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PubMed1976

The comparison of parameters estimated from several different samples by maximum likelihood.

A system of computer programs has been developed to compare the parameters of several samples taken from populations with arbitrary but known distribution functions. The user indicates which of the parameters are assumed to be equal in all populations under the null hypothesis alone or under both the null and the alternative hypotheses. The programs perform maximum likelihood estimation under the general and the restricted model and also calculate the values needed for a likelihood ratio test. The programming language used was PL/I-FORM AC. An illustrative numerical example is given.

Animals↗

PubMed2005

Models for estimating parameters of neutral detergent fiber digestion by ruminal microorganisms.

Model assumptions included number of concurrently degrading entities (or pools) and expected distributions of undegraded NDF. Degradation processes modeled included a single pool with ruminal age-constant rates (exponential distribution), a single pool with a ruminal age-dependent rate, two pools with age-constant rates, two pools with age-dependent and age-constant rates, and a continuum of pools with a gamma distribution of age-constant rates. Various sizes of ingestively masticated fragments of bermudagrass hay or corn silage were obtained via wet sieving of esophageal masticate and incubated in vitro with ruminal fluid for 0 h, every 6 h up to 48 h, and every 12 h up to 168 h. Models assuming a single pool of age-constant or age-dependent rates had larger mean residual mean squares (P < 0.05) than did the gamma mixture model or the two-pool models. Degradation rates estimated by the gamma mixture model indicated distribution of rates ranging from near exponential, age-constant distribution to a near normal bell-shaped distribution of age-constant rates for different datasets. Superior fit by the two-pool models in most datasets (83%) indicated that having two resolvable entities of potentially degradable NDF with different degradation rates was causal of a biphasic distribution of lifetimes. Increasing order of age-dependency modeled in the two-pool model improved fit and precision of estimation (standard error of estimate) for the limit parameters of time delay and indigestible NDF. Both the gamma mixture continuum of age-constant rate model and the two-pool, age-dependent models with a discrete time delay provided similar fit to data and flexibility for fitting data with lifetime distributions ranging from simple exponential to sigmodial. The two-pool, age-dependent and gamma-distributed, age-constant models were better in fitting the dominant biphasic lifetime distributions that occurred when the two pools of degrading entities were of similar size and in estimating the discrete time delay when strategic, quality data were available. Having fewer parameters (four), the gamma-distributed, age-constant model was superior when data quality was limited.

Animal Nutritional Physiological Phenomena↗

PubMed1989

Anaerobic threshold: reproducibility out from ventilatory parameter estimation.

Anaerobic threshold (AT) during exercise is usually noninvasively determined by assuming a two-segment mathematical relationship between two ventilatory parameters. In the literature, all the possible pairs of segments are first considered, and the most appropriate pair is then selected according to at least-squares method. In such a model, the AT is considered to be related to the joining point of the two segments. In order to test the reliability of the model, we compare the results of the least-squares method to those based on maximum probability method in discriminating the two regression coefficients. In order to test the reproducibility of the two different criteria, comparisons have been repeated after data have been filtered. A paired t test was used to carry out comparisons. Ventilatory parameters were collected in 10 healthy subjects during the use of a bicycle ergometer. The required power was increased every 15 s by steps of 30 W, starting from 50 W. Ve, VO2 and VCO2 have been sampled every 15 s, then the three functions--Ve versus VO2, Ve versus VCO2 and VCO2 versus VO2--were considered. Each function was stylized with two linear segments. Each segment was estimated by using a second-kind linear fitting. We verified that: (i) the AT may be reliably appreciated depending on the pair of selected parameters; (ii) only when data are smoothed is no difference between the two criteria documented (Ve vs. VO2, p = 0.99; Ve vs. VCO2, p = 0.54); (iii) no significant difference, related to smoothing, is documented both in using the least-squares method (Ve vs. VO2, p = 0.61; Ve vs. VCO2, p = 0.15) and the maximum p level criterion (Ve vs. VO2, p = 0.59; Ve vs. VCO2, p = 0.19).

Adolescent↗

PubMed2003

Physiologically based pharmacokinetic model parameter estimation and sensitivity and variability analyses for acrylonitrile disposition in humans.

