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PubMed2000

Numerical methods and parameter estimation of a structured population model with discrete events in the life history.

We consider two numerical methods for the solution of a physiologically structured population (PSP) model with multiple life stages and discrete event reproduction. The model describes the dynamic behaviour of a predator-prey system consisting of rotifers predating on algae. The nitrate limited algal prey population is modelled unstructured and described by an ordinary differential equation (ODE). The formulation of the rotifer dynamics is based on a simple physiological model for their two life stages, the egg and the adult stage. An egg is produced when an energy buffer reaches a threshold value. The governing equations are coupled partial differential equations (PDE) with initial and boundary conditions. The population models together with the equation for the dynamics of the nutrient result in a chemostat model. Experimental data are used to estimate the model parameters. The results obtained with the explicit finite difference (FD) technique compare well with those of the Escalator Boxcar Train (EBT) method. This justifies the use of the fast FD method for the parameter estimation, a procedure which involves repeated solution of the model equations.

Animals↗

PubMed1995

Theory and application of the maximum likelihood principle to NMR parameter estimation of multidimensional NMR data.

A general theory has been developed for the application of the maximum likelihood (ML) principle to the estimation of NMR parameters (frequency and amplitudes) from multidimensional time-domain NMR data. A computer program (ChiFit) has been written that carries out ML parameter estimation in the D-1 indirectly detected dimensions of a D-dimensional NMR data set. The performance of this algorithm has been tested with experimental three-dimensional (HNCO) and four-dimensional (HN(CO)-CAHA) data from a small protein labeled with 13C and 15N. These data sets, with different levels of digital resolution, were processed using ChiFit for ML analysis and employing conventional Fourier transform methods with prior extrapolation of the time-domain dimensions by linear prediction. Comparison of the results indicates that the ML approach provides superior frequency resolution compared to conventional methods, particularly under conditions of limited digital resolution in the time-domain input data, as is characteristic of D-dimensional NMR data of biomolecules. Close correspondence is demonstrated between the results of analyzing multidimensional time-domain NMR data by Fourier transformation, Bayesian probability theory [Chylla, R.A. and Markley, J.L. (1993) J. Biomol. NMR, 3, 515-533], and the ML principle.

Algorithms↗

PubMed2004

Model selection and parameter estimation for ion channel recordings with an application to the K+ outward-rectifier in barley leaf.

We present a statistical method, and its accompanying algorithms, for the selection of a mathematical model of the gating mechanism of an ion channel and for the estimation of the parameters of this model. The method assumes a hidden Markov model that incorporates filtering, colored noise and state-dependent white excess noise for the recorded data. The model selection and parameter estimation are performed via a Bayesian approach using Markov chain Monte Carlo. The method is illustrated by its application to single-channel recordings of the K(+) outward-rectifier in barley leaf.

Algorithms↗

PubMed1989

Ion-channel gating mechanisms: model identification and parameter estimation from single channel recordings.

Patch-clamp data may be analysed in terms of Markov process models of channel gating mechanisms. We present a maximum likelihood algorithm for estimation of gating parameters from records where only a single channel is present. Computer simulated data for three different models of agonist receptor gated channels are used to demonstrate the performance of the procedure. Full details of the implementation of the algorithm are given for an example gating mechanism. The effects of omission of brief openings and closings from the single-channel data on parameter estimation are explored. A strategy for discriminating between alternative possible gating models, based upon use of the Schwarz criterion, is described. Omission of brief events is shown not to lead to incorrect model identification, except in extreme circumstances. Finally, the algorithm is extended to include channel gating models exhibiting multiple conductance levels.

Animals↗

PubMed2006

Theoretical and experimental studies of parameter estimation based on chaos feedback synchronization.

In this paper, we perform theoretical and experimental studies of parameter estimation based on chaos feedback synchronization. The Chua chaotic system is applied as the original system, and its time series of a single variable is applied as a feedback variable to drive a simulative system. The simplex method is employed to minimize the synchronization error in the simulative system to iteratively approach the original system parameters. Furthermore, the effects of feedback function, feedback weight, and noise are investigated. The parameter estimation method based on feedback synchronization shows its robustness to noise perturbation. Finally, the circuit experiment of parameter estimation is implemented in order to examine its practical applicability. The original Chua circuit parameters can be well approached from its recorded time series of a single variable. The results show the parameter estimation method based on feedback synchronization may be capable of estimating real system parameters from a chaotic time series.

