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Results for “Monte Carlo Method”

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PubMed1987

Comparison of measured and calculated internal absorbed doses in a heterogeneous phantom.

The experimental validity of the MIRD (Medical Internal Radiation Dose Committee of the Society of Nuclear Medicine) internal-dose calculations was investigated. Internal radiation doses were measured in a phantom representing the MIRD mathematical phantom using a newly developed volumetric tissue-equivalent dose meter that could be moulded to reproduce the geometry of the phantom's mathematical organs. The MIRD Monte Carlo computer code ALGAM was adapted to simulate the experimental conditions and was run for each calculation with 60,000 photon histories. The experimental data and the theoretical calculations were compared for different combinations of six source organs and seven target organs using 60Co as the source of radiation. The results of this comparison indicated agreement between measured and calculated doses when the uncertainties associated with both techniques are considered. However, statistical analysis of the data also gave an indication that the Monte Carlo method might overestimate the internal absorbed doses since the agreement with the experimental data was found to be in one direction.

Cobalt Radioisotopes↗

PubMed1997

Enzyme-inhibitor association thermodynamics: explicit and continuum solvent studies.

Studying the thermodynamics of biochemical association reactions at the microscopic level requires efficient sampling of the configurations of the reactants and solvent as a function of the reaction pathways. In most cases, the associating ligand and receptor have complementary interlocking shapes. Upon association, loosely connected or disconnected solvent cavities at and around the binding site are formed. Disconnected solvent regions lead to severe statistical sampling problems when simulations are performed with explicit solvent. It was recently proposed that, when such limitations are encountered, they might be overcome by the use of the grand canonical ensemble. Here we investigate one such case and report the association free energy profile (potential of mean force) between trypsin and benzamidine along a chosen reaction coordinate as calculated using the grand canonical Monte Carlo method. The free energy profile is also calculated for a continuum solvent model using the Poisson equation, and the results are compared to the explicit water simulations. The comparison shows that the continuum solvent approach is surprisingly successful in reproducing the explicit solvent simulation results. The Monte Carlo results are analyzed in detail with respect to solvation structure. In the binding site channel there are waters bridging the carbonyl oxygen groups of Asp189 with the NH2 groups of benzamidine, which are displaced upon inhibitor binding. A similar solvent-bridging configuration has been seen in the crystal structure of trypsin complexed with bovine pancreatic trypsin inhibitor. The predicted locations of other internal waters are in very good agreement with the positions found in the crystal structures, which supports the accuracy of the simulations.

Benzamidines↗

PubMed2003

A framework for a streamline-based probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements.

PURPOSE: To establish a general methodology for quantifying streamline-based diffusion fiber tracking methods in terms of probability of connection between points and/or regions. MATERIALS AND METHODS: The commonly used streamline approach is adapted to exploit the uncertainty in the orientation of the principal direction of diffusion defined for each image voxel. Running the streamline process repeatedly using Monte Carlo methods to exploit this inherent uncertainty generates maps of connection probability. Uncertainty is defined by interpreting the shape of the diffusion orientation profile provided by the diffusion tensor in terms of the underlying microstructure. RESULTS: Two candidates for describing the uncertainty in the diffusion tensor are proposed and maps of probability of connection to chosen start points or regions are generated in a number of major tracts. CONCLUSION: The methods presented provide a generic framework for utilizing streamline methods to generate probabilistic maps of connectivity.

Anisotropy↗

PubMed1999

Fission converter and metal-oxide-semiconductor field effect transistor study of thermal neutron flux distribution in an epithermal neutron therapy beam.

The depth distribution of the thermal neutron flux is a major factor in boron neutron capture therapy (BNCT) in determining the efficiency of cell sterilization. In this paper the fission detector method is developed and applied to measure the in-phantom thermal neutron flux depth distribution. Advantages of the fission detector include small size, direct measurement of thermal neutron flux in a mixed radiation field of BNCT beam, self-calibration, and the possibility of on-line measurement. The measurements were performed at epithermal a BNCT facility. The experimental results were compared with the thermal neutron flux calculated by the Monte Carlo method and found to be in good agreement.

