PubMed Health⌕ Search

SEARCH · PubMed Health

Results for “Monte Carlo Method”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 379 records · Page 21Linked to original sources

Method of Monte Carlo simulation verification in hadron therapy with non-tissue equivalent detectors.

In hadron therapy the spectra of secondary particles can be very broad in type and energy. The most accurate calculations of tissue equivalent (TE) absorbed dose and biological effect can be achieved using Monte Carlo (MC) simulations followed by the application of an appropriate radiobiological model. The verification of MC simulations is therefore an important quality assurance (QA) issue in dose planning. We propose a method of verification for MC dose calculations based on measurements of either the integral absorbed dose or the spectra of deposited energies from single secondary particles in non-TE material detectors embedded in a target of interest (phantom). This method was tested in boron neutron capture therapy and fast neutron therapy beams.

Algorithms↗

Dual scattering foil design for poly-energetic electron beams.

The laser wakefield acceleration (LWFA) mechanism can accelerate electrons to energies within the 6-20 MeV range desired for therapy application. However, the energy spectrum of LWFA-generated electrons is broad, on the order of tens of MeV. Using existing laser technology, the therapeutic beam might require a significant energy spread to achieve clinically acceptable dose rates. The purpose of this work was to test the assumption that a scattering foil system designed for a mono-energetic beam would be suitable for a poly-energetic beam with a significant energy spread. Dual scattering foil systems were designed for mono-energetic beams using an existing analytical formalism based on Gaussian multiple-Coulomb scattering theory. The design criterion was to create a flat beam that would be suitable for fields up to 25 x 25 cm2 at 100 cm from the primary scattering foil. Radial planar fluence profiles for poly-energetic beams with energy spreads ranging from 0.5 MeV to 6.5 MeV were calculated using two methods: (a) analytically by summing beam profiles for a range of mono-energetic beams through the scattering foil system, and (b) by Monte Carlo using the EGS/BEAM code. The analytic calculations facilitated fine adjustments to the foil design, and the Monte Carlo calculations enabled us to verify the results of the analytic calculation and to determine the phase-space characteristics of the broadened beam. Results showed that the flatness of the scattered beam is fairly insensitive to the width of the input energy spectrum. Also, results showed that dose calculated by the analytical and Monte Carlo methods agreed very well in the central portion of the beam. Outside the useable field area, the differences between the analytical and Monte Carlo results were small but significant, possibly due to the small angle approximation. However, these did not affect the conclusion that a scattering foil system designed for a mono-energetic beam will be suitable for a poly-energetic beam with the same central energy. Further studies of the dosimetric properties of LWFA-generated electron beams will be done using Monte Carlo methods.

Electrons↗

Theoretical estimates of the solid angle subtended by a dual diaphragm-detector assembly for alpha sources.

Knowledge of the solid angle subtended by a detector is essential for the determination of the activity of a radioactive source. This work investigates the influence of diaphragm and source diameter, and source to diaphragm distance, on the solid angle subtended by a dual opposed alpha diaphragm-detector assembly. Expressions published by Segre, Ruby, and others, and the Monte Carlo method are used. The analytical expressions consistently produced higher estimates than the Monte Carlo method for the solid angle.

Journal Article↗

Calculation of the characteristic ratio of randomly coiled poly(L-proline).

Allowing for rotation about the Calpha-C' bond (i.e., variation of psi) and for some degree of freedom about the peptide bond (i.e., small variations of omega), the characteristic ratios, (R2)o/nl2, of the form I (cis) and form II (trans) poly(L-proline) chain have been calculated by a Monte Carlo method in which the conformational energies were used as weighting factors. The Monte Carlo method enabled short-range interactions (beyond those involved in a single residue) to be taken into account. The effect of the presence of a small amount of one form (say cis in a trans-rich chain) on (R2)o/nl2 was also investigated. The results for the trans-rich form are in good agreement with values observed experimentally in solvents in which the poly(L-proline) chain is predominantly in form II; the presence of a small amount of cis residues reduces the characteristic ratio of the trans-rich form of poly(L-proline) significantly.

Dipeptides↗

Conformational analysis of the 20-residue membrane-bound portion of melittin by conformational space annealing.

