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Biomedical subjects

K R Godfrey

Publications and source records attributed to K R Godfrey.

At least 19 recordsLinked to original sources
PubMed2001

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

A structural identifiability analysis is performed on a mathematical model for the coupled transmission of two classes of pathogen. The pathogens, classified as major and minor, are aetiological agents of mastitis in dairy cows that interact directly and via the immunological reaction in their hosts. Parameter estimates are available from experimental data for all but four of the parameters in the model. Data from a longitudinal study of infection are used to estimate these unknown parameters. A novel approach and application of structural identifiability analysis is combined in this paper with the estimation of cross-protection parameters using epidemiological data.

Animals↗
PubMed2001

An identifiability analysis of a parent-metabolite pharmacokinetic model for ivabradine.

The paper considers the structural identifiability of a parent-metabolite pharmacokinetic model for ivabradine and one of its metabolites. The model, which is linear, is considered initially for intravenous administration of ivabradine, and then for a combined intravenous and oral administration. In both cases, the model is shown to be unidentifiable. Simplification of the model (for both forms of administration) to that proposed by Duffull et al. (1) results in a globally structurally identifiable model. The analysis could be applied to the modeling of any drug undergoing first-pass metabolism, with plasma concentrations available from drug and metabolite.

Administration, Oral↗
PubMed1999

Evaluation of frequency and time-frequency spectral analysis of heart rate variability as a diagnostic marker of the sleep apnoea syndrome.

The sleep apnoea/hypopnoea syndrome (SAHS) elicits a unique heart rate rhythm that may provide the basis for an effective screening tool. The study uses the receiver operator characteristic (ROC) to assess the diagnostic potential of spectral analysis of heart rate variability (HRV) using two methods, the discrete Fourier transform (DFT) and the discrete harmonic wavelet transform (DHWT). These two methods are compared over different sleep stages and spectral frequency bands. The HRV results are subsequently compared with those of the current screening method of oximetry. For both the DFT and the DHWT, the most diagnostically accurate frequency range for HRV spectral power calculations is found to be 0.019-0.036 Hz (denoted by AB2). Using AB2, 15 min sections of non-REM sleep data in 40 subjects produce ROC areas, for the DFT, DHWT and oximetry, of 0.94, 0.97 and 0.67, respectively. In REM sleep, ROC areas are 0.78, 0.79 and 0.71, respectively. In non-REM sleep, spectral analysis of HRV appears to be a significantly better indicator of the SAHS than the current screening method of oximetry, and, in REM sleep, it is comparable with oximetry. The advantage of the DHWT over the DFT is that it produces a greater time resolution and is computationally more efficient. The DHWT does not require the precondition of stationarity or interpolation of raw HRV data.

Adult↗
PubMed1998

CODE: a deconvolution program implementing a regularization method of deconvolution constrained to non-negative values. Description and pilot evaluation.

A regularization method of deconvolution constrained to non-negative values is described. The method gives smooth estimates of the input function whilst providing a feasible fit (in terms of least squares) to measurements. A description of the program CODE (constrained deconvolution) which implements the method is given. A new methodology for a pilot evaluation of deconvolution programs is also proposed. The methodology is based on synthetic data. It employs a variety of shapes of the input function, low (1%) and high (15%) values of the measurement error, and incorporates primary (accuracy) and secondary (bias) performance measures. The performance of CODE is evaluated and it is suggested that CODE provides estimates of the input function with acceptable accuracy.

Data Interpretation, Statistical↗
PubMed1998

Nonlinear pharmacokinetics of tissue-type plasminogen activator in three animal species: a comparison of mathematical models.

A recent study presented plasma concentrations of tissue-type plasminogen activator in three different animal species and at several different dose levels. A three-compartment mammillary model with capacity-limited elimination (of Michaelis-Menten form) was postulated to describe the data. In the present study, several alternative model structures are examined with the view of determining whether better fits can be obtained, whether linear models are significantly worse than nonlinear models, and whether all three compartments are really necessary.

Animals↗
PubMed1996

A comparison of six deconvolution techniques.

We present results for the comparison of six deconvolution techniques. The methods we consider are based on Fourier transforms, system identification, constrained optimization, the use of cubic spline basis functions, maximum entropy, and a genetic algorithm. We compare the performance of these techniques by applying them to simulated noisy data, in order to extract an input function when the unit impulse response is known. The simulated data are generated by convolving the known impulse response with each of five different input functions, and then adding noise of constant coefficient of variation. Each algorithm was tested on 500 data sets, and we define error measures in order to compare the performance of the different methods.

