Alaminos-Quesada J, Gutiérrez-Montes C, Coenen W, Sánchez A L
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA, 92093-0411, USA.
Department of Mechanical and Mining Engineering, University of Jaén, Jaén, 23071, Spain.
J Fluid Mech. 2024 Apr;985. doi: 10.1017/jfm.2024.297. Epub 2024 Apr 19.
This paper investigates the transport of drugs delivered by direct injection into the cerebrospinal fluid (CSF) that fills the intrathecal space surrounding the spinal cord. Because of the small drug diffusivity, the dispersion of neutrally buoyant drugs has been shown in previous work to rely mainly on the mean Lagrangian flow associated with the CSF oscillatory motion. Attention is given here to effects of buoyancy, arising when the drug density differs from the CSF density. For the typical density differences found in applications, the associated Richardson number is shown to be of order unity, so that the Lagrangian drift includes a buoyancy-induced component that depends on the spatial distribution of the drug, resulting in a slowly evolving cycle-averaged flow problem that can be analysed with two-time scale methods. The asymptotic analysis leads to a nonlinear integro-differential equation for the spatiotemporal solute evolution that describes accurately drug dispersion at a fraction of the cost involved in direct numerical simulations of the oscillatory flow. The model equation is used to predict drug dispersion of positively and negatively buoyant drugs in an anatomically correct spinal canal, with separate attention given to drug delivery via bolus injection and constant infusion.
本文研究了通过直接注入充满脊髓周围鞘内空间的脑脊液（CSF）来输送药物的情况。由于药物扩散系数较小，先前的研究表明，中性浮力药物的扩散主要依赖于与脑脊液振荡运动相关的平均拉格朗日流。本文关注药物密度与脑脊液密度不同时产生的浮力效应。对于应用中发现的典型密度差异，相关的理查森数显示为单位量级，因此拉格朗日漂移包括一个依赖于药物空间分布的浮力诱导分量，这导致了一个可以用双时间尺度方法分析的缓慢演化的周期平均流动问题。渐近分析得出了一个用于时空溶质演化的非线性积分 - 微分方程，该方程能够以振荡流直接数值模拟成本的一小部分准确描述药物扩散。该模型方程用于预测在解剖学上正确的椎管中正负浮力药物的药物扩散情况，并分别关注推注注射和持续输注给药方式。
