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PubMed1979

A program package for simulation and parameter estimation in pharmacokinetic systems.

A set of programs is presented which has been developed for parameter estimation and simulation of models arising from pharmacokinetic applications. The programs can accommodate linear and nonlinear models with multiple inputs and multiple outputs. When the model is defined by differential equations, non-uniform repetitive dosage regimens can be handled. The model may also be entered in integrated form when single dose studies or uniform multiple dose studies are being considered. The programs employ a variable-step, variable-order integration routine to solve the model differential equations, and the Nelder-Mead simplex procedure to determine the parameter values which minimize a weighted least squares criterion. The programs have been written for an interactive time-sharing environment with the experimental data and model equations stored in files for future use.

Computers↗

PubMed1999

On the kinematic modelling and the parameter estimation of the human shoulder.

This paper presents some results on the modelling and the corresponding parameter estimation of the human shoulder. This system consists of the clavicle, the scapula, the humerus and the various joints between these bodies and the trunk through the sternum; it will be represented as a succession of a rotational joint between the sternum and the clavicle and a constant distance joint, representing the scapula between, the clavicle and the humerus head. The parameters of this system are the components of the position vectors of the joint characteristic points (the corresponding centres of the rotations). Experimental results are presented as well as a validation of the proposed model.

Acromioclavicular Joint↗

PubMed1995

Cytoplasmic incompatibility in Drosophila simulans: dynamics and parameter estimates from natural populations.

In Drosophila simulans, cytoplasmically transmitted Wolbachia microbes cause reduced egg hatch when infected males mate with uninfected females. A Wolbachia infection and an associated mtDNA variant have spread northward through California since 1986. PCR assays show that Wolbachia infection is prevalent throughout the continental US and Central and South America, but some lines from Florida and Ecuador that are PCR-positive for Wolbachia do not cause incompatibility. We estimate from natural populations infection frequencies and the transmission and incompatibility parameter values that affect the spread of the infection. On average, infected females from nature produce 3-4% uninfected ova. Infected females with relatively low fidelity of maternal transmission show partial incompatibility with very young infected laboratory males. Nevertheless, crosses between infected flies in nature produce egg-hatch rates indistinguishable from those produced by crosses between uninfected individuals. Incompatible crosses in nature produce hatch rates 30-70% as high as those from compatible crosses. Wild-caught infected and uninfected females are equally fecund in the laboratory. Incompatibility decreases with male age, and age-specific incompatibility levels suggest that males mating in nature may often be 2 or 3 weeks old. Our parameter estimates accurately predict the frequency of Wolbachia infection in California populations.

Africa, Southern↗

PubMed1992

Analysis of variance of parameter estimates: F tests and t tests.

The problem of comparing and pooling experimentally independent estimates of a parameter such as a Michaelis constant (K) has been treated as a simple analysis of variance of "within" and "between" set deviations from the fitted variable (v). As applied to assessing the reproducibility of multiple estimates of the same K, this is identical to the procedure of Duggleby (Anal. Biochem. 189, 84-87, 1990). However, the theory developed here shows that applying Duggleby's procedure to the comparison of two experiments (each consisting of multiple data sets) depends critically on the assumption of equal errors within and between the individual sets, i.e., Fvb vw = s2wv/s2bv is close to 1. Application of the method when this is not the case will underestimate the common error (s2rv), overestimate its associated degrees of freedom (vr = vb+vw), and may suggest apparently significant differences where there are none. The theory also shows that this situation is an instance of the Fisher-Behrens problem and shows how Welch's solution can be applied. This gives the between set error s2bv as the corrected estimate of the common error and the corrected degrees of freedom as a simple function of vb, vw, and Fvb vw. When the nine prephenate dehydratase data sets which originally showed three apparently significant differences were reanalyzed in this way, all the variations in K were found to be within the range of the experimental error.

Analysis of Variance↗

PubMed1999

Multi-rate nonlinear state and parameter estimation in a bioreactor.

