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 whole-brain scale. Here we present a differentiable reaction-diffusion framework that enables inference of spatially resolved tau amplification rates directly from tau PET data. By integrating MRI-informed forward simulation with error backpropagation, our approach reconstructs voxel-wise propagation kinetics across the human brain. The inferred maps revealed structured, non-uniform patterns of tau amplification, with both cross-individual consistency and substantial inter-individual variability. These patterns were distinct from observed tau burden, revealing regional vulnerability that is not apparent from static tau PET maps alone. Integration with transcriptomic data identifies 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.