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Recent Bayesian methods for the analysis of infectious disease outbreak data using stochastic epidemic models are reviewed. These methods rely on Markov chain Monte Carlo methods. Both temporal and non-temporal data are considered. The methods are illustrated with a number of examples featuring different models and datasets.
This article demonstrates the use of the Monte Carlo simulation method in physician practice valuation. The Monte Carlo method allows the valuator to incorporate probability ranges into the discounted cash flow model and obtain an output indicating the probability for specified ranges of practice valuation. Given the high level of uncertainty in projected cash flows associated with physician practices, the value of this kind of information in a practice valuation decision would quite obviously be superior to any single point estimate generated by a traditional discounted cash flow model. It is postulated that virtually all hospitals support an information system that can easily accommodate a Monte Carlo simulation.
PURPOSE: We investigated the practical application of a calculation algorithm based on the Monte Carlo method to stereotactic radiosurgery treatment planning. In radiosurgery, high dose gradients and the lack of electronic disequilibrium make high resolution matrices and high computing power and speed necessary to obtain accurate dose distribution. To date, the main obstacle to the wider-spread use of the Monte Carlo method has been the huge computing time necessary to obtain a dose distribution on current hardware. MATERIAL AND METHODS: In this project, developed within the ESPRIT program, funded by the European Union, a Parsytec CC (Cognitive Computing) computer was used with 9 processors (Power PC 604, 133 Mhz, RAM 64 Mb) with IBM AIX/EPX OS and availability for Fortran parallel codes compilation, connected to a PC for data input, results rendering, and dose distribution calculation with a conventional algorithm for comparison with the Monte Carlo code (an EGS4 user code). The module named Rapt Region Extractor performs data compression with an octree method without decreasing resolution, for RAM and computing time requirements to remain acceptable. A model of the 6 MV photon beam from Clinac 2100C Varian linear accelerator was devised, based on incident photon energy spectrum and, for each collimator dimension, on bidimensional dose distribution orthogonal to beam direction measured at SSd = SAD = 100 cm. RESULTS: Parallelization was carried out on event numbers, allowing a simulation speed to number of processor ratio close to unity. A new random number generator was used, capable of correctly running on the parallel architecture. The simulation procedure includes: 1) CT acquisition in DICOM 3.0 format, Analyze or with scanner; 2) Target delineation, treatment arc definition. 3) Dose calculation, with both conventional and Monte Carlo methods. 4) Dose distribution rendering on every transverse, sagittal or coronal planes overlapped in color wash on anatomical representation. Comparison between conventional and Monte Carlo algorithms were carried out on an anthropomorphic phantom and 10 real patients, with 2.5 mm anatomical resolution and standard deviation never exceeding 2%. A simulation with 10,000,000 events and 1% maximum variance can be run in 43'. When PTV is an homogeneous areas the differences between the two methods are around 5%, while when PTV is localized in dishomogeneous areas discrepancies reach 20% in the bone. CONCLUSIONS: In conclusion, the feasibility of direct simulation with the Monte Carlo method in radiosurgery has been demonstrated within time and hardware costs compatible with clinical practice.
The quantum Monte Carlo (QMC) technique is an extremely powerful method to treat many-body systems. Usually the quantum Monte Carlo method has been applied in cases where the interaction potential has a simple analytic form, like the 1/r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a nontrivial problem. Obtaining the potential from any grid-based finite-difference method for every walker and every step is infeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo calculation within the overall quantum Monte Carlo scheme. We have developed a modified "walk on spheres" algorithm using Green's function techniques, which can efficiently account for the interaction energy of walker configurations, typical of quantum Monte Carlo algorithms. This stochastically obtained potential can be easily incorporated with variational, diffusion, and other Monte Carlo techniques. We demonstrate the validity of this method by studying a simple problem, the polarization of a helium atom in the electric field of an infinite capacitor.
The lattice-switch Monte Carlo method, recently introduced and applied in the context of hard spheres, is extended to particles interacting through a soft potential. The method utilizes a transformation that switches between configurations of two different crystalline structures, allowing the phase space of both structures to be explored in a single simulation and the difference between their free energies to be determined directly. We apply the method to determine the fcc-hcp crystalline phase behavior of the classical Lennard-Jones solid.
