Mathematical Sciences: Wave Propagation in Excitable Media

9303502基纳研究员研究波在一维、二维和三维可兴奋介质中的传播，特别强调心脏组织。这项研究的目的是了解空间模式的动力学，特别是螺旋波和涡旋波的形成和演化，考虑到心脏组织的特殊特征，如离散性、各向异性、非均质性、几何和离子动力学。这项研究包括建立波型动力学的数学模型，对模型方程进行数学分析，开发和实现适用于大尺度背景下的波型模拟的数值算法，包括但不限于Ekonal-Curvature方法，以及将结果与现有的实验结果进行比较。虽然有许多互补和补充的问题需要解决，但这项研究的首要目标是开发一种定量可靠的全心模型，用于可视化心跳。虽然这是一个可以实现的目标，但用当今的计算机和数学模型是不可能的。这项研究的重点是开发改进的数学模型，而不是等待足够大小和速度的机器的开发。这样的模型对于扩大EKG的诊断价值，或了解梗塞和临床操作在诱发危及生命的心律失常中的作用将是非常有价值的。***

9303502 Keener The investigator studies propagation of waves in one, two and three dimensional excitable media, with a special emphasis on cardiac tissue. The goal of this study is to understand the dynamics of spatial patterns, especially the formation and evolution of spiral and scroll waves, taking into account specific features of cardiac tissue such as discreteness, anisotropy, inhomogeneity, geometry, and ionic kinetics. The study involves the construction of mathematical models for the dynamics of wave patterns, the mathematical analysis of model equations, development and implementation of suitable numerical algorithms for their simulation in large scale contexts, including but not limited to eikonal-curvature methods, and comparison of results with available experimental results. While there are many complementary and supplementary problems to address, the overriding goal of this research is to develop a quantitatively reliable whole heart model with which to vizualize the heartbeat. While this is an achievable goal, it is impossible with present day computers and mathematical models. The emphasis of this research is to develop improved mathematical models, rather than await the development of machines of sufficient size and speed. Such a model would be of great value in extending the diagnostic usefulness of the EKG, or in understanding the role of infarctions and clinical procedures in inducing life threatening cardiac arrhythmias. ***