Reentrant Arrhythmias

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Point stimuli

Reentrant arrhythmias usually form spontaneously, although they can also be intentionally initiated. The way in which they are intentionally initiated probably has little to do with how they form spontaneously. However, intentional initiation gives important insight into the nature of excitable media. It is well known that reentrant arrhythmias can be initiated intentionally by the correct application of point stimuli. This procedure has been described beautifully by Winfree (1987), with many gorgeous color plates, so here we content ourselves with a shorter, less colorful, verbal description of the process.

When a current is injected at some point to resting cardiac tissue, cells in the vicinity of the stimulus are depolarized. If the stimulus is of sufficient amplitude and duration, the cells closest to the stimulating electrode may receive a superthreshold stimulus and become excited. Cells further away from the stimulus site receive a subthreshold stimulus, so they return to rest when the stimulus ends. At the border between subthreshold and superthreshold stimulus, a wave front is formed.

Once a transition front is formed, the nonlinear dynamics and curvature determine whether it moves forward or backward. That is, if the undisturbed medium is sufficiently excitable, and the initially excited domain is sufficiently large, the wave front moves outward into the unexcited region. If, however, the unaffected medium is not excitable, but partially refractory, or the excited domain is too small, the wave front recedes and collapses.

If the stimulated medium is initially uniform, these two are the only possible responses to a stimulus. However, if the state of the medium in the vicinity of the stimulating electrode is not uniform, then there is a third possible response. Suppose, for example, that there is a gradual gradient of recovery so that a portion of the stimulated region is excitable, capable of supporting wave fronts (with positive wave speed) and the remaining portion of the stimulated region cannot support wave fronts, but only wave backs (i.e., fronts with negative speed). Then, the result of the stimulus is to produce both wave fronts and wave backs.

With a mixture of wave fronts and wave backs, a portion of the wave surface will expand, and a portion will retract. Allowed to continue in this way, a circular (two-dimensional) domain evolves into a double-armed spiral, and a spherical (three-dimensional) domain evolves into a scroll. If the domain is sufficiently large, these become self-sustained reentrant patterns.

In resting tissue with no pacemaker activity, two stimuli are required to initiate a reentrant pattern. The first is required to set up a spatial gradient of recovery. Then, if the timing and location of the second is within the appropriate range, a single action potential that propagates in the backward, but not forward, direction can be initiated. This window of time and space is called the vulnerable window or vulnerable period. If the tissue mass is large enough or if there is a sufficiently long closed one-dimensional path, the retrograde propagation initiates a self-sustained reentrant pattern of activation.

Sudden cardiac death

Death following a heart attack probably occurs via a much different mechanism. A heart attack occurs when there is a sudden occlusion of a coronary artery, stopping the flow of blood to a portion of the ventricular wall. Following this occlusion, cells become anoxic, and cell metabolism changes. There is a subsequent change in the internal osmotic pressure, followed by swelling of the cell. To prevent swelling, stretch-activated potassium channels release large quantities of potassium into the extracellular space, possibly rendering the cell self-oscillatory, but certainly changing the cell's resting potential. Gradually, gap junctions fail, and cells become electrically decoupled. Eventually, the cells die (a myocardial infarction), and form nonfunctioning scar tissue.

It is during the period of potassium extrusion preceding complete electrical decoupling that a reentrant arrhythmia is most likely to form. While the details are not known, there are several ingredients associated with their formation that are certain. First, there must be a region where propagation is blocked. Clearly, this is not sufficient, because in general, propagation simply goes around the blocked region and continues merrily on its way. However, if the region of block is on a one-dimensional conduct ing pathway and there is an alternative route by which an action potential can reach the blocked region from the opposite side, then a reentrant pattern is formed if the returning action potential successfully propagates through the blocked region in the retrograde direction. Such a region is called a region of one-way block, and we know that such regions can exist, for example, at points of fiber arborization (Section 11.1.2). One-dimensional paths with one-way block may be created by infarctions. Following occlusion of a coronary artery, tissue is highly inhomogeneous, and all sorts of strange conductive arrangements are possible, indeed likely.

A simple model shows why the initiation of a reentrant pattern is so dramatic. Suppose that there are cells located next to the exit from a one-dimensional path with one-way block (Fig. 14.24), and suppose that these cells are normally stimulated by some external pacemaker, with period T. We define the instantaneous frequency of stimulus as ATn+1 = tn+1 - tn, where tn is the nth firing. Now we take a simple kinematic description of propagation in the one-way path and suppose that the speed of propagation in the path is a function of the instantaneous period, c = c(AT). (Typically, c is an increasing function of AT.) Then the travel time around the one-way loop is CAT). In cardiac tissue, the speed of an action potential is on the order of 0.5 m/s, so that travel time around the loop is much shorter than the period of external stimulus. Thus the wave on the loop typically returns to the stimulus site long before the next external stimulus arrives (i.e., we assume that L/c < T). If this travel time is larger than the absolute refractory period Tr of the cells but smaller than T, the period of the external stimulus, then it stimulates the cells and initiates another wave around the loop. Thus,

On the other hand, if this travel time is smaller than Tr, the stimulus is not successful, and the cells must await the next external stimulus before they fire, so that

