29 citations · 86 across the 9 of their papers we have counts for
9 papers
Spreading of pathological proteins through brain networks: a case study for Alzheimers disease
G. Landi, A. Scaravelli, M. C. Tesi +1
Mathematical modeling offers a valuable approach to understanding Alzheimers disease (AD) given its complexity, unknown causes, and lack of effective treatments. Models, once valid…
Mixing, segregation, and collapse transitions of interacting copolymer rings
EJ Janse van Rensburg, E Orlandini, MC Tesi +1
A system of two self and mutual interacting ring polymers, close together in space, can display several competing equilibrium phases and phase transitions. Using Monte Carlo simula…
The role of beta-amyloid and tau proteins in Alzheimer's disease: a mathematical model on graph
Michiel Bertsch, Bruno Franchi, Maria Carla Tesi +1
In this Note we study a mathematical model for the progression of Alzheimer's Disease in the human brain. The novelty of our approach consists in the representation of the brain as…
Thermodynamic and topological properties of copolymer rings with a segregation/mixing transition
EJ Janse van Rensburg, E Orlandini, MC Tesi +1
Two ring polymers close to each other in space may be either in a segregated phase if there is a strong repulsion between monomers in the polymers, or intermingle in a mixed phase…
Sobolev-Gaffney type inequalities for differential forms on sub-Riemannian contact manifolds with bounded geometry
Annalisa Baldi, Maria Carla Tesi, Francesca Tripaldi
In this paper we establish a Gaffney type inequality, in -Sobolev spaces, for differential forms on sub-Riemannian contact manifolds without boundary, having bounded ge…
A sensitivity analysis of a mathematical model for the synergistic interplay of Amyloid beta and tau on the dynamics of Alzheimer's disease
Michiel Bertsch, Bruno Franchi, Valentina Meschini +2
We propose a mathematical model for the onset and progression of Alzheimer's disease based on transport and diffusion equations. We treat brain neurons as a continuous medium and s…
Well-posedness of a mathematical model for Alzheimer's disease
Michiel Bertsch, Bruno Franchi, Maria Carla Tesi +1
We consider the existence and uniqueness of solutions of an initial-boundary value problem for a coupled system of PDE's arising in a model for Alzheimer's disease. Apart from reac…
Microscopic and macroscopic models for the onset and progression of Alzheimer's disease
Michiel Bertsch, Bruno Franchi, Maria Carla Tesi +1
In the first part of this paper we review a mathematical model for the onset and progression of Alzheimer's disease (AD) that was developed in subsequent steps over several years.…
Alzheimer's disease: a mathematical model for onset and progression
Michiel Bertsch, Bruno Franchi, Norina Marcello +2
In this paper we propose a mathematical model for the onset and progression of Alzheimer's disease based on transport and diffusion equations. We regard brain neurons as a continuo…