Human Atrial Arrhythmogenesis and Sinus Bradycardia in KCNQ1-Linked Short QT Syndrome: Insights From Computational Modelling

Atrial fibrillation (AF) and sinus bradycardia have been reported in patients with short QT syndrome variant 2 (SQT2), which is underlain by gain-of-function mutations in KCNQ1 encoding the α subunit of channels carrying slow delayed rectifier potassium current, IKs. However, the mechanism(s) underlying the increased atrial arrhythmogenesis and impaired cardiac pacemaking activity arising from increased IKs remain unclear. Possible pharmacological interventions of AF in the SQT2 condition also remain to be elucidated. Using computational modelling, we assessed the functional impact of SQT2 mutations on human sinoatrial node (SAN) pacemaking, atrial repolarisation and arrhythmogenesis, and efficacy of the anti-arrhythmic drug quinidine. Markov chain formulations of IKs describing two KCNQ1 mutations – V141M and V307L – were developed from voltage-clamp experimental data and then incorporated into contemporary action potential (AP) models of human atrial and SAN cells, the former of which were integrated into idealised and anatomically detailed tissue models. Both mutations shortened atrial AP duration (APD) through distinct IKs ‘gain-of-function’ mechanisms, whereas SAN pacemaking rate was slowed markedly only by the V141M mutation. Differences in APD restitution steepness influenced re-entry dynamics in tissue – the V141M mutation promoted stationary and stable spiral waves whereas the V307L mutation promoted non-stationary and unstable re-entrant waves. Both mutations shortened tissue excitation wavelength through reduced effective refractory period but not conduction velocity, which served to increase the lifespan of re-entrant excitation in a 3D anatomical human atria model, as well as the dominant frequency (DF), which was higher for the V141M mutation. Quinidine was effective at terminating arrhythmic excitation waves associated with the V307L but not V141M mutation, and reduced the DF in a dose-dependent manner under both mutation conditions. This study provides mechanistic insights into different AF/bradycardia phenotypes in SQT2 and the efficacy of quinidine pharmacotherapy.

Parameters describing KCNQ1 V307L mutant and wild type (WT) I Ks were incorporated exactly as described previously (Adeniran et al., 2017). The response of WT and mutant currents to simulated voltage clamps and corresponding I-V relation and steady state activation is shown in Figures S2A,B. Furthermore, as this study focuses on I Ks in the human atria, the responses of the MC models of WT and V307L mutant I Ks to AP clamps using a (simulated) human atrial AP waveform were compared with experimental data (El Harchi et al., 2010). The resulting I Ks profiles are shown in Figure S2C, where close concordance can be seen with experiment.
The MC formulation of I Ks was subsequently employed to develop a model of the V141M mutation in KCNQ1, first described by Hong et al. (Hong et al., 2005). An additional parameter, ξ, was introduced to account for the constitutively active, voltage-independent component of I Ks observed in KCNQ1 V141M mutant channels (Hong et al., 2005;Restier et al., 2008). In the V141M mutation condition, the formulation for I Ks was thus modified to where the MC state equations were the same as given previously. The response of V141M mutant currents to simulated voltage clamps and corresponding I-V relation and steady state activation is shown in Manuscript Figure 1. It should be noted that the trace for WT I Ks in Manuscript Figure 1 is not identical to that presented in Figure S2 due to differences in both the protocol used and a large difference in temperature (given in figure legends). Transition rates for WT, V307L, and V141M mutant channels (corresponding to the MC scheme in Figure S1) are given in Figure S3.

