Importance of Geometry and Refractory Period in Sustaining Atrial Fibrillation
Testing the Critical Mass Hypothesis
Background— The critical mass hypothesis for atrial fibrillation (AF) was proposed in 1914. There has never been a systematic investigation defining the relationship between tissue geometry and AF. The purpose of this study was to determine the association among the probability of maintaining AF and the width, area, weight, effective refractory period (ERP), and wavelength in atrial tissue.
Methods and Results— Isolated canine atria (n=20) were perfused with Krebs-Henseleit solution. Baseline ERPs were obtained with and without acetylcholine (10E-3.5 mol/L) using single extra-stimulus pacing while unipolar electrograms were recorded from 250 sites. The tissue was then partitioned using bipolar radiofrequency ablation, and the ERPs were measured again with and without acetylcholine. Any section of tissue that maintained AF was divided until the arrhythmia was no longer inducible. ERPs and conduction velocities were measured in all of the sections after each ablation, and the wavelengths were calculated. The probability of AF was found to be correlated with increasing tissue areas, widths, and weights (P<0.001). The probability of AF was significantly associated with the length of the ERP and the wavelength (P<0.001). With shorter ERPs and shorter wavelengths, there was an increased probability of sustained AF.
Conclusions— The probability of sustained AF was significantly associated with increasing tissue area, width, and weight and decreasing ERPs and wavelengths. These data may lead to a better understanding of the mechanism of AF and, thus, help to design more-effective interventional procedures in the future.
Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia in the world. There are thought to be >2.3 million Americans living with AF.1 In 1914, Garrey2 hypothesized that a critical mass of tissue was necessary to maintain fibrillation.3 Garrey2 theorized that multiple wavelets circulated through the atria around transitory and shifting lines of block, activating the atria in a chaotic manner that sustained AF. Using computer modeling, researchers4,5 demonstrated that multiple wavelet reentry theoretically could be a mechanism to sustain AF. Others subsequently confirmed multiple wavelet reentry as a cause of AF in studies in animals and humans.6,7 Weiner and Rosenbluth8 introduced the concept of wavelength, defined as the product of refractory period and conduction velocity (CV), which represents the minimum path length needed for reentry in sustained AF.
The maze procedure divides the atrium into a maze and prevents macro circuit reentry, while still allowing for normal sinus activation of the atrium.9 Recent long-term follow-up data demonstrated a success rate of >92%.10 Although a successful procedure, there still remains a subset of patients for which this procedure does not cure of AF.
Kosakai11 examined their operative experience and found a decreasing success rate with increasing preoperative atrial sizes. When the left atria (LA) diameter was <45 mm, the success rate in conversion to normal sinus rhythm (NSR) after the maze was 100%. When the diameter was >87 mm, there was a 0% success rate for conversion to NSR after the maze. It is hypothesized that the maze procedure does not divide the atria into small enough sections to prevent AF in patients with enlarged atria.
It was the objective of this study to obtain a more quantitative definition of the critical geometry associated with sustained AF. This study evaluated the importance of effective refractory period (ERP), conduction velocities, wavelength, and the geometry of atrial tissue on the maintenance of sustained AF in a canine isolated atrial preparation.
Normal mongrel dogs (n=20), weighing between 20 and 30 kg, were IV anesthetized with 7.5 mg/kg propofol, intubated, and placed on a positive pressure respirator with 2% to 3% isoflurane for anesthesia throughout the procedure. A median sternotomy was performed, the heart was cradled in the pericardium, and the azygous vein was ligated and divided. The interatrial groove was dissected, separating the LA and right atria (RA). Two dissection protocols were used to isolate the LA and RA.
In the RA (n=14) preparations, the atrium was dissected from the rest of the heart and divided through the superior venae cava down to the inferior vena cava to facilitate mounting of the tissue on the electrode plaque.12 The right coronary artery was cannulated with a 16-gauge catheter.
