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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 Na-Ca-mediated waves in the ORd and TP06 models.The left and right panels show the time evolution of typical wave patterns of Na-Ca-mediated wave-types in the ORd and TP06 models, respectively. The parameter sets for the two models are as follows. ORd: GCaL = 4 and Gkr = 0.37; TP06: GCaL = 3 and Gkr = 0.5.
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pone.0130632.g007: Typical wave patterns of Na-Ca-mediated waves in the ORd and TP06 models.The left and right panels show the time evolution of typical wave patterns of Na-Ca-mediated wave-types in the ORd and TP06 models, respectively. The parameter sets for the two models are as follows. ORd: GCaL = 4 and Gkr = 0.37; TP06: GCaL = 3 and Gkr = 0.5.

Mentions: The wave patterns of the Na-Ca-mediated type are slightly different in the two models. The ORd model supports spirals that are short-lived, whereas the TP06 model does not produce any spiral waves that last for one complete rotation. Fig 7 shows the time evolution of this wave-type in both these models for the representative parameter sets provided in Fig 7 (a corresponding Video is provided below; S3 Video). After initiating the spiral, with the S1-S2 cross-field protocol, the spirals in the ORd and TP06 models show the first triggered activity because of EADs in the examples presented at times 880ms and 3320ms, respectively, after the application of the S2 stimulus. This initial triggered activity, which introduces functional heterogeneity in the medium, further exacerbates the instability of the spiral and leads to more triggered excitations and eventually induces wave turbulence in the medium. The waves in the ORd model continue to exhibit short-lived spirals, whereas the waves in the TP06 model do not exhibit spirals that sustain themselves for one complete rotation (see also S3 Video). Typical time series recordings of Vm, for this wave-type in both the models, from a point, and the power spectra (E(ω)) averaged over 2500 grid points are shown in Fig 8. Both the models show a wide spectrum of frequencies. However, the frequency of the strongest peak in E(ω) is related approximately to the inverse of the spacing between successive peaks in the time series of Vm.


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 Na-Ca-mediated waves in the ORd and TP06 models.The left and right panels show the time evolution of typical wave patterns of Na-Ca-mediated wave-types in the ORd and TP06 models, respectively. The parameter sets for the two models are as follows. ORd: GCaL = 4 and Gkr = 0.37; TP06: GCaL = 3 and Gkr = 0.5.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0130632.g007: Typical wave patterns of Na-Ca-mediated waves in the ORd and TP06 models.The left and right panels show the time evolution of typical wave patterns of Na-Ca-mediated wave-types in the ORd and TP06 models, respectively. The parameter sets for the two models are as follows. ORd: GCaL = 4 and Gkr = 0.37; TP06: GCaL = 3 and Gkr = 0.5.
Mentions: The wave patterns of the Na-Ca-mediated type are slightly different in the two models. The ORd model supports spirals that are short-lived, whereas the TP06 model does not produce any spiral waves that last for one complete rotation. Fig 7 shows the time evolution of this wave-type in both these models for the representative parameter sets provided in Fig 7 (a corresponding Video is provided below; S3 Video). After initiating the spiral, with the S1-S2 cross-field protocol, the spirals in the ORd and TP06 models show the first triggered activity because of EADs in the examples presented at times 880ms and 3320ms, respectively, after the application of the S2 stimulus. This initial triggered activity, which introduces functional heterogeneity in the medium, further exacerbates the instability of the spiral and leads to more triggered excitations and eventually induces wave turbulence in the medium. The waves in the ORd model continue to exhibit short-lived spirals, whereas the waves in the TP06 model do not exhibit spirals that sustain themselves for one complete rotation (see also S3 Video). Typical time series recordings of Vm, for this wave-type in both the models, from a point, and the power spectra (E(ω)) averaged over 2500 grid points are shown in Fig 8. Both the models show a wide spectrum of frequencies. However, the frequency of the strongest peak in E(ω) is related approximately to the inverse of the spacing between successive peaks in the time series of Vm.

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