Fig. 3: ESM approach and prediction of intra-brain tau spreading.

a Changes in the presence of a given infection-like “agent” factor (e.g., amyloid, tau misfolded proteins [MP]) at a specific brain region, “i”, are modeled as a function of the incoming “agent” from each connected region, “j” (i.e. spread effects through communicating cells), minus the local “agent” clearance. b This dynamic cause–effect model can be mathematically translated to a non-linear system of differential equations, which is dependent on the individual “agent” production rate, the clearance rate, and the inter-region brain-connectivity matrix. In the NeuroPM-box, both the production and clearance rates can be optionally modeled as time-dependent sigmoid functions¹² or as global constant values. The connectivity matrix can be estimated via diffusion MRI tractography^63,64 or an alternative technique^65,66,67. c Shows ESM results reproducing the tau deposition patterns at the first ¹⁸F-AV1451 PET evaluation (age = 71 years) of a clinically healthy female control with significant memory complaints (ADNI data, subject ID 024_S_5290). d ESM results in the same participant at the fourth time point evaluation (age = 73 years). Starting from a pathology-free stage, the model explained 86% (P < 10⁻¹⁰) of the variance in tau values across the four available time points. e ESM simulation of the whole-brain intra-brain tau spreading process from the estimated onset time of tau appearance/propagation (age = 62 years) to the last observed time point. In c–e, tau values are cortical-to-cerebellum standardized uptake value ratio (SUVr).