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PubMed1998

Noise from voltage-gated ion channels may influence neuronal dynamics in the entorhinal cortex.

Neurons of the superficial medial entorhinal cortex (MEC), which deliver neocortical input to the hippocampus, exhibit intrinsic, subthreshold oscillations with slow dynamics. These intrinsic oscillations, driven by a persistent Na+ current and a slow outward current, may help to generate the theta rhythm, a slow rhythm that plays an important role in spatial and declarative learning. Here we show that the number of persistent Na+ channels underlying subthreshold oscillations is relatively small (<10(4)) and use a physiologically based stochastic model to argue that the random behavior of these channels may contribute crucially to cellular-level responses. In acutely isolated MEC neurons under voltage clamp, the mean and variance of the persistent Na+ current were used to estimate the single channel conductance and voltage-dependent probability of opening. A hybrid stochastic-deterministic model was built by using voltage-clamp descriptions of the persistent and fast-inactivating Na+ conductances, along with the fast and slow K+ conductances. All voltage-dependent conductances were represented with nonlinear ordinary differential equations, with the exception of the persistent Na+ conductance, which was represented as a population of stochastic ion channels. The model predicts that the probabilistic nature of Na+ channels increases the cell's repertoire of qualitative behaviors; although deterministic models at a particular point in parameter space can generate either subthreshold oscillations or phase-locked spikes (but rarely both), models with an appropriate level of channel noise can replicate physiological behavior by generating both patterns of electrical activity for a single set of parameters. Channel noise may contribute to higher order interspike interval statistics seen in vitro with DC current stimulation. Models with channel noise show evidence of spike clustering seen in brain slice experiments, although the effect is apparently not as prominent as seen in experimental results. Channel noise may contribute to cellular responses in vivo as well; the stochastic system has enhanced sensitivity to small periodic stimuli in a form of stochastic resonance that is novel (in that the relevant noise source is intrinsic and voltage-dependent) and potentially physiologically relevant. Although based on a simple model that does not include all known membrane mechanisms of MEC stellate cells, these results nevertheless imply that the stochastic nature of small collections of molecules may have important effects at the cellular and network levels.

Animals↗
PubMed2006

Modeling film-coat non-uniformity in polymer coated pellets: a stochastic approach.

The objective of the present study is to include coating thickness non-uniformity in the development of a drug release model using coated ion-exchange pellets through the use of stochastic approaches. Drug release from ion-exchange resins was described using a Nernst-Plank model. Complexes of a model drug (dextromethorphan) and Dowex 50WX4-200 were prepared using a modified batch method and coated with Kollicoat SR 30D polymer. The deterministic model, validated using experimental drug release profiles for different coating thicknesses at 0%, 10%, 15%, 20% (w/w), was in agreement with the experimental data with a maximum root mean square error (RMSE) of 2.4%. An arbitrary Lagrangian-Eulerian approach was pursued to develop models of spherical pellets with non-uniform coating thicknesses. The Monte Carlo method was used to simulate the effect of the level of coating deformity on the cumulative drug release profile. Considering the co-existence of equal percentages of deformed and undeformed pellets in a batch, the cumulative release profile can vary by approximately +/-6% as a result of coating non-uniformity. The release profile obtained for a model of an arbitrary pellet with an actual non-uniform coating profile was in good agreement with the average release profile for the models of the theoretical randomly deformed pellets. The developed mathematical model is a useful tool to evaluate and predict release profiles of polymer coated ion-exchange resin complexes.

Algorithms↗
PubMed2002

Identification of determinism in noisy neuronal systems.

Most neuronal ensembles are nonlinear excitable systems. Thus it is becoming common to apply principles derived from nonlinear dynamics to characterize neuronal systems. One important characterization is whether such systems contain deterministic behavior or are purely stochastic. Unfortunately, many methods used to make this distinction do not perform well when both determinism and high-amplitude noise are present which is often the case in physiological systems. Therefore, we propose two novel techniques for identifying determinism in experimental systems. The first, called short-time expansion analysis, examines the expansion rate of small groups of points in state space. The second, called state point forcing, derives from the technique of chaos control. The system state is forced onto a fixed point, and the subsequent behavior is analyzed. This technique can be used to verify the presence of fixed points (or unstable periodic orbits) and to assess stationarity. If these are present, it implies that the system contains determinism. We demonstrate the use and possible limitations of these two techniques in two systems: the Hénon map, a classic example of a chaotic system, and spontaneous epileptiform bursting in the rat hippocampal slice. Identifying the presence of determinism in a physiological system assists in the understanding of the system's dynamics and provides a mechanism for manipulating this behavior.

