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Results for “Monte Carlo Method”

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PubMed1989

Evaluation of uncertainties for parameters in binding studies: the sum-of-squares profile and Monte Carlo estimation.

Methods for characterization and evaluation of uncertainties in the parameter values for binding experiments are presented. A sum-of-squares profile is defined and illustrated. Sum-of-squares profiles give a qualitative description of both the uncertainties and correlation of parameters. The Monte Carlo method is developed as an accurate means of evaluating uncertainties in parameter values for nonlinear models. Examples are given for both actual and synthetic data.

Binding Sites↗

PubMed1997

Design of a knowledge-based force field for off-lattice simulations of protein structure.

Prediction of protein structure from amino-acid sequence still continues to be an unsolved problem of theoretical molecular biology. One approach to solve it is to construct an appropriate (free) energy function that recognizes the native structures of some selected proteins (whose native structures are known) as the ones distinctively lowest in (free) energy and then to carry out a search of the lowest-energy structure of a new protein. In order to reduce the complexity of the problem and the cost of energy evaluation, the so-called united-residue representation of the polypeptide chain is often applied, in which each amino-acid residue is represented by only a few interaction sites. Once the global energy minimum of the simplified chain has been found, the all-atom structure can easily and reliably be constructed. The search of the lowest-energy structure is usually carried out by means of Monte Carlo methods, though use of more efficient global-optimization methods, especially those of deformation of original energy surface is potentially promising. Monte Carlo search of the conformational space can be accelerated greatly, if the chain is superposed on a discrete lattice (the on-lattice approach). On the other hand, the on-lattice approach prohibits the use of many efficient global-optimization methods, because they require both energy and its space derivatives. The on-lattice methods in which the chain is embedded in the continuous 3D space are, therefore, also worth developing. In this paper we summarize the work on the design and implementation of an off-lattice united-residue force field that is underway in our group, in cooperation with Professor HA. Scheraga of Cornell University, U.S.A.

Models, Molecular↗

PubMed1998

A general framework for random effects survival analysis in the Cox proportional hazards setting.

The use of random effects modeling in statistics has increased greatly in recent years. The introduction of such modeling into event-time analysis has proceeded more slowly, however. Previously, random effects models for survival data have either required assumptions regarding the form of the baseline hazard function or restrictions on the classes of models that can be fit. In this paper, we develop a method of random effect analysis of survival data, the hierarchical Cox model, that is an extension of Cox's original formulation in that the baseline hazard function remains unspecified. This method also allows an arbitrary distribution for the random effects. We accomplish this using Markov chain Monte Carlo methods in a Bayesian setting. The method is illustrated with three models for a dataset with times to multiple occurrences of mammory tumors for 48 rats treated with a carcinogen and then randomized to either treatment or control. This analysis is more satisfying than standard approaches, such as studying the first event for each subject, which does not fully use the data, or assuming independence, which in this case would overestimate the precision.

Animals↗

PubMed2001

Optimization of ground- and excited-state wave functions and van der Waals clusters.

A quantum Monte Carlo method is introduced to optimize excited-state trial wave functions. The method is applied in a correlation function Monte Carlo calculation to compute ground- and excited-state energies of bosonic van der Waals clusters of up to seven particles. The calculations are performed using trial wave functions with general three-body correlations.

Journal Article↗

PubMed1999

Simulation of peptide folding with explicit water--a mean solvation method.

A new approach to efficiently calculate solvent effect in computer simulation of macromolecular systems has been developed. Explicit solvent molecules are included in the simulation to provide a mean solvation force for the solute conformational search. Simulations of an alanine dipeptide in aqueous solution showed that the new approach is significantly more efficient than conventional molecular dynamics method in conformational search, mainly because the mean solvation force reduced the solvent damping effect. This approach allows the solute and solvent to be simulated separately with different methods. For the macromolecule, the rigid fragment constraint dynamics method we developed previously allows large time-steps. For the solvent, a combination of a modified force-bias Monte Carlo method and a preferential sampling can efficiently sample the conformational space. A folding simulation of a 16-residue peptide in water showed high efficiency of the new approach.

Computer Simulation↗

PubMed2005

Estimation of flux distributions with Monte Carlo functional expansion tallies.