This paper concerns real-time, multi-rate, nonlinear state and parameter estimation in a pilot-scale biochemical reactor in which cultivation of mouse-mouse hybridoma cells takes place. A multi-rate estimator is designed and implemented to estimate specific growth rate and concentrations of viable cells, total cells, glucose, glutamine, and monoclonal antibodies (MAb) in the reactor. These are estimated from frequent measurement (inferred values) of oxygen uptake rate (OUR) and infrequent and delayed measurements of the concentrations of viable cells, total cells, glucose, glutamine, and MAb. The infrequent measurements are available every 2 to 17 h with a time delay of 0.08 to 2.00 h, and OUR is inferred from dissolved oxygen concentration measurements that are available very 0.17 h. For each of the process variables, its infrequent measurement data and the profile of its estimate are presented to show the performance of the multi-rate estimator.

Animals↗

PubMed1978

ESTRIP, a BASIC computer program for obtaining initial polyexponential parameter estimates.

A new BASIC exponential stripping program, ESTRIP, allows the relatively rapid calculation of initial polyexponential parameter estimates, as does the previously published FORTRAN IV program, CSTRIP. The potential advantages of the new program are that it can be run on microcomputers and minicomputers with BASIC capability and a relatively small core and that it can be easily modified by the user.

Computers↗

PubMed1990

Nonlinear parameter estimation applied to a model of smooth pursuit eye movements.

We present a procedure that optimally adjusts specified parameters of a mathematical model to describe a set of measured data. The technique integrates a dynamic systems-simulation language with a robust algorithm for nonlinear parameter estimation, and it can be implemented on a microcomputer. Sensitivity functions are generated that indicate how the operation of the model is affected by each updated parameter. This procedure offers a greater resolution of optimal parameter values than other, less rigorous methods. To illustrate this technique we have applied it to the model of human smooth pursuit eye movements proposed by D.A. Robinson and colleagues (1986).

Eye Movements↗

PubMed1997

Multivariate time-variant identification of cardiovascular variability signals: a beat-to-beat spectral parameter estimation in vasovagal syncope.

In this paper a bivariate, time-variant model able to continuously measure the mutual interactions between heart rate and systolic blood pressure variability signals is presented. A recursive identification of the model parameters makes it possible to estimate, on a beat-to-beat basis, spectral low-frequency (LF) and high-frequency (HF) power, (LF/HF ratio) and cross-spectral (coherence and phase relationships between spectral peaks) indexes during nonstationary events. These indexes can be helpful in: 1) physiological study of autonomic nervous system mechanisms of cardiovascular control and 2) quantification and clinical evaluation of the neural and mechanical links between the two signals. In addition, an estimate of baroreceptive activation (alpha-gain) is continuously extracted. Before applying the model to cardiovascular signals, the reliability of the estimated parameters was tested on simulated signals. Subsequently, the model was applied to investigating vasovagal syncope episodes, aiming at the assessment of autonomic nervous system status and autonomic role in the dynamic phenomena which lead to syncope. The proposed model, which provides noninvasive beat-to-beat evaluation of the autonomic events, may be useful in the description of the syncopal episodes and in the comprehension of the complex physiological mechanisms of syncope.

Algorithms↗

PubMed1990

A method for binding parameters estimation of A1 adenosine receptor subtype: a practical approach.

Working with pig brain striatum in which A1 and A2 adenosine receptor subtypes coexist, we describe an uncomplicated method for unequivocally obtaining the equilibrium parameters (KD and binding capacity) of A1 receptor without interference from ligand binding to A2 receptor. Also, the equilibrium parameter estimation method we propose avoids the experimental determination of nonspecific binding by the inclusion of the corresponding unknown parameter in the function. This not only saves time but also avoids the use of expensive radioligands in saturation experiments. The method is suitable for any system with two different receptor subtypes for the same physiological ligand, and good estimates of the equilibrium parameters corresponding to the subtype displaying the higher affinity for the ligand can be obtained.

Adenosine↗

PubMed1997

Stochastic optimization algorithms of a Bayesian design criterion for Bayesian parameter estimation of nonlinear regression models: application in pharmacokinetics.

This article proposes three stochastic algorithms to optimize a Bayesian design criterion for Bayesian estimation of the parameters of nonlinear regression models; this criterion is the information expected from an experiment. The first algorithm is based on a stochastic version of the simplex with an adaptive sampling procedure. The others are stochastic approximation algorithms: the Kiefer-Wolfowitz and the pseudogradient algorithms. We first present the information criterion and the optimization algorithms. The efficiency of each algorithm for optimizing this Bayesian design criterion is then assessed by a simulation study for a nonlinear model assuming a discrete prior distribution. An application for designing an experiment to estimate the kinetics of radioiodine thyroid uptake is then proposed.

