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K R Godfrey

Publications and source records attributed to K R Godfrey.

30 records · Page 2Linked to original sources
PubMed1989

A methodology for compartmental model indistinguishability.

The problem of constructing all minimal compartmental models that are indistinguishable through input-output knowledge alone from some given model is examined. The main tool in this analysis is a set of geometric properties that can be deduced from input-output knowledge and hence must be equally true in any two indistinguishable models. These properties, together with preservation of the form of the model's transfer function(s), provide an effective means for producing a set of candidate models for indistinguishability.

Mathematics↗
PubMed1988

Numerical deconvolution using system identification methods.

A deconvolution method is presented for use in pharmacokinetic applications involving continuous models and small samples of discrete observations. The method is based on the continuous-time counterpart of discrete-time least squares system identification, well established in control engineering. The same technique, requiring only the solution of a linear regression problem, is used both in system identification and input identification steps. The deconvolution requires no a priori information, since the proposed procedure performs system identification (including optimal selection of model order), selects the form of the input function and calculates its parametric representation and its values at specified time points.

Models, Biological↗
PubMed1985

Regional specific mean expiratory gas flow from 81mKr equilibrium inhalation data.

A new method of analysing the data available from routine 81m Kr equilibrium inhalation investigations has been developed. The data for analysis are acquired from a gamma camera in the form of a sequential series of images from which multiple breath activity-time curves are generated for eight regions in the lung. The method is based on a description of the behaviour of the radioactive gas in the lung using a mathematical model. Values of specific mean expiratory gas flow, that is mean expiratory gas flow per unit lung volume, are calculated from the application of the model to the expiratory phase only of a single breath activity-time curve which is generated from the multiple breath activity-time curve using post-acquisition gating. This method overcomes the problem of non-uniform inspiratory concentration of tracer gas experienced in previously reported techniques of analysing inhalation data obtained using poorly soluble radioactive gases. The model is shown, in simulation studies, to be an adequate description of the behaviour of radioactive gas in the lung and the analysis technique is shown, in clinical studies, to be both reproducible and sensitive to disease state.

Humans↗
PubMed1984

The deterministic identifiability of nonlinear pharmacokinetic models.

This paper deals with the deterministic identifiability of nonlinear pharmacokinetic models, namely, whether the model parameters can be identified with perfect data. It is shown that the most familiar method for analyzing the deterministic identifiability of linear models, in which the Laplace transform of the observation is examined, does not work for nonlinear models. An alternative method, in which the observation is expanded as a Taylor series about t = 0, is described and is illustrated with some examples of nonlinear models familiar in the pharmacokinetics literature, in which an elimination rate is assumed capacity limited, with Michaelis-Menten kinetics.

Animals↗
PubMed1984

On the identification of Michaelis-Menten elimination parameters from a single dose-response curve.

This paper deals with aspects of the numerical identifiability of parameters of a model with a capacity-limited elimination rate using a single dose-response curve, namely, the prospects of being able to identify model parameters with any meaning from real data. The concept of linear bounds, first proposed by Tong and Metzler, is described and it is shown that if the Michaelis-Menten constant Km is greater than all the measured concentration values, approximation by a linear model is appropriate. At the other end of the scale, if Km is small compared with measured concentration values, the nonlinear response approximates to a zero-order curve.

Animals↗
PubMed1982

Comment on "Parameter and structural identifiability concepts and ambiguities: a critical review and analysis".

Identifiability of a model for the glucose tolerance test, considered by Cobelli and DiStefano [Am. J. Physiol. 239 (Regulatory Integrative Comp. Physiol. 8): R7-R24, 1980], is shown to depend on the shape of the external perturbation. For systems with two or more inputs applied simultaneously, it is essential in Laplace transform identifiability analysis to examine the Laplace transform(s) of the observation(s) rather than the individual transfer functions, which are not measurable separately.

Glucose Tolerance Test↗
PubMed1980

Identifiable pharmacokinetic models: the role of extra inputs and measurements.

Single input, single output experiments can result in nonunique solutions for the rate constants to a linear compartmental model used to describe the pharmacokinetics. Where a finite number of solutions exists, a priori knowledge has to be used to distinguish between the solutions. Where there is a infinite number of solutions, assumptions have to be made about the values of some rate constants in order to obtained a unique solution for the other. This paper considers such experiments and determines whether either the addition of an extra input (simultaneously with the first input) or the taking of an extra measurement would result in a unique solution. It is found that perturbing a second input can be useful, but only if the perturbation is of different shape from the first input. Measurements of drug in urine and metabolite in plasma are generally not helpful in resolving identifiability of the drug dynamic model. If a radioactive tracer is used, through, the second measurement (for example, by externally scanning the radioactivity of the liver) can prove useful, but only if the gain of the measuring device is known.

Administration, Oral↗
PubMedDate not supplied

The structural identifiability and parameter estimation of a multispecies model for the transmission of mastitis in dairy cows with postmilking teat disinfection.

A mathematical model for the transmission of two interacting classes of mastitis causing bacterial pathogens in a herd of dairy cows is presented and applied to a specific data set. The data were derived from a field trial of a specific measure used in the control of these pathogens, where half the individuals were subjected to the control and in the others the treatment was discontinued. The resultant mathematical model (eight non-linear simultaneous ordinary differential equations) therefore incorporates heterogeneity in the host as well as the infectious agent and consequently the effects of control are intrinsic in the model structure. A structural identifiability analysis of the model is presented demonstrating that the scope of the novel method used allows application to high order non-linear systems. The results of a simultaneous estimation of six unknown system parameters are presented. Previous work has only estimated a subset of these either simultaneously or individually. Therefore not only are new estimates provided for the parameters relating to the transmission and control of the classes of pathogens under study, but also information about the relationships between them. We exploit the close link between mathematical modelling, structural identifiability analysis, and parameter estimation to obtain biological insights into the system modelled.

Animals↗