An asymptotic method for the prediction of the anisotropic effective elastic properties of the cortical vein: superior sagittal sinus junction embedded within a homogenized cell element

Abstract

Bridging veins (BVs) are frequently damaged in traumatic brain injury due to brain-skull relative motion. These veins, connected to the superior sagittal sinus (SSS), are prone to rupture upon head impact giving rise to an acute subdural hematoma (ASDH). We modeled the biomechanical characteristics of ASDH to study the behavior of the SSS-BVs compound with its surrounding medium. The almost periodic distribution of the BVs along the SSS allowed the use of the homogenization method based on asymptotic expansion to calculate the effective elastic properties of the brain-skull interface region. The representative volume element (RVE) under study is an anisotropic equivalent medium with homogenized elastic properties, accounting for the variations of each constituent's mechanical properties. It includes the sinus, the BVs and blood, and the surrounding cerebrospinal fluid and tissue. The results show large variations in the RVE anisotropic properties depending on each constituent of the BV and, to a certain extent, on the variability of the surrounding constituents' mechanical properties.