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

Abstract

To provide the first application of fractal kinetics under steady state conditions to pharmacokinetics as a model for the enzymatic elimination of a drug from the body. A one-compartment model following fractal Michaelis-Menten kinetics under a steady state is developed and applied to concentration-time data for the cardiac drug mibefradil in dogs. The model predicts a fractal reaction order and a power law asymptotic time-dependence of the drug concentration, therefore a mathematical relationship between the fractal reaction order and the power law exponent is derived. The goodness-of-fit of the model is assessed and compared to that of four other models suggested in the literature. The proposed model provided the best fit to the data. In addition, it correctly predicted the power law shape of the tail of the concentration-time curve. 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.