With this information, we can construct the map ATn ^ ATn+1 (shown in Fig. 14.25). There are obviously two branches for this map (shown as solid curves). Of interest are the fixed points of this map, corresponding to a periodic pattern of stimulus. The fixed point on the upper branch corresponds to the normal stimulus pattern from the external source, whereas the fixed point on the lower branch corresponds to a high-frequency, reentrant, pattern. The key feature of this map is that there is hysteresis between the two fixed points. In a "normal" situation (Fig. 14.25A), with L small and T large, the period of stimulus is fixed at T. However, as L increases or as T decreases, rendering L > Trc(STn), there is a "snap" onto the smaller-period fixed point, corresponding to initiation of a reentrant pattern (Fig. 14.25B). The pernicious nature

one-way block one-way block

Figure 14.24 Diagram of a conducting path with one-way block, preventing conduction from right to left. A: Conduction of a stimulus around the loop until it encounters refractoriness and fails to propagate further. B: Conduction of a reentrant pattern circulating continuously around the loop and exiting via the entry pathway on every circuit.

of the reentrant pattern is demonstrated by the fact that increasing the period back to previous levels does not restore the low-frequency pattern—the iterates of the map stay fixed at the lower fixed point, even though there are two possible fixed points. This is because the circulating pattern acts as a retrograde source of high-frequency stimulus on the original stimulus site, thereby masking its periodic activity.

Note that there are a number of ways that this reentrant pattern might be initiated. First, following a heart attack, a growing infarcted region may lead to a gradual increase in L, initiating the reentrant pattern while keeping T fixed. On the other hand, an infarcted region may exist but remain static (L fixed), and the reentrant pattern is initiated following a decrease in T, for example, during strenuous exercise. Thus, a static one-way loop acts like a "period bomb" (rather than a time bomb), ready to go off whenever the period is sufficiently low.

V —^-

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Tr

ATn

Figure 14.25 Next-interval map for a one-way conducting loop in two cases. A: With T large, so that two stable steady solutions exist. B: With T small, so that the only steady solution corresponds to reentry.

It is possible to initiate a reentrant arrhythmia in any healthy human heart using the two-stimulus protocol. However, the reason that we do not all succumb to reentrant arrhythmias (although many of us will) is that the spontaneous generation of reentrant patterns seems to require a substantial mass of damaged tissue (in this model, sufficiently large, but not too large, L). The most dangerous time for onset of a reentrant arrhythmia following a heart attack is when the infarcted area is in this critical size domain. It is perhaps not surprising that reentrant patterns also occur with high likelihood during reperfusion after an occlusion has been removed and blood flow restored to a region of tissue damage (although a full explanation of this requires a much more detailed model and analysis than that given here).

Tachycardia and fibrillation

The two primary reentrant arrhythmias are tachycardia and fibrillation. Both of these can occur on the atria (atrial tachycardia and atrial fibrillation) or on the ventricles (ventricular tachycardia and ventricular fibrillation). When they occur on the atria, they are not life-threatening because there is little disruption of blood flow. However, when they occur on the ventricles, they are life-threatening. Ventricular fibrillation is fatal if it is not terminated quickly. Symptoms of ventricular tachycardia include dizziness or fainting, and sometimes rapid "palpitations."

Tachycardia is often classified as being either monomorphic or polymorphic, depending on the assumed morphology of the activation pattern. Monomorphic tachycardia is identified as having a simple periodic ECG, while polymorphic tachycardia is usually quasiperiodic, apparently the superposition of more than one periodic oscillation. A typical example of a polymorphic tachycardia is called torsades de pointes, and appears on the ECG as a rapid oscillation with slowly varying amplitude (Fig. 14.26). A vectorgram interpretation suggests a periodically rotating mean heart vector.

The simplest reentrant pattern is one for which the path of travel is a one-dimensional path. These were first studied by Mines (1914) when he intentionally cut a ring of tissue from around the superior vena cava and managed to initiate waves that traveled in only one direction. More complicated monomorphic tachycardias correspond to single spirals on the atrial surface (known as atrial flutter) or single scroll waves in the ventricular muscle. A three-dimensional view of a (numerically computed) monomorphic V-tach is shown in Fig. 14.27.

Stable monomorphic ventricular tachycardia is rare, as most reentrant tachycardias become unstable and degenerate into fibrillation. Thus, the clinical occurrence of stable monomorphic V-tach is considered an anomaly rather than the typical case.

Fibrillation is believed to correspond to the presence of many reentrant patterns moving throughout the ventricles in continuous, perhaps erratic, fashion, leading to an uncoordinated pattern of ventricular contraction and relaxation. A surface view of a (numerically computed) fibrillatory pattern is shown in Fig. 14.28.

The likely reason that monomorphic V-tach is rare is because there are a number of potential instabilities, although the mechanism of the instability has not been decisively determined. Some possibilities are discussed by a number of authors (Courtemanche

Figure 14.26 A six-lead ECG recording of torsades de pointes. (Zipes and Jalife, 1995, Fig. 79-1, p. 886.)

and Winfree, 1991; Karma, 1993, 1994; Panfilov and Holden, 1990; Panfilov and Hogeweg, 1995; Bar and Eiswirth, 1993; Courtemanche et al., 1993). Suffice it to say, whatever the form and evolution of a reentrant pattern, all are dangerous, so we now devote our attention to the important problem of how to get rid of a reentrant pattern, whether stable or erratic.

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