Brain-Network mathematical modeling for neurodegenerative disease

The human brain can be described as a multi-layer network. We can model neurological disease in terms of alterations of the brain network at different layers. Thus, we define an operator acting on connectivity matrices and altering the weights of the connections. In particular, we can conceptualize an operator K, that acts on a healthy brain and produces a pattern of change typical for each disease, or describes the time evolution of a diseased brain. Focusing on neurodegenerative diseases having age as a risk factor, we consider Parkinson’s and Alzheimer-Perusini’s disease. We applied our model to patients from the Parkinson’s Progression Markers Initiative (PPMI) and the Alzheimer’s Disease Neuroimaging Initiative (ADNI) datasets. We computed matrix forms of the K-operator comparing healthy control and diseased brain networks, and gained insights into the disease evolution by computing the K-operator between brains from the baseline to different follow-ups. We compared our findings with the medical literature, confirming the relevance of our results. Finally, we propose a machine-learning model to predict the patients’ disease evolution, using as the training set our findings on the K-operator for different patients.