Pre-Publicación 2023-28
Marie Haghebaert, Beatrice Laroche, Mauricio Sepúlveda:
Study of the numerical method for an inverse problem of a simplified intestinal crypt
Abstract:
In this work we consider the study of an inverse problem for an intestinal crypt model. The original model is based on the interaction of ep- ithelial cells with microbiota-derived chemicals diffusing in the crypt from the gut lumen. The 5 types of cells considered in the original model [3] were re- duced in this work to 3 types of cells for simplifications of the inverse problem. The inverse problem consists of determining the shape of the secretory cells of the deep crypt from observations of the stem cells and progenitor cells at a fixed time. The method used is the calculation of the adjoint state asso- ciated with the second-order BGK numerical scheme considered in [3], which allows calculating the critical points of the Lagrangian associated with the in- verse problem, and applying a gradient method in order to minimize the cost function. The algorithm is described, and some numerical examples are given
