Mixed-dimensional models for molecular transport in human pial perivasculature
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The nature and efficiency of molecular transport in the brain parenchyma, subarach- noid(SAS) and perivascular(PVS) spaces is an open problem in the theory of glymphatic system. The slender geometry of PVS presents a major challenge for simulating the phe- nomena on a macroscale by fully-resolved (3d-3d) models. To overcome this issue, we establish a 3d-1d model of time-dependent convection, diffusion and exchange between SAS and PVS represented by a 1d network [3]. To obtain the convective flow field inside the PVS spaces, we apply model reduction to Stokes flow in long domains with deforming annular cross-section [1]. We show well-posedness of both models and discuss their dis- cretization in terms of discontinuous Galerkin method [2]. Finally, the models are applied to study transport inside the full pial vascular network embedded in SAS.