Modelling electrophysiology of the human atria
An updated version of the Colman et al. model of the human atrial AP, which is well suited to the simulation of re-entrant atrial arrhythmias (Colman et al., 2013(Colman et al., , 2017Whittaker et al., 2017b), was used for the modelling in this study  (and is referred to as the CNZ model). The I Ks equations (native to the parent CRN model (Courtemanche et al., 1998)) were replaced with the WT formulation of I Ks , with a conductance of 0.161 nS/pF (which places the current density within the range observed in human atrial myocytes (Caballero et al., 2010) -Supplementary Figure S4). Furthermore, the MC model of I Kr /hERG developed in our previous study (Whittaker et al., 2017a) was incorporated into the CNZ model with the conductance set to 0.0111 • [ + ] 0.59 , where [ + ] is the extracellular potassium concentration (allowing for simulation of drug binding of quinidine to I Kr see Supplementary Methods 1.5). The resulting WT AP had an APD 90 of 250.0 ms at 1 Hz, which is well within the experimentally-measured range of APDs in human atrial myocytes (Bosch et al., 1999;Calum J Redpath, 2006;Dobrev and Ravens, 2003;Katoh et al., 2005;Kim et al., 2002;Pau et al., 2007)see Table S1. This ensured that the role of I Kr on the AP remained the same as in the original Colman et al. model, based on the original data from human atrial myocytes (Courtemanche et al., 1998;Wang et al., 1994).
A family of regional cell models was developed based on experimentally-measured changes in maximal current density of several ionic currents in different regions of the atria (Colman et al., 2013), where conductance changes were implemented relative to the baseline right atrium (RA) model. Data from canine atrial myocytes were used primarily (Burashnikov et al., 2004;Cha et al., 2005;Datino et al., 2010;Ehrlich et al., 2003;Feng et al., 1998;Li et al., 2001), as these are much more readily available than human atrial data (Caballero et al., 2010;Gong et al., 2008;Katoh et al., 2005). Changes to maximal ionic conductances used to create a family of regional cell models can be seen in Table S2. The response of regional cell models to SQT2 mutants at 1 Hz is shown in Figure  S5.
APD restitution curves were measured using an S1-S2 protocol. 400 conditioning S1 stimuli were delivered at a pacing frequency of 1 Hz (stimulus strength 20 pA/pF and duration 2.0 ms), following which an S2 stimulus was applied at varying intervals. APD restitution curves were generated by plotting the APD (measured from the maximum upstroke velocity to the point at which the membrane potential crossed −70 mV) against the corresponding diastolic interval (DI), which was computed using DI = S2 -APD, where S2 denotes the S1-S2 interval. Maximum slope of restitution was determined as the maximal derivate of APD against DI.

Modelling the effects of AF-induced remodelling
In this study, as a theoretical consideration, the effects of AF-induced electrical remodelling were simulated using the same approach adopted in previous studies (Colman et al., 2013(Colman et al., , 2017. Evidence of AF-induced remodelling in the SQTS is currently lacking; nevertheless, it is useful to consider electrical remodelling which could potentially arise from persistent forms of AF induced by genetic mutations in the SQTS. Consistent with experimental evidence (Bosch et al., 1999;Wagoner et al., 1999;Workman et al., 2001), AF-induced remodelling of atrial myocytes was assumed to markedly reduce the maximal conductance of I CaL , I to , and I Kur , whereas the conductance of I K1 , I Ks , and I NaCa were all increased. A list of parameter changes in the AF model relative to the baseline sinus rhythm (SR) model is given in Table S3. In addition, in tissue simulations with AF-induced electrical remodelling, the value of the diffusion coefficient, D, was reduced by 40% in order to simulate possible connexin and structural remodelling (a reduction in D increases the effective tissue size) associated with AF (Colman et al., 2013(Colman et al., , 2017. As structural/connexin remodelling may occur without electrical remodelling, simulations were also performed with D reduced by 40% but no AFinduced electrical remodelling. A comparison of the CNZ model AP under SR and AF remodelling conditions at 1 Hz is shown and compared to experimentally-measured human atrial APs from Dobrev et al. (Dobrev and Ravens, 2003), Bosch et al. (Bosch et al., 1999), Workman et al. (Workman et al., 2001), van Wagoner et al. (Van Wagoner and Nerbonne, 2000), and Voigt et al. (Voigt et al., 2012) in Figure S6. The simulated AF conditions produced changes to the AP which were strongly concordant with those observed experimentally; namely, (i) the markedly shortened APD associated with AF-induced electrical remodelling, and (ii) the more triangular AP morphology. In SQT2 mutation conditions, the simplifying assumption was made that electrical remodelling associated with AF was identical to that in the absence of SQTS gene mutations (minus effects on I Ks ), and was thus also implemented using the parameters given in Table S3. It should also be noted that whereas remodelling of I Kur under AF conditions was included in the model based on certain experimental data (Caballero et al., 2010;Christ et al., 2004;Wagoner et al., 1997), other studies have reported no changes in I Kur under human AF remodelling conditions (not shown in Table S3) (Bosch et al., 1999;Workman et al., 2001).
Reduced I Kur was included in this study as it better reproduced the AP morphology associated with AF remodelling.

