Parameter estimation in a crossbridge muscle model

Models of muscle crossbridge dynamics have great potential for understanding muscle contraction and having a wide range of application. However, the estimation of many model parameters, most of which are difficult to measure, limits their applicability. This study developed a method of estimating parameters in the Distribution Moment crossbridge model from measurements of force-length and force-velocity relationships in cat soleus single muscle fibers. Analysis of the parameter estimates showed that the detachment rate parameters had more uncertainty than the attachment rate parameter, which could reflect physiological variations in the contractile protein content and in the response of muscle to lengthenings.     

Parameter estimation for a point-source diffusion-decay morphogen model

Journal of Mathematical Biology - In this paper we present a novel method for finding unknown parameters for an unknown morphogen. We postulate the existence of an unknown morphogen in a given...     

Parameter estimation in a generalized discrete-time model of density dependence

Flexible discrete-time per-capita-growth-rate models accommodating a variety of density-dependent relationships offer parsimonious explanations for the variation of population abundance through time. However, the accuracy of standard approaches to parameter estimation and confidence interval construction for such models has not been explored in a generalized setting or with consideration of limited sample sizes typical for ecology. Here, we use simulated data to quantify the relative effects of sample size, population perturbations, and environmental stochasticity on statistical inference. We focus on the key parameters that inform population dynamic predictions in a generalized Beverton–Holt model. We find that reliable parameter estimation requires data spanning ranges where both low and high density dependence act. However, the asymptotic distribution of the likelihood ratio test statistic can be fairly accurate for constructing confidence regions even when point estimation is poor. Consideration of the joint profile likelihood surface is shown to be useful for assessing reliability of point estimates and dynamical population predictions. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Parameter estimation in a Gompertzian stochastic model for tumor growth

The problem of estimating parameters in the drift coefficient when a diffusion process is observed continuously requires some specific assumptions. In this paper, we consider a stochastic version of the Gompertzian model that describes in vivo tumor growth and its sensitivity to treatment with antiangiogenic drugs. An explicit likelihood function is obtained, and we discuss some properties of the maximum likelihood estimator for the intrinsic growth rate of the stochastic Gompertzian model. Furthermore, we show some simulation results on the behavior of the corresponding discrete estimator. Finally, an application is given to illustrate the estimate of the model parameters using real data.     

A nonlinear viscoelastic model of lung tissue mechanics.

There have been a number of attempts recently to use linear models to describe the low-frequency (0-2 Hz) dependence of lung tissue resistance (Rti) and elastance (Eti). Only a few attempts, however, have been made to account for the volume dependence of these quantities, all of which require the tissues to be plastoelastic. In this paper we specifically avoid invoking plastoelasticity and develop a nonlinear viscoelastic model that is also capable of accounting for the nonlinear and frequency-dependent features of lung tissue mechanics. The model parameters were identified by fitting the model to data obtained in a previous study from dogs during sinusoidal ventilation. The model was then used to simulate pressure and flow data by use of various types of ventilation patterns similar to those that have been employed experimentally. Rti and Eti were estimated from the simulated data by use of four different estimation techniques commonly applied in respiratory mechanics studies. We found that the estimated volume dependence of Rti and Eti is sensitive to both the ventilation pattern and the estimation technique, being in error by as much as 217 and 22%, respectively.     

Parameter estimation for a leaky integrate-and-fire neuronal model from ISI data

The Ornstein-Uhlenbeck process has been proposed as a model for the spontaneous activity of a neuron. In this model, the firing of the neuron corresponds to the first passage of the process to a constant boundary, or threshold. While the Laplace transform of the first-passage time distribution is available, the probability distribution function has not been obtained in any tractable form. We address the problem of estimating the parameters of the process when the only available data from a neuron are the interspike intervals, or the times between firings. In particular, we give an algorithm for computing maximum likelihood estimates and their corresponding confidence regions for the three identifiable (of the five model) parameters by numerically inverting the Laplace transform. A comparison of the two-parameter algorithm (where the time constant tau is known a priori) to the three-parameter algorithm shows that significantly more data is required in the latter case to achieve comparable parameter resolution as measured by 95% confidence intervals widths. The computational methods described here are a efficient alternative to other well known estimation techniques for leaky integrate-and-fire models. Moreover, it could serve as a template for performing parameter inference on more complex integrate-and-fire neuronal models.     