Multislice spiral CT scanners allow to acquire multiple slices simultaneously. With increasing numbers of slices, not only the total extent of slice collimation increases, but also the contribution of scatter radiation to the detector signal. A fast method for calculating the scatter signal would offer the possibility to correct the measured detector signal. Monte Carlo methods allow to simulate the paths of photons through a 3D volume, both in a patient- and scanner-specific fashion. If a scatter photon leaves the volume, its path can be followed and its interaction with an element of the detector be checked. This conventional way of calculating the scatter signal is time-consuming. In order to reduce the calculation time, a more efficient method was developed (Method of Weights). Every time an interaction occurs inside of the 3D volume, the probability of a detector hit due to photon scattering is calculated for each detector channel. The respective value is added to the scatter signal per detector with the corresponding weight. Simulated values of scatter-to-primary-signal ratios were confirmed by data available in the literature. Both the conventional and fast methods for the calculation of scatter signals yielded identical values within the range of statistical accuracy. Assuming the same computing time, the standard deviation for the conventional method was 5 times higher than for the fast one. The presented method allows to significantly reduce the computation time. It may therefore provide a basis for "real time" methods to correct for the scatter signal, especially in case of increasing numbers of slices.
A Monte Carlo method has been developed for generating the conformations of short single-stranded DNAs from arbitrary starting states. The chain conformers are constructed from energetically favorable arrangements of the constituent mononucleotides. Minimum energy states of individual dinucleotide monophosphate molecules are identified using a torsion angle minimizer. The glycosyl and acyclic backbone torsions of the dimers are allowed to vary, while the sugar rings are held fixed in one of the two preferred puckered forms. A total of 108 conformationally distinct states per dimer are considered in this first stage of minimization. The torsion angles within 5 kcal/mole of the global minimum in the resulting optimized states are then allowed to vary by +/- 10 degrees in an effort to estimate the breadth of the different local minima. The energies of a total of 2187 (3(7)) angle combinations are examined per local conformational minimum. Finally, the energies of all dinucleotide conformers are scaled so that the populations of differently puckered sugar rings in the theoretical sample match those found in nmr solution studies. This last step is necessitated by limitations in the theoretical methods to predict DNA sugar puckering accurately. The conformer populations of the individual acyclic torsion angles in the composite dimer ensembles are found to be in good agreement with the distributions of backbone conformations deduced from nmr coupling constants and the frequencies of glycosyl conformations in x-ray crystal structures, suggesting that the low energy states are reasonable. The low energy dimer forms (consisting of 150-325 conformational states per dimer step) are next used as variables in a Monte Carlo algorithm, which generates the conformations of single-stranded d(CXnG) chains, where X = A, T and n = 3, 4, 5. The oligonucleotides are built sequentially from the 5' end of the chain using random numbers to select the conformations of overlapping dimer units. The simulations are very fast, involving a total of 10(6) conformations per chain sequence. The potential errors in the buildup procedure are minimized by taking advantage of known rotational interdependences in the sugar-phosphate backbone. The distributions of oligonucleotide conformations are examined in terms of the magnitudes, positions, and orientations of the end-to-end vectors of the chains. The differences in overall flexibility and extension of the oligomers are discussed in terms of the conformations of the constituent dinucleotide steps, while the general methodology is discussed and compared with other nucleic acid model building techniques.
We demonstrate the applicability of the reactive Monte Carlo (RxMC) simulation method [J. K. Johnson, A. Z. Panagiotopoulos, and K. E. Gubbins, Mol. Phys. 81, 717 (1994); W. R. Smith and B. Tríska, J. Chem. Phys. 100, 3019 (1994)] for calculating the shock Hugoniot properties of a material. The method does not require interaction potentials that simulate bond breaking or bond formation; it requires only the intermolecular potentials and the ideal-gas partition functions for the reactive species that are present. By performing Monte Carlo sampling of forward and reverse reaction steps, the RxMC method provides information on the chemical equilibria states of the shocked material, including the density of the reactive mixture and the mole fractions of the reactive species. We illustrate the methodology for two simple systems (shocked liquid NO and shocked liquid N2), where we find excellent agreement with experimental measurements. The results show that the RxMC methodology provides an important simulation tool capable of testing models used in current detonation theory predictions. Further applications and extensions of the reactive Monte Carlo method are discussed.
