A mathematical macroscopic model for the onset and progression of Alzheimer's disease

Fino, Angela (2018) A mathematical macroscopic model for the onset and progression of Alzheimer's disease. [Laurea magistrale], Università di Bologna, Corso di Studio in Matematica [LM-DM270]
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In this work we deal with the study of a macroscopic mathematical model which describes the onset and progression of Alzheimer’s disease (AD) in the human brain. In particular, we analyze in detail the well-posedness of the model itself. The model is based on the so-called “amyloid cascade hypothesis” together with the “prionoid hypothesis”, which represents the spreading of the disease through neuron-to-neuron transmission. In particular, from a mathematical point of view, the model consists of a transport equation for a probability measure, coupled with a nonlinear Smoluchowski-type system with a diffusion term. In view of the features of the biological phenomena we are dealing with, the main hallmark of such a system is that the two groups of equations cannot be separated and they must be considered together. The main tools to prove existence and uniqueness of the solution of the problem coupled with appropriate initial and boundary conditions are: the definition of an appropriate metric space obtained by endowing with the Wasserstein distance the space of Borel probability measures supported on a bounded interval; the transport of measures along the characteristics of the transport equation; an ad hoc formulation of the classical contraction theorem and a priori estimates for solutions of the reaction diffusion equations.

Tipologia del documento
Tesi di laurea (Laurea magistrale)
Autore della tesi
Fino, Angela
Relatore della tesi
Corso di studio
Curriculum A: Generale e applicativo
Ordinamento Cds
Parole chiave
transport and diffusion equations Smoluchowski equations mathematical models of Alzheimer’s disease beta-amyloid aggregation prion-like transmission neural damage
Data di discussione della Tesi
14 Dicembre 2018

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