A Simulation Study of the Role of Mechanical Stretch in Arrhythmogenesis during Cardiac Alternans

Figure 1. (Left) Dynamic restitution curves plotting APD against the preceding DI for the middle cell for different values of Gs. For each chosen value of Gs, given in the legend, a 7-cm cable was paced at the middle at an initial BCL of 600 ms for a period of 300 beats. BCL was then reduced by 100 ms and cable was paced for a further 300 beats. This process was repeated but each time BCL, is reduced by 100 ms if it is greater than 300 ms, by 10 ms if it is greater than 250 ms, and by 1 ms if it is greater than 190 ms. APD were plotted versus the preceding DI for seven values of BCL (190, 200, 210, 240, 300, 400, and 600 ms). (Right) The CV restitution curves for different values of Gs were determined by plotting CV against the preceding DI. To this end, for each value of Gs, the 1D cable was paced at the boundary using a similar pacing protocol, and the CV was measured at steady state for each BCL as the distance between two points, positioned at 0.5 and 1 cm from the PS, divided by the front arrival times between these points. To see this figure in color, go online.

Figure 2. CV vs X (distance) along a 7-cm cable, calculated for a BCL of 300 ms under four situations of MEF (left) and for different values of Gs (right). To see this figure in color, go online.

Figure 3. Time evolution of V (top), Isac (middle), Dm (middle), and λ (bottom) for the cells positioned 1 cm (left) and 6 cm (right) from the PS, when MEF is off (black solid lines) and when MEF is on, and F = 1 in the stretch-dependent conduction in Eq. 1. (red dashed-dotted lines), and for Gs=50μS/μF, and when MEF is on, and λ = 1 in Isac (Eq. 7) (blue dashed lines) when a 7-cm cable is paced at the boundary with BCL = 400 ms and decreased gradually to BCL = 300 ms, and then paced periodically with BCL = 300 ms until a steady state is reached. To see this figure in color, go online.

Figure 4. Spatiotemporal evolution of V when MEF is off (a), when MEF is on (set Gs=50μS/μF) (b), when MEF is on Isac (c), and when MEF is on λ (d) for several beats at steady state when a 7-cm cable is paced at the boundary with BCL = 190 ms (starting at BCL = 400 ms and decreased gradually to BCL = 190 ms and then paced periodically with BCL = 190 ms until a steady state is reached). To see this figure in color, go online.

Figure 5. Time evolution of V (bottom), Isac (middle), and λ (top) for the cells positioned 2 cm (left) and 6 cm (right) from the PS for Gs=0μS/μF (MEF is off; black solid line) and for Gs=50μS/μF (MEF is on; red dashed-dotted line) when a 7-cm cable is paced at the boundary with BCL = 400 ms and decreased gradually to BCL = 190 ms and then paced periodically with BCL = 190 ms until a steady state is reached. To see this figure in color, go online.

Figure 6. APDs (top) and CVs (bottom) vs X (distance) along a 7-cm cable for the same two consecutive beats at steady state calculated for a BCL of 190 ms and when MEF is off (black solid lines) and MEF is on (red dashed-dotted lines). To see this figure in color, go online.

Figure 7. Magnitude of the amplitude of alternans at steady state for different values of Gs, when a 7-cm cable is paced at the boundary with BCL = 400 ms and decreased gradually to BCL = 190 ms, and then paced periodically with BCL = 190 ms. APD at 90% repolarization was adopted as a measure of APD. To see this figure in color, go online.

Figure 8. Plot showing the different patterns of alternans that are formed because of the Isac in the plane of Gs and BCL when a 7-cm cable is paced at the boundary with BCL = 400 ms and decreased gradually to a BCL in the range of 187–206 ms until a steady state is reached. As shown, the formed patterns are no alternans (black circles), concordant alternans (blue squares), and discordant alternans (red triangles). To see this figure in color, go online.

Figure 9. Spatiotemporal evolution of V when MEF is off (a), MEF is on (b), MEF is on Isac (c), and when MEF is on λ (d) for Gs=50μS/μF and for several beats at steady state when a 7-cm cable is paced at the boundary with BCL = 180 ms (starting at BCL = 400 ms and decreased gradually to BCL = 180 ms). To see this figure in color, go online.

Figure 10. APDs (top) and CVs (bottom) vs X (distance) along a 7-cm cable, for the same two consecutive beats at steady state, calculated for a BCL of 180 ms and when MEF is off (black solid lines) and MEF is on (red dashed-dotted lines). To see this figure in color, go online.

Figure 11. Magnitude of the amplitude of alternans at steady state for different values of Gs when a 7-cm cable is paced at the boundary with BCL = 400 ms and decreased gradually to BCL = 180 ms and then paced periodically with BCL = 180 ms. APD at 90% repolarization was adopted as a measure of APD. To see this figure in color, go online.

Figure 12. Spatiotemporal evolution of V when MEF is off (a), and on (b), Isac (c), λ (d) for Es=0ms and Gs=80μS/μF for several beats at intermediate states (A) and steady states (B), when a 7-cm cable is paced at the boundary, starting at BCL = 400 ms, and decreased gradually to BCL = 180 ms. (Ab) The wave front (red star) of the 62nd beat (beat no. 62) hits the refractory tail of the preceding wave. (Bb) The waves of the even paced beats collide with the preceding waves of the odd beats at the vicinity of PS. To see this figure in color, go online.