Work

Directional flow in perivascular networks: mixed finite elements for reduced-dimensional models on graphs

Year: 2024

Type: article

Abstract: Flow of cerebrospinal fluid through perivascular pathways in and around the brain may play a crucial role in brain metabolite clearance. While the driving forces of such flows remain enigmatic, experiments have shown that pulsatility is central. In this work, we present a novel network model for simulating pulsatile fluid flow in perivascular networks, taking the form of a system of Stokes-Brinkman equations posed over a perivascular graph. We apply this model to study physiological questions concerning the mechanisms governing perivascular fluid flow in branching vascular networks. Notably, our findings reveal that even long wavelength arterial pulsations can induce directional flow in asymmetric, branching perivascular networks. In addition, we establish fundamental mathematical and numerical properties of these Stokes-Brinkman network models, with particular attention to increasing graph order and complexity. By introducing weighted norms, we show the well-posedness and stability of primal and dual variational formulations of these equations, and that of mixed finite element discretizations.

Source: Journal of Mathematical Biology

DOI: 10.1007/s00285-024-02154-0

Authors: Ingeborg G. Gjerde, Miroslav Kuchta, Marie E. Rognes, Barbara Wohlmuth

Institutions: Norwegian Geotechnical Institute, Simula Research Laboratory, Technical University of Munich

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,890

Funders: European Commission, Deutsche Forschungsgemeinschaft, Norges Forskningsråd, H2020 European Research Council