Parameter estimation and sensitivity analysis of a nonlinearly elastic static lung model

A model for the static pressure-volume behavior of the lung parenchyma based on a pseudo-elastic strain energy function was tested. Values of the model parameters and their variances were estimated by an optimal least-squares fit of the model-predicted pressures to the corresponding data from excised, saline-filled dog lungs. Although the model fit data from twelve lungs very well, the coefficients of variation for parameter values differed greatly. To analyze the sensitivity of the model output to its parameters, we examined an approximate Hessian, H, of the least-squares objective function. Based on the determinant and condition number of H, we were able to set formal criteria for choosing the most reliable estimates of parameter values and their variances. This in turn allowed us to specify a normal range of parameter values for these dog lungs. Thus the model not only describes static pressure-volume data, but also uses the data to estimate parameters from a fundamental constitutive equation. The optimal parameter estimation and sensitivity analysis developed here can be widely applied to other physiologic systems.     

Parameter identification for systems of nonlinear differential equations by the example of Lotka-Volterra model

In this article we study the inverse problem of finding coefficients of Lotka-Volterra equations from one given solution. The conditions of existence and uniqueness of the inverse problem are found.     

Parameter estimation and model selection for Neyman-Scott point processes

This paper proposes an approximative method for maximum likelihood estimation of parameters of Neyman-Scott and similar point processes. It is based on the point pattern resulting from forming all difference points of pairs of points in the window of observation. The intensity function of this constructed point process can be expressed in terms of second-order characteristics of the original process. This opens the way to parameter estimation, if the difference pattern is treated as a non-homogeneous Poisson process. The computational feasibility and accuracy of this approach is examined by means of simulated data. Furthermore, the method is applied to two biological data sets. For these data, various cluster process models are considered and compared with respect to their goodness-of-fit.     

Cell mechanics studied by a reconstituted model tissue

Tissue models reconstituted from cells and extracellular matrix (ECM) simulate natural tissues. Cytoskeletal and matrix proteins govern the force exerted by a tissue and its stiffness. Cells regulate cytoskeletal structure and remodel ECM to produce mechanical changes during tissue development and wound healing. Characterization and control of mechanical properties of reconstituted tissues are essential for tissue engineering applications. We have quantitatively characterized mechanical properties of connective tissue models, fibroblast-populated matrices (FPMs), via uniaxial stretch measurements. FPMs resemble natural tissues in their exponential dependence of stress on strain and linear dependence of stiffness on force at a given strain. Activating cellular contractile forces by calf serum and disrupting F-actin by cytochalasin D yield "active" and "passive" components, which respectively emphasize cellular and matrix mechanical contributions. The strain-dependent stress and elastic modulus of the active component were independent of cell density above a threshold density. The same quantities for the passive component increased with cell number due to compression and reorganization of the matrix by the cells.     

Parameter estimation in a stochastic model of the tubuloglomerular feedback mechanism in a rat nephron

A key parameter in the understanding of renal hemodynamics is the gain of the feedback function in the tubuloglomerular feedback mechanism. A dynamic model of autoregulation of renal blood flow and glomerular filtration rate has been extended to include a stochastic differential equations model of one of the main parameters that determines feedback gain. The model reproduces fluctuations and irregularities in the tubular pressure oscillations that the former deterministic models failed to describe. This approach assumes that the gain exhibits spontaneous erratic variations that can be explained by a variety of influences, which change over time (blood pressure, hormone levels, etc.). To estimate the key parameters of the model we have developed a new estimation method based on the oscillatory behavior of the data. The dynamics is characterized by the spectral density, which has been estimated for the observed time series, and numerically approximated for the model. The parameters have then been estimated by the least squares distance between data and model spectral densities. To evaluate the estimation procedure measurements of the proximal tubular pressure from 35 nephrons in 16 rat kidneys have been analyzed, and the parameters characterizing the gain and the delay have been estimated. There was good agreement between the estimated values, and the values obtained for the same parameters in independent, previously published experiments.     

