A Survey of Pathways for Mechano-Electric Coupling in the Atria

Mechano-electric coupling (MEC) in the atrial tissue has received sparse investigation to date, despite the well-known association between chronic atrial dilation and atrial fibrillation (AF). Of note, no fewer than six different mechanisms pertaining to stretch-activated channels, cellular conductance and geometric effects have been identified in the literature as potential players. In this mini review, we briefly survey each of these pathways to MEC. We then perform single cell and tissue simulations in presence of various combination of the mechanisms and applied stretch, in order to assess the relative significance of each mechanism in determining action potential duration, conduction velocity and rotor stability. For chronic stretch, we find that stretch-induced alterations in membrane capacitance decrease conduction velocity and increase action potential duration. In the presence of passive atrial stretch, stretch-activated channels play the largest role, leading to after-depolarizations and rotor hypermeandering.

• Several pathways for mechano-electric feedback exist, including stretch-activated channels (non-specific and permeable to potassium ions), stretch-induced alterations in cell membrane capacitance and intra-cellular calcium handling, geometric effects and effects mediated by non-cardiomyocytes. • Passive atrial strains need to be considered when incorporating mechano-electro feedback in atrial electrophysiology models.

Introduction
Arrhythmias are one of the major causes of death worldwide, accounting for 17 million deaths each year (Srinivasan and Schilling, 2018). Despite being disturbances of the propagation of electrical signals in the heart, their devastating impact is caused by their perturbation of the heart's mechanical function. This relationship between electrical impulses and cardiac contraction is mediated by wellknown electro-mechanical coupling pathways, involving intracellular calcium handling. It is also known that cardiac mechanics can influence the propagation of the electrical potential in the heart, although these mechano-electric coupling (MEC) mechanisms have received much less attention so far. Nevertheless, MEC effects can have a critical influence on cardiac function. The initiation of an arrhythmia through a high-impulse impact on the chest (commotio cordis) (Kohl et al., 1999) and the termination of the arrhythmia using a similar mechanism (Pennington et al., 1970) are some of the most dramatic manifestations of MEC.
MEC is expected to also play an important role in atrial arrhythmias, particularly in atrial fibrillation (AF), the most common sustained arrhythmia. AF is characterised by a rapid, irregular and ultimately inefficient contraction of the atria. It affected 32.5 million people worldwide in 2010 and its incidence in Western Europe is expected to rise to 3% of all adults aged over 20 by 2030 (Kirchhof et al., 2016). AF is independently associated with a two-fold increase in all-cause mortality and is strongly associated with stroke, heart failure and cognitive impairment (Kirchhof et al., 2016). AF is thus often accompanied by substantial decreases in quality of life and a high rate of hospitalizations (Calkins et al., 2012) and, altogether, the economic burden of AF already amounts to 1% of total healthcare costs in the UK (Kirchhof et al., 2016).
The electrophysiological mechanisms underlying AF are notoriously complex. As a consequence, treatment to restore sinus rhythm to AF patients is unfortunately relatively inefficient. Catheter ablation, arguably the most successful form of rhythm control treatment, suffers from 3-year recurrence rates as high as 53% for a single procedure, which improve to 73% only following repeat procedures (Ganesan et al., 2013).
Chronic atrial stretch (i.e. atrial dilation) is considered both a predisposing factor for AF and a consequence of AF-induced structural remodelling (Schotten et al., 2003) and, as such, has been used to predict the success of catheter ablations in AF (Berruezo et al., 2007;Varela et al., 2017). Animal and human studies of chronic atrial stretch widely demonstrate an enhanced sensitivity to AF induction and (often heterogeneous) conduction slowing but variable or negligible effects on the effective refractory period (ERP), as recently reviewed by (Thanigaimani et al., 2017). The mechanisms through which atrial dilation may promote AF are complex and may involve activation of multi-organ signalling pathways and a concomitant development of atrial fibrosis (Schotten et al., 2003) and inflammation (Verheule et al., 2004). Other direct pathways may involve an increase in the atrial surface area available for re-entrant electrical circuits and enhanced conductance of stretch-activated channels experienced by hypertrophied cardiomyocytes (Kamkin et al., 2000).
Acute atrial stretch is also known to lead to a plethora of electrophysiological changes, although many studies offer contradictory findings, particularly in relation to stretch-induced changes in ERP (Ravelli, 2003). Most animal and human studies suggest that acute atrial stretch leads to a reduction in overall conduction velocity (CV), an increase in CV heterogeneity and increased susceptibility to AF (Coronel et al., 2010;Ravelli et al., 2011;Thanigaimani et al., 2017;Walters et al., 2014). Stretch-induced afterdepolarizations and ectopic beats have also been reported (Franz, 2000).
Despite all the evidence for the important role MEC can play in atrial arrhythmias, there have been few computational modelling studies investigating the pathways through which MEC can contribute to atrial arrhythmias. When included, only certain MEC pathways have been considered in each study (Kuijpers et al., 2011(Kuijpers et al., , 2007 making it difficult to assess which of the MEC contributions are likely to play the most significant role in the genesis and maintenance of AF. Furthermore, most of the methodology for incorporating MEC in atrial models borrows heavily from ventricular studies, not making allowance for important effects such as the large passive strain experienced by the atria during ventricular contraction (Hoit, 2014). In this article, we aim to catalogue the proposed MEC pathways and perform initial simulations to assess their potential role in atrial arrhythmogenesis. We expect this to contribute to the creation of a set of standard mechanisms for incorporating MEC in computational simulations of atrial electrophysiology.

