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At least 91 records · Page 5Linked to original sources
PubMed1995

On the parameter estimation for diffusion models of single neuron's activities. I. Application to spontaneous activities of mesencephalic reticular formation cells in sleep and waking states.

For the Ornstein-Uhlenbeck neuronal model a quantitative method is proposed for the estimation of the two parameters characterizing the unknown input process, namely the neuron's mean input per unit time mu and the infinitesimal standard deviation per unit time sigma. This method is based on the experimentally observed first- and second-order moments of interspike intervals. The dependence of the estimates mu and ŝigma on the moments of the observed interspike intervals and on the neuronal parameters is clarified, and a comparison is made between the estimates based on the classical Wiener model and those yielded by the Ornstein-Uhlenbeck model. Comprehensive tables are included in which the displayed values of mu and ŝigma have been calculated in terms of physiologically realistic pairs of first- and second-order moments. Our method is finally applied to interspike interval data recorded from neurons in the mesencephalic reticular formation of the cat during hypothetical sleep, slow-wave sleep stage, and wake stage.

Animals↗
PubMed1980

Identification and parameter estimation of the mechanical ventilatory system.

Oesophageal pressure and mouth volume were measured by oesophageal balloon and pneumotachography, respectively, in 10 men (both normal and diseases) under different experimental conditions, i.e. spontaneous ventilation, quasi-static manoeuvres and respiration at high frequencies. The recorded data were then analyzed by an identification and parameter estimation computer programme, to determine a mathematical model for the process. Contrary to other recently published papers dealing with frequency analysis, we studied a time-dependent model, represented by a linear time-invariant differential equation. The results were quite satisfactory since a relatively second-order model seems to be adequate for describing the process. Differences in the parameter values between normal and diseased subjects were characterized by increases in the patients' lung viscous component. In conclusion, our identification test results in the mechanical ventilatory system seem to indicate that a simple second-order mathematical model is consistent with the experimental data.

Adult↗
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↗
PubMedDate not supplied

Parameter estimation in six numeric models of transperitoneal transport of glucose.

Six competing kinetic models of transperitoneal glucose transport were formulated and validated. The models were designed to elucidate the presence or absence of diffusive, nonlymphatic convective and lymphatic convective solute transport. The validation procedure included an assessment of theoretical and practical identifiability, goodness of fit, residual error analysis, and plausibility of parameter estimates. Experimental results were obtained from 21 patients without diabetes. The validation procedure demonstrated that the model that only included diffusion was superior to the other models. Theoretically, both nonlymphatic convective and lymphatic convective transports might exist. However, neither the ultrafiltration sieving coefficient nor the lymphatic flow rate were practically identifiable, probably because any amount of glucose transported by nonlymphatic convective and lymphatic convective transport mechanisms was negligible compared with the amount transported by diffusion. Based on these results, there appear to be problems measuring convective solute transport parameters when the solute transport is in the dialysate-to-blood direction while the fluid transport is in the blood-to-dialysate direction.

Adult↗
PubMed1995

A model of fluid resuscitation following burn injury: formulation and parameter estimation.

A dynamic compartmental model is developed to describe the redistribution of fluid and albumin between the circulation and the intact and injured interstitia following burn injury in humans. Transcapillary fluid and albumin exchange is described by a coupled Starling mechanism, while the effect of the burn is represented by time-dependent perturbations to all three compartments. The unknown model parameters are determined for two groups of patients, having less than and greater than 25% total body surface area burns, by statistical fitting of model predictions to patient data from two sources. The parameters include the perturbations to the fluid filtration coefficients in uninjured and injured tissue, GkF,Tl and GkF,BT, respectively, the relaxation coefficient, r, which describes the exponential decay of the perturbations, and the exudation factor, EXFAC, which relates the protein concentration in the exudate to that in the injured tissue. Perturbations to other parameters, including the membrane permeability-surface area product and the albumin reflection coefficient in the injured and uninjured tissues, are determined based on interrelationships with GkF,Tl and GkF,BT. The values of GkF,BT, when corrected for tissue destruction and decreased post-injury perfusion, are in reasonable agreement with the limited experimental data available from the literature. The model and its parameters are further validated by comparing the simulated patient responses to the clinical data used in the parameter estimation as well as to data available from two additional sources.

Body Fluid Compartments↗
PubMed1982

Aspects of parameter estimation in ascertainment sampling schemes.

It has recently been suggested that ascertainment sampling estimation procedures commonly used are not fully efficient in that the number of unobserved families is an unknown parameter that should be estimated (contrary to common practice) along with the genetic parameters for fully efficient estimation. It has also been suggested that the frequency distribution of family size contains unknown parameters that should similarly be estimated with the genetic parameters. These two suggestions are considered in this paper. It is shown by means of an equivalence theorem that in both cases the estimates and their variances obtained by adopting the suggested procedure are identical with those found by ignoring the unobserved families and by ignoring the family-size distribution. This demonstration leads to a formal justification of further procedures, in particular: (1) use of "method-of-moments" estimators, (2) ignoring the ascertainment scheme in some cases when estimating parameters, and (3) forming estimates of parameters when various parts of the data are obtained by different ascertainment schemes.

