Deterministic and stochastic models of drug transport and reaction kinetics in heterogeneous media

Pharmacokinetics describes the course of a drug through the body and is the main quantitative tool used in all stages of drug discovery, development, and administration. Most pharmacokinetic models are based on the assumption that drug transport and reaction kinetics occur in a homogenous environment. However, the spaces in the body are usually confined and heterogeneous. Consequently, the transport and chemical reaction processes occurring within them can become anomalous. Evidence of this result includes emergent power law behaviour. The objective of this thesis is to apply concepts from physics to develop more physiologically-accurate models of drug processes occurring in the body in the presence of spatial and/or temporal heterogeneity.; Several complementary models were developed to investigate drug elimination kinetics in a heterogeneous environment. Fractal drug kinetics under Michaelis-Menten conditions was developed and implemented using a continuous, deterministic fractal compartmental model. Using a parameter optimization method based on a simulated annealing algorithm, the model was found to provide an improved fit to experimental data for the cardiac drug mibefradil.; The theory of fractal elimination kinetics was then tested using a stochastic method based on an interacting random walk model. It was found that short-term correlations between drug molecules produced Michaelis-Menten elimination kinetics while long-term correlations produced fractal kinetics. By combining both effects, the fractal Michaelis-Menten theory was reproduced. The model was then expanded into a continuous time random walk model to include the effects of temporal heterogeneity in the form of Levy-distributed long-time trapping of drug molecules in temporary traps.; Power law behaviour does not always indicate fractal kinetics. A two-compartment model for the anticancer drug paclitaxel was used to demonstrate that it can be produced by the competition between two saturable processes. The power exponent of the long-time tail of the concentration-time curve was correlated with the power exponent describing the nonlinear dose-dependence of two pharmacokinetic measures.; Finally, a physiologically-based flow network model was used to show that the organ-level dynamics of drug metabolism can be reproduced at the level of the functional unit of the liver. Different types of spatial heterogeneity that mimicked pathological conditions were found to lead to either fractal or fractal Michaelis-Menten kinetics.