Multiarm spirals in a two-dimensional cardiac substrate

Abstract

A variety of chemical and biological nonlinear excitable media, including heart tissue, can support stable, self-organized waves of activity in a form of rotating single-arm spirals. In particular, heart tissue can support stationary and meandering spirals of electrical excitation, which have been shown to underlie different forms of cardiac arrhythmias. In contrast to single-arm spirals, stable multiarm spirals (multiple spiral waves that rotate in the same direction around a common organizing center) have not been demonstrated and studied yet in living excitable tissues. Here, we show that persistent multiarm spirals of electrical activity can be induced in monolayer cultures of neonatal rat heart cells by a short, rapid train of electrical point stimuli applied during single-arm-spiral activity. Stable formation is accomplished only in monolayers that show a relatively broad and steep dependence of impulse wavelength and propagation velocity on rate of excitation. The resulting multiarm spirals emit waves of electrical activity at rates faster than for single-arm spirals and exhibit two distinct behaviors, namely "arm-switching" and "tip-switching." The phenomenon of rate acceleration due to an increase in the number of spiral arms possibly may underlie the acceleration of functional reentrant tachycardias paced by a clinician or an antitachycardia device.

Fig. 1.

Initiation of a double-arm spiral in a cultured cardiac monolayer (see Movie 1). (A) Transmembrane voltage (fluorescence) was measured optically from a hexagonal area of monolayer with 8.5-mm edge and color-coded from blue (rest) to red (fully depolarized). Planes I-IV show voltage snapshots at four points in time. Motions of spiral wave tips (i.e., centers of wave rotation) are represented by PS trajectories in x, y, and t space (23). PS with clockwise and anticlockwise chirality are shown in yellow and purple, respectively. A clockwise single-arm spiral (labeled 1 on plane I) is paced by a pulse train (white bars on the left) at a point on the monolayer periphery (labeled P on plane II). During pacing (planes II and III), new waves of opposite chirality form in pairs (•) and annihilate either by merging in pairs or colliding individually against the monolayer boundary (*). After pacing terminates, two spirals having the same chirality as the initial spiral survive and form a stable two-arm spiral (plane IV, arms labeled 1 and 2). (x, y, and t bars are 2 mm, 2 mm, and 300 ms, respectively.) (B) A 5.4-s voltage trace from a site labeled B in the bottom plane in A. White frame denotes trace during A. Numbers I-IV denote the times of voltage snapshots (planes) from A. Multiplication of arms (from 1 to 2) accelerates the rate of cell firing from 3.7 to 4.9 Hz. (C) PS trajectories (white lines) in the plane of monolayer during 2-s rotation, before (Left) and after the formation (shown in A) of stable two-arm spiral (Right). Note that PS trajectories generally follow the longitudinal direction of anisotropy (indicated by double-headed arrow).

Fig. 3.

Interactions between two corotating spiral arms in cardiac monolayers. Phase snapshots reveal two scenarios, AS (A) and TS (B). Initially (top frames), each arm (A1, A2) and its tip (T1, T2) have the same index number (T1-A1 and T2-A2 pairs). During AS, arms collide in the center and switch to the other tip (forming T1-A2 and T2-A1 pairs). During TS, tips (phase singularities) drift and switch position, while arms do not collide (T1-A1 and T2-A2 pairs remain intact). Time between frames is 40 ms in A and 50 ms in B.(C) Tip (T1, T2) trajectories during 1.5 s of the same two-arm spiral. Repetitive alternations of TS and AS in this case produce a helical pattern in a space-time plot. In the x-y plane (cell monolayer plane), the tips traverse virtually the same closed path (data not shown). (x, y, and t bars are 2 mm, 2 mm, and 150 ms, respectively) (Color bars in A-C are -π to π.) D and E are voltage traces at sites far from tips (periphery) and between tips (central zone), respectively, as marked by D and E in the bottom plane of C. White frames in C-E denote the same time intervals as during A and B. During AS (A), cells fire in both the central zone and periphery, whereas during TS (B), conduction is blocked in the central zone. Alternating AS and TS in this case corresponds to a 2:1 propagation block in the central zone (E).

Fig. 2.

Stable two-arm (A) and three-arm (B) (see Movie 2) spirals in cardiac monolayers. Transmembrane voltage (fluorescence) is coded from blue to red. Frames read columnwise, left to right, and span one full rotation of each arm. Time between frames is 50 ms in A and 45 ms in B. Each arm is labeled by number, and wavefront direction is indicated by arrows. Spiral arms rotate at the same frequency, interact in a complex fashion in the central zone, and maintain a separation of ≈180° (two-arm) or ≈120° (three-arm) in the periphery. Note that spiral arms are short in length due to the relatively small size of the cardiac monolayer compared with the WL of propagated waves.

Fig. 4.

Steady-state rate dependences of percentage APD (A), CV (B), and WL (C) in cardiac monolayers (filled symbols) and computer models (open symbols). Cultures of neonatal rat myocytes where only single-arm spirals and no acceleration could be induced (n = 64) are denoted by “SA,” and those with inducible multiarm spirals (n = 11) are labeled “MA.” A FitzHugh-Nagumo-type computer model with inducible multiarm spirals by Vasiev (12) with k = 4.86 is denoted by “V,” and a model by Ermakova et al. (13) with C₂ = 0.75 is denoted by “E.” (See Computational Methods for details). Data are linearly fit by using the expression % y = -α × (x - 2) + 100. For computer models, α is not significantly different from 0, and linear fit is not shown.