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.

脑脊液在蛛网膜下腔，即围绕脊髓的细长环形通道中的运动，表现出由心动周期和呼吸周期引起的压力振荡驱动的振荡速度分量。最近提出了一个时均运移方程来描述沿运河的溶质运移，从而避免了计算由这种快速振荡引起的浓度波动的需要。在此，通过与跨越数百个振荡周期的直接数值模拟的结果进行比较，来测试此时间平均描述的准确性和局限性，以生成溶质的显着分散。数值结果与分析模型的预测结果之间的比较包括流速场和流动参数选定值的瞬态溶质弥散事件的量化，以及两种不同的理想的规范化椎管几何形状。这些比较清楚地表明了分析模型的时间平均描述的准确性，这被认为以直接数值模拟所涉及的计算成本的一小部分提供了良好的保真度。直接数值模拟和直接数值模拟均发现，沿离心管的离心管偏心率变化在溶质运移动力学中起着重要作用，导致封闭的拉格朗日循环涡流的出现，可能阻碍溶质沿管的扩散。时间平均结果。