Algorithms↗

PubMed2002

Impact of omission or replacement of data below the limit of quantification on parameter estimates in a two-compartment model.

PURPOSE: To evaluate the influence of omission and replacement approaches for data below the limit of quantification (LOQ) on the estimation of pharmacokinetic parameters for two-compartment models when using nonlinear mixed-effect models. METHOD: Nine data sets were simulated according to a two-compartment intravenous bolus model with interindividual and residual variabilities, and a sparse sampling strategy was adopted. The data sets differed with respect to area-under-the-curve (AUC) ratio (0.1. 0.2, 0.3) and half-life ratio (0.03, 0.1, 0.3) between the distribution and elimination phases. For each of the nine data sets, six reduced data sets were created by omitting 5%, 10%, 20%, 30%, 40%, or 50% of the lowest concentration values. For each of the reduced data sets only one simple correction procedure to handle observations below LOQ was applied. All the values below the LOQ were deleted, and the first one was replaced by half of the LOQ value. Population parameters were estimated for each of the 117 resulting data sets (one initial, six reduced, and six "corrected" data sets for each of the nine cases). This approach was also applied on a real data set of patients administered multiple i.v. bolus doses. RESULTS: For many of the data sets, particularly when a large fraction of the data was omitted, one or several population parameters were biased. When there was bias, clearance (CL) usually was underestimated, whereas peripheral volume was overestimated. The parameters related to the distribution phase (central volume and intercompartmental clearance) were less affected, and changes were not systematic. The correction procedure markedly decreased overall bias on the fixed effect of the parameters. Results for the real data were similar. CONCLUSION: Omission of data below the LOQ value may induce a not negligible bias on fixed-effect parameter estimates. The influence of the omission of values below LOQ was related to the underlying shape of the concentration-time profile and fraction of omitted observations. The use of a simple replacement rule seems to reduce this bias in estimates but needs further investigation.

Models, Theoretical↗

PubMed2007

Improved usability of the minimal model of insulin sensitivity based on an automated approach and genetic algorithms for parameter estimation.

Minimal model analysis of glucose and insulin data from an IVGTT (intravenous glucose tolerance test) is widely used to estimate insulin sensitivity; however, the use of the model often requires intervention by a trained operator and some problems can occur in the estimation of model parameters. In the present study, a new method for minimal model analysis, termed GAMMOD, was developed based on genetic algorithms for the estimation of model parameters. Such an algorithm does not require the fixing of initial values for the parameters (that may lead to unreliable estimates). Our method also implements an automated weighting scheme not requiring manual intervention of the operator, thus improving the usability of the model. We studied a group of 170 women with a history of previous gestational diabetes. Results obtained by GAMMOD were compared with those obtained by MINMOD (a traditional gradient-based algorithm for minimal model analysis). Insulin sensitivity by GAMMOD was (3.86+/-0.19) compared with (4.33+/-0.20) x 10(-4) micro-units.ml(-1) x min(-1) by MINMOD; glucose effectiveness was 0.0236+/-0.0005 compared with 0.0229+/-0.0005 min(-1) respectively. The difference in the estimation by the two methods was within the precision expected for such metabolic parameters and is probably of no clinical relevance. Moreover, both the coefficient of variation of the estimated parameters and the error of fit were generally lower in GAMMOD, despite the fact that it does not require manual intervention. In conclusion, the GAMMOD approach for parameter estimation in the minimal model provides a reliable estimation of the model parameters and improves the usability of the model, thus facilitating its further use and application in a clinical context.

Adult↗

PubMed2000

On the design of optimal dynamic experiments for parameter estimation of a Ratkowsky-type growth kinetics at suboptimal temperatures.

