A Mathematical Head/Brain Model for Investigation of Damping Characteristics of SAS in Low Velocity Head Impacts

摘要

Blunt head impact arising from vehicular collisions, sporting injuries, and falls leads to relative motion between the brain and skull and an increase in contact and shear stresses in the meningeal region, and leading to traumatic brain injuries. While there have been many finite element studies of the brain/head models there are limited analytical models. The goal of the present paper is to mathematically model subarachnoid space (SAS) and the meningeal layers and to investigate the motion of the brain relative to the skull, and their damping characteristics, during blunt head impacts. Based on the experimental studies of Hardy et al [6] the elasticity of the springs and damping constants of the dashpots were determined. The nonlinear governing integro-differential equations were formed and solved. The results of the analytical method are validated by performing an explicit finite element analysis. Acceptable agreement between these two methods is observed. The elastic deformation of the spherical shell, the brain motion during the impact, and contact conditions between the brain and the skull were determined. The results were also compared with experimental studies on Nahum [7], The results give the contact threshold of the skull/brain, and represent the relevant velocity of this event. It was concluded that the proposed analytical model is a reliable model to parametrically study the damping characteristic of the head/brain system.