Mathematical Models of Blast-Induced TBI: Current Status, Challenges, and Prospects

Abstract

Blast-induced traumatic brain injury (TBI) has become a signature wound of recent military activities and is the leading cause of death and long-term disability among U.S. soldiers. The current limited understanding of brain injury mechanisms impedes the development of protection, diagnostic, and treatment strategies. We believe mathematical models of blast wave brain injury biomechanics and neurobiology, complemented with in vitro and in vivo experimental studies, will enable a better understanding of injury mechanisms and accelerate the development of both protective and treatment strategies. The goal of this paper is to review the current state of the art in mathematical and computational modeling of blast-induced TBI, identify research gaps, and recommend future developments. A brief overview of blast wave physics, injury biomechanics, and the neurobiology of brain injury is used as a foundation for a more detailed discussion of multiscale mathematical models of primary biomechanics and secondary injury and repair mechanisms. The paper also presents a discussion of model development strategies, experimental approaches to generate benchmark data for model validation, and potential applications of the model for prevention and protection against blast wave TBI.

A computational model coupling mechanics and electrophysiology in spinal cord injury

“…To the best of the knowledge of the authors and as suggested by a recent review (Gupta and Przekwas 2013), this model is the first of the kind. It is constituted of four main building blocks whose parameters have been taken from actual experiments, leaving only seven remaining free parameters.…”

“…Computational biomechanics simulations making use of finite element schemes have recently allowed for the identification of stress extrema and/or patterns at the tissue (Moore et al 2009;Nyein et al 2010;Cloots 2011;Cloots et al 2013;Gupta and Przekwas 2013) and cell scales (Jerusalem and Dao 2012) during TBI events (see these references for a complete literature review). Conversely, recent work building on the observation of "leaky" voltage-gated sodium ion channel after trauma (Wang et al 2009) has proposed a model of the resulting hyperpolarization-(left-)shifts of the ion channel current (Boucher et al 2012).…”

The Modeling of Shock-Wave Pressures, Energies, and Temperatures Within the Human Brain Due to Improvised Explosive Devices (IEDs) Using the Transport and Burgers' Equations

“…This graph, illustrating a solution for the Burgers' equation, is again non-linear. In Figure 7B, there is similar spatially-axial behavior, except for the periodicity and the presence of under-pressures with-respect-to time, the latter of which [8] suggests may be due to compression of the skull and recoil of the brain. However, the graph's solution-curve-like the Transport equation from which it is derived-is linear, as will be described in the section Preamble to Cauchy Problem when the equation is solved.…”

“…The authors' assertions here could be correctly founded, given that any phase difference in an emitted wave, possibly due to differing experimental setup, could conceivably affect the periodicity of the incoming, transmitted, and reflected waves' peaks and troughs. As suggested above, this may further tie in with the compression of the skull and recoil of the brain, [8], but in ways that are dictated by the physical positioning and directional nature of both the apparatus and the emitted waves, respectively. If this is so, then one could potentially explain either the presence or absence of apparently inconsistently occurring under-pressures that were previously unexplained.…”

“…At the time, the reasons for these apparent under-pressures were not clear, [8], but can be described, not only by application of more appropriate sinusoidal boundary conditions shown below, but also because of the reflection and transmission coefficients associated with each wave rebounding within the skull and brain. For example, it is known that when impact waves are reflected from a surface, they often display a trough immediately after rebounding (as opposed to the original incoming peak) due to the nature of the reflection coefficients vs. t and x.…”