News Archive

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. 

Check out the latest article from C.B. Leimer Saglio, S. Pagani, P.F. Antonietti, and me, "A high-order discontinuous Galerkin method for the numerical modeling of epileptic seizures" recently published in Computers & Mathematics with Applications. 

This work employs the monodomain model, coupled with specific models characterizing ion concentration dynamics, to mathematically describe brain tissue electrophysiology at the organ scale. This multiscale model is discretized in space with the high-order discontinuous Galerkin method on polygonal and polyhedral grids. 

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.

Our last preprint "Structure-preserving local discontinuous Galerkin discretization of conformational conversion systems" from P.F. Antonietti, S. Gómez, I. Perugia, and me is now out on ArXiv. 

This work investigates a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretization with the backward Euler time-integration method. We prove a discrete entropy-stability inequality, which we use to show the existence of discrete solutions, as well as to establish the convergence of the scheme by means of some discrete compactness arguments.

Check out our last article, "Polytopal mesh agglomeration via geometrical deep learning for three-dimensional heterogeneous domains", which has been recently published in Mathematics and Computers in Simulation. 

In this work, we propose a bisection model based on Graph Neural Networks to partition a suitable connectivity graph of computational three-dimensional meshes. Our algorithm can agglomerate meshes of a domain composed of heterogeneous media, automatically respecting the underlying heterogeneities. Moreover, we demonstrate that our algorithm also shows a good level of generalization when applied to complex geometries, such as three-dimensional geometries reconstructed from medical images. Finally, the model’s capability to perform agglomeration in heterogeneous domains is evaluated when integrated into a polytopal discontinuous Galerkin finite element solver.  

Check out the latest article from P.F. Antonietti, S. Gomez, I. Perugia, and me, "A structure-preserving LDG discretization of the Fisher–Kolmogorov equation for modeling neurodegenerative diseases" recently published in Mathematics and Computers in Simulation. 

This work presents a structure-preserving, high-order, unconditionally stable numerical method for approximating the solution to the Fisher–Kolmogorov equation on polytopal meshes, with a particular focus on its application in simulating misfolded protein spreading in neurodegenerative diseases.