Critical Requirements for the Initiation of a Cardiac Arrhythmia in Rat Ventricle: How Many Myocytes?

Abstract

Cardiovascular disease is the leading cause of death worldwide due in a large part to arrhythmia. In order to understand how calcium dynamics play a role in arrhythmogenesis, normal and dysfunctional Ca²⁺ signaling in a subcellular, cellular, and tissued level is examined using cardiac ventricular myocytes at a high temporal and spatial resolution using multiscale computational modeling. Ca²⁺ sparks underlie normal excitation-contraction coupling. However, under pathological conditions, Ca²⁺ sparks can combine to form Ca²⁺ waves. These propagating elevations of (Ca²⁺)_i can activate an inward Na⁺-Ca²⁺ exchanger current (I_NCX) that contributes to early after-depolarization (EADs) and delayed after-depolarizations (DADs). However, how cellular currents lead to full depolarization of the myocardium and how they initiate extra systoles is still not fully understood. This study explores how many myocytes must be entrained to initiate arrhythmogenic depolarizations in biophysically detailed computational models. The model presented here suggests that only a small number of myocytes must activate in order to trigger an arrhythmogenic propagating action potential. These conditions were examined in 1-D, 2-D, and 3-D considering heart geometry. The depolarization of only a few hundred ventricular myocytes is required to trigger an ectopic depolarization. The number decreases under disease conditions such as heart failure. Furthermore, in geometrically restricted parts of the heart such as the thin muscle strands found in the trabeculae and papillary muscle, the number of cells needed to trigger a propagating depolarization falls even further to less than ten myocytes.

Keywords: arrhythmia; computational model; heart failure; ventricular myocyte network.

Figure A1

The number of cells needed to initiate a propagating AP increases as the gap junction conductance increases. The base gap junction conductance used in the simulations is 2400 ns. The formula and R² for trendline is included in the inset.

Figure A2

1-D Simulation with 5 cells fail to produce an action potential that can propagate between cells. Cell numbers 50, 100, 150, and 200 overlap.

Figure A3

The number of cells needed to initiate a propagating AP increases as the maximal Na⁺-Ca²⁺ exchanger maximal current density increases (equivalent to increase expression. The base value of v_ncx used in the simulation is 750 s⁻¹. The formula and R² for trendline is included in the inset.

Figure 1

(A) Schematic of a 1-D tissue, myocytes are coupled by the gap junction conductance G^k_gap. Stimulus is applied to the end of the cable at cell 0 or cell 200. (B). Current injection into the first 7 myocytes (magenta) results in propagating action potential in 1-D cable of myocytes, (C) the current-injection induced action potential triggers calcium release in the 1-D cable of myocytes.

Figure 2

(A) Action potential propagation is shown at different times (20 milliseconds (ms), 40 ms, 60 ms, and 80 ms) during the simulation in the 2-D network of 100 × 100 rat ventricular myocytes. (B) The corresponding Ca²⁺ wave propagation in the 2-D network.

Figure 3

Comparison of simulated heart failure vs. control for the rat ventricular myocyte model. The model was paced in a single myocyte for 20 s so that steady-state pacing was obtained. (A) Changes in the membrane potential during an action potential. (B) The myoplasmic Ca²⁺ concentration during an AP. (C) The RyR2 open probability. (D) The network SR Ca²⁺ concentration.

Figure 4

(A) Changes in I_NCX during the depolarization of myocytes due to the activating Ca²⁺ release. (B) Under HF conditions, opening 10 RyR2 channels in 50% of the release units results in a propagating action potential. (C) The Ca²⁺ rises slowly in the triggered myocytes resulting in depolarization. The action potential spreads rapidly to other myocytes activating calcium release. (D) Table showing dependence of number of myocytes to propagate AP as a function of the fraction of activated Ca²⁺ release units in 1-D, 2-D, and 3-D tissue.

Figure 5

(A) The 1-D structure that extends from the atrioventricular bundle. (B) The computational approach representing a trabecula attached to the ventricular wall.

Figure 6

By injecting current results in a propagating action potential at along the line of 2 × 2 × 5 myocytes. The movies of the simulation are available in Supplementary Videos S5 and S6.

Figure 6

By injecting current results in a propagating action potential at along the line of 2 × 2 × 5 myocytes. The movies of the simulation are available in Supplementary Videos S5 and S6.

Figure 7

(A) The schematic of 1-D tissue where the current is injected into the myocytes with red filling, the myocytes with black filling are the unstimulated myocytes. (B). Schematic of the 2-D tissue when the stimulated myocytes are not neighbors but there are some unstimulated myocytes between them.