In this talk, we present a new mathematical model describing the interplay between biological tissue atrophy driven by the diffusion of a biological agent and its applications to neurodegenerative diseases. The model of study comprises a Fisher-Kolmogorov equation for species diffusion, incorporating both dispersion and proliferation effects, coupled with a elasticity equation governing tissue atrophy. This mass loss process is described through a morpho-elastic framework, where mass loss and tissue elasticity together shape the resulting tissue morphology. The model integrates the morpho-elastic response with a biological agent concentration by introducing an evolution law for inelastic strain, governed by the agent concentration through a logistic-type differential equation. We present the application of this model to the onset and development of Alzheimer’s disease, where the equations describe the propagation of misfolded tau-proteins and the ensuing brain atrophy characteristic of the disease. To address the inherited complexities numerically, we propose a Discontinuous Galerkin (DG) method for spatial discretization, while time integration relies on the Crank-Nicolson method. We present convergence tests to validate the DG method in the uncoupled case, discuss the results concerning the theoretical outcomes and validate the model in the coupled framework. Moreover, we have applied the model to simulate Alzheimer's disease on a real brain geometry, where we observed outcomes consistent with the anticipated biological behaviour of prion-like protein diffusion and tissue atrophy. As an introduction to future studies, we also present the results of a simulation incorporating a nonlinear constitutive law for tissue elasticity.