Analytical Solution and Exposure Analysis of a Pharmacokinetic Model with Simultaneous Elimination Pathways and Endogenous Production: The Case of Multiple Dosing Administration

Statistical Analysis of Two-Compartment Pharmacokinetic Models with Drug Non-adherence

Poor drug adherence is considered one of major barriers to achieving the clinical and public health benefits of many pharmacotherapies. In the current paper, we aim to investigate the impact of dose omission on the plasma concentrations of two-compartment pharmacokinetic models with two typical routes of drug administration, namely the intravenous bolus and extravascular first-order absorption. First, we reformulate the classical two-compartment pharmacokinetic models with a new stochastic feature, where a binomial random model of dose intake is integrated. Then, we formalize the explicit expressions of expectation and variance for trough concentrations and limit concentrations, with the latter proved of the existence and uniqueness for steady-state distribution. Moreover, we mathematically demonstrate the strict stationarity and ergodicity of trough concentrations as a Markov chain. In addition, we numerically simulate the impact of drug non-adherence to different extents on the variability and regularity of drug concentration and compare the drug pharmacokinetic preference between one and two compartment pharmacokinetic models. The results of sensitivity analysis also suggest the drug non-adherence as one of the most sensitive model parameters to the expectation of limit concentration. Our modelling and analytical approach can be integrated into the chronic disease models to estimate or quantitatively predict the therapy efficacy with drug pharmacokinetics presumably affected by random dose omissions.

Statistical analysis of one-compartment pharmacokinetic models with drug adherence

Pharmacokinetics is a scientific branch of pharmacology that describes the time course of drug concentration within a living organism and helps the scientific decision-making of potential drug candidates. However, the classical pharmacokinetic models with the eliminations of zero-order, first-order and saturated Michaelis-Menten processes, assume that patients perfectly follow drug regimens during drug treatment, and the significant factor of patients' drug adherence is not taken into account. In this study, therefore, considering the random change of dosage at the fixed dosing time interval, we reformulate the classical deterministic one-compartment pharmacokinetic models to the framework of stochastic, and analyze their qualitative properties including the expectation and variance of the drug concentration, existence of limit drug distribution, and the stochastic properties such as transience and recurrence. In addition, we carry out sensitivity analysis of drug adherence-related parameters to the key values like expectation and variance, especially for the impact on the lowest and highest steady state drug concentrations (i.e. the therapeutic window). Our findings can provide an important theoretical guidance for the variability of drug concentration and help the optimal design of medication regimens. Moreover, The developed models in this paper can support for the potential study of the impact of drug adherence on long-term treatment for chronic diseases like HIV, by integrating disease models and the stochastic PK models.

Constant infusion case of one compartment pharmacokinetic model with simultaneous first-order and Michaelis-Menten elimination: analytical solution and drug exposure formula

The main objective of this article is to propose the closed-form solution of one-compartment pharmacokinetic model with simultaneous first-order and Michaelis-Menten elimination for the case of constant infusion. For the case of bolus administration, we have previously established a closed-form solution of the model through introducing a transcendent X function. In the same vein, we found here a closed-form solution of constant infusion could be realized through introducing another transcendent Y function. For the general case of constant infusion of limited duration, the closed-form solution is then fully expressed using both X and Y functions. As direct results, several important pharmacokinetic surrogates, such as peak concentration [Formula: see text] and total drug exposure AUC[Formula: see text], are found the closed-form expressions and ready to be analyzed. The new pharmacokinetic knowledge we have gained on these parameters, which largely exhibits in a nonlinear feature, is in clear contrast to that of the linear case. Finally, with a pharmacokinetic model adapted from that formerly reported on phenytoin, we numerically analyzed and illustrated the roles of different model parameters and discussed their influence on drug exposure. To conclude, the present findings elucidate the intrinsic quantitative structural properties of such pharmacokinetic model and provide a new avenue for future modelling and rational drug designs.

Exact solutions and equi-dosing regimen regions for multi-dose pharmacokinetics models with transit compartments

Compartmental models which yield linear ordinary differential equations (ODEs) provide common tools for pharmacokinetics (PK) analysis, with exact solutions for drug levels or concentrations readily obtainable for low-dimensional compartment models. Exact solutions enable valuable insights and further analysis of these systems. Transit compartment models are a popular semi-mechanistic approach for generalising simple PK models to allow for delayed kinetics, but computing exact solutions for multi-dosing inputs to transit compartment systems leading to different final compartments is nontrivial. Here, we find exact solutions for drug levels as functions of time throughout a linear transit compartment cascade followed by an absorption compartment and a central blood compartment, for the general case of n transit compartments and M equi-bolus doses to the first compartment. We further show the utility of exact solutions to PK ODE models in finding constraints on equi-dosing regimen parameters imposed by a prescribed therapeutic range. This leads to the construction of equi-dosing regimen regions (EDRRs), providing new, novel visualisations which summarise the safe and effective dosing parameter space. EDRRs are computed for classical and transit compartment models with two- and three-dimensional parameter spaces, and are proposed as useful graphical tools for informing drug dosing regimen design.