Algorithms↗
PubMed1994

Identifiability and indistinguishability of nonlinear pharmacokinetic models.

Three nonlinear model structures of interest in pharmacokinetics are analyzed to determine whether the unknown, independent, model parameters can be deduced if perfect input-output data were available. This is the problem of identifiability. The method used is based on the local state isomorphism theorem. In certain circumstances, the modeler may be undecided between several model structures and it is then of interest to determine whether different model structures can be distinguished from perfect input-output data. This is the problem of model indistinguishability. The technique used, again based on the local state isomorphism theorem, parallels the similarity transformation approach for linear systems described previously in this journal. The analysis is performed on three two-compartment examples having one linear and one nonlinear (Michaelis-Menten) elimination pathway. In each model there is, on physiological and other grounds, some uncertainty over the precise location (central compartment or peripheral compartment) of one of the elimination pathways.

Models, Biological↗
PubMed1994

Indistinguishability for a class of nonlinear compartmental models.

Indistinguishability, as applied to nonlinear compartmental models, is analyzed by means of the local state isomorphism theorem. The method of analysis involves the determination of all local, diffeomorphic transformations connecting the state variables of two models. This is then applied to two two-compartment models, in the first instance with linear eliminations, and then with the addition of eliminations with Michaelis-Menten kinetics. In the nonlinear example, the state transformation turns out to be linear or possibly affine. It is found that the nonlinear analysis could be eased by splitting the state isomorphism equations into those of the initial linear models together with extra equations due to the nonlinearities.

Kinetics↗
PubMed1993

Modelling circadian variation in the pharmacokinetics of non-steroidal anti-inflammatory drugs.

A one-compartment model with first-order absorption has provided good fits to five sets of indomethacin data and four sets of ketoprofen data taken at different times of day. There was substantial variation in the model parameters with time of administration and most of the features of this variation applied equally to both drugs. From the data examined, the source of variation appears to be mainly in the absorption phase and this was confirmed using a chronokinetic analysis, in which simultaneous fits were obtained with time-variant rate parameters. However, there may also be circadian variation in protein binding. The danger of quoting parameter values for either of these two drugs based on administration at a single time of day has been illustrated, and this may well be true for other drugs.

Adult↗
PubMed1992

Structural identifiability of the parameters of a nonlinear batch reactor model.

The similarity transformation approach is used to analyze the structural identifiability of the parameters of a nonlinear model of microbial growth in a batch reactor in which only the concentration of microorganisms is measured. It is found that some of the model parameters are unidentifiable from this experiment, thus providing the first example of a real-life nonlinear model that turns out not to be globally identifiable. If it is possible to measure the initial concentration of growth-limiting substrate as well, all model parameters are globally identifiable.

Bacteria↗
PubMed1991

Optimal tumor targeting by antibodies: development of a mathematical model.

A mathematical model has been developed to optimize tumor targeting with labeled antibodies. The model is compartmental and nonlinear, incorporating saturable binding. Published parameter values have been used in the model, and the resulting stiff differential equations have been solved using FACSIMILE, a computer package that can simulate very stiff differential systems. Results show that successful tumor targeting depends on an optimal combination of antibody dose, affinity, and molecular size. The model has allowed an assessment to be made of the complicated and interrelated dynamic relationships that these factors have on tumor targeting. It has also offered an explanation for previously unsatisfactory results from tumor targeting with labeled antibodies. The structural identifiability of the model parameters is also analyzed and it is shown that, with the prior knowledge of some parameters which is likely in practice, the remaining model parameters are uniquely identifiable.

Algorithms↗
PubMed1990

Global identifiability of the parameters of nonlinear systems with specified inputs: a comparison of methods.

The two methods available for analyzing the global structural identifiability of the parameters of a nonlinear system with a specified input function, the Taylor series approach and the similarity transformation approach, are compared and contrasted through application to three examples. It is shown that, as for linear systems, it is very difficult to predict which of the available methods will result in the least effort for a particular example. The role of modern symbolic manipulation packages in the analysis is assessed. The third example proves intractable using the similarity transformation approach as originally formulated, but the analysis is completed using a reformulation that exploits the polynominal form of the system equations in the example.

Biometry↗
PubMed1990

Theoretical considerations for improving tumour targeting.

