Hydrodynamic Modeling of Cerebrospinal Fluid Motion Within the Spinal Cavity

Abstract

The fluid that resides within cranial and spinal cavities, cerebrospinal fluid (CSF), moves in a pulsatile fashion to and from the cranial cavity. This motion can be measured by magnetic resonance imaging (MRI) and may be of clinical importance in the diagnosis of several brain and spinal cord disorders such as hydrocephalus, Chiari malformation, and syringomyelia. In the present work, a geometric and hydrodynamic characterization of an anatomically relevant spinal canal model is presented. We found that inertial effects dominate the flow field under normal physiological flow rates. Along the length of the spinal canal, hydraulic diameter was found to vary significantly from 5 to 15 mm. The instantaneous Reynolds number at peak flow rate ranged from 150 to 450, and the Womersley number ranged from 5 to 17. Pulsatile flow calculations are presented for an idealized geometric representation of the spinal cavity. A linearized Navier–Stokes model of the pulsatile CSF flow was constructed based on MRI flow rate measurements taken on a healthy volunteer. The numerical model was employed to investigate effects of cross-sectional geometry and spinal cord motion on unsteady velocity, shear stress, and pressure gradient fields. The velocity field was shown to be blunt, due to the inertial character of the flow, with velocity peaks located near the boundaries of the spinal canal rather than at the midpoint between boundaries. The pressure gradient waveform was found to be almost exclusively dependent on the flow waveform and cross-sectional area. Characterization of the CSF dynamics in normal and diseased states may be important in understanding the pathophysiology of CSF related disorders. Flow models coupled with MRI flow measurements may become a noninvasive tool to explain the abnormal dynamics of CSF in related brain disorders as well as to determine concentration and local distribution of drugs delivered into the CSF space.