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PubMed1994

MC-Fit: using Monte-Carlo methods to get accurate confidence limits on enzyme parameters.

A program is described for estimating enzymatic parameters from experimental data using Apple Macintosh computers. MC-Fit uses iterative least-square fitting and Monte-Carlo sampling to get accurate estimates of the confidence limits. This approach is more robust than the conventional covariance matrix estimation, especially in cases where experimental data is partially lacking or when the standard error on individual measurements is large. This happens quite often when analysing the properties of variant enzymes obtained by mutagenesis, as these can have severely impaired activities and reduced affinities for their substrates.

Confidence Intervals↗
PubMed2003

Modeling leaching of viruses by the Monte Carlo method.

A predictive screening model was developed for fate and transport of viruses in the unsaturated zone by applying the final value theorem of Laplace transformation to previously developed governing equations. A database of input parameters allowed Monte Carlo analysis with the model. The resulting kernel densities of predicted attenuation during percolation indicated very small, but finite probabilities of failure for all homogeneous USDA classified soils to attenuate reovirus 3 by 99.99% in one-half meter of gravity drainage. The logarithm of saturated hydraulic conductivity and water to air-water interface mass transfer coefficient affected virus fate and transport about 3 times more than any other parameter, including the logarithm of inactivation rate of suspended viruses. Model results suggest extreme infiltration events may play a predominant role in leaching of viruses in soils, since such events could impact hydraulic conductivity. The air-water interface also appears to play a predominating role in virus transport and fate. Although predictive modeling may provide insight into actual attenuation of viruses, hydrogeologic sensitivity assessments for the unsaturated zone should include a sampling program.

Air↗
PubMed2000

Library design in combinatorial chemistry by Monte Carlo methods.

Strategies for searching the space of variables in combinatorial chemistry experiments are presented, and a random energy model of combinatorial chemistry experiments is introduced. The search strategies, derived by analogy with the computer modeling technique of Monte Carlo, effectively search the variable space even in combinatorial chemistry experiments of only modest size. Efficient implementations of the library design and redesign strategies are feasible with current experimental capabilities.

Combinatorial Chemistry Techniques↗
PubMed1991

On the multiple-minima problem in the conformational analysis of polypeptides. V. Application of the self-consistent electrostatic field and the electrostatically driven Monte Carlo methods to bovine pancreatic trypsin inhibitor.

In connection with the accompanying paper to test various models for the hydration of polypeptides, we have explored a limited portion of the conformational energy hyperspace of the small protein bovine pancreatic trypsin inhibitor (BPTI) with the aid of two search methods developed in this laboratory. A series of low-energy conformations was obtained as a result of this study. These conformations constitute a set of local minima in the conformational energy space of the molecule as described by the ECEPP/2 (Empirical Conformational Energy Program for Peptides) potential energy function, without the inclusion of hydration. Five different initial conformations were used in this exploration: the first corresponds to an energy-refined structure based on the crystallographic coordinates (4PTI) provided by Deisenhofer and Steigemann and reported previously by Meirovitch and Scheraga. The remaining four initial conformations were obtained by using a Variable-Target-Function procedure, applied to the experimental Cartesian coordinates (5PTI) reported by Wlodawer et al. The self-consistent electrostatic field (SCEF) and the electrostatically driven Monte Carlo (EDMC) methods were used to search the conformational space. The SCEF and EDMC methodologies assume that a polypeptide or protein molecule is driven toward the native structure mainly by the action of the electrostatic interactions. Application of these methodologies led to a set of conformations (up to 50 kcal/mol lower than the starting ones) with ECEPP/2 energies lower than any of those that we had previously found. Application of both methods to the initial conformation generated from 4PTI led to a series of low-energy conformations exhibiting similar rms deviations with respect to the experimental data (4PTI) as did the starting conformation. However, statistical analysis of the runs that had started from the conformations generated by using the variable-target-function procedure (and applying the EDMC method) indicated that the rms deviations of the atomic positions of the new low-energy conformations tended to increase as the energy improved, when compared with the X-ray data from which the starting conformations had been generated. The structures with the lowest energies also had radii of gyration smaller than the experimentally observed one. These results indicated a need to include hydration in the potential function, and provided the conformations used in the accompanying paper to test various hydration models.

