Periodic Reporting for period 4 - Waterscales (Mathematical and computational foundations for modeling cerebral fluid flow.)
Période du rapport: 2021-10-01 au 2023-03-31
Your brain has its own waterscape: whether you are reading or sleeping, fluid flows through or along the brain and clears waste in the process. These physiological processes are crucial for the well-being of the brain. In spite of their importance we understand them but little. Mathematics and numerics are starting to play a crucial role in gaining new insight. Indeed, medical doctors express an urgent need for modeling and simulation of brain clearance and solute transport through the brain, to overcome limitations in traditional techniques. Surprisingly little attention has been paid to the numerics of the brain’s waterscape however, and fundamental knowledge is missing.
In response, the Waterscales ambition is to establish mathematical and computational foundations for predictively modeling fluid flow and solute transport through and around the brain across scales – from the cellular to the organ level. We address this overarching vision by specific scientific aims ranging from developing new mathematics and new simulation technology to gaining new insight into human physiology. Specifically, our objectives are:
- to pioneer mathematical models for describing the complex interplay between the mechanics of the brain and its electrochemistry; between blood flow, tissue fluid flow, brain pulsatility and glial cell activity;
- to design and analyze robust, high-fidelity multiscale numerical methods and computational technology for simulating physiological brain processes spanning multiple length scales;
- to evaluate and improve the predictive capabilities of computational models of the brain’s waterscape, both using mathematical techniques alone and through comparison with clinical and experimental data.
In response, the Waterscales ambition is to establish mathematical and computational foundations for predictively modeling fluid flow and solute transport through and around the brain across scales – from the cellular to the organ level. We address this overarching vision by specific scientific aims ranging from developing new mathematics and new simulation technology to gaining new insight into human physiology. Specifically, our objectives are:
- to pioneer mathematical models for describing the complex interplay between the mechanics of the brain and its electrochemistry; between blood flow, tissue fluid flow, brain pulsatility and glial cell activity;
- to design and analyze robust, high-fidelity multiscale numerical methods and computational technology for simulating physiological brain processes spanning multiple length scales;
- to evaluate and improve the predictive capabilities of computational models of the brain’s waterscape, both using mathematical techniques alone and through comparison with clinical and experimental data.
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.
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.
A key Waterscales result is the establishment of an internationally-recognized and vibrant scientific environment at Simula Research Laboratory, Oslo, Norway, researching numerical mathematics for brain multiphysics and targeting dual scientific impact: both within applied mathematics and in medicine. The Waterscales models, methods and insights enable high-fidelity in-silico studies of the brain’s waterscape across scales, with ample opportunities for further mathematical and more applied study. The processes at hand are associated with neurodegenerative diseases such as e.g. dementia and with brain swelling caused by e.g. stroke The Waterscales project provides the field and its clinical collaborators with a sorely needed, new avenue of investigation to understand these conditions, with tremendous long-term impact.