Saturable Fractal Pharmacokinetics and Its Applications - Mathematical Methods and Models in Biomedicine - page 327

Saturable Fractal Pharmacokinetics
and Its Applications

Rebeccah E. Marsh and Jack A. Tuszy nski

1 Introduction

In this chapter we discuss an application of fractal kinetics under steady state
conditions to model 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. 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 provides the best fit to the data.
In addition, it correctly predicts the power law shape of the tail of the concentration-
time curve. The new fractal reaction order can be explained in terms of the
complex geometry of the liver, the organ responsible for eliminating the drug.
Furthermore, we investigate the potential for identifying global characteristics in
the pharmacokinetics of the anticancer drug paclitaxel. An analysis of data in
the literature yields both clearance curves and dose-dependency curves that are
accurately described by power laws with similar exponents.
Pharmacokinetics is the study of the absorption, distribution, metabolism, and
eventual elimination (ADME) of a drug from the body [ 19 ]. It is fundamental in
developing dosing regimes, predicting the behavior of new drugs, and estimating
their therapeutic effects. For numerous compounds, such as anesthetics, cardiac
drugs, and chemotherapeutic drugs, quantitative knowledge about the interaction
of the drug with the body is of vital importance to its successful therapeutic applica-
tions. Pharmacological data usually consist of discrete values of the concentration
of a drug in the plasma or blood as a function of time. A plot of these values

R.E. Marsh ￿ J.A. Tuszy nski ( )
Department of Physics, University of Alberta, Edmonton, AB, Canada, T6G 2J1
e-mail: [e-mail] ; [e-mail]