A physiologically based pharmacokinetic (PBPK) model of acrylonitrile (ACN) and cyanoethylene oxide (CEO) disposition in humans was developed and is based on human in vitro data and scaling from a rat model (G. L. Kedderis et al., 1996, TOXICOL: Appl. Pharmacol.140, 422-435) for application to risk assessment. All of the major biotransformation and reactivity pathways, including metabolism of ACN to glutathione conjugates and CEO, reaction rates of ACN and CEO with glutathione and tissues, and the metabolism of CEO by hydrolysis and glutathione conjugation, were described in the human PBPK model. Model simulations indicated that predicted blood and brain ACN and CEO concentrations were similar in rats and humans exposed to ACN by inhalation. In contrast, rats consuming ACN in drinking water had higher predicted blood concentrations of ACN than humans exposed to the same concentration in water. Sensitivity and variability analyses were conducted on the model. While many parameters contributed to the estimated variability of the model predictions, the reaction rate of CEO with glutathione, hydrolysis rate for CEO, and blood:brain partition coefficient of CEO were the parameters predicted to make the greatest contributions to variability of blood and brain CEO concentrations in humans. The main contributor to predicted variance in human blood ACN concentrations in people exposed through drinking water was the Vmax for conversion of ACN to CEO. In contrast, the main contributors for variance in people exposed by inhalation were expected to be the rate of blood flow to the liver and alveolar ventilation rate, with the brain:blood partition coefficient also contributing to variability in predicted concentrations of ACN in the brain. Expected variability in blood CEO concentrations (peak or average) in humans exposed by inhalation or drinking water was modest, with a 95th-percentile individual expected to have blood concentrations 1.8-times higher than an average individual.

Acrylonitrile↗

PubMed1987

PEDA: a microcomputer program for parameter estimation and dosage adjustment in clinical practice.

PEDA, an integrated program in BASIC for implementation on microcomputers, has been developed for use in clinical practice to assist dosage adjustment for individual patients. A parameter optimization for individual patients is based on the principle of Bayes' theory and Maximum Likelihood Estimation, and utilizes a prior information on the distribution of population pharmacokinetic parameters, means and variances, as well as serum drug concentrations. The program can accommodate a one-compartment open linear model and a non-linear model at steady state (Michaelis-Menten model) and handle both uniform and non-uniform multiple dosage regimens mostly arising from clinical settings. Clinical examples which demonstrate the ability and the flexibility of the program are provided. The program may also be used as an aid for instruction in clinical pharmacokinetics.

Adult↗

PubMed2005

Genetic algorithms for parameter estimation in mathematical modeling of glucose metabolism.

Direct measurement of hormones secretion and kinetics in glucose metabolism is not feasible in the clinical practice, being highly invasive. As their knowledge is important in the diagnosis of metabolic disorders, thanks to mathematical models based on non-invasive tests, estimation of hormones behaviour is obtained. Unfortunately, traditional model estimation can suffer for convergence problems, and it can be strongly dependent on the parameters initial value. To overcome these limitations, Genetic algorithms (GAs) were tested on a group of 49 subjects. The stochastic nature of GAs allowed overcoming the initialization problem. Moreover, GAs significantly improved the accuracy of fit.

Algorithms↗

PubMed2006

Hodgkin-Huxley type ion channel characterization: an improved method of voltage clamp experiment parameter estimation.

The Hodgkin-Huxley formalism for quantitative characterization of ionic channels is widely used in cellular electrophysiological models. Model parameters for these individual channels are determined from voltage clamp experiments and usually involve the assumption that inactivation process occurs on a time scale which is infinitely slow compared to the activation process. This work shows that such an assumption may lead to appreciable errors under certain physiological conditions and proposes a new numerical approach to interpret voltage clamp experiment results. In simulated experimental protocols the new method was shown to exhibit superior accuracy compared to the traditional least squares fitting methods. With noiseless input data the error in gating variables and time constants was less than 1%, whereas the traditional methods generated upwards of 10% error and predicted incorrect gating kinetics. A sensitivity analysis showed that the new method could tolerate up to approximately 15% perturbation in the input data without unstably amplifying error in the solution. This method could also assist in designing more efficient experimental protocols, since all channel parameters (gating variables, time constants and maximum conductance) could be determined from a single voltage step.

Animals↗

PubMed1977

Respiratory parameter estimation using forced oscillatory impedance data.