Computational Modelling of Arrhythmias
In this section, we briefly revisit the current standard methods for incorporating MEC in EP simulations, which have, in general, been created to study mechano-electric effects in the ventricles. We then discuss the alterations to these models that may make them more suitable for modelling MEC in the atria, before introducing the MEC pathways under study.
To date, computational models of arrhythmias usually restrict themselves to electrophysiology, disregarding any changes to atrial EP properties that may arise from the cardiac mechanical function. These studies typically involve the following steps: 1. Modelling the propagation of the action potential (AP) in tissue using an existing electrophysiological (EP) model; 2. Introducing forward electro-mechanical coupling by computing the active tension, Ta, generated by local changes in transmembrane voltage, Vm. This can be accomplished in two different formalisms: • a direct phenomenological relationship, usually an ordinary differential equation where changes in Ta depend explicitly on Vm (Nash and Panfilov, 2004;Panfilov et al., 2007). This is the usual approach employed when using a phenomenological EP model with a reduced number of channels, such as the Fenton-Karma (Fenton and Karma, 1998) or the Aliev-Panfilov (Aliev and Panfilov, 1996) EP models.
• a detailed physiological description of myofilament physiology, where intracellular calcium and its binding to sarcolemmal buffers mediate the relationship between Ta and V m (Land et al., 2017;Rice et al., 2008). This approach is usually employed when the EP model is very detailed and already involves explicit calculations of intracellular calcium concentration and calcium buffer dynamics.
3. Calculating the deformation (strains) experienced by the heart in response to the active tension Ta. This represents solving a classical solid mechanics problem, which relies on assumptions about the mechanical properties of myocardium. Most studies treat the myocardium as a hyperelastic medium. A detailed review of the constitutive models used to describe the passive mechanical properties of the myocardium can be found in (Avazmohammadi et al., 2019).
Although the template above can be used as a starting point for modelling MEC in the atria, differences between atrial and ventricular function should be taken into account: • Most of the strain experienced by the atria is passive ( Fig 1A). This is caused by both ventricular contraction and passive filling of the atria with blood (reservoir phase; systolic strain s = 29-48%) and subsequently by emptying of atrial blood to the ventricles (conduit phase; early diastolic strain e = 9-27%). Echocardiographic and CINE MRI studies suggest that these passive atrial strains greatly exceed those experienced during active atrial contraction (booster pump; active strain a = 8-20%). All quoted LA strains are adapted from the review by (Hoit, 2017) and are given as absolute values, with the atrial at its smallest size (just before the QRS complex) as the reference configuration. s corresponds to atrial stretch, whereas e and a are a measure of atrial contraction.
These measurements are typically performed by measuring changes in the length of a contour on a 2D atrial image and therefore the measured strain values do not represent length changes across the direction of maximum stretch/contraction, i.e. principal strain values. They are furthermore measured across large segments of the atria and therefore likely not to be representative of true regional strains. Finally, differences in imaging technique and methodology lead to a large spread in measured strain values (Tobon-Gomez et al., 2013). • To date, few studies have characterised the mechanical properties of the atria and, when this is has been done, a large variability in properties has been found across subjects and atrial regions (Bellini et al., 2013). It is also not clear what the appropriate boundary conditions in atrial mechanical models are (Di Martino et al., 2011). Atrial-specific constitutive models have not yet been adopted in most studies, except for the model proposed in (Bellini et al., 2013).

