A model of competing saturable kinetic processes with application to the pharmacokinetics of the anticancer drug paclitaxel.

A saturable multi-compartment pharmacokinetic model for the anti-cancer drug paclitaxel is proposed based on a meta-analysis of pharmacokinetic data published over the last two decades. We present and classify the results of time series for the drug concentration in the body to uncover the underlying power laws. Two dominant fractional power law exponents were found to characterize the tails of paclitaxel concentration-time curves.

Emergence of power laws in the pharmacokinetics of paclitaxel due to competing saturable processes.

Purpose: This study presents the results of power law analysis applied to the pharmacokinetics of paclitaxel. Emphasis is placed on the role that the power exponent can play in the investigation and quantification of nonlinear pharmacokinetics and the elucidation of the underlying physiological processes.

Methods: Forty-one sets of concentration-time data were inferred from 20 published clinical trial studies, and 8 sets of area-under-the-curve (AUC) and maximum concentration (Cmax) values as a function of dose were collected.

Use of a simulated annealing algorithm to fit compartmental models with an application to fractal pharmacokinetics.

Increasingly, fractals are being incorporated into pharmacokinetic models to describe transport and chemical kinetic processes occurring in confined and heterogeneous spaces. However, fractal compartmental models lead to differential equations with power-law time-dependent kinetic rate coefficients that currently are not accommodated by common commercial software programs. This paper describes a parameter optimization method for fitting individual pharmacokinetic curves based on a simulated annealing (SA) algorithm, which always converged towards the global minimum and was independent of the initial parameter values and parameter bounds.

Modeling fractal-like drug elimination kinetics using an interacting random-walk model.

We introduce an interacting random-walk model to describe the residence time of drug molecules undergoing a series of sojourn times in the body before being permanently eliminated under either homogeneous or heterogeneous conditions. We show that short-term correlations between drug molecules lead to Michaelis-Menten kinetics while long-term correlations lead to transient fractal-like kinetics. By combining both types of correlation, fractal-like Michaelis-Menten kinetics are achieved, and the simulations confirm previous analytical results.

Fractal michaelis-menten kinetics under steady state conditions: Application to mibefradil.

Purpose: 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.

Materials And Methods: 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.