Limits...
A Comparative Study of Early Afterdepolarization-Mediated Fibrillation in Two Mathematical Models for Human Ventricular Cells.

Zimik S, Vandersickel N, Nayak AR, Panfilov AV, Pandit R - PLoS ONE (2015)

Bottom Line: We find that the two models produce qualitatively similar results in terms of exhibiting Na-Ca-mediated wave patterns that are more chaotic than those for the Ca-mediated and phase waves.The Na-Ca-mediated waves in the ORd model show short-lived spirals but the TP06 model does not.The TP06 model supports more Ca-mediated spirals than those in the ORd model, and the TP06 model exhibits more phase-wave patterns than does the ORd model.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Centre for Condensed Matter Theory, Indian Institute of Science, Bangalore, Karnataka, India.

ABSTRACT
Early afterdepolarizations (EADs), which are abnormal oscillations of the membrane potential at the plateau phase of an action potential, are implicated in the development of cardiac arrhythmias like Torsade de Pointes. We carry out extensive numerical simulations of the TP06 and ORd mathematical models for human ventricular cells with EADs. We investigate the different regimes in both these models, namely, the parameter regimes where they exhibit (1) a normal action potential (AP) with no EADs, (2) an AP with EADs, and (3) an AP with EADs that does not go back to the resting potential. We also study the dependence of EADs on the rate of at which we pace a cell, with the specific goal of elucidating EADs that are induced by slow or fast rate pacing. In our simulations in two- and three-dimensional domains, in the presence of EADs, we find the following wave types: (A) waves driven by the fast sodium current and the L-type calcium current (Na-Ca-mediated waves); (B) waves driven only by the L-type calcium current (Ca-mediated waves); (C) phase waves, which are pseudo-travelling waves. Furthermore, we compare the wave patterns of the various wave-types (Na-Ca-mediated, Ca-mediated, and phase waves) in both these models. We find that the two models produce qualitatively similar results in terms of exhibiting Na-Ca-mediated wave patterns that are more chaotic than those for the Ca-mediated and phase waves. However, there are quantitative differences in the wave patterns of each wave type. The Na-Ca-mediated waves in the ORd model show short-lived spirals but the TP06 model does not. The TP06 model supports more Ca-mediated spirals than those in the ORd model, and the TP06 model exhibits more phase-wave patterns than does the ORd model.

No MeSH data available.


Related in: MedlinePlus

Typical wave patterns of phase waves in the ORd and TP06 models.The left and right panels show the time evolution of phase waves in the ORd and TP06 models, respectively, when an assymetric pulse is applied. The parameter sets for the two models are as follows. ORd: GCaL = 4 and Gkr = 0.2; TP06: GCaL = 5 and Gkr = 0.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4488347&req=5

pone.0130632.g011: Typical wave patterns of phase waves in the ORd and TP06 models.The left and right panels show the time evolution of phase waves in the ORd and TP06 models, respectively, when an assymetric pulse is applied. The parameter sets for the two models are as follows. ORd: GCaL = 4 and Gkr = 0.2; TP06: GCaL = 5 and Gkr = 0.

Mentions: In the ORd model, the phase waves usually evolve into spirals or periodic wavetrains when we apply a single, asymmetric pulse. On the other hand, this wave-type shows a variety of patterns in the TP06 model [23], which include various unusual manifestations; e.g., in addition to spirals, point sources, and lines of point sources have been shown to emerge. We show the time-evolution of this wave-type, for both these models, in Fig 11 for specific parameter sets (also see S5 Video). In the ORd model, after some initial trains of waves emerge spontaneously from the point of application of the initial stimulus, excitations, triggered by EADs, lead to backfiring of waves (see left panel at 3680 ms in Fig 11 and S5 Video), and these backfired waves eventually evolve into spirals of phase waves. In the TP06 model, however, the trains of waves are not disrupted by any triggered excitations during their propagation and the wave trains continue to progress undisturbed for more than 20s. The time series and the averaged power spectrum of this wave-type are shown in Fig 12. In both the models, E(ω) shows a prominent peak. The peak frequency is the frequency of the spirals in the ORd model, and in the TP06 model, it is the frequency of the periodic wave trains. Phase-wave patterns with uninterrupted wave-trains, similar to those in the TP06 model, can also be produced in the ORd model as we reduce the value of GKr; Fig 13 shows one such example. However, in the ORd model, the amplitude of the waves decay with time and the medium eventually relaxes to a steady state with a potential ≃ −10mV. Once the medium attain this steady state, it becomes completely refractory and does not allow the conduction of any external stimulus. This happens when the cells in the medium exhibit the AP type (4) (Fig 2) where GKr is reduced to a level that the repolarizing power of the cell is obliterated. The points where this steady state occurrs in the GCaL-GKr parameter space are marked by magenta-colored circles in Fig 4.


