Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation

Nayak, Alok Ranjan; Pandit, Rahul

doi:10.3389/fphys.2014.00207

Cited by 12 publications

(8 citation statements)

References 105 publications

(272 reference statements)

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“…We initiate spiral and scroll waves in our simulation domain by using the S1-S2 cross-field protocol [26,29]. For this we apply a stimulus (S1) of strength 150 pA for 3 ms to the left edge, of our 2D domain, or the left face, for our three dimensions of simulation domain.…”

Section: B Methodsmentioning

confidence: 99%

Turbulent states and their transitions in mathematical models for ventricular tissue: The effects of random interstitial fibroblasts

Nayak

Pandit

2015

Phys. Rev. E

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We study the dynamical behaviors of two types of spiral- and scroll-wave turbulence states, respectively, in two-dimensional (2D) and three-dimensional (3D) mathematical models, of human, ventricular, myocyte cells that are attached to randomly distributed interstitial fibroblasts; these turbulence states are promoted by (a) the steep slope of the action-potential-duration-restitution (APDR) plot or (b) early afterdepolarizations (EADs). Our single-cell study shows that (1) the myocyte-fibroblast (MF) coupling G_{j} and (2) the number N_{f} of fibroblasts in an MF unit lower the steepness of the APDR slope and eliminate the EAD behaviors of myocytes; we explore the pacing dependence of such EAD suppression. In our 2D simulations, we observe that a spiral-turbulence (ST) state evolves into a state with a single, rotating spiral (RS) if either (a) G_{j} is large or (b) the maximum possible number of fibroblasts per myocyte N_{f}^{max} is large. We also observe that the minimum value of G_{j}, for the transition from the ST to the RS state, decreases as N_{f}^{max} increases. We find that, for the steep-APDR-induced ST state, once the MF coupling suppresses ST, the rotation period of a spiral in the RS state increases as (1) G_{j} increases, with fixed N_{f}^{max}, and (2) N_{f}^{max} increases, with fixed G_{j}. We obtain the boundary between ST and RS stability regions in the N_{f}^{max}-G_{j} plane. In particular, for low values of N_{f}^{max}, the value of G_{j}, at the ST-RS boundary, depends on the realization of the randomly distributed fibroblasts; this dependence decreases as N_{f}^{max} increases. Our 3D studies show a similar transition from scroll-wave turbulence to a single, rotating, scroll-wave state because of the MF coupling. We examine the experimental implications of our study and propose that the suppression (a) of the steep slope of the APDR or (b) EADs can eliminate spiral- and scroll-wave turbulence in heterogeneous cardiac tissue, which has randomly distributed fibroblasts.

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Section: B Methodsmentioning

confidence: 99%

Turbulent states and their transitions in mathematical models for ventricular tissue: The effects of random interstitial fibroblasts

Nayak

Pandit

2015

Phys. Rev. E

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“…The development of control strategies for the elimination of spiral-and scroll-wave turbulence is of paramount importance in searching for low-amplitude defibrillation schemes. One such scheme, which has been especially successful in the elimination of spiral-wave turbulence in a variety of mathematical models for cardiac tissue [3,4,21,[54][55][56], eliminates spiral waves by electrical stimulation on a square mesh. We investigate the efficacy of such a control scheme in the TP06, MM1 WT, MM2 WT, MM1 MUT, and MM2 MUT models.…”

Section: Appendix D: Control Of Spiral Wavesmentioning

confidence: 99%

Comparisons of wave dynamics in Hodgkin-Huxley and Markov-state formalisms for the sodium (Na) channel in some mathematical models for human cardiac tissue

Mulimani

Nayak

Pandit

2020

Phys. Rev. Research

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We compare and contrast the excitation properties of cardiac myocytes and cardiac tissue modeled by (a) a Hodgkin-Huxley-model (HHM) and (b) Markov-chain-model (MM) formalisms for the sodium (Na) ion channel. Specifically, we bring out the differences between HHM and MM formalisms, for both wild-type (WT) and mutant (MUT) models, for ion-channel kinetics, single-myocyte action potentials, and the spatiotemporal evolutions of spiral and scroll waves in different mathematical models of cardiac tissue. We show that the kinetic properties of Na ion channels are not the same for HHM and MM models; in particular, the range of values of the trans-membrane potential V m , in which there is a significant window current, depends significantly on these models, so there are marked differences in the opening times of the Na ion channels, the maximal amplitude of the Na current, and the presence or absence of a late Na current. Furthermore, these changes lead to different excitation behaviors in cardiac tissue; specifically, two of the WT models show stable spiral waves, but the other one shows meandering and transiently breaking spiral waves. Our results are based on extensive direct numerical simulations of waves of electrical activation in these models, in two-and three-dimensional (2D and 3D) homogeneous simulation domains and also in domains with localized heterogeneities, either obstacles with randomly distributed inexcitable regions or mutant cells in a wild-type background. Our study brings out the sensitive dependence of spiral-and scroll-wave dynamics on these five models and the parameters that define them. We list desiderata for a good model for the Na wild-type ion channel; we use these desired properties to select one of the MM models that we study.

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“…We use the S1-S2 cross-field protocol [21] to initiate spiral waves in a square simulation domain of side L = 256 mm. In this protocol, we apply S1 and S2 stimuli with strengths 150 pA/pF for 3 ms.…”

Section: Modelmentioning

confidence: 99%

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and Purkinje fibers

2017

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We present systematic numerical studies of the possible effects of the coupling of human endocardial and Purkinje cells at cellular and two-dimensional tissue levels. We find that the autorhythmic-activity frequency of the Purkinje cell in a composite decreases with an increase in the coupling strength; this can even eliminate the autorhythmicity. We observe a delay between the beginning of the action potentials of endocardial and Purkinje cells in a composite; such a delay increases as we decrease the diffusive coupling, and eventually a failure of transmission occurs. An increase in the diffusive coupling decreases the slope of the action-potential-durationrestitution curve of an endocardial cell in a composite. By using a minimal model for the Purkinje network, in which we have a two-dimensional, bilayer tissue, with a layer of Purkinje cells on top of a layer of endocardial cells, we can stabilize spiral-wave turbulence; however, for a sparse distribution of Purkinje-ventricular junctions, at which these two layers are coupled, we can also obtain additional focal activity and many complex transient regimes. We also present additional effects resulting from the coupling of Purkinje and endocardial layers and discuss the relation of our results to the studies performed in anatomically accurate models of the Purkinje network.

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Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation

Cited by 12 publications

References 105 publications

Turbulent states and their transitions in mathematical models for ventricular tissue: The effects of random interstitial fibroblasts

Turbulent states and their transitions in mathematical models for ventricular tissue: The effects of random interstitial fibroblasts

Comparisons of wave dynamics in Hodgkin-Huxley and Markov-state formalisms for the sodium (Na) channel in some mathematical models for human cardiac tissue

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and Purkinje fibers

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