Pathways for Mechano-Electric Coupling in the Atria
In this section, we survey the pathways for MEC that are likely to play a role in the atria, as show in the diagram in Fig 2. The source of experimental data for these pathways is heterogeneous and often comes from ventricular cells or models. When relevant for the simulations we carried out, we provide expressions relating the considered pathways and the local stretch, .  represents the fractional stretch experienced by local myocytes.  = 1 corresponds to the reference, no-stretch configuration. More rigorously, = √det( ) where C is the right Cauchy-Green deformation tensor.
Figure 2: Mechano-electric coupling pathways considered in this study. Those in yellow font are also studied using simulations.

Mechanically gated channels
Several mechanically gated channels have been identified in the human heart. These include stretchactivated channels (SACs) and volume-activated channels as well as putative channels activated by changes in membrane curvature or thickness. In addition to all these, it is known that the properties of several ionic currents, such as INa, ICaL, IKATP and IK1, can be affected by mechanical stimuli, as detailed in a recent review (Peyronnet et al., 2016). Here, we will focus on stretch-activated channels, which are arguably the most important mediators of MEC at the ionic channel-level.
Stretch-activated channels (SACs) are protein complexes that span the sarcolemma and whose open probability increases in the presence of local membrane stretch. SACs can be divided into two broad categories: K+ permeable SACs (SAC_K) and non-specific SACs (SAC_NS).

Non-Specific
Stretch-Activated Channels K + -Permeable As with other potassium currents, the reversal potential for SAC_K is slightly more negative than the resting membrane potential (RMP). SAC_K thus contributes to the hyperpolarization/repolarization of the cell and, when activated, can shorten the action potential duration (APD) and the effective refractory period (ERP) and make RMP more negative (Peyronnet et al., 2016). There are several molecular candidates for SAC_K, such as TREK-1, TREK-2 and TRAAK. We model SAC_K as proposed by (Healy and McCulloch, 2005):

Alterations in Conductance
where u is the transmembrane potential scaled to the [0, 1] interval, as is typically done in lowdimensional ionic models such as the Fenton-Karma model (Fenton and Karma, 1998). gSAC_K , the channel conductance, has a value of 0.024 A as previously proposed (Healy and McCulloch, 2005).
SAC_NS, on the other hand, are permeable to a wider range of ions, placing their reversal potential between -20 and 0 mV (Peyronnet et al., 2016). If active during the repolarisation phases of the action potential, SAC_NS can increase APD and ERP and also make the RMP less negative. Piezo 1 or 2 and TRP channels are the most likely candidates for SAC_NS's molecular counterpart. SAC_NS are modelled as a passive current (Zeng et al., 2000): with gSAC_NS = 0.024 A and urev = 0.837.
Models of SAC_K and SAC_NS typically assume that these channels are either homogeneously distributed across the heart or that there is a ventricular transmural gradient (Healy and McCulloch, 2005). It is usually assumed that the channels' response does not depend on whether the sensed stretch is longitudinal or transverse relative to the myofibres. The response of these channels to an external stretch is also assumed to be instantaneous. Few experimental studies have specifically focused on atrial cells -an exception is (Kamkin et al., 2003).
Whereas most of these studies used ventricular geometries and/or ventricular ionic models, some have focused on the atria, including atrial ionic models that include AF remodelling (Brocklehurst et al., 2017) and atrial geometries (Kuijpers et al., 2011(Kuijpers et al., , 2007. Other atrial studies have included externally-imposed stretches (although not designed to mimic the ones experienced by the atria) and found that these affected the anchoring of spiral waves, often in the presence of other arrhythmogenic effects (Yamazaki et al., 2009(Yamazaki et al., , 2012.

Atrial myocyte capacitance
Some studies have shown a dependence of the capacitance of the cardiomyocyte cell membrane on local stretch (Mills et al., 2008). Although the sparsity of experimental data leads to ambiguities in the optimal choice of model, we follow here the Hill function formalism previously introduced for ventricular cells (Oliveira et al., 2015): Here, we treat the myocyte capacitance as a relative variable, with Cm = 1 A s/m 2 in the absence of stretch.