Biophysical Phenomena↗

PubMed1997

Estimating residence times and their associated errors in patient absorbed-dose calculation.

OBJECTIVE: An approach for estimating organ residence times (tau) and their errors in patient internal emitter radiation dosage calculations has been determined. METHODS: Using a modeling algorithm and its associated parameters, chimeric anti-CEA monoclonal antibody (cT84.66) patient organ uptake data and residence times of source organ activity were calculated. Through the covariance matrix of the model's parameters and subsequent Monte Carlo simulations, errors in organ residence time (gamma tau) also were estimated RESULTS: These relative tau errors were found to be model-dependent; increasing as the number of organs being simultaneously modeled in a set of two patients being considered for 90Y-cT84.66 radioimmunotherapy. CONCLUSION: Use of modeling and Monte Carlo methods provide a general, direct procedure for calculating the degree of accuracy of activity integrals and other mathematical functions of kinetic variables.

Algorithms↗

PubMed2004

The importance of accounting for the uncertainty of published prognostic model estimates.

OBJECTIVES: Reported is the importance of properly reflecting uncertainty associated with prognostic model estimates when calculating the survival benefit of a treatment or technology, using liver transplantation as an example. METHODS: Monte Carlo simulation techniques were used to account for the uncertainty of prognostic model estimates using the standard errors of the regression coefficients and their correlations. These methods were applied to patients with primary biliary cirrhosis undergoing liver transplantation using a prognostic model from a historic cohort who did not undergo transplantation. The survival gain over 4 years from transplantation was estimated. RESULTS: Ignoring the uncertainty in the prognostic model, the estimated survival benefit of liver transplantation was 16.7 months (95 percent confidence interval [CI], 13.5 to 20.1), and was statistically significant (p < .001). After adjusting for model uncertainty using the standard errors of the regression coefficients, the estimated survival benefit was 17.5 months (95 percent CI, -3.9 to 38.5) and was no longer statistically significant. An additional adjustment for the correlation between regression coefficients widened the 95 percent confidence interval slightly: the estimated survival benefit was 17.0 months (95 percent CI: -4.6 to 38.6). CONCLUSIONS: It is important that the precision of regression coefficients is available for users of published prognostic models. Ignoring this additional information substantially underestimates uncertainty, which can then impact misleadingly on policy decisions.

Cohort Studies↗

PubMed2002

Using stochastic risk assessment in setting information priorities for managing dioxin impact from a municipal waste incinerator.

The objectives of this study were to assess site-specific carcinogenic risk of incinerator-emitted dioxins in a manner reflecting pollutant transfer across multimedia and multi-pathways. The study used site-specific environmental and exposure information and combined the Monte Carlo method with multimedia modeling to produce probability distributions of risk estimates. The risk estimates were further categorized by contaminated environmental media and exposure pathways that are experienced by human receptors in order to pinpoint significant sources of risk. Rank correlation coefficients were also calculated along with the Monte Carlo sampling to identify key factors that influenced estimation of risk. The results showed that ingestion accounted for more than 90% of the total risk and that risk control on ingestion of eggs, aboveground vegetables, and poultry should receive priority. It was also found that variation of parameters with variability accounted for around 35% of the total risk variance, while uncertainty contributed to the remaining 65%. Intake rates of aboveground vegetables, eggs, and poultry were the key parameters with the largest contribution to variance. In addition, sufficient sampling and analysis of dioxin contents in eggs, aboveground vegetables, poultry, soil, and fruit should be performed to improve risk estimation because the variation in concentrations in these media accounted for the largest overall risk variance. Finally, focus should be placed on reduction of uncertainty associated with the risk estimation through ingestion of aboveground vegetables, eggs, poultry, fruit, and soil because the risk estimates associated with these exposure pathways had the largest variance.

Animals↗

PubMed2005

A diffusion quantum Monte Carlo study on the lowest singlet and triplet electronic states of BN molecule.

