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

该提案的广泛目标是创建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进行的电激活。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浸入流体中的移动弹性边界的问题，例如心脏流体动力学，鱼类游泳和细菌运动。这些进展也使得流体与弹性器官或生物体的神经力学模型之间的相互作用的建模变得可行。该项目将重点开发和实施两个问题的模型：1）通过管状心脏泵送的液体运输，以及2）水母钟脉动产生的喂养电流。该提案利用现有的计算算法进行流体-结构相互作用，而数学新奇在于将该技术与活边界相耦合。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Ca 2+模型将噪声起搏细胞触发的动作电位与张力的产生耦合。高度可变形的心管和水母钟的非胡克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。这项工作将结合联合收割机计算，数学和实验工具，最终回答生物体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、弹性和泵送管状心脏和水母钟的流体动力学的综合数学模型。虽然这些组件的建模和仿真已经取得了很大的进步，耦合这些领域仍然难以捉摸。激励这项研究的工作命题是，建模完整的神经力学系统是更容易为两个选定的问题比几乎任何其他鉴于其相对简单。这项研究的结果也可能为其他基本生物学问题的综合模型的发展提供一个框架，例如废物通过肠道的运动和调节，空气通过肺部，淋巴通过淋巴系统。该建议的教育重点是为数学家和生物学家实施以生物学数学建模为中心的统一培训计划。拟议的教育活动将包括第一年的流行病学研讨会，生物学家和数学家的比较生物力学的数学建模课程和相关文本，以及加拉帕戈斯中心数学生物学家的暑期课程。这个教育计划的动机是，它将是至关重要的，以培养数学和生物学学生在这个接口，以上升到科学的挑战，将在21世纪世纪。

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.