Animals↗
PubMedDate not supplied

Reconstruction of optical properties of low-scattering tissue using derivative estimated through perturbation Monte-Carlo method.

An iterative method for the reconstruction of optical properties of a low-scattering object, which uses a Monte-Carlo-based forward model, is developed. A quick way to construct and update the Jacobian needed to reconstruct a discretized object, based on the perturbation Monte-Carlo (PMC) approach, is demonstrated. The projection data is handled either one view at a time, using a propagation-backpropagation (PBP) strategy where the dimension of the inverse problem and consequently the computation time are smaller, or, when this approach failed, using all the views simultaneously with a full dataset. The main observations and results are as follows. 1. Whereas the PMC gives an accurate and quick method for constructing the Jacobian the same, when adapted to update the computed projection data, the data are not accurate enough for use in the iterative reconstruction procedure leading to convergence. 2. The a priori assumption of the location of inhomogeneities in the object reduces the dimension of the problem, leading to faster convergence in all the cases considered, such as an object with multiple inhomogeneities and data handled one view at a time (i.e., the PBP approach). 3. On the other hand, without a priori knowledge of the location of inhomogeneities, the problem was too ill posed for the PBP approach to converge to meaningful reconstructions when both absorption and scattering coefficients are considered as unknowns. Finally, to bring out the effectiveness of this method for reconstructing low-scattering objects, we apply a diffusion equation-based algorithm on a dataset from one of the low-scattering objects and show that it fails to reconstruct object inhomogeneities.

Algorithms↗
PubMed2005

An efficient Monte Carlo method for estimating Ne from temporally spaced samples using a coalescent-based likelihood.

This article presents an efficient importance-sampling method for computing the likelihood of the effective size of a population under the coalescent model of Berthier et al. Previous computational approaches, using Markov chain Monte Carlo, required many minutes to several hours to analyze small data sets. The approach presented here is orders of magnitude faster and can provide an approximation to the likelihood curve, even for large data sets, in a matter of seconds. Additionally, confidence intervals on the estimated likelihood curve provide a useful estimate of the Monte Carlo error. Simulations show the importance sampling to be stable across a wide range of scenarios and show that the N(e) estimator itself performs well. Further simulations show that the 95% confidence intervals around the N(e) estimate are accurate. User-friendly software implementing the algorithm for Mac, Windows, and Unix/Linux is available for download. Applications of this computational framework to other problems are discussed.

Algorithms↗
PubMed2006

Digitally reconstructed radiograph generation by an adaptive Monte Carlo method.

Digitally reconstructed radiograph (DRR) generation is an important step in several medical imaging applications such as 2D-3D image registration, where the generation of DRR is a rate-limiting step. We present a novel DRR generation technique, called the adaptive Monte Carlo volume rendering (AMCVR) algorithm. It is based on the conventional Monte Carlo volume rendering (MCVR) technique that is very efficient for rendering large medical datasets. In contrast to the MCVR, the AMCVR does not produce sample points by sampling directly in the entire volume domain. Instead, it adaptively divides the entire volume domain into sub-domains using importance separation and then performs sampling in these sub-domains. As a result, the AMCVR produces almost the same image quality as that obtained with the MCVR while only using half samples, and increases projection speed by a factor of 2. Moreover, the AMCVR is suitable for fast memory addressing, which further improves processing speed. Independent of the size of medical datasets, the AMCVR allows for achieving a frame rate of about 15 Hz on a 2.8 GHz Pentium 4 PC while generating reasonably good quality DRR.

Algorithms↗
PubMed2003

Comparison of dose calculation algorithms with Monte Carlo methods for photon arcs.

