Effects of Conduction Block and Reentry on Evolution of Spiral Waves

doi:10.19596/j.cnki.1001-246x.8552

Abstract

Abstract:

We study conduction block and reentry induced by conduction velocity restitution, and their effects on the evolution of spiral waves. Simulation shows that the shape of stable spiral waves, Eckhaus instability and Doppler instability of spiral waves are associated with conduction block and reentry. The stable spiral wave exhibits concave or rhombic shape as the conduction block reduces its symmetry. The Eckhaus instability of spiral waves emerges as serious conduction blocks and the accompanying reentry initiated far from the spiral wave tip. In the case that serious conduction blocks begin near the spiral wave tip, the spiral wave meanders, and then the wave arms near the tip compress in one direction but elongate in other direction, which lead to the Doppler instability of spiral waves. This work tries to expound mechanisms of the evolution of spiral waves in the sight of cellular and electrical level.

Key words: conduction velocity restitution, conduction block, reentrant, spiral waves, cellular automata

Chengqian LI, Furong GUAN, Minyi DENG. Effects of Conduction Block and Reentry on Evolution of Spiral Waves[J]. Chinese Journal of Computational Physics, 2023, 40(1): 117-126.

Figures/Tables 10

Fig.1 Examples of the emergence of (a) conduction block and (b) reentry (The square frames and the figures represent cells and their state values, respectively.)

Fig.2 Patterns of stable spiral waves without CVR at t=30 000 and γ=2 (a)α=2 300, β=34;(b)α=1 400, β=40; (c)α=1 500, β=40; (d)α=2 600, β=36(The white, dark and gray represent the state of rest, excited and refractory, respectively. Deeper gray indicates smaller value of refractory state.)

Fig.3 The concave shape of spiral wave due to CVR and its relation with conduction block (a)~(c)spiral wave patterns; (d)~(f)local state distributions in concave region; (g)~(i)local state distributions in non-concave region (The square frames and figures in local state distributions are the same as in Fig. 1. Colors in patters represent the same as in Fig. 2. The cell with attention is signed with a circle. The end of arrow is at the point where electrical signal arrives, and beginning of the arrow is the source of electrical signal. Parameters are the same as in Fig. 2(a).)

Fig.4 Rhombic shape of spiral wave due to CVR and its relation with conduction block (a)~(c)spiral wave patterns; (d)~(f) local state distributions reflecting conduction blocks along the diagonal direction (Colors in patterns and signals in state distributions represent the same as in Fig. 3. Parameters are the same as in Fig. 2(b).)

Fig.5 Eckhaus instability due to CVR and its relation with conduction block and reentry (a) and (b) patterns during Eckhaus instability process; (c) and (d) local state distributions reflecting the conduction block; (e) and (f) local state distributions reflecting the reentry (Colors in patters and signals in state distributions represent the same as in Fig. 3. Parameters are the same as in Fig. 2(c).)

Fig.6 Doppler instability due to CVR and its relation with conduction block (a)~(d)patterns during Doppler instability process; (e)~(h)local state distributions reflecting the conduction block (Colors in patter and signals in state distributions represent the same as in Fig. 3. Parameters are the same as in Fig. 2(d).)

Table 1 Conduction time of a pulse from a cell at (69, 77) in Fig. 3 and excitation situation of its neighbors

单位距离传导时间	激发正向邻居	激发斜向邻居
40	失败	成功
35	成功	失败
37	成功	失败
24	失败	失败
21	失败	失败
21	失败	成功

Table 2 Conduction time of a pulse from a cell at (46, 84) in Fig. 3 and excitation situation of its neighbors

单位距离传导时间	激发正向邻居	激发斜向邻居
27	成功	成功
27	成功	成功
29	成功	失败
30	成功	失败
30	成功	失败
28	成功	成功

Table 3 Conduction time of a pulse from a cell at (75, 71) in Fig. 4 and excitation situation of its neighbors

单位距离传导时间	激发正向邻居	激发斜向邻居
24	失败	失败
45	成功	成功
41	成功	失败
43	成功	失败
38	成功	失败

Fig.7 Evolution types of spiral waves under different parameters as CVR is considered (〇, ▽and △ represent stable spiral waves, Eckhaus instability and Doppler instability, respectively.)

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