To determine the relative importance of factors influencing tumour uptake of antibodies, we used a mathematical model to simulate intravenous injection of substances of varying molecular sizes and tumour-binding affinities at several dose levels. The FACSIMILE program was used to simulate the time course of tumour uptake of the tumour-binding substance by calculating the instantaneous tumour content (TC) and tumour:background uptake ratios (UR). Relative total doses to tumour and normal tissue were calculated by integration of TC/time curves. The model was used to make theoretical predictions on the effects of altering different parameters. The size of the injected dose in relation to the number of tumour receptors was crucial:if too low, uptake could not be improved by manipulating other variables, and if too high, the UR for large binding molecules was reduced. Using the standard scanning dose of labelled antibody, absolute numbers of labelled molecules binding to tumour could be increased by injection of a large excess of unlabelled molecules. Given an adequate dose, peak tumour content increased with increasing affinity up to receptor saturation. The peak uptake ratio rose progressively with affinity for a small ligand, but reached a relatively low plateau for antibody due to constant high background levels. At low doses such as those currently administered for diagnostic scanning with antibody, no effect of increasing affinity was predicted.

Antibodies, Monoclonal↗
PubMed1989

Effect of dose, molecular size, affinity, and protein binding on tumor uptake of antibody or ligand: a biomathematical model.

A mathematical model has been developed to determine the best approach to improving tumor targeting with antibody. The amount of antibody in the tumor (tumor content) and the tumor:normal tissue antibody concentration ratio (uptake ratio) were calculated over 12 days from injection, using the computer program FACSIMILE to solve the stiff nonlinear differential equations describing the system. Results indicate that success requires an optimal combination of dose, size, and binding affinity of antibody. Increasing the dose to 100 times that presently used for scanning increased both the percentage of injected antibody in the tumor and the uptake ratio by up to 2 orders of magnitude to maximal values determined by affinity. This result could be achieved by coinjecting unlabeled antibody. Increasing affinity from Keq = 10(9) to 10(13)M-1 increased the uptake ratio from 5 to 100 for whole antibody and to 550 for a small ligand, at the calculated optimal dose, but had no effect at the current scanning dose. With decreasing molecular size at average affinity, the same maximum tumor content and uptake ratio were achieved but progressively earlier. At high affinity there was a substantial advantage for a small ligand compared with whole antibody in terms of uptake ratio (550 versus 100) and tumor:normal tissue integral dose ratio (330 versus 60). The uptake of a small ligand was not increased by binding to plasma protein but with increasing time the tumor content was higher than without protein binding.

Animals↗
PubMed1989

The problem of model indistinguishability in pharmacokinetics.

The problem of model indistinguishability is introduced in the context of linear compartmental models in pharmacokinetics. The two most widely used methods of analyzing model indistinguishability are described. It is shown that as the number of compartments increases, one approach, based on the Laplace transforms of the observations, although conceptually simple, can result in very large numbers of candidate models to be examined for indistinguishability, while the other approach, based on similarity transformations, although systematic, often results in very difficult algebraic expressions. These problems can be eased by the use of some simple geometrical rules, used at the outset of an indistinguishability analysis. The approach is illustrated by application of two 2-compartment drug, 2-compartment metabolite models.

Models, Biological↗
PubMed1989

Similarity transformation approach to identifiability analysis of nonlinear compartmental models.

Through use of the local state isomorphism theorem instead of the algebraic equivalence theorem of linear systems theory, the similarity transformation approach is extended to nonlinear models, resulting in finitely verifiable sufficient and necessary conditions for global and local identifiability. The approach requires testing of certain controllability and observability conditions, but in many practical examples these conditions prove very easy to verify. In principle the method also involves nonlinear state variable transformations, but in all of the examples presented in the paper the transformations turn out to be linear. The method is applied to an unidentifiable nonlinear model and a locally identifiable nonlinear model, and these are the first nonlinear models other than bilinear models where the reason for lack of global identifiability is nontrivial. The method is also applied to two models with Michaelis-Menten elimination kinetics, both of considerable importance in pharmacokinetics, and for both of which the complicated nature of the algebraic equations arising from the Taylor series approach has hitherto defeated attempts to establish identifiability results for specific input functions.

Kinetics↗
PubMed1989

Parameter space boundaries for unidentifiable compartmental models.

Methods for dealing with unidentifiable compartmental models are first reviewed, emphasizing the parameter interval analysis and exhaustive modeling approaches. More general methods are presented for generating the set of all nonnegative parameter solutions that localize the parameters within bounded regions of parameter space and extend previously published parameter bounding strategies. Each point of these regions is an equivalent solution of the parameter identification problem. If a point on the boundary is selected, at least one of the parameters vanishes and an equivalent submodel is obtained. This property shows the close relationship between the exhaustive modeling and parameter interval analysis approaches.

Mathematics↗