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Results for “Monte Carlo Method”

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PubMed2000

Comparative evaluation of scatter correction techniques in 3D positron emission tomography.

Much research and development has been concentrated on the scatter compensation required for quantitative 3D positron emission tomography (PET). Increasingly sophisticated scatter correction procedures are under investigation, particularly those based on accurate scatter models and iterative reconstruction-based scatter compensation approaches. The main difference among the correction methods is the way in which the scatter component in the selected energy window is estimated. Monte Carlo methods provide further insight and might in themselves offer a possible correction procedure. Five scatter correction methods were compared in this study where applicable: the dual-energy window (DEW) technique, the convolution-subtraction (CVS) method, two variants of the Monte Carlo-based scatter correction technique (MCBSCI and MCBSC2) and our newly developed statistical reconstruction-based scatter correction (SRBSC) method. These scatter correction techniques were evaluated using Monte Carlo simulation studies, experimental phantom measurements and clinical studies. Accurate Monte Carlo modelling is still the gold standard since it allows the separation of scattered and unscattered events and comparison of the estimated and true unscattered component. In this study, our modified version of Monte Carlo-based scatter correction (MCBSC2) provided a good contrast recovery on the simulated Utah phantom, while the DEW method was found to be clearly superior for the experimental phantom studies in terms of quantitative accuracy at the expense of a significant deterioration in the signal-to-noise ratio. On the other hand, the immunity to noise in emission data of statistical reconstruction-based scatter correction methods makes them particularly applicable to low-count emission studies. All scatter correction methods gave very good activity recovery values for the simulated 3D Hoffman brain phantom, which averaged within 3%. The CVS and MCBSC 1 techniques tended to overcorrect while SRBSC undercorrected for scatter in most regions of this phantom. It was concluded that all correction methods significantly improve the image quality and contrast compared to the case where no correction is applied. Generally, it was shown that the differences in the estimated scatter distributions did not have a significant impact on the final quantitative results. The DEW method showed the best compromise between ease of implementation and quantitative accuracy, but entailed a significant deterioration in the signal-to-noise ratio.

Algorithms↗

PubMed1995

Normalized average glandular dose in magnification mammography.

PURPOSE: To evaluate the normalized average glandular dose (the average glandular dose per unit entrance skin exposure) in magnification mammography. MATERIALS AND METHODS: Photon transport in the breast was simulated by using Monte Carlo methods. A semielliptical cylinder containing glandular and adipose tissue was used to simulate the breast. Measured mammography spectra for a molybdenum target-molybdenum filter unit were utilized. The normalized average glandular dose was calculated as a function of half-value layer, tube voltage, breast thickness, and breast composition for typical magnification geometries. RESULTS: The normalized average glandular dose in magnification mammography is 7%-25% lower than that with the contact (nonmagnification) technique because of the effects of partial irradiation, smaller field size, and greater percentage depth dose gradient at the reduced source-to-skin distance. CONCLUSION: The normalized average glandular dose in magnification mammography is lower than that in contact mammography. The average glandular dose in magnification mammography, however, is still substantially greater due to the two to three times greater entrance skin exposure.

Female↗

PubMed2002

Dosimetry characteristics of degraded electron beams investigated by Monte Carlo calculations in a setup for intraoperative radiation therapy.

Degraded electron beams, as used for intraoperative radiation therapy (IORT) or similar complicated dosimetric situations, have different characteristics compared to conventional electron therapy beams. If international dosimetry protocols are applied in a direct manner to such degraded beams, uncertainties will be introduced in the absorbed dose determination. The Monte Carlo method has been used to verify experimentally determined relative absorbed dose distributions and output factors in an IORT geometry. Monte Carlo generated dose distributions are mostly within +/-2% or +/-2 mm of measured data. The simulated output variation between the IORT cones (relative output factors) are mostly within 2% of measured values. By comparing IORT and conventional electron beam characteristics (e.g. energy spectra, angular distributions and the contributions of different system components to these quantities) limitations and uncertainties of commonly used dosimetric techniques in IORT electron fields are quantified. The intraoperative treatment field contains a larger amount of scattered electrons, which leads to a broader energy spectrum as well as a wider angular distribution of electrons at the phantom surface. The dose from the scattered electrons can contribute up to 40% of the total dose at a depth of dose maximum, compared to approximately 10% for standard beams. A study of the energy spectra at the reference depth reveals that an uncertainty of the order of 1% can be introduced if ionization chamber based dosimetry is used to determine output factors for the investigated IORT system. We recommend that relative absorbed dose distributions and output factors in IORT electron beams and for similar complicated dosimetric situations should be determined with detectors having a small energy and angular dependence (e.g. diamond detectors or p-Si diodes).

