Tumor growth model for ductal carcinoma: from in situ phase to stroma invasion

Thierry Colin (1) , Olivier Gallinato (1) , Clair Poignard (1) , Olivier Saut (1)

1 MC2 - Modélisation, contrôle et calcul

We propose a tumor growth model, based on partial differential equations, for breast ductal carcinoma. In particular, we focus on the transition from the in situ stage to the invasive phase, under the action of specific enzymes: matrix metalloproteinases (MMPs), that are produced by cancer cells. Advection equations describe the movement of biological cells, generated by cancer cell proliferation that exerts pressure on the surrounding tissues. In its early phase, ductal carcinoma remains confined to the galactophoric duct due to the membrane. However, as soon as MMPs enzymes are produced, they are able to degrade the membrane, which leads to cancer invasion. The specificity of the model lies in the description of these phenomena and the modeling of the duct membrane degradation, thanks to nonlinear Kedem-Kalchalski type transmission conditions to describe the pressure.

Mots clés: tumor growth model; nonlinear advection equations; Kedem-Katchalsky conditions; breast cancer; metalloproteinases

Domaines: Equations aux dérivées partielles [math.AP]; Cancer; Modélisation et simulation

Thierry Colin, Olivier Gallinato, Clair Poignard, Olivier Saut. Tumor growth model for ductal carcinoma: from in situ phase to stroma invasion. [Research Report] RR-8502, 2014, pp.31. ⟨hal-00962163v1⟩