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The problem of ordering and mapping genes on the basis of recombinant data and radiation hybrid data is formulated as a problem of Bayesian inference for an unknown permutation. The challenging computational problems posed by this approach are shown to be resolvable using Markov chain Monte Carlo methods.
A simple protein model restricted to the face-centered cubic lattice has been studied. The model interaction scheme includes attractive interactions between hydrophobic (H) residues, repulsive interactions between hydrophobic and polar (P) residues, and orientation-dependent P-P interactions. Additionally, there is a potential that favors extended beta-type conformations. A sequence has been designed that adopts a native structure, consisting of an antiparallel, six-member Greek-key beta-barrel with protein-like structural degeneracy. It has been shown that the proposed model is a minimal one, i.e., all the above listed types of interactions are necessary for cooperative (all-or-none) type folding to the native state. Simulations were performed via the Replica Exchange Monte Carlo method and the numerical data analyzed via a multihistogram method.
A water beam imaging system (WBIS) has been developed and used to verify dose distributions for intensity modulated radiotherapy using dynamic multileaf collimator. This system consisted of a water container, a scintillator screen, a charge-coupled device camera, and a portable personal computer. The scintillation image was captured by the camera. The pixel value in this image indicated the dose value in the scintillation screen. Images of radiation fields of known spatial distributions were used to calibrate the device. The verification was performed by comparing the image acquired from the measurement with a dose distribution from the IMRT plan. Because of light scattering in the scintillator screen, the image was blurred. A correction for this was developed by recognizing that the blur function could be fitted to a multiple Gaussian. The blur function was computed using the measured image of a 10 cm x 10 cm x-ray beam and the result of the dose distribution calculated using the Monte Carlo method. Based on the blur function derived using this method, an iterative reconstruction algorithm was applied to recover the dose distribution for an IMRT plan from the measured WBIS image. The reconstructed dose distribution was compared with Monte Carlo simulation result. Reasonable agreement was obtained from the comparison. The proposed approach makes it possible to carry out a real-time comparison of the dose distribution in a transverse plane between the measurement and the reference when we do an IMRT dose verification.
Our purpose is to directly measure mammographic x-ray spectra with collimators and a low-efficiency CdZnTe detector developed recently and to find out the best fit response function of CdZnTe detector to correct the measured spectra. Photon spectra (target Mo or Rh) produced by a mammographic x-ray unit at 25-32 kV and 240 mAs (= 3 times of 80 mAs) and transmitted through 0.03 mm Mo or 0.025 mm Rh filter and object (0.1 mm Al to 0.8 mm Al phantoms) have been analyzed. Since detected spectra were distorted by the response of CdZnTe detector and did not present the true photon spectra, the correction was applied by the stripping procedure. The response function of detector used in this procedure has been determined by the evaluation of interactions (K-escape, coherent scattering, and Compton scattering processes) and incomplete charge collection calculated using the Monte Carlo method. We have used Kalpha1, Kalpha2, Kbeta1, Kbeta2 radiations of Cd, Zn, and Te, respectively and have used the weight function for the incomplete charge collection and have considered Compton scattering. The Monte Carlo simulations were continued by changing the important factors (mean path length of hole lambda(h), dead layer of the CZT crystal and weight factor Wq) of incomplete charge collection until the best fit response function was found out. Corrected photon spectra were compared with the mammographic x-ray spectral data of Bureau of Radiological Health (BRH) measured using a Ge detector. Attenuation curves of aluminum for 25-32 kV were calculated from the corrected photon spectra and compared with the attenuation curves measured using an ionization chamber. These results obtained using the CdZnTe detector agreed with the mammographic x-ray spectral data of BRH and attenuation curves obtained by the ionization chamber.
Currently, there is a trend away from the use of single (often conservative) estimates of risk to summarize the results of risk analyses in favor of stochastic methods which provide a more complete characterization of risk. The use of such stochastic methods leads to a distribution of possible values of risk, taking into account both uncertainty and variability in all of the factors affecting risk. In this article, we propose a general framework for the analysis of uncertainty and variability for use in the commonly encountered case of multireplicative risk models, in which risk may be expressed as a product of two or more risk factors. Our analytical methods facilitate the evaluation of overall uncertainty and variability in risk assessment, as well as the contributions of individual risk factors to both uncertainty and variability which is cumbersome using Monte Carlo methods. The use of these methods is illustrated in the analysis of potential cancer risks due to the ingestion of radon in drinking water.
If a patient is treated in a hospital, drugs are administered at 'deterministic', known times. However, if the patient is not supervised the times of drug intake may be less 'deterministic' and less well known. It seems therefore worthwhile to make a theoretical experiment in which one assumes that drugs are applied according to a random process. In the present article it is proposed that shot noise models could be used to represent concentration curves in such situations. By means of Monte Carlo methods different measures of random drug excess are described. An included program may encourage readers to consider these methods and to perform computer experiments.
