Mathematical Sciences: Traveling Waves in Excitable Media

9525766泰森行波为多种生物系统的通讯和空间组织提供了一种机制，如神经肌肉组织中的膜去极化波、果蝇胚胎中的有丝分裂波、黏菌聚集期间的环磷酸腺苷波，以及在敏感种群中传播的感染波。这些和其他兴奋性的例子共享许多共同的特征，这些特征可以用可兴奋介质的通用数学模型来表达。这位研究人员和他的同事使用成熟的理论工具和新的计算方法研究了这种模型中的波传播，主要集中在三维可激发介质中的旋转涡旋波。当涡卷波围绕其中心的“细丝”旋转时，该细丝根据某些仍鲜为人知的运动定律在空间中缓慢移动。研究人员开发了高效而准确的计算工具，基于可激发介质的元胞自动机模型，以模拟大区域中涡旋细丝在长时间内的运动。哺乳动物心脏的厚壁脑室是一种传播电化学波的三维可兴奋介质。通过调节细胞内钙水平，这些波控制着心脏的跳动。在正常的心跳中，电波会诱导左心室的肌肉纤维同步收缩，血液会有效地从心跳腔中排出。但在病理情况下(颤动和纤颤)，心跳会退化为本项目所研究的那种旋转的涡旋波。旋转的涡卷波导致肌肉纤维不同步收缩，因此当其他部分收缩时，腔室的一部分得到放松。结果是，腔内的血液没有得到有效的泵送，心脏必须进行除颤才能挽救受害者的生命。为了了解室颤的根本原因和有效的治疗方法，需要更好地了解三维可激发介质中旋转涡旋波的发生、发展和湮灭，这是本项目的基本目标。

9525766 Tyson Traveling waves of excitation provide a mechanism for communication and spatial organization in a variety of biological systems, such as waves of membrane depolarization in neuromuscular tissue, waves of mitosis in fruit fly embryos, waves of cyclic AMP during slime mold aggregation, and waves of infection spreading through susceptible populations. These and other examples of excitability share many common features that can be expressed in generic mathematical models of excitable media. The investigator and his colleague study wave propagation in such models using established theoretical tools and new computational approaches, focusing primarily on rotating scroll waves in three-dimensional excitable media. As a scroll waves rotates around its central "filament," the filament moves slowly through space according to certain laws of motion that are still poorly understood. The investigators develop efficient and accurate computational tools, based on a cellular automaton model of excitable media, in order to simulate the motion of scroll filaments in large domains over long periods of time. The thick-walled ventricle of the mammalian heart is a three-dimensional excitable medium that propagates waves of electrochemical activity. By modulating intracellular calcium levels, these waves control the beating of the heart. During a normal heartbeat the wave induces the muscle fibers of the left ventricle to contract synchronously and blood is efficiently expelled from the chamber. But under pathological conditions (flutter and fibrillation), the heartbeat degenerates into a rotating scroll wave of the sort studied in this project. The rotating scroll wave causes the muscle fibers to contract asynchronously, so that part of the chamber is relaxed when other parts are contracting. As a result the blood within the chamber is not pumped efficiently and the heart must be "defibrillated" to save the victim's life. To understand the fundamental causes of ventricular fibrillation and its effective treatment, one needs a better understanding of the onset, development and annihilation of rotating scroll waves in three-dimensional excitable media, which is the basic goal of this project.