Modeling of the brain movement and cerebrospinal fluid flow within porous subarachnoid space under translational impacts

Traumatic brain injury remains a significant global health concern, requiring advanced understanding and mitigation strategies. In current brain concussion research, there is a significant knowledge gap: the critical role of transient cerebrospinal fluid (CSF) flow in the porous subarachnoid space (SAS) has long been overlooked. To address this limitation, we are developing a simplified mathematical model to investigate the CSF pressurization in the porous arachnoid trabeculae and the resulting motion of brain matter when the head is exposed to a translational impact. The model simplifies the head into an inner solid object (brain) and an outer rigid shell (skull) with a thin, porous fluid gap (SAS). The CSF flow in the impact side (coup region) and the opposite side (contrecoup region) is modeled as porous squeezing and expanding flows, respectively. The flow through the side regions, which connect these regions, is governed by Darcy's law. We found that the porous arachnoid trabeculae network significantly dampens brain motion and reduces pressure variations within the SAS compared to a SAS without the porous arachnoid trabeculae (AT). This effect is particularly pronounced under high-frequency, periodic acceleration impacts, thereby lowering the risk of injury. The dampening effect can be attributed to the low permeability of the AT, which increases resistance to fluid movement and stabilizes the fluid and pressure responses within the SAS, thereby reducing extreme pressure fluctuations and brain displacement under impact. This work provides a foundational understanding of CSF flow dynamics, paving the way for innovative approaches to brain injury prevention and management.