Traumatic brain injuries, the leading cause of death and disability in children and young adults, are the result of a rapid acceleration or impact of the head. In recent years, a global effort to better understand the biomechanics of TBI has been undertaken, with many laboratories creating detailed computational models of the head and brain. For these models to produce realistic results they require accurate regional constitutive data for brain tissue. However, there are large differences in the mechanical properties reported in the literature. These differences are likely due to experimental parameters such as specimen age, brain region, species, test protocols, and fiber direction which are often not reported. Furthermore, there is a dearth of reported viscoelastic properties for brain tissue at large-strain and high rates. Mouse, rat, and pig brains are impacted at 10/s to a strain of ~36% using a custom-built micro-indenter with a 125 μm radius. It is shown that the resultant mechanical properties are dependent on specimen-age, species, and region, under identical experimental parameters.
We show that porcine brain matter can be modelled accurately as a very soft rubberlike material using the Mooney-Rivlin strain energy function, up to strains as high as 60%. This result followed from simple shear experiments performed on small rectangular fresh samples (2.8 cm 3 and 1.2 cm 3 ) at quasi-static strain rates. They revealed a linear shear stress-shear strain relationship (R 2 > 0.97), characteristic of Mooney-Rivlin materials at large strains. We found that porcine brain matter is about 30 times less resistant to shear forces than a silicone gel. We also verified experimentally that brain matter exhibits the positive Poynting e↵ect of nonlinear elasticity, and numerically that the stress and strain fields remain mostly homogeneous throughout the thickness of the samples in simple shear.
The classical flexure problem of non-linear incompressible elasticity is revisited assuming that the bending angle suffered by the block is specified instead of the usual applied moment. The general momentbending angle relationship is then obtained and is shown to be dependent on only one non-dimensional parameter: the product of the aspect ratio of the block and the bending angle. A Maclaurin series expansion in this parameter is then found. The first-order term is proportional to µ, the shear modulus of linear elasticity; the second-order term is identically zero, because the moment is an odd function of the angle; and the third-order term is proportional to µ(4β −1), where β is the non-linear shear coefficient, involving third-order and fourth-order elasticity constants. It follows that bending experiments provide an alternative way of estimating this coefficient, and the results of one such experiment are presented. In passing, the coefficients of Rivlin's expansion in exact non-linear elasticity are connected to those of Landau in weakly (fourth-order) non-linear elasticity.
The brain is a complex organ made up of many different functional and structural regions consisting of different types of cells such as neurons and glia, as well as complex anatomical geometries. It is hypothesized that the different regions of the brain exhibit significantly different mechanical properties, which may be attributed to the diversity of cells and anisotropy of neuronal fibers within individual brain regions. The regional dynamic mechanical properties of P56 mouse brain tissue in vitro and in situ at velocities of 0.71–4.28 mm/s, up to a deformation of 70 μm are presented and discussed in the context of traumatic brain injury. The experimental data obtained from micro-indentation measurements were fit to three hyperelastic material models using the inverse Finite Element method. The cerebral cortex elicited a stiffer response than the cerebellum, thalamus, and medulla oblongata regions for all velocities. The thalamus was found to be the least sensitive to changes in velocity, and the medulla oblongata was most compliant. The results show that different regions of the mouse brain possess significantly different mechanical properties, and a significant difference also exists between the in vitro and in situ brain.
Shearing is induced in soft tissues in numerous physiological settings. The limited experimental data available suggest that a severe strain-stiffening effect occurs in the shear stress when soft biological tissues are subjected to simple shear in certain directions. This occurs at relatively small amounts of shear (when compared with the simple shear of rubbers). This effect is modelled within the framework of nonlinear elasticity by consideration of a class of incompressible anisotropic materials. Owing to the large stresses generated for relatively small amounts of shear, particular care must be exercised in order to maintain a homogeneous deformation state in the bulk of the specimen. The results obtained are relevant to the development of accurate shear test protocols for the determination of constitutive properties of soft tissues. It is also demonstrated that there is a fundamental ambiguity in determining the normal stresses in simple shear when soft tissues are modelled as incompressible hyperelastic materials owing to the arbitrary nature of the hydrostatic pressure term. Two physically well-motivated approaches to determining the pressure are presented here, and the resulting hydrostatic stresses are compared and contrasted. The possible generation of cavitational damage owing to critical hydrostatic stress levels is briefly discussed.
A constitutive model based on an assumption regarding the general response to hydrostatic pressure is proposed for the moderate deformations of slightly compressible (or nearly incompressible) rubber. It is shown that an excellent fit is obtained with the available experimental data for a particularly simple form of strain-energy density. The data considered are from those material characterization tests that involve only moderate deformations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.