Tahmina Akhter | Applied Math, University of Waterloo
Stochastic effects and Fractal Kinetics in the Pharmacokinetics of drug transport
Pharmacokinetics (PK) attempts to model the progression and time evolution of a drug in the human body from administration to the elimination stage. It is the primary quantitative approach used in drug discovery/development (in the pharma industry). The overwhelming majority of PK models are based on equilibrium kinetics with all the reaction kinetics occurring in a well-mixed, homogeneous environment. Of course as is well known, the human body is comprised of heterogeneous media with non-equilibrium chemical kinetics. As a result, the transport processes and reaction mechanisms are often atypical. In this thesis, we apply ideas from stochastic processes and fractal kinetics in order to better capture the time course of a drug through the body when there is spatial and temporal heterogeneity. We discuss the limitations of the Langevin equation and Bourret's approximation and apply Van Kampen's approach to the random differential equations arising from the stochastic formulation of a standard one compartmental pk model. Although one compartment models can produce good fits if a drug disperses rapidly so that equilibrium is achieved (in all tissues) swiftly, in general they are oversimplifications of a complex process. Thus we also extend the two compartmental model Kearns et. al., to incorporate fractal Michaelis Menten kinetics and compare with experimental data from the literature for paclitaxel. Finally, we conclude with a discussion and appraisal of the contribution in the thesis to the field of pharmacokinetics.