Modelling and direct numerical simulation of flow and solute dispersion in the spinal subarachnoid space.

Abstract The motion of the cerebrospinal fluid in the spinal subarachnoid space, a slender annular canal surrounding the spinal cord, exhibits an oscillatory velocity component driven by the pressure oscillations induced by the cardiac and respiratory cycles. A time-averaged transport equation has been recently proposed for describing solute transport along the canal, circumventing the need to compute the concentration fluctuations resulting from this fast oscillatory motion. The accuracy and limitations of this time-averaged description are tested here by means of comparisons with results of direct numerical simulations spanning hundreds of oscillation cycles, as needed to generate significant dispersion of the solute. The comparisons between the numerical results and the predictions of the analytical model include velocity fields and quantifications of transient solute-dispersion events for selected values of the flow parameters and two different idealized, canonical geometries of the spinal canal. The comparisons clearly demonstrate the accuracy of the time-averaged description of the analytical model, which is seen to provide a good fidelity at a fraction of the computational cost involved in the direct numerical simulations. The variations of canal eccentricity along the spinal canal are found to play an important role in the dynamics of the solute transport, leading to the emergence of closed recirculating Lagrangian vortices that may hinder solute dispersion along the canal, as revealed by both direct numerical simulations and time-averaged results.