MATHEMATICAL MODEL FOR SIMULATION OF MORPHOLOGICAL CHANGES ASSOCIATED TO CRYPT FISSION IN THE COLON

Author(s)

Romanazzi, Giuseppe ; Settanni, Giuseppina

• Document type: Journal article
• Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S; v. 15, n. 12, p. 25-pg., 2022-03-22.

Abstract

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. (AU)

• FAPESP's process: 17/05519-5 - Multiscale modeling and numerical simulation of the firsts steps of the formation of colorectal cancer
• Grantee: Giuseppe Romanazzi
• Support Opportunities: Regular Research Grants
• FAPESP's process: 17/16960-4 - Model and numerical simulations of the fission process of abnormal crypts in the colon epithelium
• Grantee: Giuseppe Romanazzi
• Support Opportunities: Research Grants - Visiting Researcher Grant - International