Ab initio calculation of both the lowest singlet and triplet electronic states of BN has been performed by the fixed-node Ornstein-Uhlenbeck diffusion quantum Monte Carlo method with the floating spherical Gaussian orbitals and spherical Gaussian geminals. The Monte Carlo calculation gives equilibrium bond lengths and equilibrium harmonic frequencies of 1.3317(7) A and 1529(7) cm(-1), respectively, for the lowest triplet state and 1.2751(7) A and 1709(8) cm(-1), respectively, for the lowest singlet state. Also, the Monte Carlo calculation reports an energy separation of 178(83) cm(-1) between the two electronic states and recommends the ground state is the lowest triplet state.

Journal Article↗

PubMed2005

Predicting the effect of various ISA penetration grades on pedestrian safety by simulation.

Intelligent speed adaption (ISA) is one type of vehicle-based intelligent transportation systems (ITS), which warns and regulates driving speed according to the speed limits of the roads. Early field studies showed that ISA could reduce general mean speed levels and their variances in different road environments. This paper studies the effects of various ISA penetration grades on pedestrian safety in a single lane road. A microscopic traffic simulation tool, TPMA, was further developed and used to implement different ISA penetration grades. Momentary spot speed and traffic flow data are first logged in the traffic simulation for later prediction of pedestrian safety. Then a hypothetical vehicle-pedestrian collision model is extended from early researches in order to estimate two safety indicators: probability of collision, and risk of death. Finally, Monte Carlo method is applied iteratively to compute those safety indices. The computational result shows that raising ISA penetration in traffic flow will reduce both the probability of mid-block collision between vehicle and pedestrian and the risk of death in the collision accidents. Furthermore, the decrease of the risk of death will be more prominent than that of the collision probability according to this method.

Acceleration↗

PubMed1994

A simplified amino acid potential for use in structure predictions of proteins.

A simplified description and a corresponding force field for polypeptides is introduced. Each amino acid residue is reduced to one interaction site, representing the backbone, and one or two side chain sites depending on its size and complexity. Site-site interactions are parameterized after a hydrophobicity criterium. The treatment of backbone sites is in addition designed to reproduce typical polypeptide hydrogen bonding patterns, as well as yielding conformations in accord with the allowed phi and psi angles through an effective angle potential. There are no explicit charges in the model. The derived energy functions, which are based on thermodynamic data and sterical consideration of allowed backbone conformations, correspond to the introduction of an effective potential. The model is tested on two small proteins, avian pancreatic polypeptide and a parathyroid hormone-related protein, by simulating folding from an initially extended state using Monte Carlo methods. The reduced amino acid description is able to satisfactorily reproduce the experimentally determined native structures.

Amino Acids↗

PubMed1992

Spontaneous regression of residual tumour burden: prediction by Monte Carlo simulation.

Current cancer treatment protocols are designed to release the tumour burden down to a small number of cells. In this study, we use Monte Carlo simulations to show that small populations of cells with intrinsic cell loss rates comparable to the cell loss rates observed clinically in human tumours, may regress spontaneously. Large populations of cells tend to grow under the same conditions of cell loss that result in extinction of small clones. Furthermore, minor variations in the intrinsic cell death probability near 0.50 result in large differences in the number of surviving cells calculated at the 100th generation. When Monte Carlo simulations of clonal growth resulted in clones with large populations (> 50 cells), the population as a whole behaved in a deterministic fashion (logarithmic growth) similar to those observed in clinically observed neoplasms and consistent with other published models of tumour growth. These findings provide a plausible explanation for the clinically observed failure of tumours to recur in instances where tumour burden remains following cancer therapy. The findings also demonstrate the usefulness of the Monte Carlo method to simulate biologic events in populations where the fate of each member of a population can be modeled probabilistically.

Cell Death↗

PubMed2002

Empirical description and Monte Carlo simulation of fast neutron pencil beams as basis of a treatment planning system.

