Frontiers in Applied Mathematics and Statistics (Aug 2018)
Adoption of the Transport and Burgers' Equations in Modeling Neurological Shock-Waves in the Human Brain Due to Improvised Explosive Devices (IEDs)
Abstract
This paper considers the propagation of neurological shock-waves in the human head due to improvised explosive devices (IEDs). The models adopted here use various mathematical techniques, including adoption and application of the two most important partial differential equations (PDEs) in this area, such as the Burgers' and Transport equations—together with a discussion of the inherent mechanics witnessed during experiments. In particular, only a one-dimensional model of the propagation of an intense acoustic compression wave—known as a shock-wave—traveling from air into the human head, is analyzed, using experimental data taken from existing literature. Computer simulations of these models also reproduce published experimental measurements of these acoustic dynamic pressures within the human brain, with graphs describing shock-wave motion in both two- and three- dimensions. There follows analysis and explanations of this phenomena, developed more thoroughly, to explain in detail features of experimentally-observed dynamic-pressures resulting in the brain, after a transitory shock-wave rapidly passes through the human head. The final part of this paper leads to further mathematical exposition—intended to be discussed within future publications—of dynamic-pressures, the latter being explained more comprehensively, and in greater detail, for clarity, especially in terms of the inherent physics and mechanical properties of the ensuing dynamics.
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