Optimising muscle parameters in musculoskeletal models using Monte Carlo simulation

The use of musculoskeletal simulation software has become a useful tool for modelling joint and muscle forces during human activity, including in reduced gravity because direct experimentation is difficult. Knowledge of muscle and joint loads can better inform the design of exercise protocols and exercise countermeasure equipment. In this study, the LifeModeler? (San Clemente, CA, USA) biomechanics simulation software was used to model a squat exercise. The initial model using default parameters yielded physiologically reasonable hip-joint forces but no activation was predicted in some large muscles such as rectus femoris, which have been shown to be active in 1-g performance of the activity. Parametric testing was conducted using Monte Carlo methods and combinatorial reduction to find a muscle parameter set that more closely matched physiologically observed activation patterns during the squat exercise. The rectus femoris was predicted to peak at 60.1% activation in the same test case compared to 19.2% activation using default parameters. These results indicate the critical role that muscle parameters play in joint force estimation and the need for exploration of the solution space to achieve physiologically realistic muscle activation.     

Mobile shielding evaluation on the fetal dose during a breast radiotherapy using Monte Carlo simulation

PurposeEvaluation of the out-of-field dose is an important aspect in radiotherapy. Due to the fetus radiosensitivity, this evaluation becomes even more conclusive when the patient is pregnant. In this work, a linear accelerator Varian Clinac 2100c operating at 6 MV, a pregnant anthropomorphic phantom (Maria), and different shields added above the abdominal region of the phantom were used for the analysis based on MCNPX. Methods: The simulations were performed for the medial and lateral projections, using either an open field collimation (10×16 cm²) or a multileaf collimator. The added shields (M1 and M2) were designed based on models proposed by Stovall et al. [1], intending to reduce the deposited dose on the fetus and related structures. Results: The presence of the shields showed to be effective in reducing the doses on the fetus, amniotic sac, and placenta, for example. A reduction of about 43% was found in the dose on the fetus when M2 was added, using the open field collimation, in comparison with the situation with no shield, being the lateral projection the main responsible for the dose. The use of MLC significatively reduced the doses in different structures, including on the fetus and amniotic sac, for example, in comparison to the open field situation. A slight increment on the dose in organs such as the eyes, thyroid and brain was found in both collimation systems, due to the presence of the shields. The contribution of the leakage radiation from the tube head of the linear accelerator was found to be in the order of µGy, being reduced by the presence of the M2 shield. Conclusion: Using the shields showed to be an essential feature in order to reduce the dose not only on the fetus, but also in important structures responsible to its development.     

Quantitative modelling of DNA damage using Monte Carlo track structure method

This paper presents data on modelling of DNA damage induced by electrons, protons and alpha-particles to provide an insight into factors which determine the biological effectiveness of radiations of high and low linear energy transfer (LET). These data include the yield of single- and double-strand breaks (ssb, dsb) and base damage in a cellular environment. We obtain a ratio of 4–15 for ssb:dsb for solid and cellular DNA and a preliminary ratio of about 2 for base damage to strand breakage. Data are also given on specific characteristics of damage at the DNA level in the form of clustered damage of varying complexity, that challenge the repair processes and if not processed adequately could lead to the observed biological effects. It is shown that nearly 30% of dsb are of complex form for low-LET radiation, solely by virtue of additional breaks, rising to about 70% for high-LET radiation. Inclusion of base damage increases the complex proportion to about 60% and 90% for low- and high-LET radiation, respectively. The data show a twofold increase in frequencies of complex dsb from low-LET radiation when base damage is taken into account. It is shown that most ssb induced by high-LET radiation have associated base damages, and also a substantial proportion is induced by low-energy electrons. Received: 20 September 1998 / Accepted in revised form: 15 December 1998     

Modeling of primary photosynthetic processes using the kinetic Monte Carlo method

Processes that occur in the ensemble of photosynthetic electron transport systems have been modeled using a kinetic Monte Carlo method. The size of a simulated ensemble (3–5 million elementary photosynthetic chains) corresponds to the number of photosynthetic reaction centers in a plant cell. The method enables one to modify the structure of a model system according to different concepts of the organization of processes in a photosynthetic membrane. Using this model, the experimental kinetics of the chlorophyll fluorescence induction associated with the Photosystem II and the redox transformations of a photoactive pigment of the Photosystem I have been successfully reproduced. The model was verified by comparing the calculated fluorescence induction curves to experimental curves, obtained in the presence of various photosynthesis inhibitors and under temperature inactivation of the Photosystem II donor side.     

