Border-collision bifurcations in cardiac muscle

一般认为，发生在空间定位的组织中的分叉可以破坏整个心脏电活动的时空波的稳定性，导致心动过速甚至纤颤。因此，刻画分叉的特征并开发控制方法是很重要的。他们使用一个由一块周期性起搏的青蛙心肌组成的简单试验台，使用几种技术来验证他们的假设。他们正在使用新的起搏方案和同时测量跨膜电压和细胞内钙离子来研究分叉附近诱导反应的稳定性。这些模型非常简单，可以逐个动物地调整模型的参数，这使得可以与实验进行详细的比较。列举了模型可用的长期解，并与实验结果进行了密切的比较，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，并提供了对模型的测试。研究人员还在研究对观察到的分叉的闭环反馈抑制，并特别关注在控制算法中使用细胞内钙浓度的知识。该计划将在水平和垂直整合的环境中培训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，需要每个团队成员的独特背景和专业知识来有效地解决研究问题，将定量科学和工程学的实验和理论方法结合起来。研究人员还参与了对当地中学的宣传，向学生展示这项研究，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.