In the LA preparations (n=6), the heart lung block was removed, the lungs were cleanly dissected from the heart, and the pulmonary veins were divided ≈1 cm from their insertion into the LA. The ventricles and RA were excised. The circumflex artery was dissected up to the aortic root and distally to beyond the last atrial branch, and all of the ventricular branches were ligated. The circumflex artery was cannulated with a 16-gauge catheter.13 The LA was divided through the right and left superior veins, unfolded, and mounted on the electrode plaque.
Before the isolated atrial preparations were mounted to the electrode plaque in the bath, the appendages were ablated using bipolar radiofrequency energy (AtriCure Inc.). The clamp created transmural lesions (≈1 mm wide) that prevented electrical conduction across the lesion. The epicardial surface was mounted on a flat electrode platform containing 256 unipolar electrodes with an interelectrode distance of 5 mm. The atrial appendage of each preparation was placed into a slot in the electrode template that allowed the atrium to lie flat.
The preparation was kept in a temperature-controlled bath at 37°C and perfused with a Krebs-Henseleit (KH) solution at a rate of 8 to 10 mL/min (≈50 mm Hg). The composition of the KH solution was as follows (mmol/L): Na+, 143; K+, 4.7; Cl−, 128; Ca2+ 1.25, HCO3−, 25; Mg2+, 1.2; and dextrose, 11.1. The solution was oxygenated with 95% O2 and 5% CO2 (pH=7.4). The preparations were continuously superfused with KH (Figure 1).
Pacing sites were marked such that pacing was always performed from the same sites. Pacing was conducted at 1.5 times the pacing threshold. The S1S1 interval used for all of the pacing was 300 ms. The ERP was determined at each pacing site by incrementally decreasing the S1S2 interval by 5 ms until capture no longer occurred. The ERP was defined as the shortest S1S2 interval that captured the atrium.
After the baseline ERP values were determined, at each marked pacing site, the solution was switched to KH solution with acetylcholine at a concentration of 10−3.5 M.12 The electrical activity of the atria was recorded using an in-house designed system (Figure 2a). If the preparation continuously fibrillated for >30 s, it was considered a sustained episode of AF (Figure 2b). The perfusion solution was then switched to KH alone until the arrhythmia terminated. The radiofrequency bipolar ablation device was used to divide the arrhythmogenic sections of the preparation. ERPs were again recorded at all of the sites with and without acetylcholine (Figure 2c). Any section that maintained an arrhythmia after the first ablation (Figure 2d) was subsequently divided again. The ERPs were again determined with and without acetylcholine. This process continued until all of the sections no longer maintained an arrhythmia.
At the conclusion, a lissamine green dye bolus was injected into the preparation to ensure that there were no perfusion abnormalities. Any sections of the atrium that were not well perfused were excluded from the data analysis. The atrial sections were photographed with a high-resolution digital camera and permanently fixed in 10% buffered formalin. The digital photos were analyzed (Scion Image and Adobe Photoshop 7.0) to determine the minimum and maximum height; the minimum, maximum, and average width; and the area of all sections created (Figure 3). The fixed atrial sections were then dissected, and only atrial myocardium was weighed.
The electrograms recorded during pacing at 300 ms were analyzed to calculate the activation sequence and the CVs.14 The mean, maximum, and minimum CVs and SDs for each section were calculated. Wavelength was calculated as the product of the average CV and the ERP of each section of atrium.8
All of the data were expressed as mean±SD. Analysis of variance with multiple comparisons was used for comparisons of >2 groups. Multiple comparisons were made with a post hoc test (Fishers lysergic acid diethylamide). A multivariable logistical regression was performed to develop a model for the associations among the probability of AF, ERP, and area. A P<0.05 was considered significantly different (SYSTAT Software Inc.).