Modelling electrophysiology of the human sinoatrial node
The recently-developed human sinoatrial node (SAN) model of Fabbri et al. (Fabbri et al., 2017), referred to as the FS model, was used to simulate primary pacemaking in the human heart in this study. The native equations for I Ks were replaced with the MC formulation developed in this study, with the maximal conductance set to a value of 0.00965 nS/pF. This gave a natural cycle length of 818 ms, which is in good agreement with the value of 828 ± 21 ms measured experimentally by Verkerk et al. (Verkerk et al., 2007). It should be noted that this involved updating the reversal potential, E Ks , from the potentially unphysiological value of −49 mV in the original model, to the more realistic value of ~−75 mV for consistency with CNZ human atrial simulations. This meant that the new formulation of I Ks in the updated FS model is always an outward current, and thus current density had to be reduced in order to give the same contribution from I Ks as in the original model. Furthermore, it also meant that I Ks always shortens the APD as it is an outward current exclusively, so the APD 50 and APD 90 values are smaller than published values from the original FS model (Fabbri et al., 2017).
The effects of autonomic modulation by 10 nM acetylcholine (ACh) in the FS model were simulated through a −7.5 mV shift in funny current (I f ) activation, a 3.1% reduction in L-type calcium channel current (I CaL ) maximum conductance, and a 7% decrease in sarcoplasmic reticulum Ca 2+ uptake (in addition to the effects of the acetylcholine-activated potassium current, I K,ACh ) (Fabbri et al., 2017). A comparison between FS model AP characteristics (in the absence of autonomic modulation) and experimentally-measured values is shown in Figure S7. The diastolic depolaristion rate (DDR) was calculated using DDR = (TOP−MDP)/(t TOP −t MDP ), where TOP is the take-off (threshold) potential, MDP is the maximum diastolic potential (i.e. the minimum potential attained), and t TOP and t MDP are the times at which the TOP and MDP occur, respectively.

Modelling pharmacological actions of quinidine
In this study, the actions of quinidine on human atrial electrophysiology were represented using the same formulations and IC 50 (half maximal inhibitory concentration) values presented in our previous study (Whittaker et al., 2017a). Briefly, in that study, state-dependent models of the actions of quinidine were developed for I Na and I Kr , and a simple pore block approach was used to describe block of I CaL , I to , I Ks , I K1 , and I NaL (late sodium current block was not included in the present study). Quinidine block of I Kur was additionally accounted for in the present study (Nenov et al., 1998). In the simple pore block theory (Brennan et al., 2009), the maximal conductance g i of an ionic current type i is modified in a concentration-dependent manner, such that where g control,i represents the maximal conductance of the i channel in drug-free conditions, [D] is the concentration of the drug, and nH is the Hill coefficient. A summary of IC 50 values for quinidine block of multiple ionic currents is given in Table S4.
As described previously (Whittaker et al., 2017a), quinidine was assumed to bind to activated, inactivated, and rested sodium channels. The formulation for I Na is thus given by the guarded receptor equations where g Na is the maximal channel conductance, b A , b I , and b R are the fractional blocks of activated, inactivated, and resting states, respectively, m is the activation gate, h and j are the fast and slow inactivation gates of the sodium channel, respectively, E Na is the Na + reversal potential, and all other parameters retain their previous definitions. Binding and unbinding rates of quinidine to sodium channels are given in Table S5, and model fits to experimental data (Koumi et al., 1992) are shown in Figure S8.
Quinidine was assumed to block the open and inactivated states of hERG channels (Whittaker et al., 2017a), which was modelled through addition of drug-bound open and inactivated states to the MC model of I Kr /hERG used in this study. The formulation for I Kr is given by where g Kr is the maximal channel conductance, O an open state, I an inactivated state, C1, C2, and C3 are closed states, O* and I* represent drug-bound open and inactivated states, respectively, E Kr is the K + reversal potential, and k X and l X are binding and unbinding rate constants for states of type X, respectively. Binding and unbinding rates of quinidine to hERG channels are given in Table S6, and model fits to experimental data (McPate et al., 2008;Paul et al., 2002) are shown in Figure S9. Full details of the parameter estimation procedure for drug binding models of quinidine are given in our previous study (Whittaker et al., 2017a).

Tissue simulations
Propagation of excitation waves in tissue was described using the monodomain equation (Clayton et al., 2011), where V is the transmembrane voltage, D is the tensor of diffusion coefficients, I ion is the total ionic current, and C m is the membrane capacitance. Eq. (S34) was solved using a finite difference PDE solver based on the explicit forward Euler method and Strang splitting scheme . The pseudo-ECG (pECG) was calculated according to (Plonsey and Barr, 2013), i.e.
where Φ is a unipolar potential generated by the multicellular tissue preparation, r is the distance between a source point (x, y, z) and the coordinate of a virtual electrode (x', y', z'), and Ω is the domain of integration (i.e. atrial tissue volume).

