Closed form solutions and dominant elimination pathways of simultaneous first-order and Michaelis-Menten kinetics

Steady-State Drug Exposure of Repeated IV Bolus Administration for a One Compartment Pharmacokinetic Model with Sigmoidal Hill Elimination

Drugs exhibiting nonlinear pharmacokinetics hold significant importance in drug research and development. However, evaluating drug exposure accurately is challenging with the current formulae established for linear pharmacokinetics. This article aims to investigate the steady-state drug exposure for a one-compartment pharmacokinetic (PK) model with sigmoidal Hill elimination, focusing on three key topics: the comparison between steady-state drug exposure of repeated intravenous (IV) bolus ( AUC ss ) and total drug exposure after a single IV bolus ( AUC 0 - ∞ ); the evolution of steady-state drug concentration with varying dosing frequencies; and the control of drug pharmacokinetics in multiple-dose therapeutic scenarios. For the first topic, we established conditions for the existence of AUC ss , derived an explicit formula for its calculation, and compared it with AUC 0 - ∞ . For the second, we identified the trending properties of steady-state average and trough concentrations concerning dosing frequency. For the third, we developed formulae to compute dose and dosing time for both regular and irregular dosing scenarios. As an example, our findings were applied to a real drug model of progesterone used in lactating dairy cows. In conclusion, these results provide a theoretical foundation for designing rational dosage regimens and conducting therapeutic trials.

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.

Oral drug delivery systems using core-shell structure additive manufacturing technologies: a proof-of-concept study

OBJECTIVES

The aim of this study was to couple fused deposition modelling 3D printing with melt extrusion technology to produce core-shell-structured controlled-release tablets with dual-mechanism drug-release performance in a simulated intestinal fluid medium. Coupling abovementioned technologies for personalized drug delivery can improve access to complex dosage formulations at a reasonable cost. Compared with traditional pharmaceutical manufacturing, this should facilitate the following: (1) the ability to manipulate drug release by adjusting structures, (2) enhanced solubility and bioavailability of poorly water-soluble drugs and (3) on-demand production of more complex structured dosages for personalized treatment.

METHODS

Acetaminophen was the model drug and the extrusion process was evaluated by a series of physicochemical characterizations. The geometries, morphologies, and in vitro drug-release performances were compared between directly compressed and 3D-printed tablets.

KEY FINDINGS

Initially, 3D-printed tablets released acetaminophen more rapidly than directly compressed tablets. Drug release became constant and steady after a pre-determined time. Thus, rapid effectiveness was ensured by an initially fast acetaminophen release and an extended therapeutic effect was achieved by stabilizing drug release.

CONCLUSIONS

The favourable drug-release profiles of 3D-printed tablets demonstrated the advantage of coupling HME with 3D printing technology to produce personalized dosage formulations.

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.

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

In this paper, a typical pharmacokinetic (PK) model is studied for the case of multiple intravenous bolus-dose administration. This model, of one-compartment structure, not only exhibits simultaneous first-order and Michaelis-Menten elimination, but also involves a constant endogenous production. For the PK characterization of the model, we have established the closed-form solution of concentrations over time, the existence and local stability of the steady state. Using analytical approaches and the concept of corrected concentration, we have shown that the area under the curve ([Formula: see text]) at steady state is higher compared to that at the single dose ([Formula: see text]). Moreover, by splitting the dose and dosing interval into halves, we have revealed that it can result in a significant decrease in the steady-state average concentration. These model-based findings, which contrast with the current knowledge for linear PK, confirm the necessity to revisit drugs exhibiting nonlinear PK and to suggest a rational way of using mathematical analysis for the dosing regimen design.

Mathematical analysis and drug exposure evaluation of pharmacokinetic models with endogenous production and simultaneous first-order and Michaelis-Menten elimination: the case of single dose

Drugs with an additional endogenous source often exhibit simultaneous first-order and Michaelis-Menten elimination and are becoming quite common in pharmacokinetic modeling. In this paper, we investigate the case of single dose intravenous bolus administration for the one-compartment model. Relying on a formerly introduced transcendent function, we were able to analytically express the concentration time course of this model and provide the pharmacokinetic interpretation of its components. Using the concept of the corrected concentration, the mathematical expressions for the partial and total areas under the concentration time curve (AUC) were also given. The impact on the corrected concentration and AUC is discussed as well as the relative contribution of the exogenous part in presence of endogenous production. The present findings theoretically elucidate several pharmacokinetic issues for the considered drug compounds and provide guidance for the rational estimation of their pharmacokinetic parameters.

Impact of saturable distribution in compartmental PK models: dynamics and practical use

We explore the impact of saturable distribution over the central and the peripheral compartment in pharmacokinetic models, whilst assuming that back flow into the central compartiment is linear. Using simulations and analytical methods we demonstrate characteristic tell-tale differences in plasma concentration profiles of saturable versus linear distribution models, which can serve as a guide to their practical applicability. For two extreme cases, relating to (i) the size of the peripheral compartment with respect to the central compartment and (ii) the magnitude of the back flow as related to direct elimination from the central compartment, we derive explicit approximations which make it possible to give quantitative estimates of parameters. In three appendices we give detailed explanations of how these estimates are derived. They demonstrate how singular perturbation methods can be successfully employed to gain insight in the dynamics of multi-compartment pharmacokinetic models. These appendices are also intended to serve as an introductory tutorial to these ideas.

Steady-state volume of distribution of two-compartment models with simultaneous linear and saturated elimination

The model-independent estimation of physiological steady-state volume of distribution ([Formula: see text]), often referred to non-compartmental analysis (NCA), is historically based on the linear compartment model structure with central elimination. However the NCA-based steady-state volume of distribution ([Formula: see text]) cannot be generalized to more complex models. In the current paper, two-compartment models with simultaneous first-order and Michaelis-Menten elimination are considered. In particular, two indistinguishable models [Formula: see text] and [Formula: see text], both having central Michaelis-Menten elimination, while first-order elimination exclusively either from central or peripheral compartment, are studied. The model-based expressions of the steady-state volumes of distribution [Formula: see text] and their relationships to NCA-based [Formula: see text] are derived. The impact of non-linearity and peripheral elimination is explicitly delineated in the formulas. Being concerned with model identifiability and indistinguishability issues, an interval estimate of [Formula: see text] is suggested.