Spatiotemporal modeling of tau aggregation following traumatic brain injury: implications for chronic traumatic encephalopathy.

Chronic traumatic encephalopathy (CTE) is a progressive neurodegenerative disorder associated with repetitive traumatic brain injury (TBI) and characterized by abnormal tau aggregation. Although biological and clinical evidence link head trauma to tau pathology, the mechanistic pathway connecting mechanical impact to biochemical progression remains insufficiently defined. This research introduces a mathematical model designed to predict the spatiotemporal evolution of tau accumulation following TBI. The formulation is based on an Avrami-type nucleation-growth framework, originally developed for phase transformations in materials, here adapted to represent the initiation and expansion of tau aggregates. Nucleation rate and growth velocity are treated as time-dependent parameters to capture realistic pathological dynamics. Temporal kinetics are calibrated using experimental data from mouse models of tauopathy, ensuring agreement with observed global progression. Spatial heterogeneity is incorporated through a mechanical field derived from finite element simulations, enabling regions exposed to higher post-impact strain to exhibit faster local transformation. This integrated biomechanical-mathematical approach provides a quantitative link between injury-induced deformation and tau aggregation, offering a basis for identifying mechanically vulnerable regions that may be predisposed to CTE-related pathology.