Mathematical Sciences: Nonlinear Differential and Integral Equations in Physiology

数学科学：生理学中的非线性微分方程和积分方程

• 批准号: 9303706
• 负责人: Bard Ermentrout
• 金额: $ 23.5万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-15 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9303706&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Differential; Integral

9303706 Ermentrout The proposer continues his work on the modelling of central pattern generators with particular application to the lamprey spinal cord. He collaborates with several physiologists on modelling of the propagation and genesis of electrical activity in muscular and nervous tissues. Techniques for reducing complex membrane models to ``connectionist'' models and the requisite numerical routines will be developed. Interactive computational tools for solving of parabolic PDES and integral equations that arise in biological models will also be developed. The formation of regular patterns of muscular contraction activity is critical in many living systems. This proposal aims to study the common features of this organization. The rhythmic waves of contraction as food moves down the small intestine, the small regular changes in diameter of blood vessels, and the regular beating of the heart are all controlled by oscillating electrical activity of cells. Understanding such patterned oscillators is critical in developing a fundamental understanding of physiological structures and functions. Moreover, irregularities in these activities can lead to diseased states and in some cases even death. Mathematical models of interacting rhythmical units can shed light on how the units normally behave and interact, how irregularities in the units arise, and sometimes on how to reset them to their normal mode. The proposer continues his work on such models as well as the development of computational tools to aid in this type of modeling. ***

9303706提议人继续其中央模式发生器的建模工作，特别是在七鳃鳗脊髓上的应用。他与几位生理学家合作，对肌肉和神经组织中电活动的传播和起源进行建模。将开发将复杂的膜模型简化为“连接主义”模型的技术和必要的数值例程。还将开发用于求解生物模型中出现的抛物型偏微分方程组和积分方程式的交互式计算工具。在许多生命系统中，肌肉收缩活动规律模式的形成是至关重要的。本提案旨在研究该组织的共同特点。食物沿小肠向下移动时收缩的有节奏的波，血管直径的小而有规律的变化，以及心脏的有规律的跳动，都由细胞的振荡电活动控制。了解这种图案化的振荡器对于发展对生理结构和功能的基本理解至关重要。此外，这些活动的不规则性可能导致疾病状态，在某些情况下甚至死亡。相互作用的有节奏的单元的数学模型可以阐明这些单元的正常行为和相互作用，单元中的不规则现象是如何出现的，有时还可以说明如何将它们重新设置为正常模式。提出者继续他在这类模型上的工作，以及帮助这类建模的计算工具的开发。***