This project will develop mathematical models to study the link between electrophysiology, metabolism, and hemodynamics in the human brain. The human brain, accounting for only 2% of total body weight, consumes about 20% of the oxygen supply to produce energy needed to support its functions. Brain functions depend in a crucial way on the vascular system delivering oxygen and metabolites where needed and removing waste products in a timely fashion. Several questions related to the coordination of blood flow and brain activity level are still waiting for a definite answer, for example why an oversupply of oxygenated blood is delivered to activated brain regions. Understanding the coupling between brain electrophysiological activity and cerebral blood flow is crucial in many brain studies, and a model explaining the mechanism connecting cerebral electrophysiology and hemodynamics will be the key to interpret experimental data. The metabolic processes guaranteeing brain functions require a coordination between different types of brain cells, neurons and astrocytes, and are the crucial link between electrophysiology and hemodynamics. Multiscale, multi-physiology mathematical models are necessary to evaluate the feasibility of proposed interaction mechanisms, test novel oxygen transport paradigms, and understand the interplay between local and global brain phenomena. This project will open a mathematical window on the interactions and feedback of different human brain functions, with potential to uncover metabolic or vascular causes behind some brain disease states. Students will be trained through involvement in the research project.

The integrated spatially distributed mathematical models developed as part of the project will be used to understand the signaling mechanisms linking neural activation to changes in the cerebral metabolism and hemodynamics, with a particular interest in the role of oxygen in normal brain activity and in the presence of cortical spreading depolarization waves related to migraine and traumatic brain injury. The new predictive computational models for the electric, metabolic, and blood flow dynamics of brain activation under normal and abnormal conditions will be based on ordinary and partial differential equations and will account for multiple spatial and temporal time scales. Modeling challenges arise from the need to interface brain functions at widely different spatial and temporal scales, involving quantities as different as electric charges and biochemical species concentrations. The design of a model capable of relating phenomena occurring in the gap junctions to changes at the organ level, e.g., in the concentrations of biochemical species or hemodynamic response, will be a great asset for the mathematical modeling community and may serve as a template for a variety of spatial and temporal multiscale paradigms. The models will depend on a multitude of parameters, whose estimation will be carried out within a Bayesian framework utilizing the tools developed for computational inverse problems. An important contribution of the project will be the quantification of uncertainty in the model predictions, which will indicate how much variability can be expected.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Zhilan Feng
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Case Western Reserve University
United States
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