The fast neutron beam, used for fast neutron therapy in Essen, is produced by the nuclear reaction of a 14 MeV cyclotron-based deuteron beam on a thick beryllium target. The resulting neutron beam has a continuous energy spectrum with a mean and a maximum energy equal to 5.5 and 18 MeV, respectively. The dose delivered to the patient is computed by a treatment planning system (TPS) based on an empirical model, in which the dose components (neutron and photon) are described by analytical functions. In order to improve the dose calculation, and thus to use the fast neutron beam for other applications (e.g., Boron Neutron Capture Enhancement of Fast Neutron Therapy), in this work we aim to develop a new TPS. For this purpose, a model based on pencil beams of mono-energetic neutrons has been created. The neutron energy ranged from 0.25 MeV up to 17.25 MeV by steps of 0.5 MeV in order to cover the energy range of the Essen facility. The Monte Carlo method was then used to simulate the transport of neutrons within such pencil beams in a homogeneous water phantom. By using Monte Carlo techniques, it is possible to distinguish the energy deposition due to a primary collision in water to that due to scattered neutrons. The energy deposition due to pencil beams of 2.224 MeV photons, coming from hydrogen neutron capture reaction in the phantom or in the collimator, was also determined. In order to complete this work, air filled cylinders have been introduced in the water phantom. It is shown that the resulting depth dose curves for primary neutrons can be easily derived using the homogeneous phantom, and that the description of the effect on scattered neutron dose distribution is more complex. In this work we demonstrate the relevance of Monte Carlo simulations of mono-energetic neutron pencil beams for purposes of neutron treatment planning. Some additional work is still required to describe a clinical situation (continuous energy neutron spectrum) as well as to experimentally validate the method described here.

Adipose Tissue↗

PubMed1989

A nonlinear least squares program, MULTI(FILT), based on fast inverse Laplace transform for microcomputers.

A nonlinear curve fitting program MULTI(FILT) into which the fast inverse Laplace transform (FILT) is incorporated was developed on a microcomputer. FILT is an algorithm for the numerical inversion of Laplace-transformed equations (image equations) to generate the corresponding real time courses. The pharmacokinetic models can be defined in the form of Laplace-transformed equations as a subroutine in MULTI(FILT). MULTI(FILT) achieves the numerical inversion of the defined image equations according to FILT and the subsequent curve-fitting of the inverse-transformed time courses to the experimental data points to estimate the pharmacokinetic parameters by the nonlinear least-squares method. MULTI(FILT) has a function to impose constraints on the pharmacokinetic parameters. In order to verify the reliability of MULTI(FILT), the pharmacokinetic parameters estimated by MULTI(FILT) were compared with those by MULTI using 100 time courses which were artificially generated according to the Monte Carlo method, based on data for theophylline and bishydroxycoumarin. The estimated pharmacokinetic parameters by MULTI(FILT) agreed with those by MULTI. Thus, it is suggested that FILT, developed in the field of electronic technology, is also useful in the pharmacokinetic field.

Mathematics↗

PubMedDate not supplied

The albedo effect on neutron transmission probability.

The aim of this study is to evaluate the albedo effect on the neutron transmission probability through slab shields. For this reason we have considered an infinite homogeneous slab having a fixed thickness equal to 20 lambda (lambda is the mean free path of the neutron in the slab). This slab is characterized by the factor Ps (scattering probability) and contains a vacuum channel which is formed by two horizontal parts and an inclined one (David, M. C. (1962) Duc and Voids in shields. In Reactor Handbook, Vol. III, Part B, p. 166). The thickness of the vacuum channel is taken equal to 2 lambda. An infinite plane source of neutrons is placed on the first of the slab (left face) and detectors, having windows equal to 2 lambda, are placed on the second face of the slab (right face). Neutron histories are sampled by the Monte Carlo method (Booth, T. E. and Hendricks, J. S. (1994) Nuclear Technology 5) using exponential biasing in order to increase the Monte Carlo calculation efficiency (Levitt, L. B. (1968) Nuclear Science and Engineering 31, 500-504; Jehouani, A., Ghassoun, J. and Abouker, A. (1994) In Proceedings of the 6th International Symposium on Radiation Physics, Rabat, Morocco) and we have applied the statistical weight method which supposes that the neutron is born at the source with a unit statistical weight and after each collision this weight is corrected. For different values of the scattering probability and for different slopes of the inclined part of the channel we have calculated the neutron transmission probability for different positions of the detectors versus the albedo at the vacuum channel-medium interface. Some analytical representations are also presented for these transmission probabilities.

