Spatially Conserved Spiral Wave Activity during Human Atrial Fibrillation

Abstract

Background:

Atrial fibrillation (AF) is the most common cardiac arrhythmia in the world and increases the risk for stroke and morbidity. During AF the electrical activation fronts are no longer coherently propagating through the tissue and, instead, show rotational activity, consistent with spiral wave activation, focal activity, collision or partial versions of these spatial patterns. An unexplained phenomenon is that although simulations of cardiac models abundantly demonstrate spiral waves, clinical recordings often show only intermittent spiral wave activity.

Methods:

In-silico data was generated using simulations in which spiral waves were continuously created and annihilated and in simulations in which a spiral wave was intermittently trapped at a heterogeneity. Clinically, spatio-temporal activation maps were constructed using 60s recordings from a 64 electrode catheter within the atrium of N=34 patients (N=24 persistent AF). The location of clockwise and counterclockwise rotating spiral waves was quantified and all intervals during which these spiral waves were present were determined. For each interval, the angle of rotation as a function of time was computed and used to determine whether the spiral wave returned “in step” or changed phase at the start of each interval.

Results:

In both simulations, spiral waves did not come back in phase and were “out-of-step”. In contrast, spiral waves returned in step in the majority (68%; p=0.05) of patients. Thus, the intermittently observed rotational activity in these patients is due to a temporally and spatially conserved spiral wave and not due to ones that are newly created at the onset of each interval.

Conclusions:

Intermittency of spiral wave activity represents conserved spiral wave activity of long, but interrupted duration or transient spiral activity, in the majority of patients. This finding could have important ramifications for identifying clinically important forms of AF and in guiding treatment.

Graphical Abstract

Introduction

Atrial fibrillation (AF) is the most common cardiac arrhythmia that affects approximately 30 million patients worldwide ^{1, 2}. During AF the electrical spatio-temporal organization of the atria becomes disorganized, which results in reduced cardiac output and is associated with serious health complications, including stroke, heart failure and increased mortality ³. Even though the exact spatio-temporal organization of AF is still under debate, spiral waves of electrical activation have been proposed to play a role ⁴. Indeed, spiral wave activity has been investigated and demonstrated in numerous computational studies of cardiac tissue ⁴, starting with early work on sheets of cellular automata ⁵, and extending to patient-specific, whole heart simulations ^{6, 7}.

Clinically and experimentally, spiral waves were first demonstrated in animal tissue, where voltage sensitive dyes can be applied to visualize electrical activity, and in intact pig hearts using ultrasound techniques ^{8, 9}. In humans, in whom such visualization techniques are currently not available, spiral wave activity has been recorded using endocardial basket electrodes that cover the majority (>70%) of the atria with a spatial resolution of approximately 5–10 mm and a temporal resolution of 1 ms ^10–12. In addition, spiral wave activity has been observed using various smaller catheter configurations ^{13, 14}, and using a non-invasive electrode vests on the chest of patients, which uses inverse solution techniques to determine the spatio-temporal activity of the tissue ¹⁵. Finally, spiral wave activity in the atria of explanted human hearts, in which voltage sensitive dyes can be used, has also been demonstrated ¹⁶.

In both the invasive and non-invasive techniques, observed spiral wave patterns were found to be intermittent but spatially conserved: the spiral wave tips intermittently return to approximately the same location ^{17, 18}. It is currently not known if this intermittence is a manifestation of a spatially conserved spiral wave that is temporarily obscured due to mapping limitations or if de-novo spiral waves are intermittently created in the same region. This distinction can have important implications. Intermittent creation of new spiral waves would indicate that AF is propagated by multiple wavelets. On the other hand, a conserved spiral wave that is intermittently visible at a specific location would indicate that AF is perpetuated by a limited number of spiral waves. The former may represent a less organized form of AF, and that elimination of a spiral wave tip is unlikely to have beneficial effects. The latter may indicate more organized AF, and that targeting the spatially conserved spiral wave tip may have therapeutic relevance ¹².