Ca 2+ handling and other intracellular processes
It is increasingly recognised that stretch can also affect intracellular processes, including the release of bound calcium from troponin C in myofilaments (Schönleitner et al., 2017;ter Keurs et al., 1998) and an increase in the open probability of ryanodine receptors, through the so-called X-ROS signalling processes (Prosser et al., 2011). These effects can lead to changes in electrophysiology by affecting Ca 2+ handling within myocytes, with some authors even proposing that they may be responsible for ectopic beats (ter Keurs et al., 1998;Timmermann et al., 2019). Moreover, alterations in intracellular Ca 2+ induced by stretch may also affect the conductivity of ionic channels sensitive to intracellular Ca 2+ , as discussed in more detail in (Calaghan et al., 2003). These Ca 2+ -mediated mechanisms are not amenable to study using simplified models of electrophysiology and will therefore not be examined in the current study. There are reviewed in more detail in (Timmermann et al., 2017). We also do not consider here the interesting effects stretch may have on gene expression in cardiomyocytes and other cellular constituents of the myocardium. These effects are reviewed in detail in (Saucerman et al., 2019).

Effect of stretch on non-cardiomyocytes
As arrhythmic mechanisms are unveiled, the role of cardiac cells other than atrial cardiomyocytes has become increasingly prominent. Atrial fibrotic remodelling is believed to be of particular importance, as fibrotic regions are known to be sites of slow and/or discontinuous conduction velocity (Nguyen et al., 2014) and likely rotor anchoring sites (Roy et al., 2018). Less is known about how fibrosis may play a role in arrhythmia mechanisms through MEC. Its high stiffness relative to healthy myocardium suggests that cardiomyocytes surrounding areas of fibrosis may undergo comparatively smaller deformations than areas of healthy myocardium further afield. This could further contribute to heterogeneities in EP properties across the atria, promoting arrhythmias (Weise and Panfilov, 2012). Further characterisation of the electrical and mechanical properties of non-cardiomyocytes is needed to study these effects in more detail.

Geometric effects and effects on conductivity
In some studies, the change in pathlength of the trajectory of the action potential induced by stretch has also been incorporated, as suggested by (Colli Franzone et al., 2017;Nash and Panfilov, 2004;Panfilov et al., 2007;Quarteroni et al., 2017) among others. In practical terms, this corresponds to solving the diffusion PDE governing the propagation of the action potential in a deforming geometry rather than in undeformed (material) coordinates. This approximation assumes that conduction velocity is dominated by intracellular conductivity, disregarding conduction delays at (intercellular) gap junctions. However, experimental studies suggest that conduction velocity across the cytoplasm of cardiomyocytes is several orders of magnitude higher than CV across gap junctions in 1D tissue strands, making conduction of the electrical signal almost saltatory (Rohr, 2004). This supports the suggestion that the geometric implications of the stretch of the cytoplasm of cardiomyocytes are negligible (Pfeiffer et al., 2013).
The conduction velocity in cardiomyocytes embedded in 3D tissue, nevertheless, appears to depend more on cytoplasmic conduction, presumably due to the averaging effects of lateral gap junctions (Rohr, 2004). This suggests that modelling the geometric effect of stretch on conduction velocity may be more complex than what has hitherto been considered.
In addition to the above, it is not clear whether electrical conductivity (typically incorporated in the electrical diffusion tensor, D, in modelling studies) is directly affected by stretch. Some studies have suggested that intercellular connectivity at gap junctions may be increased (Zhuang et al., 2000) or decreased (Kamkin et al., 2005;Mills et al., 2008) by stretch, whereas other have proposed that intracellular conductivity increases with (moderate) strains (McNary et al., 2008). Other studies have instead modelled the geometric effect of stretch by assuming a reduction in the number of gap junctions per unit length of chronically dilated atrial myocardium (Kuijpers et al., 2007) or alterations in the space constant of the tissue (Oliveira et al., 2015).

Methods
To further investigate which of the above MEC ways may have the largest contribution for atrial arrhythmogenesis, we conducted some initial computational simulations in a cuboid geometry exposed to different stretch protocols. Of the above pathways, we focused on stretch-activated channels and stretch-induced changes in membrane capacitance, as we found these were some of the best candidates for easy inclusion in future atrial EP simulations: the selected pathways are comparatively well-characterised experimentally and amenable to being included in EP simulations with only minor alterations. We therefore did not explicitly model the more complex stretch-induced geometric effects in this study.

