A Multiscale Model for Aberrant Crypt Foci

Colorectal cancer is believed to be initiated in colonic crypts as consequence of several genetic mutations in normal cells. Clusters of abnormal crypts, called Aberrant Crypt Foci (ACF), are thought to be the rst manifestation of a possible carcinogenic process. Assuming that the formation of an ACF is due to the accumulation of abnormal cells we use multiscale technics to study their evolution. Starting from a 3-d crypt model we make its projection in a plane and then build a model in which the colon is a 2-d structure with crypts periodically distributed. Inside the crypts, the dynamics of the abnormal cells is governed by a convective-diffusive model, whose unknowns are the cell density of abnormal cells and a pressure. Outside the crypts, in the inter-cryptal region, a proliferative-diffusive model is assumed for the dynamics of abnormal cells. For the numerical implementation of this model, it is used a technique based on heterogeneous multiscale methods. Two scales are employed: a macro-scale and a micro-scale. The macro-scale corresponds to the region of the colon where the evolution of ACF is taking place, whilst the micro-scale is related to the region occupied by each crypt and its inter-cryptal region. Pressure and cell density are computed at the macro-scale level using the micro-scale structure in a neighborhood of the quadrature macro-scale points. This strategy reduces the computational cost of the simulations. Numerical results, simulating the ACF evolution, are shown and discussed