Geometry Reduced Order Modeling (GROM) with application to modeling of glymphatic function

Computational modeling of the brain has become a key part of understanding how the brain clears metabolic waste, but patient-specific modeling on a significant scale is still out of reach with current methods. We introduce a novel approach for leveraging model order reduction techniques in computational models of brain geometries to alleviate computational costs involved in numerical simulations. Using image registration methods based on magnetic resonance imaging, we compute inter-brain mappings which allow previously computed solutions on other geometries to be mapped on to a new geometry. We investigate this approach on two example problems typical of modeling of glymphatic function, applied to a dataset of 101 MRI of human patients. We discuss the applicability of the method when applied to a patient with no known neurological disease, as well as a patient diagnosed with idiopathic Normal Pressure Hydrocephalus displaying significantly enlarged ventricles. In each of our two example problems, we achieve a speedup of more 750 times compared to the full order problem, while introducing a comparably small additional system assembly overhead. The reduced solutions recover the full order solution with an error of less than 10% in most cases.

Statement of significance: In many fields, model order reduction is a key technique in enabling high-throughput numerical simulations, but remains largely unexploited for biomedical modeling of the brain. In this work, we introduce a novel technique for building reduced representations integrating simulations performed on other brain geometries derived from MRI. Using this technique, we may leverage a dataset of previous solutions to accelerate simulations on new geometries, making patient-specific modeling more feasible.