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Genigraphics® has been producing output from PowerPoint® longer than anyone in the industry; dating back to when we helped Microsoft® design the PowerPoint® software. US and Canada: 1-800-790-4001 Email: info@genigraphics.com [This sidebar area does not print.] The Interaction of Fixed Compressive Deformation and Translational Shear Deformation in Rat Brain Tissue Lauren N. Leahy, Henry W. Haslach, Jr., Adam H. Hsieh University of Maryland – College Park Lauren Leahy University of Maryland – College Park Email: leahy@terpmail.umd.edu Contact 1. H. W. Haslach Jr., L. N. Leahy, P. Riley, R. Gullapalli, S. Xu, and A. H. Hsieh (2014). Solid - Extracellular Fluid Interaction and Damage in the Mechanical Response of Rat Brain Tissue under Confined Compression. Journal of the Mechanical Behavior of Biomedical Materials 29, 138-150. DOI 10.1016/j.jmbbm.2013.08.027 2. Henry W. Haslach, Jr. (2014). A Non-equilibrium Model for Rapid Finite Deformation of Hydrated Soft Biological Tissue in Uniaxial Confined Compression. Acta Mechanica. DOI 10.1007/s00707-014-1100-x 3. H. W. Haslach, Jr. (2005). Nonlinear Viscoelastic, Thermodynamically Consistent, Models for Biological Soft Tissue. Biomechanics and Modeling in Mechanobiology 3, 172 - 189 4. D. Van Essen (1997). A tension-based theory of morphogenesis and compact wiring in the central nervous system. Nature 385, 313-318. 5. A. Verkman (2013). Diffusion in the extracellular space in brain and tumors. Physical Biology 10, 1-8. References Brain tissue is a biphasic material, consisting of both solid and fluid matter that is not naturally load bearing. It is unknown how the solid and fluid parts interact when the tissue experiences a mechanical insult or how this interaction can lead to physical damage. Extracellular fluid, comprising about 20% of the brain’s volume, may interact with the solid matter when the tissue is under an external mechanical insult. Introduction Unconfined Compression: These tests provide information about the ECF-solid phase interaction in which the ECF-flow is multi-axial. Applying deformation to the tissue disrupts its equilibrium balance of hydrostatic pressure. The lateral dimension changes are measured as the specimen is compressed to indicate that the tissue is compressible due to ECF loss. The speed of relaxation is measured by the stress relaxation fraction defined as the fraction of stress recovered at 60 seconds. The stress relaxation fraction is greater for tests performed at a faster rate. Combined Linear Translational Shear and Unconfined Compression: Brain tissue can experience internal deformation waves which consist of both longitudinal and shear components simultaneously (translational shear and compressive waves). Unconfined compression is applied before the translational shear test is applied due to fixture machine limitations. The residual normal stresses are estimated from the unconfined compression tests after 60 seconds of relaxation. The influence of extracellular fluid on the mechanical response appears as traits in the stress strain graphs under different testing variables. Shear stress increases when there is either an increase in deformation rate or compression percentage. The relaxation speed is greater for faster deformation rate tests which can be seen in the comparison of figure 5 and 6. The specimens that are not compressed tend to have a stress response that is concave up (Fig. 12), indicating hardening, which increases in concavity with respect to an increase in deformation rate. The specimens that are compressed prior to shear deformation tend to have more linear and slightly concave down stress responses (Fig. 13). Hypothesis Methods and Materials Unconfined Compression: During unconfined compression tests, the tissue’s interstitial fluid may move in all directions within the tissue causing transverse stress due to the drag force between the fluid and solid phase. The compression may increase the hydrostatic pressure and induce axonal stretching. The solid matter’s resistance of ECF flow is possibly caused by the further restriction of extracellular space in the compressed tissue. Combined Linear Translational Shear and Unconfined Compression: Since the unconfined compression causes a residual normal stress prior to the shear deformation, the principal stress directions are not parallel and perpendicular to the test plates because these tests are not in simple shear. The speed of relaxation which is likely directly linked to the ECF flow is greater after a faster deformation rate than a slow rate and exceeds the relaxation speed of axons when in tension. The faster relaxation rate is possibly due to a higher ECF hydrostatic pressure induced from the faster deformation rate that drives the ECF redistribution which is usually assumed responsible for the relaxation in stress. The relaxation rate of the compressed tests may be explained by the compressive pressure which may force the ECF into substructures