The brain network damage provoked by a neurological disease can be modeled as the result of the action of an operator, $K$, acting on the brain, inspired by physics. Here, we explore the matrix formulation of $K$, analyzing eigenvalues and eigenvectors, with heuristic considerations on different techniques to approximate it. The primary objective of this paper is to lay the foundational groundwork for an innovative framework aimed at the development of predictive models regarding the progression of neurodegenerative diseases. This endeavor will leverage the potential of integrating these novel representations of brain damage with advanced machine-learning techniques. A case study based on real-world data is here presented to support the proposed modeling.