force or blood volume (decreased cardiac output), or a disruption of the electrical signal in an otherwise mechanically adequate heart may be the primary dysfunction. Of course, these disruptions are rarely completely independent, as diseased and damaged tissue often results in an increased likelihood of electrical malfunction.

One challenge presented by the cardiac system is to understand the physiological mechanisms underlying the electrical signal, so as to understand the mechanisms of the variety of arrhythmias and to learn how to control or prevent these arrhythmias. A substantial amount of ongoing research is aimed at understanding the dynamics of cardiac cells using mathematical and computational models. There is a long history to this direction of investigation, which has its origins with the Hodgkin-Huxley equations. The Hodgkin-Huxley theory was extended to cardiac cells by Noble, Beeler-Reuter, and others. More recently, detailed cellular ionic models have been developed by, for instance, Luo and Rudy (1994), Jafri et al. (1998), and Puglisi and Bers (2001).

In spite of the remarkable success of these models, they all fall short of providing an understanding of many important arrhythmias. This short-coming is illustrated by the history of antiarrhythmic drugs. Many of the so-called antiarrhythmic drugs are known to be ion channel blockers. When they were first discovered, it was thought that arrhythmias were caused by overactive ion channels and if these were blocked, then the arrhythmias could be prevented. Indeed, tests on single cells and small patches of tissue verified this conjecture. However, when drugs were tested in the CAST and SWORD clinical trials (CAST Investigators, 1989; Waldo et al., 1996), it was discovered that many of these drugs were actually proarrhythmic. The fundamental difficulty was that an understanding of how single cells or small patches of tissue behave or respond to drugs does not answer the question of how the entire spatiotemporal system will behave. (While some arrhythmias are the result of cellular automaticity and ectopic foci, which occur when a cell or small collection of cells oscillates without external stimulus and thereby takes over as the pacemaker of the heart, the most significant life-threatening arrhythmias are maintained because they are spatiotemporal patterns and cannot occur in single cells or small patches of tissue.) In the case of the CAST and SWORD studies, the lack of a suitable spatiotemporal model led people astray. They relied instead on their best guess, but their best guess was wrong. It is now recognized that almost all drugs that were previously classified as antiarrhythmic are actually proarrhythmic. It is also now recognized that the response of a single cell to ion-channel blockers does not adequately predict the response at the spatiotemporal level.

Thus, the challenge is to develop mechanistic, functionally integrated, multiscale mathematical models of the heart from molecular to



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