The results comparing the LA and RA are summarized in Tables 1 and 2⇓. The term “whole section” refers to either the RA or LA before any ablations were performed, that is, the atrium in its entirety. The term “all sections” is used to describe an analysis performed when all of the varying sized sections, including the whole, were combined for that test. This distinction allowed differentiation of innate properties of the native atria from any that could be artifacts from either time in the bath or the ablative procedures.
The RA was significantly larger than the LA. However, the LA was significantly heavier than the RA. The mean maximum widths of the whole RA and LA were not statistically different.
There were no differences between the left and right whole atria ERPs in the absence of acetylcholine (Table 2). When acetylcholine was added, the mean ERP in the whole RA was significantly less than in the whole LA. When both RA and LA sections were analyzed in the absence of acetylcholine, the RA was found to have significantly shorter ERPs than the LA. There was no difference in the ERP for all of the sections between the right and the left in the presence of acetylcholine.
The impact of the ablations on the ERP was evaluated. Without acetylcholine, the RA ERPs trended toward decreasing values with each additional ablation (P=0.077). This trend was not observed in the LA (P=0.278). With the addition of acetylcholine, the ERP in the RA significantly increased over time from the beginning of the study to the end (25.91±10.49 ms to 42.35±21.58 ms; P<0.001). There was no change in the ERP of the LA preparation over time (P=0.130) with the addition of acetylcholine.
All of the CVs were calculated at a paced cycle length of 300 ms. An analysis of all sections combined found no significant difference in mean CVs for those sections that were perfused with acetylcholine and those that were not (P=0.476). Examination of each atrium individually and all of its CV parameters showed no difference between the average minimum CV, the average maximum CV, or the mean CV when comparing the whole RA preparation perfused with and without acetylcholine. The average maximum CV and the overall mean CV were unchanged in the LA whole preparation with and without acetylcholine present.
The RA and LA preparations were compared for differences in minimum, maximum, and mean CV values and their SDs. There was a significant difference in the mean CV for all of the data points collected in the whole section, with the LA having a faster mean CV than the RA. The SDs for the measurement of mean CVs in all of the sections were also significantly different, with the RA having a greater SD than the LA. The maximum CV values in the whole atrial preparations were greater in the right than the left. However, when the maximum CV values were examined in all of the sections, there was no significant difference. The minimum CVs were significantly less in the RA than the LA in the whole atrial preparations and when all of the sections were combined. When the CVs were analyzed in relation to ablations, there was no change in the RA (P=0.485) or the LA (P=0.320). The SDs for this evaluation were also not statistically different (RA, P=0.204; LA, P=0.129).
Mean wavelength was calculated by multiplying the mean CV by the ERP. When the mean wavelengths without acetylcholine were compared among all of the sections, there was a significant difference between the LA and RA, with the right having a shorter mean wavelength. Comparison of mean wavelengths in the presence of acetylcholine showed no statistical difference. There was no change over time when the mean wavelengths for all of the sections were pooled and compared after each ablation (P=0.508). There was found to be no change in the wavelength after each ablation when each atrium was analyzed individually (RA, P=0.595; LA, P=0.945).
The probability of AF was analyzed with a univariable logistical regression. The impact of ERP, area, maximum width, minimum width, average width, maximum height, minimum height, weight, CVs, CV SDs, wavelength, and atria were evaluated. The results of the univariable logistical regression are presented in Table 2. McFadden Rho squared values between 0.2 and 0.4 are considered satisfactory.15
In summary, decreasing ERPs (P<0.001), increasing areas (P<0.001) (Figure 4a), increasing maximum and minimum widths (P<0.001), increasing average widths (P<0.001), increasing weights (P<0.001), maximum CV (P=0.001), and decreasing wavelengths (P<0.001) were all found to be significantly associated with an increased probability of sustained AF (Table 3). The factors that did not correlate with an increasing probability of sustained AF were maximum (P=0.654) and minimum (P=0.154) heights, mean CVs (P=0.319) or their SDs (P=0.516), and minimum CVs (P=0.299). A multivariable analysis was performed using combinations of ERP, wavelength, weight, area, CV, maximum width, and average width (Table 2 and Figures 4 and 5⇓).