This paper proposes a novel computational approach employing a Monte Carlo method, aimed at an improved understanding of the dynamics and energetics of activated ions in sustained off-resonance irradiation collisionally activated dissociation (SORI-CAD) experimental events of Fourier transform ion cyclotron resonance mass spectrometry (FTICRMS). In SORI-CAD events, internal energies of activated ions are complicatedly associated with their motion undergoing off-resonance excitation (i.e. alternate accelerations and decelerations) and inherently stochastic ion-neutral collisions. Several types of pseudo-random generators were adapted to probability density functions (PDFs) which characterize the ion-neutral collision process. Simulated ion trajectories involve the realistic feature of pressurized SORI-CAD events, such as a collisional damping and those which have not been illustrated in conventional analytical approaches. The proposed method can simulate the time-varying translational and internal energies of activated ions. The present result suggests that the internal energy of a SORI-activated ion should be inversely proportional to the cube of the SORI excitation frequency offset. Copyright 1999 John Wiley & Sons, Ltd.
We have been able by a Monte Carlo technique to generate the point spread function (PSF) for light in tissue for a generalized range of tissue characteristics. We have demonstrated that these can be described by an equation containing a gaussian, diffusion and exponential term. The PSF equation will allow one to estimate the limits of spatial resolution achievable with near infrared (NIR) imaging systems, and may be used in image deconvolution algorithms. Additionally an equation has been derived describing the average photon pathlength through the tissue. Finally, the light transmission and reflection (backscattering) have been illustrated as functions of scattering and absorption coefficients. These results can be used in attempting to quantify data from non-invasive NIR spectroscopy systems.
The results of a dynamical Monte-Carlo study on the coil-globule and globule-coil transitions are presented. Self-avoiding chains of lengths N = 32 and 64 are investigated. The kinetic model included two- and three-bonds flips. The relaxation of the chain was induced by the abrupt change of the interaction between the monomers. The time evolution of the radius of gyration and the number of intramolecular contacts was obtained. It is established that the transition to the compact state occurs due to the contacts between the monomers close to each other along the chain. The results obtained are compared with the predictions of analytical theories.
By analogy with Monte Carlo algorithms, we propose new strategies for design and redesign of small molecule libraries in high-throughput experimentation, or combinatorial chemistry. Several Monte Carlo methods are examined, including Metropolis, three types of biased schemes, and composite moves that include swapping or parallel tempering. Among them, the biased Monte Carlo schemes exhibit particularly high efficiency in locating optimal compounds. The Monte Carlo strategies are compared to a genetic algorithm approach. Although the best compounds identified by the genetic algorithm are comparable to those from the better Monte Carlo schemes, the diversity of favorable compounds identified is reduced by roughly 60%.
A Monte Carlo method has been used to model the measurement of cisplatin uptake with in vivo X-ray fluorescence. A user-code has been written for the EGS4 Monte Carlo system that incorporates linear polarisation and multiple element fluorescence extensions. The yield of fluorescent photons to the mainly Compton scattered background is computed for our detector arrangement. The detector consists of a mutually orthogonal arrangement of X-ray tube, aluminium polariser and high purity germanium scintillation detector. The influence of tube voltage on the minimum detectable concentration is modelled for 100 through 150 kVp X-radiation. The code is able to predict absorbed dose to the patient which will influence the optimal choice of tube voltage. The influence of alterations to collimator design and scatterer construction can also be examined. A minimum detectable concentration of 50 ppm is determined from measurements with a 115 kVp X-ray source and a 615 ppm cisplatin sample in a water phantom.