Electrons↗

PubMed1994

Monte Carlo likelihood in the genetic mapping of complex traits.

Many of the likelihoods arising in the analysis of complex genetic traits, particularly in linkage analysis, are computationally infeasible. Where exact likelihoods cannot be computed, Monte Carlo estimates of likelihoods may provide a satisfactory alternative. Although simulation on pedigrees is straightforward, simulation conditional upon observed phenotypic data is not. However, recent advances in Markov chain Monte Carlo methods have provided a method well suited to this problem. From realizations of underlying genes, simulated under a genetic model, conditional upon observed data, a Monte Carlo estimate of this likelihood surface can be formed. Various sampler and model modifications are needed to enhance the statistical efficiency of the Monte Carlo estimator; as these methods become increasingly developed, this approach becomes a useful tool in resolving the genes contributing to the phenotypes associated with genetically complex diseases.

Algorithms↗

PubMed1999

Domain-wall free energy of spin-glass models: numerical method and boundary conditions.

An efficient Monte Carlo method is extended to evaluate directly domain-wall free energy for randomly frustrated spin systems. Using the method, critical phenomena of spin-glass phase transition are investigated in the 4d+/-J Ising model under the replica boundary condition. Our values of the critical temperature and exponent, obtained by finite-size scaling, are in good agreement with those of the standard Monte Carlo and the series expansion studies. In addition, two exponents, the stiffness exponent and the fractal dimension of the domain wall, which characterize the ordered phase, are obtained. The latter value is larger than d-1, indicating that the domain wall is really rough in the 4d Ising spin-glass phase.

Journal Article↗

PubMed2001

High-resolution multipoint linkage-disequilibrium mapping in the context of a human genome sequence.

A new method is presented for fine-scale linkage disequilibrium (LD) mapping of a disease mutation; it uses multiple linked single-nucleotide polymorphisms, restriction-fragment-length polymorphisms, or microsatellite markers and incorporates information from an annotated human genome sequence (HGS) and from a human mutation database. The method takes account of population demographic effects, using Markov chain Monte Carlo methods to integrate over the unknown gene genealogy and gene coalescence times. Information about the relative frequency of disease mutations in exons, introns, and other regions, from mutational databases, as well as assumptions about the completeness of the gene annotation, are used with an annotated HGS, to generate a prior probability that a mutation lies at any particular position in a specified region of the genome. This information is updated with information about mutation location, from LD at a set of linked markers in the region, to generate the posterior probability density of the mutation location. The performance of the method is evaluated by simulation and by analysis of a data set for diastrophic dysplasia (DTD) in Finland. The DTD disease gene has been positionally cloned, so the actual location of the mutation is known and can be compared with the position predicted by our method. For the DTD data, the addition of information from an HGS results in disease-gene localization at a resolution that is much higher than that which would be possible by LD mapping alone. In this case, the gene would be found by sequencing a region < or =7 kb in size.

Algorithms↗

PubMed1998

Solvent relaxation by uniformly magnetized solute spheres. The classical-quantal connection.

