Influence of high deformation rate, brain region, transverse compression, and specimen size on rat brain shear stress morphology and magnitude.

An external mechanical insult to the brain, such as a blast, may create internal stress and deformation waves, which have shear and longitudinal components that can induce combined shear and compression of the brain tissue. To isolate the consequences of such interactions for the shear stress and to investigate the role of the extracellular fluid in the mechanical response, translational shear stretch at 10/s, 60/s, and 100/s translational shear rates under either 0% or 33% fixed transverse compression is applied without preconditioning to rat brain specimens. The specimens from the cerebrum, the cerebellum grey matter, and the brainstem white matter are nearly the full length of their respective regions. The translational shear stress response to translational shear deformation is characterized by the effect that each of four factors, high deformation rate, brain region, transverse compression, and specimen size, have on the shear stress magnitude averaged over ten specimens for each combination of factors. Increasing the deformation rate increases the magnitude of the shear stress at a given translational shear stretch, and as tested by ANOVAs so does applying transverse fixed compression of 33% of the thickness. The stress magnitude differs by the region that is the specimen source: cerebrum, cerebellum or brainstem. The magnitude of the shear stress response at a given deformation rate and stretch depends on the specimen length, called a specimen size effect. Surprisingly, under no compression a shorter length specimen requires more shear stress, but under 33% compression a shorter length specimen requires less shear stress, to meet a required shear deformation rate. The shear specimen size effect calls into question the applicability of the classical shear stress definition to hydrated soft biological tissue.

Crack Propagation and Its Shear Mechanisms in the Bovine Descending Aorta.

Aortic dissection and rupture may involve circumferential shear stress in the circumferential-longitudinal plane. Inflation of bovine descending aortic ring specimens provides evidence of such shear from the non-uniform circumferential distortion of radial lines drawn on the circumferential-radial ring face. Delamination without tensile peeling induces cracks that propagate nearly circumferentially in the circumferential-longitudinal plane from the root of a radial cut representing rupture initiation in a ring. Translational shear deformation tests of small rectangular aortic wall blocks in the circumferential and longitudinal direction measure the consequences of such shear on substructures in the aortic wall, in particular the collagen fibers. The two directions of shear deformation produce no statistical difference in the shear stress response of the wall. Possibly, the interfiber connections between collagen fibers are put into tension by either translational shear deformation so that the stress measured reflects the tensile response of these connections. Wall rupture may involve failure of these connections; such failure is supported by the voids parallel to the collagen fibers observed in a histological study after translational shear. Further, interstitial fluid is redistributed by shear as evidenced by the measured weight loss of a set of specimens during the translational shear of blocks. Because the mass changes, mathematical modeling of aortic tissue in vitro as incompressible is an approximation. These observations suggest that no simple modification of classical rupture theories, whether based on energy functions, stress or strain, suffices to predict the rupture of hydrated soft biological tissue that has complex substructures.

Transient solid-fluid interactions in rat brain tissue under combined translational shear and fixed compression.

An external mechanical insult to the brain may create internal deformation waves, which have shear and longitudinal components that induce combined shear and compression of the brain tissue. To isolate such interactions and to investigate the role of the extracellular fluid (ECF) in the transient mechanical response, translational shear stretch up to 1.25 under either 0 or 33% fixed normal compression is applied without preconditioning to heterogeneous sagittal slices which are nearly the full length of the rat brain cerebrum. The normal stress contribution is estimated by separate unconfined compression stress-stretch curves at 0.0667/s and 1/s engineering strain rates to 33% strain. Unconfined compression deformation causes lateral dimension expansion less than that predicted for an incompressible material under large deformation and often a visible loss of internal fluid from the specimen so that the bulk brain tissue is not incompressible in vitro, as sometimes assumed for mathematical modeling. The response to both slow 0.001/s and moderate 1/s shear translational stretch rates is deformation rate dependent and hardening under no compression but under 33% compression is nearly linear perhaps because of increased solid-solid friction. Both shear and normal stress relaxation are faster after the fast rate deformation possibly because higher deformation rates produce higher ECF hydrostatic pressure that primarily drives stress relaxation. The experimental results on ECF behavior guide the form of our nonlinear viscoelastic mathematical model. Our data are closely fit by non-equilibrium evolution equations that involve at most three specimen-specific empirical parameters and that are based on the idea that stretch of axons and glial processes resists load-induced ECF pressure.

Solid-extracellular fluid interaction and damage in the mechanical response of rat brain tissue under confined compression.

The mechanical processes that underlie mild traumatic brain injury from physical insults are not well understood. One aspect in particular that has not been examined is the tissue fluid, which is known to be critical in the mechanical function of other organs. To investigate the contributions of solid-fluid interactions to brain tissue mechanics, we performed confined compression tests, that force the extracellular fluid (ECF) to flow in the direction of the deformation, on 6.35mm diameter, 3mm long cylindrical samples excised from various regions of rat brains. Two types of tests in deformation control, (1) quasi-static, slow and moderate constant strain rate tests at 0.64×10(-5)/s, 0.001/s and 1/s to large strains and (2) several applications of slow linear deformation to 5% strain each followed by stress relaxation are employed to explore the solid-fluid interaction. At slow and moderate compressive strain rates, we observed stress peaks in the applied strain range at about 11%, whose magnitudes exhibited statistically significant dependence on strain rate. These data suggest that the ECF carries load until the tissue is sufficiently damaged to permit pathological fluid flow. Under the slow ramp rate in the ramp-relaxation cycles protocol, commonly used to estimate permeability, the stress relaxes to zero after the first cycle, rather than to a non-zero equilibrium stress corresponding to the applied strain, which further implicates mechanical damage. Magnetic resonance imaging (MRI) of changes in tissue microstructure during confined compression, before and after compression, provides further evidence of tissue damage. The solid-fluid interactions, reflected in the morphology of the stress-stretch curves and supported by the MRI data, suggest that increases in hydrostatic pressure in the ECF may contribute to mechanical damage of brain tissue.