Left atrial effective conducting size predicts atrial fibrillation vulnerability in persistent but not paroxysmal atrial fibrillation

Abstract Background The multiple wavelets and functional re‐entry hypotheses are mechanistic theories to explain atrial fibrillation (AF). If valid, a chamber's ability to support AF should depend upon the left atrial size, conduction velocity (CV), and refractoriness. Measurement of these parameters could provide a new therapeutic target for AF. We investigated the relationship between left atrial effective conducting size (LAECS), a function of area, CV and refractoriness, and AF vulnerability in patients undergoing AF ablation. Methods and Results Activation mapping was performed in patients with paroxysmal (n = 21) and persistent AF (n = 18) undergoing pulmonary vein isolation. Parameters used for calculating LAECS were: (a) left atrial body area (A); (b) effective refractory period (ERP); and (c) total activation time (T). Global CV was estimated as √A/T. Effective atrial conducting size was calculated as LAECS=A/(CV×ERP). Post ablation, AF inducibility testing was performed. The critical LAECS required for multiple wavelet termination was determined from computational modeling. LAECS was greater in patients with persistent vs paroxysmal AF (4.4 ± 2.0 cm vs 3.2 ± 1.4 cm; P = .049). AF was inducible in 14/39 patients. LAECS was greater in AF‐inducible patients (4.4 ± 1.8 cm vs 3.3 ± 1.7 cm; P = .035, respectively). The difference in LAECS between inducible and noninducible patients was significant in patients with persistent (P = .0046) but not paroxysmal AF (P = .6359). Computational modeling confirmed that LAECS > 4 cm was required for continuation of AF. Conclusions LAECS measured post ablation was associated with AF inducibility in patients with persistent, but not paroxysmal AF. These data support a role for this method in electrical substrate assessment in AF patients.


| INTRODUCTION
The multiple wavelet hypothesis, initially proposed by Moe  Another important mechanistic theory of AF, that of "functional re-entry," was proposed by Allessie et al 5 in an ex vivo study of rabbit atria. In this study, rotating re-entry occurred in the absence of an anatomical obstacle. Subsequent studies further demonstrated functional, anatomic, and micro re-entry to be driving mechanisms in animal models of AF. 6,7 In the modern era two new technologies (intracardiac phase mapping 8 and electrocardiographic imaging 9 ) have also been used to demonstrate, albeit controversially, the occurrence of rotors in human AF, described previously as drivers of function re-entry. 10 Since directly mapping activation in AF is challenging, our ability to deliver therapies based on such mechanisms is currently limited.
Nevertheless, a key concept of these hypotheses is that a critical mass of tissue is required to facilitate the perpetuation of AF. 11 Whether chamber size determines the capacity of the chamber to sustain multiple re-entrant wavelets will depend on the electrical properties (conduction velocity [CV] and refractoriness) of that chamber. 12 A technique to quantify the electrical substrate size of an atrium, based on a limited set of measurements collectible within a clinically applicable timescale, would allow interventional AF treatments to be individualized. We therefore propose a metric termed "Effective Conducting Size" (units, cm) which is a function of total atrial area, CV, and a single-site measurement of refractoriness. We hypothesize that the ability of a chamber to support AF is related to Effective Conducting Size, independent of the use of antiarrhythmic medication.

| AF vulnerability
Following ERP measurements, an AF induction protocol was performed by pacing from the ablation catheter at the left atrial posterior wall. The protocol consisted of sensed doubles (S1 = 600 milliseconds; S2 = 400 milliseconds, decreasing in 10 milliseconds steps to atrial ERP), sensed triples S1 = 600 milliseconds; S2 =ERP + 50 milliseconds, S3 =ERP + 50 milliseconds, decreasing in 10 millisecond steps to atrial ERP) and incremental pacing, decreasing in 10 millisecond intervals from 450 milliseconds to loss of 1:1 atrial capture. 13 Each step in the induction protocol was carried out once before moving onto the subsequent step. If AF was not induced by this protocol the entire protocol was repeated for a second time.
Sustained AF was defined as AF continuing for greater than 30 seconds. If AF resolved to an organized tachycardia, overdrive pacing was used to terminate the tachycardia. Sustained AF was terminated by electrical cardioversion if required.  14,15 AF is sustained in this model by multiple wavelets undergoing functional re-entry and wave break. 15 The ionic conductance of I K1 was modified to reproduce the average ERP of the inducible persistent AF patients in this study (G K1 = 1.8 mS/cm 2 ), to attain ERP = 231 milliseconds. AF was initiated by cross-field stimulation.

