Using Homogenization by Asymptotic Expansion for Micro – Macro Behavior Modeling of Traumatic Brain Injury

Bridging veins are frequently damaged in traumatic brain injury. These veins are prone to rupture in their subdural portion upon head impact, due to brain-skull relative motion, giving rise to an acute subdural hematoma. To understand the biomechanical characteristics of this hematoma, we take into account the periodical distribution of bridging veins in the sagittal plane. This allowed the use of the method of homogenization by asymptotic expansion to calculate the homogenized elastic properties of the brain-skull interface region. The geometry of this zone was simplified and a representative volume element was developed comprising: sinus, bridging vein, blood circulating inside them, surrounding cerebrospinal fluid and tissues. The heterogeneous elementary cell is transformed to an anisotropic homogenous equivalent medium and the homogenized elastic properties were calculated. The macroscopic homogenized properties resulted from the current study can be incorporated into a finite element model of the human head at macroscopic scale. The main results of this homogenization theory are the calculation of the local stress field into the elementary cell, as well as its homogeneous anisotropic properties at the macroscopic scale.