The objective of this study is to seek an accurate and efficient method to calculate the dose distribution of a photon arc. The algorithms tested include Monte Carlo, pencil beam kernel (PK), and collapsed cone convolution (CCC). For the Monte Carlo dose calculation, EGS4/DOSXYZ was used. The SRCXYZ source code associated with the DOSXYZ was modified so that the gantry angle of a photon beam would be sampled uniformly within the arc range about an isocenter to simulate a photon arc. Specifically, photon beams (6/18 MV, 4 x 4 and 10 x 10 cm2) described by a phase space file generated by BEAM (MCPHS), or by two point sources with different photon energy spectra (MCDIV) were used. These methods were used to calculate three-dimensional (3-D) distributions in a PMMA phantom, a cylindrical water phantom, and a phantom with lung inhomogeneity. A commercial treatment planning system was also used to calculate dose distributions in these phantoms using equivalent tissue air ratio (ETAR), PK and CCC algorithms for inhomogeneity corrections. Dose distributions for a photon arc in these phantoms were measured using a RK ion chamber and radiographic films. For homogeneous phantoms, the measured results agreed well (approximately 2% error) with predictions by the Monte Carlo simulations (MCPHS and MCDIV) and the treatment planning system for the 180 degrees and 360 degrees photon arcs. For the dose distribution in the phantom with lung inhomogeneity with a 90 degrees photon arc, the Monte Carlo calculations agreed with the measurements within 2%, while the treatment planning system using ETAR, PK and CCC underestimated or overestimated the dose inside the lung inhomogeneity from 6% to 12%.

Algorithms↗
PubMed2006

Simultaneous determination of equivalent dose to organs and tissues of the patient and of the physician in interventional radiology using the Monte Carlo method.

This study presents the results of computations of organ equivalent doses and effective doses for the patient and the primary physician during an interventional cardiological examination. The simulations were carried out for seven x-ray spectra (between 60 kVp and 120 kVp) using the Monte Carlo code MCNP. The voxel-based whole-body model VIP-Man was employed to represent both the patient and the physician, the former lying on the operation table while the latter standing 15 cm from the patient at about waist level behind a lead apron. The x-rays, which were generated by a point source positioned around the table and were directed with a conical distribution, irradiated the patient's heart under five major projections used in a coronary angiography examination. The mean effective doses under LAO45, PA, RAO30, LAO45/CAUD30 and LLAT irradiation conditions were calculated as 0.092, 0.163, 0.161, 0.133 and 0.118 mSv/(Gy cm2) for the patient and 1.153, 0.159, 0.145, 0.164 and 0.027 microSv/(Gy cm2) for the shielded physician. The effective doses for the patient determined in this study were usually lower than the literature data obtained through measurements and/or calculations and the discrepancies could be attributed to the fact that this study computes the effective doses specific to the VIP-Man body model, which lacks an ovarian contribution to the gonadal equivalent dose. The effective doses for the physician agreed reasonably well with the literature data.

Adult↗
PubMed2003

Direct simulation Monte Carlo method for the Uehling-Uhlenbeck-Boltzmann equation.

In this paper we describe a direct simulation Monte Carlo algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady-state distribution.

Journal Article↗
PubMed2004

[Calibration of a whole body counter using Monte Carlo methods].

Radioactive substances in the human body can be identified and quantified by gamma spectroscopy using whole body counters. Counting efficiencies needed for calculation of incorporated activities are generally determined from measurements of phantoms simulating shape and density of a human and filled with known activity concentrations. The Cologne whole body counter setup was simulated using the EGSnrc Monte Carlo code system. The simulations did reproduce the spectra and efficiencies from phantom measurements (within +/- 2% for K-40). Variations of the phantom position alongside the stretcher resulted in parabola-shaped courses with efficiency changes of up to 5%. Nuclides which are inaccessible to phantom measurements can be quantified by weighted summation of efficiencies generatedfrom simulation offictitious monoenergetic gamma emitters. For I-131, a strong dependence upon the activity distribution inside the body was observed in simulations with a simplified model of the human body Inclusion of the skeleton in the model had a rather small effect. The efficiency decreases linearly with body length by up to 6% when body mass is kept constant. This has to be taken into account when the activity needs to be determined with high precision. For in vivo counting in the context of radiation protection, however, efficiencies can be deduced with sufficient accuracy from measurements or simulations of simple phantoms.