One-dimensional (1D) tissue models
An electrically-homogeneous, isotropic right atrial 1D strand of 100 nodes with spacing 0.25 mm was used to assess the effects of KCNQ1 mutations on the effective refractory period (ERP), conduction velocity (CV), and wavelength of re-entry (WL) (Whittaker et al., 2017b). Steady state variables from single cell models across a range of basic cycle lengths (BCL) at intervals of 10 ms were saved and read into the 1D model as initial conditions for computation of steady-state restitution curves for ERP, CV, and WL. When measuring the ERP, a threshold of −20 mV was used to define atrial activation (Whittaker et al., 2017b). The CV was determined by computing the quotient of the distance of the centre section of the 1D strand and the activation time of the same section by an excitation wave. The simulated CV in the 1D strand under baseline conditions was 0.7 ms −1 , close to experimental measurements in the RA free wall (Fedorov et al., 2010). Tissue WL was calculated according to WL = CV × ERP.

Two-dimensional (2D) tissue models
In order to characterise spiral wave dynamics in WT and SQT2 mutant tissue, an isotropic 2D sheet of electrically-homogeneous atrial tissue with dimensions 100×100 mm 2 and spatial step 0.25 mm was employed (Whittaker et al., 2017b). Spiral waves were initiated using a cross-field S1-S2 stimulation protocol, wherein one edge of the sheet was paced with four conditioning S1 stimuli at a BCL of 400 ms using steady-state initial conditions obtained in a single cell environment, followed by application of an S2 stimulus of area 50×50 mm 2 in the lower left quadrant of the sheet (Whittaker et al., 2017b). The S2 stimulus was applied at time, t = ERP+20 ms, which caused a uni-directional conduction block and resulted in development of a spiral wave under all conditions investigated. The resulting behaviour over a 5.0 s simulation period was recorded. The cores of spiral waves were tracked using the method of identifying phase singularities with time-delay embedding of the transmembrane potential (Bray and Wikswo, 2002) (using a time delay of τ = 10.0 ms).

Heterogeneous three-dimensional (3D) anatomical human atria geometry
The behaviour of re-entrant excitation waves in an anatomically-realistic setting was determined using a 3D human atria structured grid geometry based on the Visible Female dataset (Seemann et al., 2006), as has been employed in several of our previous studies (Colman et al., 2013(Colman et al., , 2017Kharche et al., 2012;Whittaker et al., 2017b). Fibre orientations were incorporated using a semiautomatic rule-based approach (Krueger et al., 2011(Krueger et al., , 2013, and the 3D geometry was segmented into the same distinct regions of the human atria as described in (Colman et al., 2013;Whittaker et al., 2017b). The transverse value of the diffusion coefficient, D, was set to 0.1 mm 2 ms −1 , where an anisotropy ratio of 3:1 was applied in directions longitudinal and transverse to fibres in the atrial working myocardium, and a ratio of 9:1 along the fast conducting bundles of the Bachmann's bundle, crista terminalis, and pectinate muscles (Colman et al., 2013;Whittaker et al., 2017b). The spacing between nodes, Δx, was set to Δx = 0.33 mm as determined by the data set resolution (Seemann et al., 2006). The 3D anatomical human atria geometry segmentation and fibre orientations are shown in Figure S10, as well as measured atrial activation times, which were in close agreement with experimental measurements (Lemery et al., 2007). Following stimulation of the SAN region (modelled electrically as CT tissue for simplicity (Colman et al., 2013(Colman et al., , 2017), the excitation spread radially outwards, first entering the LA at 29 ms (cf. 31±13 ms (Lemery et al., 2007)), fully activating the RA after 91 ms (cf. 93±17 ms (Lemery et al., 2007)), and with a latest LA activation time of 107 ms (cf. 116±118 ms (Lemery et al., 2007)).
In this study, re-entrant scroll waves were initiated using the phase distribution method (Biktashev and Holden, 1998)for detailed descriptions and illustrations of the phase distribution method see (Biktashev and Holden, 1998;Colman et al., 2017;Whittaker et al., 2017b). Where sustained reentrant activity was initiated, a power spectrum was obtained through Fourier transform analysis of pECG time series (the virtual electrode was placed approximately in the centre of the RA cavity).
The dominant frequency (DF) was computed using Matlab based on the largest peak in the power spectrum density (Whittaker et al., 2017b). It should be noted that this simple approach to computing the DF, described in our previous studies (Colman et al., 2013;Whittaker et al., 2017b), is different from the more commonly used definition (e.g. see Ng et al. (Ng et al., 2006)). For simulating the effects of quinidine on re-entrant wave patterns, state variables for each node within the 3D anatomical model were saved after 2.5 s of a 10.0 s episode of sustained re-entrant activity in drugfree conditions. These were then used as initial conditions for new 3D simulations of duration 7.5 s (giving 10.0 s activity overall) in which 1, 2 or 5 μM quinidine was applied immediately. Where applicable, the final 5.0 s of activity was analysed to compute the DF.

