Reaction-Diffusion Model of Cortical Atrophy Spread during Early Stages of Alzheimer's Disease

Abstract

1.This study introduces a reaction-diffusion model of atrophy spread across the rhinal cortex during early stages of Alzheimers disease. Our finite elements model of atrophy spread is motivated by histological evidence of a spatio-temporally specific pattern of neurofibrillary tau accumulation, and evidence of grey matter atrophy correlating with sites of neurofibrillary tau accumulation. The goal is to estimate disease-related parameters such as the origin of atrophy, the speed at which atrophy spreads, and the stage of the disease. We solve a constrained optimization problem using the adjoint state method and gradient descent to match modeled cortical thickness to observed cortical thickness as calculated from 3T MRI scans. Simulation testing shows that disease-related parameters can be estimated accurately with as little as 2 years of annual observations, depending on the stage of the disease. Case studies of 3 subjects suggests that we can pinpoint the origin of atrophy to the anterior transentorhinal cortex, and that the speed of atrophy spread is less than 1 mm per year. In the future, this type of modeling could be useful to stage the progression of the disease prior to the onset of clinical symptoms. 2. Author SummaryMisfolded tau proteins are associated with Alzheimers disease. They are known to accumulate and spread across the rhinal cortex, which is an area of the temporal lobe. Recent imaging studies suggest that we can detect grey matter thinning that occurs in pattern similar to tau spread. In this study, we introduce a model of disease spread to examine where thinning begins, how fast it spreads, and the stage of the disease. The results show that the origin of thinning corresponds with the earliest known location of tau accumulation, and spreads at a rate of less than 1 mm per year. Future work may focus on staging the progression of the disease using this type of model.