Fractal Michaelis-Menten Kinetics Under Steady State Conditions: Application to Mibefradil

Abstract

A simple one-compartment model with steady state fractal Michaelis-Menten kinetics describing drug elimination from the body most accurately describes the pharmacokinetics of mibefradil in dogs. The new fractal reaction order can be explained in terms of the complex geometry of the liver, the organ responsible for eliminating the drug.

A physiologically-based flow network model for hepatic drug elimination I: regular lattice lobule model

“…To address the above shortcomings several explanations have been proposed, including a stochastic random walk model for the drug molecules (Wise et al [4] ), convective-diffusive transit behaviour in the liver (Norwich and Siu [5]), gamma-distributed drug residence time (Wise [6]), transient fractal kinetics (Anacker and Kopelman [2]), and fractal Michaelis-Menten kinetics (Marsh and Tuszynski [7]). All of these studies, however, represented an organ as a homogenous compartment that is not realistic, i.e.…”

The Changing Face of the Rate Concept in Biopharmaceutical Sciences: From Classical to Fractal and Finally to Fractional

“…Processes like dissolution and release, which are based on diffusion principles, have been modeled with this type of kinetics (5). Moreover, time-dependent coefficients have been used to explain the pharmacokinetics of calcium (6) and mibefradil (7)(8)(9). The heterogeneous character of the drug processes in the gastrointestinal lumen (10,11) has also been analyzed with fractal and fractal kinetics principles (12), and this has led to the development of the heterogeneous tube model for the gastrointestinal absorption (13,14).…”

Pharmacokinetics and Pharmacodynamics

“…The basis of the compartment model is equilibrium systems, homogeneity, and mass transfer between compartments. A compartment is defined as the number of drug molecules having the same probability of undergoing a set of chemical kinetic processes (Marsh and Tuszynski 2006). The mass transfer of drug molecules between compartments is described by kinetic rate constants.…”

“…Application of fractals to pharmacokinetics has been used for drug release and dissolution (as shown in Sect. 3), absorption (Macheras and Argyrakis 1997), and fractal compartment models (Fuite et al 2002;Marsh and Tuszynski 2006). Excellent reviews of these fractal concepts applied to pharmacokinetics have been published (Dokoumetzidis et al 2004;Pang et al 2007).…”