Pharmacokinetics with intravenous infusion of two-compartment model based on Liu process

By describing the absorption, distribution, metabolism, and excretion of drugs, pharmacokinetics helps to find optimal therapies for patients and speed up drug development. In pharmacokinetics, dynamic uncertainties, such as fluctuations in hormone levels and external environment factors, are ubiquitous. Due to sparse clinical data and patient disease specificity, these uncertainties are mainly epistemic uncertainties rather than aleatory uncertainties, which cannot be handled well by probability theory based methods. Therefore, several pharmacokinetics based on uncertain differential equations under the framework of uncertainty theory were investigated, which all considered one compartment models. Noting that many drugs follow two compartment kinetics, this article proposes a two compartment pharmacokinetic model based on uncertain differential equations. Based on the proposed model, several essential pharmacokinetic parameters are investigated, which are important information required by regulatory bodies to approve drugs for public use. Estimation for unknown parameters in the model are given. Finally, a real data analysis using lidocaine drug concentration illustrates our methodology in details.