Modeling molecular transport in the human intracranial space

Molecular transport in perivascular spaces (PVSs) plays an important role in clearance and delivery in the human brain. Previous studies indicate rapid movement of molecules in the subarachnoid space (SAS) and PVSs surrounding pial arteries, however, the exact mechanisms are not fully understood. Moreover, computational investigations of the phenomena in terms of fully resolved $3d$-$3d$ models are prohibitively expensive due to the complex geometry of the PVSs. To address these challenges, we introduce a $3d$-$1d$ model [1, 2] of the convective and diffusive transport in the PVS and the parenchyma. We discuss approximation properties of the reduced-order model and describe the finite element discretization of the resulting coupled system. Our implementation isolates the mixed-dimensional coupling and leverages existing FEniCS functionality for the remaining parts. Using recent imaging data of the human pial vasculature we finally showcase capabilities of the model/solver by studying brain clearance on the whole organ scale.

References¶

[1] Masri, R., Kuchta, M., & Riviere, B. (2023). Discontinuous Galerkin methods for 3D-1D systems. arXiv preprint arXiv:2312.16565.

[2] Masri, R., Zeinhofer, M., Kuchta, M., & Rognes, M. E. (2023). The modelling error in multi-dimensional time-dependent solute transport models. arXiv preprint arXiv:2303.17999.