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

Area of Science:

• Neuroscience
• Fluid Dynamics
• Mathematical Biology

Background:

• Cerebrospinal fluid (CSF) flow via perivascular pathways is vital for brain metabolite clearance.
• The precise mechanisms driving these flows, particularly pulsatility, remain incompletely understood.

Purpose of the Study:

• To develop and analyze a novel network model for simulating pulsatile fluid flow in perivascular networks.
• To investigate the physiological mechanisms governing perivascular fluid flow in branching vascular networks.

Main Methods:

• A network model based on a system of Stokes-Brinkman equations posed over a perivascular graph was developed.
• Mathematical and numerical properties of the Stokes-Brinkman network models were established, considering increasing graph complexity.
• Well-posedness and stability of variational formulations and mixed finite element discretizations were demonstrated using weighted norms.

Main Results:

• The model demonstrates that arterial pulsations can induce directional perivascular fluid flow, even in asymmetric, branching networks.
• The study reveals fundamental mathematical and numerical properties of the proposed Stokes-Brinkman network models.
• The stability and well-posedness of the numerical methods used for simulation were confirmed.

Conclusions:

• Pulsatile flow in perivascular networks is a key factor in brain metabolite clearance.
• The developed network model provides a robust framework for studying brain fluid dynamics.
• Mathematical analysis confirms the reliability of the model for complex vascular network simulations.