Arrhythmia Mechanisms and Spontaneous Calcium Release: II - From Calcium Spark to Re-entry and Back

Motivation The role of sub-cellular spontaneous calcium release events (SCRE) in the development of arrhythmia associated with atrial and ventricular tachycardia and fibrillation has yet to be investigated in detail. SCRE may underlie the emergence of spontaneous excitation in single cells, resulting in arrhythmic triggers in tissue. Furthermore, they can promote the substrate for conduction abnormalities. However, the potential interactions with re-entrant excitation have yet to be explored. The primary aim of this study was therefore to apply a novel computational approach to understand the multi-scale coupling between re-entrant excitation and SCRE. Methods A general implementation of Spontaneous Release Functions - which reproduce the calcium dependent SCRE dynamics of detailed cell models at a significantly reduced computational cost - was used to reproduce SCRE in tissue models. Arrhythmic dynamics, such as rapid pacing and re-entry, were induced in the tissue models and the resulting interactions with SCRE were analysed. Results In homogeneous tissue, the emergence of a spontaneous beat from a single source was observed and the positive role of coupling was demonstrated. Conduction block could be promoted by SCRE by both inactivation of the fast sodium channel as well as focal pacing heterogeneity interactions. Sustained re-entrant excitation promoted calcium overload, and led to the emergence of focal excitations both after termination of re-entry and also during re-entrant excitation. These results demonstrated a purely functional mechanism of re-entry and focal activity localisation, related to the unexcited spiral wave core. Conclusions SCRE may interact with tissue excitation to promote and perpetuate arrhythmia through multiple mechanisms, including functional localisation and mechanism switching. These insights may be particularly relevant for successful pharmacological management of arrhythmia.

Tachycardia and fibrillation describe rapid cardiac arrhythmias which interrupt the regular 3 electrical activity of the heart and can lead to reduced cardiac output and sudden cardiac death 4 [1]. The underlying rapid and irregular electrical activation of cardiac tissue may be mediated by 5 abnormal spontaneous pacing (focal ectopic activity), self-perpetuating re-entrant excitation, or 6 a complex interplay between both mechanisms [1,2]. Management of these arrhythmias is 7 typically challenging, often requiring invasive procedures such as implanted defibrillators or 8 catheter ablation; even these interventions have limited success rates [3,4]. Improved 9 understanding of the mechanisms underlying the genesis, perpetuation and recurrence of rapid 10 arrhythmias is vital for the development of improved treatment strategies.

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The potential links between stochastic sub-cellular dynamics of the intracellular calcium (Ca 2+ ) 3 In this manuscript, the multi-scale framework presented in the preceding study is applied to: (i) 4 highlight the mechanisms of synchronisation of SCRE to form an ectopic beat, and (ii) investigate 5 the role of SCRE variability in its SR-Ca 2+ dependence; (iii) demonstrate different mechanisms of 6 SCRE mediated conduction block; and (iv) investigate the coupling between SCRE and re-entry 7 underlying sustained arrhythmia. The results illustrate the general mechanisms of coupling 8 between SCRE and arrhythmia, present a novel mechanism of functional localisation of focal and 9 re-entrant excitation, and represent an initial step towards full assessment of the importance and 10 mechanisms of SCRE in cardiovascular disease morbidity and mortality.

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Multi-scale modelling of spontaneous calcium release events 13 This section only briefly outlines the detailed methods presented in the preceding study, 17

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The basis of the computational framework is a structurally idealised model of spatio-temporal 19 calcium handling which is capable of reproducing SR-Ca 2+ dependent SCRE ( Figure 1A). The  Figure 1D) -can be randomly sampled from the appropriate inverse functions in order to 25 generate SCRE which vary in timing and morphology with the given SR-Ca 2+ dependence. These 26 SRF can then be incorporated into Hodgkin-Huxley type non-spatial cell models and in idealised 27 and realistic tissue models, allowing simulations of SCRE at the tissue scale ( Figure 1E).
where t i is the initiation time of the SCRE, t f is the end time (duration, λ, thus = t f -t i ), t p is the time 19 of the peak of the waveform and N RyR_O peak is the peak of open proportion RyR. The amplitude, 20 N RyR_O peak , depends directly on the duration, and the peak time, t p , approximately varies evenly 21 within the duration; the waveform is therefore completely described by two parameters: Duration, λ:  in ms) must be determined, in addition to the probability of release, P(SCR).

