用运动控制器来终止心律失常

doi:10.19596/j.cnki.1001-246x.8243

摘要/Abstract

摘要：

采用Luo-Rudy相Ⅰ心脏模型对通过局部电击使细胞复极化来消除心脏中的螺旋波和时空混沌进行数值模拟。提出利用控制器局部电击螺旋波波头周围的心肌细胞来抑制螺旋波的旋转，使螺旋波漂移出边界，进而控制螺旋波和时空混沌。数值模拟表明：适当选择控制的格点数和膜电位控制阈值，螺旋波和时空混沌都可以被抑制。最少的控制格点数为9个，最短的单螺旋波控制时间小于150 ms，最短的时空混沌控制时间小于500 ms。

关键词: 心律失常, 螺旋波, 时空混沌, 膜电位控制阈值

Abstract:

A control method suppressing spiral wave and spatiotemporal chaos by using local electric shock produced by moving controller is proposed. The local electric shock is to myocardial cells around spiral wave tip to suppress the rotation of spiral wave tip, causing spiral wave tip to move out of the boundary. We studied numerically with Luo-Rudy phase I heart model. It shows that with appropriate number of grid points controlled by local electrical shock and the control thresholds of membrane potential, both spiral wave and spatiotemporal chaos can be suppressed. The minimum number of controlled grid points is 9. The shortest control times of spiral wave and spatiotemporal chaos are less than 150 ms and 500 ms, respectively.

Key words: arrhythmia, spiral wave, spatiotemporal chaos, control threshold of membrane potential

中图分类号:

O415.5

白婧, 黄志精, 唐国宁. 用运动控制器来终止心律失常[J]. 计算物理, 2021, 38(3): 352-360.

Jing BAI, Zhijing HUANG, Guoning TANG. Terminating Arrhythmia by Using Motion Controller[J]. Chinese Journal of Computational Physics, 2021, 38(3): 352-360.

图/表 9

图1 在n-Vc参数平面上(a)螺旋波和(b)时空混沌的可控制区(□这个可控点及上方各点没有数值模拟确认。实线及上方为可控区，下方为不可控区。在虚线上方控制(Ⅰ)区螺旋波被快速控制。在可控制区(Ⅱ)螺旋波不能被快速控制。)

Fig.1 Controllable regions of (a) spiral wave and (b) spatiotemporal chaos in the n-Vc parameter plane (□ and the points above □ are controllable points that have not been confirmed by numerical simulation. The area above the solid curve is controllable area and the rest is uncontrollable area. The area above the dotted line in (a) is controllable area (Ⅰ) in which spiral wave can be controlled quickly. The other is controllable area (Ⅱ) in which spiral wave cannot be controlled quickly.)

图2 在n-Vc参数平面上(a)螺旋波和(b)时空混沌的控制时间分布

Fig.2 Control time distribution of (a) spiral wave and (b) spatiotemporal chaos in the n-Vc plane

图3 ${\bar G}$si= 0.02 mS ·cm-2时平均膜电位差随时间的变化 (a) Vc=-78 mV，n= 9；(b)Vc=-73.5 mV，n= 9；(c) Vc=-73.5 mV，n= 10；(d) Vc= -65 mV，n= 15；(e) Vc= -65 mV，n= 16；(f) Vc= -62.5 mV，n= 16；(g) Vc= -62.5 mV，n= 25；(h) Vc= -59 mV，n= 16；(i) Vc= -59 mV，n= 25

Fig.3 Evolution of the mean membrane potential difference at ${\bar G}$si= 0.02 mS ·cm-2 (a) Vc=-78 mV, n= 9; (b) Vc=-73.5 mV, n= 9; (c) Vc=-73.5 mV, n= 10; (d) Vc= -65 mV, n= 15; (e) Vc= -65 mV, n= 16; (f) Vc= -62.5 mV, n= 16; (g) Vc= -62.5 mV, n= 25; (h)Vc= -59 mV, n= 16; (i) Vc= -59 mV, n= 25

图4 在${\bar G}$si= 0.02 mS ·cm-2，Vc = -73 mV和n = 10的情况下不同时刻的膜电位斑图 (a) t = 4 ms；(b) t = 20 ms；(c) t = 48 ms；(d) t = 104 ms

Fig.4 Patterns of membrane potential at different moments for ${\bar G}$si= 0.02 mS ·cm-2, Vc = -73 mV and n = 10 (a) t = 4 ms; (b) t = 20 ms; (c) t = 48 ms; (d) t = 104 ms

图5 图 4中各斑图的局部放大

Fig.5 Local blowup of patterns shown in Fig. 4

图6 在${\bar G}$si= 0.02 mS ·cm-2，Vc= -60 mV和n= 16情况不同时刻的膜电位斑图 (a) t= 4 ms；(b) t= 40 ms；(c) t= 248 ms；(d) t= 456 ms；(e) t= 712 ms；(f) t= 1 180 ms；(g) t= 1 560 ms；(h) t= 1 660 ms；(i) t= 1 760 ms

Fig.6 Patterns of membrane potential at different moments for ${\bar G}$si= 0.02 mS ·cm-2, Vc= -60 mV and n= 16 (a) t= 4 ms; (b) t= 40 ms; (c) t= 248 ms; (d) t= 456 ms; (e) t= 712 ms; (f) t= 1 180 ms; (g) t= 1 560 ms; (h) t= 1 660 ms; (i)t= 1 760 ms

图7 在${\bar G}$si= 0.02 mS ·cm-2螺旋波波头轨迹(a) Vc= -60 mV，n = 16；(b) Vc = -73 mV，n = 10

Fig.7 Trajectories of spiral wave tip at G si= 0.02 mS ·cm-2 (a) Vc= -60 mV, n = 16; (b) Vc= -73 mV, n = 10

图8 在${\bar G}$si= 0.05 mS ·cm-2平均膜电位差随时间的变化(a) Vc= -72.5 mV，n = 10；(b) Vc= -72.5 mV，n = 20；(c) Vc= -63 mV，n = 20

Fig.8 Evolution of the mean membrane potential difference at ${\bar G}$si= 0.05 mS ·cm-2 (a) Vc= -72.5 mV, n = 10; (b) Vc= -72.5 mV, n = 20; (c) Vc= -63 mV, n = 20

图9 在${\bar G}$si= 0.05 mS ·cm-2，Vc= -66.5 mV和n = 12情况下不同时刻的膜电位斑图(a) t = 0 ms；(b) t = 20 ms；(c) t = 40 ms；(d) t = 140 ms；(e) t = 440 ms；(f) t = 800 ms；(g) t = 1 340 ms；(h) t = 1 580 ms；(i) t = 1 700 ms

Fig.9 Patterns of membrane potential at different moments for ${\bar G}$si= 0.05 mS ·cm-2, Vc= -66.5 mV and n = 12 (a) t = 0 ms; (b) t = 20 ms; (c) t = 40 ms; (d) t = 140 ms; (e) t = 440 ms; (f) t = 800 ms; (g) t = 1 340 ms; (h) t = 1 580 ms; (i) t = 1 700 ms

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