Numerical algorithm for morphogen synthesis region identification with indirect image-type measurement data

Abstract

Diffusion–reaction models are used to describe development processes in the framework of morphogen theory. The images of the concentration fields for the subset of the interacting morphogens are available. In order to interpret this data in terms of the model parameters, the inverse source problem is stated. The sensitivity operator, composed of the independent adjoint problem solutions ensemble, allows transforming the inverse problem to the family of nonlinear ill-posed operator equations. The equations are solved with the Newton–Kantorovich-type algorithm. The approach is applied to the morphogen synthesis region identification problem for the model of regulation of the renewing zone size in biological tissue.