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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of pharmacokinetics and pharmacodynamics 8 (1980), S. 633-648 
    ISSN: 1573-8744
    Keywords: compartmental analysis ; dynamic response ; identification ; linear systems ; modeling ; parameter estimation ; pharmacokinetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Single input, single output experiments can result in nonunique solutions for the rate constants of 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 an infinite number of solutions, assumptions have to be made about the values of some rate constants in order to obtain a unique solution for the others. 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, though, 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.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    European journal of nuclear medicine 10 (1985), S. 321-331 
    ISSN: 1619-7089
    Keywords: Krypton ; 81 m ; Lung ; Mathematical model ; Gas flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract A new method of analysing the data available from routine 81 m 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.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of pharmacokinetics and pharmacodynamics 22 (1994), S. 229-251 
    ISSN: 1573-8744
    Keywords: compartmental models ; identification ; indistinguishability ; Michaelis-Menten kinetics ; model discrimination ; nonlinear systems ; pharmacokinetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of pharmacokinetics and pharmacodynamics 12 (1984), S. 177-191 
    ISSN: 1573-8744
    Keywords: compartmental analysis ; identification ; Michaelis-Menten kinetics ; nonlinear systems ; pharmacokinetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of pharmacokinetics and pharmacodynamics 16 (1988), S. 85-107 
    ISSN: 1573-8744
    Keywords: numerical deconvolution ; algorithm for deconvolution ; linear systems analysis ; system identification ; least squares fitting ; calculation of drug input rates ; input response in pharmacokinetic systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract 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 prioriinformation, 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.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of pharmacokinetics and pharmacodynamics 12 (1984), S. 193-221 
    ISSN: 1573-8744
    Keywords: compartmental analysis ; identification ; Michaelis-Menten kinetics ; nonlinear systems ; pharmacokinetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of pharmacokinetics and pharmacodynamics 17 (1989), S. 229-267 
    ISSN: 1573-8744
    Keywords: compartmental models ; drug-metabolite models ; identifiability ; model indistinguishability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract 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 to two 2-compartment drug, 2-compartment metabolite models.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of pharmacokinetics and pharmacodynamics 19 (1991), S. 227-260 
    ISSN: 1573-8744
    Keywords: antibodies ; compartmental models ; identifiability ; nonlinear models ; tumor targeting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Journal of pharmacokinetics and pharmacodynamics 24 (1996), S. 283-299 
    ISSN: 1573-8744
    Keywords: constrained optimization ; cubic splines ; deconvolution ; Fourier transforms ; genetic algorithms ; maximum entropy ; system identification
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
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