Simulation of shear shock waves in the human head for traumatic brain injury

We have recently observed, experimentally, that shear shock waves are generated deep inside the brain starting from a low initial acceleration (sub-concussive range). This observation has motivated the development of simulation tools to model shear shock waves in the human head. Current numerical methods that describe nonlinear shear wave propagation are in retarded time which makes them unidirectional, and they are valid for small angles only. A full-wave model would capture a much wider range of shock wave physics that occurs during a traumatic event. Here we present: 1) a nonlinear system of conservation laws that models the propagation of linearly-polarized shear waves in 2D, 2) a model of the attenuation/dispersion in soft solids using relaxation mechanisms, 3) numerical simulations of (1)-(2) using the Piecewise Parabolic Method (PPM). This system is solved using an unsplit and conservative implementation of PPM with a local Lax-Friedrichs flux, coupled with second-order splitting in time. The 2D method is validated with planar and focusing experimental results. Lastly, a complex geometry of human skull CT-scan is used as the 2D computational domain for simulating the propagation of shear shocks in brain mimicking gelatin phantom.