Pattern Formation in Semi-Discrete Excitable Media

半离散可激励介质中的图案形成

• 批准号: 9703630
• 负责人: Stuart Hastings
• 金额: $ 6万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-08-15 至 2000-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9703630&HistoricalAwards=false
• 关键词: Pattern; Formation; Semi; Discrete; Excitable

Hastings 9703630 Semi-discrete models of excitable media consist of coupled systems of ordinary differential equations, with each unit describing the electrical kinetics in a single "cell". They are intermediate between continuous (pde) models and purely discrete models, or cellular automata. The investigator studies whether principles developed for cellular automata models apply to the more realistic semi-discrete case. He considers specific models developed from experimental data to give quantitative descriptions of neural behavior. A model of special interest is that of Morris and Lecar, describing voltage oscillations in barnacle muscle fiber. This model has different features from the well-known FitzHugh-Nagumo system, features that are found in a number of experimental settings and that, moreover, appear amenable to mathematical analysis. The investigator explores the role of various parameters in the system in the propagation of spatial patterns. Among the factors to be considered are excitation threshold, coupling strength, relative rates of fast and slow processes, spatial geometry of the medium, and the relative time spent in the excited and refractory states. The goal of this project is to develop an understanding of pattern formation in semi-discrete excitable media. The main intended application is to neurobiology, though excitable media are found in many biological and chemical systems. Isolated cells are called ``excitable'' if they exhibit a threshold phenomenon in response to a brief external stimulus, but cannot support continued oscillations on their own. A semi-discrete model describes collections of excitable neurons coupled by a linear or nonlinear diffusion mechanism. Examples include nerve, cardiac, and muscle tissue, supporting phenomena such as wave propagation down a myelinated axon, waves of electrical stimulation that sweep through heart muscles, and spreading cortical depression, a brain wave phenomenon.

黑斯廷斯9703630 可激发介质的半离散模型由常微分方程的耦合系统组成，每个单元描述单个“细胞”中的电动力学。 它们介于连续（pde）模型和纯离散模型或细胞自动机之间。 研究人员研究是否原则开发的元胞自动机模型适用于更现实的半离散的情况下。 他考虑了从实验数据中开发的特定模型，以定量描述神经行为。 一个特别有趣的模型是Morris和Lecar的模型，描述了藤壶肌肉纤维中的电压振荡。 这个模型有不同的功能，从著名的FitzHugh-Nagumo系统，功能，发现在一些实验设置，而且，似乎经得起数学分析。 研究人员探讨了空间模式传播中系统中各种参数的作用。 要考虑的因素包括激发阈值、耦合强度、快过程和慢过程的相对速率、介质的空间几何形状以及在激发态和不应态中花费的相对时间。 这个项目的目标是在半离散可激发介质中发展图案形成的理解。 主要的预期应用是神经生物学，虽然可兴奋介质在许多生物和化学系统中发现。 如果孤立的细胞对短暂的外部刺激表现出阈值现象，但不能自己支持持续的振荡，那么它们被称为“可兴奋的”。 半离散模型描述了由线性或非线性扩散机制耦合的可兴奋神经元的集合。 例子包括神经，心脏和肌肉组织，支持现象，如波传播下有髓鞘的轴突，电刺激波扫过心脏肌肉，和扩散皮层抑制，脑波现象。