A non-autonomous delay differential equation model of cancer chemotherapy

Harsh Jain
Mathematical Biosciences Institute, The Ohio State University

(November 3, 2011 10:30 AM - 11:30 AM)

A non-autonomous delay differential equation model of cancer chemotherapy

Abstract

A new approach to anti-cancer therapy modeling is presented, that reconciles existing observations for the combined action of carboplatin (a Pt-based chemotherapeutic agent) and ABT-737 (a small molecule inhibitor of Bcl-2/xL) against ovarian cancers. To accurately simulate the action of these compounds, an age-structure together with a delay is imposed on proliferating cancer cells, and detailed biochemistry of Bcl-xL-mediated apoptotic pathways is incorporated. The model is calibrated versus in vitro experimental results, and is then used to predict optimal doses and administration time scheduling for the treatment of a tumor growing in vivo. The age-structured model gives rise to a 1D hyperbolic Partial Differential Equation which can be reduced to a nonlinear, non-autonomous Delay Differential Equation by projecting along the characteristics. I prove the existence of periodic solutions and derive conditions for their stability. This has clinical implications since it leads to a lower bound for the amount of therapy required to effect a cure.