Mathematical and computational foundations for modeling cerebral fluid flow (Waterscales) is a research project funded by the European Research Council through a 2016 Starting Grant within PE1 (Mathematics) to Dr. Marie E. Rognes hosted by Simula Research Laboratory, Norway. The 5-year project runs from 2017 to 2022.

Overall ambition

The overall objective of the Waterscales project is to establish the mathematical, numerical and computational foundations for predictively modeling fluid flow and solute transport through the brain across spatiotemporal scales – from the cellular to the organ level.

Research objectives

To approach its overall ambition, the Waterscales project will target five main scientific objectives (Objectives 1–5). Objectives 1–3 represent largely independent directions of pioneering mathematical model and numerical method development, Objective 4 focuses on new computational abstractions and algorithm development, while Objective 5 collects and evaluates the results of Objectives 1–4 via goal-oriented model adaptivity:

  • Objective 1: To integrate cellular features into tissue level models of the brain’s waterscape and to understand how properties and structures are propagated in discretizations of these models.
  • Objective 2: To couple vascular and perivascular features with tissue level models of the brain’s waterscape and to understand how to best discretize such models.
  • Objective 3: To develop and analyze mathematical models and associated numerical schemes that connect mechanical and electrochemical features of the brain’s waterscape across spatiotemporal scales
  • Objective 4: To design numerical algorithms and software abstractions that allow for high-level specification and high-performance forward and reverse solution of models with multiscale features
  • Objective 5: To evaluate and improve the predictive capabilities of mathematical models of the brain’s waterscape, both theoretically and through comparison with experimental data