It is generally known that accurate model building, i.e., proper model structure selection and reliable parameter estimation, constitutes an essential matter in the field of predictive microbiology, in particular, when integrating these predictive models in food safety systems. In this context, Versyck et al. (1999) have introduced the methodology of optimal experimental design techniques for parameter estimation within the field. Optimal experimental design focuses on the development of optimal input profiles such that the resulting rich (i.e., highly informative) experimental data enable unique model parameter estimation. As a case study, Versyck et al. (1999) [Versyck, K., Bernaerts, K., Geeraerd, A.H., Van Impe, J.F., 1999. Introducing optimal experimental design in predictive modeling: a motivating example. Int. J. Food Microbiol., 51(1), 39-51] have elaborated the estimation of Bigelow inactivation kinetics parameters (in a numerical way). Opposed to the classic (static) experimental approach in predictive modelling, an optimal dynamic experimental setup is presented. In this paper, the methodology of optimal experimental design or parameter estimation is applied to obtain uncorrelated estimates of the square root model parameters [Ratkowsky, D.A., Olley, J., McMeekin, T.A., Ball, A., 1982. Relationship between temperature and growth rate of bacterial cultures. J. Bacteriol. 149, 1-5] describing the effect of suboptimal growth temperatures on the maximum specific growth rate of microorganisms. These estimates are the direct result of fitting a primary growth model to cell density measurements as a function of time. Apart from the design of an optimal time-varying temperature profile based on a sensitivity study of the model output, an important contribution of this publication is a first experimental validation of this innovative dynamic experimental approach for uncorrelated parameter identification. An optimal step temperature profile, within the range of model validity and practical feasibility, is developed for Escherichia coli K12 and successfully applied in practice. The presented experimental validation result illustrates the large potential of the dynamic experimental approach in the context of uncorrelated parameter estimation. Based on the experimental validation result, additional remarks are formulated related to future research in the field of optimal experimental design.

Escherichia coli↗

PubMed1995

Screening for Down syndrome during the first and second trimesters: impact of risk estimation parameters.

OBJECTIVES: To evaluate impact of risk estimation parameters for screening for Down Syndrome during the first and second trimesters. METHODS: We prospectively examined for their performance in the prenatal prediction of trisomy 21, alphafetoprotein (AFP), unconjugated estriol (uE3), total human chorionic gonadotropin (hCG), and its free subunits (free alpha-hCG, free beta-hCG) at both the first and second trimesters, and the impact of three sets of published risk estimation parameters. A total of 14,612 pregnancies were studied. All Down syndrome specimens (12 and 11 cases for first and second trimesters, respectively) and a sample of the unaffected pregnancies were analyzed. RESULTS: The median multiple of median (MoM) for total hCG was lower in the first trimester (1.83 vs. 2.01 in the second trimester) but no loss in discriminative power was observed if the lower variability of the results in the first trimester is taken into account (interquartile range of 0.251 vs. 0.338). The choice of distribution parameters did not alter significantly the detection rates for the various combinations of markers (p > 0.05). False positive rates were affected significantly however and for the combination AFP-uE3-free beta-hCG they varied from 14.6% to 22.6% (p < 0.001). CONCLUSIONS: Our results suggest that specific distribution parameters would be necessary to account for the lower variability of the markers in the first trimester and the peculiarity of the total hCG assay we used.

Adult↗

PubMed1990

Estimation of regurgitant volume and orifice in aortic regurgitation combining CW Doppler and parameter estimation in a Windkessel-like model.

A method for noninvasive estimation of regurgitant orifice and volume in aortic regurgitation is proposed and tested in anesthetized open chested pigs. The method can be used with noninvasive measurement of regurgitant jet velocity with continuous wave ultrasound Doppler measurements together with cuff measurements of systolic and diastolic systemic pressure in the arm. These measurements are then used for parameter estimation in a Windkessel-like model which include the regurgitant orifice as a parameter. The aortic volume compliance and the peripheral resistance are also included as parameters measurements in the open chest pigs are used. Electromagnetic flow measurements in the ascending aorta and pulmonary artery are used for control, and a correlation between regurgitant volume obtained from parameter estimation and electromagnetic flow measurements of 0.95 over a range from 2.1 to 17.8 mL is obtained.

