A Viscoelastic Model for High Strain Rate Loading of the Human Calvarium

Brain injury resulting from exposure to blast continues to be a significant problem in the military community. In order to understand the response of the human brain under various high-rate mechanical insults to the head, the way in which the load is transmitted through the skull must be accurately characterized. The bones of the human calvarium comprise a sandwich structure with two dense layers of cortical bone separated by porous cancellous bone. Although the high strain-rate behavior of human calvarium cortical bone has been previously studied, the viscoelasticity of the porous diploe layer has remained to be characterized. Due to the presence of fluids in the porous layer, the diploe may be expected to exhibit considerable strain-rate related stiffening and dissipative properties. The primary objective of this dissertation is to investigate the viscoelasticity of the calvarium at strain-rates characteristic of blast loading.
For modeling the stiff bending response while retaining accurate through-the-thickness response of the calvarium sandwich structure, it is essential to describe the thicknesses and mechanical properties of the individual layers. As a secondary objective, the layer thicknesses and how they vary across the calvarium, which is unavailable in the literature, was studied through micro computed tomography (μCT) of through-the-thickness cylindrical samples (cores) from the calvarium using an objective methodology of distinction of the three layers. It was established that the outer cortical table is at an average 68% thicker than the inner.
The same cores were tested under dynamic compression and cyclic compression-tension loading (1 to 20 kHz) in the direction normal to the surface of the skull, for obtaining viscoelastic properties of the calvarium. These composite properties, which included the contribution of the two cortical layers and the diploe layer, were decomposed into effective properties of the individual layers using geometrically accurate FE models of the composite core specimens built using their μCT images.
Dynamic tension tests were conducted on coupon samples from the cortical layer. Two phase micro finite element (µFE) models specific to each tested coupon, developed from their μCT images, were used to account for specimen porosity and identify the Young’s modulus of the bone phase (18.5 ± 3.5 GPa) through optimization to match the coupon structural response (12.0 ± 3.3 GPa). The cortical modulus was found to vary between the superior and inferior aspects of the calvarium. These properties were used in the cortical layers of the FE models of the cores for derivation of the effective viscoelastic properties of the diploe layer. Interestingly, the effective diploe layer quasi-static modulus (273 ± 125 MPa) and the fractional viscoelastic modulus (3.3 ± 1.2) varied between the frontal and parietal bones. The extent of viscoelastic stiffening of the porous diploe layer is much greater than that observed for cortical bone and it was capable of dissipating far more energy. The viscoelastic model of the calvarium, including the material properties and geometric measurements, developed in this study can be used by researchers to accurately model the effect of blast on the human brain for understanding the mechanism of blast-induced traumatic brain injury.
A simplified plane-strain FE model using the layer thicknesses and properties found in this study showed that viscoelasticity of the calvarium and it’s between subjects variation may have very little influence on brain deformation caused by blast. On the other hand variation in calvarium layer thicknesses could result in substantial change of brain deformation, caused by blast. The effect of variation in layer thicknesses was found to be comparable to the combined influence of the scalp and the cerebrospinal fluid layers.