南开大学机器人与信息自动化研究所

Institute of Robotics and Automatic Information System

2013年春季先进机器人与MEMS技术系列学术讲座

Seminar Series：Advanced Robotics & MEMS

题目：

PartI：Mathematical Models of Morphogenesis

PartII：Mathematical Models of Cardiac Arrhythmias

报告人：prof. *Alan Garfinkel*

单位：Medicine (Cardiology) at UCLA, USA

时间：2013年10月14日（周一）14:30-16:30&2013年10月15日（周二）14:30-16:30

地点：计算机与控制工程学院419会议室 （原附中）

Bio:Alan Garfinkel is Professor of Medicine (Cardiology) at UCLA. His undergraduate and graduate degrees were in mathematics and philosophy. His research uses mathematical modeling to study cardiac arrhythmias and the development of biological morphogenesis, and has been sponsored by the US National Institutes of Health and the National Science Foundation.

abstractI：In 1952, a revolutionary paper by Alan Turing introduced the idea that morphogenesis, the emergence of spatial structure, can be explained by bifurcations in the solutions to Partial Differential Equations representing the interactions of chemical morphogens reacting and diffusing through space. Turing’s original model produced simple patterns of spots or stripes. Since the discovery of physiological morphogens in the past few decades, even this simple model has had successful applications.

The growing maturity of the applications has now led modelers to more complex scenarios. Developments have included the extension of the original model to include cell density variables, the inclusion of mechanical factors, the extension to 3D spatial domains, and the study of patterns, such as branching structures, that occur far from the linear instability first studied by Turing. We will review examples of these new developments in the field of physiology and pathophysiology, exploring applications of Turing--‐style modeling to simple spot and stripe patterns, for example, in vascular calcification, and to more advanced morphologies such as branching patterns as seen in the lung and kidney.

abstractII：Sudden cardiac death is generally due to an arrhythmia, a disturbance in the electrical behavior of the heart. In the normally functioning heart, a wave of contraction in the heart muscle pumps the blood to the body. This wave of contraction is created by a wave of electrical activation of cardiac cells, a phenomenon which is described by a Partial Differential Equation (PDE) whose local dynamics describe the electrophysiology of the cell, and whose spatial term represents the anisotropic diffusion of ionic currents.

Arrhythmias can be divided into cellular disturbances, which can be modeled using the Ordinary Differential Equations (ODE) describing the single cell, and tissue level disturbances, which h require the full PDE of cardiac conduction. We will present examples of each. Early Afterdepolarizations are cellular level arrhythmias that correspond to bifurcations in the cellular ODE, while ventricular fibrillation is a tissue level conduction disturbance that is modeled by bifurcations in the conduction PDE.

The mathematical approach enables us to discover the mechanisms behind these arrhythmias, as well as to devise therapeutic strategies.