Comparison with an alternative human atria model
The human atrial cell model of Grandi et al. (Grandi et al., 2011), referred to in this study as the GB model, was used for comparative simulations. The GB model is largely derived from different experimental data to the CNZ model, and thus has a different AP morphology. The MC formulation of I Ks was incorporated into the GB model with a conductance of 0.012 nS/pF (it should be noted that is significantly smaller than the conductance used in the CNZ model, due to inherent differences in the role of I Ks between the models). This gave an APD 90 in the WT condition of 306.0 ms, close to that of the original published model (Grandi et al., 2011). APD restitution curves were computed using the same method that was used in the CNZ model (with the membrane potential threshold adjusted to −65 mV due to the slow repolarisation tail in the GB model).

Determinants of APD restitution steepness
Supplementary simulations were conducted in order to investigate why two KCNQ1 mutations which both cause a 'gain-of-function' in I Ks produced opposite effects on the maximum slope of restitution, shown in Figure S11. These investigations revealed the following: (1) A linear increase in the maximal conductance of I Ks in the WT condition, in order to match roughly the degree of APD shortening in the V307L mutation condition, increased the slope of restitution to an even greater extent than observed under V307L conditions. (2) Addition of the instantaneous voltage-independent component (ξ) in the V307L mutation condition dramatically reduced the maximum slope. (3) The maximum slope under V141M mutation conditions in which either (i) only ξ was considered or (ii) kinetics were kept the same but ξ was removed, remained much smaller than in the WT condition. These three observations suggest that increased I Ks early during the AP, either due to slower deactivation under SQT2 mutation conditions or presence of a constitutively active component, reduces the maximum slope of restitution. (4) A final hypothetical V141M mutation condition without ξ and with a 2.5-fold increase in maximal conductance of I CaL showed a restitution steepness close to that of the WT condition. This suggests that the effects of ξ on reducing I CaL are also an important factor in determining restitution steepness, in agreement with a previous study that suggested restitution of I CaL is a primary determinant of the steepness of APD restitution (Qu et al., 1999).

Comparison with an alternative human atria model
In comparative simulations using the GB model, the V141M and V307L KCNQ1 mutations produced much more modest APD shortening than in the CNZ model (due to smaller maximal I Ks conductance and lesser activation of I Ks during the AP; Figure S12). Nonetheless, a greater APD shortening under V141M mutation conditions than V307L mutation conditions was observed, consistent with CNZ model simulations (Supplementary Table S8). Furthermore, opposing effects on the maximal slope of APD restitution were similarly observed (decreased steepness for the V141M mutation and increased steepness for the V307L mutation). These findings are reassuring; in the CNZ model, greater APD shortening associated with the V141M mutation was responsible for the higher DF of re-entrant excitations than under V307L mutation conditions, and steepness of APD restitution in SQT2 mutation conditions mediated spiral wave dynamics. Both of these important determinants of tissue-level re-entrant wave behaviour were reproduced using the GB modelan alternative, wellestablished human atrial AP model (Grandi et al., 2011).

Effects of AF-induced electrical and structural remodelling on SQT2 phenotype
In the 3D anatomical human atria, the effects of quinidine on arrhythmic atrial excitation waves are shown in Manuscript Figure 7. Supplementary simulations were performed in order to investigate potential interactions between AF remodelling and KCNQ1 mutations. When AF-induced structural/connexin remodelling (40% reduction in D) was included, either alone or combined with electrical remodelling, quinidine was ineffective at pharmacological conversion of arrhythmic excitation waves under both mutation conditions ( Figure S13). However, quinidine still reliably decreased the DF in a dose-dependent manner. Figure (Dobrev and Ravens, 2003), (C) Bosch et al. (Bosch et al., 1999), (D) Workman et al. (Workman et al., 2001), (E) van Wagoner et al. (Van Wagoner and Nerbonne, 2000), and (F) Voigt et al. (Voigt et al., 2012). In all panels, a marker to the left of the APs represents a membrane potential of 0 mV, and the scale inset corresponds to 100 ms and 30 mV along the x and y axes, respectively.

