Our last preprint "A whole-brain model of amyloid beta accumulation and cerebral hypoperfusion in Alzheimer's disease" from A. Ahern, A. Goriely, E. Kuhl, P.F. Antonietti, and me is now out on ArXiv and MOX Report. 

Evidence suggests that amyloid beta and cerebrovascular pathology are mutually reinforcing; in particular, amyloid beta suppresses perfusion by constricting capillaries, and hypoperfusion promotes the production of amyloid beta. Here, we propose a whole-brain model coupling amyloid beta and blood vessel through a hybrid model consisting of a reaction-diffusion system for the protein dynamics and porous-medium model of blood flow within and between vascular networks. Simulations in realistic brain geometries demonstrate the emergence of multistability, implying that a sufficiently large pathogenic protein seeds is necessary to trigger disease outbreak. Motivated by the "two-hit vascular hypothesis" of Alzheimer's disease that hypoperfusive vascular damage triggers amyloid beta pathology, we also demonstrate that localized hypoperfusion, in response to injury, can destabilize the healthy steady state and trigger brain-wide disease outbreak. 

We are excited to share that our last preprint, "A novel mathematical and computational framework of amyloid-beta triggered seizure dynamics in Alzheimer's disease", from C.B. Leimer Saglio, S. Pagani, P.F. Antonietti and me, is now out on ArXiv. 

In this work, we introduce a novel mathematical model that extends the Barreto-Cressman ionic formulation by incorporating multiple mechanisms of calcium dysregulation induced by amyloid-beta. Numerical simulations performed on idealized and realistic brain geometries demonstrate that progressive amyloid-beta accumulation leads to severe alterations in calcium homeostasis, increased neuronal hyperexcitability, and pathological seizure propagation.

Polygonal and Structure-Preserving Methods for PDEs Discretization

Mathematical Modeling of Neurodegenerative Diseases