Variability and singularity arising from poor compliance in a pharmacokinetic model II: the multi-oral case

Abstract : We study a simplified model for the drug concentration in the case of multiple oral doses and in a situation of poor patient compliance. Our model is a stochastic one, which is able to take into account an irregular drug intake schedule. This article is the second in a series of three. It presents a multi-oral version of the results given in [11], that dealt with the multi IV case. Under some assumptions, we study features of the drug concentration that have practical implications, such as its variability and the regularity of its probability distribution. We consider four variants: continuous-time, with either deterministic or random doses, and discrete-time, also with either deterministic or random doses. Our computations allow one to assess in a precise way the effect of various significant parameters such as the mean rate of intake, the elimination rate, the absorption rate and the mean dose. They quantify how much poor compliance will affect the regimen. To appreciate this impact, we provide detailed comparisons with the variability of concentration in the cases of both a fully compliant patient and a population of fully compliant patients with log-normaly distributed pharmacokinetic parameters. Besides, the discrete-time versions of our models reveal unexpected links with possibly multifractal measures known in mathematics as infinite Bernoulli convolutions. Analogously to the multi-IV case, we find that the distribution of the concentration in this model is either absolutely continuous or purely singular, depending on a relevant parameter. Our results complement the ones in [11] and help understanding the consequences of poor compliance. They may have practical outcomes in terms of drug dosing and scheduling.
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Journal of Mathematical Biology, Springer Verlag (Germany), 2016, 〈10.1007/s00285-016-1041-1〉
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Lisandro J. Fermin, Jacques Lévy Véhel. Variability and singularity arising from poor compliance in a pharmacokinetic model II: the multi-oral case. Journal of Mathematical Biology, Springer Verlag (Germany), 2016, 〈10.1007/s00285-016-1041-1〉. 〈hal-00868621〉

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