Collision-based spiral acceleration in cardiac media: roles of wavefront curvature and excitable gap

Abstract

We have previously shown in experimental cardiac cell monolayers that rapid point pacing can convert basic functional reentry (single spiral) into a stable multiwave spiral that activates the tissue at an accelerated rate. Here, our goal is to further elucidate the biophysical mechanisms of this rate acceleration without the potential confounding effects of microscopic tissue heterogeneities inherent to experimental preparations. We use computer simulations to show that, similar to experimental observations, single spirals can be converted by point stimuli into stable multiwave spirals. In multiwave spirals, individual waves collide, yielding regions with negative wavefront curvature. When a sufficient excitable gap is present and the negative-curvature regions are close to spiral tips, an electrotonic spread of excitatory currents from these regions propels each colliding spiral to rotate faster than the single spiral, causing an overall rate acceleration. As observed experimentally, the degree of rate acceleration increases with the number of colliding spiral waves. Conversely, if collision sites are far from spiral tips, excitatory currents have no effect on spiral rotation and multiple spirals rotate independently, without rate acceleration. Understanding the mechanisms of spiral rate acceleration may yield new strategies for preventing the transition from monomorphic tachycardia to polymorphic tachycardia and fibrillation.

Figure 1

Characteristics of spiral tip dynamics in multiwave spirals. (A) Color-coded tip trajectories. Signs next to the tip numbers denote spiral chiralities. (B) Distances between spiral tip pairs as a function of time. Oscillations in top and bottom rows are due to tip rotations during each cycle. Note that for different cases (rows) the tip-tip distances (black traces) and the mean tip-tip distance (red solid trace) vary distinctly with time, whereas the mean tip-tip distance averaged over the shown time (red dashed line) is comparable among all cases. (C) Tip velocity magnitudes over time, with color coding as in A. (D) Changes in tip cycle length (i.e., period of wave revolution around the tip) over time. Black traces in C and D show corresponding 1/0 cases. The average values from B–D for multiwave and single spiral cases are given in Table 2.

Figure 2

Maps of mean CL, DI, APD, CV, and κ for single and multiwave spirals. Values in the maps are obtained by averaging over the same 10–56 cycles of spiral activity shown in the first column of Fig. S4 for 1/0 cases and in Fig. 1A for 2/1 and 3/1 cases. Color scales are conserved to facilitate comparisons between single (1/0) and multiwave (2/1 and 3/1) spiral maps. The spatially averaged mean values from these maps (ignoring boundaries) are given in Table 2.

Figure 3

Effects of wave curvature on CV_s and action potential depolarization. (A) Mean ΔCV_s spatial maps. (B) ΔCV_s-curvature relationship for single (black line) and multiwave (red line) spirals. For each point in space, ΔCV_s values represent the difference between the CV_s from Fig. 2 and CV_r from plane-wave restitution curves (Fig. S3) at the corresponding DI from Fig. 2. (C) Assessment of the depolarization phase of the action potential. Representative phase portraits are shown for single (black solid line) and multiwave (red solid line) spirals at a position far from spiral tips and collision sites (denoted by ⊗ in A), as well as corresponding plane waves (dashed lines) at the same DI. Note that despite their positive curvatures, wavefronts in accelerated multiwave spirals (τ_V1 and G_fi) exhibit faster depolarization (including higher (dV_m/dt)^max) compared to plane waves at the same DI.

Figure 4

Effect of increased medium size on multiwave spiral activity. (A) The 3 × 3 cm² tissue domain with 3/1 τ_v1 multiwave spiral was gradually expanded to 8 × 8 cm². The resulting tip trajectories and intertip distances (A1) along with the CL_s (A2), κ (A3), and ΔCV_s (A4) distributions remained similar to those in the 3 × 3 cm² domain. As a result, the same degree of rate acceleration persisted. (B) The 3/1 τ_v1 multiwave spiral was reinitiated in an 8 × 8 cm² tissue domain at rest by forming phase singularities at the corners of a 2 × 2 cm² square in the center. The tip trajectories (B1), along with the CL_s (B2), κ (B3), and ΔCV_s (B4) behaved as in the single spiral case, and no rate acceleration occurred. Note that compared to A, the mean intertip distance was increased and the positive ΔCV_s regions were present only at collision sites.

Figure 5

Mechanisms of acceleration in multiwave spirals. (A) Mutual entrainment and advancement of individual spiral phases in multiwave spirals. (A1) Isochrone lines during rotation of a single spiral. Red arrows denote rotational phase of the spiral at times t₁–t₄. (A2) Wavefront collision between two spirals yields faster phase advancement. Isochrones t₁–t₄ show the same time interval as in A1. Note negative curvature at t₃ and the greater advancement of spiral phase between t₂ and t₃ and between t₃ and t₄ compared to A1. (B) Schematic of a spiral CL (CL_s) reduction (rate acceleration) due to the application of external stimulus. Two tissues with different excitation threshold versus premature interval curves at the spiral tip are shown in blue and orange. The negative curvature due to wave collision creates excess depolarizing current, which is equivalent to a suprathreshold stimulus. If I_stim, the current supplied to the spiral tip from the site of collision, is sufficient to excite downstream tissue near the tip, it will advance the spiral phase and decrease the CL. Note that the difference between CL_s and minimum CL at which tissue can be excited represents the available room for rate acceleration. The slope of the curve and the amount of supplied excitatory current, I_stim, determine ΔCL and the resulting degree of rate acceleration (ΔCL/(CL_s − ΔCL)).