RATIONALE AND OBJECTIVES: Large magnetic entities, with diameters in the range of 4 nm to 4 microns, are becoming of increasing interest for magnetic resonance imaging (MRI). The smaller are iron oxide nanoparticles, used for the RE system, and the larger are deoxygenated blood cells, for functional MRI. It can be useful to model such systems as magnetized solute spheres in water. Classical computations of 1/T2 have been reported for the larger particles, in the micron range, where the computational complexities are simplified by Monte Carlo methods. For smaller particles, the quantum mechanical (quantal) expressions for outer sphere relaxation, for both 1/T1 and 1/T2, have been available for some time, and are particularly simple to apply at MRI fields. The questions that arise, and which the author addresses, are how to interrelate the classical and quantal approaches and when to use which. METHODS: The author compares published results of Monte Carlo calculations of 1/T2 for diamagnetic polystyrene solute spheres of various sizes in water, made paramagnetic by addition of dysprosium-(DTPA)2-, with quantum mechanical outer sphere theory applied to the same system. The latter includes the usual assumption of motional narrowing and yields both 1/T1 and 1/T2. RESULTS: For particles with diameters less than about 1 micron, both approaches give identical results for 1/T2. For larger particles, the conditions for motional narrowing breakdown, and quantal theory overestimates 1/T2. In addition, in the particular system studied, relaxation becomes so effective near solute that there is insufficient time for all water molecules to experience their maximal effect. Classical theory handles this well whereas quantal theory does not. CONCLUSIONS: In comparing the classical and quantal approaches, one balances computational complexity but broader applicability with more limited but far simpler mathematics. In addition, because the quantal approach shows that 1/T1 and 1/T2 are intimately related, the author suggests, by analogy, how to extend classical methods to computation of 1/T1.

Contrast Media↗

PubMed1980

A criterion for the establishment of a stable polymorphism of higher order with an application to the evolution of polymorphism.

This note gives some further useful properties of the constant fitness selection model for multiple alleles which pertain to the effects of adding a new allele to n preexisting alleles in stable equilibrium. In particular the conditions are derived for the establishment of a stable equilibrium involving all n + 1 alleles. For 3 alleles (i.e. n = 2) I give a complete qualitative solution, including the case of the replacement of one diallelic polymorphism by another. As an application I discuss a possible mechanism for the evolution of polymorphism using Monte Carlo methods similar to Lewontin, Ginzburg and Tuljapurkar (1978).

Alleles↗

PubMed1987

Phantom equivalent thicknesses in diagnostic radiology.

Some measurements in diagnostic radiology must be done with phantoms. The most frequently used phantoms are water, plexiglass, aluminium and copper. It is interesting to know the equivalent thicknesses between these phantoms in order to be able to relate these values to real anatomical organs of known thicknesses. The use of antiscatter grids, the choice of intensifier screens, the beam size and in general the scattering parameters considerably change the equivalent thicknesses. Many situations have been simulated by the Monte Carlo method and equivalent thicknesses are presented.

Humans↗

PubMed2002

CdZnTe detector in diagnostic x-ray spectroscopy.

A method to utilize CdZnTe (CZT) detectors in diagnostic x-ray spectroscopy is described in this article. Spectral distortion due to transmission of primary x rays, the escape of cadmium- and tellurium-K fluorescent x rays, and tailing was severe in measured x-ray spectra. Therefore, correction for the distortion was performed with the stripping method using response functions. The response functions were calculated with the Monte Carlo method. The Hecht equation was employed to approximate the effects of carrier trapping in the calculations. The parameters in the Hecht equation, the mean-free path (lambda) of electrons and holes, were determined such that the tailing in calculated response functions fit that in measured gamma-ray spectra. Corrected x-ray spectra agreed well with the reference spectra measured with an HPGe detector. The results indicate that CZT detectors are suitable for diagnostic x-ray spectroscopy with appropriate corrections.

Algorithms↗

PubMed2000

A virtual linear accelerator for verification of treatment planning systems.

