## Abstract

This paper presents a coupled experimental/modeling study of the mechanical response of porcine brain under high strain rate loading conditions. Essentially, the stress wave propagation through the brain tissue is quantified. A Split-Hopkinson Pressure Bar (SPHB) apparatus, using a polycarbonate (viscoelastic) striker bar was employed for inducing compression waves for strain rates ranging from 50 – 750 s-1. The experimental responses along with high speed video showed that the brain tissue’s response was nonlinear and inelastic. Also, Finite Element Analysis (FEA) of the SHPB tests revealed that the tissue underwent a non-uniform stress state during testing when glue is used to secure the specimen with the test fixture. This result renders erroneous the assumption of uniaxial loading. In this study, the uniaxial volume averaged stress-strain behavior was extracted from the FEA to help calibrate inelastic constitutive equations.

## Introduction

Traumatic brain injury (TBI), due to mechanical insult of the head, is a leading cause of death and life-long disability in the United States. The Center for Disease Control (CDC) has estimated that, on average, 1.4 million Americans sustain TBI every year, 20% of which are the result of motor vehicle-traffic accidents. In order to develop effective protective measures, better knowledge of injury mechanisms and the corresponding biomechanics of injury development in the brain are needed. SPHB is a novel experimental set-up to test and study the mechanical behavior of brain at injurious (high strain rates) loading conditions.

Contour plots of the loading direction stress (${\sigma}_{33}$) at different stages of the true stress-stress curve at a compressive strain rate of 750 s-1. The specimen sample is a solid cylindrical disk and compressive ${\sigma}_{33}$ in the plot ordinate is treated as positive, while the contour level compressive ${\sigma}_{33}$are negative.
To effectively model TBI conditions, the material properties of the brain in the range susceptible to traumatic injuries need to be understood. The authors discovered no studies to date that address the mechanical response of the brain in the range of 50 -750 s-1.Consequently, our research goal is first to present high strain rate data for porcine brain at strain rates in the range 50 -750 s-1, and second to study the stress state and inertial effects of the specimen during a SHPB test using FEA. An additional goal is to verify the assertion of Song et al. (2007)[1] on specimen geometry modification to counter inertial effects during high strain rate compression.

## Materials and Methods

### Sample Preparation

Porcine heads of healthy pigs were procured from a local abattoir in Maben, MS. These porcine heads (covered in plastic wrapping) were then stored in an iced container (~42oF) and transported to Mississippi State University College of Veterinary Medicine, Starkville, MS. There, porcine brain samples were extracted and stored in containers filled with Phosphate Buffered Saline (PBS). PBS solution was chosen, because of its similar osmolarity and ion concentration as CSF (Prevost et al., 2010).These containers were then stored in a cooler (~45 oF) and transported to the Center for Advanced Vehicular Systems (CAVS) for sample preparation. Standard bio-hazard safety protocols were followed. Using a cylindrical die of 30mm inner diameter, brain samples were extracted and cut to an average thickness of 15mm (Figure A.3). This gave an aspect ratio of 0.5, which was based on the work conducted by Gray and Blumenthal (2000). Brain extractions and dissection required approximately 1 hour for completion, and all compression experiments were conducted within 3 hour post-mortem. In all, 20 porcine brains were used for testing, with 35 extracted viable samples that were tested. Due to the loss of samples in the experiments (sample problems, incision errors, variation in cross-section thickness and unsuccessful testing), results of 26 samples (that came from 15 porcine brains) were successfully obtained and used for the following analyses. Details of the samples obtained and porcine brains used along with testing conditions are given in Table 1. No preconditioning was performed for our testing as specified by Fung (1993) as quasi-static preconditioning has no meaning for high strain rate testing as conducted in this study.

## References

1. Song, B., Chen, W., Ge, Y., Weerasooriya, Y., (2007), “Dynamic and Quasi-static Compressive Response of Porcine Muscle,” J Biomech, 40 pp. 2999–3005.

Citation: R. Prabhu, M. F. Horstemeyer, J. Bouvard, J. Sherburn, L. N. William, E. B. Marin, J. Liao, (Mar 2011), “Coupled Experiment/Finite Element Simulation On High Rate Mechanical Response Of Porcine Brain”. (Accepted article, In press, Journal of The Mechanical Behavior of Biomedical Materials; [[1]])