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PubMed1988

The effect of random measurement errors on kinetic transport parameter estimation.

Saturation kinetics experiments, in which uptake U of a substance across a transport barrier is measured as a function of initial concentration difference C, are used to describe transport of nutrients. Many such processes are characterized by low- and high-affinity systems in which kinetic parameters Vmax and Km differ by orders of magnitude. Transformations of equations to straight-line relationships between U and C are popular methods of parameter estimation. The aims of this study are (1) to show effects of random errors in U measurement on Vmax and Km estimation in a two-affinity process under several transformations: Lineweaver-Burk (1/U vs. 1/C), Hanes (C/U vs. C), Eadie-Hofstee (U/C vs. U), and Wolff (U vs. U/C), and (2) to indicate strategies for minimizing effects of errors. Two transport properties will illustrate: an ideal process of low- (Vmax = 100, Km = 10) and high-affinity (Vmax = 1, Km = .1) systems to which random error is added, and experimental uptake of 5-methyltetrahydrofolic acid by isolated hepatocytes.

Age Factors↗

PubMed1987

Neurotransmission parameters estimated from miniature endplate current growth phase.

A numerical model of miniature endplate current (mepc) generation was fitted to the rising phase of individual mepcs recorded at the frog neuromuscular junction, and estimates of 6 transmission parameters were obtained. Model fitting was enabled by assuming literature values for geometric parameters and determining single channel current by noise analysis, the channel closing rate constant from the mepc decay, and acetylcholine hydrolysis parameters from mepcs recorded in esterase-blocked endplates. Under control conditions, mean estimates were: number of molecules in a quantum = 29,000, diffusion coefficient = 2.8 X 10(-6) cm2s-1, endplate receptor density = 8500 micron-2, forward binding rate constant = 7.6 X 10(8) M-1s-1, equilibrium dissociation constant = 58 microM and channel opening rate constant = 8100 s-1.

Animals↗

PubMed1987

Genetic parameter estimates for preweaning growth traits in Santa Gertrudis cattle.

Genetic parameters were estimated for birth weight and weaning weight from records collected on 1,894 Santa Gertrudis calves (939 bulls, 955 heifers) during the 8-yr period, 1978 through 1985. Variance and covariance components were estimated separately by sex and combined across sexes utilizing mixed-model, least-squares procedures (Henderson's Method 3). The mathematical model assumed for estimating variance and covariance components by sex included effects of year, sire-within-year and age of dam. Also, calf weaning age was included as covariate for birth weight and weaning weight. Estimates were obtained across sexes utilizing the same model, with the addition of effects of sex of calf and the sex-of-calf X age-of-dam interaction. Heritabilities and genetic and phenotypic correlations were estimated using paternal half-sib techniques. The heritability estimate for birth weight for bulls was 1.6 times larger than that for heifers (.38 +/- .12 vs .24 +/- .10). Conversely, the heritability estimate for weaning weight for heifers was 1.5 times larger than that for bulls (.45 +/- .12 vs .30 +/- .11). However, based upon their approximate standard errors, neither of these differences was significant. Heritability estimates calculated across sexes were .32 +/- .07 and .42 +/- .08 for birth weight and weaning weight, respectively. Estimates of genetic and phenotypic correlations of birth weight and weaning weight by sex were .43 +/- .21 and .31, respectively, for bulls and .33 +/- .22 and .27, respectively, for heifers. Calculated across sexes, the genetic correlation was .40 +/- .14 and the phenotypic correlation was .29.

Animals↗

PubMed1992

Arm function after axillary dissection for breast cancer: a pilot study to provide parameter estimates.

Sixty-three women participated in a study in Calgary, Alberta to assess the rate of arm recovery and factors affecting it up to one year after axillary node dissection for breast cancer. Outcomes included objective measures of swelling, mobility, and strength, and subjective assessments of pain (at rest and with movement) and stiffness. Approximately 42% of women had residual impairment of at least one type one year after surgery, the most common problems being pain (16%) and reduced grip strength (16%). Except for lymphedema, measurements one year after surgery showed little change from measurements at 6 months, suggesting that the shorter follow-up may be appropriate for assessing the long term effects of axillary dissection. Lymphedema was the only sequela which increased over time. The results provide parameter estimates for designing studies to evaluate the role of physiotherapy after axillary dissection.

Arm↗

PubMed1992

Parameter estimation for carcass traits including growth information of Simmental beef cattle using restricted maximum likelihood with a multiple-trait model.

