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The glymphatic system (GS) hypothesis states that advective driven cerebrospinal fluid (CSF) influx from the perivascular spaces into the interstitial fluid space rapidly transport solutes and clear waste from brain. However, the presence of advection in neuropil is contested and solutes are claimed to be transported by diffusion only. To address this controversy, we implemented a regularized version of the optimal mass transport (rOMT) problem, wherein the advection/diffusion equation is the only a priori assumption required. rOMT analysis with a Lagrangian perspective of GS transport revealed that solute speed was faster in CSF compared to grey and white matter. Further, rOMT analysis also demonstrated 2-fold differences in regional solute speed within the brain. Collectively, these results imply that advective transport dominates in CSF while diffusion and advection both contribute to GS transport in parenchyma …