Action Potentials↗
PubMed2007

Mass fluctuation kinetics: capturing stochastic effects in systems of chemical reactions through coupled mean-variance computations.

The intrinsic stochastic effects in chemical reactions, and particularly in biochemical networks, may result in behaviors significantly different from those predicted by deterministic mass action kinetics (MAK). Analyzing stochastic effects, however, is often computationally taxing and complex. The authors describe here the derivation and application of what they term the mass fluctuation kinetics (MFK), a set of deterministic equations to track the means, variances, and covariances of the concentrations of the chemical species in the system. These equations are obtained by approximating the dynamics of the first and second moments of the chemical master equation. Apart from needing knowledge of the system volume, the MFK description requires only the same information used to specify the MAK model, and is not significantly harder to write down or apply. When the effects of fluctuations are negligible, the MFK description typically reduces to MAK. The MFK equations are capable of describing the average behavior of the network substantially better than MAK, because they incorporate the effects of fluctuations on the evolution of the means. They also account for the effects of the means on the evolution of the variances and covariances, to produce quite accurate uncertainty bands around the average behavior. The MFK computations, although approximate, are significantly faster than Monte Carlo methods for computing first and second moments in systems of chemical reactions. They may therefore be used, perhaps along with a few Monte Carlo simulations of sample state trajectories, to efficiently provide a detailed picture of the behavior of a chemical system.

Algorithms↗
PubMed2006

Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems.

BACKGROUND: We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness. RESULTS: We have developed a new procedure based on the scatter search methodology for nonlinear optimization of dynamic models of arbitrary (or even unknown) structure (i.e. black-box models). In this contribution, we describe and apply this novel metaheuristic, inspired by recent developments in the field of operations research, to a set of complex identification problems and we make a critical comparison with respect to the previous (above mentioned) successful methods. CONCLUSION: Robust and efficient methods for parameter estimation are of key importance in systems biology and related areas. The new metaheuristic presented in this paper aims to ensure the proper solution of these problems by adopting a global optimization approach, while keeping the computational effort under reasonable values. This new metaheuristic was applied to a set of three challenging parameter estimation problems of nonlinear dynamic biological systems, outperforming very significantly all the methods previously used for these benchmark problems.

Algorithms↗
PubMed1994

Subthreshold frequency selectivity in avian auditory thalamus.

1. We studied the frequency responses of neurons in the nucleus ovoidalis (OV), the principal thalamic auditory relay nucleus of the chicken, in the subthreshold range of membrane potentials. The frequency response is the impedance amplitude profile evident in the voltage response to a broadband stimulus. The stimulus was a deterministic periodic current input of small amplitude, sweeping through a specified frequency range. We used whole-cell, tight-seal recording techniques in slices to study the voltage responses and membrane properties in current and voltage clamp. 2. Generally, low-frequency resonant humps with peak impedances of approximately 6 Hz characterized the frequency responses of OV neurons. This resonance was the principal determinant for frequency selectivity in the majority of OV neurons expressing only a tonic mode of firing. 3. The 6-Hz resonance was voltage dependent and most distinct where the activation ranges of a hyperpolarization activated inward current (IH) and a persistent Na+ current tend to overlap. The potential range for optimal resonance often included the resting potential. 4. Application of the Na+ current antagonist, tetrodotoxin, blocked the persistent Na+ current and most of the resonant hump at depolarized levels but did not affect the resonant peak along the frequency axis. Thus the persistent Na+ current may serve to amplify the resonance. 5. Extracellular application of Cs+, but not Ba2+, blocked a voltage sag during pulsed hyperpolarization as well as the IH current. Application of Cs+ also eliminated the 6-Hz resonance. An IH seems, therefore, instrumental for the resonance. 6. A minority of neurons that expressed low-threshold Ca2+ spikes and burst firing at hyperpolarized states displayed voltage oscillations at 2-4 Hz, spontaneously or in response to pulsatile stimuli. Application of Ni2+ blocked the oscillations and the low-threshold spikes, presumably produced by a T-type Ca2+ current. The resonance at 6 Hz, however, was only slightly affected by Ni2+. A T-type current, therefore, is critical for the 2- to 4-Hz oscillations. 7. Membrane resonance may dominate the power spectrum of subthreshold potential fluctuations. The resonance demonstrated in vitro may be stabilized by experimental procedures; its frequency may be different and more variable in vivo. Resonances in thalamic neurons may play a role in auditory signal processing in birds.

