  Aggregates of misfolded tau proteins (or just '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) scans can be used quantify the extend of abnormal tau spread.
Such PET-based image biomarkers are a promising technology for AD diagnosis and
prognosis. Here, we propose to calibrate an organ-scale biophysical
mathematical model using longitudinal PET scans to extract characteristic
growth patterns and spreading of tau. The biophysical model is a
reaction-advection-diffusion partial differential equation (PDE) with only two
scalar unknown parameters, one representing the spreading (the diffusion part
of the PDE) and the other one the 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 we perform a preliminary evaluation on clinical scans from the ADNI
dataset. We study whether such model calibration is possible and investigate
the sensitivity of such calibration to the time between consecutive scans and
the presence of atrophy. Our findings show that despite using only two
calibration parameters, the model can reconstruct clinical scans quite
accurately. We discovered that small time intervals between scans and the
presence of background noise create difficulties. Our reconstructed model fits
the data well, yet the study on clinical data also reveals shortcomings of the
simplistic model. Interestingly, the parameters show significant variability
across patients, an indication that these parameters could be useful
biomarkers.