In this study, we examined 60s intracardiac recordings in AF patients in whom spiral waves were intermittently present at a particular spatial location. We focused on both the most prominent counter clockwise and clockwise rotating spiral wave and identified the time intervals in which the tips started at the conserved location and could be continuously followed. We then determined the angle of rotation (AR) of these spiral waves as a function of time for each of the intervals. For an intermittently present spiral wave, the AR would show different behavior depending on whether the spiral comes back “in-step” or not. These two possible continuity scenarios are schematically shown in Fig. 1, where we have plotted measured values of AR as dots before and after an intermittency period (shown in gray). To facilitate the visualization of the angle, we show AR (mod 2π), so that the angle restarts at 0 once it crosses 2π. Before the intermittency period, the AR can be fitted by a constantly growing solution ${AR}_{cons}$, which increases monotonically by 2π during every rotation period of the spiral wave (solid line). Following the period of intermittency, the measured AR comes back either in phase (in-step; top panel Fig. 1) or out of phase (“out-of-step”; lower panel Fig. 1) with ${AR}_{cons}$. In the latter case, there will be a clear difference between the measured AR and ${AR}_{cons}$ extrapolated to later times. In contrast, in the former case, the two ARs will overlap again after the intermittency period. In this study, we show that the majority of patients display spiral waves that come back in phase, suggesting that the observed re-entry is caused by the same spiral wave.

Figure 1.

Premise of the study. Clinically measured Angle of Rotation (AR; red dots) in an interval during which the spiral wave is present can be accurately fitted by a solution that increases constantly and monotonically (mod 2π; blue line). After a period of obscurity, the AR re-appears and is either in-step (top) or out-of-step (bottom) with the constantly increasing solution.

Methods

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Clinical Mapping

We studied N=34 patients from three different centers with AF undergoing ablation for routine indications. Details for patients in our population are presented in Table 1. Electrical signals were recorded from multipolar catheters comprising 64 electrodes (FIRM, Abbott, IL; Constellation, Boston Scientific, MA) that were placed in each atrium with a temporal resolution of 1ms (Fig. S1). Their locations were registered in each patient’s atrial geometry using standard mapping systems (NavX, St Jude Medical, MN). This multipolar system has been reported to have sufficient spatial resolution to resolve electrical activation patterns observed in optical mapping studies of human AF ¹⁹. Electrograms for 60s intervals were annotated for activation times, using a previously detailed method ²⁰. This method first computes the dominant frequency (DF) of the electrogram. Then, it constructs a recomposed signal by adding, for each time point, a single-period sinusoidal wave with frequency equal to the DF and amplitude equal to the absolute value of the electrogram slope (dV/dt) when this slope is negative or equal to zero when this slope is positive. The final signal is the sum of all these single-period waves, which has a sinusoidal morphology oscillating around zero and crosses zero at maximum −dV/dt, identifiable as the electrode’s activation time. Using the activation times for all electrograms, we computed the mean activation time for each patient. The activation times were also used to compute the phase φ(x,y,t) of the signal for all times t and at all positions (x,y) on a square 8×8 grid ¹⁰. These phase maps were then interpolated on a 29×29 grid.

Table 1.

Patient demographics

	n=34	%
Type of AF
Long-standing persistent AF	6	17.7%
Persistent (n, %)	18	52.9%
Paroxysmal (n, %)	10	29.4%
Duration of AF (months, mean±SD)	60.3±50.3
Demographics
Age (y, mean±SD)	63.8±9.7
Sex (female)	11	32.4%
Race (self-reported)
African American	2	5.9%
Asian	1	2.9%
White	28	73.5%
Unknown	3	8.8%
BMI (kg/m2, mean±SD)	28.7±4.9
Comorbidities
LA Size
Enlarged	23	68%
Diameter (mm, mean±SD)	50.5±8.0
LVEF (%)	53.9±9.7
CHA2DS2VASc (mean±SD)	2.0±1.5
CHF (n, %)	4	11.8%
Hypertension (n, %)	21	55.9%
Hyperlipidemia (n, %)	22	52.9%
Coronary Artery Disease (n, %)	6	11.8%
Diabetes (n, %)	6	17.7%
TIA/CVA (n, %)	1	2.9%
CKD (n, %)	0	2.9%
OSA (n, %)	7	20.6%