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Implementations were presented where these parameters were either directly set 13 (corresponding to a specific dataset; Direct Control implementation), fit to the dynamics of the 14 3D cell model in multiple conditions (Dynamic Fit SRF implementation; Figure 1C), or where the 15 SR-Ca 2+ -dependence of the distributions was determined through controllable inputs (General 16 Dynamic SRF implementation; Figure 1C). Whereas a primary aim of the previous study was to 17 develop an approach to allow direct translation of 3D cell modelling studies to the organ scale, 18 the General Dynamic SRF implementation ( Figure 1D) offers the most powerful approach to 19 conduct the mechanistic investigation of this study's ambitions. In this implementation, the SRF 20 input parameters (P(SCR), t i_sep , CF ti,Sep , k F1 , k F1 , MD), which define the inverse functions from 21 which the actual waveform parameters are sampled (equations 6-9), are determined from the SR-  to the unexcited core illustrated in A) is highlighted in red in the recovery time map and green in 40 the activation maps. Note the correlation between activation source and this highlighted region.
1 C -Mechanism switching between re-entrant and focal excitation, showing the AP from a 2 randomly selected cell (a) and temporal snapshots associated with the transition from re-entry 3 to focal activity (b) and focal activity to re-entry (c). Snapshots corresponds to the temporal range 4 illustrated by the grey and white bars with solid (re-entry to focal) and broken (focal to re-entry) 5 borders.  3 Furthermore, these lower probability events indicate the presence of a minimal substrate for the 4 emergence of focal activity which may arise with very low probability under conditions without 5 significant single-cell SCRE; certainly, the mechanism by which focal activity emergences permits 6 this possibility: consider the potential rare occurrence associated with low-probability SCRE in 7 which the activity is localised and the large amplitude releases are well timed relative to 8 surrounding tissue to initiate TA. It is possible that these low probability events play an important 9 role in the spontaneous initiation of arrhythmia in predominantly healthy patients. Full 10 characterisation of this minimal substrate is therefore vital for quantitative assessment of the 11 potential importance of these events; such work is currently being carried out.

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The mechanisms by which a suitably timed focal excitation can result in conduction block and the 14 onset of self-perpetuating re-entrant excitation have been extensively studied previously (e.g.

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[20]); the present study also demonstrates a feedback mechanism by which re-entrant excitation  I would like to thank Dr Izzy Jayasinghe, University of Leeds, for providing experimental data used 10 in Figure 7, and also to Dr Al Benson for providing comments and feedback on the manuscript.    6 shown) and the blue trace to the simulations illustrated in (ii), in which DADs inhibit the 7 propagation of excitation following the applied stimulus. B -AP traces (i) and temporal snapshots 8 (ii) of SCRE focal activity resulting in conduction block due to transmural AP heterogeneity in the 9 ventricular wall. The purple trace in (i) corresponds to the homogeneous condition, in which the 10 focal excitation propagates uniformly; the blue trace corresponds to the heterogeneous condition 11 in which focal excitation propagates non-uniformly following conduction block. 1 2 Figure 5: Coupling between re-entry and SCRE. A -SR-Ca 2+ concentration (i) and V m (ii) 3 associated with sustained re-entry followed by self-termination (at around 8 s), simulations 4 without SCRE (purple) and with the General Dynamic SRF model with two different thresholds 5 (orange, 1.125 mM; blue, 1.0 mM). B -Temporal snapshots of voltage in the 2D sheet associated 6 with the traces shown in A, showing self-termination (i) and the emergence of delayed (ii, 7 corresponding to the orange traces in A) and rapid (iii, corresponding to the blue trace in A) focal 8 excitations. C -Examples of non-localised focal excitations emerging in the 2D sheet (i) and 3D 9 whole atria models (ii). and then focal excitations. Highlighted region (circle) illustrates the island of large SR-Ca 2+ 6 associated with the unexcited scroll wave core (i-iv) and its correlation with the focus of ectopic 7 activation (vi-vii). B -Examples of recovery time maps (a) and focal activation maps (b) for 6 8 independent simulations (i-vi) associated with the self-termination of re-entry followed by 9 ectopic excitation. The contour surrounding the region of longest recovery time (corresponding 10 to the unexcited core illustrated in A) is highlighted in red in the recovery time map and green in 11 the activation maps. Note the correlation between activation source and this highlighted region. 1 randomly selected cell (a) and temporal snapshots associated with the transition from re-entry 2 to focal activity (b) and focal activity to re-entry (c). Snapshots corresponds to the temporal range 3 illustrated by the grey and white bars with solid (re-entry to focal) and broken (focal to re-entry) 4 borders.

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Page 27 of 27 1 2 Figure 7: Mechanisms of coupling between SCRE and arrhythmia. Cellular cross section data 3 (part 2) provided by Dr. Izzy Jayasinghe, University of Leeds. Illustration of atrial heterogeneity 4 (part 6) reproduced with permission from [20]. All other illustrations utilise data from this or the 5 related study.