| Statistical analysis
Data analysis were performed using SPSS statistics (IBM, Version 22) and Prism (GraphPad Software, Version 7). Continuous variables were expressed as a mean ± standard deviation. Comparison of means between groups was performed using the Mann-Whitney U test for independent samples. Categorical variables were compared using χ 2 test. P < .05 was considered statistically significant.

| Measured parameters and calculated parameters
Mean left atrial body area was 86.

2D simulations
Baseline parameter sets were chosen to model multiple wavelet re-entry with the ERP tuned to match the mean value for the inducible persistent AF patients. AF was sustained for this set-up ( Figure 6A) with a calculated LA ECS = 6.18 cm (filled hexagon; Figure 6D). The effects of ablation and antiarrhythmic drugs on arrhythmia inducibility were tested by altering the conducting area of the domain and I K1 channel conductance, respectively. When atrial area was modified by ablation, a critical LA ECS > 4 cm was required for maintenance of AF. AF was sustained for atrial areas of 80 cm 2 (LA ECS = 4.5 cm, filled circle; Figure 6D) or larger, whilst reducing the atrial area to 70 cm 2 (LA ECS = 3.9 cm; empty circle; Figure 6D) resulted in AF termination ( Figure 6B). When modifications in ERP and CV were modeled by the application of sotalol, a critical LA ECS > 4 cm was still required for maintenance of AF. AF was sustained at an ERP of 290 milliseconds (LA ECS = 4.6; filled triangle; Figure 6D), but not at an ERP of 320 milliseconds (LA ECS = 4 cm; empty triangle; Figure   6D) ( Figure 6C). Modifying ERP through changes in G K1 conductance also modified CV, such that CV = 86 cm/s at ERP = 320 milliseconds and CV = 83 cm/s at ERP = 290 milliseconds. In 76% of the simulations, AF sustained after pulmonary vein isolation ( Figure 8A). Applying a box isolation lesion set further reduced LA ECS and terminated AF in 67% of simulation set-ups using the inferior line that resulted in the lowest LA ECS . Figure 8B shows an example in which AF was inducible with the smallest area of isolated tissue owing to a resultant atrial area of 121 cm 2 and corresponding LA ECS of 5.82 cm. Figure 8C shows the same anatomy, ERP and CV properties as Figure 8B. In this case, increasing the area of the isolated posterior box resulted in a LA ECS of 3.94 cm, and termination of AF. In contrast, Figure 8D demonstrates a case in which AF is still inducible following the largest box isolation lesion set with an ERP of 230 milliseconds and LA ECS remaining above 4 cm (LA ECS = 4.18 cm).
By additionally increasing ERP to 250 milliseconds, through modeling the effects of sotalol, LA ECS is decreased less than 4 cm (LA ECS = 3.84 cm) and AF terminates ( Figure 8E).

| DISCUSSION
In this study, we sought to design and test a clinically applicable These findings support a future role for LA ECS in guiding interventional, pharmacological or combined therapies for persistent AF.

