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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 Ca-mediated waves in the ORd and TP06 models.The left and right panels show the time evoultion of typical wave patterns of the Ca-mediated wave-type in the ORd and TP06 models, respectively. The parameter sets for the two models are as follows. ORd: GCaL = 4 and Gkr = 0.275; TP06: GCaL = 3.5 and Gkr = 0.
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pone.0130632.g009: Typical wave patterns of Ca-mediated waves in the ORd and TP06 models.The left and right panels show the time evoultion of typical wave patterns of the Ca-mediated wave-type in the ORd and TP06 models, respectively. The parameter sets for the two models are as follows. ORd: GCaL = 4 and Gkr = 0.275; TP06: GCaL = 3.5 and Gkr = 0.

Mentions: These waves are initially driven by INa, but the fraction of wavefronts mediated by INa decreases in the course of time and eventually the waves are totally mediated by ICaL, within the 10s of the duration of simulation (see S1 Video). The TP06 model supports more spirals than does the ORd model, because the spiral arms in the former are narrower than in the latter, perhaps because the duration of the secondary oscillations (see Fig 2) is larger in the ORd model than in the TP06 model. Fig 9 shows the time evolution of a spiral, initiated by the S1-S2 cross-field protocol, into multiple spirals in both these models (see also S4 Video). The time-series of Vm and the averaged power spectrum, obtained as in the earlier subsection (Na-Ca-mediated waves), is shown in Fig 10. Both these models show a prominent peak in the E(ω), which indicates the frequency of the small oscillations in the time-series of Vm that oscillates about a voltage higher than −50 mV. This peak frequency also corresponds to the frequency of rotation of the spirals in the medium. In Fig 10, the value of this peak frequency is 3.5 Hz in the ORd model, and 5.18 Hz in the TP06 model; these values increase with an increase of GCaL. The wave patterns of this wave-type in both the models are similar, to the extent that there are multiple stable spirals (Fig 9), and E(ω) exhibits a single prominent peak corresponding to the rotation frequency of the spirals.


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 Ca-mediated waves in the ORd and TP06 models.The left and right panels show the time evoultion of typical wave patterns of the Ca-mediated wave-type in the ORd and TP06 models, respectively. The parameter sets for the two models are as follows. ORd: GCaL = 4 and Gkr = 0.275; TP06: GCaL = 3.5 and Gkr = 0.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0130632.g009: Typical wave patterns of Ca-mediated waves in the ORd and TP06 models.The left and right panels show the time evoultion of typical wave patterns of the Ca-mediated wave-type in the ORd and TP06 models, respectively. The parameter sets for the two models are as follows. ORd: GCaL = 4 and Gkr = 0.275; TP06: GCaL = 3.5 and Gkr = 0.
Mentions: These waves are initially driven by INa, but the fraction of wavefronts mediated by INa decreases in the course of time and eventually the waves are totally mediated by ICaL, within the 10s of the duration of simulation (see S1 Video). The TP06 model supports more spirals than does the ORd model, because the spiral arms in the former are narrower than in the latter, perhaps because the duration of the secondary oscillations (see Fig 2) is larger in the ORd model than in the TP06 model. Fig 9 shows the time evolution of a spiral, initiated by the S1-S2 cross-field protocol, into multiple spirals in both these models (see also S4 Video). The time-series of Vm and the averaged power spectrum, obtained as in the earlier subsection (Na-Ca-mediated waves), is shown in Fig 10. Both these models show a prominent peak in the E(ω), which indicates the frequency of the small oscillations in the time-series of Vm that oscillates about a voltage higher than −50 mV. This peak frequency also corresponds to the frequency of rotation of the spirals in the medium. In Fig 10, the value of this peak frequency is 3.5 Hz in the ORd model, and 5.18 Hz in the TP06 model; these values increase with an increase of GCaL. The wave patterns of this wave-type in both the models are similar, to the extent that there are multiple stable spirals (Fig 9), and E(ω) exhibits a single prominent peak corresponding to the rotation frequency of the spirals.

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