Numerical analysis of finite element methods for the diffusion, cell proliferation model in the colon epithelium with viscoelastic properties

Abstract

In this project, we propose a multiscale model and a numerical strategy to obtain a computational simulation of the initial phases of the cancerinogenesis process in the colon. Our goal is to model and simulate the formation of adenomas in the colon starting by considering the multiscale interactions of the colonic cells acting in the cavities of the colon epithelium (called crypts). The candidate multiscale model is three dimensional in space and is based on a continuum system of PDEs for the cell dynamics coupled with a viscoelastic model that describe the deformations of the epithelium tissue, the crypt fission, and the formation of adenomas. The numerical methods here proposed to approximate the multiscale interactions of the transient cells with the tissue in the colon epithelium, are in the framework of the "Heterogeneous Multiscale Methods". Since the human colon presents millions of crypts, each with hundreds of transit cells that cab be responsible for the formation of adenomas in the colon, we will use a multiscale strategy during the implementation of the numerical method to have an ecient numerical methodology that yields to a balance between accuracy and memory/computational cost. This work is an extension of the research that has been developed by Prof. G. Romanazzi and his collaborators in Coimbra and Bari during the last eight years in the area of the mathematical modelling and numerical simulation of the firsts stages of the formation of colorectal cancer. The novelties of this proposal regard in using: (1) multiscales to model the initial phases (initiation and promotion) of the carcinogenesis in the colon that have been never modeled by using many scales (2) a three dimensional modelling to describe the formation of adenomas(3) the viscoelastic properties of the epithelium tissue, (4) a crypt fission modelling, and (5) an efficient multiscale strategy. (AU)