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At least 235 records · Page 13Linked to original sources

Kinetic model of glucose-6-phosphate dehydrogenase from red blood cells. Parameter estimation from progress curves and simulation of regulatory properties.

A kinetic model of human and mouse glucose-6-phosphate dehydrogenase is presented which takes into account the substrates and all inhibitors of significant importance in the red cell. The parameter values were estimated by analysis of progress curves. The applicability of a new method based on non-linear regression to complex enzyme kinetics was proved. The in vivo-regulation of glucose-6-phosphate dehydrogenase is examined by determining elasticity coefficients and by using simple simulation experiments. The model is convenient to describe the behaviour of enzyme activity under physiological conditions.

Adenosine Triphosphate↗

Pharmacokinetic calculator program for generation of initial parameter estimates from a three-compartment infusion model.

A polyexponential curve-stripping program, KIN, is described for use on the HP-41CV programmable calculator. The program may be used in the analysis of plasma-concentration-time curves for a three-compartment intravenous bolus or infusion model with linear elimination processes. The coefficients and hybrid rate constants of the exponential function are then used to compute pharmacokinetic parameters (volume of the central compartment, intercompartmental rate transfer constants), which may be used as initial estimates of model parameters in non-linear regression curve-fitting procedures.

Computers↗

All maps of parameter estimates are misleading.

Maps are frequently used to display spatial distributions of parameters of interest, such as cancer rates or average pollutant concentrations by county. It is well known that plotting observed rates can have serious drawbacks when sample sizes vary by area, since very high (and low) observed rates are found disproportionately in poorly-sampled areas. Unfortunately, adjusting the observed rates to account for the effects of small-sample noise can introduce an opposite effect, in which the highest adjusted rates tend to be found disproportionately in well-sampled areas. In either case, the maps can be difficult to interpret because the display of spatial variation in the underlying parameters of interest is confounded with spatial variation in sample sizes. As a result, spatial patterns occur in adjusted rates even if there is no spatial structure in the underlying parameters of interest, and adjusted rates tend to look too uniform in areas with little data. We introduce two models (normal and Poisson) in which parameters of interest have no spatial patterns, and demonstrate the existence of spatial artefacts in inference from these models. We also discuss spatial models and the extent to which they are subject to the same artefacts. We present examples from Bayesian modelling, but, as we explain, the artefacts occur generally.

Bayes Theorem↗

A new method of parameter estimation from progress curves.

A mathematical procedure is presented which permits kinetic parameters to be determined from progress curve data. The method is applicable to any kind of enzymatic reaction which can be described by a single rate equation. A general criterion is derived to check the accuracy of the method. An application to a simulated 2-substrate reaction is given.

Half-Life↗

Simulation studies of influenza epidemics: assessment of parameter estimation and sensitivity.

The influenza simulation model of Elveback et al is used to evaluate the accuracy of the maximum likelihood procedure of Longini et al for estimating the secondary attack rate in households. The sample population from the Tecumseh Respiratory Illness Study is mapped into the simulation model and simulations are carried out over a range of parameter values and conditions, some of which were derived from influenza seasons in Tecumseh and from the Seattle Flu Study for the years 1975-1980. The estimation procedure is found to be quite robust for parameter values preset within appropriate limits for influenza. However, a significant difference is found between the preset and estimated household contact parameter for epidemics of medium and high intensity when the preset value is zero. Incremental increases in the household contact parameter are shown to produce marked increases in the overall infection attack rate demonstrating that household spread is an important link in maintaining infection in other mixing groups such as schools, preschool groups and neighbourhood clusters of households.

Adolescent↗

Parameter estimation in studying circadian rhythms.

In the model under consideration for the circadian rhythm study there are three unknown physiological parameters involved: the level, the amplitude and the phase. This paper concerns the estimation of the group level, group amplitude and group phase of a certain group of individuals based on their time series data. Special attention is paid to the amplitude and phase parameters, and solutions are obtained for both the small-sample and the large-sample cases.

Circadian Rhythm↗

The regulation of malaria parasitaemia: parameter estimates for a population model.

Classical studies of non-immune individuals infected with Plasmodium falciparum reveal that the infection may be regulated for long periods at a relatively stable parasite density, despite the enormous growth potential of a parasite that continually replicates within host erythrocytes. This suggests that the parasite population may be controlled by density-dependent mechanisms, and in theory the most obvious of these is competition between parasites for host erythrocytes. Here we evaluate the role of this mechanism in the regulation of parasitaemia, by modelling the basic population interaction between parasites and erythrocytes in a form that allows all the essential parameters to be estimated from clinical data. Our results show that competition cannot account for the total regulation of P. falciparum, but when combined with immune mechanisms it may play a more important role than is generally supposed. Further analysis of the model indicates that in the long term, parasite replication at low parasite densities can contribute significantly to the high degree of anaemia observed in natural infection, a conclusion which is not obvious from simple clinical observation.

Anemia↗

Model parameter estimation and analysis: understanding parametric structure.

We developed three algorithms to facilitate an analysis of the parameter combinations (PASS points) that fit experimental data to a desired degree of accuracy. The clustering algorithm separates PASS points into clusters (PASS clusters) as a preliminary step for the following geometrical parametric analyses. The PASS region reconstruction algorithm defines the space of a PASS cluster to allow further parametric structural analysis. The feasible parameter space expansion algorithm produces a complete PASS cluster to be used for model predictions to evaluate the effects of variability and uncertainty. These algorithms are demonstrated using two pharmacokinetic models; a single compartment model for procainamide and a three-compartment physiologically based model for benzene. We found a more thorough representation of the parameter space than previously considered. Thus, we obtained model predictions that describe better the variability in population responses. In addition, we also parametrically identified a subpopulation that may have a higher risk for cancer.

Algorithms↗

Estimating parameters for psychometric functions using the four-point sampling method.

Although a psychometric function describing a subject's responses to some physical stimuli is of considerable value, characterizing such functions is time consuming and, hence, is not carried out routinely in psychophysical experiments. A principal reason for the lack of efficiency in characterizing a psychometric function is the use of sampling methods that either converge on a single point on the psychometric function, such as the PEST method, or which distribute observations uniformly over a wide range, such as the constant stimuli method. As an alternative, a multimodal four-point sampling method has been proposed [C. F. Lam, J. H. Mills, and J. R. Dubno, J. Acoust. Soc. Am. 99, 3689-3693 (1996)]. A psychometric function is then fitted to the four points (each with several trials) to estimate the threshold and slope parameters of the psychometric function. Adaptive methods, such as the up-down methods [H. Levitt, J. Acoust. Soc. Am. 49, 467-477 (1971)], can be used to provide good initial estimates of the threshold and spread parameters of a psychometric function described by a logistic function. In ongoing studies of age-related changes in auditory masking and discrimination, this new four-point sampling method has been applied to determine psychometric functions for absolute thresholds as a function of duration, thresholds in simultaneous and forward masking, frequency discrimination, and intensity discrimination in both young and aged human subjects. Results indicate that a reduction in data collection time of about 50% with no increase in variance can be achieved. This increase in efficiency applies to simple detection tasks by normal hearing subjects as well as to complex discrimination tasks by older subjects with hearing loss.

Adult↗

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↗

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↗

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↗

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↗

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↗

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↗

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↗

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↗