Monte Carlo methods provide a powerful technique for estimating the average radiation flux in a volume (or across a surface) in cases where analytical solutions may not be possible. Unfortunately, Monte Carlo simulations typically provide only integral results and do not offer any further details about the distribution of the flux with respect to space, angle, time or energy. In the functional expansion tally (FET) a Monte Carlo simulation is used to estimate the functional expansion coefficients for flux distributions with respect to an orthogonal set of basis functions. The expansion coefficients are then used in post-processing to reconstruct a series approximation to the true distribution. Discrete event FET estimators are derived and their application in estimating radiation flux or current distributions is demonstrated. Sources of uncertainty in the FET are quantified and estimators for the statistical and truncation errors are derived. Numerical results are presented to support the theoretical development.

Algorithms↗

PubMedDate not supplied

Activity measurements with radionuclide calibrators in the Czech Republic.

Since radionuclide calibrators are used in nuclear medicine for the determination of the activity of radiopharmaceuticals administered to patients, it is important to ensure their long-term accuracy. Results of the checks performed in the Czech Republic during the year 2002 are given, together with a short overview of previous years. For the CMI 4pigamma ionization chamber, against which all the calibrators are checked, we calculated the response function and basic characteristics by a Monte Carlo method, using the MCNP4C code.

Algorithms↗

PubMed1999

New Monte Carlo algorithms for protein folding.

Over the past three decades, a number of powerful simulation algorithms have been introduced to the protein folding problem. For many years, the emphasis has been placed on how to both overcome the multiple minima problem and find the conformation with the global minimum potential energy. Since the new view of the protein folding mechanism (based on the free energy landscape of the protein system) arose in the past few years, however, it is now of interest to obtain a global knowledge of the phase space, including the intermediate and denatured states of proteins. Monte Carlo methods have proved especially valuable for these purposes. As well as new, powerful optimization techniques, novel algorithms that can sample much a wider phase space than conventional methods have been established.

Algorithms↗

PubMed2003

Monte Carlo study of TLD measurements in air cavities.

Thermoluminescent dosimeters (TLDs) are used for verification of the delivered dose during IMRT treatment of head and neck carcinomas. The TLDs are put into a plastic tube, which is placed in the nasal cavities through the treated volume. In this study, the dose distribution to a phantom having a cylindrical air cavity containing a tube was calculated by Monte Carlo methods and the results were compared with data from a treatment planning system (TPS) to evaluate the accuracy of the TLD measurements. The phantom was defined in the DOSXYZnrc Monte Carlo code and calculations were performed with 6 MV fields, with the TLD tube placed at different positions within the cylindrical air cavity. A similar phantom was defined in the pencil beam based TPS. Differences between the Monte Carlo and the TPS calculations of the absorbed dose to the TLD tube were found to be small for an open symmetrical field. For a half-beam field through the air cavity, there was a larger discrepancy. Furthermore, dose profiles through the cylindrical air cavity show, as expected, that the treatment planning system overestimates the absorbed dose in the air cavity. This study shows that when using an open symmetrical field, Monte Carlo calculations of absorbed doses to a TLD tube in a cylindrical air cavity give results comparable to a pencil beam based treatment planning system.

Algorithms↗

PubMedDate not supplied

Uncertainty analysis of field placement error measurements using digital portal and simulation image correlations.

An uncertainty analysis of a field placement error measurement method using correlations between digital portal and simulation images has been performed. This analysis used the Monte Carlo method to simulate random uncertainties arising in image registration and portal field edge detection. The uncertainty analysis used data from a field placement error study to predict the dependences of the measurement method upon image matchpoint number and spatial distribution, image registration, and uncertainties arising in the detection and description of the field edge in a portal image. It was shown that the uncertainty in the field registration had the most significant effect upon the measurement uncertainty, whereas the number of matchpoints had an extremely limited effect (beyond the minimum required for the mathematical procedure used in registration). In contrast, it was shown that an accurate field placement error measurement required that the number of pixels describing a field edge used for comparisons should exceed 20, thus automatically setting a minimum field length necessary for field placement comparisons. It was also shown that the spatial uniformity of the matchpoints in an image pair had a limited effect upon the field placement error measurement, provided that the points are distributed over about 15% of the image area.

Humans↗

PubMed2004

A 3-D computational model predicts that cell deformation affects selectin-mediated leukocyte rolling.

