A Mathematical Model of Chemotaxis in Cancer Treatment

Abstract

Chemotaxis is the directed movement of cells or organisms in response to a chemical gradient. This process is critical in many biological systems. In the context of cancer, chemotaxis plays a significant role in how cancer cells migrate and invade surrounding tissues. Our goal is to design a mathematical model that utilizes chemo-attractants to draw cancer cells towards the core of the tumor domain. We include therapeutic agents to eradicate cancer cells concentrated at the core of the tumor domain. To that aim, we set up a coupled system of partial differential equations that describes the interactions and dynamics of the following components: cancer cells concentration, chemo-attractants concentration, and cancer killer agents concentration. The model components are designed to manipulate the spatial distribution and eradication of cancer cells within the tumor microenvironment over time. Each term in the equations of those components plays a specific role to that end. Our simulations confirm that the combined therapy is highly effective in reducing tumor burden. Counter-intuitively, we find that chemotactic drift alone can achieve up to a 78% reduction in tumor mass within one unit of dimensionless time by inducing overcrowding at the tumor core, while the addition of therapy further enhances eradication and accelerates tumor suppression.