Biomedical Engineering Reference
In-Depth Information
therapy of tachycardia, even without a detailed mathematical analysis of these
arrhythmias (29). Thus, although the precise mathematical analysis of the circu-
lation of reentrant waves on one-dimensional rings is necessarily sophisticated,
cardiologists have been able to devise a qualitative understanding of the phe-
nomena that enables them to make clinical decisions without carrying out the
mathematics.
Other reentrant arrhythmias are not as well understood and are not as easily
treated. Many theoretical and experimental studies have documented spiral
waves circulating stably in two dimensions and scroll waves circulating in three
dimensions (30,31). Since real hearts are three dimensional, and there is still no
good technology to image excitation in the depth (as opposed to the surface) of
the cardiac tissue, the actual geometry of excitation waves in cardiac tissue as-
sociated with some arrhythmias is not as well understood and is now the subject
of intense study. From an operational point of view, I suggest that any arrhyth-
mia that CANNOT be cured by a small localized lesion in the heart will best be
described by rotating spiral or scroll waves. Such rhythms include atrial and
ventricular fibrillation. In these rhythms, there is evidence that there is strong
fractionation (breakup) of excitation waves giving rise to multiple small spiral
waves and patterns of shifting blocks (32). Tachycardias can also arise in the
ventricles in other patients than those who have experienced a heart attack, or
perhaps occasionally in hearts with completely normal anatomy, and in these
individuals it is likely that spiral and scroll waves are the underlying geometries
of the excitation. A particularly dangerous arrhythmia, polymorphic ventricular
tachycardia (in which there is a continually changing morphology of the electro-
cardiogram complexes), is probably associated with meandering spiral and scroll
waves (30).
4.
FUTURE PROSPECTS
To date, there have been significant advances in developing a theoretical
understanding of the mechanisms underlying complex cardiac arrhythmia and
this remains an extremely active area for research. Certain trends are clear. The
advances in computational ability, combined with improved understanding of
the ionic mechanisms of the action potential, are combining to make feasible
simulations of extremely complex mathematical models of cardiac propagation
using physiological and anatomical parameters that are increasingly close to
those found in real hearts (33,34) (for an excellent review, see this volume, Part
III, chapter 3.2, by Winslow). Although it is not yet possible to combine realistic
mathematical models of the electrical activity with realistic mechanical models
of the heart's pumping, computational advances in modeling the mechanical
properties of whole hearts have succeeded in generating flow patterns in the
beating heart similar to what is observed (35). Given current trends and the de-
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