Calibration of Biophysical Models for tau-Protein Spreading in Alzheimer's Disease from PET-MRI

Aggregates of misfolded tau proteins (or just \emph{"tau"} for brevity) play a crucial role in the progression of Alzheimer's disease (AD) as they correlate with cell death and accelerated tissue atrophy. Longitudinal positron emission tomography (PET) is used to measure the extent of tau inclusions; and PET-based image biomarkers are a promising technology for AD diagnosis and prognosis. Here, we propose to combine an organ-scale biophysical mathematical model and longitudinal PET to extract characteristic growth patterns and spreading of tau. The biophysical model is a reaction-advection-diffusion partial differential equation (PDE) with only two unknown parameters representing the spreading (the diffusion part of the PDE) and growth of tau (the reaction part of the PDE). The advection term captures tissue atrophy and is obtained from diffeomorphic registration of longitudinal magnetic resonance imaging (MRI) scans. We describe the method, present a numerical scheme for the calibration of the growth and spreading parameters, perform a sensitivity study using synthetic data, and apply it to clinical scans from the ADNI dataset. Despite having only two parameters, the model can reconstruct clinical scans quite accurately.