quenching and heating procedure similar in spirit to simulated annealing, are tested on a simple two-dimensional spin system (xy model) and on a model in vacuo polypeptide system. In the coupled Monte Carlo chain algorithms, we find that the net mobility of the composite chain is determined by the competition between the characteristic time of coupling between adjacent chains and the degree of overlap of their distributions. Extensive studies of all methods are carried out to obtain optimal sampling conditions. In particular, the most efficient parallel-tempering procedure is to attempt to swap configurations after very few Monte Carlo updates of the composite chains. Furthermore, it is demonstrated that, contrary to expectations, the deterministic procedure does not improve the sampling rate over that of parallel tempering.

Journal Article↗

PubMed2004

Lower and upper bounds for the absolute free energy by the hypothetical scanning Monte Carlo method: application to liquid argon and water.

The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy S and free energy F by analyzing Boltzmann samples obtained by Monte Carlo or molecular dynamics techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by gradually placing the molecules in their positions at i using transition probabilities (TPs). At each step of the process the system is divided into two parts, the already treated molecules (the "past"), which are fixed, and the as yet unspecified (mobile) "future" molecules. Obtaining the TP exactly requires calculating partition functions over all positions of the future molecules in the presence of the frozen past, thus it is customary to invoke various approximations to best represent these quantities. In a recent publication [Proc. Natl. Acad. Sci. USA 101, 9235 (2004)] we developed a version of HS called complete HSMC, where each TP is calculated from an MC simulation involving all of the future molecules (the complete future); the method was applied very successfully to Lennard-Jones systems (liquid argon) and a box of TIP3P water molecules. In its basic implementation the method provides lower and upper bounds for F, where the latter can be evaluated only for relatively small systems. Here we introduce a new expression for an upper bound, which can be evaluated for larger systems. We also propose a new exact expression for F and verify its effectiveness. These free energy functionals lead to significantly improved accuracy (as applied to the liquid systems above) which is comparable to our thermodynamic integration results. We formalize and discuss theoretical aspects of HSMC that have not been addressed in previous studies. Additionally, several functionals are developed and shown to provide the free energy through the analysis of a single configuration.

Argon↗

PubMed1990

Evaluation of inter- and intramolecular primary structure homologies of interferons by a Monte Carlo method.

Using Sellers TT algorithm, primary structure repeats have been described for interferon (IFN)-alpha, -beta 1, and gamma. To reevaluate these results and to extend them to IFN-beta 2 (interleukin-6), a modified algorithm was developed that uses a metric to define the "best" partial homology of two peptide sequences and to compare it to those detected in random permutations of the peptide. Using this approach, the known structural homologies of IFN-alpha with IFN-beta 1 and of human (Hu) IFN-gamma with murine (Mu) IFN-gamma were identified correctly. However, the primary structure repeats in the amino acid sequences of IFN-alpha, -beta 1, and -gamma turned out to be no better than those detectable in random permutations of these sequences. These results were confirmed using a different, nonlinear metric. A previously used approach to demonstrate significance was shown to produce false-positive results. No significant primary structure homologies were detected among IFN-beta 1, -beta 2, and -gamma. In contrast to the amino acid sequence analysis, the DNA sequence of HuIFN-beta 1 contained a significant repeat that had no significant counterpart in MuIFN-beta or in IFN-alpha. In conclusion, some previously reported results obtained with Sellers TT algorithm on amino acid sequences are easily explained as random similarities, and it is therefore strongly recommended that a method like ours should be used to control significance.

Algorithms↗

PubMed1997

A Monte Carlo method for finding important ligand fragments from receptor data.

A simulated annealing method for finding important ligand fragments is described. At a given temperature, ligand fragments are randomly selected and randomly placed within the given receptor cavity, often replacing or forming bonds with existing ligand fragments. For each new ligand fragment combination, the bonded, nonbonded, polarization and solvation energies of the new ligand-receptor system are compared to the previous configuration. Acceptance or rejection of the new system is decided using the Boltzmann distribution e-E/kT, where E is the energy difference between the old and new systems, k is the Boltzmann constant and T is the temperature. Thus, energetically unfavorable fragment switches are sometimes accepted, sacrificing immediate energy gains in the interest of findings a system with minimum energy. By lowering the temperature, the rate of unfavorable switches decreases and energetically favorable combinations become more difficult to change. The process is terminated when the frequency of switches becomes too small. As a test, the method predicted positions and types of important ligand fragments for neuraminidase that were in accord with the known ligand, sialic acid.