The conformational space of the 20-residue membrane-bound portion of melittin has been investigated extensively with the conformational space annealing (CSA) method and the ECEPP/3 (Empirical Conformational Energy Program for Peptides) algorithm. Starting from random conformations, the CSA method finds that there are at least five different classes of conformations, within 4 kcal/mol, which have distinct backbone structures. We find that the lowest energy conformation of this peptide from previous investigations is not the global minimum-energy conformation (GMEC); but it belongs to the second lowest energy class of the five classes found here. In four independent runs, one conformation is found repeatedly as the lowest energy conformation of the peptide (two of the four lowest energy conformations are identical; the other two have essentially identical backbone conformations but slightly different side-chain conformations). We propose this conformation, whose energy is lower than that found previously by 1.9 kcal/mol, as the GMEC of the ECEPP/3 force field. The structure of the proposed GMEC is less helical and more compact than the previous one. It appears that the CSA method can find several classes of conformations of a 20-residue peptide starting from random conformations utilizing only its amino acid sequence information. The proposed GMEC has also been found with a modified electrostatically driven Monte Carlo method [D. R. Ripoll, A. Liwo, and H. A. Scheraga (1998) "New Developments of the Electrostatically Driven Monte Carlo Method: Test on the Membrane-Bound Portion of Melittin," Biopolymers, Vol. 46, pp. 117-126].

Algorithms↗

Refinements to the geometry factor used in the AAPM Task Group Report No. 43 necessary for brachytherapy dosimetry calculations. American Association of Physicists in Medicine.

Determination of the geometry factor is necessary for brachytherapy dosimetry calculations as recommended by the AAPM Task Group No. 43 (TG-43). The equivalence and errors associated with use of a point source approximation for an extended line segment source are examined. For all angles, the error using the point source approximation is less than 2% for distances in which the ratio of radius to active source length, (r/L), exceed about 3.6. A novel approach to determining the geometry factor using Monte Carlo methods is discussed in which the particle flux emanates from the active source and streams with no interactions occurring within the source or phantom. This method was performed for determining the geometry factor along the transverse axis for six brachytherapy sources. Differences in the geometry factor exceeding 2% between the point source approximation and that obtained using Monte Carlo methods occurred at distances ranging from 0.5 to 5 mm from the source center along the transverse plane. The merits of the Monte Carlo approach for solving the geometry factor are discussed in light of using a point or line source approximation for calculating additional brachytherapy dosimetry parameters.

Algorithms↗

Cool walking: a new Markov chain Monte Carlo sampling method.

Effective relaxation processes for difficult systems like proteins or spin glasses require special simulation techniques that permit barrier crossing to ensure ergodic sampling. Numerous adaptations of the venerable Metropolis Monte Carlo (MMC) algorithm have been proposed to improve its sampling efficiency, including various hybrid Monte Carlo (HMC) schemes, and methods designed specifically for overcoming quasi-ergodicity problems such as Jump Walking (J-Walking), Smart Walking (S-Walking), Smart Darting, and Parallel Tempering. We present an alternative to these approaches that we call Cool Walking, or C-Walking. In C-Walking two Markov chains are propagated in tandem, one at a high (ergodic) temperature and the other at a low temperature. Nonlocal trial moves for the low temperature walker are generated by first sampling from the high-temperature distribution, then performing a statistical quenching process on the sampled configuration to generate a C-Walking jump move. C-Walking needs only one high-temperature walker, satisfies detailed balance, and offers the important practical advantage that the high and low-temperature walkers can be run in tandem with minimal degradation of sampling due to the presence of correlations. To make the C-Walking approach more suitable to real problems we decrease the required number of cooling steps by attempting to jump at intermediate temperatures during cooling. We further reduce the number of cooling steps by utilizing "windows" of states when jumping, which improves acceptance ratios and lowers the average number of cooling steps. We present C-Walking results with comparisons to J-Walking, S-Walking, Smart Darting, and Parallel Tempering on a one-dimensional rugged potential energy surface in which the exact normalized probability distribution is known. C-Walking shows superior sampling as judged by two ergodic measures.

Journal Article↗

Hierarchical Bayesian modeling of spatially correlated health service outcome and utilization rates.

We present Bayesian hierarchical spatial models for spatially correlated small-area health service outcome and utilization rates, with a particular emphasis on the estimation of both measured and unmeasured or unknown covariate effects. This Bayesian hierarchical model framework enables simultaneous modeling of fixed covariate effects and random residual effects. The random effects are modeled via Bayesian prior specifications reflecting spatial heterogeneity globally and relative homogeneity among neighboring areas. The model inference is implemented using Markov chain Monte Carlo methods. Specifically, a hybrid Markov chain Monte Carlo algorithm (Neal, 1995, Bayesian Learning for Neural Networks; Gustafson, MacNab, and Wen, 2003, Statistics and Computing, to appear) is used for posterior sampling of the random effects. To illustrate relevant problems, methods, and techniques, we present an analysis of regional variation in intraventricular hemorrhage incidence rates among neonatal intensive care unit patients across Canada.

