A Multi-Scale Finite Element Model for Shock Wave-Induced Axonal Brain Injury

Abstract

Traumatic brain injuries (TBIs) involve a significant portion of human injuries resulting from a wide range of civilian accidents as well as many military scenarios. Axonal damage is one of the most common and important pathologic features of traumatic brain injury. Axons become brittle when exposed to rapid deformations associated with brain trauma. Accordingly, rapid stretch of axons can damage the axonal cytoskeleton, resulting in a loss of elasticity and impairment of axoplasmic transport. Subsequent swelling of the axon occurs in discrete bulb formations or in elongated varicosities that accumulate organelles. Ultimately, swollen axons may become disconnected [1]. The shock waves generated by a blast, subject all the organs in the head to displacement, shearing and tearing forces. The brain is especially vulnerable to these forces — the fronts of compressed air waves cause rapid forward or backward movements of the head, so that the brain rattles against the inside of the skull. This can cause subdural hemorrhage and contusions. The forces exerted on the brain by shock waves are known to damage axons in the affected areas. This axonal damage begins within minutes of injury, and can continue for hours or days following the injury [2]. Shock waves are also known to damage the brain at the subcellular level, but exactly how remains unclear. Kato et al., [3] described the effects of a small controlled explosion on rats’ brain tissue. They found that high pressure shock waves led to contusions and hemorrhage in both cortical and subcortical brain regions. Based on their result, the threshold for shock wave-induced brain injury is speculated to be under 1 MPa. This is the first report to demonstrate the pressure-dependent effect of shock wave on the histological characteristics of brain tissue. An important step in understanding the primary blast injury mechanism due to explosion is to translate the global head loads to the loading conditions, and consequently damage, of the cells at the local level and to project cell level and tissue level injury criteria towards the level of the head. In order to reach this aim, we have developed a multi-scale non-linear finite element modeling to bridge the micro- and macroscopic scales and establish the connection between microstructure and effective behavior of brain tissue to develop acceptable injury threshold. Part of this effort has been focused on measuring the shock waves created from a blast, and studying the response of the brain model of a human head exposed to such an environment. The Arbitrary Lagrangian Eulerian (ALE) and Fluid/Solid Interactions (FSI) formulation have been used to model the brain-blast interactions. Another part has gone into developing a validated fiber-matrix based micro-scale model of a brain tissue to reproduce the effective response and to capturing local details of the tissue’s deformations causing axonal injury. The micro-model of the axon and matrix is characterized by a transversely isotropic viscoelastic material and the material model is formulated for numerical implementation. Model parameters are fit to experimental frequency response of the storage and loss modulus data obtained and determined using a genetic algorithm (GA) optimizing method. The results from macro-scale model are used in the micro-scale brain tissue to study the effective behavior of this tissue under injury-based loadings. The research involves the development of a tool providing a better understanding of the mechanical behavior of the brain tissue against blast loads and a rational multi-scale approach for driving injury criteria.