Algorithms↗

PubMed1998

Monte Carlo method to study the proton fluence for treatment planning.

The proton beam at the Hahn Meitner Institute (HMI) in Berlin will be used for proton therapy of eye melanoma in the near future. As part of the pre-therapeutic studies, Monte Carlo calculations have been performed to investigate the primary fluence distribution of the proton beam including the influence of scattering foils, range shifters, modulator wheels, and collimators. Any material in the beam path will modify the therapeutic beam because of energy loss, multiple scattering, range straggling, and nuclear reactions. The primary fluence information is a pre-requisite for most pencil-beam treatment planning algorithms. The measured beam penumbra has been used as one of the parameters to characterize a proton beam for further calculations in a treatment planning algorithm. However, this phenomenological quantity represents only indirect information about the properties of the proton beam. In this work, an alternative parameterization of the beam exiting the vacuum window of the accelerator, as well as the beam right in front of the patient collimator, is introduced. A beam is fully characterized if one knows (for instance from Monte Carlo simulations) the particle distribution in energy, position, and angle, i.e., the phase space distribution. Therefore, parameters derived from this distribution can provide an alternative input in treatment planning algorithms. In addition, the method of calculation is introduced as a tool to investigate the influence of modifications in the beam delivery system on the behavior of the therapeutic proton beam.

Algorithms↗

PubMed2003

Modeling of daily operation in proton radiotherapy by Monte Carlo method.

A simple model for efficiency analysis of daily operation in proton radiotherapy is applied to numerical calculation with fixed time advancing. For the simplifying, man power is assumed to be enough and troubles in the equipments are ignored. To generate random numbers which become the time for adjusting the patient position and for waiting the next patient, typical probability distributions are utilized in the simulation. By using the simulation, treatment capacity of a facility is estimated for different number of treatment rooms to know the efficient number of gantries for proton radiotherapy.

Computer Simulation↗

PubMed2002

Energy-based reconstruction of a protein backbone from its alpha-carbon trace by a Monte-Carlo method.

An automatic procedure is proposed for reconstruction of a protein backbone from its C(alpha)-trace; it is based on optimization of a simplified energy function of a peptide backbone, given its alpha-carbon trace. The energy is expressed as a sum of the energies of interaction between backbone peptide groups that are not neighbors in the sequence, the energies of local interactions within all amino acid residues, and a harmonic penalty function accounting for the conservation of standard bond angles. The energy of peptide group interactions is calculated using the assumption that each peptide group acts as a point dipole. For local interaction energy, use is made of a two-dimensional Fourier series expansion of the energies of model terminally blocked amino acid residues, calculated with the Empirical Conformational Energy Program for Peptides (ECEPP/3) force field in the angles lambda((1)) and lambda((2)) defining the rotation of peptide groups adjacent to a C(alpha) carbon atom about the corresponding C(alpha) em leader C(alpha) virtual-bond axes. To explore all possible rotations of peptide groups within a fixed C(alpha)-trace, a Monte Carlo search is carried out. The initial lambda angles are calculated by aligning the dipoles of the peptide groups that are close in space, subject to the condition of favorable local interactions. After the Monte Carlo search is accomplished with the simplified energy function, the energy of the structure is minimized with the ECEPP/3 force field, with imposition of distance constraints corresponding to the initial C(alpha)-trace geometry. The procedure was tested on model alpha-helices and beta-sheets, as well as on the crystal structure of the immunoglobulin binding protein (PDB code: 1IGD, an alpha/beta protein). In all cases, complete backbone geometry was reconstructed with a root-mean-square (rms) deviation of 0.5 A from the all-atom target structure.

Algorithms↗

PubMed2001

Linkage analysis of a complex pedigree with severe bipolar disorder, using a Markov chain Monte Carlo method.

Recently developed algorithms permit nonparametric linkage analysis of large, complex pedigrees with multiple inbreeding loops. We have used one such algorithm, implemented in the package SimWalk2, to reanalyze previously published genome-screen data from a Costa Rican kindred segregating for severe bipolar disorder. Our results are consistent with previous linkage findings on chromosome 18 and suggest a new locus on chromosome 5 that was not identified using traditional linkage analysis.