Bayes Theorem↗

Using robotics to fold proteins and dock ligands.

The problems of protein folding and ligand docking have been explored largely using molecular dynamics or Monte Carlo methods. These methods are very compute intensive because they often explore a much wider range of energies, conformations and time than necessary. In addition, Monte Carlo methods often get trapped in local minima. We initially showed that robotic motion planning permitted one to determine the energy of binding and dissociation of ligands from protein binding sites (Singh et al., 1999). The robotic motion planning method maps complicated three-dimensional conformational states into a much simpler, but higher dimensional space in which conformational rearrangements can be represented as linear paths. The dimensionality of the conformation space is of the same order as the number of degrees of conformational freedom in three-dimensional space. We were able to determine the relative energy of association and dissociation of a ligand to a protein by calculating the energetics of interaction for a few thousand conformational states in the vicinity of the protein and choosing the best path from the roadmap. More recently, we have applied roadmap planning to the problem of protein folding (Apaydin et al., 2002a). We represented multiple conformations of a protein as nodes in a compact graph with the edges representing the probability of moving between neighboring states. Instead of using Monte Carlo simulation to simulate thousands of possible paths through various conformational states, we were able to use Markov methods to calculate the steady state occupancy of each conformation, needing to calculate the energy of each conformation only once. We referred to this Markov method of representing multiple conformations and transitions as stochastic roadmap simulation or SRS. We demonstrated that the distribution of conformational states calculated with exhaustive Monte Carlo simulations asymptotically approached the Markov steady state if the same Boltzman energy distribution was used in both methods. SRS permits one to calculate contributions from all possible paths simultaneously with far fewer energy calculations than Monte Carlo or molecular dynamics methods. The SRS method also permits one to represent multiple unfolded starting states and multiple, near-native, folded states and all possible paths between them simultaneously. The SRS method is also independent of the function used to calculate the energy of the various conformational states. In a paper to be presented at this conference (Apaydin et al., 2002b) we have also applied SRS to ligand docking in which we calculate the dynamics of ligand-protein association and dissociation in the region of various binding sites on a number of proteins. SRS permits us to determine the relative times of association to and dissociation from various catalytic and non-catalytic binding sites on protein surfaces. Instead of just following the best path in a roadmap, we can calculate the contribution of all the possible binding or dissociation paths and their relative probabilities and energies simultaneously.

Algorithms↗

Theoretical study of transition state structure and reaction enthalpy of the F + H2-->HF + H reaction by a diffusion quantum Monte Carlo approach.

Ab initio calculations of transition state structure and reaction enthalpy of the F + H2-->HF + H reaction has been carried out by the fixed-node diffusion quantum Monte Carlo method in this study. The Monte Carlo sampling is based on the Ornstein-Uhlenbeck random walks guided by a trial wave function constructed from the floating spherical Gaussian orbitals and spherical Gaussian geminals. The Monte Carlo calculated barrier height of 1.09(16) kcal/mol is consistent with the experimental values, 0.86(10)/1.18(10) kcal/mol, and the calculated value from the multireference-type coupled-cluster (MRCC) calculation with the aug-cc-pVQZ(F)/cc-pVQZ(H) basis set, 1.11 kcal/mol. The Monte Carlo-based calculation also gives a similar value of the reaction enthalpy, -32.00(4) kcal/mol, compared with the experimental value, -32.06(17) kcal/mol, and the calculated value from a MRCC/aug-cc-pVQZ(F)/cc-pVQZ(H) calculation, -31.94 kcal/mol. This study clearly indicates a further application of the random-walk-based approach in the field of quantum chemical calculation.

Journal Article↗

Metropolis sampling in pedigree analysis.

This paper reviews and develops the applications of Markov chain Monte Carlo methods in pedigree analysis, with particular stress on the Metropolis algorithm. In likelihood based genetic analyses, standard deterministic algorithms often fail because of the computational complexity of the observed pedigree data under a proposed genetic model. The new Monte Carlo methods permit approximate maximum likelihood estimation in the presence of such complexity. Monte Carlo implementation of the EM algorithm is the key to successful maximum likelihood analysis. Gibbs sampling and the Metropolis algorithm are alternative ways of defining Markov chains for performing the E step of the EM algorithm. Two applications illustrate the power and simplicity of the Metropolis algorithm. One of these applications involves a discrete model for variance component analysis of quantitative traits; the other application involves a Monte Carlo version of location scores for multipoint linkage analysis.