Spatial point pattern analysis provides a statistical method to compare an observed spatial pattern against a hypothesized spatial process model. The G statistic, which considers the distribution of nearest neighbor distances, and the K statistic, which evaluates the distribution of all neighbor distances, are commonly used in such analyses. One method of employing these statistics involves building a simulation envelope from the result of many simulated patterns of the hypothesized model. Specifically, a simulation envelope is created by calculating, at every distance, the minimum and maximum results computed across the simulated patterns. A statistical test is performed by evaluating where the results from an observed pattern fall with respect to the simulation envelope. However, this method, which differs from P. Diggle's suggested approach, is invalid for inference because it violates the assumptions of Monte Carlo methods and results in incorrect type I error rate performance. Similarly, using the simulation envelope to estimate the range of distances over which an observed pattern deviates from the hypothesized model is also suspect. The technical details of why the simulation envelope provides incorrect type I error rate performance are described. A valid test is then proposed, and details about how the number of simulated patterns impacts the statistical significance are explained. Finally, an example of using the proposed test within an exploratory data analysis framework is provided.
AIM: To develop limited sampling strategy (LSS) for estimation of C(max) and AUC(0-t) and assessing the bioequivalence of two pioglitazone hydrochloride (PGT) preparations. METHODS: Healthy subjects (n = 20), enrolled in a bioequivalence study, were received 30 mg PGT po of reference or test formulation. The plasma concentration of PGT was determined by the validated HPLC method. A multiple linear regression analysis of the Cmax and AUC(0-t) against the PGT concentration for the reference formulation was carried out to develop LSS models to estimate these parameters. The models were internally validated by the Jackknife method and externally validated using simulated sets generated by Monte Carlo method. The best model was employed to assess bioequivalence of the two PGT formulations. RESULTS: The linear relationship between pharmacokinetics parameters and single concentration point was poor. Several models for these parameters estimation met the predefined criteria (r2 > 0.9). The Jackknife validation procedure revealed that LSS models based on two sampling times (C1, C2.5 and C1.5, C2.5 for C(max); C1.5, C9 and C2.5, C9 for AUC(0-t) predict accurately. Mean prediction errors (MPE) were less than 3%, and mean absolute prediction error (MAE) were less than 9%. The prediction error (PE) beyond 20% was less than 5% of total samples. Model external validation by Monte Carlo simulated data indicated that the most informative sampling combinations were C1.5, C2.5 for C(max), and C1.5, C9 for AUC(0-t), respectively. MPE and MAE of the proposed models were less than 5% , and 9% respectively. The PE beyond 20% was less than 5% of the total. Bioequivalence assessment of the two PGT formulations, based on the best LSS models, provided results similar to those obtained using all the observed concentration-time data points, and indicated that the two PGT formulations were bioequivalent. CONCLUSION: The LSS method for bioequivalence assessment of PGT formulations was established and proved to be applicable and accurate. Thus, it could be considered appropriate for PGT bioequivalence study with inexpensive cost of sampling acquisition and analysis. Key words: pioglitazone hydrochloride; limited sampling strategy; Monte Carlo simulation; bioequivalence
MOTIVATION: The availability of a huge amount of molecular data concerning various biochemical reactions provoked numerous attempts to study the dynamics of cellular processes by means of kinetic models and computer simulations. Biochemical processes frequently involve small numbers of molecules (e.g. a few molecules of a transcriptional regulator binding to one 'molecule' of a DNA regulatory region). Such reactions are subject to significant stochastic fluctuations. Monte Carlo methods must be employed to study the functional consequences of the fluctuations and simulate processes that cannot be modelled by continuous fluxes of matter. This provides the motivation to develop software dedicated to Monte Carlo simulations of cellular processes with the rigorously proven Gillespie algorithm. RESULTS: STOCKS, software for the stochastic kinetic simulation of biochemical processes is presented. The program uses a rigorously derived Gillespie algorithm that has been shown to be applicable to the study of prokaryotic gene expression. Features dedicated to the study of cellular processes are implemented, such as the possibility to study a process in the range of several cell generations with the application of a simple cell division model. Taking expression of Escherichia coli beta-galactosidase as an example, it is shown that the program is able to simulate systems composed of reactions varying in several orders of magnitude by means of reaction rates and the numbers of molecules involved. AVAILABILITY: The software is available at ftp://ibbrain.ibb.waw.pl/stocksand http://www.ibb.waw.pl/stocks. SUPPLEMENTARY INFORMATION: Parameters of the model of prokaryotic gene expression are available in example files of software distribution.
