Structural defects lead to dynamic entrapment in cardiac electrophysiology

Abstract

Biological networks are typically comprised of many parts whose interactions are governed by nonlinear dynamics. This potentially imbues them with the ability to support multiple attractors, and therefore to exhibit correspondingly distinct patterns of behavior. In particular, multiple attractors have been demonstrated for the electrical activity of the diseased heart in situations where cardioversion is able to convert a reentrant arrhythmia to a stable normal rhythm. Healthy hearts, however, are typically resilient to abnormal rhythms. This raises the question as to how a healthy cardiac cell network must be altered so that it can support multiple distinct behaviors. Here we demonstrate how anatomic defects can give rise to multi-stability in the heart as a function of the electrophysiological properties of the cardiac tissue and the timing of activation of ectopic foci. This leads to a form of hysteretic behavior, which we call dynamic entrapment, whereby the heart can become trapped in aberrant attractor as a result of a transient change in tissue properties. We show that this can lead to a highly inconsistent relationship between clinical symptoms and underlying pathophysiology, which raises the possibility that dynamic entrapment may underlie other forms of chronic idiopathic illness.

Fig 1. Model setup for simulating anatomically defined reentry.

The tissue has a circumference of 50mm and a width of 9mm, and contains a pacemaker site (dark grey cells) and a narrowing “wedge” which allows for the possibility of unidirectional block due to asymmetric source-sink relationships.

Fig 2. Stable system behaviors.

(a) Sinus Rhythm with Clockwise Conduction, SR_cond, requires that the wedge conducts in the clockwise direction; (b) Sinus Rhythm with Clockwise Block, SR_block, requires that the wedge be non-conducting; (c) Counter-Clockwise Reentry, CCWR, requires that the wedge conducts in the counter-clockwise direction; (d) Clockwise Reentry, CWR, requires that the wedge conducts in the clockwise direction.

Fig 3. Regions of parameter space and their supported stable behaviors.

The jagged edges reflect the discrete nature of the system as well as the relatively coarse sampling of parameter space. The asterisks correspond to the points in Table 1.

Fig 4. Mechanism of dynamic entrapment: parameter oscillation.

A shift in behavior (SR_cond to CCWR) occurs when ΔV _repol rises above a critical value and the system enters region 3 of R-ΔV _repol space (at 2,000ms & 17,000ms); CCWR does not revert back to SR_cond despite reversal of ΔV _repol back into region 2 (at 5,000ms & 20,000ms). The inverse occurs when ΔV _repol falls below another critical value and the system enters region 1 of parameter space (at 9,000ms & 24,000ms); the system returns to SR_cond and remains there even when the system returns to region 2 (at 13,000ms & 28,000ms).

Fig 5. Effect of oscillation frequency on the occurrence of dynamic entrapment.

The bottom panels show the cycle length of activation of a single cell in the circuit. Values below 1000ms correspond to rapid activation during CCWR. The cycle length during SR_cond varies with ΔV _repol as this alters action potential duration of the pacemaker cells. (a) The frequency of dynamic entrapment, i.e. transitions from SR_cond to CCWR (shaded in grey), corresponds to that of the oscillating parameter provided it is low enough. (b) Dynamic entrapment occurs irregularly and less frequently when the frequency is higher due to a beating effect, where the brief incursions of the parameter into Region 3 must occur while there is a wavefront attempting to traverse the isthmus from the right.

Fig 6. Inducibility of reentry by premature depolarization.

Grey and black areas represent ectopic activations that successfully induced reentry (CCWR and CWR respectively), while white area represents those which failed to induce reentry and left the system in SR_cond. Y-axis: coupling interval of external stimulus (ms) relative to pacemaker firing; x-axis: location of premature activation on disc (degrees).