A single-snapshot inverse solver for two-species graph model of tau pathology spreading in human Alzheimer's disease.

We propose a method that uses a two-species ordinary differential equation (ODE) model for subject-specific misfolded tau protein spreading in Alzheimer's disease (AD) and calibrates it from magnetic resonance imaging (MRI) and positron emission tomography (PET) scans. The ODE model is a variant of the heterodimer Fisher-Kolmogorov (HFK) model. The unknown model parameters are the initial condition (IC) for tau and three scalar parameters representing the migration, proliferation, and clearance of tau proteins. Driven by imaging data, these parameters are estimated by formulating a constrained optimization problem with a sparsity regularization for the IC. This optimization problem is solved with a projection-based quasi-Newton algorithm. We evaluate the performance of our method on both synthetic and clinical data. Subjects are from the AD Neuroimaging Initiative (ADNI) datasets: 455 cognitively normal (CN), 212 mild cognitive impairment (MCI), and 45 AD subjects. We compare the performance of our approach to the commonly used Fisher-Kolmogorov (FK) model with a fixed IC at the entorhinal cortex (EC). Our method demonstrates an average improvement of 19.6% relative error compared to the FK model on the AD dataset. HFK also achieves an R-squared score of 0.591 for fitting AD data compared with 0.256 from FK model results with IC fixing at EC. The inverted IC from our scheme indicates that the EC is the most likely initial seeding region if subcortical regions are excluded from the analysis. However, other regions also have probability to be the IC seeding regions. Furthermore, for cases that have longitudinal data, we estimate a subject-specific AD onset time.