The Sodium Iodide detector NaI(Tl) presents a great efficiency for gamma-photon and the X-ray detection. The purpose of the present work is to study this efficiency versus different parameters that are related to the detection phenomenon. This has been achieved by using both analytical method and Monte Carlo simulation which give the same results. We have found that the intrinsic efficiency has a minimum at d/R approximately 0.7 (d is the source-NaI(Tl) distance and R is the NaI(Tl) radius). In order to explain this minima we have used the Dirac theory for the mean chord 1 of photons in the NaI(Tl) crystal and we have determined asymptotic limits of the efficiency corresponding to the following asymptotic limits of the mean chord: 1 = L (L: NaI(Tl) length) for large d/R and 1 = 4/3R for small d/R for point source. For distributed source (disk) the minimum is less pronounced and the asymptotic limit of the intrinsic efficiency is less than for the punctual source for small d/R while they are the same for large d/R. The total efficiency falls down at the d/R ratio corresponding to the minimum of the gamma-photons mean chord in the NaI(Tl) crystal so for a good photon detection we have shown that the source detector distance must respect the inequality: d/R < 0.01.
Monte Carlo methods for computing various statistical aspects of turbulent diffusion with long range correlated and even fractal random velocity fields are described here. A simple explicit exactly solvable model with complex regimes of scaling behavior including trapping, subdiffusion, and superdiffusion is utilized to compare and contrast the capabilities of conventional Monte Carlo procedures such as the Fourier method and the moving average method; explicit numerical examples are presented which demonstrate the poor convergence of these conventional methods in various regimes with long range velocity correlations. A new method for computing fractal random fields involving wavelets and random plane waves developed recently by two of the authors [J. Comput. Phys. 117, 146 (1995)] is applied to compute pair dispersion over many decades for systematic families of anisotropic fractal velocity fields with the Kolmogorov spectrum. The important associated preconstant for pair dispersion in the Richardson law in these anisotropic settings is compared with the one obtained over many decades recently by two of the authors [Phys. Fluids 8, 1052 (1996)] for an isotropic fractal field with the Kolmogorov spectrum. (c) 1997 American Institute of Physics.
Simulation of detector calibration using the Monte Carlo method is very convenient. The computational calibration procedure using the MCNP code was validated by comparing results of the simulation with laboratory measurements. The standard source used for this validation was a disc-shaped filter where fission and activation products were deposited. Some discrepancies between the MCNP results and laboratory measurements were attributed to the point source model adopted. In this paper, the standard source has been simulated using both point and surface source models. Results from both models are compared with each other as well as with experimental measurements. Two variables, namely, the collimator diameter and detector-source distance have been considered in the comparison analysis. The disc model is seen to be a better model as expected. However, the point source model is good for large collimator diameter and also when the distance from detector to source increases, although for smaller sizes of the collimator and lower distances a surface source model is necessary.
In this work we propose the regional Monte Carlo (RMC) method of dose calculation. This method combines the Monte Carlo (MC) algorithm and a non-MC algorithm (such as the convolution method) for optimal speed and accuracy in dose calculation for both photon and electron beams and for various irradiation and patient geometries. For specific regions in the geometry where high accuracy is required but difficult to obtain with analytical or empirical calculations, such as critical organs surrounded by complicated inhomogeneities, the MC algorithm is used. For regions with simple geometries, or where a high degree of dose accuracy is not critical, the non-MC algorithm is used to increase speed. There are two aspects of the RMC method. The first one involves determining critical regions and boundaries, and the other involves the actual implementation and mixing of the two computational algorithms. Two examples of different geometries are used to illustrate the different ways to apply the RMC method. The possibility to extend the method to more complicated geometries and inhomogeneities, as well as the ability of the method to incorporate different calculation algorithms, are also discussed.
Backscatter factors were determined for x-ray beams relevant to diagnostic radiology using Monte Carlo methods. The phantom size considered most suitable for calibration of dosimeters is a cuboid of 30 x 30 cm2 front surface and 15 cm depth. This phantom size also provides a good approximation to adult patients. Three different media were studied: water, PMMA and ICRU tissue; the source geometry was a point source with varying field size and source-to-phantom distance. The variations of the backscatter factor with phantom medium and field geometry were examined. From the obtained data, a set of backscatter factors was selected and proposed for adoption as a standard set for the calibration of dosimeters to be used to measure diagnostic reference doses.