We developed a general procedure for estimating the transmission probability adjusting for covariates when susceptibles are exposed to several infectives concurrently and taking correlation within transmission units into account. The procedure is motivated by a study estimating efficacy of pertussis vaccination based on the secondary attack rate in a rural sub-Saharan community (Niakhar, Senegal) and illustrated with simulations. The procedure is also appropriate to estimate the pairwise transmission probability in transmission studies of live vaccine virus in a collection of transmission units, such as day-care centres or retirement centres. Previously, analyses either excluded transmission units with multiple infectives or ignored co-infectives. Excluding transmission units with multiple infectives is statistically less efficient and ignoring co-infectives can lead to biased estimation. Modelling is carried out by regressing the latent pairwise transmission probability from each infective to a susceptible on covariates and specifying a transmission linkage function linking the latent pairwise transmission probability to the overall transmission probability. Parameters are estimated using Markov chain Monte Carlo methods.
Nonstationary noise analysis of electrophysiological data is applied to the estimation of the single-channel current, i, and the number of active channels, N(C), whenever they cannot be determined directly due to limited resolution. Using least squares methods, the accuracy of estimating i and N(C) chiefly depends on the statistical error of the ensemble variance. It is shown that if the correlation among the binned data points is taken into account correctly, the variability of i and N(C) can be remarkably reduced and exact confidence limits of the parameters can be calculated. Least-squares methods are introduced which consider the measured error-covariance matrix of the binned variance in a model-independent fashion. Employing Monte Carlo methods, it is demonstrated that both the error predictions and the confidence limits are correct. The method is used to investigate the performance of nonstationary noise analysis at low channel open-probabilities. The application of the approach to simulated data as well as to experimental, i.e. non-ideal, data is discussed.
The mean energy of the energy spectrum is an essential parameter for the dosimetry of therapeutic electron beams. Frequently it is assumed that the mean energy of such beams remains constant across the beam and only its degradation with depth is considered. The present work analyzes the variation of the mean energy of primary electrons with depth and lateral position in an electron beam using the Monte Carlo method. Results are compared with relations commonly employed for determination of mean energy at a depth. For the variation of the mean electron energy with depth in broad beams, good agreement was found between Monte Carlo results and an analytic continuous slowing down expression, which takes the variation of radiation stopping power with depth into account. Due to the calculated lateral variation of the mean energy, the relative absorbed dose profile determined with an air ionization chamber in a clinical beam should differ by less than 1% from the measured ionization profile.
We propose an alternative stochastic strategy to search secondary structures based on the generalized simulated annealing (GSA) algorithm, by using conformational preferences based on the Ramachandran map. We optimize the search for polypeptide conformational space and apply to peptides considered to be good alpha-helix promoters above a critical number of residues. Our strategy to obtain conformational energies consist in coupling a classical force field (THOR package) with the GSA procedure, biasing the Phi x Psi backbone angles to the allowed regions in the Ramachandran map. For polyalanines we obtained stable alpha-helix structures when the number of residues were equal or exceeded 13 amino acids residues. We also observed that the energy gap between the global minimum and the first local minimum tends to increase with the polypeptide size. These conformations were generated by performing 2880 stochastic molecular optimizations with a continuum medium approach. When compared with molecular dynamics or Monte Carlo methods, GSA can be considered the fastest.
Despite the large number of single-stepping source pulsed and high dose-rate (HDR) remote after-loading devices in clinical use, the published literature contain little data characterizing dose-rate distributions around the high-intensity (4 x 10(3)-4 x 10(4) microGy m2h-1) 192Ir sources currently used in these devices. We have used the Monte Carlo method to calculate complete two-dimensional dose-rate distributions about the most widely used high dose-rate source design, as well as the Nucletron pulsed dose-rate (PDR) 192Ir source. A Monte Carlo photon transport code, incorporating the detailed internal geometry of the source, was used to calculate the dose rate per unit air-kerma strength in water medium on the transverse bisecting axis over the 0.15-12 cm distance range. In addition, polar dose profiles were calculated at distances ranging from 0.25 to 5 cm. The PDR and HDR dose-rate distributions are tabulated using the formalism endorsed by the Interstitial Collaborative Working Group and the AAPM Task Group 43, and includes dose-rate constant, radial dose function, anisotropy function, geometry function, and anisotropy factors. The dose-rate constants, lambda, of the MicroSelectron/HDR and PDR sources were found to be 1.115 and 1.128 cGy h-1 per unit air-kerma strength, respectively, in good agreement with previously published data for low dose-rate interstitial 192Ir sources. Oblique filtration by the high-density iridium metal core resulted in deviations from anisotropy as large as 35%-55% near the longitudinal axis of the source. Dose-rate distributions are also presented in Cartesian ("away" and "along") coordinates.
