On reduced-order modeling of drug dispersion in the spinal canal

The optimization of intrathecal drug delivery procedures requires a deeper understanding of flow and transport in the spinal canal. Numerical modeling of drug dispersion is challenging due to the disparity in time scales: dispersion occurs over 1 hour, while cerebrospinal fluid pulsations driven by cardiac motion occur on a 1-second scale. Patient-specific predictions in clinical settings demand simplified descriptions that focus on drug-dispersion times, bypassing the rapid concentration oscillations caused by cyclic motion. A previously derived reduced-order model involving convective transport driven by mean Lagrangian drift is tested here through comparisons with MRI-informed direct numerical simulations (DNS) of drug dispersion in a cervical-canal model featuring nerve rootlets and denticulate ligaments. The comparisons demonstrate that the reduced model is able to describe precisely drug transport, enabling drug-dispersion predictions at a fraction of the computational cost involved in the DNS. Approximate descriptions assuming convective transport to be governed by the mean Eulerian velocity are found to significantly underpredict drug dispersion, highlighting the critical role of mean Lagrangian motion. Our results also confirm the substantial influence of microanatomical features on drug dispersion, consistent with earlier analyses. A key additional finding from the DNS is that molecular diffusion has a negligible impact on drug dispersion, with the mean drift of fluid particles primarily dictating the evolution of the drug distribution-an insight valuable for future modeling efforts.