Leukocyte recruitment to sites of inflammation is initiated by their tethering and rolling on the activated endothelium under flow. Even though the fast kinetics and high tensile strength of selectin-ligand bonds are primarily responsible for leukocyte rolling, experimental evidence suggests that cellular properties such as cell deformability and microvillus elasticity actively modulate leukocyte rolling behavior. Previous theoretical models either assumed cells as rigid spheres or were limited to two-dimensional representations of deformable cells with deterministic receptor-ligand kinetics, thereby failing to accurately predict leukocyte rolling. We therefore developed a three-dimensional computational model based on the immersed boundary method to predict receptor-mediated rolling of deformable cells in shear flow coupled to a Monte Carlo method simulating the stochastic receptor-ligand interactions. Our model predicts for the first time that the rolling of more compliant cells is relatively smoother and slower compared to cells with stiffer membranes, due to increased cell-substrate contact area. At the molecular level, we show that the average number of bonds per cell as well as per single microvillus decreases with increasing membrane stiffness. Moreover, the average bond lifetime decreases with increasing shear rate and with increasing membrane stiffness, due to higher hydrodynamic force experienced by the cell. Taken together, our model captures the effect of cellular properties on the coupling between hydrodynamic and receptor-ligand bond forces, and successfully explains the stable leukocyte rolling at a wide range of shear rates over that of rigid microspheres.

Biophysics↗

PubMed1997

A Weibull regression model with gamma frailties for multivariate survival data.

Frequently in the analysis of survival data, survival times within the same group are correlated due to unobserved co-variates. One way these co-variates can be included in the model is as frailties. These frailty random block effects generate dependency between the survival times of the individuals which are conditionally independent given the frailty. Using a conditional proportional hazards model, in conjunction with the frailty, a whole new family of models is introduced. By considering a gamma frailty model, often the issue is to find an appropriate model for the baseline hazard function. In this paper a flexible baseline hazard model based on a correlated prior process is proposed and is compared with a standard Weibull model. Several model diagnostics methods are developed and model comparison is made using recently developed Bayesian model selection criteria. The above methodologies are applied to the McGilchrist and Aisbett (1991) kidney infection data and the analysis is performed using Markov Chain Monte Carlo methods.

Bayes Theorem↗

PubMed1991

Nonparametric analysis of covariance for comparing change in randomized studies with baseline values subject to error.

Change from baseline to a follow-up examination can be compared among two or more randomly assigned treatment groups by using analysis of variance on the change scores. However, a generally more sensitive (powerful) test can be performed using analysis of covariance (ANOVA) on the follow-up data with the baseline data as a covariate. This approach is not without potential problems, though. The assumption of ordinary ANCOVA of normally distributed errors is speculative for many variables employed in biomedical research. Furthermore, the baseline values are inevitably random variables and often are measured with error. This report investigates, in this situation, the validity and relative power of the ordinary ANCOVA test and two asymptotically distribution-free alternative tests, one based on the rank transformation and the other based on the normal scores transformation. The procedures are illustrated with data from a clinical trial. Normal and several nonnormal distributions, as well as varying degree of variable error, are studied by Monte Carlo methods. The normal scores test is generally recommended for statistical practice.

Analysis of Variance↗

PubMed1990

Studies on response characteristics of drug ISE's (VII)--performance and theoretical treatment of microcells connected in series.

A new type of MCCS (microcells connected in series) has been constructed and its performances investigated. It has been applied to the determination of streptomycin. The sensitivity and accuracy have been increased significantly. A theoretical model for the error of determination using the MCCS has been suggested and proved experimentally using the Monte Carlo method, and the error model proposed in Ref. [1] revised.

Electrodes↗

PubMed2000

Aspects of fast-ion dosimetry.

A first step in the dosimetry of fast-ion beams is the determination of accurate Bragg (ionization) functions. Bragg functions for several substances have been measured and calculated for 3480 MeV carbon ions. In the measurements, the ions first traverse an absorber in which the energy is reduced to either 1900 or 1200 MeV, then a "range gauge" followed by a thin ionization chamber. Functions are calculated with an analytical method using convolutions of straggling functions. This approach gives results without the stochastic variations implicit in Monte Carlo methods. The comparison of measured and calculated functions shows how reliable the calculations are. An important part of the calculations is the determination of the total range of the ions. The range can be determined from the Bragg function. The measured range is given by the sum of the thickness of the absorber and the residual range measured with the range gauge. For water, the range is about 150 mm, and the precision of the measurements is +/-0.05 mm. Because the ion energy at the surface of the absorber fluctuates with time, measurements with water are used to define this energy. Thus the ranges (or average stopping powers) in absorbers are obtained relative to those in water. Measured ranges R(m) are compared with ranges R(0) calculated with a current version of the Bethe theory. For light absorbers (atomic number Z < 20), differences between R(m) and R(0) are less than +/-0.3 mm; for Z > 20 differences are between 0 and +/-0.6 mm. This agreement between calculated and measured ranges confirms the value I = 80 eV for water measured earlier for protons. The ionization by nuclear fragments is obtained from the difference between measured and calculated ionization functions, and has little influence on the ranges of the primary ions.

