About the project
Neurodegenerative diseases are a pressing concern in Europe and Alzheimer's disease costs was estimated to 100-200 billion euros in the European union in 2010 alone. To address the looming Alzheimer's disease crisis medical researchers are asking fundamental questions about metabolic waste clearance in the brain. New theories have upended centuries of previous medical opinion; however these theories are not without controversy and the experimental methods themselves have been called into question. Mathematical modeling have revealed deficiencies and revised the new theories; but these mathematical models fall short due to a lack of accounting for complex geometries, neglecting coupling effects, multi-physics, or relevant time scales. As such, advancing the mathematical modeling of the medical theories is a timely subject and is getting increased attention.
This proposal aim to provide the next generation of mathematical models and software tools for this important medical problem. In particular, we address appropriate mathematical models that encompass not only multi-physics effects at both short and long time-scales but also involve fundamental questions of the appropriate preconditioning of monolithic multi-scale solvers. In our solution algorithms we employ a newly developed multi-level component where Laplace operators of mixed fractionality are utilised at the interface. This utility has not been explored for multi-physics problems despite their canonical appearance.
Research council of Norway, Independent projects - project number 301013. Total budget approx 11,6 mill NOK.