Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

A Mathematical Exploration of the Development and Therapeutic Implications of Anti-Cancer Drug Resistance
Jan Gevertz

Last modified: 2014-06-09


Practically all chemotherapeutic agents, and many newer targeted cancer therapeutics, lead to drug resistance. Drug resistance can arise due to a number of different intracellular and microenvironmental causes. Further, drug resistance may be pre-existing, or can be acquired in response to treatment. For an individual cancer patient, there is essentially no way to know if they harbor pre-existing resistant cells, and what forms of resistance they have or will develop to a given treatment protocol. With the goal of better understanding drug resistance and its implications for treatment, we have developed a hybrid discrete-continuous mathematical model to compare different timings and mechanisms of drug resistance. In the hybrid model, drug dynamics are described through partial differential equations, and a particle-spring approach is used to model individual cells which can grow, divide, and interact with other cells in their immediate neighborhood. Our preliminary model findings examine the consequences of having either pre-existing or acquired drug resistance. We examine two types of
simulations that share the following common features: spatial configurations of cancer cells and vasculature (initial conditions extracted from patient-specific histological data), mechanism of drug action, and cause of drug resistance. However, in the first simulation, we have assumed that drug resistance existed prior to the start of treatment, and in the second simulation, we have assumed that drug resistance is acquired in response to treatment. From these preliminary results, we are beginning to form hypotheses on which modes/timing of drug resistance lead to more aggressive tumors, and how to optimally design therapeutic protocols given the uncertainty of whether drug resistance is pre-existing or acquired. I will also discuss future directions for this project.