Animals↗
PubMed1988

Sexual partner selectiveness effects on homosexual HIV transmission dynamics.

Deterministic simulation models are used to show that HIV transmission dynamics in homosexual populations can be strongly affected by sexual partner selectiveness. The type of selectiveness or biased mixing examined is where individuals with similar new partnership formation rates are more likely to form a pair than would be expected by chance. The effect of such selectiveness could be strong even when the total number and distribution of new sexual partnerships and sex acts remains constant. This means that in order to predict the future course of HIV transmission and identify the populations at highest risk, we must have information not only on the frequency of new sexual partnerships and types of sex acts, but also on who has sex with whom. Given high sexual partner selectiveness, some groups of homosexuals with low rates of sex and new sex partners would take many decades before a single introduction would generate an epidemic. Epidemics in these groups can be markedly accelerated by only modest contact with higher risk groups. Even in very low activity groups, which if isolated would have no epidemic, an important proportion of their members can be infected when they are not selective. The relative risks of AIDS in groups making high numbers of new sexual partnerships compared to groups making low numbers are markedly affected by sexual partner selectiveness. The models developed were examined using information collected in 1984 from the Coping and Change Study in collaboration with the Chicago Multicenter AIDS Cohort Study. This population was divided into activity groups by the rate at which individuals established new sexual partnerships and then a structure of new sexual partnerships between these activity groups was defined consistent with available data. Even without introducing any behavior change in the models, the proportion of the homosexual population infected was seen to level off temporarily at around 50% after several years as a consequence of saturation in the high risk groups when lower risk groups were not yet being consumed by the epidemic process. Most sex in the study population is casual or anonymous. The sample selection procedures were biased toward individuals who engage in such sex. There is, however, a large group of individuals that avoids the casual and anonymous sex scene. Simulated epidemics indicated that under a variety of conditions, the population that does not engage in casual and anonymous sex could experience an epidemic of HIV infection quite some time after the epidemic in the population that does has waned.(ABSTRACT TRUNCATED AT 400 WORDS)

Acquired Immunodeficiency Syndrome↗
PubMedDate not supplied

A novel mechanism for irregular firing of a neuron in response to periodic stimulation: irregularity in the absence of noise.

Irregular firing of action potentials (AP's) is a characteristic feature of neurons in the brain. The variability has been attributed to noise from various sources. This study illustrates an alternative mechanism, namely, deterministic irregularity within a model of ionic conductances. Specifically, a model based on modern measurements of the Na+ and K+ current components from the squid giant axon fires irregularly in response to a continuous train of near-threshold current pulses. The interspike interval histogram from these simulations is multi-modal, a result which in other systems has been attributed to stochastic resonance. Moreover, the simulations exhibited short burst of spikes followed by relatively long quiescent periods, a result suggestive of patterned input to the model even though the input consisted of a train of regularly spaced current pulses. The variability of firing is attributable to variations in AP parameters, in particular AP amplitude. The action potential for squid giant axons is not all-or-none. Rather, it is fundamentally a continuous function of stimulus amplitude. That is, the membrane lacks a threshold. Variation in AP amplitude, and to a lesser extent, AP duration, can produce variations in the time to a subsequent AP, which represents a paradigm shift for understanding irregular neuronal firing. The emphasis is not as much on events prior to an AP as it is on the AP's themselves.

Acoustic Stimulation↗
PubMed1999

Dissociation of HIV-1 from follicular dendritic cells during HAART: mathematical analysis.

