With each heartbeat, the heart wall contracts as a wave of electrical activation spreads though it [1]. In a normally operating heart, successive waves travel in an orderly way, resulting in a coordinated contraction of the ventricles. Under some conditions, however, rapid self-sustaining rotary waves can be set up, resulting in tachycardia, fibrillation and death. In vivo experiments show that fibrillation is associated with the presence of rotating waves of electrical excitation [4-6]. These waves are similar to the spiral waves seen in chemical and physical systems such as the Belousov-Zhabotinskii reaction [2,3,7].
Despite gross nonuniformities and structural discontinuities, the ventricular myocardium can be modeled mathematically as a homogeneous excitable medium, using nonlinear partial differential equations to describe transmembrane ionic fluxes. Such models indicate that spiral waves or rotors centering on a phase singularity are inducible by a precisely timed stimulus of appropriate amplitude. Once initiated, these rotating waves are remarkably stable and rarely disappear spontaneously. Current research focuses on the circumstances which lead to initiation of spiral waves in vivo, on the mechanism of their stability and on the conditions necessary to stop them. A significant factor is that adult myocarium may be thick enough to support three- dimensional waves or vortices, and that this can leads to instability even when the myocardium is stable in two dimensions. Furthermore, in three dimensions the spiral waves are gound to propagate around vortex filaments (corresponding to phase singularities) which may form knotted paths. These results have implications for the timing, strength and orientation of counter-shock therapy, and have successfully predicted the merits of larger, rather than smaller, shocks.
Dr. Winfree is currently developing a new kind of instrument for doing optical tomography of chemical gels in which propagating nonlinear waves form three-dimensional vortices ad vortex rings. It will permit, for the first time, three-dimensional visualization of the chemical gradients that arise by reaction and diffusion in excitable materials. Graduate students in Physics, Optical Sciences and Ecology and Evolutionary Biology have participated in this development, which includes mechanical components, organic chemistry, image processing and software aspects. A second current project is the development of a device for detecting fluorescence of heart cells during ventricular fibrillation in living dogs. In this collaborative effort, experimental aspects are being done by colleagues at Edmonton, Alberta, with theoretical aspects being developed at the University of Arizona.
Another project is the development of methods to deduce the activity of the heart from the fluctuations of the very weak magnetic field that it generates. In the last 30 years, biomagnetism has made dramatic advances with the development of sensitive quantum magnetometers (SQUIDs). These are noninvasive and permit source localization when electrocardiography is not applicable, due to the averaged nature of the measurements, or due to electrical isolation of the sources for the body surface (like brain, fetus, etc.). In the future, SQUIDs will become a major diagnostic took, replacing less informative and riskier catheter procedures to localize the electric sources of arrhythmias and other heart malfunctions. The cost of SQUID measurements is high due to the low temperature requirements, but development of ceramics with superconductive properties at moderately low temperatures should drive down the cost.
Brio and colleagues are addressing a fundamental, clinically important problem: detection of reentry current in atrial flutter. This electrical wave front in the heart tissue. The goal is to determine the center, the size and regions of slow conduction velocity of the animal magnetocardiograms, and a new two-conductivity model of the excitable medium that extends existing static models. The model will distinguish intra- and extracellular currents and allow more accurate prediction of the magnetic field.