A Biophysical Model of Shape Changes due to Atrophy in the Brain with Alzheimer's Disease

This paper proposes a model of brain deformation triggered by atrophy in Alzheimer's Disease (AD). We introduce a macroscopic biophysical model assuming that the density of the brain remains constant, hence its volume shrinks when neurons die in AD. The deformation in the brain parenchyma minimizes the elastic strain energy with the prescribed local volume loss. The cerebrospinal fluid (CSF) is modelled differently to allow for fluid readjustments occuring at a much faster time-scale. PDEs describing the model is discretized in staggered grid and solved using Finite Difference Method. We illustrate the power of the model by showing different deformation patterns obtained for the same global atrophy but prescribed in gray matter (GM) or white matter (WM) on a generic atlas MRI, and with a realistic AD simulation on a subject MRI. This well-grounded forward model opens a way to study different hypotheses about the distribution of brain atrophy, and to study its impact on the observed changes in MR images.