Single Cell Simulations
To study the effect of MEC on EP properties, we solved, in a single cell, the 3-variable Fenton Karma model (Fenton and Karma, 1998) reparameterised to approximate the action potential from AFremodelled atrial cells (Goodman et al., 2005;Roy et al., 2018). We scaled V, the transmembrane potential, such that V=0 corresponds to -80 mV and V=1, to 3.6 mV, as typically done when using the Fenton-Karma model in the atria (Roy et al., 2018). Using a forward Euler scheme (t = 5 s) implemented in Matlab, we incorporated each of the following mechanisms: a) K + permeable stretch activated channels (eq 1) b) Non-specific stretch activated channels (eq 2) c) Stretch-induced changes in membrane capacitance (eq 3) d) Simultaneous presence of effects a-c.
In the presence of:
Time-variable stretch with a peak of 30% whose time course mimics the global left atrial strains measured using echocardiography (see Fig 1B), with data taken from (Montserrat et al., 2015). Negative stretches (contractions) were not taken into account, as in previous studies (Panfilov et al., 2007;Timmermann et al., 2017). These measured strains were synchronised with the action potential, such that the active contraction of the LA (A in Fig 1A) took place 10 ms after the upstroke of the action potential for every cell.
The conditions imposed in 2 aimed to model a chronic stretch situation, whereas 3 sought to model the passive stretch experienced by the atria during the normal reservoir phase. To allow comparisons between conditions 2 and 3, we used similar stretch values for condition 3 as in condition 2. We chose these strain values to match those used in the experiments from which the used MEC pathway formalisms were derived.
Resting membrane potential (RMP) and 90% action potential durations (APD90) and restitution curves were calculated for all combinations (a-d and 1-3) and compared to baseline values.

Tissue Simulations
We additionally solved the monodomain equation on a 60 x 60 x 1.8 mm 3 grid, using the same remodelled atrial Fenton-Karma model. We used an in-house MPI C solver, with centred finite differences (x = 0.3 mm) and a forward Euler scheme (t = 5 s). Neumann boundary conditions were implemented in all simulations. Action potentials were initiated by raising the transmembrane potential in the left-most 5 cells (corresponding to 1.5 mm) at the boundary of the tissue at a basic cycle length of 400 ms.
Simulations were performed for all combinations of effects a-d and stretch protocols 1-3 sensed uniformly by the entire tissue in isotropic conditions with a diffusion coefficient of 0.1 mm 2 /ms, corresponding to a baseline mean conduction velocity of approximately 60 cm/s, typical of AF remodelled atria (Varela et al., 2016). Anisotropic conditions with Dlongitudinal = 0.3 mm 2 /ms and Dtransverse = 0.03 mm 2 /ms, with fibres aligned with y-axis (orthogonal to the direction of propagation of the action potential) were also employed.
Conduction velocity and APD90 were computed across the tissue, as detailed in (Varela et al., 2013). We additionally initiated a rotor using a cross-field protocol in the centre of the cuboid of tissue and tracked its position for 2s, as described in (Roy et al., 2018). The presence of constant stretches of up to 3% led to small changes in AP morphology (Fig 3), with observable changes only under the effect of Cm, which broadens the action potential and increases the RMP. As shown in Fig 4, SAC_K had a negligible effect on APD90 (Fig 3A) whereas ISAC_NS tended to shorten it ( Fig 3B) and stretch-induced alterations in Cm, to increase it (Fig 3C). When combining all three effects APD90 was changed by less than 2%, except for a constant stretch of 3% where it increased by 7% at a BCL of 400 ms mostly due to capacitance effects (Fig 3D and Fig 6A). These changes did not depend on the BCL used (Fig 4). Under the action of a time-dependent stretch mimicking the global passive stretch experienced by the left atrium during the reservoir phase (scaled to 30%, see Figure 5A), AP underwent minimal changes -see Fig 5b. However, the timing of the passive stretch relative to the AP led to the appearance of some after-depolarizations, driven by ISAC_NS. We note that ISAC_K has the opposite effect to ISAC_NS at this time, causing a repolarization dip in the action potential. For the current parameterisation of the SAC channels, the combined effect of these MEC pathways gives rise to an afterdepolarization. Cm does not play a role in appearance of these changes in V after the action potential.

