Modelos de reacción difusión para el registro de imágenes médicas.

Abstract

In the present work, we study an inverse problem that consists of a minimization problem of a linearized image registration model for glioma growth, which is subject to a system of parabolic partial differential equations, with homogeneous Dirichlet and Neumann boundary conditions non-homogeneous, which describes the evolution of the glioma density, together with a vectorial transport equation that defines the border that the glioma occupies. The objective function to be minimized is based on the Landmark-Based Registration technique, which is used in the image registration of medical images. Finally, the existence of a solution to this minimization problem is shown. Furthermore, first-order optimality conditions are derived using the associated Lagrangian, and the corresponding adjoint state.