Coupled solutions of one- and two-compartment pharmacokinetic models with first-order absorption
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ORIGINAL PAPER
Coupled solutions of one- and two-compartment pharmacokinetic models with first-order absorption N. Asmanova • G. Koloskov • A. I. Ilin
Received: 2 December 2012 / Accepted: 6 March 2013 / Published online: 10 April 2013 Ó Springer Science+Business Media New York 2013
Abstract This work emphasizes the importance of the fact, that plasma concentration profiles of one- and two-compartment linear pharmacokinetic (PK) models with firstorder absorption introduce an uncertainty in data interpretation. PK-curve fitting results in a pair of valid solutions (coupled solutions), for which the derived PK parameters (such as AUC, MRT, Cmax, tmax, initial and terminal slope) are identical. Therefore, to make a proper choice of PK parameters of the drug in question, more information has to be considered, for example, which one of the solutions is more correlated with corresponding data, observed after iv administration. Comparison of different types of PK models and discussion on the transitions between the coupled solutions was carried out using a novel symbolic notation to provide more clarity and to simplify parameter indexing. Presented results were obtained by combined means of the method of statistic moments, Laplace transform and illustrated by the numerical experiment. Keywords Flip-flop phenomenon Coupled solutions Vanishing exponential Statistical moments Pharmacokinetics
Introduction Basic concern of the inverse problems management in pharmacokinetic (PK) modelling is instability and non-
N. Asmanova G. Koloskov (&) A. I. Ilin Scientific Centre for Anti-Infectious Drugs, Almaty, Kazakhstan e-mail: [email protected] A. I. Ilin e-mail: [email protected]
uniqueness of solutions [1, 2]. While the instability of solution is a well known source of headache for software developers, the question of non-uniqueness is not always an issue for particular models. Perhaps, this is why it attracts much less attention and consequently its presence is often attributed to the unusual circumstances. Consider, for example so-called flip-flop phenomenon, when generally adopted relation between the rate constants of drug absorption (ka) and elimination (k10) ka [ k10 inverses to k10 [ ka. This phenomenon is traditionally attributed to the onecompartment linear model [3, 4, 5], and is usually referred to the work of Byron and Notari [6], despite that paper considered a two-compartment model as it clearly stated in its title. Besides, the non-uniqueness is usually attributed to be a property of particular drug [7–9], rather than an intrinsic feature of the model used. More general approach is presented in [1, 10], which special feature is an attempt to bind the non-uniqueness of solution of the two-compartment model with the intrinsic properties of the function that describes concentration changes in the central compartment. Perhaps, the reason that the results of [1, 10] did not get a proper reflection in common practice of presentation of the outcome of PK studies, lies in the shift of the attention focus to the a
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