Modelling, numerical analysis and computational simulation of the colon adenoma growing during the absorption of drug released from polymers

Abstract

We propose a modeling, and a numerical analysis of finite element methods implemented for simulating the colon adenoma formation and growing during the absorption of antitumor drugs released from polymers. We use a partial differential equation model to simulate the drug release and the adenoma dynamics under the effect of the absorbed drug. The adenoma formation in the colon is due to an abnormal cell differentiation acting in the cavities spread in the colon epithelium called crypts. This process is modeled by a differential equation system, that is coupled with a model for crypt deformations, to simulate the adenoma formation and growing due to a cell hyper-proliferation. The drug release from polymers is modeled by another system of differential equations for the dissolved and free drug concentration that can be absorbed by the tumor adenoma. This concentration depends on the viscoelastic properties of the polymer matrix where the drug is initially linked. The full model proposed is multiscale:in the cell scale (microscale) we use a differential system that describes the cell dynamics in the colon epithelium, and also the drug release and absorption in the tissue; whereas in the tissue scale (macroscale) we model the epithelium deformation, the crypt fission and the following adenoma dynamics. This project has relevant novelties in the modeling, numerical analysis and simulations as follows:(1) modeling of the first steps of carcinogenesis in the colon epithelium coupled with its viscoelastic deformations and crypt fission, (2) drug release and absorption in the epithelium that acts and affect the adenoma growing, (3) numerical analysis of the methods used, (4) development of a multiscale numerical strategy that is efficient to simulate the dynamics of adenomas under the antitumor drug effect. (AU)