Angle of Rotation (AR) analysis

Using the interpolated phase maps, we computed spiral wave tip locations using the Hilbert transform as detailed earlier ¹⁰. The tip locations were used to create tip density maps, computed as the ratio of the time that a tip is present and the total recording time. Thus, this quantity can take on values between 0 (tip never present at that location) and 1 (tip always present). The location of the maximum tip density for both the clockwise (CW) and counterclockwise (CCW) rotating spiral was determined. Using these locations, we determined all time intervals for which a CW and CCW spiral wave tip was initiated in a 9×9 square centered at the location of the maximum tip density, corresponding to a 3×3 electrode area, and could be followed smoothly such that the change in tip location between successive time points was less than 1 electrode spacing. Only intervals with a duration that was at least the mean activation time were considered. This procedure resulted in N_CW and N_CCW intervals during which the CW and CCW tip location started near the maximum tip density location and could be smoothly followed.

To compute the angle of rotation (AR) of a spiral wave, we compared the phase of each grid point within a circle of radius R* and centered at the tip location to a fixed and generic phase map φ₀. Computing the AR using such a comparison is less prone to noise than, for example, computing the AR from activation fronts. The phases of this fixed map were determined by the polar angle of the line connecting the tip location and the grid point. This procedure is illustrated in Fig. 2A–C for a CCW spiral. The fixed map, indicated by the gray scale dots, starts at 0, and increases in the clockwise direction by 2π. The phase map of the CCW rotating spiral wave is shown at three different time points using a color scale, with blue/red corresponding to 0/2π. For each grid point within the circle, we computed the phase difference between the clinical and the fixed phase map: Δφ(t)=mod(φ-φ₀,2π). This difference should be roughly constant for each point if the clinical spiral wave is not too distorted. To compute the spiral wave’s AR at each time, we then computed the mean phase difference, using the circular average:

$$AR\left(t\right)=\text{atan}\left(\sum \text{sin(Δφ(t))}/\sum \text{cos(Δφ(t))}\right)$$

where the sum is over all grid points within the circle. This procedure was carried out for both the CW and CCW tip during N_CW and N_CCW, respectively.

Figure 2.

Computing the AR. A-C: The successive snapshots of a CCW rotating spiral wave, visualized using a phase map with the phase represented by a color map and shown for three different timepoints. At each grid point within the circle with radius R*, the phase is compared to a static phase map, represented by the gray scale.

Error analysis

To determine whether a clinical CW spiral wave remains in step throughout the recording, we compared AR_CW to a linearly progressing solution ${AR}_{cons}\left(t\right)=\text{2π}\mathrm{t}/\mathrm{T}\text{+}{AR}_0$, where ${AR}_0$ is the value of ${AR}_{cons}$ at t=0 and where T is the period. Specifically, we computed, for each time t_i within the N_CW intervals, the difference between AR_CW(t_i) and AR_cons(t_i), ${\mathrm{\Delta }AR}_{CW}\left(t_i\right)={AR}_{CW}\left(t_i\right)-{AR}_{cons}\left(t_i\right)$ taken to be between $-\mathrm{\pi }\text{and}\mathrm{\pi }$. The total error Err_CW, which is a function of both T_cons and initial value ${RA}_0$, was then computed as the root mean square (RMS) value:

$${Err}_{CW}=\sqrt{\frac{\sum _i{\left({\mathrm{\Delta }AR}_{CW}\left(t_i\right)\right)}^2}{n_{CW}}}$$

where the sum is over all points that are part of the N_CW intervals. This error was computed for a range of values of T_cons (±100 ms) centered around the mean of the electrode activation times. For each value of T_cons, ${AR}_0$ was varied between 0 and 2π in steps of 2π/T_cons. This computation allowed us to determine the optimal values for T_cons and ${AR}_0$, T_opt and ${AR}_{0,opt}$, that minimized ${Err}_{CW}$. For a spiral wave that always comes back perfectly in phase, this error would be minimal. For randomly and uniformly distributed ${\mathrm{\Delta }AR}_{CW}$ between $-\mathrm{\pi }\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{\pi }$, the average error equates to $\mathrm{\pi }/\sqrt{3}$. The RMS error for the CCW rotating spiral wave, ${Err}_{CCW}$, was determined in a similar fashion and the total error ${Err}_{tot}$ for all spiral waves was computed as the average over both chiralities.