Parameter estimation of a plant uptake model for cyanide: application to hydroponic data

A plant uptake model is applied to describe free cyanide and ferrocyanide transport and fate in willow (Salix eriocephala var. Michaux) grown in hydroponics. The model is applied to experimental data to determine best-fit parameter values, their associated uncertainty, and their relative importance to field-scale phytoremediation applications. The fitted model results, using least-squares optimization of the observed log concentrations, indicate that free cyanide volatilization from leaf tissue and free cyanide cell wall adsorption were negligible. The free cyanide maximum uptake rate and assimilate (noncyanide 15N) first-order leaf loss rate were the only coefficients that significantly affected the model goodness of fit and were concurrently sensitive to data uncertainty in the parameter optimization. Saturation kinetics may be applicable for free cyanide uptake into plants, but not for ferrocyanide uptake, which may occur via preferential protein-mediated or inefficient transpiration stream uptake. Within the free cyanide system, the relative magnitudes of the saturation uptake parameters and the demonstration of an active role for plants in uptake relative to transpiration suggest the potential importance of preferential diffusion through the cell membranes as reported in the literature, rather than protein-mediated uptake. The fitted 13-parameter model matched the observed data well except for the predicted stem and leaf tissue assimilate concentrations, which were significantly underestimated, particularly in the free cyanide system. These low predicted values, combined with the slightly underestimated solution free cyanide removal, suggest that noncyanide 15N redistribution in phloem should be considered.     

Parameter estimation for a mathematical model of the cell cycle in frog eggs.

Parameter values for a kinetic model of the nuclear replication-division cycle in frog eggs are estimated by fitting solutions of the kinetic equations (nonlinear ordinary differential equations) to a suite of experimental observations. A set of optimal parameter values is found by minimizing an objective function defined as the orthogonal distance between the data and the model. The differential equations are solved by LSODAR and the objective function is minimized by ODRPACK. The optimal parameter values are close to the "guesstimates" of the modelers who first studied this problem. These tools are sufficiently general to attack more complicated problems, where guesstimation is impractical or unreliable.     

Parameter estimation in a model for multidimensional recording of neuronal data: a Gibbsian approximation approach

This article proposes improved numerical procedures for estimating parameters in a spatiotemporal lattice model introduced for the analysis of cortical activities monitored from arrays of diodes. The numerical algorithms are based on approximations inspired by statistical physics. Both Gibbsian and mean-field approximations are used; they allow for computing local conditional probabilities inside the lattice. The statistical procedures rely on the computation of pseudomaximum-likelihood estimators. The estimators are evaluated on the basis of Monte Carlo simulations. These simulations show that mean-field approximations are useful for reducing the variance of estimators when the data are recorded from arrays of 144 diodes (which are in accordance with standard practice). In light of these improved methods, we give new interpretations for a data set obtained from optical recording of a Guinea pig's auditory cortex in response to pure tone stimulations.     

Parameter estimation of a monod-type model. Part I: Theoretical identifiability and sensitivity analysis

Summary Parameter estimation of a Monod-type model based on the study of the theoretical identifiability of the model followed by the sensitivity analysis of the state variables with respect to parameters is presented. Theorerical identifiability allows to establish the unicity of the solution. On the other hand, sensitivity analysis throws light on the conditions that make parameters identifiable. Thus, the introduction of additional parameters, especially substrate maintenance and death constant, increases the estimation difficulty.     

