Alzheimer's disease: a mathematical model for onset and progression

Area of Science:

• Neuroscience
• Mathematical Biology
• Computational Neuroscience

Background:

• Alzheimer's disease (AD) is a progressive neurodegenerative disorder.
• Understanding AD's onset and progression is crucial for developing effective treatments.

Purpose of the Study:

• To propose a novel mathematical model for Alzheimer's disease (AD) onset and progression.
• To incorporate key pathological mechanisms of AD, including amyloid aggregation and prion-like spread.

Main Methods:

• Developed a mathematical model using transport and diffusion equations.
• Modeled neurons as a continuous medium, categorized by malfunctioning degree.
• Utilized Smoluchowski equations for amyloid concentration and a kinetic-type transport equation for neuron malfunctioning distribution.

Main Results:

• Simulated the diffusion and agglomeration of amyloid polymers.
• Modeled neuron-to-neuron prion-like transmission as a disease spread mechanism.
• Numerical simulations qualitatively matched clinical images of AD distribution across disease stages.

Conclusions:

• The proposed mathematical model provides a framework for understanding AD progression.
• The model captures essential disease mechanisms, offering insights into spatio-temporal spread.
• Simulations show good qualitative agreement with in-vivo observations of Alzheimer's disease patterns.