To determine whether the computed RMS error was smaller than expected by chance, we increased the start time of each interval by a random amount, taken from a uniform distribution between 0 and T_opt. For this new, randomized sequence of intervals, we again computed the RMS error between AR_cons (with period T_opt) and the clinical phase. Since the starting times are shuffled, we adjusted the value of ${AR}_0$ such that it minimized the error. This procedure was repeated 1,000 times, resulting in a probability distribution of errors, which can be compared to the error obtained from the clinical data to determine the probability that the clinical data is in step by chance. As an alternative method to assess the likelihood that the clinical data is in phase, we randomly shuffled the order of the N_CW intervals while keeping the intervals between successive intervals constant. Again, for each shuffled sequence, we first computed the optimal ${AR}_0$ by minimizing the difference between AR_CW and AR_cons using the period of the clinical recording T_opt and then computed the error between the constant phase solution and the shuffled clinical data.

In addition, we generated in silico data in which the AR in each interval, taken to be of constant duration, was linearly progressing but started at a random initial value. This data sequence, comprising of N_int intervals, was then compared to AR_cons with different start values AR₀, which was adjusted to minimize the RMS error. This was repeated 1,000 times, resulting in a probability distribution for the RMS error. Note that the error for each point within each interval is identical so that the total error is simply the average error for each interval.

Electrogram quality assessment

The quality of an electrogram recording was computed using the amplitude of the recomposed signal, which encodes the maximum −dV/dt of the electrogram. For each electrogram, the average of the amplitudes during the intermittency and during the spiral wave intervals were computed. The two resulting distributions were compared using the Wilcoxon rank sum test.

Statistics

Continuous normally distributed variables are summarized by means and standard deviations and evaluated by Student t tests for independent samples. Where the Shapiro-Wilk test indicated non-normal distributions, variables are summarized by medians and interquartile ranges and evaluated with Mann-Whitney U tests. Correlation was tested by computing Pearson’s linear correlation coefficient. A P of 0.05 was considered statistically significant.

Study approval

Written, informed consent was granted for all patients prior to enrollment in National Institutes of Health protocols (NCT01248156), which were approved by UCSD and Stanford Institutional Review Boards.

Results

In silico data

We first generated in silico data by simulating an electrophysiological model, the Fenton-Karma model ²¹, in a two-dimensional square domain of size 7.5cmx7.5cm with non-conducting boundaries (for details, see Supplemental Material). We used parameter values that resulted in spiral defect chaos, characterized by the continuous creation and annihilation of spiral waves ²². Therefore, in this simulation, spiral wave tips are expected to be created de novo, resulting in ARs that will not be in phase and will be out-of-step.

Fig. 3A shows a snapshot of a simulation, with tips indicated by solid circles and the activation variable displayed using a color, with red corresponding to activation and blue to deactivation. We identified tip trajectories that started in a square domain of size 1cmx1cm, centered in the computational domain, and that could be continuously followed for a duration of at least one spiral wave rotation. During a simulation that represented 60s, we identified 31 intermittently present CW trajectories that corresponded to rotating spiral waves (Fig. 3B). The median lifetime of these trajectories, which were present for 27% of the total simulation time, was 406 (206–766) ms.

Figure 3.

Out-of-step spiral waves in a computational model. A: Snapshot of a simulation of the Fenton-Karma model, carried out using a 7.5cmx7.5cm square domain with non-conducting boundaries. Spiral wave tips are indicated by black dots and the variable representing the membrane potential is shown in a color map with red/blue corresponding to activated/recovered tissue. B: Sample of tip trajectories for CW rotating spiral waves. Each color represents a different trajectory that started at the central region of the computational domain. C: Folded-time plot (black) of the AR vs. time (normalized by the optimal period T). The red line corresponds to the constantly increasing phase solution that minimizes the RMS error. D: Snapshots of a simulation of a clockwise rotating spiral wave, intermittently trapped by a heterogeneity with radius R=0.225 cm, indicated by the dashed circle. Black dots: spiral wave tips. E: Distance of the spiral wave tip from the center of the heterogeneity as a function of time. Red bars indicate periods during which the spiral wave is trapped by the heterogeneity. F: Folded-time plot of the AR vs. normalized time for the intermittently trapped spiral wave.

