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

职业：MPS-BIO：神经机械泵的数学建模和实验

• 批准号: 1151478
• 负责人: Laura Miller
• 金额: $ 50.42万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1151478&HistoricalAwards=false
• 关键词: CAREER; MPS; BIO; Mathematical; Modeling

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.

该提案的总体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起搏细胞作用的电激活。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没在流体中的弹性边界的问题，例如心脏流体动力学、鱼类游泳和细菌运动等问题。这些进步还使得对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进行建模变得可行。该项目将重点开发和实施此类模型来解决两个问题：1）通过管状心脏泵送的流体运输，2）水母钟的脉动产生的喂养流。该提案利用现有的流体-结构相互作用计算算法，而数学新颖性在于将该技术与生活边界相结合。该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，将嘈杂的起搏器细胞触发的动作电位与通过适当的肌肉和 Ca2+ 模型产生的张力结合起来。高度可变形心管和水母钟的非胡克材料特性和几何形状也将使用离散微分几何进行量化和精确建模。这项工作将结合计算、数学和实验工具，最终回答有机生物学五个重大挑战之一中提出的一些问题：整合生命和物理系统。将开发泵管状心脏和水母钟的神经生物学、肌肉力学、弹性和流体动力学的综合数学模型。虽然在对每个组件进行单独建模和仿真方面已经取得了巨大进步，但这些领域的耦合仍然难以实现。推动这项研究的工作主张是，考虑到这两个选定的问题相对简单，对完整的神经力学系统进行建模比几乎任何其他问题都更容易处理。这项研究的结果还可能为开发其他基本生物学问题的综合模型提供框架，例如废物通过肠道、空气通过肺部以及淋巴液通过淋巴系统的运动和调节。该提案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、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文本，以及北卡罗来纳大学加拉帕戈斯中心的数学生物学家暑期项目。该教育计划的动机是，为了应对 21 世纪将提出的科学挑战，对数学和生物学学生进行这一界面的培训至关重要。