Border-collision bifurcations in cardiac muscle

这项研究计划的目的是了解发生在小块心肌的电反应分叉的起源。通常认为，在空间定位的组织中发生的分叉可以使整个心脏中的电活动的时空波不稳定，从而导致心动过速或甚至纤维性颤动。因此，重要的是要描述的分叉和发展的方法，他们的控制。研究人员假设，过渡到交替是由边界碰撞分叉介导的。他们使用一个简单的试验台，由一块起搏的青蛙心肌组成，他们使用几种技术来测试他们的假设。他们正在使用新的起搏协议和跨膜电压和细胞内钙的同时测量，以研究分叉附近诱导反应的稳定性。他们还在开发心脏膜的数学模型，该模型包含短期记忆和细胞内离子浓度。该模型足够简单，模型的参数可以在动物的基础上进行调整，这允许与实验进行详细比较。列举模型的可用长期解决方案并与实验结果进行密切比较，使实验数据具有一致性，为全面了解心脏组织反应铺平了道路，并提供了模型的测试。研究人员还在研究观察到的分叉的闭环反馈抑制，特别是专注于在控制算法中使用细胞内钙浓度的知识。该计划将在横向和纵向整合的环境中培养本科生和研究生以及博士后助理。此外，他们将接受培训，在团队中工作，每个团队成员的独特背景和专业知识需要有效地解决研究问题，结合实验和理论方法来定量科学和工程。研究人员还参与了当地中学的外联活动，向学生展示研究成果，并与教师合作开发相关课程材料。

The purpose of this research program is to understand the origins of bifurcations that occur in the electrical response of small pieces of cardiac muscle. It is generally believed that bifurcations occurring in spatially-localized tissue can destabilize spatial-temporal waves of electrical activity in the whole heart, leading to tachycardia or even fibrillation. Thus, it is important to characterize the bifurcations and develop methods for their control. The researchers hypothesize that the transition to alternans is mediated by a border-collision bifurcation. Using a simple test-bed, consisting of a piece of periodically-paced frog myocardium, they are using several techniques to test their hypotheses. They are using new pacing protocols and simultaneous measurement of the transmembrane voltage and intracellular calcium to investigate the stability of the induced responses in the vicinity of the bifurcation. They are also developing mathematical models of the cardiac membrane that incorporates short-term memory and intracellular ionic concentrations. The models are simple enough that the parameters of the model can be adjusted on an animal-by- animal basis, which allows for a detailed comparison with the experiments. The enumeration of the available long-time solutions of the model and close comparison to the experimental results is lending coherence to the experimental data, paving the way for a complete understanding of the cardiac tissue response and providing a test of the models. The researchers are also investigating close-loop feedback suppression of the observed bifurcation and are especially focusing on using knowledge of the intracellular calcium concentration in the control algorithm.The program will train undergraduate and graduate students, and post-doctoral associates within a horizontally and vertically integrated environment. In addition, they will be trained to work in teams where the unique background and expertise of each team member is needed to effectively tackle the research question, combining both experimental and theoretical approaches to quantitative science and engineering. The researchers are also involved with outreach to local middle schools to showcase the research to students and to work with teachers to develop related curricular materials.