The frequency dependency of the magnitude and phase angle of total respiratory impedance was measured in apneic dogs at functional residual capacity during forced oscillation by a special electronics unit. Regression analysis of these data yielded estimates of total respiratory resistance (RFO), inertance (IFO), and compliance (CFO). After correcting for the effects of the endotracheal tube, mean control values (+/-SE) of RFO, IFO, and CFO for the clinically normal dogs were 1.30+/-0.10 cmH2O-1-1-s, 0.0114+/-0.0022 cmH2O-1-1-s2, and 0.0306+/-0.0009 1-cm H2O-1, respectively. Estimates obtained with added resistance, a less dense gas, and abdominal weighting were consistent with predicted effects. In four dogs with mild respiratory symptoms, mean RFO was significantly elevated with no change in IFO or CFO. Independent measurements of resistance and compliance during tidal ventilation correlated well with RFO (r=0.87) and CFO (r=0.80), but RFO and CFO were, on the average, 71% of the tidal breathing values. Thus, the method provides precise estimates of RFO, IFO, and CFO, and allows detection of small changes in these parameters.

Airway Resistance↗

PubMed2004

Spatial analysis of 3' phosphoinositide signaling in living fibroblasts: II. Parameter estimates for individual cells from experiments.

Fibroblast migration is directed by gradients of platelet-derived growth factor (PDGF) during wound healing. As in other chemotactic systems, it has been shown recently that localized stimulation of intracellular phosphoinositide (PI) 3-kinase activity and production of 3' PI lipids in the plasma membrane are important events in the signaling of spatially biased motility processes. In turn, 3' PI localization depends on the effective diffusion coefficient, D, and turnover rate constant, k, of these lipids. Here we present a systematic and direct comparison of mathematical model calculations and experimental measurements to estimate the values of the effective 3' PI diffusion coefficient, D, turnover rate constant, k, and other parameters in individual fibroblasts stimulated uniformly with PDGF. In the context of our uniform stimulation model, the values of D and k in each cell were typically estimated within 10-20% or less, and the mean values across all of the cells analyzed were D = 0.37 +/- 0.25 microm2/s and k = 1.18 +/- 0.54 min(-1). In addition, we report that 3' PI turnover is not affected by PDGF receptor signaling in our cells, allowing us to focus our attention on the regulation of 3' PI production as this system is studied further.

Cells, Cultured↗

PubMed1982

Analytical approximations of sensitivities of steady state predictions to errors in parameter estimation.

The sensitivity theory is applied to derive a linear approximation to the functional dependence of some steady state quantities of therapeutic significance on pharmacokinetic parameters obtained from the biexponential response to a single drug dose. The error of a steady state prediction depends in general on two terms. The first one may be viewed as an approximate sensitivity of the prediction to the parameter errors, and this depends solely on the algebraic relation between the prediction and the parameters. The second term is the relative error in parameters, and this may be affected by experimental design and the method of data analysis. Comparisons are made with Monte Carlo simulations and "a posteriori" estimates of variance of a prediction.

Kinetics↗

PubMed1984

Estimating parameters of the family-size distribution in ascertainment sampling schemes: numerical results.

It is argued that, in any ascertainment sampling scheme using data from families of various sizes, there is never any need to assume a particular form for the (unknown) family-size distribution. There exists a simple conditional method, making no assumptions about the family-size distribution, that is always preferable to the assumption of any particular distributional form. Furthermore, the simplicity of the conditional method gives insights into properties of estimates of genetic and ascertainment parameters, which are not available when a particular form for the family-size distribution is assumed.

Biometry↗

PubMed1994

Structure identifiability in metabolic pathways: parameter estimation in models based on the power-law formalism.

An important step in understanding a metabolic pathway is to identify its structure, in terms of the flow of material and information. In pursuing this goal, the available information for a given system is usually obtained from experiments in vitro and comes from different sources. Frequently, the final set of regulatory signals acting in the system in vivo is unclear, and some kind of test is needed on the intact system. Besides defining an appropriate experimental approach, identification of the regulatory pattern needs a theoretical framework in which the different experimental measurements can be evaluated and a final picture can be agreed on. Mathematical approaches based on sensitivity coefficients provide a useful tool for addressing this problem. Within this framework, the appropriate parameters are related to both the structure of the reaction network and the signals that regulate the target system. Thus the identification of the regulatory structure can be related to the estimation of the appropriate set of parameters. In pursuing this goal, we will show the limitations of using steady-state measurements and the usefulness of using dynamic data. We suggest a way to test the regulatory pattern in a given metabolic pathway by combining both kinds of data, and we show, by using a reference system, the potential of the method suggested.

Metabolism↗

PubMedDate not supplied

Logistic growth curve of chickens: a comparison of techniques to estimate parameters.

