CAREER: MPS-BIO: Mathematical Modeling and Experiments of Neuromechanical Pumping

这项提议的主要目标是建立器官和生物体的电生理学和神经力学的数学模型，其动力学依赖于环境线索和通过起搏细胞的作用而产生的电激活。计算流体动力学的最新进展使研究人员能够有效地探索涉及移动浸入流体中的弹性边界的问题，如心脏流体动力学、鱼类游泳和细菌运动等问题。这些进展也使得对流体和弹性器官或生物体的神经力学模型之间的相互作用进行建模成为可能。该项目将重点开发和实施这类模型，以解决两个问题：1)通过泵送管状心脏的液体传输，以及2)由水母铃声脉动产生的摄食电流。这一提议利用了现有的流体-结构相互作用的计算算法，而数学上的新奇之处在于将这项技术与生物边界相结合。这些模型将整合动作电位传导、肌肉收缩、组织运动和流体运动之间的反馈。例如，将开发数学模型，通过适当的肌肉和钙离子模型，将嘈杂的起搏细胞触发的动作电位与张力的产生耦合起来。高度可变形的心脏导管和水母铃铛的非Hookean材料特性和几何形状也将被量化，并使用离散微分几何精确建模。这项工作将结合计算、数学和实验工具，最终回答生物生物学五大挑战之一提出的一些问题：整合生命和物理系统。将开发神经生物学、肌肉力学、弹性和流体动力学的综合数学模型，用于泵送管状心脏和水母铃声。虽然在单独对这些组件进行建模和仿真方面取得了很大进展，但将这些领域结合起来仍然是难以捉摸的。激励这项研究的工作命题是，考虑到这两个问题的相对简单性，对这两个选定问题的完整神经机械系统建模比几乎任何其他问题都更容易处理。这项研究的结果也可能为开发其他基本生物学问题的综合模型提供一个框架，例如废物通过肠道的移动和调节，空气通过肺的移动，以及淋巴通过淋巴系统的移动和调节。这项建议的教育重点是实施以生物数学建模为中心的数学家和生物学家的统一培训计划。拟议的教育活动将包括第一年的流行病学研讨会，为生物学家和数学家开设的比较生物力学数学建模课程和相关教材，以及北卡罗来纳大学加拉帕戈斯中心为数学生物学家举办的暑期课程。这一教育计划的动机是这样一个事实，即在这一界面上培训数学和生物学生将是至关重要的，以应对将在21世纪提出的科学挑战。

The broad goal of this proposal is to create mathematical models of the electrophysiology and neuromechanics of an organ and organism whose dynamics rely on environmental cues and electrical activation through the action of pacemaker cells. Recent advancements in computational fluid dynamics have enabled researchers to efficiently explore problems that involve moving elastic boundaries immersed in fluids for problems such as cardiac fluid dynamics, fish swimming, and the movement of bacteria. These advances have also made modeling the interaction between a fluid and a neuromechanical model of an elastic organ or organism feasible. This project will focus on the development and implementation of such models for two problems: 1) fluid transport through the pumping of tubular hearts, and 2) feeding currents generated by the pulsation of jellyfish bells. This proposal leverages existing computational algorithms for fluid-structure interactions, whereas the mathematical novelty lies in coupling this technology to living boundaries. The models will integrate feedback between the conduction of action potentials, the contraction of muscles, the movement of tissues, and fluid motion. For example, mathematical models will be developed that couple action potentials triggered by noisy pacemaker cells to the generation of tension through appropriate muscle and Ca2+ models. The non-Hookean material properties and geometry of highly deformable heart tubes and jellyfish bells will also be quantified and accurately modeled using discrete differential geometry. This work will combine computational, mathematical, and experimental tools to ultimately answer some of questions posed in one of the five grand challenges in organismal biology: Integrating living and physical systems. Integrative mathematical models of the neurobiology, muscular mechanics, elasticity, and fluid dynamics of pumping tubular hearts and jellyfish bells will be developed. While great strides have been made in the modeling and simulation of each of these components separately, coupling these fields remains elusive. The working proposition that motivates this research is that modeling the complete neuromechanical system is more tractable for the two selected problems than almost any other given their relative simplicity. The results of this research may also provide a framework for the development of integrative models of other fundamental biological problems such as the movement and regulation of waste through the intestines, air through the lungs, and lymph through the lymphatic system. The educational focus of this proposal is to implement a unified training program for mathematicians and biologists centered on mathematical modeling in biology. The proposed educational activities will include a first year seminar in epidemiology, a course and associated text on mathematical modeling in comparative biomechanics for biologists and mathematicians, and a summer program for mathematical biologists at the UNC Galapagos Center. This educational program is motivated by the fact that it will be critical to train mathematics and biology students at this interface in order to rise to the scientific challenges that will be posed during the 21st century.