Interdisciplinary Undergraduate Workshop on Dynamics of Excitable Systems

This project is a component of a larger effort is to develop the foundations of modeling, synthesis and development of verified medical device software and systems from verified closed-loop models of the device and organ(s). This research spans both implantable medical devices such as cardiac pacemakers and physiological control systems such as drug infusion pumps which have multiple networked medical systems. Here we focus on an education and outreach activity associated with the project.

Eighteen undergraduate students from around the country gathered at Rochester Institute of Technology (RIT) in Rochester, New York January 8-14 to take part in the Workshop on Excitable Systems supported by the National Science Foundation. Led by Elizabeth Cherry from RIT and Flavio Fenton from the Georgia Institute of Technology, the workshop gave students an opportunity to learn about excitable and oscillatory systems from theoretical, experimental, and computational perspectives. A key goal of the workshop was to provide students with an interdisciplinary perspective; to help do so, the participants were assembled into teams that included at least two different majors. Lectures on the mathematics of dynamical systems, including fixed points, bifurcations, oscillations, and chaos were interspersed with chemical and physical demonstrations of these properties through systems like the oscillating Briggs-Rauscher reaction and the propagating Belousov-Zhabotinsky reaction as well as a saline oscillator and a candle oscillator that can exhibit chaos. Computational exercises involving the logistic map, the pendulum, and the FitzHugh-Nagumo equations helped students understand how the mathematics they learned and the physical systems could be understood geometrically. As the week progressed, students were given an introduction to cardiac action potentials and electrical waves, which can describe normal and abnormal cardiac rhythms, and also studied the heart by dissecting preserved sheep hearts in groups. The workshop culminated in a project that used GPU-accelerated web-based codes to map out the dynamics of parameter space in a popular cardiac model. The students' results will be incorporated in a manuscript currently in preparation. Variations on the January workshop will be offered for the next three years and will touch on the different areas of expertise of the eight-institution collaborative grant, led by Scott Smolka of Stony Brook University, that supports the project. New topics may include formal verification techniques from computer science and pacemaker algorithms from engineering.