Supplementary Videos
Video S1: Initiation and conduction of spiral waves in a 2D idealised geometry in the WT condition. Re-entry was initiated using an S1-S2 protocol: following propagation of a planar wave elicited with four conditioning S1 stimuli at a BCL of 400 ms, an S2 stimulus was applied in the lower left quadrant of the patch. The initiated spiral wave meanders out of the tissue boundaries after ~3.7 s.
Video S2: Initiation and conduction of spiral waves in a 2D idealised geometry in the WT-V141M condition. Re-entry was initiated using an S1-S2 protocol: following propagation of a planar wave elicited with four conditioning S1 stimuli at a BCL of 400 ms, an S2 stimulus was applied in the lower left quadrant of the patch. The initiated spiral wave persists as a stationary, stable wave for the duration of the simulation.
Video S3: Initiation and conduction of spiral waves in a 2D idealised geometry in the V141M condition. Re-entry was initiated using an S1-S2 protocol: following propagation of a planar wave elicited with four conditioning S1 stimuli at a BCL of 400 ms, an S2 stimulus was applied in the lower left quadrant of the patch. The initiated spiral wave persists as a stationary, stable wave for the duration of the simulation.
Video S4: Initiation and conduction of spiral waves in a 2D idealised geometry in the WT-V307L condition. Re-entry was initiated using an S1-S2 protocol: following propagation of a planar wave elicited with four conditioning S1 stimuli at a BCL of 400 ms, an S2 stimulus was applied in the lower left quadrant of the patch. The initiated spiral wave persists as a meandering but stable wave for the duration of the simulation.
Video S5: Initiation and conduction of spiral waves in a 2D idealised geometry in the V307L condition. Re-entry was initiated using an S1-S2 protocol: following propagation of a planar wave elicited with four conditioning S1 stimuli at a BCL of 400 ms, an S2 stimulus was applied in the lower left quadrant of the patch. The initiated spiral wave spontaneously degenerates into multiple waves, persisting for the duration of the simulation.
Video S6: Re-entrant scroll waves in the WT condition initiated in the 3D anatomical human atria model shown from two views-looking at the RA posterior wall (left) and into the cavities (right). A single scroll wave completes two circuits in the RA before self-terminating after ~0.6 s.
Video S7: Re-entrant scroll waves in the WT-V141M condition initiated in the 3D anatomical human atria model shown from two views-looking at the RA posterior wall (left) and into the cavities (right). Re-entry is driven by a single stationary scroll wave in the RA which follows a circuit along the junction of the crista terminalis and pectinate muscles, persisting for the duration of the simulation.
Video S8: Re-entrant scroll waves in the V141M condition initiated in the 3D anatomical human atria model shown from two views-looking at the RA posterior wall (left) and into the cavities (right). Re-entry is driven by a single stationary scroll wave in the right atrial appendage, persisting for the duration of the simulation.
Video S9: Re-entrant scroll waves in the WT-V307L condition initiated in the 3D anatomical human atria model shown from two views-looking at the RA posterior wall (left) and into the cavities (right). Scroll waves meander significantly throughout the atria, before settling into a persistent, anatomical re-entry around the opening of the inferior vena cava which lasts for the remainder of the simulation.
Video S10: Re-entrant scroll waves in the V307L condition initiated in the 3D anatomical human atria model shown from two views-looking at the RA posterior wall (left) and into the cavities (right). The initiated scroll wave moves unpredictably at first, then occasionally breaks and forms multiple wavelets which meander and collide. Re-entry ultimately settles into a persistent, anatomical re-entry around the opening of the inferior vena cava which lasts for the remainder of the simulation.
Video S11: Re-entrant scroll waves in the WT-V307L condition under application of 2 μM quinidine in the 3D anatomical human atria model shown from two views-looking at the RA posterior wall (left) and into the cavities (right). Following application of quinidine, the wavelength of re-entrant excitations is increased, which leads to termination of re-entry after ~7.5 s.