Multiscale Multiphysiology Models of the Brain

这个项目将开发数学模型来研究人类大脑中电生理学、新陈代谢和血液动力学之间的联系。人类大脑只占总体重的2%，却消耗了大约20%的氧气供应，以产生维持其功能所需的能量。大脑的功能在很大程度上取决于血管系统，在需要的地方输送氧气和代谢物，并及时清除废物。与血液流动和大脑活动水平的协调有关的几个问题仍在等待确定的答案，例如，为什么过量的含氧血液被输送到激活的大脑区域。了解脑电生理活动和脑血流之间的耦合在许多脑研究中是至关重要的，而解释脑电生理和血流动力学之间的机制的模型将是解释实验数据的关键。保证大脑功能的代谢过程需要不同类型的脑细胞、神经元和星形胶质细胞之间的协调，是电生理学和血流动力学之间的关键纽带。多尺度、多生理学的数学模型对于评估所提出的相互作用机制的可行性、测试新的氧运输范例以及理解局部和全局脑现象之间的相互作用是必要的。该项目将为人类不同大脑功能的相互作用和反馈打开一扇数学窗口，有可能揭示某些大脑疾病状态背后的代谢或血管原因。学生将通过参与研究项目来接受培训。作为该项目的一部分，开发的综合空间分布数学模型将用于了解将神经激活与大脑新陈代谢和血液动力学变化联系起来的信号机制，特别关注氧气在正常大脑活动中的作用，以及与偏头痛和创伤性脑损伤相关的皮质扩散性去极化波的存在。正常和异常情况下脑激活的电、代谢和血流动力学的新预测计算模型将基于常微分方程组和偏微分方程组，并将考虑多时空尺度。建模的挑战来自于需要在非常不同的空间和时间尺度上连接大脑功能，涉及到不同的数量，如电荷和生化物种浓度。设计一种能够将缝隙连接中发生的现象与器官水平的变化联系起来的模型，例如生化物种的浓度或血液动力学反应，将是数学模型界的一大财富，并可作为各种空间和时间多尺度范例的模板。这些模型将依赖于许多参数，这些参数的估计将在贝叶斯框架内利用为计算反问题开发的工具进行。该项目的一个重要贡献将是量化模型预测中的不确定性，这将表明可以预期的变异性有多大。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.