Computational modeling of brain tissue biomechanics at high strain rates
Abstract
Traumatic brain injury (TBI) has become a significant public health concern. However, despite decades of biomechanics and pathology research, the exact mechanism of injury is poorly understood. Because the injury is inherently mechanical, an accurate description of brain tissue mechanics is essential to better understanding and preventing TBI. Historically, brain tissue has been modeled as a linear or nonlinear viscoelastic material. However, the extracellular fluid in brain tissue is believed to significantly impact the stress distributions and deformations at higher strain rates, such as would occur during an impact or blast injury. Nevertheless, few studies have examined brain tissue as a porous material, and none have employed a nonlinear porous description. In the present work, the theoretical basis for describing gray matter is discussed. As a side-development, it is shown that the two classical porous material theories–Biot's poroelastic theory and continuum mixture theory–are in fact derived from the same thermodynamic constraints and are equivalent. Subsequently, the numerical methods available to simulate brain tissue mechanics are discussed in detail. Ultimately, the finite element method was selected, and a new quadratic, axisymmetric element is developed. The new element is validated against a one-dimensional wave propagation problem. The primary application of the new finite element code is to determine the material properties of gray matter based on highs strain rate compression experimental data. An inverse approach is presented, which resulted in a best fit with mean absolute percent error of approximately 58%. Despite the high error, the model successfully demonstrated that the use of a porous media model captures key features of high strain rate compression behavior in brain tissue and better unifies the quasistatic and high strain rate stress-strain response. The finite element model is also applied to explore two aspects of brain tissue mechanics. First, a series of simulations at various strain rates are evaluated in order to determine the range of strain rates in which the behavior of brain tissue diverges substantially from a polymeric solid. Subsequently, a model of wave propagation in a cylinder of brain tissue is described, and the pressure wave attenuation and frequency response of are evaluated. The successful development of a nonlinear, porous material finite element description of brain tissue represents an improvement in the available analytical tools for studying brain tissue mechanics. Further development and application of the methods presented here may help improve understanding of the brain's response under impact loading and ultimately allow for the development of better preventative technologies.
Degree
Ph.D.
Advisors
Nauman, Purdue University.
Subject Area
Mechanics|Mechanical engineering|Biomechanics
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