Characterising model dynamics using sparse grid interpolation: Parameter estimation of cholera

Sparse grid interpolation is a popular numerical discretization technique for the treatment of high dimensional, multivariate problems. We consider the case of using time-series data to calibrate epidemiological models from both phenomenological and mechanistic perspectives using this computational tool. By capturing the dynamics underlying both global and local spaces, our algorithm identifies potentially optimal regions of the parameter space and directs computational effort towards resolving the dynamics and resulting fits of these regions. We demonstrate how sparse grid interpolants can be effectively deployed to fit available data and discriminate between competing hypotheses to explain the current cholera epidemic in Yemen.     

Finite element analysis of vertebral body mechanics with a nonlinear microstructural model for the trabecular core.

In this study, a finite element model of a vertebral body was used to study the load-bearing role of the two components (shell and core) under compression. The model of the vertebral body has the characteristic kidney shape transverse cross section with concave lateral surfaces and flat superior and inferior surfaces. A nonlinear unit cell based foam model was used for the trabecular core, where nonlinearity was introduced as coupled elastoplastic beam behavior of individual trabeculae. The advantage of the foam model is that architecture and material properties are separated, thus facilitating studies of the effects of architecture on the apparent behavior. Age-related changes in the trabecular architecture were considered in order to address the effects of osteoporosis on the load-sharing behavior. Stiffness changes with age (architecture and porosity changes) for the trabecular bone model were shown to follow trends in published experimental results. Elastic analyses showed that the relative contribution of the shell to the load-bearing ability of the vertebra decreases with increasing age and lateral wall curvature. Elasto-plastic (non-linear) analyses showed that failure regions were concentrated in the upper posterior region of the vertebra in both the shell and core components. The ultimate load of the vertebral body model varied from 2800 N to 5600 N, depending on age (architecture and porosity of the trabecular core) and shell thickness. The model predictions lie within the range of experimental results. The results provide an understanding of the relative role of the core and shell in vertebral body mechanics and shed light on the yield and post-yield behavior of the vertebral body.     

Parameter estimation of a monod-type model. Part II: Use of a neural network with associative memories

Summary On the basis of a previous study related with parameter identifiability and sensitivity analysis of a Monod-type model, a parameter estimation method based on Artificial Neural Networks (ANN) with Associative Memories (AMs) is presented. A combination of an iterative procedure and a convergence index given by AMs allows to confirm the nature of relations existing between state variables and parameters which were found in the first part of the study. The convergence criterion is particularly well adapted to showing various influences of state variables on parameter estimation of such a model.     

Parameter estimation for a temperature-dependent development model of Thrips palmi Karny (Thysanoptera: Thripidae)

Development of immature Thrips palmi Karny was investigated at 12.5, 15, 17.5, 20, 22.5, 25, 27.5, 30, 32.5, and 35 °C, 20–40% RH and a photoperiod of 14:10 (L:D) h. Developmental time decreased with increasing temperature up to 32.5 °C in all stages. The total developmental time was longest at 12.5 °C (64.2 days) and shortest at 32.5 °C (9.2 days). The lower developmental threshold was 10.6, 10.6, 9.1, and 10.7 °C for egg, larva, prepupa, and pupa, respectively. The thermal constant required to complete the respective stage was 71.7, 59.2, 18.1, and 36.8DD. The lower threshold temperature and thermal constant were 10.6 °C and 183.3DD, respectively, for total immature development. The nonlinear relationship between developmental rate and temperature was well described by the modified Sharpe and DeMichele biophysical model (r² = 0.905–0.998). The distribution of developmental completion of each stage was described by the 3-parameter Weibull function (r² = 0.855–0.927). The temperature-dependent developmental models of T. palmi developed in this study could be used to predict its seasonal phenology in field and greenhouse vegetable crops.