A Comparative Study of Early Afterdepolarization-Mediated Fibrillation in Two Mathematical Models for Human Ventricular Cells.

Zimik S, Vandersickel N, Nayak AR, Panfilov AV, Pandit R - PLoS ONE (2015)

Typical wave patterns of phase waves in the ORd and TP06 models.The left and right panels show the time evolution of phase waves in the ORd and TP06 models, respectively, when an assymetric pulse is applied. The parameter sets for the two models are as follows. ORd: GCaL = 4 and Gkr = 0.2; TP06: GCaL = 5 and Gkr = 0.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4488347&req=5

pone.0130632.g011: Typical wave patterns of phase waves in the ORd and TP06 models.The left and right panels show the time evolution of phase waves in the ORd and TP06 models, respectively, when an assymetric pulse is applied. The parameter sets for the two models are as follows. ORd: GCaL = 4 and Gkr = 0.2; TP06: GCaL = 5 and Gkr = 0.
Mentions: In the ORd model, the phase waves usually evolve into spirals or periodic wavetrains when we apply a single, asymmetric pulse. On the other hand, this wave-type shows a variety of patterns in the TP06 model [23], which include various unusual manifestations; e.g., in addition to spirals, point sources, and lines of point sources have been shown to emerge. We show the time-evolution of this wave-type, for both these models, in Fig 11 for specific parameter sets (also see S5 Video). In the ORd model, after some initial trains of waves emerge spontaneously from the point of application of the initial stimulus, excitations, triggered by EADs, lead to backfiring of waves (see left panel at 3680 ms in Fig 11 and S5 Video), and these backfired waves eventually evolve into spirals of phase waves. In the TP06 model, however, the trains of waves are not disrupted by any triggered excitations during their propagation and the wave trains continue to progress undisturbed for more than 20s. The time series and the averaged power spectrum of this wave-type are shown in Fig 12. In both the models, E(ω) shows a prominent peak. The peak frequency is the frequency of the spirals in the ORd model, and in the TP06 model, it is the frequency of the periodic wave trains. Phase-wave patterns with uninterrupted wave-trains, similar to those in the TP06 model, can also be produced in the ORd model as we reduce the value of GKr; Fig 13 shows one such example. However, in the ORd model, the amplitude of the waves decay with time and the medium eventually relaxes to a steady state with a potential ≃ −10mV. Once the medium attain this steady state, it becomes completely refractory and does not allow the conduction of any external stimulus. This happens when the cells in the medium exhibit the AP type (4) (Fig 2) where GKr is reduced to a level that the repolarizing power of the cell is obliterated. The points where this steady state occurrs in the GCaL-GKr parameter space are marked by magenta-colored circles in Fig 4.

Bottom Line: We find that the two models produce qualitatively similar results in terms of exhibiting Na-Ca-mediated wave patterns that are more chaotic than those for the Ca-mediated and phase waves.The Na-Ca-mediated waves in the ORd model show short-lived spirals but the TP06 model does not.The TP06 model supports more Ca-mediated spirals than those in the ORd model, and the TP06 model exhibits more phase-wave patterns than does the ORd model.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Centre for Condensed Matter Theory, Indian Institute of Science, Bangalore, Karnataka, India.

ABSTRACT
Early afterdepolarizations (EADs), which are abnormal oscillations of the membrane potential at the plateau phase of an action potential, are implicated in the development of cardiac arrhythmias like Torsade de Pointes. We carry out extensive numerical simulations of the TP06 and ORd mathematical models for human ventricular cells with EADs. We investigate the different regimes in both these models, namely, the parameter regimes where they exhibit (1) a normal action potential (AP) with no EADs, (2) an AP with EADs, and (3) an AP with EADs that does not go back to the resting potential. We also study the dependence of EADs on the rate of at which we pace a cell, with the specific goal of elucidating EADs that are induced by slow or fast rate pacing. In our simulations in two- and three-dimensional domains, in the presence of EADs, we find the following wave types: (A) waves driven by the fast sodium current and the L-type calcium current (Na-Ca-mediated waves); (B) waves driven only by the L-type calcium current (Ca-mediated waves); (C) phase waves, which are pseudo-travelling waves. Furthermore, we compare the wave patterns of the various wave-types (Na-Ca-mediated, Ca-mediated, and phase waves) in both these models. We find that the two models produce qualitatively similar results in terms of exhibiting Na-Ca-mediated wave patterns that are more chaotic than those for the Ca-mediated and phase waves. However, there are quantitative differences in the wave patterns of each wave type. The Na-Ca-mediated waves in the ORd model show short-lived spirals but the TP06 model does not. The TP06 model supports more Ca-mediated spirals than those in the ORd model, and the TP06 model exhibits more phase-wave patterns than does the ORd model.

No MeSH data available.


Related in: MedlinePlus