Follicular dendritic cells (FDC) provide a reservoir for HIV type 1 (HIV-1) that may reignite infection if highly active antiretroviral therapy (HAART) is withdrawn before virus on FDC is cleared. To estimate the treatment time required to eliminate HIV-1 on FDC, we develop deterministic and stochastic models for the reversible binding of HIV-1 to FDC via ligand-receptor interactions and examine the consequences of reducing the virus available for binding to FDC. Analysis of these models shows that the rate at which HIV-1 dissociates from FDC during HAART is biphasic, with an initial period of rapid decay followed by a period of slower exponential decay. The speed of the slower second stage of dissociation and the treatment time required to eradicate the FDC reservoir of HIV-1 are insensitive to the number of virions bound and their degree of attachment to FDC before treatment. In contrast, the expected time required for dissociation of an individual virion from FDC varies sensitively with the number of ligands attached to the virion that are available to interact with receptors on FDC. Although most virions may dissociate from FDC on the time scale of days to weeks, virions coupled to a higher-than-average number of ligands may persist on FDC for years. This result suggests that HAART may not be able to clear all HIV-1 trapped on FDC and that, even if clearance is possible, years of treatment will be required.

Anti-HIV Agents↗
PubMed2003

Modeling variability and uncertainty associated with inhaled weapons-grade PuO2.

The work presented relates to developing a stochastic version of the ICRP 66 respiratory tract deposition model and applying the stochastic model to characterize the variability/uncertainty associated with inhaled PuO2 for a hypothetical population of nuclear workers engaged in light work-related exercise. The parameter uncertainty/variability distributions used are essentially the same as the FORTRAN-based stochastic deposition model of Bolch et al. known as LUDUC (LUng Dose Uncertainty Code). Based on Crystal Ball software, this stochastic deposition model includes particle polydispersity, which Bolch et al. did not discuss. This paper first compares model-simulated regional deposition probability distributions to deterministic results based on LUDEP (LUng Dose Evaluation Program) software, which implements the ICRP 66 deterministic deposition model. For these comparisons, a particle density of 3 g cm(-3) (for hypothetical radioactive particles) was used. The range of possible depositions generated by LUDUC and the Crystal Ball program results revealed LUDEP's limitations. Even though LUDEP tends to use parameters that represent average parameter values for adult males, it overestimates deposition in the lower regions of the lung for most of the population. The Crystal Ball program was then used to generate radioactivity intake distributions for single and multiple PuO2 particle intakes by a hypothetical population of nuclear workers for the stochastic intake (STI) paradigm. These distributions of radioactivity intake are evaluated for the five primary regions of the respiratory tract as defined in the ICRP Publication 66. The results reveal that when a particle has been deposited, the radioactivity is likely to be low if it is in the lower regions (< 10 Bq for the bb and AI regions), but it may be quite large in the upper regions (as much as 600 Bq for the ET1, and ET2 regions), and the distributions for radioactivity become less and less skewed to the right, as particles penetrate deeper within the respiratory tract.

Administration, Inhalation↗
PubMed2006

Prediction of the variance of stereological volume estimates from systematic sections using computer-intensive methods.

The Cavalieri method is an unbiased estimator of the total volume of a body from its transectional areas on systematic sections. The coefficient of error (CE) of the Cavalieri estimator was predicted by a computer-intensive method. The method is based on polynomial regression of area values on section number and simulation of systematic sectioning. The measurement function is modelled as a quadratic polynomial, with an error term superimposed. The relative influence of the trend and the error component is estimated by techniques of analysis of variance. This predictor was compared with two established short-cut estimators of the CE based on transitive theory. First, all predictors were applied to data sets from six deterministic models with analytically known CE. For these models, the CE was best predicted by the older short-cut estimator and by the computer-intensive approach, if the measurement function had finite jumps. The best prediction was provided by the newer short-cut estimator when the measurement function was continuous. The predictors were also applied to published empirical datasets. The first data set consisted of 10 series of areas of systematically sectioned rat hearts with 10-13 items, the second data set consisted of 13 series of systematically sampled transectional areas of various biological structures with 38-90 items. On the whole, similar mean values for the predicted CE were obtained with the older short-cut estimator and the computer-intensive method. These ranged in the same order of magnitude as resampling estimates of the CE from the empirical data sets, which were used as a cross-check. The mean values according to the newer short-cut CE estimator ranged distinctly lower than the resampling estimates. However, for individual data sets, it happened that the closest prediction as compared to the cross-check value could be provided by any of the three methods. This finding is discussed in terms of the statistical variability of the resampling estimate itself.

Analysis of Variance↗
PubMed1984

The California Automated Mortality Linkage System (CAMLIS).