Algorithms↗

PubMed2000

Parameter estimates for greasy fleece weight of Rambouillet sheep at different ages.

Variance components for greasy fleece weight in Rambouillet sheep were estimated. Greasy fleece weight was modeled either as repeated measurements on the same trait or as different traits at different ages. The original data were separated according to the age of the ewe at shearing into three classes; 1 yr, 2 and 3 yr, and older than 3 yr. An animal model was used to obtain estimates of genetic parameters with a REML algorithm. Total numbers of animals in pedigrees for the different age classes were 696, 729, and 573, respectively, and 822 for the repeated measures model across ages. The animal model included direct genetic, permanent environmental, and residual environmental random effects and fixed effects for age of ewe, shearing date as contemporary group, and number of lambs born. Days between shearings was used as a covariate. Single-trait analyses were initially done to obtain starting values for multiple-trait analyses. A repeated measures model across ages was also used. Estimates of heritability by age group were .42, .50, and .58 from three-trait (age class) analyses and for the repeated measures model the estimate was .57. Estimates of genetic correlations between fleece yields for 1 yr and 2 and 3 yr, 1 yr and >3 yr, and 2 and 3 yr and >3 yr classes were .88, .89, and .97, respectively. These estimates of genetic correlations suggest that a repeated measures model for greasy fleece weight is adequate for making selection decisions.

Aging↗

PubMed2003

Simulation and parameter estimation of dynamics of synaptic depression.

Synaptic release was simulated using a Simulink sequential storage model with three vesicular pools. Modeling was modular and easily extendable to the systems with greater number of vesicular pools, parallel input, or time-varying parameters. Given an input (short or long tetanic trains, patterned or random stimulation) and the storage model, the vesicular release, the replenishment of various vesicular pools, and the vesicular content of all pools could be simulated for the time-invariant and time-varying storage systems. From the input stimuli and either a noiseless or a noisy output, the parameters of such storage systems could also be estimated using the optimization technique that minimizes in the least square sense the error between the observed release and the predicted release. All parameters of the storage model could be evaluated with sufficiently long input-output data pairs. Not surprisingly, the parameters characterizing the processes near the release locus, such as the fractional release and the size of the immediately available pool and its coupling to the small store, as well as the state variables associated with the immediately available pool, such as its vesicular content and replenishment, could be determined with fewer stimuli. The possibility of estimating parameters with random inputs extends the applicability of the method to in vivo synapses with the physiological inputs. The parameter estimation was also possible under the time-variant, but slowly changing, conditions as well as for open systems that are part of larger vesicular storage systems but whose parameters can either not be reliably determined or are of no interest. The quality of parameter estimation was monitored continuously by comparing the observed and predicted output and/or estimated parameters with the true values. Finally, the method was tested experimentally using the rat phrenic-diaphragm neuromuscular junction.

Long-Term Synaptic Depression↗

PubMed1977

Kinetic parameter estimation by numerical algorithms and multiple linear regression: theoretical.

A new method is presented for the determination of kinetic parameters based on a functional relationship among experimental data derived from the postulated model. The data, even though containing errors, are manifestations of this relationship, which should be satisfied by parameters fitted to the system. The procedure involves the use of numerical integration and/or differentiation of the data, followed by multiple linear regression. It does not require initial estimates or repetitive iteration for linear systems and can be applied to nonlinear models. The accuracy of estimated parameter depends on the goodness of the particular numerical approximation method used.

Computers↗

PubMedDate not supplied

Nonlinear gradient isotherm parameter estimation for proteins with consideration of salt competition and multiple forms.

Salt gradients in ion-exchange chromatography are routinely used to speed separation of proteins and to concentrate products, but systematic optimization of these gradients requires protein equilibrium data as a function of salt concentration. An understanding of conformational changes, aggregation, and salt effects, which include both competition and affinity modulation, is important for equilibrium isotherm parameter estimation. In this study, gradient elution of bovine serum albumin (BSA) in anion exchange was well predicted by a salt-modulated nonlinear isotherm which considers salt competition. The isotherm was able to predict BSA gradient elution from batch equilibrium data. The same isotherm was also able to predict elution for various gradient slopes when fitted to an intermediate slope gradient experiment. If multiple forms due to aggregation or denaturation exist, isotherm parameters are readily averaged in batch experiments because of the long equilibration times. Similarly, gradient experiments yield averaged parameters because the salt gradient tends to merge the closely eluting forms. However, in isocractic elution, if the reaction rate is not rapid enough to give a merged peak, the estimated isotherm parameters are only fair predictors of gradient behavior and vice versa. Slower flow rates in isocratic elution can help reduce the discrepancy by allowing forms to merge through interconversion. As an alternative to determining averaged parameters, consideration of two binding forms, using VERSE-LC, an advanced rate model, gave good agreement with experimental data over the entire range of salt gradient durations.

