A one-dimensional model for the pulsating flow of cerebrospinal fluid in the spinal canal

The monitoring of intracranial pressure (ICP) fluctuations, which is needed in the context of a number of neurological diseases, requires the insertion of pressure sensors, an invasive procedure with considerable risk factors. Intracranial pressure fluctuations drive the wave-like pulsatile motion of cerebrospinal fluid (CSF) along the compliant spinal canal. Systematically derived simplified models relating the ICP fluctuations with the resulting CSF flow rate can be useful in enabling indirect evaluations of the former from non-invasive magnetic resonance imaging (MRI) measurements of the latter. As a preliminary step in enabling these predictive efforts, a model is developed here for the pulsating viscous motion of CSF in the spinal canal, assumed to be a linearly elastic compliant tube of slowly varying section, with a Darcy pressure-loss term included to model the fluid resistance introduced by the trabeculae, which are thin collagen-reinforced columns that form a web-like structure stretching across the spinal canal. Use of Fourier-series expansions enables predictions of CSF flow rate for realistic anharmonic ICP fluctuations. The flow rate predicted using a representative ICP waveform together with a realistic canal anatomy is seen to compare favourably with in vivo phase-contrast MRI measurements at multiple sections along the spinal canal. The results indicate that the proposed model, involving a limited number of parameters, can serve as a basis for future quantitative analyses targeting predictions of ICP temporal fluctuations based on MRI measurements of spinal-canal anatomy and CSF flow rate.