The California Automated Mortality Linkage System (CAMLIS), established in 1981 to facilitate the conduct of follow-up studies in the State of California, employs a combination of deterministic and probabilistic linkage decision criteria to perform the death clearance function. The system was evaluated against four traditional death clearance procedures and the performance of each procedure measured in terms of measures of sensitivity and specificity. Only one procedure was associated with a specificity lower than 0.99; for that one, the specificity was 0.93. There was much greater fluctuation in the observed sensitivity levels. In one of the procedures, CAMLIS demonstrated a sensitivity of 0.97 versus 0.79 for the Social Security Administration. A comparison against the National Death Index (NDI) produced sensitivities of 0.89 for CAMLIS and 0.94 for the NDI. An assessment of manual search procedures using a file of Japanese names produced a CAMLIS sensitivity measure of 0.92 compared with 0.93 for the manual search. Another manual search procedure using microfiche copies of the state death index produced a CAMLIS sensitivity of 0.97; in this evaluation, the sensitivity of the manual search was defined as 1.0. Another measure of performance of a death clearance procedure is its predictive value in identifying a person who has died; CAMLIS generated predictive values in these evaluations that ranged from 0.93 through 0.99, contrasted with the NDI value of 0.59.

California↗
PubMed2002

Statistical determination of cost-effectiveness frontier based on net health benefits.

Statistical methods are given for producing a cost-effectiveness frontier for an arbitrary number of programs. In the deterministic case, the net health benefit (NHB) decision rule is optimal; the rule funds the program with the largest positive NHB at each lambda, the amount a decision-maker is willing to pay for an additional unit of effectiveness. For bivariate normally distributed cost and effectiveness variables and a specified lambda, a statistical procedure is presented, based on the method of constrained multiple comparisons with the best (CMCB), for determining the program with the largest NHB. A one-tailed t test is used to determine if the NHB is positive. To obtain a statistical frontier in the lambda-NHB plane, we develop a method to produce the region in which each program has the largest NHB, by pivoting a CMCB confidence interval. A one-sided version of Fieller's theorem is used to determine the region where the NHB of each program is positive. At each lambda, the pointwise error rate is bounded by a prespecified alpha. Upper bounds on the familywise error rate, the probability of an error at any value of lambda, are given. The methods are applied to a hypothetical clinical trial of antipsychotic agents.

Algorithms↗
PubMed1998

Power spectral density of unevenly sampled data by least-square analysis: performance and application to heart rate signals.

This work studies the frequency behavior of a least-square method to estimate the power spectral density of unevenly sampled signals. When the uneven sampling can be modeled as uniform sampling plus a stationary random deviation, this spectrum results in a periodic repetition of the original continuous time spectrum at the mean Nyquist frequency, with a low-pass effect affecting upper frequency bands that depends on the sampling dispersion. If the dispersion is small compared with the mean sampling period, the estimation at the base band is unbiased with practically no dispersion. When uneven sampling is modeled by a deterministic sinusoidal variation respect to the uniform sampling the obtained results are in agreement with those obtained for small random deviation. This approximation is usually well satisfied in signals like heart rate (HR) series. The theoretically predicted performance has been tested and corroborated with simulated and real HR signals. The Lomb method has been compared with the classical power spectral density (PSD) estimators that include resampling to get uniform sampling. We have found that the Lomb method avoids the major problem of classical methods: the low-pass effect of the resampling. Also only frequencies up to the mean Nyquist frequency should be considered (lower than 0.5 Hz if the HR is lower than 60 bpm). We conclude that for PSD estimation of unevenly sampled signals the Lomb method is more suitable than fast Fourier transform or autoregressive estimate with linear or cubic interpolation. In extreme situations (low-HR or high-frequency components) the Lomb estimate still introduces high-frequency contamination that suggest further studies of superior performance interpolators. In the case of HR signals we have also marked the convenience of selecting a stationary heart rate period to carry out a heart rate variability analysis.

Cardiac Pacing, Artificial↗
PubMed2003

Correlation dimension and the largest Lyapunov exponent characterization of RR interval.

OBJECTIVE: To search for evidence of deterministic chaos and to characterise it quantitatively in RR intervals of different subjects. METHOD: An improved Grassberger-Procaccia (GP) algorithm was proposed for computing the correlation dimensions (CD) of RR intervals in ten healthy young men, ten healthy old men, and ten atrial fibrillation (AF) patients. Analysis was also performed by calculating the largest Lyapunov exponents. RESULT: It was found that the cardiac systems of healthy young men are some 7-8 dimensional complex dynamic systems, while those of healthy old men are 6-6.5 dimensional, and those of AF patients had dimensions of about 4-4.5. The young men had the largest Lyapunov exponents of about 0.019-0.23, the largest Lyapunov exponents of old men was 0.12-0.16, and that of AF patients was 0.083-0.123. CONCLUSION: The above results demonstrated that the RR intervals could be chaotic. The decrease in the CDs and the largest Lyapunov exponents as we move from the young to the old and then to the AF patients reflects the loss of complexity as the heart becomes less healthy. Therefore, correlation dimension and the largest Lyapunov exponent could be used as some novel non-invasive analysis tools for clinical cardiology.