Parameters of a mathematical function of growth, fit to the body weight curve of two randombred control populations of each sex of chickens from hatching through 45 weeks of age, were estimated. The logistic function was chosen from among growth formulae that express rate of gain as a function of weight at a given time and gain to be made. Two logistic parameters, growth-rate constant and age at the point of inflection, were estimated by the methods of sample quantiles and nonlinear regression from weekly mean body weights of 225 males and 281 females of the Rhode Island Red (RIR) line, and 164 males and 239 females of the White Leghorn (WL) line. Males had a larger growth-rate constant than females of the same line. The RIR line had a larger rate constant than the WL line, for each sex. Age at the point of inflection was similar for males and females in the RIR line, but smaller for males than females in the WL line. Sample quantiles yielded larger, less precise estimates of the growth-rate constant than nonlinear regression. Estimates of age at the point of inflection were usually smaller using sample quantiles.

Aging↗

PubMed2001

Material parameter estimation with terahertz time-domain spectroscopy.

Imaging systems based on terahertz (THz) time-domain spectroscopy offer a range of unique modalities owing to the broad bandwidth, subpicosecond duration, and phase-sensitive detection of the THz pulses. Furthermore, the possibility exists for combining spectroscopic characterization or identification with imaging because the radiation is broadband in nature. To achieve this, we require novel methods for real-time analysis of THz waveforms. This paper describes a robust algorithm for extracting material parameters from measured THz waveforms. Our algorithm simultaneously obtains both the thickness and the complex refractive index of an unknown sample under certain conditions. In contrast, most spectroscopic transmission measurements require knowledge of the sample's thickness for an accurate determination of its optical parameters. Our approach relies on a model-based estimation, a gradient descent search, and the total variation measure. We explore the limits of this technique and compare the results with literature data for optical parameters of several different materials.

Algorithms↗

PubMed2000

Endogenous model state and parameter estimation from an extensive batch experiment.

In this paper an extensive batch experiment of endogenous process behavior in an aerobic biodegradation process is presented. From these experimental data, comprising measurements of MLVSS (mixed liquor volatile suspended solids) and respiration rate, in a first step the states and unknown parameters in a four-compartmental model are reconstructed analytically. Subsequently, for a selected set of states and parameters, using the results of the previous step, a recursive state estimation procedure, in particular an Extended Kalman filter-based observer, is applied to deal with the noise properties of the data appropriately. From this it appears that the initially proposed model structure, and especially the hydrolysis term, has to be modified.

Aerobiosis↗

PubMed2001

Stability parameter estimation at ambient temperature from studies at elevated temperatures.

The determination of specific kinetic constants k(i) in pH-profile studies is often undertaken at ambient temperature. However, when dealing with a drug substance that is stable at ambient temperature, the pH-profile study is conducted at a chosen elevated temperature and the kinetic parameters are given at this particular elevated temperature. But in stability studies we generally need kinetic constants at ambient or storage temperature for practical reasons (information and storage conditions of formulation). To assess this ambient kinetic information from studies at elevated temperatures, cumulative sequential steps are usually employed with very few statistical concerns on the final estimates. The statistical problems on these final estimates in cumulative procedures are highlighted in many papers. Because these stability parameters are useful for drug formulation and storage conditions, good practical decisions have to be made on the basis of statistically unbiased identified parameters. We propose in this paper a nonlinear model that allows the direct determination of specific activation energies E(ai) that are linked to the specific kinetic constants k(i). Hence, a mathematical relationship between drug concentration C, pH, temperature T, and time t is obtained. Kinetic data from acetylsalicylic acid (ASA) hydrolysis (first-order kinetics) are used to validate the model. The results show that it is possible to obtain directly, by an extrapolation procedure, the kinetic parameters (specific kinetic constants k(i), specific activation energies E(ai), and dissociation constant pK(a)) at low temperature from data gathered at elevated temperatures using more meaningful statistics.

Data Interpretation, Statistical↗

PubMed2005

A kinetic model and its parameter estimation for the process of binding copper to human serum albumin by a voltammetric method.

Linear sweep anodic stripping voltammetry was applied to determine the concentration of free copper ions in the process of binding copper to human serum albumin (HSA) on the mercaptoethane sulfonate modified gold electrode surface. A kinetic model of two consecutive steps for the process of binding copper to HSA was first proposed on the basis of the electrochemical results and compared with a parallel kinetic response model by using residual analysis. The experimental data of the stripping peak currents with time was fitted according to the model and the kinetic parameters, binding rate constants, k1 and k2, were estimated to be 0.411 and 0.055 min(-1), respectively.

Copper↗

PubMed1997

Linear and nonlinear ARMA model parameter estimation using an artificial neural network.

This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.

Computer Simulation↗