A master stability function approach to cardiac alternans

Lai, Yi Ming; Veasy, Joshua; Coombes, Stephen; Thul, Rüdiger

doi:10.1007/s41109-019-0199-z

Cited by 4 publications

(4 citation statements)

References 45 publications

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“…3 and 4. This is consistent with our earlier findings, which have demonstrated a rich pattern space of subcellular Ca 2+ alternans [12,13].…”

Section: Bufferssupporting

confidence: 94%

“…Crucially, the shape of the Ca 2+ alternans may depend on the form of coupling. In a recent model of Ca 2+ cycling, Ca 2+ alternans emerge for dominant cytosolic coupling via the traditional period-doubling bifurcation, where an eigenvalue of the associated linearised map exits the unit disk through −1 35 along the real axis [12,13]. Here, each node exhibits alternating Ca 2+ dynamics, and neighbouring nodes (or nodes in different parts of a cell) oscillate out-ofphase with each other.…”

mentioning

confidence: 99%

“…1, 2, 6 and 8 illustrate, the Ca 2+ profiles across the network exhibit significant variability. In a PWL model, these patterns can be classified and understood from 345 a linear stability analysis, which can be performed in closed form[12,13]. On the other hand, the nonlinear model requires direct simulations, which are computationally more expensive and limited in scope as to what parameter values to sample.As stated above, our focus here is on tubulated myocytes.…”

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confidence: 99%

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Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans

Lai

Coombes

Thul

2019

Preprint

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In cardiac myocytes, calcium cycling links the dynamics of the membrane potential to the activation of the contractile filaments. Perturbations of the calcium signalling toolkit have been demonstrated to disrupt this connection and lead to numerous pathologies including cardiac alternans. This rhythm disturbance is characterised by alternations in the membrane potential and the intracellular calcium concentration, which in turn can lead to sudden cardiac death. In the present computational study, we make further inroads into understanding this severe condition by investigating the impact of calcium buffers and L-type calcium channels on the formation of subcellular calcium alternans when calcium diffusion in the sarcoplasmic reticulum is strong. Through numerical simulations of a two dimensional network of calcium release units, we show that increasing calcium entry is proarrhythmogenic and that this is modulated by the calcium-dependent inactivation of the L-type calcium channel. We also find that while calcium buffers can exert a stabilising force and abolish subcellular Ca 2+ alternans, they can significantly shape the spatial patterning of subcellular calcium alternans. Taken together, our results demonstrate that subcellular calcium alternans can emerge via various routes and that calcium diffusion in the sarcoplasmic reticulum critically determines their spatial patterns. alternans, saddle-node bifurcation 1. Intoduction Cardiac arrhythmias constitute a leading public health problem and cause most cases of sudden cardiac death. In the US alone, sudden cardiac death accounts for approximately 300, 000 − 450, 000 lives every year [1]. Among the many forms of cardiac arrhythmias, cardiac alternans feature prominently. This 5 rhythm disturbance at the level of a single cardiac myocyte is characterised by alternating patterns of the membrane potential and the intracellular calcium (Ca 2+ ) concentration on successive beats. For instance, at one beat, a long action potential duration (APD) is accompanied by a large intracellular Ca 2+ transient, while on the next beat, the APD is shortened concomitant with a 10 small amplitude Ca 2+ transient. As a consequence, contractile efficiency is impaired, which in turn can cause a detrimental reduction in blood flow. In early experimental studies, the intracellular Ca 2+ concentration was averaged across a cardiac myocyte. The advent of high-resolution microscopy revealed that alternating Ca 2+ dynamics were already present at individual Ca 2+ release units 15 (CRU). While one CRU follows a pattern of large-small-large Ca 2+ transients, neighbouring CRUs exhibit small-large-small Ca 2+ transients. Crucially, both CRUs experience the same membrane potential. These findings gave rise to the concept of subcellular Ca 2+ alternans [2-10] and illustrated that nonlinear processes govern cardiac dynamics across multiple scales: the cell wide membrane 20 potential and the Ca 2+ fluxes restricted to single dyadic clefts.The existence of subcellular Ca 2+ alternans reinforces the n...

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“…3 and 4. This is consistent with our earlier findings, which have demonstrated a rich pattern space of subcellular Ca 2+ alternans [12,13].…”

Section: Bufferssupporting

confidence: 94%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans

Lai

Coombes

Thul

2019

Preprint

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“…The indirect coupling scheme in HR model is investigated with MSF and quantified the significance of coupling strength of the synchronization [17,34,35]. Highly complex network of networks such as calcium release unit in Cardiac myocytes and stability changes with different network patterns were studied using MSF, the effectiveness of plotting Zero-contour shown in [36]. MSF for a multiplex networks with nonidentical inner coupling between layers is discussed in [37].…”

Section: Introductionmentioning

confidence: 99%

Stability of synchronisation manifold in coupled fractional order nonlinear oscillators: a master stability function approach

Rajagopal¹,

Jafari

Duraisamy³

et al. 2023

Preprint

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Master stability function (MSF) plays a substantial role in understanding the synchronisation behaviour of coupled nonlinear oscillators. Recent attention in the fractional calculus and its applications in nonlinear dynamics has expanded to investigate the network dynamics of them. Hence, we derive the MSF for couped fractional order nonlinear oscillators and investigate their relation with coupling strength and fractional order. To make the comparison between integer and fractional order MSF, we have used well known nonlinear oscillators for investigation. Similar to the integer order, the fractional order coupled nonlinear oscillators too exhibit MSFs which are analysed for existence of negative with in the finite interval of normalized coupling parameter value. We have used the same classifications of integer order MSFs to define different classes for fractional order MSF’s. By using numerical simulations, we could show that majority of fractional order coupled oscillators exhibit higher classes of MSF confirming better synchronisation compared to their integer order counterparts.

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Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans

Lai

Coombes

Thul

2020

Communications in Nonlinear Science and Numerical Simulation

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A master stability function approach to cardiac alternans

Cited by 4 publications

References 45 publications

Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans

Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans

Stability of synchronisation manifold in coupled fractional order nonlinear oscillators: a master stability function approach

Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans

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