Tissue Simulations
Tissue-level simulations confirmed the APD trends seen in single-cell simulations, with modest APD increases driven by stretch-induced capacitive changes, as shown in Fig 6a. The inclusion of SAC_NS led to a marginal increase in CV, which was dwarfed by the reduction in CV (10% for a 3% uniform permanent stretch) induced by stretch modulation of Cm -see Fig 6b. Similar relative changes in APD90 and CV were observed in isotropic and anisotropic conditions. Simulated rotors traced the stable epitrochoidal meandering pattern characteristic of this model in both baseline conditions and in the presence of uniform constant stretch -see Figure 7A. In the presence of the time-dependent stretch and the associated after-depolarizations, however, the hypermeandering greatly increased and the rotors terminated early by interacting with tissue boundaries in our model ( Figure 7B).

Discussion
In this manuscript, we surveyed the main mechanisms responsible for mechano-electric feedback, highlighting how they apply to the atria. We stress, in particular, how the atria are subjected to large physiological external strains, which have typically not been considered when studying MEF in these chambers. With the parameters used, we found stretch-induced capacitance effects to dominate over effects mediated by stretch-activated channels. In the presence of all effects, we saw an increase in APD and a decrease in CV in the presence of constant stretch in both single-cell and tissue conditions. In the presence of variable stretch mimicking the passive strain experienced by the atria, small afterdepolarisations were observed. These greatly increased the meandering of rotors in our tissue model and led them to quickly terminate by interacting with tissue borders. Further simulations will study the implication of these effects to atrial arrhythmias in greater depth.
We found that external stretches in atrial reservoir function may lead to EP changes similar to afterdepolarizations, with can be of relevance for the generation of ectopic beats. The observed afterdepolarizations come from a balance between the two stretch-activated currents. We note that the afterdepolarizations are likely to take a different form for different parameterisations of ISAC_K and ISAC_NS which are compatible with experimental data. It is not clear whether these afterdepolarizations are relevant in atrial tissue, which typically does not undergo realistic haemodynamic stretches in experimental EP studies. In the atria, stretch is also expected to be heterogeneous. If relevant, these MEC effects are likely to be particularly significant in the presence of asynchronous atrial activation, such as in AF, where they can contribute to heterogeneity in EP properties. We found, in particular, that the presence of these stretch-induced after-depolarizations causes rotors to hypermeander, which may complicate their termination using ablation procedures.
In the current study, we restricted ourselves to three reasonably well-characterised effects that are easy to implement in EP simulations: non-specific and K + -permeable stretch-activated current and stretch-induced alterations in Cm. We found that the effect of Cm alterations, modelled using a previously proposed formalism, led to larger changes in EP properties (namely CV and APD90) than the other pathways surveyed in this article. Our study used a basic cycle length of 400 ms, and a 3-variable model of electrophysiology parameterized to model AF-remodelled atrial cells. We were able to capture slight changes in APD due to stretch and the reduction in CV with stretch generally seen at atrial-level studies in the presence of chronic stretch (Ravelli, 2003;Schotten et al., 2003). For the time being, we did not take into account the additional MEC pathways such as alterations in intra-cellular calcium handling or geometrical effects. Similarly, inhomogeneous stretches (passive or due to active atrial contraction), the presence of heterogeneous fibrosis or gradients in mechanical or EP properties across the atria will be addressed in future studies.
Progress in studying the contributions of MEC to atrial EP, especially to atrial arrhythmias, is dependent on more detailed atrial-specific experimental characterization of the different MEC pathways. This will enable the parallel creation of more realistic computational models, which include MEC effects. In particular, it is not clear how some of the surveyed MEC pathways (e.g. conductance alterations under stretch) may depend on the direction of the applied stretch. This will be essential for future adequate modelling of MEC in realistic atrial geometries, which include the anisotropy induced by the complex atrial fibre orientations and region-specific strains.

Conclusions
In this paper, we discuss the many pathways through which MEC can affect atrial EP. We stress that the stretches that atria are subjected to are substantially different from those experienced by the ventricles and that this should be taken into account in atrial EP models than include MEC. In our simulations, we found that accounting for passive atrial stretches similar to those observed in healthy atria led to after-depolarisations and enhanced rotor meandering. We also observed reductions in CV and increases in APD90 in the presence of chronic stretch, consistent with experimental studies. These findings suggest that MEC effects should be are likely to play an important role in the atria. Further experimental characterization of MEC pathways and modelling studies are required to better understand MEC's role in atrial arrhythmias such as AF.