Monte Carlo Method↗

PubMed1999

A Bayesian hierarchical approach for combining case-control and prospective studies.

Motivated by the absolute risk predictions required in medical decision making and patient counseling, we propose an approach for the combined analysis of case-control and prospective studies of disease risk factors. The approach is hierarchical to account for parameter heterogeneity among studies and among sampling units of the same study. It is based on modeling the retrospective distribution of the covariates given the disease outcome, a strategy that greatly simplifies both the combination of prospective and retrospective studies and the computation of Bayesian predictions in the hierarchical case-control context. Retrospective modeling differentiates our approach from most current strategies for inference on risk factors, which are based on the assumption of a specific prospective model. To ensure modeling flexibility, we propose using a mixture model for the retrospective distributions of the covariates. This leads to a general nonlinear regression family for the implied prospective likelihood. After introducing and motivating our proposal, we present simple results that highlight its relationship with existing approaches, develop Markov chain Monte Carlo methods for inference and prediction, and present an illustration using ovarian cancer data.

Bayes Theorem↗

PubMed1990

How big is the universe of exons?

If genes have been assembled from exon subunits, the frequency with which exons are reused leads to an estimate of the size of the underlying exon universe. An exon database was constructed from available protein sequences, and homologous exons were identified on the basis of amino acid identity; statistically significant matches were determined by Monte Carlo methods. It is estimated that only 1000 to 7000 exons were needed to construct all proteins.

Amino Acid Sequence↗

PubMed2004

Analysis of histamine release assays using the Bootstrap.

The data from several types of bioassays is usually presented as a quotient as an intuitive parameter and a means of comparing results between experiments. For the example we considered here, we look at experiments with an experiment-wide negative control used to generate percent activity quotients from each experimental group. We asked if there was a valid means to statistically evaluate the transformed rather than the raw data. The experimental system chosen was a dose response of the agonist compound 48/80, which causes release of histamine from mast cells, thus providing test data from replicates of n=24. Descriptive statistics, the Ryan-Joiner test for normality of distribution of data, and normal probability plots confirm the normality of the distribution of data at each dose level. In parametric analysis, when the control group was treated as an errorless constant, there was a distinct consistent bias in the standard error of the data of 10% or less, which was not present if the control group's mean was treated as a variable with experimental error. This would be of minor interest in qualitative studies and might be safely ignored, but might be of considerable importance in quantitative assessments of activity using confidence intervals. When using Bootstrap estimates of standard error and probability plots of the bootstrap samples, the transformed data does not deviate significantly from normality. The standard, bias-corrected percentile limits (BCa), and empirical percentile methods gave very similar results when using resampling statistics to generate the transformed data from groups of n=6. Sample size can be as low as n=4 and still provide useful results. Thus, we have shown that resampling (i.e., bootstrap, Monte Carlo method, computer-intensive methods) can produce the data transform as well as provide confidence intervals using this type of raw data in small groups (n=4 to 6), giving improved statistical analysis of the transformed data (ratio estimates) without accepting a bias from methodology ignoring variation in the control group.

Animals↗

PubMed2005

The correction for attenuation due to measurement error: clarifying concepts and creating confidence sets.

The correction for attenuation due to measurement error (CAME) has received many historical criticisms, most of which can be traced to the limited ability to use CAME inferentially. Past attempts to determine confidence intervals for CAME are summarized and their limitations discussed. The author suggests that inference requires confidence sets that demarcate those population parameters likely to have produced an obtained value--rather than indicating the samples likely to be produced by a given population--and that most researchers tend to confuse these 2 types of confidence sets. Three different Monte-Carlo methods are presented, each offering a different way of examining confidence sets under the new conceptualization. Exploring the implications of these approaches for CAME suggests potential consequences for other statistics.

Humans↗