Animals↗

PubMed2005

Enhanced parameter estimation from noisy PET data: Part I--methodology.

RATIONALE AND OBJECTIVES: The reliability of positron emission tomographic (PET) images depends on the number of annihilation events that are detected. Short image durations are required to capture rapid tracer dynamics, and the resultant images are noisy. Consequently, direct parameter estimation from time-activity curves at high resolution often is unreliable. If adjacent voxels are combined into larger regions of interest the reliability of parameter estimation may be improved, but at the expense of decreased spatial resolution. In this report, a method is presented that provides an alternative to degrading image resolution. MATERIALS AND METHODS: Following the approach of Kimura et al, voxels are grouped not by spatial proximity, but by the similarity of their kinetics. Parameter estimation is performed on these groups, and derived parameters are assigned to all members of the group. Spatial information thus is preserved, but at the expense of parametric discretization. An improvement to the method of Kimura et al is described, in which data are grouped using principal components derived from artificial data. RESULTS: The application of the method is demonstrated by analysis of PET images of human lungs obtained by the nitrogen-13 infusion-washout technique. In a comparison of the accuracy of parameter estimates, the enhanced method is shown to outperform the original method at all noise levels, with the difference increasing as the amount of noise increases. The robustness of this parameter estimation method in the presence of noise is described in part II of this report in this issue of Academic Radiology. CONCLUSION: A method is described that provides demonstrably robust parameter estimates from noisy PET data, while not compromising image resolution.

Humans↗

PubMed1997

Using principal-components regression to stabilize EMG-muscle force parameter estimates of torso muscles.

Models for estimating muscle force from surface electromyographic (EMG) recordings require parameter estimates with low intertrial variability. The inclusion of multiple muscles in multivariate statistical models can lead to multicollinearity, especially when there are significant correlations between synergist muscles. One result of multicollinearity is that parameter estimates are very sensitive to changes in the independent variables. This study compared the parameter variability of multiple regression and principal-components regression techniques when applied to a six muscle EMG analysis of the lumbar region of the torso. Nine subjects participated. Twenty-three percent of the traditional multiple-regression parameters had incorrect signs, but none of the principal-components regression parameters did. The principal-components regression technique also produced parameter estimates having an order of magnitude smaller parameter variability. It was concluded that principal-components regression is an effective method of mitigating the effect of multicollinearity in torso EMG models.

Adult↗

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↗

PubMed2005

Kinetic parameters estimation in an anaerobic digestion process using successive quadratic programming.

In this work, an optimization method is implemented in an anaerobic digestion model to estimate its kinetic parameters and yield coefficients. This method combines the use of advanced state estimation schemes and powerful nonlinear programming techniques to yield fast and accurate estimates of the aforementioned parameters. In this method, we first implement an asymptotic observer to provide estimates of the non-measured variables (such as biomass concentration) and good guesses for the initial conditions of the parameter estimation algorithm. These results are then used by the successive quadratic programming (SQP) technique to calculate the kinetic parameters and yield coefficients of the anaerobic digestion process. The model, provided with the estimated parameters, is tested with experimental data from a pilot-scale fixed bed reactor treating raw industrial wine distillery wastewater. It is shown that SQP reaches a fast and accurate estimation of the kinetic parameters despite highly noise corrupted experimental data and time varying inputs variables. A statistical analysis is also performed to validate the combined estimation method. Finally, a comparison between the proposed method and the traditional Marquardt technique shows that both yield similar results; however, the calculation time of the traditional technique is considerable higher than that of the proposed method.

Acetic Acid↗

PubMed1979

Kinetic parameter estimation by numerical algorithms and multiple linear regression: application to pharmacokinetics.

Two numerical examples are presented to illustrate the application of the proposed method of parameter estimation in pharmacokinetics. Results for a system exemplifying first-order kinetics indicate that parameters estimated by the proposed procedure compare favorably with those estimated by a nonlinear regression method. In a simulated example characterized by Michaelis-Menten elimination kinetics, the accuracy of the estimated parameters was comparable to that expected, verifying the validity of the method. The importance of the numerical approximation algorithms was demonstrated also.