Algorithms↗

A finite element approach for modeling photon transport in tissue.

The use of optical radiation in medical physics is important in several fields for both treatment and diagnosis. In all cases an analytic and computable model of the propagation of radiation in tissue is essential for a meaningful interpretation of the procedures. A finite element method (FEM) for deriving photon density inside an object, and photon flux at its boundary, assuming that the photon transport model is the diffusion approximation to the radiative transfer equation, is introduced herein. Results from the model for a particular case are given: the calculation of the boundary flux as a function of time resulting from a delta-function input to a two-dimensional circle (equivalent to a line source in an infinite cylinder) with homogeneous scattering and absorption properties. This models the temporal point spread function of interest in near infrared spectroscopy and imaging. The convergence of the FEM results are demonstrated, as the resolution of the mesh is increased, to the analytical expression for the Green's function for this system. The diffusion approximation is very commonly adopted as appropriate for cases which are scattering dominated, i.e., where mu s >> mu a, and results from other workers have compared it to alternative models. In this article a high degree of agreement with a Monte Carlo method is demonstrated. The principle advantage of the FE method is its speed. It is in all ways as flexible as Monte Carlo methods and in addition can produce photon density everywhere, as well as flux on the boundary. One disadvantage is that there is no means of deriving individual photon histories.

Health Physics↗

Linkage analysis with sequential imputation.

Multilocus calculations, using all available information on all pedigree members, are important for linkage analysis. Exact calculation methods in linkage analysis are limited in either the number of loci or the number of pedigree members they can handle. In this article, we propose a Monte Carlo method for linkage analysis based on sequential imputation. Unlike exact methods, sequential imputation can handle large pedigrees with a moderate number of loci in its current implementation. This Monte Carlo method is an application of importance sampling, in which we sequentially impute ordered genotypes locus by locus, and then impute inheritance vectors conditioned on these genotypes. The resulting inheritance vectors, together with the importance sampling weights, are used to derive a consistent estimator of any linkage statistic of interest. The linkage statistic can be parametric or nonparametric; we focus on nonparametric linkage statistics. We demonstrate that accurate estimates can be achieved within a reasonable computing time. A simulation study illustrates the potential gain in power using our method for multilocus linkage analysis with large pedigrees. We simulated data at six markers under three models. We analyzed them using both sequential imputation and GENEHUNTER. GENEHUNTER had to drop between 38-54% of pedigree members, whereas our method was able to use all pedigree members. The power gains of using all pedigree members were substantial under 2 of the 3 models. We implemented sequential imputation for multilocus linkage analysis in a user-friendly software package called SIMPLE.

Genetic Linkage↗

Monte Carlo simulations in SPET and PET.

Monte Carlo methods are extensively used in Nuclear Medicine to tackle a variety of problems that are difficult to study by an experimental or analytical approach. A review of the most recent tools allowing application of Monte Carlo methods in single photon emission tomography (SPET) and positron emission tomography (PET) is presented. To help potential Monte Carlo users choose a code, we present advantages and disadvantages of the different types of Monte Carlo codes currently available for SPET and PET, discuss common and specific features of the codes, classify the codes with respect to these features, comment key properties for a code to be appropriate for a given purpose and, at last, we consider the possibility of going towards a standardisation of the description of the codes which could facilitate their comparison.

Computer Simulation↗

Comparison of the Batho, ETAR and Monte Carlo dose calculation methods in CT based patient models.

This paper shows the contribution that Monte Carlo methods make in regard to dose distribution calculations in CT based patient models and the role it plays as a gold standard to evaluate other dose calculation algorithms. The EGS4 based BEAM code was used to construct a generic 8 MV accelerator to obtain a series of x-ray field sources. These were used in the EGS4 based DOSXYZ code to generate beam data in a mathematical water phantom to set up a beam model in a commercial treatment planning system (TPS), CADPLAN V.2.7.9. Dose distributions were calculated with the Batho and ETAR inhomogeneity correction algorithms in head/sinus, lung, and prostate patient models for 2 x 2, 5 x 5, and 10 X 10 cm2 open x-ray beams. Corresponding dose distributions were calculated with DOSXYZ that were used as a benchmark. The dose comparisons are expressed in terms of 2D isodose distributions, percentage depth dose data, and dose difference volume histograms (DDVH's). Results indicated that the Batho and ETAR methods contained inaccuracies of 20%-70% in the maxillary sinus region in the head model. Large lung inhomogeneities irradiated with small fields gave rise to absorbed dose deviations of 10%-20%. It is shown for a 10 x 10 cm2 field that DOSXYZ models lateral scatter in lung that is not present in the Batho and ETAR methods. The ETAR and Batho methods are accurate within 3% in a prostate model. We showed how the performance of these inhomogeneity correction methods can be understood in realistic patient models using validated Monte Carlo codes such as BEAM and DOSXYZ.