Calibration↗
PubMed2000

Sequential monte carlo methods To train neural network models

We discuss a novel strategy for training neural networks using sequential Monte Carlo algorithms and propose a new hybrid gradient descent sampling importance resampling algorithm (HySIR). In terms of computational time and accuracy, the hybrid SIR is a clear improvement over conventional sequential Monte Carlo techniques. The new algorithm may be viewed as a global optimization strategy that allows us to learn the probability distributions of the network weights and outputs in a sequential framework. It is well suited to applications involving on-line, nonlinear, and nongaussian signal processing. We show how the new algorithm outperforms extended Kalman filter training on several problems. In particular, we address the problem of pricing option contracts, traded in financial markets. In this context, we are able to estimate the one-step-ahead probability density functions of the options prices.

Journal Article↗
PubMed2003

Convolution/superposition using the Monte Carlo method.

The convolution/superposition calculations for radiotherapy dose distributions are traditionally performed by convolving polyenergetic energy deposition kernels with TERMA (total energy released per unit mass) precomputed in each voxel of the irradiated phantom. We propose an alternative method in which the TERMA calculation is replaced by random sampling of photon energy, direction and interaction point. Then, a direction is randomly sampled from the angular distribution of the monoenergetic kernel corresponding to the photon energy. The kernel ray is propagated across the phantom, and energy is deposited in each voxel traversed. An important advantage of the explicit sampling of energy is that spectral changes with depth are automatically accounted for. No spectral or kernel hardening corrections are needed. Furthermore, the continuous sampling of photon direction allows us to model sharp changes in fluence, such as those due to collimator tongue-and-groove. The use of explicit photon direction also facilitates modelling of situations where a given voxel is traversed by photons from many directions. Extra-focal radiation, for instance, can therefore be modelled accurately. Our method also allows efficient calculation of a multi-segment/multi-beam IMRT plan by sampling of beam angles and field segments according to their relative weights. For instance, an IMRT plan consisting of seven 14 x 12 cm2 beams with a total of 300 field segments can be computed in 15 min on a single CPU, with 2% statistical fluctuations at the isocentre of the patient's CT phantom divided into 4 x 4 x 4 mm3 voxels. The calculation contains all aperture-specific effects, such as tongue and groove, leaf curvature and head scatter. This contrasts with deterministic methods in which each segment is given equal importance, and the time taken scales with the number of segments. Thus, the Monte Carlo superposition provides a simple, accurate and efficient method for complex radiotherapy dose calculations.

Algorithms↗
PubMed2004

Projective quantum monte carlo method for the anderson impurity model and its application to dynamical mean field theory.

We develop a projective quantum Monte Carlo algorithm of the Hirsch-Fye type for obtaining ground state properties of the Anderson impurity model. This method is employed to solve the self-consistency equations of dynamical mean field theory. It is shown that the approach converges rapidly to the ground state so that reliable zero-temperature results are obtained. As a first application, we study the Mott-Hubbard metal-insulator transition of the frustrated one-band Hubbard model, reconfirming the numerical renormalization group results.

Journal Article↗
PubMed2007

Predicting costs over time using Bayesian Markov chain Monte Carlo methods: an application to early inflammatory polyarthritis.

This article focuses on the modelling and prediction of costs due to disease accrued over time, to inform the planning of future services and budgets. It is well documented that the modelling of cost data is often problematic due to the distribution of such data; for example, strongly right skewed with a significant percentage of zero-cost observations. An additional problem associated with modelling costs over time is that cost observations measured on the same individual at different time points will usually be correlated. In this study we compare the performance of four different multilevel/hierarchical models (which allow for both the within-subject and between-subject variability) for analysing healthcare costs in a cohort of individuals with early inflammatory polyarthritis (IP) who were followed-up annually over a 5-year time period from 1990/1991. The hierarchical models fitted included linear regression models and two-part models with log-transformed costs, and two-part model with gamma regression and a log link. The cohort was split into a learning sample, to fit the different models, and a test sample to assess the predictive ability of these models. To obtain predicted costs on the original cost scale (rather than the log-cost scale) two different retransformation factors were applied. All analyses were carried out using Bayesian Markov chain Monte Carlo (MCMC) simulation methods.

Adult↗