We next computed the AR of the spiral wave during these identified intermittency intervals. This AR can, in principle, be computed as the angle between the activation front, which initiates at the spiral wave tip, and an arbitrary fixed line. As the spiral wave completes a cycle, this angle should increase by 2π. However, determining the activation front, especially in the clinical recordings, is prone to noise and is thus challenging. We therefore used a different methodology, in which the computed phases at discrete points surrounding the spiral wave tip are compared to a static phase map. This methodology, illustrated in Fig. 2 and further detailed in Methods, thus computes an average AR, which is less prone to noise.

Once the AR was computed as a function of time, we compared it to an AR that increases at a constant rate, AR_cons, with a period T. By systematically changing the period and starting value of AR_cons we found values that minimized the RMS error ${Err}_{CW}$ (Methods). The optimal period for our in silico data was found to be T_opt=114ms, which was within the interquartile range of spiral wave periods as determined during each of the 31 intervals: 104 (84–118) ms. Using this optimal period and the optimal starting value, we computed the RMS error and found that ${Err}_{CW}$=0.52π. This is close to the mean RMS value expected for drawing random numbers from a uniform distribution between −π and π, which can be computed as $\mathrm{\pi }/\sqrt{3}=0.577\mathrm{\pi }$. As expected, when plotting the AR of the spiral wave over the entire period, using a “folded-time” representation where time is restarted at 0 every 2T, the values of AR for each time point are not centered around the optimal, constant solution but are filling the entire space (Fig. 3C).

In additional simulations, we investigated whether a spiral wave that is intermittently or permanently trapped at an heterogeneity comes back in step or not. These simulations were carried by introducing a circular heterogeneity within the computational domain. As shown in a previous study ²³, a single meandering spiral wave that encounters this heterogeneity can be trapped at the heterogeneity. For large heterogeneity strengths, this trapping is permanent while for low heterogeneity strengths the trapping can be intermittent. In the latter case, the spiral wave will eventually meander away from the heterogeneity (Fig. 3D). This sequence can repeat itself, resulting in the intermittent trapping of a spiral wave (Fig. 3E). For this intermittent case, we computed the AR as a function of time and determined AR_cons that minimized the RMS error. A folded-time representation of the AR shows that its value is again filling the entire space (Fig. 3F). Thus, as in the spiral defect chaos simulation, the intermittently trapped spiral wave does not come back in phase but is, instead, out-of-step. Finally, as a control, we repeated this calculation but now for a spiral wave that is permanently trapped at a heterogeneity. After artificially creating intermittent intervals, we find, as expected, that the spiral wave comes back in-step (Fig. S2).

Clinical data

Fig. 4A shows the trajectories of the tips of the most prominent CW and CCW spiral wave in a 67 year old female patient during persistent AF. These trajectories reveal that these tips are only intermittently present during the recording. Fig. 4B shows a snapshot of the corresponding phase map, which, for ease of visualization, is shown by mapping the electrode locations within the atrium onto a square, flat grid (Fig. S1). Two clear rotational sources are present: one CW rotating spiral wave (black arrow and black tip) and one CCW rotating spiral wave (white arrow and white tip). The tip density map for CW and CCW rotating spiral wave tips, obtained by tracking these tips for the entire 60s recording, shows two regions of elevated density (Fig. 4C). These locations, marked by a black and white X, respectively, correspond to the tip location shown in the snapshot (Fig. 4C). During the analyzed 60s interval, we found that the CW spiral wave was present during N_CW=53 intervals of varying lengths, for a total of 42% of the recording time, and its period was computed as 194±7ms. The CCW spiral wave was present during N_CCW=50 intervals (73% of the time), with a period of 191±6ms.

Figure 4.

Spiral wave dynamics during AF. A: Trajectories of CW and CCW spiral waves for a 67 year old female patient during AF. B: Snapshot of the phase map during persistent AF in the patient. Two rotating spiral waves are observable (scale bar: 4 mm). C: Tip density map of the patient, obtained using a 60s recording of AF, showing a region of elevated tip density for both CW (black X) and CCW rotational activity (white X).

