Asymptotic time dependence in the fractal pharmacokinetics of a two-compartment model

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. Short infusion times led to a power exponent of -1.57 ± 0.14, while long infusion times resulted in tails with roughly twice the exponent. Curves following intermediate infusion times were characterized by two power laws. An initial segment with the larger slope was followed by a long-time tail characterized by the smaller exponent. The area under the curve and the maximum concentration exhibited a power law dependence on dose, both with compatible fractional power exponents. Computer simulations using the proposed model revealed that a two-compartment model with both saturable distribution and elimination can reproduce both the single and crossover power laws. Also, the nonlinear dose-dependence is correlated with the empirical power law tails. The longer the infusion time the better the drug delivery to the tumor compartment is a clinical recommendation we propose.

Comment on "Asymptotic time dependence in the fractal pharmacokinetics of a two-compartment model"

A clarification is due about the paper by Chelminiak [Phys. Rev. E 72, 031903 (2005)]. In changing notation at the beginning, the authors incur an unfortunate error that significantly impacts the rest of the paper.

Combinatorial design of passive drug delivery platforms

We introduce a novel computational approach to designing passive drug delivery systems based on porous materials such as hydrogels. Our approach uses three tools: a method to establish the exact release pattern from all possible loading sites inside a given hydrogel; a method to generate a large number of hydrogel structures to be tested numerically, and finally an optimization algorithm which leads to the selection of optimal hydrogel structures. Using this approach, we show that controlled release curves can be obtained by using a genetic algorithm for the optimization step. Strategies to generalize this approach to other systems are also discussed.

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. The goodness-of-fit of the model is assessed and compared to that of four other models suggested in the literature.

RESULTS

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.

CONCLUSION

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.

Application of a random network with a variable geometry of links to the kinetics of drug elimination in healthy and diseased livers

This paper discusses an application of a random network with a variable number of links and traps to the elimination of drug molecules from the body by the liver. The nodes and links represent the transport vessels, and the traps represent liver cells with metabolic enzymes that eliminate drug molecules. By varying the number and configuration of links and nodes, different disease states of the liver related to vascular damage have been simulated, and the effects on the rate of elimination of a drug have been investigated. Results of numerical simulations show the prevalence of exponential decay curves with rates that depend on the concentration of links. In the case of fractal lattices at the percolation threshold, we find that the decay of the concentration is described by exponential functions for high trap concentrations but transitions to stretched exponential behavior at low trap concentrations.