Adult↗
PubMed1996

Quantal transmitter release at somatic motor-nerve terminals: stochastic analysis of the subunit hypothesis.

Here we analyze the problem of determining whether experimentally measured spontaneous miniature end-plate currents (MEPCs) indicate that quanta are composed of subunits. The properties of MEPCs at end plates with or without secondary clefts at the neuromuscular junction are investigated, using both stochastic and deterministic models of the action of a quantum of transmitter. It is shown that as the amount of transmitter in a quantum is increased above about 4000 acetylcholine (ACh) molecules there is a linear increase in the size of the MEPC. It is possible to then use amplitude-frequency histograms of such MEPCs to detect a subunit structure, as there is little potentiation effect above 4000 ACh molecules. Autocorrelation and power spectral analyses of such histograms establish that their subunit structure can be detected if the coefficient of variation of the subunit size is less than about 0.12 or, if electrical noise is added, about 0.1. Positive gradients relate the rise time and half-decay times of MEPCs to their amplitude, even in the absence of potentiating effects; these gradients are shallower at motor nerve terminals that possess secondary clefts. The effect of asynchronous release of subunits is also investigated. The criteria determined by this analysis for identifying a subunit composition in the quantum are applied to an amplitude-frequency histogram of MEPCs recorded from a small group of active zones at a visualized amphibian motor-nerve terminal. This did not provide evidence for a subunit structure.

Acetylcholine↗
PubMed2002

Parental assignment in fish using microsatellite genetic markers with finite numbers of parents and offspring.

Deterministic predictions for the proportion of offspring assigned to different numbers of parent-pairs are developed in order to investigate the power of microsatellite loci for parental assignment in fish species. Comparisons with stochastic simulation results show that predictions based on exclusion probabilities are accurate, provided that the number of parents involved in the crosses is large. Accounting for sampling of parents gave very accurate predictions for a small number of parents and a single biallelic locus. For large numbers of loci or large numbers of alleles per locus stochastic simulations are, however, the only available method to predict the power of assignment of a particular set of loci when the number of parents is small. Nine 5-allele loci or six 10-allele loci with equifrequent alleles, are sufficient for assigning, with certainty, parents to 99% of the fish resulting from either 100 or 400 crosses. Results simulating a set of highly polymorphic microsatellites developed for Atlantic salmon show that the four most informative loci are sufficient to assign at least 99% of the offspring to the correct pair with 100 crosses involving 100 males and 100 females. An additional locus is required for correctly assigning 99% of the offspring when the 100 crosses are produced with 10 males and 10 females.

Animals↗
PubMed2005

A stochastic model of elbow flexion strength for subjects with and without long head biceps tear.

The classical approach of musculoskeletal modeling is to predict muscle forces and joint torques with a deterministic model constructed from parameters of an average subject. However, this type of model does not perform well for outliers, and does not model the effects of parameter variability. In this study, a Monte-Carlo model was used to stochastically simulate the effects of variability in musculoskeletal parameters on elbow flexion strength in healthy normals, and in subjects with long head biceps (LHB) rupture. The goal was to determine if variability in elbow flexion strength could be quantifiably explained with variability in musculoskeletal parameters. Parameter distributions were constructed from data in the literature. Parameters were sampled from these distributions and used to predict muscle forces and joint torques. The median and distribution of measured joint torque was predicted with small errors (< 5%). Muscle forces for both cases were predicted and compared. In order to predict measured torques for the case of LHB rupture, the median force and mean cross-sectional area in the remaining elbow flexor muscles is greater than in healthy normals. The probabilities that muscle forces for the Tear case exceed median muscle forces for the No-Tear case are 0.98, 0.99 and 0.79 for SH Biceps, brachialis and brachioradialis, respectively. Differences in variability of measured torques for the two cases are explained by differences in parameter variability.

Computer Simulation↗