Macroscopic description of flow and transport through the trabecular network of the subarachnoid space
Phys. Rev. Fluids 11, 054102 – Published 11 May, 2026
DOI: https://doi.org/10.1103/nkz4-brp5
Abstract
The pulsating motion of the cerebrospinal fluid in the subarachnoid space (SAS) surrounding the brain and the spinal cord is known to be affected by the presence of trabeculae, which are thin collagen-reinforced fibers that form a dispersed web-like structure stretching across the SAS. Previous analyses employed a homogenized approach comprising macroscopic conservation equations for flow and transport in porous media, an approximation justified by the disparity of scales present in the problem. Here, we assess the accuracy of these macroscopic equations by comparing their predictions with direct numerical simulations performed in a parallel-plate channel containing a random array of circular cylinders, used as a canonical representation of the SAS. The comparisons cover physiologically relevant ranges of the governing flow parameters. The results show that the unsteady Brinkman equation, when supplemented with an appropriately selected permeability, accurately captures the momentum balance. In contrast, the study of solute dispersion under the oscillatory flow conditions characteristic of the SAS demonstrates that the macroscopic transport equation for fibrous porous media—derived under the assumption of quasisteady microscopic flow—tends to overpredict streamwise dispersion while underpredicting local transverse dispersion across near-wall Stokes layers. These findings suggest that macroscopic transport models incorporating unsteady, shear-enhanced mixing effects at the microscopic scale are needed to accurately describe the influence of trabeculae on solute dispersion, with implications for intrathecal drug delivery and related clinical processes.
