Phase-locking behaviors in an ionic model of sinoatrial node cell and tissue

Huang, Xiaodong; Mi, Yuanyuan; Qian, Yu; Hu, Gang

doi:10.1103/physreve.83.061917

Cited by 16 publications

(16 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Bifurcation analyses using mathematical models revealed very complex nonlinear dynamics [25–28], some of them can be used to explain the mechanisms of sinus node dysfunction. The nonlinear dynamical responses of a pacemaker cell to periodic stimulations have been extensively investigated by Guevara, Glass, Shrier, and colleagues [29–36] and by others [37–39] in both experimental and theoretical studies.…”

Section: Nonlinear and Stochastic Dynamics In The Heartmentioning

confidence: 99%

“…In a series of studies by Guevara, Glass, Shrier and colleagues [29–36] as well as by other authors [37–39], the nonlinear dynamics of periodic stimulated pacemaker cells has been studied both experimentally and theoretically. These cells exhibit phase-locking behavior at different locking ratios, exhibiting the devil’s staircase (Figs.…”

Section: Nonlinear Dynamics Of the Pacemaking Systemmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear and stochastic dynamics in the heart

et al. 2014

Self Cite

View full text Add to dashboard Cite

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

show abstract

Section: Nonlinear and Stochastic Dynamics In The Heartmentioning

confidence: 99%

Section: Nonlinear Dynamics Of the Pacemaking Systemmentioning

confidence: 99%

Nonlinear and stochastic dynamics in the heart

et al. 2014

Self Cite

View full text Add to dashboard Cite

show abstract

“…For SAN tissue, the heterogeneous rabbit SAN model [ 36 , 37 ] is used. There are some other models describing more details of physiological processes in SAN cell (e.g., calcium cycling) [ 38 ].…”

Section: Methodsmentioning

confidence: 99%

“…However, in previous studies, SAN dynamics was usually investigated using simple systems (e.g., a single cell or oscillator [ 19 , 20 , 23 ] or homogeneous tissue [ 33 ]). In fact, SAN tissue constitutes a heterogeneous system [ 34 , 35 ], which may exhibit some interesting phase-locking behaviors [ 36 ]. Furthermore, in the presence of the geometric complexity brought by atrial strands, the phase-locking dynamics may show some new characteristics, which better approach the actual dynamics in the heart realistically.…”

Section: Introductionmentioning

confidence: 99%

The Functions of Atrial Strands Interdigitating with and Penetrating into Sinoatrial Node: A Theoretical Study of the Problem

Huang

Cui

2015

PLoS ONE

Self Cite

View full text Add to dashboard Cite

The sinoatrial node (SAN)-atrium system is closely involved with the activity of heart beating. The impulse propagation and phase-locking behaviors of this system are of theoretical interest. Some experiments have revealed that atrial strands (ASs) interdigitate with and penetrate into the SAN, whereby the SAN-atrium system works as a complex network. In this study, the functions of ASs are numerically investigated using realistic cardiac models. The results indicate that the ASs penetrating into the central region of the SAN play a major role in propagating excitation into the atrium. This is because the threshold SAN-AS coupling for an AS to function as an alternative path for propagation is lower at the center than at the periphery. However, ASs penetrating into the peripheral region have a great effect in terms of enlarging the 1:1 entrainment range of the SAN because the automaticity of the SAN is evidently reduced by ASs. Moreover, an analytical formula for approximating the enlargement of the 1:1 range is derived.

show abstract

“…Phase synchronization is defined as the locking of the phases of coupled oscillators [ 13 , 14 ]. Specifically, let ϕ 1,2 ( t ) be the instantaneous phases of the coupled oscillators; phase synchronization is said to be achieved if | ϕ 1 ( t ) – ( m / n ) ϕ 2 ( t )| < c , where c ∊ [0, π ] is a constant and m and n are two integers.…”

Section: Introductionmentioning

confidence: 99%

Experimental Study of the Irrational Phase Synchronization of Coupled Nonidentical Mechanical Metronomes

Song

Liu

et al. 2015

PLoS ONE

View full text Add to dashboard Cite

It has recently been observed in numerical simulations that the phases of two coupled nonlinear oscillators can become locked into an irrational ratio, exhibiting the phenomenon of irrational phase synchronization (IPS) [Phys. Rev. E 69, 056228 (2004)]. Here, using two coupled nonidentical periodic mechanical metronomes, we revisit this interesting phenomenon through experimental studies. It is demonstrated that under suitable couplings, the phases of the metronomes indeed can become locked into irrational ratios. Numerical simulations confirm the experimental observations and also reveal that in the IPS state, the system dynamics are chaotic. Our studies provide a solid step toward further studies of IPS.

show abstract

Phase-locking behaviors in an ionic model of sinoatrial node cell and tissue

Cited by 16 publications

References 57 publications

Nonlinear and stochastic dynamics in the heart

Nonlinear and stochastic dynamics in the heart

The Functions of Atrial Strands Interdigitating with and Penetrating into Sinoatrial Node: A Theoretical Study of the Problem

Experimental Study of the Irrational Phase Synchronization of Coupled Nonidentical Mechanical Metronomes

Contact Info

Product

Resources

About