A virtual linear accelerator is implemented into a commercial pencil-beam-based treatment planning system (TPS) with the purpose of investigating the possibility of verifying the system using a Monte Carlo method. The characterization set for the TPS includes depth doses, profiles and output factors, which is generated by Monte Carlo simulations. The advantage of this method over conventional measurements is that variations in accelerator output are eliminated and more complicated geometries can be used to study the performance of a TPS. The difference between Monte Carlo simulated and TPS calculated profiles and depth doses in the characterization geometry is less than +/-2% except for the build up region. This is of the same order as previously reported results based on measurements. In an inhomogeneous, mediastinum-like case, the deviations between TPS and simulations are small in the unit-density regions. In low-density regions, the TPS overestimates the dose, and the overestimation increases with increasing energy from 3.5% for 6 MV to 9.5% for 18 MV. This result points out the widely known fact that the pencil beam concept does not handle changes in lateral electron transport, nor changes in scatter due to lateral inhomogeneitics. It is concluded that verification of a pencil-beam-based TPS with a Monte Carlo based virtual accelerator is possible, which facilitates the verification procedure.

Algorithms↗

PubMed1999

Monte Carlo-based inverse treatment planning.

A Monte Carlo based inverse treatment planning system (MCI) has been developed which combines arguably the most accurate dose calculation method (Monte Carlo particle transport) with a 'guaranteed' optimization method (simulated annealing). A distribution of photons is specified in the tumour volume; they are transported using an adjoint calculation method to outside the patient surface to build up an intensity distribution. This intensity distribution is used as the initial input into an optimization algorithm. The dose distribution from each beam element from a number of fields is pre-calculated using Monte Carlo transport. Simulated annealing optimization is then used to find the weighting of each beam element, to yield the optimal dose distribution for the given criteria and constraints. MCI plans have been generated in various theoretical phantoms and patient geometries. These plans show conformation of the dose to the target volume and avoidance of critical structures. To verify the code, an experiment was performed on an anthropomorphic phantom.

Algorithms↗

PubMed2001

Comparing Bayesian neural network algorithms for classifying segmented outdoor images.

In this paper we investigate the Bayesian training of neural networks for region labelling of segmented outdoor scenes; the data are drawn from the Sowerby Image Database of British Aerospace. Neural networks are trained with two Bayesian methods, (i) the evidence framework of MacKay (1992a,b) and (ii) a Markov Chain Monte Carlo method due to Neal (1996). The performance of the two methods is compared to evaluating the empirical learning curves of neural networks trained with the two methods. We also investigate the use of the Automatic Relevance Determination method for input feature selection.

Algorithms↗

PubMed2004

Evidence for a novel late-onset Alzheimer disease locus on chromosome 19p13.2.

Late-onset familial Alzheimer disease (LOFAD) is a genetically heterogeneous and complex disease for which only one locus, APOE, has been definitively identified. Difficulties in identifying additional loci are likely to stem from inadequate linkage analysis methods. Nonparametric methods suffer from low power because of limited use of the data, and traditional parametric methods suffer from limitations in the complexity of the genetic model that can be feasibly used in analysis. Alternative methods that have recently been developed include Bayesian Markov chain-Monte Carlo methods. These methods allow multipoint linkage analysis under oligogenic trait models in pedigrees of arbitrary size; at the same time, they allow for inclusion of covariates in the analysis. We applied this approach to an analysis of LOFAD on five chromosomes with previous reports of linkage. We identified strong evidence of a second LOFAD gene on chromosome 19p13.2, which is distinct from APOE on 19q. We also obtained weak evidence of linkage to chromosome 10 at the same location as a previous report of linkage but found no evidence for linkage of LOFAD age-at-onset loci to chromosomes 9, 12, or 21.

Adult↗

PubMed2001

Errors-in-variables in joint population pharmacokinetic/pharmacodynamic modeling.

Pharmacokinetic (PK) models describe the relationship between the administered dose and the concentration of drug (and/or metabolite) in the blood as a function of time. Pharmacodynamic (PD) models describe the relationship between the concentration in the blood (or the dose) and the biologic response. Population PK/PD studies aim to determine the sources of variability in the observed concentrations/responses across groups of individuals. In this article, we consider the joint modeling of PK/PD data. The natural approach is to specify a joint model in which the concentration and response data are simultaneously modeled. Unfortunately, this approach may not be optimal if, due to sparsity of concentration data, an overly simple PK model is specified. As an alternative, we propose an errors-in-variables approach in which the observed-concentration data are assumed to be measured with error without reference to a specific PK model. We give an example of an analysis of PK/PD data obtained following administration of an anticoagulant drug. The study was originally carried out in order to make dosage recommendations. The prior for the distribution of the true concentrations, which may incorporate an individual's covariate information, is derived as a predictive distribution from an earlier study. The errors-in-variables approach is compared with the joint modeling approach and more naive methods in which the observed concentrations, or the separately modeled concentrations, are substituted into the response model. Throughout, a Bayesian approach is taken with implementation via Markov chain Monte Carlo methods.