(Co)variance component estimates were computed for retail cuts per day of age (kilograms per day), cutability (percentage of carcass weight), and marbling score (1 through 11) using a multiple-trait sire model. Restricted maximum likelihood estimates of (co)variance components were obtained via an expectation-maximization algorithm. Carcass data consisted of 8,265 progeny records collected by U.S. Simmental producers. Growth trait information (birth weight, weaning weight, and[or] postweaning gain) for those progeny with carcass data and an additional 5,405 contemporaries formed the complete data set for analysis. A total of 420 sires were represented. Three models differing in number of traits were investigated: 1) carcass traits with growth traits, 2) carcass traits only, and 3) single trait. The final models did not include postweaning gain because of convergence problems. Parameter estimates for all three models were essentially the same. Heritability estimates were .30, .18, and .23 for retail cuts per day, cutability, and marbling score, respectively. Correlations between growth and carcass traits were low except for those with retail cuts per day, which were moderate and positive. The additional information gained by adding growth traits to the carcass-traits-only evaluation lowered prediction error variances most for retail cuts per day. Little change in prediction error variances was found for cutability and marbling score. Inclusion of growth traits in future sire evaluations for carcass traits will benefit the evaluation of retail cuts per day but have considerably less effect on cutability and marbling score.

Analysis of Variance↗

PubMed1988

Effect of blood curve smearing on the accuracy of parameter estimates obtained for 82Rb/PET studies of blood-brain barrier permeability.

82Rb in conjunction with positron emission tomography (PET) has been used to estimate the blood to brain transport rate constant (K1) for Rb and the regional brain/tumour blood volume (Vb). Errors in K1 and Vb depend upon the accuracy of the measured arterial blood radioactivity and PET-monitored brain radioactivity. Arterial blood is usually sampled by placing a catheter in the radial artery and measuring the radioactivity in blood passing continuously in front of a detector or by counting discrete blood samples in a well scintillation detector. In either case, the passage of blood through catheter/pump tubing produces a smearing of the waveform as well as a delay in the arrival of radioactivity at the blood sampling site. The change in shape of the blood curve is significant for bolus-type injections and results in large errors in those model parameters which contribute substantially to the initial phase of the brain activity curve. We report here the results of computer simulations and an analysis of patient data which suggest that parameter estimation errors due to smearing and time shift may be large (greater than 50%) but that these errors can be minimised by the use of deconvolution techniques.

Blood-Brain Barrier↗

PubMed1985

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.

Animals↗

PubMed1989

Sensitivity analysis of the systemic circulation with a view to computer simulation and parameter estimation.

A sensitivity analysis study has been performed on a seven-parameter model of the systemic vascular bed in order to obtain structure reductions appropriate for simulation and estimation. This analysis considers separately the systolic and diastolic transfer functions between arterial and venous pressures in order to divide a non-linear problem in two distinct linear problems. The results obtained refer to nominal parameter values corresponding to normal circulatory conditions in man and supply guide-lines for an application-oriented selection of reduced models. Simple resistance-compliance models are preferred because the inertial effects appear to have only slight influence. In particular, the choice of a five-parameter model seems to be convenient for simulation purposes. An additional structure reduction is suggested to reach reliable results in parameter estimation problems. The resulting model is characterized by three elements: peripheral resistance, arterial compliance and venous compliance.

Blood Circulation↗

PubMed1985

Parameter estimates for a QALY utility model.

This paper discusses a utility model for quality adjusted life years (QALY). According to this model, the utility of Y years of survival in health state Q is bYrH(Q), where b is a scaling constant and r and H(Q) are parameters. The parameter r is shown to be interpretable as a representation of a patient's risk attitude with respect to survival duration. The parameter H(Q) represents the proportionate reduction in the utility of survival when health state Q prevails. Methods are described for estimating these parameters from the results of an individual patient utility assessment. Results are then reported for empirical estimation of parameters r and H(Q) from the preference judgments of a sample of 46 coronary artery disease patients. In this empirical study, health state Q takes on two values--survival with angina pectoris and survival free from angina pectoris. Estimated values of parameters r and H(Q) are discussed in relation to the decision analysis of coronary artery bypass graft surgery. Finally, it is argued that the model deserves consideration as a medical utility model, despite some preliminary evidence that assumptions of the model are descriptively false, because it provides a simple representation of the utility of survival duration and health quality. These aspects of health outcomes are known to be critically important in the expected utility analysis of health decisions.

Angina Pectoris↗

PubMed1992

A relation between the Akaike criterion and reliability of parameter estimates, with application to nonlinear autoregressive modelling of ictal EEG.

The Akaike minimum information criterion provides a means to determine the appropriate number of lags in a linear autoregressive model of a time series. We show that the Akaike criterion is closely related to the reliability estimates of successively determined parameters of a linear autoregressive (LAR) model. A similar criterion may be applied to determine whether the addition of a nonlinear term to an LAR model provides a statistically significant improvement in the description of the time series. As an example, we use this method to identify quadratic contributions to a nonlinear autoregressive characterization of a typical 3/s spike and wave seizure discharge.

Data Interpretation, Statistical↗

PubMed1978

Program to estimate parameters of linear systems without numerical differentiation.

This paper describes a computer program for estimating the parameters of a linear differential equation systen with constant coefficients by use of a nonlinear least-squares method. For minimization the sum of squares of an existing standard program, the Gauss-Newton gradient procedure, is employed. The differential equation system is solved by the Taylor expansion method. The advantage of this approach is that the derivatives with respect to the parameters are available without numerical differentiation. Therefore the inaccuracy inherent in numerical differentiation and the problem of choosing the modification of the parameters are eliminated. The given procedure is applicable for all the first order gradient methods. The presented method was tested with generated data from a four-compartmental model.