Algorithms↗

A comparison of the Low Mode and Monte Carlo conformational search methods.

The Low Mode (LM) and Monte Carlo (MC) conformational search methods were compared on three diverse molecular systems; (4R, 5S, 6S, 7R)-hexahydro-5,6-dihydroxy-1,3,4,7-tetrakis(phenylmethyl)-2H-1,3-diazapin-2-one (1), 2-methoxy-2-phenyl-2-triflouromethyl-N-alpha-methyl benzyl propanamide (2) and a trimeric 39-membered polyazamacrolide (3). We find that either method, or a combination of the methods, is equally efficient at searching the conformational space of the smaller molecular systems while a 50:50 hybrid of Low Mode and Monte Carlo is most efficient at searching the space of the larger molecular system.

Algorithms↗

Fractal structure and conformational entropy of protein chain.

The structures of 25 proteins arbitrarily chosen are investigated by fractal geometry, and their fractal dimensions (Df) and conformational entropies S(NO) are calculated by Havlin-Ben Avraham and Monte Carlo method, respectively. Comparison of the Df and S(NO) give the relation: Df = 1.532 - 3.00 x 10(-4) S(NO). The entropy data obtained by Monte Carlo method for the chain of random self-avoiding walks confirm the prediction of renormalization group: S(NO) = 1.544NO + 0.1667 In NO + 0.1570 where NO is the number of residues in a protein chain. Both the Df and S(NO) reflect the conformational properties of a protein molecular chain. The idea resulting from the present communication suggests that the thermodynamic behaviours of proteins may be related to multifractals.

Mathematics↗

Information dynamics in carcinogenesis and tumor growth.

The storage and transmission of information is vital to the function of normal and transformed cells. We use methods from information theory and Monte Carlo theory to analyze the role of information in carcinogenesis. Our analysis demonstrates that, during somatic evolution of the malignant phenotype, the accumulation of genomic mutations degrades intracellular information. However, the degradation is constrained by the Darwinian somatic ecology in which mutant clones proliferate only when the mutation confers a selective growth advantage. In that environment, genes that normally decrease cellular proliferation, such as tumor suppressor or differentiation genes, suffer maximum information degradation. Conversely, those that increase proliferation, such as oncogenes, are conserved or exhibit only gain of function mutations. These constraints shield most cellular populations from catastrophic mutator-induced loss of the transmembrane entropy gradient and, therefore, cell death. The dynamics of constrained information degradation during carcinogenesis cause the tumor genome to asymptotically approach a minimum information state that is manifested clinically as dedifferentiation and unconstrained proliferation. Extreme physical information (EPI) theory demonstrates that altered information flow from cancer cells to their environment will manifest in-vivo as power law tumor growth with an exponent of size 1.62. This prediction is based only on the assumption that tumor cells are at an absolute information minimum and are capable of "free field" growth that is, they are unconstrained by external biological parameters. The prediction agrees remarkably well with several studies demonstrating power law growth in small human breast cancers with an exponent of 1.72+/-0.24. This successful derivation of an analytic expression for cancer growth from EPI alone supports the conceptual model that carcinogenesis is a process of constrained information degradation and that malignant cells are minimum information systems. EPI theory also predicts that the estimated age of a clinically observed tumor is subject to a root-mean square error of about 30%. This is due to information loss and tissue disorganization and probably manifests as a randomly variable lag phase in the growth pattern that has been observed experimentally. This difference between tumor size and age may impose a fundamental limit on the efficacy of screening based on early detection of small tumors. Independent of the EPI analysis, Monte Carlo methods are applied to predict statistical tumor growth due to perturbed information flow from the environment into transformed cells. A "simplest" Monte Carlo model is suggested by the findings in the EPI approach that tumor growth arises out of a minimally complex mechanism. The outputs of large numbers of simulations show that (a) about 40% of the populations do not survive the first two-generations due to mutations in critical gene segments; but (b) those that do survive will experience power law growth identical to the predicted rate obtained from the independent EPI approach. The agreement between these two very different approaches to the problem strongly supports the idea that tumor cells regress to a state of minimum information during carcinogenesis, and that information dynamics are integrally related to tumor development and growth.

Information Theory↗