Algorithms↗

PubMed1999

Fetal dose assessment from invasive special procedures by Monte Carlo methods.

The assessment of fetal dose from a special procedure in the clinical environment is difficult as patient size, fluoroscopic beam motion, and imaging sequences vary significantly from study to study. Fetal dose is particularly difficult to estimate when the fetus is exposed partially or totally to scatter radiation from images taken in other locations of the mother's body. A method to reliably estimate fetal dose has been developed by using template based input files for the Monte Carlo radiation transport code MCNP. Female patient phantoms at 0, 3, 6, and 9 months of pregnancy and source terms for common diagnostic tube potentials are used to rapidly build an input file for MCNP. The phantoms can be easily modified to fit patient shape. The geometry and beam location for each type of image acquired (i.e. fluoroscopy, spot filming, etc.) is verified by the use of a 3D visualization code (Sabrina). MCNP is then run to estimate the dose to the embryo/fetus and the exposure to skin entrance (ESE) for the beam being modeled. The actual ESE for the beam is then measured with ion chambers and the fetal dose is determined from the MCNP supplied ratio of ESE to fetal dose. Runs are made for each type of imaging and the doses are summed for the total fetal dose. For most procedures, the method can provide an estimate of the fetal dose within one day of the study. The method can also be used to prospectively model a study in order to choose imaging sequences that will minimize fetal dose.

Biophysical Phenomena↗

PubMed1999

Bayesian phylogenetic inference via Markov chain Monte Carlo methods.

We derive a Markov chain to sample from the posterior distribution for a phylogenetic tree given sequence information from the corresponding set of organisms, a stochastic model for these data, and a prior distribution on the space of trees. A transformation of the tree into a canonical cophenetic matrix form suggests a simple and effective proposal distribution for selecting candidate trees close to the current tree in the chain. We illustrate the algorithm with restriction site data on 9 plant species, then extend to DNA sequences from 32 species of fish. The algorithm mixes well in both examples from random starting trees, generating reproducible estimates and credible sets for the path of evolution.

Algorithms↗

PubMed2006

Thermodynamic properties of Ag2O--B2O3 glasses by a modified scale-transformed energy space sampling Monte Carlo method.

The density of states of Ag(2)O--B(2)O(3) glasses has been calculated by using a modified scale-transformed energy space sampling algorithm. This algorithm combines the scale-transformed energy space sampling algorithm and the Wang-Landau method. It is shown how the two algorithms can be combined to improve the efficiency of calculation. The thermodynamic properties, in particular the specific heat C(V), of the above-mentioned glass system is studied. At temperatures above 80 K, the value of specific heat C(v) is close to 22 J/mol/K. At low temperatures, the deviations of C(v) from a T(3) behavior are discernible, that is, C(v)/T(3) exhibits a hump at T = 7 K, which is in good agreement with the reported experimental behavior.

Algorithms↗

PubMed2006

A Monte Carlo method to calculate the average solid angle subtended by a right cylinder to a source that is circular or rectangular, plane or thick, at any position and orientation.

This note describes the development of a short program for a personal computer to calculate the solid angle subtended by a right cylinder detector to a circular or rectangular, plane or thick source at any position and orientation to the cylinder. The program also calculates the number of hits on the cylinder side and on each end, and the average pathlength through the detector volume (assuming no scattering or absorption). The current performance of personal computers makes it realistic to model the order of 10(9) simulations of radiation emission and achieve accuracies of solid angle estimates typically better than 0.03%.

Algorithms↗

PubMed1996

[Dynamics of the haplotype frequencies in populations: study using the Monte Carlo method].

A program that simulates random genetic drift, random mating, recombination, natural selection, and mutation process was developed to study the influence of these processes on the evolutionary dynamics of haplotype frequencies in populations. The program can track nine sites, each including up to 15 alleles. The program application was illustrated by the study of frequency dynamics in the HOXB haplotypes (17q) in different populations. The simulation results confirmed the hypothesis, which was proposed on the basis of the experimental data, that, in the absence of recurrent mutations, population mixing, and natural selection, the harmonic mean of the effective population size from the moment of New World colonization up to now was more than 1000.

Alleles↗