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.

Keywords: biomechanics; blast injury; mathematical model; neurobiology; traumatic brain injury.

Figure 1

(A) Ideal shock wave pressure profile (Friedlander curve) and (B) example of complex overpressure pattern inside a vehicle subjected to a blast mine (NATO, 2007).

Figure 2

CFD simulation of a blast wave impacting a sold block; four time instances of pressure fields showing shock reflection from the front face, diffraction around the block, and back reflection behind the block.

Figure 3

Coupled simulations of CFD blast wave and FEM biomechanics of a human head. Pressure profiles in the air and in the brain during intracranial pressure wave penetration. Note that the intracranial pressure wave is faster than the incident shock wave in the air.

Figure 4

Schematic of brain-CSF interaction in linear and rotational acceleration.

Figure 5

A schematic of time-structured secondary brain injury mechanisms and potential windows for pharmacological intervention.

Figure 6

Schematic of the simulation framework, tools and interfaces, and expected results.

Figure 7

3D Anatomical/geometric models of a human body and head, and a virtual rat.

Figure 8

Whole body cardiovascular system model “embedded” in the tissue biomechanics model used to study blast-induced elastic waves.

Figure 9

Example coupled CFD-FEM simulation results of a blast wave diffraction around, and transmission through a human head. A sequence of four time instances.

Figure 10

Whole body multi-compartmental human cardiovascular system and the cerebral perfusion (circle of Willis) models.

Figure 11

Integrated biomechanical, electrokinetic, and metabolic model of an in vitro neuron exposed to mechanical stretching.

Figure 12

A human head phantom in the shock tube for testing blast wave loading (Przekwas et al., 2011).