Taking Math to Heart: Mathematical Challenges in Cardiac Electrophysiology

O nhiswebsite, University of Utahmathematicsprofessor JamesKeener poses the question, “Did you know that heart attacks can give you mathematics!?” Indeed, there are a host of important research problems in cardiology that appear ideal for unified attack by mathematicians, clinicians, and biomedical engineers.What follows is a survey of six ongoing Challenge Problems that (i) seem tractable and (ii) draw from a variety of mathematical subdisciplines. We hope that this article will serve as a “call to arms” for mathematicians so that we, as a community, can contribute to an improved understanding of cardiac abnormalities. The emphasis of this article will be on cardiac electrophysiology, because some of the most exciting research problems in mathematical cardiology involve electrical wave propagation in heart tissue. The quantitative study of electrophysiology has a fascinating history, with its notable milestones touched by tragedy and triumph. Nearly a century has passed since the tragically premature death of George Ralph Mines (1886–1914), a brilliant physiologist who apparently died from self-experimentation in his laboratory. Perhaps Mines would be comforted to know that his pioneering research continues to influence the mathematical study of reentrant arrhythmia (see Temporal Pattern Challenge below). Nearly half a century afterMines’s death, in a stunningly elegant blendofmathematicsand experimentation,British physiologists Alan Hodgkin and Andrew Huxley introduced amodel of electrical propagation in the squid giant axon [11]. Their mathematical model