of the tissue and may expand the extracellular space, changing the tortuosity of the tissue. This could allow the fluid to flow more freely when redistributing. These tests also verify that under combined shear and compression the stress response is rate dependent, as is well known. Combined Sinusoidal Translational Shear and Unconfined Compression: One interpretation is that, in vivo, the ECF reduces the shear stress on the cells and helps protect the cells during everyday motions of the head. The fluid resists the shear deformation which is resisted even more drastically with a faster deformation rate or a larger deformation. The hydrostatic pressure due to the compression could stiffen the shear stress magnitude by increasing the tensions in the neuronal axons and glial processes that maintain the shape of the tissue and resist sliding of the solid components. The “shoulder” portrayed in the compression sinusoidal tests could be related to an artifact known as a “toe” in other biomaterials when experiencing an axial deformation. This phenomenon is likely linked to the viscoelastic properties of the tissue and the interaction of the ECF and the solid matter. The two set sinusoidal tests show that something is changing within the material during the dwell time. The fluid likely changed the tortuosity of the material due to the initial loading which may have caused axonal stretching or other forms of damage. Damage would affect the internal flow pathways for the fluid which would affect the mechanical response. It is currently hypothesized that during the initial loading, damage in the form of gaps within the tissue may have formed. Due to the pressure difference between the fluid and the gaps, the fluid would redistribute during the dwell time. Once the gaps have filled with fluid and the second round of cycles begins, the pressure for the extra fluid within these gaps rises much more so than the original set of cycles. Discussion ECF behavior strongly influences the mechanical viscoelastic response of rat brain cerebrum tissue due to an applied deformation. The ECF behavior may be directly linked to the initial mechanical mechanism that induces damage within brain tissue that may lead to mTBI. Conclusions One mechanical cause of tissue damage under an external mechanical insult is increased hydrostatic pressure in, and pathological flow of, the extracellular fluid (ECF) that may stretch axons, rupture cells, disassociate axonal-glial interconnections, or produce relative motion of substructures in the heterogeneous tissue. Results Figure 3. (Left) BOSE unconfined compression apparatus Figure 4. (Right) BOSE translational shear apparatus Figure 1. (Left) Specimen that are the full length of the cerebrum shows heterogeneity of tissue tested. Figure 2. (Right) Rat Brain Schematic Combined Sinusoidal Translational Shear and Unconfined Compression: Sinusoidal tests simulate the longitudinal and shear components which exist due to an internal deformation wave. The response of the stress is nonsymmetrical and quasi-periodic for both compressed and non-compressed specimens. The time shift between the displacement and the stress response changes between cycles. “Shoulders” are present in the compressed tests which could be due to the increase in hydrostatic pressure from the compression applied prior to testing. The stress response amplitudes to sinusoidal translational shear decrease on subsequent cycles in an exponential manner. An increase in displacement amplitude correlates to an increase in the stress peaks. An increase in compression correlates to an increase in the stress peaks. A larger displacement amplitude creates a stress response in which the peaks drop more quickly within the first few cycles. (Fig. 7,8,9,10) Figure 5. (Left) Combined linear translational shear and unconfined compression (33%) at 0.001/s strain rate. Figure 6. (Right) Combined linear translational shear and unconfined compression (33%) at 1/s strain rate. Sinusoidal tests were performed with multiple sets of cycles, 10 sinusoidal displacement controlled periods followed by a dwell that holds the displacement at 0 then the 10 sinusoidal cycles are repeated. It is hypothesized that the fluid redistributes during a dwell time in between the sets of cycles which accounts for a change in the mechanical response between the sets of cycles (Fig. 14). Figure 11. Unconfined Compression 1/s k= 0.01887, E= 120.4 Pa Figure 12. Translational Shear 0% compression, 1/s Figure 13. Combined Translational Shear And Unconfined Compression 33% compression, 0.001/s Figure 7. (Left, Top) Stress response to sinusoidal translational shear at 1Hz, 0% Compression, 12.5% strain Figure 8. (Right Top) Stress response to 1Hz, 33% compression, 12.5% strain Figure 9. (Left, Bottom) Stress response to 1Hz, 0% compression, 25% strain Figure 10. (Right, Bottom) Stress response to 1Hz, 33% compression, 25% strain Figure 14. Translational sinusoidal shear at 1Hz, 0% compression, 25% strain, 120s dwell time.