Numerical Simulation of Focused Shock Shear Waves in Soft Solids and a Two-Dimensional Nonlinear Homogeneous Model of the Brain

Journal of Biomechanical Engineering
Bruno GiammarinaroGianmarco Pinton

Abstract

Shear waves that propagate in soft solids, such as the brain, are strongly nonlinear and can develop into shock waves in less than one wavelength. We hypothesize that these shear shock waves could be responsible for certain types of traumatic brain injuries (TBI) and that the spherical geometry of the skull bone could focus shear waves deep in the brain, generating diffuse axonal injuries. Theoretical models and numerical methods that describe nonlinear polarized shear waves in soft solids such as the brain are presented. They include the cubic nonlinearities that are characteristic of soft solids and the specific types of nonclassical attenuation and dispersion observed in soft tissues and the brain. The numerical methods are validated with analytical solutions, where possible, and with self-similar scaling laws where no known solutions exist. Initial conditions based on a human head X-ray microtomography (CT) were used to simulate focused shear shock waves in the brain. Three regimes are investigated with shock wave formation distances of 2.54 m, 0.018 m, and 0.0064 m. We demonstrate that under realistic loading scenarios, with nonlinear properties consistent with measurements in the brain, and when the shock wave propagation...Continue Reading

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Citations

May 27, 2017·International Journal for Numerical Methods in Biomedical Engineering·W YeM Rochette
Mar 13, 2019·International Journal for Numerical Methods in Biomedical Engineering·Bharat B TripathiGianmarco F Pinton
Aug 20, 2019·Proceedings. Mathematical, Physical, and Engineering Sciences·Michel DestradeGiuseppe Saccomandi

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