Mathematical model for simulation of morphological changes associated to crypt fission in the colon

Abstract

<p style='text-indent:20px;'>Morphological changes due to colorectal cancer propagation by an abnormal crypt fission is an interesting application arising in medicine and biology, that we try to analyse by a differential equations model coupled with a discrete crypt fission model. A colonic crypt can slowly change its shape in three steps: growth, bifurcation and fission. Fission is a rare event in a normal tissue, however if transit cells are unable to differentiate, due to an activation of Wnt signaling, then it may become fast and uncontrolled and cause a formation of aberrant crypt foci (ACF), defined as clusters of aberrant crypts. The differential equation system is composed by a convective diffusive equation for transit cell density and an elliptic equation for cell pressure, both defined on a manifold. The discrete crypt fission model acts in a set of adjacent crypts in order to investigate the ACF dynamics, due to a differentiation block. By using a Galerkin finite element method we solve numerically the differential equation model and show some interesting results about an ACF formation caused by a deformation and fission of abnormal crypts.</p>