Biomedical subjects

M J Chappell

Publications and source records attributed to M J Chappell.

13 recordsLinked to original sources

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↗

PubMed1998

A procedure for generating locally identifiable reparameterisations of unidentifiable non-linear systems by the similarity transformation approach.

A method is presented for the generation of locally identifiable reparameterisations of non-linear systems which have been shown to be unidentifiable via application of the similarity transformation approach. The existence of the reparameterised system in terms of the maximum permissible number of locally identifiable parameters is provided and is crucially dependent upon the ability to find the rank deficiency of an appropriate (and possibly infinite) jacobian matrix. The reparameterisation procedure is described in detail, and is illustrated with application to two known non-trivial examples of unidentifiable non-linear systems.

Mathematics↗

PubMed1996

Structural identifiability of models characterizing saturable binding: comparison of pseudo-steady-state and non-pseudo-steady-state model formulations.

A two-state variable model in which saturable binding takes place is studied. Two mathematical representations of the same model are considered, one a standard chemical kinetics type of polynomial system, the other a reduced model formed from the original system via a pseudo-steady-state approximation. For a particular experiment the structural identifiability of the set of unknown parameters of each model is examined using the similarity transformation approach. The analysis shows that when the pseudo-steady-state approximation is made a certain degree of structural identifiability is lost in the sense that fewer individual parameters can be uniquely identified.

Kinetics↗

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↗

PubMed1995

Structural identifiability and indistinguishability of certain two-compartment models incorporating nonlinear efflux from the peripheral compartment.

A two-compartment model is considered where both compartments are observed and where the transfer efflux from the peripheral compartment may take three different nonlinear forms. The structural identifiability of the set of unknown parameters of each possible model is examined using the similarity transformation approach. Using the recent extension of this approach the indistinguishability of pairs of the postulated systems is also considered.

Animals↗

PubMed1995

Model based calculation for effective cancer radioimmunotherapy.

The major problem of tumour radioimmunotherapy remains the low tumour antibody uptake and this leads to inadequate tumour irradiation. The antibody characteristics which influence uptake have been identified and quantified previously using a non-linear compartmental model that simulates antibody distribution to tumour and body after intravenous injection. The model has now been extended, in combination with MIRD dosimetry tables, to calculate the integral tumour/body radiation dose for a range of antibody masses (1, 10 and 50 mg), sizes (binding site fragments and whole molecules) and affinities (K = 10(9)-10(13) mol-1). Antibody requirements for delivering 60 Gy to the tumour over 11.6 days were calculated for 131I and 90Y-labelled antibodies and included the effect of widely varying dose rates. The model predicted that intact antibodies of high affinity (10(11)-10(13) mol-1) produced effective tumour radiation doses with acceptable whole body radiation levels. By contrast, antibody fragments gave higher body radiation levels and required larger injected activity because of renal excretion. The model predicted higher therapeutic indices for 90Y-labelled antibody compared with 131I.

Antibody Affinity↗

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↗