Monte Carlo method for bioluminescence tomography

Bioluminescence imaging plays an important role in the areas of cancer biology, cell biology, gene therapy, and so on. The 2D planar bioluminescent imaging has been transformed into a 3D framework by bioluminescence tomography (BLT) that enables bioluminescent source reconstruction in a mouse using a modality fusion approach. To solve this BLT problem, a geometrical model of the mouse is usually built from a CT/micro-CT/micro-MRI scan, which facilitates the assignment of optical parameters to various anatomical regions in the model. This optical model is then used to facilitate BLT. The forward model is based on Monte Carlo simulation to calculate the diffuse light flux on the surface of the mouse. The forward model data are used to define the imaging system and perform the BLT reconstruction. In this paper, we report the reconstruction of sources inside a heterogeneous highly scattering physical phantom to demonstrate the feasibility of this Monte Carlo based BLT method.     

A multiple-start Monte Carlo docking method.

We present a method to search for possible binding modes of molecular fragments at a specific site of a potential drug target of known structure. Our method is based on a Monte Carlo (MC) algorithm applied to the translational and rotational degrees of freedom of the probe fragment. Starting from a randomly generated initial configuration, favorable binding modes are generated using a two-step process. An MC run is first performed in which the energy in the Metropolis algorithm is substituted by a score function that measures the average distance of the probe to the target surface. This has the effect of making buried probes move toward the target surface and also allows enhanced sampling of deep pockets. In a second MC run, a pairwise atom potential function is used, and the temperature parameter is slowly lowered during the run (Simulated Annealing). We repeat this procedure starting from a large number of different randomly generated initial configurations in order to find all energetically favorable docking modes in a specified region around the target. We test this method using two inhibitor-receptor systems: Streptomyces griseus proteinase B in complex with the third domain of the ovomucoid inhibitor from turkey, and dihydrofolate reductase from E. coli in complex with methotrexate. The method could consistently reproduce the complex found in the crystal structure searching from random initial positions in cubes ranging from 25 A to 50 A about the binding site. In the case of SGPB, we were also successful in docking to the native structure. In addition, we were successful in docking small probes in a search that included the entire protein surface.     

Studies on evolutionary and selective properties of hypercycles using a Monte Carlo method

Summary The most relevant properties of hypercycles were previously studied mainly from a theoretical point of view. We have developed a Monte Carlo method simulating hypercyclic organization to obtain information about the dynamics of this prebiotic organization. Nucleation, growth, and selective properties have been tested and the results obtained are in good agreement with those of the theoretical predictions. The influence of hypercyclic organization of the error threshold has also been studied. As a consequence of the emergence of a hypercycle, the value of this threshold decreases. The amount of this decrease depends on the population size. Moreover, for some interval of quality factor values, either the hypercycle organization or an error catastrophe can be produced, depending on the initial conditions. The influence of these phenomena on both the dynamic behavior and evolutionary advantages of the hypercycle, as well as their decisive roles on genome size, are discussed.Presented at the FEBS Symposium on Genome Organization and Evolution, held in Crete, Greece, September 1–5, 1986     

Time accelerated Monte Carlo simulations of biological networks using the binomial tau-leap method

SUMMARY: Developing a quantitative understanding of intracellular networks requires simulations and computational analyses. However, traditional differential equation modeling tools are often inadequate due to the stochasticity of intracellular reaction networks that can potentially influence the phenotypic characteristics. Unfortunately, stochastic simulations are computationally too intense for most biological systems. Herein, we have utilized the recently developed binomial tau-leap method to carry out stochastic simulations of the epidermal growth factor receptor induced mitogen activated protein kinase cascade. Results indicate that the binomial tau-leap method is computationally 100-1000 times more efficient than the exact stochastic simulation algorithm of Gillespie. Furthermore, the binomial tau-leap method avoids negative populations and accurately captures the species populations along with their fluctuations despite the large difference in their size. AVAILABILITY: http://www.dion.che.udel.edu/multiscale/Introduction.html. Fortran 90 code available for academic use by email. SUPPLEMENTARY INFORMATION: Details about the binomial tau-leap algorithm, software and a manual are available at the above website.     

Bayesian adaptive Markov chain Monte Carlo estimation of genetic parameters

Accurate and fast estimation of genetic parameters that underlie quantitative traits using mixed linear models with additive and dominance effects is of great importance in both natural and breeding populations. Here, we propose a new fast adaptive Markov chain Monte Carlo (MCMC) sampling algorithm for the estimation of genetic parameters in the linear mixed model with several random effects. In the learning phase of our algorithm, we use the hybrid Gibbs sampler to learn the covariance structure of the variance components. In the second phase of the algorithm, we use this covariance structure to formulate an effective proposal distribution for a Metropolis-Hastings algorithm, which uses a likelihood function in which the random effects have been integrated out. Compared with the hybrid Gibbs sampler, the new algorithm had better mixing properties and was approximately twice as fast to run. Our new algorithm was able to detect different modes in the posterior distribution. In addition, the posterior mode estimates from the adaptive MCMC method were close to the REML (residual maximum likelihood) estimates. Moreover, our exponential prior for inverse variance components was vague and enabled the estimated mode of the posterior variance to be practically zero, which was in agreement with the support from the likelihood (in the case of no dominance). The method performance is illustrated using simulated data sets with replicates and field data in barley.     

