Transverse propagation in an expanded PSpice model for cardiac muscle with gap-junction ion channels

Abstract

Transverse propagation was previously found to occur in a two-dimensional model of cardiac muscle using the PSpice software program for electronic circuit design and analysis. Longitudinal propagation within each chain, and transverse propagation between parallel chains, occurred even when there were no gap-junction (g-j) channels inserted between the simulated myocardial cells either longitudinally or transversely. In those studies, there were pronounced edge (boundary) effects and end-effects even within single chains. Transverse velocity increased with increase in model size. The present study was performed to examine boundary effects on transverse propagation velocity when the length of the chains was held constant at 10 cells and the number of parallel chains was varied from 3 to 5, to 7, to 10, and to 20. The number of g-j channels was either zero, both longitudinally and transversely (0/0), or 100/100. Some experiments were also made at 100/0, 1/1, and 10/10. Transverse velocity and overall velocity (both longitudinal and transverse components) was calculated from the measured total propagation time (TPT), i.e., the elapsed time between when the first action potential (AP) and the last AP crossed the zero potential level. The transverse g-j channels were placed only at the ends of each chain, such that propagation would occur in a zigzag pattern. Electrical stimulation was applied intracellularly between cells A1 and A2. It was found that, with no g-j channels (0/0), overall velocity increased almost linearly when more and more chains were placed in parallel. In contrast, with many g-j channels (100/100), there was a much flatter relationship between overall velocity and number of parallel chains. The difference in velocities with 0/0 channels and 100/100 channels was reduced as the number of chains was increased. In conclusion, edges have important effects on propagation velocity (overall and transverse) in cardiac muscle simulations.

Figure 1

The model for cardiac muscle used for PSpice analysis of propagation. Each chain contained 10 cells, connected longitudinally by cell junctions. The number of chains placed in parallel was varied from 3 (chains A-C), to 5 (chains A-E), to 7 (chains A-G), to 10 (chains A-J), and to 20 (chains A-T). The longitudinal resistance between chains (R_ol2) had a standard value of 200 KΩ.

Figure 2

AP records obtained in the model for cardiac muscle when there were no gj-channels, either longitudinally or transversely (0/0). A: 3 chains in parallel. B: 5 chains in parallel. C: 7 chains in parallel. D: 10 chains in parallel. Voltage probes were placed only in cells 1, 5 and 10 of each chain in order to reduce the complexity.

Figure 3

AP records obtained in the cardiac muscle model when there were many (100) gj-channels, both longitudinally and transversely (100/100). The transverse gj-channels were placed only at the ends of the chains (e.g., at cells A10-B10, cells B1-C1, cells C10-D10, etc), giving a zigzag pattern. Voltage probes were placed only in cells 1, 5, and 10 of each chain. A: 3 chains in parallel. B: 5 chains in parallel. C: 7 chains in parallel. D: 10 chains in parallel.

Figure 4

Cardiac action potential records obtained from the 10 × 20 model (10 cells per chain, 20 parallel chains) for different numbers of gj-channels. The number of gj-channels, longitudinal to transverse, is indicated as a ratio. A: 0/0 channels. B: 1/1 channels. C: 10/10 channels. D: 100/100 channels. Voltage probes were placed only in the end cells of each chain (cells 1 and 10), to reduce complexity.

Figure 5

Graphic summary of the results obtained for no gj-channels (0/0) or 100 gj-channels (100/100). The number of parallel chains is given on the abscissa. A: TPT measured. B: Transverse velocity calculated from the TPT and distance traveled. C: Overall velocity calculated from the TPT and distance traveled. The myocardial cells were assumed to be 150 μm in length and 16 μm in diameter.