Gerrymandering in the heart: How tissue heterogeneities promote premature ventricular contractions

Figures

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  Figure 1. “Critical mass” is the basis for triggered activities. (A) cell model and tissue models. The size of the cell is 120 × 30 × 12 μm. In tissue, cells are coupled by gap junctions. (B) Ca2+ waves in one cell (cell #3) in tissue do not cause triggered activity. Blue represents DAD− cells, and red represents DAD+ cells. Top panels show snapshots of subcellular [Ca2+]i. Black line: membrane potential. Because the tissue size is very small, membrane potentials are almost identical. Red line: average [Ca2+]i. The tissue was paced until it reached the steady state. Green arrow indicates the last pacing beat (time = 0 ms) (see Video S1). The uncoupled case is shown in Figure S2A. (C) Ca2+ waves must occur in at least three out of five cells (cells 2, 4, and 5) to overcome source-sink mismatch. Blue represents DAD− cells, and red represents DAD+ cells (see Video S2). The uncoupled case is shown in Figure S2B.

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  Figure 2. Gerrymandering and its effect on PVCs. (A) 5 × 5 tissue. Red circle in the left panel: DAD+ cell. Blue circle in the left panel: DAD− cell. Nine out of 25 cells (36%) are DAD+. In homogeneous tissue, Ca2+ waves induce a DAD but cannot initiate a PVC. Top panels show snapshots of subcellular [Ca2+]i. The membrane potential was recorded from “∗” in the left panel. Green arrow indicates the last pacing beat. Because cells are well coupled, membrane potentials are almost identical (see Video S3). (B) Gap junction conductance was reduced (left panel), and a PVC occurred. Membrane potentials were recorded from “∗a” and “∗b” in the left panel. 67% (above the threshold) of cells are DAD+ in the top right corner, and 19% of cells are DAD+ in the remaining part of the tissue. The membrane potential elevates in the top right corner first. Then, an AP wave starts and spreads to the remaining part of the tissue (see Video S4). (C) Gap junction conductance was reduced (left panel) in a different way. 33% of cells are DAD+ in the top left corner, and 38% of cells are DAD+ in the remaining part of the tissue. In this case, PVCs were not observed since DAD+ cells could not overcome source-sink…

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  Figure 3. Space constant and PVCs. (A) Schematic illustration of how shorter space constant promotes local potential elevation. The distance that the membrane voltage drops to 36.8% of the source cell value is called a “space constant.” If the space constant becomes smaller, the moving average fluctuates more. Blue line: large space constant. Red: small space constant. (B) 1.5 cm × 1.5 cm tissue. The tissue was bisected into two regions. The right side of the tissue has a higher gap junction conductance of 110 nS, whereas the left side has a lower gap junction conductance of 39.6 nS (left panel). The right panel indicates the locations of PVC initiation points from 100 simulations (different random number seeds). The left side (shorter space constant side) was the origin of all PVCs across all 100 simulations. Note that Ca2+ waves occur uniformly randomly in tissue. (C) Top panels: snapshots of membrane potential. Bottom panels: snapshots of [Ca2+]i (see Video S6).

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  Figure 4. PVCs tend to start from poorly coupled regions. (A) 1.5 cm × 1.5 cm tissue. The highest gap junction conductance is 550 nS, and the lowest one is 5.5 nS. The center of tissue has the shortest space constant, and a PVC was initiated near the center. Note that Ca2+ waves occur uniformly randomly in tissue. Top panels: snapshots of membrane potential. Bottom panels: snapshots of [Ca2+]i (see Video S7). (B) 1.5 cm × 1.5 cm tissue. The left edge has the shortest space constant, and a PVC was initiated near the left edge. Top panels: snapshots of membrane potential. Bottom panels: snapshots of [Ca2+]i (see Video S8). Additional simulations with different seeds of the random number generator are shown in Figure S2.

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  Figure 5. Tissue shapes affect PVCs formation. (A) Homogeneous 1.5 cm × 1.5 cm tissue (control). The red region in the left panel contains DAD+ cells. Due to source-sink mismatch, only a DAD was observed (see Video S12). (B) The hole can promote PVCs. The simulation parameters are identical to those in Figure 5A except the hole. With the hole, the number of DAD+ cells reached the critical mass within the green box. The hole plays the role of a blank vote (a neutral element in the local source-sink balance) (see Video S13). (C) When DAD+ cells are close to the corner (or edge), PVCs occur readily. DAD+ cells are surrounded by DAD− cells in every direction when DAD+ cells are located at the center (Figure 5A). However, at the corner, DAD+ cells are surrounded by DAD− cells only in two directions. The number of DAD+ cells reached the critical mass within the green box (see Video S14).