BACKGROUND: According to early clinical trials, vascular brachytherapy performed prior to or shortly after angioplasty is very effective in reducing restenosis rates. The purpose of this study was to investigate the effects of a novel radioactive catheter that allows simultaneous balloon angioplasty and beta-particle irradiation in the prevention of restenosis. MATERIAL AND METHODS: The balloon surface of an angioplasty catheter was impregnated with the radioisotope(32)P. Dosimetry calculations using a Monte Carlo method were performed at a radial distance of 0.2 mm from the balloon surface. Rabbit iliac arteries were dilated and simultaneously irradiated with a dose of 20 Gy delivered to the adventitia. Control arteries were only dilated and not irradiated. Neointimal areas, cell numbers and the perimeter of the arteries were measured by histomorphometry after 6 weeks. RESULTS: Neointima formation was reduced after balloon dilatation and simultaneous beta-particle irradiation using the(32)P impregnated angioplasty catheter as compared to balloon dilatation alone with a non-impregnated catheter (0.09+/-0.06 vs 0.27+/-0.09 mm(2)neointimal area and 168+/-45 vs 360+/-133 cells/0.05 mm(2)neointima, P<0.001 vs control, respectively). In addition, balloon dilatation with the(32)P impregnated angioplasty catheter increased the vessel perimeter as compared to balloon dilatation with a non-impregnated catheter (4. 7+/-0.2 vs 3.9+/-0.3 mm, P<0.001 vs control). CONCLUSIONS: Simultaneous balloon dilatation and vascular brachytherapy with a novel(32)P impregnated angioplasty catheter markedly reduces restenosis in vivo by preventing neointimal hyperplasia and constrictive vascular remodelling.
RATIONALE AND OBJECTIVES: The author performed this study to test a technique for validating the logit regression method for summary receiver operating characteristic (ROC) meta-analysis, perform initial validation studies, and identify areas for further investigation. MATERIALS AND METHODS: Monte Carlo simulation was performed by using a custom macro program for a personal computer spreadsheet. The program creates simulated data sets based on user-specified parameters, performs a meta-analysis on the data sets, and logs the results so the accuracy and variability of the method can be measured. The program can also be used to measure the effects of changes in study design and meta-analysis parameters. RESULTS: For the base case of a small meta-analysis (10 studies) of small trials (mean, 50 patients), the meta-analysis results closely matched the input sensitivity and specificity when they were less than 80%. Systematic errors, if any, were small. At sensitivities and specificities greater than 80%, the true sensitivity or specificity was underestimated by up to 2% in the meta-analysis. Confidence intervals calculated with the summary ROC curve were reasonably conservative, although they too fell below the true results when sensitivity or specificity was greater than 80%. The underestimation was eliminated when the simulation was repeated for a much larger trial (mean, 1,000 cases per study)--even with a sensitivity and specificity of 98%. CONCLUSION: The Littenberg-Moses method for summary ROC meta-analysis is effective for obtaining an accurate summary estimate of diagnostic test performance, although the continuity correction introduces a small downward bias in the meta-analysis of small trials.
A semianalytical technique to study the charged-particle transport in one-dimensional finite media is developed. For this purpose, the transport equation is written in the form of coupled integral equations, separating the spatial and energy-angle transmissions. Legendre polynomial representation for the source, flux, and scattering kernel are used to solve the equations. For evaluation of the spatial transmission, discrete ordinate representation in space, energy, and direction cosine is used for the particle and source flux. The integral equations are then solved by the fast iteration technique. The computer code CHASFIT, written on the basis of the above formulation, is described. The fast convergence of the iteration process which is characteristic of charged-particle transport is demonstrated. Convergence studies are carried out with a number of mesh points and polynomial approximations. The method is applied to study the depth-dose distributions due to 140-, 200-, 300-, 400-, 600-, and 740-MeV protons incident normally on a 30-cm-thick tissue slab. The values of the quality factor at the surface and at 5 cm depth, as well as the total average quality factor, are calculated. The results thus obtained are compared with those predicted by the Monte Carlo method. This method can also be applied to multienergy, multiregion systems with arbitrary degree of anisotropy.
Multipoint linkage analysis is being performed routinely in medical genetic studies to localize disease genes. This likelihood-based method is very computationally intensive. Exact computations are thus formidable for problems with large number of genetic markers and complex pedigrees. This paper proposes a Monte Carlo method to estimate the required likelihoods. The space of multilocus genotypes is sampled using a hybrid algorithm with a mixture of Gibbs samplers and Metropolis jumping kernels. These samples are essentially realizations of a Markov chain, and are distributed approximately according to the conditional genotype distribution given the observed phenotypic data. We present a simulation study with several eight-point analyses to demonstrate the feasibility of the current method.