In line with its core ambition, the Waterscales project has developed ground-breaking methodology in the form of new mathematical models, new numerical methods and new simulation technology to create a new avenue for understanding the mechanisms underlying brain fluid flow, solute transport and clearance. Since the project’s start in 2017 and until today in 2023, mathematical modeling of cerebral fluid flow has developed from its infancy to starting to unleash its full potential. Using mathematics and numerics, we have successfully evaluated existing - and launched new - scientific hypotheses in neuroscience.
Specifically, the Waterscales project has
(i) developed reliable and efficient computational methods for simulating the interplay between the brain and its fluid environment. Our findings are described in a series of articles in numerical mathematics, scientific computing and neurofluids journals.
(ii) derived new mathematical and computational models for fluid flow and transport in long, slender channels such as the perivascular spaces of the brain, with high approximation fidelity at low computational cost. In addition to publishing our findings in applied mathematics and physics journals, we have organized several meetings on this topic, playing a key role in consolidating the European mixed-dimensional numerics community.
(iii) formulated new mathematical models and numerical methods for describing the distribution and evolution of ion concentrations in brain tissue at the microscale. Most mathematical models for brain cells are commonly based on the assumption that ionic concentrations are spatially constant. However, understanding variations in ionic concentrations are important in connection with neurological conditions such as e.g. migraine or epilepsy.
(iv) designed numerical algorithms and software abstractions that allow for high-level specification and high-performance forward and reverse solution of models with multiscale features. In addition to distributing these general algorithms within the open source and widely-available FEniCS- and Dolfin-adjoint project softwares, we have authored an easily accessible monograph describing a complete pipeline from imaging to simulation of brain multiphysics complemented by open access data sets and software.
(v) introduced new algorithms for fast uncertainty quantification in complex (brain) geometries and new models studying the interplay between brain clearance and neurodegenerative disease, and used high-dimensional inverse modeling to discover human brain clearance characteristics.
Finally, by organization of minisymposia, conferences and seminars, the Waterscales project has created meeting grounds for scientific discussion and knowledge exchange on the topic of cerebral fluid flow and transport across scientific disciplines and across the world.
