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PubMed1987

A note on confidence intervals with extended least squares parameter estimates.

It has previously been shown that the extended least squares (ELS) method for fitting pharmacokinetic models behaves better than other methods when there is possible heteroscedasticity (unequal error variance) in the data. Confidence intervals for pharmacokinetic parameters, at the target confidence level of 95%, computed in simulations with several pharmacokinetic and error variance models, using a theoretically reasonable approximation to the asymptotic covariance matrix of the ELS parameter estimator, are found to include the true parameter values considerably less than 95% of the time. Intervals with the ordinary least squares method perform better. Two adjustments to the ELS confidence intervals, taken together, result in better performance. These are: (i) apply a bias correction to the ELS estimate of variance, which results in wider confidence intervals, and (ii) use confidence intervals with a target level of 99% to obtain confidence intervals with actual level closer to 95%. Kineticists wishing to use the ELS method may wish to use these adjustments.

Kinetics↗

PubMed1984

Parameter estimation using the quasi-linear viscoelastic model proposed by Fung.

Using the quasi-linear viscoelastic model proposed by Fung for the description of the viscoelastic properties of soft biological tissues, the parameters governing their time-dependent behavior are commonly estimated from relaxation experiments. Exact quantification is possible from the response to a step change in the strain. Since it is physically impossible to realize a true step change in the strain, in practice the response to a steplike strain change is used. In the present study the discrepancies between the exact and the estimated parameter values are investigated using a hypothetical quasi-linear viscoelastic material. The parameter tau 1, governing the fast viscous phenomena, is found to be subject to the largest errors. Methods for obtaining better estimates of tau 1 are outlined in a number of special cases.

Biomedical Engineering↗

PubMed1991

Investigation of parameter estimator and adaptive controller for assist pump by computer simulation.

The multi-output adaptive controller of a left ventricular assist device (LVAD) was studied by computer simulation. The controller regulated two outputs--mean aortic pressure (mAoP) and mean atrial pressure (mLAP)--by regulating vacuum pressure (input). The autoregressive models were used to describe the circulatory system. The parameters of the models were estimated by the recursive least squares method. Based on the autoregressive models, the vacuum pressure minimizing a performance index was searched. The index used was the weighted summation of the square errors. Responses of the adaptive controller were simulated when the contractility of the left ventricle was decreased at various rates and the peripheral resistance was changed. Both the mAoP and mLAP were controlled to their predicted values in the steady state. The steady-state errors of the mAoP were less than a few mm Hg, and those of the mLAP were lower than 1 mm Hg. Consequently, the estimated parameters can be regarded as true parameters, and the adaptive controller has the potential to control more than two outputs. The multioutput adaptive controller studied is useful in controlling the LVAD according to the change in circulatory condition.

Aorta, Thoracic↗

PubMed1982

Parameter estimation of transpulmonary mechanics by a nonlinear inertive model.

Transpulmonary mechanics of anesthetized intubated dogs were studied during control breathing and hemorrhage-induced hyperventilation by least-mean-squares parameter estimation using several model versions. The classical elastance-resistance model was modified to include nonlinear elastic and viscous pressure terms with and without a linear inertive pressure component. Inclusion of the nonlinear terms decreased the root-mean-square error of fitting (q) of the classical model on the average to 67% in the control period and to 58% during hyperventilation. An additional decrease due to inertance was 4% (control) and 22% (hyperventilation) and was associated with acceptable estimates of inertance [0.056 +/- 0.02 (SD) and 0.063 +/- 0.008 cmH2O . l-1 . s2, respectively]. When inertance alone was added to the classical model, negligible improvement in q and unrealistic values of inertance were obtained. Conventional measures (Edyn and midvolume resistance) were close to the corresponding least-mean-squares estimates (E and R) of all model versions, except that in hyperventilation neglecting the inertance caused Edyn to markedly overestimate E of nonlinear inertive model.

Animals↗

PubMed1976

CSTRIP, a fortran IV computer program for obtaining initial polyexponential parameter estimates.

A new exponential stripping program, CSTRIP, has been developed. This program overcomes the problems associated with the use of previously published techniques and enables the rapid economical calculation of initial polyexponential parameter estimates. Values for the coefficients and exponents of the exponential terms are calculated as well as estimates of lag times. An exhaustive search procedure ensures that the results are comparable to, or better than, those obtained by manual residual methods.

Computers↗

PubMed1984

PHARM--an interactive graphic program for individual and population pharmacokinetic parameter estimation.

This paper describes a new computer program PHARM to estimate individual or population pharmacokinetic parameters in nonlinear models. PHARM is an interactive program which uses graphic facilities to display data and results. The structural model can be defined using differential or integrated equations. The user can also define an error model associated with experimental data. The nonlinear mixed effect model is used to estimate the mean population parameters and their interindividual variability. The maximum likelihood and Bayesian criteria are used to estimate simultaneously the error and structural model parameters.

Computers↗

PubMed1992

Model parameters estimation when the evoked potential recordings are affected by a random scale factor.

In many situations an important source of the average evoked potentials (EPs) variability is a random scale factor affecting each recording. As a result, the outcome of any EP detection method may be greatly affected. However, using an appropriate probabilistic model these scale factor can be estimated, and the performance of any available detection index improved by data rescaling. In this paper the Maximum Likelihood Estimators of the waveform of the response and the scale factor affecting both background noise and this waveform are obtained. Also, an iterative algorithm for model parameters estimation is presented and its convergence is examined in a simulation study. The Linear Discriminant function is computed using simulated test data in both situations, before and after rescaling of recordings. The performance of these statistics is evaluated by mean of ROC curves.

Algorithms↗

PubMed1989

Source parameter estimation in inhomogeneous volume conductors of arbitrary shape.

In this paper it is demonstrated that the use of a direct matrix inverse in the solution of the forward problem in volume conduction problems greatly facilitates the application of standard, nonlinear parameter estimation procedures for finding the strength as well as the location of current sources inside an inhomogeneous volume conductor of arbitrary shape from potential measurements at the outer surface (inverse procedure). This, in turn, facilitates the inclusion of a priori constraints. Where possible, the performance of the method is compared to that of the Gabor-Nelson method. Applications are in the fields of bioelectricity (e.g., electrocardiography and electroencephalography).

Electric Conductivity↗

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

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↗

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↗