Modeling of the transient cerebrospinal fluid flow under external impacts

Abstract

In this paper, a theoretical model is developed to describe the cerebrospinal fluid (CSF) flow in the subarachnoid space as the head is exposed to sudden external impacts. Although extensive study has been performed, there is a lack of understanding of the transient CSF flow and its critical role in the concussion process. The problem involves a solid object, i.e. brain matter, bathed in a liquid environment, i.e. CSF, and enclosed in a rigid container, i.e. the skull. The relative motion of the inner object to the container causes a squeezing flow on one side of the object, and an expanding flow on the other side. The fluid pressure response underlies the damping effect on the object. To capture these features, both the inner object and the outer container are modeled as cylinders of different sizes. Constant acceleration is imposed on the container. The pressurization of the fluid and the resultant motion of the inner cylinder are analytically predicted. It shows that the relative motion of the inner object is very sensitive to the gap thickness and the density difference between the object and the surrounding liquid. The squeeze-damping effect of the CSF can effectively prevent direct contact between the inner object and the container. The paper presented herein, solving a fundamental fluid mechanics problem, reveals the critical physics involved in the response of the brain matter to external impacts on the head. It also provides interesting insights on the development of a new type of vibration isolation system for biomimetic applications.