Electrons↗

PubMed1999

Quantification of intracellular metabolic fluxes from fractional enrichment and 13C-13C coupling constraints on the isotopomer distribution in labeled biomass components.

A method for the quantification of intracellular metabolic flux distributions from steady-state mass balance constraints and from the constraints posed by the measured 13C labeling state of biomass components is presented. Two-dimensional NMR spectroscopy is used to analyze the labeling state of cell protein hydrolysate and cell wall components. No separation of the biomass hydrolysate is required to measure the degree of 13C-13C coupling and the fractional 13C enrichment in various carbon atom positions. A mixture of [1-13C]glucose and uniformly labeled [13C6]glucose is applied to make fractional 13C enrichment data and measurements of the degree of 13C-13C coupling informative with respect to the intracellular flux distribution. Simulation models that calculate the complete isotopomer distribution in biomass components on the basis of isotopomer mapping matrices are used for the estimation of intracellular fluxes by least-squares minimization. The statistical quality of the estimated intracellular flux distributions is assessed by Monte Carlo methods. Principal component analysis is performed on the outcome of the Monte Carlo procedure to identify groups of fluxes that contribute major parts to the total variance in the multiple flux estimations. The methods described are applied to a steady-state culture of a glucoamylase-producing recombinant Aspergillus niger strain.

Aspergillus niger↗

PubMed2001

A model to determine the initial phase space of a clinical electron beam from measured beam data.

Advanced electron beam dose calculation models for radiation oncology require as input an initial phase space (IPS) that describes a clinical electron beam. The IPS is a distribution in position, energy and direction of electrons and photons in a plane in front of the patient. A method is presented to derive the IPS of a clinical electron beam from a limited set of measured beam data. The electron beam is modelled by a sum of four beam components: a main diverging beam, applicator edge scatter, applicator transmission and a second diverging beam. The two diverging beam components are described by weighted sums of monoenergetic diverging electron and photon beams. The weight factors of these monoenergetic beams are determined by the method of simulated annealing such that a best fit is obtained with depth-dose curves measured for several field sizes at two source-surface distances. The resulting IPSs are applied by the phase-space evolution electron beam dose calculation model to calculate absolute 3D dose distributions. The accuracy of the calculated results is in general within 1.5% or 1.5 mm; worst cases show differences of up to 3% or 3 mm. The method presented here to describe clinical electron beams yields accurate results, requires only a limited set of measurements and might be considered as an alternative to the use of Monte Carlo methods to generate full initial phase spaces.

Biophysical Phenomena↗

PubMed2004

Accounting for center-of-mass target motion using convolution methods in Monte Carlo-based dose calculations of the lung.

We have applied convolution methods to account for some of the effects of respiratory induced motion in clinical treatment planning of the lung. The 3-D displacement of the GTV center-of-mass (COM) as determined from breath-hold exhale and inhale CT scans was used to approximate the breathing induced motion. The time-course of the GTV-COM was estimated using a probability distribution function (PDF) previously derived from diaphragmatic motion [Med. Phys. 26, 715-720 (1990)] but also used by others for treatment planning in the lung [Int. J. Radiat. Oncol., Biol., Phys. 53, 822-834 (2002); Med. Phys. 30, 1086-1095 (2003)]. We have implemented fluence and dose convolution methods within a Monte Carlo based dose calculation system with the intent of comparing these approaches for planning in the lung. All treatment plans in this study have been calculated with Monte Carlo using the breath-hold exhale CT data sets. An analysis of treatment plans for 3 patients showed substantial differences (hot and cold spots consistently greater than +/- 15%) between the motion convolved and static treatment plans. As fluence convolution accounts for the spatial variance of the dose distribution in the presence of tissue inhomogeneities, the doses were approximately 5% greater than those calculated with dose convolution in the vicinity of the lung. DVH differences between the static, fluence and dose convolved distributions for the CTV were relatively small, however, larger differences were observed for the PTV. An investigation of the effect of the breathing PDF asymmetry on the motion convolved dose distributions showed that reducing the asymmetry resulted in increased hot and cold spots in the motion convolved distributions relative to the static cases. In particular, changing from an asymmetric breathing function to one that is symmetric results in an increase in the hot/cold spots of +/- 15% relative to the static plan. This increase is not unexpected considering that the target spends relatively more time at inhale as the asymmetry decreases (note that the treatment plans were generated using the exhale CT scans).

Body Burden↗