Penetrating gunshots to the head after close-range shooting: Dynamics of waves and the effect of brain tissue rheology

Abstract

Formation of the brain tissue backspatter after penetrating gunshots to the head is preceded and driven by formation and evolution of the bullet channel, which is filling with air and/or muzzle gases or issuing them with tissue fragments or without them. This process is explored here in a model situation in the framework of the dynamics of waves in brain tissue affected by its realistic rheological behavior, fragmentation, and gas dynamics in the evolving bullet channel. As a rheological model of the brain tissue, a new strain-energy function W, introduced in the accompanying work, is employed, which expresses the strain energy as a rational function of the principal invariants of the Cauchy tensor C. This strain-energy function W generates a hyperelastic constitutive equation, which resembles the behavior of brain tissues, i.e., reveals a much stronger resistance to compression than to stretching and strongly nonlinear response in simple shear. This new rheological model belongs to the class of hyperelastic models used for description of hydrogels. The equations of motion supplemented by this rheological model reveal the dynamics of the compression and rarefaction waves propagating through the brain tissue following the formation of the bullet channel. These waves are reflected from the skull and the bullet channel. In parallel, gas dynamics of air and/or muzzle gases flowing into or issued outward of the bullet channel, and stretching-driven fragmentation of the brain tissue are evolving in concert with the wave dynamics in the brain tissue. This allows for prediction of backspatter of the brain tissue resulting from a short-range shooting.