Neurodegenerative diseases have a significant global impact, affecting millions of individuals worldwide. Some of them, known as proteinopathies (for example, Alzheimer's and Parkinson's diseases), are characterized by the accumulation and propagation of toxic proteins known as prions. Mathematical models of prion dynamics play a crucial role in understanding disease progression. Several models have been proposed to describe the misfolding process, with various levels of detail. In this context, we introduce and analyze a discontinuous Galerkin method on polytopal grids (PolyDG) for the semi-discrete approximation of different nonlinear models of population dynamics, such as the Fisher-Kolmogorov, and the heterodimer model. \par Protein agglomerations cause the eventual degeneration of neurons and brain atrophy. We aim to propose a novel multiphysics model describing the spreading of a pathogen causing atrophy in the medium. The model's novelty relies on a new constitutive equation for the inelastic stress tensor component used to model tissue atrophy. The coupling with the atrophy model is achieved by introducing a variable representing tissue loss proportion assumed to follow a logistic-type ordinary differential equation that depends on the species concentration. We carry out realistic simulations in three-dimensional and two-dimensional patient-specific brain geometries reconstructed from magnetic resonance images.