Family Characteristics↗
PubMedDate not supplied

A calculator program for least-squares parameter estimation according to the one-compartment kinetic model with zero-order input.

A calculator program that performs a nonlinear least-squares fit to data conforming to the one-compartment model with zero-order input is described. The program, which is designed for the Hewlett-Packard HP-41 CV calculator, is based on the Gauss-Newton iterative algorithm as modified by Hartley. A subroutine for calculation of initial parameter estimates is incorporated into the program. Plasma concentration data relative to a single oral dose of a sustained-release theophylline formulation are used to demonstrate the practical application of the program.

Computers↗
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↗
PubMed1984

Statistical prediction of drug stability based on nonlinear parameter estimation.

The classical approach in Arrhenius prediction of drug stability uses two sequential steps of linear regression involving (a) a function of drug content versus time to obtain the rate constants (k) at several elevated temperatures and (b) the relationship of logarithm of mean k versus reciprocal temperature to predict the room temperature rate constant and hence the shelf-life of the drug. Uncertainties in drug content determinations are often neglected in the second regression. The classical approach also provides a wide and unsymmetrical 95% confidence interval for the predicted shelf-life. We have developed equations which allow for direct statistical prediction of shelf-life using observed values of drug content, time, and temperature. Nonlinear regression analysis was employed to provide parameter estimates of drug shelf-life and the energy of activation. The developed approach was shown to provide good estimates of shelf-life with meaningful statistics of reactions over a wide range of stability and energetics, with various kinetic orders, with different levels of noise in the data, and with different types of data structure. Comparison between the nonlinear approach and the classical approach showed that the nonlinear approach provided better mean estimates of shelf-life with much smaller and more symmetrical 95% confidence intervals than the classical approach. The method appears sufficiently robust and wide-ranging as to be potentially applicable for the prediction of the drug stability of pharmaceutical products.

Chemistry, Pharmaceutical↗
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↗
PubMed1995

Parameter estimation of labial movements in speech production: implications for speech motor control.

Central to theories of speech motor control are estimates on magnitudes of lip activity expressed in terms of central tendency, variability, and interrelatedness. In fact, the tenability of each of two competing theories of motor control for speech production rests solely on the observation of the predicted direction of the correlation coefficient (one positive and one negative) that indexes the relationship of concurrent lip activity. Each theory, however, predicts a relationship that is the complete opposite of the relationship predicted by the other. That is, one theory proposes that the labial system functions on the basis of complementary variation, whereas the other assumes positive covariation, or complementary modulation. In apparent contradiction, each prediction has been observed under laboratory conditions. The explanation for this apparent contradiction resides in the small sample sizes upon which each estimate was based. The minimum number of observations that are necessary to achieve accurate estimates of lip displacement parameters has remained unclear. This paper addresses three fundamental questions: (a) how many observations of on-task behavior are necessary to accurately estimate mean and variance values for the magnitude of upper lip displacement in a speech production experiment?, (b) what is the analogous number of observations for estimating the same values of lower lip displacement (together with the mandible) in the same context?, and (c) how many observations are necessary to accurately estimate the correlation coefficient indexing the relationship of lip displacements during the production of speech? Answers to these questions are accomplished through a review of estimator properties, a Monte Carlo computer simulation, and through laboratory observations.(ABSTRACT TRUNCATED AT 250 WORDS)

Humans↗
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↗
PubMed1995

Misclassification of a prognostic dichotomous variable: sample size and parameter estimate adjustment.

Under general conditions, Lagakos showed that for an explanatory variable observed with error, the asymptotic relative efficiency (ARE) when using the observed rather than the true values in linear models, logistic models and proportional hazards models for survival is the square of the correlation between the true and observed variables. The result is useful for sample size adjustment when this correlation is estimable. Often, one cannot observe correct values of the explanatory variable under any circumstances. We show, however, that under the models considered by Lagakos for a dichotomous explanatory variable, the ARE equals the kappa statistic in a read-reread protocol. Consequently, one need not know 'truth' in this situation to estimate the ARE and to adjust sample size to maintain desired power; divide the estimated sample size obtained with the assumption of no measurement error by the consistent estimate of the kappa statistic (which is unlikely to be zero or negative). We then develop heuristically an adjusted estimate of the beta parameter in a proportional hazards survival model. The work was motivated by analyses of the Childhood Brain Tumour Consortium database. Examples from this database illustrate the method.

Brain Neoplasms↗