Computers↗

PubMed1987

Identifiability: the first step in parameter estimation.

The observations in an experiment define a set of observational parameters that are functions of the basic kinetic parameters of the model of the system. The problem of identifiability is concerned with whether the observational parameters uniquely specify the basic kinetic parameters. As such, it depends only on the functional relation between the two levels of parameters and not on errors of observation and the estimation procedure. It should be checked before doing the experiment. Given initial estimates of the basic kinetic parameters, identifiability can be checked, in a local sense, from data generated by simulating the experiment on the model.

Computer Simulation↗

PubMed1988

Relationships among growth hormone and prolactin secretory parameter estimates in Holstein bulls and their predicted differences for lactational traits.

Selection of dairy sires is based on the production records of their female ancestors, half-sibs and daughters. No trait expressed by the sire is used. Concentrations of growth hormone (GH) and prolactin (PRL), hormones produced in both males and females that are fundamental in lactation, may be correlated with production. A study was conducted to determine whether measures of these hormones in the sire would be useful predictors of lactational ability of daughters. Blood samples were collected at 15-min intervals for 8 h from 26 Holstein bulls (5.5 yr of age) that had one progeny summary available. Plasma concentrations of GH and PRL were quantified and the mean and baseline concentrations and the frequency and mean amplitude of the secretory peaks were determined for each bull. Concentrations among these values and bulls' predicted differences (PD) were determined. Significant negative correlations were detected for frequency of GH peaks and PD for yield of milk, fat and protein; correlations were positive for PRL baseline concentrations and PD for fat and protein (P less than .10), and correlations were negative for frequency of PRL peaks and PD for milk, fat and protein (P less than .10). Addition of estimates of bull hormone secretory parameters to breeding values based on performance of relatives considerably improved the accuracy (R2) for predicting progeny performance from sire information. Certain characteristics of the patterns of GH and PRL secretion may be heritable and aid in identification of superior dairy animals.

Animals↗

PubMed1990

Transducer characterization from pressure amplitude distribution measurements using a Kalman filter as parameter estimation algorithm.

The amplitude and frequency contents of a received ultrasound pulse depends on the spatial pressure amplitude distribution of the sound field, as produced by the transducer in the medium, and on the position and orientation of the reflecting surface in this field. Often, the geometry of the reflecting surface and the acoustical properties of the medium are known or can be estimated. Then it is practical to determine the transducer parameters in order to calculate the distortion of a reflected ultrasound pulse. Apart from geometrical parameters such as size and mechanical focusing, the surface velocity amplitude distribution (SVAD) of a transducer is of major importance. For some transducer configurations this SVAD may be described with a limited number of parameters. This paper presents a method, based on a Kalman filter algorithm, to assess the transducer parameters by measurement of the spatial sound field pressure amplitude distribution in various planes for different emission frequencies. Comparison of the measured pressure amplitudes with those calculated using the estimated values of the parameters shows that this method yields reliable results.

Acoustics↗

PubMedDate not supplied

Identifiability and parameter estimation.

In experiments on biological systems one often cannot measure all state variables (compartments). Given a particular experiment of that type, a basic kinetic parameter may have no effect on the observations; such a parameter is an insensible parameter for that experiment. A parameter may influence the observations and not be uniquely determinable; such a parameter is nonidentifiable for that experiment. Only identifiable parameters can be estimated uniquely, by that experiment. I review the basic theory to check identifiability for a nominal value of a parameter (local identifiability), and present some examples of problems that may arise in estimation.

Kinetics↗

PubMed1986

Logistic curve fitting and parameter estimation using nonlinear noniterative least-squares regression analysis.

A microcomputer program has been developed for the fitting of the logistic curve to biological, medical, and other experimental data. In addition to supplying estimates for all of the logistic curve parameters, the program provides the fitted result for each input datum thus allowing for the immediate assessment of the logistic curve and detection of possible outliers.

Biometry↗

PubMed1990

Parameter estimation in a three-compartment model for blood alcohol curves.

Models of alcohol input and absorption are crucial to the description and understanding of the effects of alcohol in the human body. In this paper, the pharmacokinetics of alcohol after oral administration are described by a three-compartment model with a supposed concentration-dependent absorption and elimination. The absorption of alcohol from the small intestine into the blood is represented by a first-order rate constant ka. To describe the delay in peak concentration of alcohol the gastric emptying rate is represented as a first-order parameter with a feedback control depending on the amount of alcohol remaining in the stomach. The alcohol ingestion can then be represented as a bolus input. The elimination process is described by a model similar to the Michaelis-Menten model for enzyme kinetics. Parameters are estimated by means of an iterative algorithm minimizing a non-linear function. A good fit of the model was obtained for blood alcohol curves from six men and six women who each had received an alcohol dose of 28.5 g on three consecutive days. It is concluded that the model can be recommended to describe adequately the absorption and elimination of alcohol.

Adult↗

PubMed1986

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↗