Bistable Spiral Wave Dynamics in Electrically Excitable Media

Overview

Journal Phys Rev E

Publisher American Physical Society

Specialty Biophysics

Date 2024 Jan 20

PMID 38243532

Authors

Zhaoyang Zhang

Yuhao Zhang

Zhilin Qu

Affiliations

Soon will be listed here.

Abstract

We show that a positive feedback loop between sodium current inactivation and wave-front ramp-up speed causes a saddle-node bifurcation to result in bistable planar and spiral waves in electrically excitable media, in which both slow and fast waves are triggered by different stimulation protocols. Moreover, the two types of spiral wave conduction may interact to give rise to more complex spiral wave dynamics. The transitions between different spiral wave behaviors via saddle-node bifurcation can be a candidate mechanism for transitions widely seen in cardiac arrhythmias and neural diseases.

References

Chen Y, Yi F, Li X, Wang C, Chen L, Yang X . Resveratrol attenuates ventricular arrhythmias and improves the long-term survival in rats with myocardial infarction. Cardiovasc Drugs Ther. 2008; 22(6):479-85. DOI: 10.1007/s10557-008-6141-8. View

Luo C, Rudy Y . A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. Circ Res. 1991; 68(6):1501-26. DOI: 10.1161/01.res.68.6.1501. View

Hochner B, Spira M . Two distinct propagating regenerative potentials in a single ethanol-treated axon. Brain Res. 1986; 398(1):164-8. DOI: 10.1016/0006-8993(86)91262-x. View

Zhang Z, Brugada P, Weiss J, Qu Z . Phase 2 Re-Entry Without I: Role of Sodium Channel Kinetics in Brugada Syndrome Arrhythmias. JACC Clin Electrophysiol. 2023; 9(12):2459-2474. PMC: 11348283. DOI: 10.1016/j.jacep.2023.08.027. View

Ito , GLASS . Spiral breakup in a new model of discrete excitable media. Phys Rev Lett. 1991; 66(5):671-674. DOI: 10.1103/PhysRevLett.66.671. View

Weiss J, Garfinkel A, Karagueuzian H, Qu Z, Chen P . Chaos and the transition to ventricular fibrillation: a new approach to antiarrhythmic drug evaluation. Circulation. 1999; 99(21):2819-26. DOI: 10.1161/01.cir.99.21.2819. View

Jiruska P, de Curtis M, Jefferys J, Schevon C, Schiff S, Schindler K . Synchronization and desynchronization in epilepsy: controversies and hypotheses. J Physiol. 2012; 591(4):787-97. PMC: 3591697. DOI: 10.1113/jphysiol.2012.239590. View

Karma . Meandering transition in two-dimensional excitable media. Phys Rev Lett. 1990; 65(22):2824-2827. DOI: 10.1103/PhysRevLett.65.2824. View

Fenton F, Cherry E, Hastings H, Evans S . Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity. Chaos. 2003; 12(3):852-892. DOI: 10.1063/1.1504242. View

10.

Rinzel J, Keller J . Traveling wave solutions of a nerve conduction equation. Biophys J. 1973; 13(12):1313-37. PMC: 1484363. DOI: 10.1016/S0006-3495(73)86065-5. View

11.

Davidenko J, Pertsov A, Salomonsz R, Baxter W, Jalife J . Stationary and drifting spiral waves of excitation in isolated cardiac muscle. Nature. 1992; 355(6358):349-51. DOI: 10.1038/355349a0. View

12.

Vasiev , Hogeweg , Panfilov . Simulation of dictyostelium discoideum aggregation via reaction-diffusion model. Phys Rev Lett. 1994; 73(23):3173-3176. DOI: 10.1103/PhysRevLett.73.3173. View

13.

Zhang Z, Qu Z . Life and death saddles in the heart. Phys Rev E. 2021; 103(6-1):062406. PMC: 10066710. DOI: 10.1103/PhysRevE.103.062406. View

14.

Medlock L, Shute L, Fry M, Standage D, Ferguson A . Ionic mechanisms underlying tonic and burst firing behavior in subfornical organ neurons: a combined experimental and modeling study. J Neurophysiol. 2018; 120(5):2269-2281. DOI: 10.1152/jn.00340.2018. View

15.

Panfilov A . Spiral breakup as a model of ventricular fibrillation. Chaos. 2003; 8(1):57-64. DOI: 10.1063/1.166287. View

16.

Schiff S, Huang X, Wu J . Dynamical evolution of spatiotemporal patterns in mammalian middle cortex. Phys Rev Lett. 2007; 98(17):178102. PMC: 2039901. DOI: 10.1103/PhysRevLett.98.178102. View

17.

Zhang Z, Qu Z . Bistable nerve conduction. Biophys J. 2022; 121(18):3499-3507. PMC: 9515125. DOI: 10.1016/j.bpj.2022.08.006. View

18.

Luo C, Rudy Y . A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circ Res. 1994; 74(6):1071-96. DOI: 10.1161/01.res.74.6.1071. View

19.

Mackie G, Meech R . Separate sodium and calcium spikes in the same axon. Nature. 1985; 313(6005):791-3. DOI: 10.1038/313791a0. View

20.

Qu Z, Xie F, Garfinkel A, Weiss J . Origins of spiral wave meander and breakup in a two-dimensional cardiac tissue model. Ann Biomed Eng. 2000; 28(7):755-71. DOI: 10.1114/1.1289474. View