On disease and healing: a theoretical sketch - Mannone, Maria; Fazio, Peppino; Ribino, Patrizia; Marwan, Norbert (Frontiers in Applied Mathematics and Statistics, 2024)
The onset and progression of a neurological disease can often be explained in terms of brain-network alteration. They can be formalized as the action of an operator representing the disease, the so-called K-operator, acting on the network. The healing process can thus be seen as the inverse of the disease mechanism. However, perfect healing is often impossible to achieve. Here, we formalize the ideal healing in terms of perturbative variation of the possible partial healing. The modeling and analytical strategy is based on techniques from theoretical physics, with the language of matrix operators. In addition, Using the language of category theory, we also formalize the progressive abstraction from the reality of diseased patients to the definition of a disease and the comparison between different diseases as a natural transformation between colimits. This theoretical presentation can provide a new, interdisciplinary perspective on neurological investigation and possibly foster new theoretical-experimental developments.