Animals↗

PubMed1990

Evaluation of six gentamicin nomograms using a bayesian parameter estimation program.

A new set of guidelines for the administration of gentamicin was developed by estimating steady-state peak and trough gentamicin concentrations for simulated patients with known weights and creatinine clearances. The most appropriate doses to achieve target peak concentrations of 5-10 mg/L and troughs of less than 2 mg/L were then tabulated. The performance of these new guidelines was assessed using data collected from 60 patients who had received gentamicin and had at least two serum concentration measurements. Individual estimates of clearance and volume of distribution were obtained using a Bayesian parameter estimation program and these estimates were used to predict the steady-state peak and trough concentrations that would arise from the new guidelines and five other previously published nomograms (Mawer, Chan, Hull-Sarubbi, Rule of Eight, and Dettli). The new guidelines, the Dettli nomogram, and the Hull-Sarubbi table achieved similar percentages (52-57%) of patients within the target ranges (5-10 mg/L for peak and less than 2 mg/L for trough), although 28% of patients had predicted peak concentrations below 5 mg/L with the new method compared to 15% with the other two. Only 38% of patients were within both ranges when the Mawer nomogram and the Rule of Eight methods were used. Since a large percentage of patients would have achieved concentrations outside of the target ranges no matter which nomogram was used, serum concentration monitoring is still recommended to confirm dose requirements.

Bayes Theorem↗

PubMed1994

Modelling the impact of mass vaccination against hepatitis B. I. Model formulation and parameter estimation.

A new model of the transmission dynamics of hepatitis B virus in countries with high transmission rates is presented. The model is age and sex stratified, and includes details of host demography. Details of hepatitis B natural history, such as the existence of infectious and non-infectious carriers, are included. The biological assumptions of the model are discussed in full and related to the model's equations. Hepatitis B epidemiological data is reviewed with special emphasis on the estimation of model parameter values from field data. A full set of model parameter values are derived. Possible uses of the model in the assessment of strategies of mass vaccination are discussed.

Adolescent↗

PubMed1992

Transport parameter estimation from lymph measurements and the Patlak equation.

Two methods of estimating protein transport parameters for plasma-to-lymph transport data are presented. Both use IBM-compatible computers to obtain least-squares parameters for the solvent drag reflection coefficient and the permeability-surface area product using the Patlak equation. A matrix search approach is described, and the speed and convenience of this are compared with a commercially available gradient method. The results from both of these methods were different from those of a method reported by Reed, Townsley, and Taylor [Am. J. Physiol. 257 (Heart Circ. Physiol. 26): H1037-H1041, 1989]. It is shown that the Reed et al. method contains a systematic error. It is also shown that diffusion always plays an important role for transmembrane transport at the exit end of a membrane channel under all conditions of lymph flow rate and that the statement that diffusion becomes zero at high lymph flow rate depends on a mathematical definition of diffusion.

Animals↗

PubMedDate not supplied

Aquifer parameter estimation from surface resistivity data.

This paper is devoted to the additional use, other than ground water exploration, of surface geoelectrical sounding data for aquifer hydraulic parameter estimation. In a mesoscopic framework, approximated analytical equations are developed separately for saline and for fresh water saturations. A few existing useful aquifer models, both for clean and shaley sandstones, are discussed in terms of their electrical and hydraulic effects, along with the linkage between the two. These equations are derived for insight and physical understanding of the phenomenon. In a macroscopic scale, a general aquifer model is proposed and analytical relations are derived for meaningful estimation, with a higher level of confidence, of hydraulic parameter from electrical parameters. The physical reasons for two different equations at the macroscopic level are explicitly explained to avoid confusion. Numerical examples from existing literature are reproduced to buttress our viewpoint.

Electricity↗