The overall success rate of the maze procedure is reported to be >90%.10,16 Patients with enlarged atria and those that have been in sustained AF for an extended period of time preoperatively have a much lower success rate.10,11 Garrey2 hypothesized almost a century ago that there was a critical mass, above which AF was sustained and below which it could be prevented. This study supports this hypothesis, with increasing tissue surface area correlating significantly with the probability of sustaining AF (Figures 4 and 5⇑).
Atrial remodeling, with the increase in atrial fibrosis, can slow CV and can shorten the refractory period in atria with long-standing AF.17,18 The duration of preoperative AF is known to be a negative predictor for the success of the maze procedure.10 The results of this investigation demonstrate the importance of the duration of the ERP, with shorter ERPs more likely to sustain AF. Multivariable logistical regression models demonstrate that increasing tissue size and decreasing ERPs increase the probability of sustained AF (Figure 4b).
When all of the geometric data were analyzed for any correlations with AF, all of the variables correlated well, except for the maximum and minimum heights. This was because the height was not varied during the study.
Two types of logistical regression models were used. Univariable logistical regression models were used to evaluate all of the parameters to determine the probability of inducing sustained AF. ERP and wavelength were the 2 variables determined to have the best fit and the greatest association with the probability of sustained AF. The variables area, weight, maximum width, minimum width, and average width were all significant but were not determined to have as good of a fit. This demonstrates that the area needed to maintain AF is dependent on functional factors like ERP. The variables of minimum height, maximum height, CV, or CV SD were not significantly associated with predicting the probability of inducing sustained AF. This was in part because of these variables not having been modulated. This does not mean that CV is not important; it was just relatively consistent throughout the duration of the experiment. It is important to note that there was no difference between the probability of inducing sustained AF if the study occurred in the RA or the LA. Whereas, clinically, AF is often associated with the LA, it is also known, clinically, that the refractory periods in the LA are shorter than in the RA. This is consistent with the findings in this study that show an increased probability of AF with decreasing refractory period.
The multivariable logistic regression combined variables and analyzed both geometric variables and physiological variables to create models for predicting the probability of inducing sustained AF. A series of equations was developed from these models. Table 4 can be used to predict the probability of a section of canine atria fibrillating when particular variables are entered into the equations. The first model presented used the variables of ERP and area. The data in Figure 4 allows for a better appreciation of the impact of ERP and area on the probability of inducing sustained AF. As the area decreased and the ERP increased, the probability of inducing sustained AF significantly decreased. However, with the same ERP, as the tissue area increased, so did the probability of AF. This held true for the graphs that substituted wavelength for ERP, and when the geometric variable was weight, average width, or maximum width instead of area. This has important relevance to the clinical problem of increasing failure rates of the maze in patients with increased atrial size and patients with longstanding AF and decreased ERPs.
The present study represents a first attempt to quantify the relationship between geometric and functional electrophysiological variables and the inducibility of AF in the atrium. In this model, only the width and ERP were modulated. A more complete model will require modifying CV, as well as the height of the tissue. Finally, the model will need to be extended to the entire intact atrium. Although the model was developed in normal tissue, it still has significance for diseased atria. No matter what the underlying pathology, the underlying substrates are still ERP, CV, geometry, and premature impulse formation. As an example, in patients with persistent AF, ERP is decreased. The present model predicts the effects of inducibility with altered ERPs (Figure 6). Nonetheless, the model will have to be tested in diseased tissue. The model is also clinically relevant to those groups of patients with enlarged atria, who, although they have had a complete maze procedure (including PV isolation), still have AF. Using this approach, it may be possible to simulate the effect of different lesion sets on the inducibility of AF.
Supported in part by National Institutes of Health grant no. RO1-HL32257.
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