Cancer progression determined by cancer stem cells: the dynamics of growth and therapy

L.M. BARBERIS; L. BENITEZ; C.A. CONDAT

Cusco

Congreso; X Congreso Latinoamericano de Biología Matemática (SOLABIMA 17); 2017

Sociedad Latinoamericana de Biomatemática

We use a system of coupled differential equations to investigate the consequences of the cancer stem cell hypothesis. This hypothesis states that cancer growth is mediated by cancer stem cells, which are pathological variants of normal stem cells. These cells are assumed to be therapy-resistant and thus responsible for the development of tumor recurrence. Cancer stem cells may divide symmetrically, generating two new cancer stem cells or two differentiated cancer cells, or asymmetrically, generating one cancer stem cell and one differentiated cancer cell. We describe a tumor formed by cancer stem cells and differentiated cancer cells that are allowed to compete for the available resources. We find the fixed points of the system, analyze their stability and investigate the system evolution, finding that the tumor grows following two dynamic behaviors, which are selected by the relation between the cancer stem cell differentiation rate and its duplication rate. Both behavior types can be related to available experimental data. The system evolution after the application of different therapies can also be predicted. In particular, we can describe the experimentally observed increase in the cancer stem cell fraction after therapy.