Anticoagulants↗

PubMed2005

Multiscale modeling of lipids and lipid bilayers.

A multiscale modeling approach is applied for simulations of lipids and lipid assemblies on mesoscale. First, molecular dynamics simulation of initially disordered system of lipid molecules in water within all-atomic model was carried out. On the next stage, structural data obtained from the molecular dynamics (MD) simulation were used to build a coarse-grained (ten sites) lipid model, with effective interaction potentials computed by the inverse Monte Carlo method. Finally, several simulations of the coarse-grained model on longer length- and time-scale were performed, both within Monte Carlo and molecular dynamics simulations: a periodical sample of lipid molecules ordered in bilayer, a free sheet of such bilayer without periodic boundary conditions, formation of vesicle from a plain membrane, process of self-assembly of lipids randomly dispersed in volume. It was shown that the coarse-grained model, developed exclusively from all-atomic simulation data, reproduces well all the basic features of lipids in water solution.

Computer Simulation↗

PubMed2004

Monte Carlo as a four-dimensional radiotherapy treatment-planning tool to account for respiratory motion.

Four-dimensional (4D) radiotherapy is the explicit inclusion of the temporal changes in anatomy during the imaging, planning and delivery of radiotherapy. Temporal anatomic changes can occur for many reasons, though the focus of the current investigation was respiration motion for lung tumours. The aims of the current research were first to develop a 4D Monte Carlo methodology and second to apply this technique to an existing 4D treatment plan. A 4D CT scan consisting of a series of 3D CT image sets acquired at different respiratory phases was used. Deformable image registration was performed to map each CT set from the end-inhale respiration phase to the CT image sets corresponding with subsequent respiration phases. This deformable registration allowed the contours drawn on the end-inhale CT to be automatically drawn on the other respiratory phase CT image sets. A treatment plan was created on the end-inhale CT image set and then automatically created on each of the 3D CT image sets corresponding with subsequent respiration phases, based on the beam arrangement and dose prescription in the end-inhale plan. Dose calculation using Monte Carlo was simultaneously performed on each of the N (=8) 3D image sets with 1/N fewer particles per calculation than for a 3D plan. The dose distribution from each respiratory phase CT image set was mapped back to the end-inhale CT image set for analysis. This use of deformable image registration to merge all the statistically noisy dose distributions back onto one CT image set effectively yielded a 4D Monte Carlo calculation with a statistical uncertainty equivalent to a 3D calculation, with a similar calculation time for the 3D and 4D methods. Monte Carlo as a dose calculation tool for 4D radiotherapy planning has two advantages: (1) higher accuracy for calculation in electronic disequilibrium conditions, such as those encountered during lung radiotherapy, and (2) if deformable image registration is used, the calculation time for Monte Carlo is independent of the number of 3D CT image sets constituting a 4D CT, unlike other algorithms for which the calculation time scales linearly with the number of 3D CT image sets constituting a 4D CT.

Algorithms↗

PubMed1997

A flexible approach to time-varying coefficients in the Cox regression setting.

Research on methods for studying time-to-event data (survival analysis) has been extensive in recent years. The basic model in use today represents the hazard function for an individual through a proportional hazards model (Cox, 1972). Typically, it is assumed that a covariate's effect on the hazard function is constant throughout the course of the study. In this paper we propose a method to allow for possible deviations from the standard Cox model, by allowing the effect of a covariate to vary over time. This method is based on a dynamic linear model. We present our method in terms of a Bayesian hierarchical model. We fit the model to the data using Markov chain Monte Carlo methods. Finally, we illustrate the approach with several examples.

Bayes Theorem↗