Pattern Formation in a β-Amyloid Plaque Model for Alzheimer's Disease

Pattern Formation in a β-Amyloid Plaque Model for Alzheimer's Disease

Alvin Sherman Library

Alzheimer's disease is a neurodegenerative disorder with complex physiological mechanism that are not fully understood. Over 7 million Americans are known to be living with the disease, and an Alzheimer's diagnosis accounts for 60-70% of dementia cases. Current hypotheses attribute the cause to an interplay between β-Amyloid plaques and neurofibrillary tangles, resulting in central nervous system disruption and decline in cognitive functioning. In this project, we study a spatial dynamical system model that incorporates the interaction between β-Amyloid monomers, oligomers, microglia, and interleukins in the context of plaque aggregation. We establish conditions for the existence and stability of a spatially homogenous steady state, representing a disease-free equilibrium solution and other balanced and spatially uniform conditions for the concentrations of monomers, oligomers, plaques, microglia, and interleukins depending on parameter values. We then investigate the impact of microglial attraction to oligomers in developing a taxis-driven bifurcation of the steady state for spatial pattern formation. Formation of these spatial patterns corresponds to plaque formation in the brain as observed in Alzheimer's disease, representing the distribution of plaque as a result of aggregation. Exploration of this model is representative of larger research on the mechanisms behind β-Amyloid aggregation and the usefulness of mathematical modeling in representing the complex physiology behind the disease.