| Atrial size, electrical remodeling, and AF vulnerability
Left atrial dilatation is a well-described risk factor for the development of AF and is associated with disease severity and outcome post ablation. 18 22 and an association between reduced CV, atrial dilation, and arrhythmias has also been shown in human studies. 23 In the present study, we found no significant relationship between left atrial size and ERP or total activation time in patients with either paroxysmal and persistent AF, although a nonsignificant trend toward shorter ERP and longer total activation time were noted in persistent patients with inducible vs noninducible AF. Therefore, there is a need to consider both atrial size and electrical conduction together (for example using LA ECS ) in individual patients to predict response to treatments for arrhythmias.

|
The concept of Re-entry, wavelength, and atrial substrate size The concept of "atrial substrate size" was originally communicated by Moe in terms of a dimensionless quantity termed the fibrillation number. 19 In a study by Hwang et al, 24  predicting arrhythmia vulnerability in a canine study. 26 Given the interaction between atrial size, refractoriness, CV, and AF vulnerability, we incorporated these parameters into a new metric termed LA ECS . This metric differs from the fibrillation number previously described 19,24 by using atrial surface area rather than a characteristic length constant such as atrial diameter which we believe is likely to better capture the complex geometrical remodeling present in AF patients. 27 We extended the above findings to a population of AF patients by demonstrating that wavelength is significantly shorter and LA ECS significantly greater in persistent AF patients with inducible vs noninducible AF ( Figure 4F). LA ECS also notably identified a population of patients with persistent AF who were not AF-inducible after PVI and who, from an electrophysiological standpoint, appear to behave more like

| Clinical relevance
This study highlights the physiological difference between categories of AF and suggests a possible methodology by which arrhythmia in line with success rates of pulmonary vein isolation in this population. 29 Notably, however, even persistent AF patients with LA ECS < 4 cm were noninducible after pulmonary vein isolation, suggesting that isolation of PV triggers could be successful in this subpopulation. Conversely, in patients with LA ECS > 4 cm, additional substrate modification is likely to be required. In these patients, initial trigger-dependent AF may have evolved to multiple wavelet/re-entry based AF due to progressive structural and electrical remodeling. 30 In recent years, additional catheter ablation strategies have been suggested in persistent AF patients [31][32][33] , however, the optimal treatment approach remains unclear. 34 According to the present data targeted strategies to reduce LA ECS (Figures 6D and 8 to prolong atrial refractoriness. Our modeling data highlights how in certain cases even a large posterior box isolation set does not reduce the LA ECS sufficiently to terminate AF and this is only achieved through an additional increase in ERP. As such, knowledge of LA ECS could be used to guide ablation during the initial ablation procedure or to guide the selection of additional ablation vs. antiarrhythmic drugs for the management of recurrent arrhythmia after initial ablation. Such management strategies require investigation in prospective randomized trials.

| LIMITATIONS
This was a prospective simulation/clinical study to evaluate a new clinically applicable concept. Since there were a low number of recurrence events in the cohort, it was not possible to formally test the predictive power of LA ECS in a statistical model including other clinical parameters associated with AF vulnerability and recurrence. ERP was measured at a single site in the left atrium which may not be fully reflective of the heterogeneity in refractoriness seen in patients with persistent AF. Some patients were maintained on antiarrhythmic drugs periprocedurally. While the effects of these in terms of CV and refractoriness will be accounted for in the LA ECS concept, it is not possible to predict how discontinuation of medications post procedure may affect the vulnerability to AF in a particular patient from these data.
Therefore, LA ECS measured in the study may not reflect the true LA ECS once antiarrhythmic drugs are either discontinued or resumed post procedure. This study focused on multiple wavelet mechanisms of AF only. It is possible that this hypothesis may hold for other forms of re-entry in including micro-entrant circuits and rotors however this was not explored in the modeling work carried out here. Similarly, we did not examine the potential roles of the right atrium in arrhythmogenesis in these patients.

| CONCLUSION
LA ECS was significantly associated with the ability to induce AF in patients post first-time ablation for persistent, but not paroxysmal AF. These data support the mechanistic hypotheses of re-entry in the population of persistent AF patients studied. The LA ECS metric may be useful for predicting AF vulnerability and guiding arrhythmia management in such patients.