Modeling a neurological disorder as the result of an operator acting on the brain: A first sketch based on network channel modeling

The brain is a complex network, and diseases can alter its structures and connections between regions. Therefore, we can try to formalize the action of diseases by using operators acting on the brain network. Here, we propose a conceptual model of the brain, seen as a multilayer network, whose intra-lobe interactions are formalized as the diagonal blocks of an adjacency matrix. We propose a general and abstract definition of disease as an operator altering the weights of the connections between neural agglomerates, that is, the elements of the brain matrix. As models, we consider examples from three neurological disorders: epilepsy, Alzheimer-Perusini's disease, and schizophrenia. The alteration of neural connections can be seen as alterations of communication pathways, and thus, they can be described with a new channel model.