Kinetics↗

PubMed2004

Effects of censoring on parameter estimates and power in genetic modeling.

Genetic and environmental influences on variance in phenotypic traits may be estimated with normal theory Maximum Likelihood (ML). However, when the assumption of multivariate normality is not met, this method may result in biased parameter estimates and incorrect likelihood ratio tests. We simulated multivariate normal distributed twin data under the assumption of three different genetic models. Genetic model fitting was performed in six data sets: multivariate normal data, discrete uncensored data, censored data, square root transformed censored data, normal scores of censored data, and categorical data. Estimates were obtained with normal theory ML (data sets 1-5) and with categorical data analysis (data set 6). Statistical power was examined by fitting reduced models to the data. When fitting an ACE model to censored data, an unbiased estimate of the additive genetic effect was obtained. However, the common environmental effect was underestimated and the unique environmental effect was overestimated. Transformations did not remove this bias. When fitting an ADE model, the additive genetic effect was underestimated while the dominant and unique environmental effects were overestimated. In all models, the correct parameter estimates were recovered with categorical data analysis. However, with categorical data analysis, the statistical power decreased. The analysis of L-shaped distributed data with normal theory ML results in biased parameter estimates. Unbiased parameter estimates are obtained with categorical data analysis, but the power decreases.

Computer Simulation↗

PubMed2004

Fast and robust parameter estimation for statistical partial volume models in brain MRI.

Due to the finite spatial resolution of imaging devices, a single voxel in a medical image may be composed of mixture of tissue types, an effect known as partial volume effect (PVE). Partial volume estimation, that is, the estimation of the amount of each tissue type within each voxel, has received considerable interest in recent years. Much of this work has been focused on the mixel model, a statistical model of PVE. We propose a novel trimmed minimum covariance determinant (TMCD) method for the estimation of the parameters of the mixel PVE model. In this method, each voxel is first labeled according to the most dominant tissue type. Voxels that are prone to PVE are removed from this labeled set, following which robust location estimators with high breakdown points are used to estimate the mean and the covariance of each tissue class. Comparisons between different methods for parameter estimation based on classified images as well as expectation--maximization-like (EM-like) procedure for simultaneous parameter and partial volume estimation are reported. The robust estimators based on a pruned classification as presented here are shown to perform well even if the initial classification is of poor quality. The results obtained are comparable to those obtained using the EM-like procedure, but require considerably less computation time. Segmentation results of real data based on partial volume estimation are also reported. In addition to considering the parameter estimation problem, we discuss differences between different approximations to the complete mixel model. In summary, the proposed TMCD method allows for the accurate, robust, and efficient estimation of partial volume model parameters, which is crucial to a variety of brain MRI data analysis procedures such as the accurate estimation of tissue volumes and the accurate delineation of the cortical surface.

Artifacts↗

PubMed1996

Effect of intravascular ligand binding on parameter estimates derived from tracer kinetic modelling.

The purpose of this study was to assess the effect of intravascular ligand binding on parameter estimates derived from tracer kinetic modelling. To this end intravascular ligand kinetics between the free and a bound compartment in plasma and the exchange of tracer between the capillary space and tissue were analysed using a simple compartment model. The effect of non-equilibrated intravascular compartments on parameter estimates was evaluated in a computer simulation. It was found that three kinetic situations must be distinguished. If the intravascular compartments are fully equilibrated when the ligand reaches the target organ, intravascular binding simply acts as a scale factor for the transport-related parameter K1. If the intravascular kinetics is very slow, only minimal binding will occur. In between there is a range where ongoing equilibration leads to time variability of K1. Since tracer kinetic modelling usually does not account for such time variability, the parameter estimates become biased, the degree of the bias depending on the intravascular binding kinetics. Furthermore the bias may be dependent on receptor density, meaning that model-derived receptor estimates are not linearly related to the true receptor density. It is concluded that intravascular ligand binding can severely affect parameter estimates derived from tracer kinetic modelling. Especially disturbing are effects due to ongoing intravascular equilibration following the arrival of the ligand in the target organ. These can be avoided by letting the ligand equilibrate with blood in a syringe prior to injection.

Blood Vessels↗