Spatially resolved mapping of tau amplification rates via differentiable simulation of prion-like propagation.

Neurodegenerative diseases exhibit characteristic yet heterogeneous patterns of pathological spread, whose underlying determinants remain unclear. A central challenge is that inferring spatially heterogeneous propagation kinetics from neuroimaging data constitutes a high-dimensional inverse problem that has remained intractable at the whole-brain scale. Here, we present a differentiable reaction-diffusion framework that enables inference of spatially resolved tau amplification rates from tau PET data. By integrating MRI-informed forward simulation with error backpropagation, our approach reconstructs subject-specific voxel-wise maps of tau amplification rates across the human brain. Analysis of the inferred maps showed that the amplification rates have a positive spatial association with amyloid PET, suggesting that they capture aspects of regional vulnerability to amyloid-driven tau accumulation. Furthermore, integration with transcriptomic data identified gene expression programs associated with regional variation in amplification. These findings provide a data-driven framework linking molecular architecture to large-scale propagation dynamics in neurodegeneration.