Genome-wide tagging SNPs with entropy-based Monte Carlo method.

The number of common single nucleotide polymorphisms (SNPs) in the human genome is estimated to be around 3-6 million. It is highly anticipated that the study of SNPs will help provide a means for elucidating the genetic component of complex diseases and variable drug responses. High-throughput technologies such as oligonucleotide arrays have produced enormous amount of SNP data, which creates great challenges in genome-wide disease linkage and association studies. In this paper, we present an adaptation of the cross entropy (CE) method and propose an iterative CE Monte Carlo (CEMC) algorithm for tagging SNP selection. This differs from most of SNP selection algorithms in the literature in that our method is independent of the notion of haplotype block. Thus, the method is applicable to whole genome SNP selection without prior knowledge of block boundaries. We applied this block-free algorithm to three large datasets (two simulated and one real) that are in the order of thousands of SNPs. The successful applications to these large scale datasets demonstrate that CEMC is computationally feasible for whole genome SNP selection. Furthermore, the results show that CEMC is significantly better than random selection, and it also outperformed another block-free selection algorithm for the dataset considered.     

Building proteins from C alpha coordinates using the dihedral probability grid Monte Carlo method.

Dihedral probability grid Monte Carlo (DPG-MC) is a general-purpose method of conformational sampling that can be applied to many problems in peptide and protein modeling. Here we present the DPG-MC method and apply it to predicting complete protein structures from C alpha coordinates. This is useful in such endeavors as homology modeling, protein structure prediction from lattice simulations, or fitting protein structures to X-ray crystallographic data. It also serves as an example of how DPG-MC can be applied to systems with geometric constraints. The conformational propensities for individual residues are used to guide conformational searches as the protein is built from the amino-terminus to the carboxyl-terminus. Results for a number of proteins show that both the backbone and side chain can be accurately modeled using DPG-MC. Backbone atoms are generally predicted with RMS errors of about 0.5 A (compared to X-ray crystal structure coordinates) and all atoms are predicted to an RMS error of 1.7 A or better.     

Phylogenetic tree construction using sequential stochastic approximation Monte Carlo

Monte Carlo methods have received much attention recently in the literature of phylogenetic tree construction. However, they often suffer from two difficulties, the curse of dimensionality and the local-trap problem. The former one is due to that the number of possible phylogenetic trees increases at a super-exponential rate as the number of taxa increases. The latter one is due to that the phylogenetic tree has often a rugged energy landscape. In this paper, we propose a new phylogenetic tree construction method, which attempts to alleviate these two difficulties simultaneously by making use of the sequential structure of phylogenetic trees in conjunction with stochastic approximation Monte Carlo (SAMC) simulations. The use of the sequential structure of the problem provides substantial help to reduce the curse of dimensionality in simulations, and SAMC effectively prevents the system from getting trapped in local energy minima. The new method is compared with a variety of existing Bayesian and non-Bayesian methods on simulated and real datasets. Numerical results are in favor of the new method in terms of quality of the resulting phylogenetic trees.     

Pulse pressure variation tracking using sequential Monte Carlo methods

The pulse pressure variation (PPV) is a measure of the respiratory effect on the variation of systemic arterial blood pressure (ABP) in patients receiving full mechanical ventilation. It is a promising predictor of increases in cardiac output due to an infusion of fluid. We describe a novel automatic algorithm to estimate the PPV of ABP signals recorded under full respiratory support. The algorithm utilizes our recently developed sequential Monte Carlo method (SMCM), which is called a maximum a-posteriori adaptive marginalized particle filter (MAM-PF). MAM-PF estimates the state-space model parameters of the ABP signal continuously and its upper and lower envelopes are derived as a combination of those parameter estimates. Then, the continuous PPV values can be easily obtained based on those estimated envelopes. We report the assessment results of the proposed algorithm on real ABP signals.     

A Monte Carlo method for the simulation of kinetie models

The purpose of this note is to illustrate the feasibility of simulating kinetic systems, such as commonly encountered in photosynthesis research, using the Monte Carlo (MC) method. In this approach, chemical events are considered at the molecular level where they occur randomly and the macroscopic kinetic evolution results from averaging a large number of such events. Their repeated simulation is easily accomplished using digital computing. It is shown that the MC approach is well suited to the capabilities and resources of modern microcomputers. A software package is briefly described and discussed, allowing a simple programming of any kinetic model system and its resolution. The execution is reasonably fast and accurate; it is not subject to such instabilities as found with the conventional analytical approach.Abbreviations MC Monte Carlo - RN random number - PSU photosynthetic unit Dedicated to Prof. L.N.M. Duysens on the occasion of his retirement.