We next determined for both spiral waves the rotation angle AR_CW and AR_CCW as a function of time during the intervals they were observed. We then computed the difference between these angles and a rotation angle AR_cons that linearly increased from 0 to 2π every T ms and that started with angle ${AR}_0$ (Methods). Minimizing the RMS error by varying T resulted in an optimal period for both waves of T_opt=190 ms (Fig. S3A). This period also corresponds to the maximum value in the histogram of all activation times (Fig. S3B).

Using the folded-time representation, we visualized the angle for all relevant intervals (Fig. 5A&B). In these plots, and as in Fig. 3, the best fit AR_cons is presented as a red line, while the symbols correspond to clinical data. Although fluctuations are present, both AR_CW and AR_CCW are concentrated in a band around the red line rather than being completely dispersed. The latter would have been expected if the AR of the spiral waves started at a random value at the beginning of each interval. This is also reflected by the RMS errors of both the CW and the CCW spiral wave, which were found to be 0.19π and 0.17π, respectively. This suggests that these spiral waves are conserved throughout the recording: the observed rotational activity in each interval is not due to a de-novo spiral wave, but corresponds to the same spiral wave that is intermittently obscured during the recording.

Figure 5.

Spiral waves coming back in step during AF in a 67 year old female patient. A&B: Folded-time plots of the AR for the CW (A) and CCW (B) spiral waves. Clinical data points are shown as black dots and the best linearly progressing solution is shown as a red line. C&D: Probability distribution obtained by randomizing the clinical sequence, together with the clinical error, shown as a cyan symbol.

To determine how likely the errors are due to chance, we shifted the start of each interval by a number randomly chosen between 0 and T_opt. We then computed the RMS error for this shuffled sequence for all possible values of AR₀ and chose the minimum error. Repeating this many times allowed us to construct a probability density function (Methods). Consistent with the folded-time plot, the RMS error of the clinical data (red symbol) is well outside this probability density function (Fig. 5C&D). Thus, the likelihood that the observed AR conservation is due to chance is negligible for both spiral waves.

We repeated this analysis for N=34 AF patients (24 persistent or long-standing persistent and 10 paroxysmal) in which a CW or CCW spiral wave was present for at least 10% of the recording time. In most patients, we were able to identify both a CW and a CCW spiral wave, resulting in 32 CW and 29 CCW spiral waves. Spiral wave locations were distributed throughout the atrium and included the left atrium (LA) roof, posterior LA, anterior septal LA, LA posterior right superior pulmonary vein, near the mitral valve, and near the base of the LA appendage. These spiral waves were present for 32% (23%–45%) of the total recording duration, equating to 19s (14s-27s) (Fig. 6A). We computed the fraction of intermittent spiral waves in four successive non-overlapping 15 s recording windows. For spiral waves that came back in-step, we found that this fraction was 0.22/0.29/0.28/0.21 for CW spiral waves and 0.28/0.25/0.27/0.20 for CCW spiral waves. This finding that spiral waves were approximately evenly distributed throughout the recording is consistent with earlier work ¹⁸. Furthermore, the spiral wave period was found to be 206±31ms. The RMS error for the CW spiral waves was found to be ${Err}_{CW}$=0.45π (0.36π −0.48π) and for the CCW spiral waves ${Err}_{CCW}$=0.44π (0.38π −0.48π). The distributions for the CW and CCW errors were not significantly different (p>0.05) and the RMS error of all spiral waves for these patients was found to be ${Err}_{tot}$=0.45π (0.38π–0.48π) (Fig. 6A). Additional examples, illustrating patients with a small and relatively large ${Err}_{tot}$ are presented in Fig. S4.

Figure 6.

AF Wave Dynamics for all patients. A: Boxplot of the fraction of time the spiral wave was detectable (left) and of the RMS error. The red line represents the median, the box represents the 25%–75% range, and the whiskers correspond to the extreme values. B: Probability distribution of the RMS error of computer generate data in which the AR in an interval is linearly increasing with a initial value that is chosen at random for each of the N_int intervals. C: Clinical error vs number of intervals for all CW (red) and CCW (black) rotating spiral waves. The dashed and dotted lines correspond to 5% and 1% chance of finding this error, based on the distributions shown in B.

Comparing the clinical data to a probability distribution obtained by shuffling the sequence may be underestimating the likelihood that a spiral wave comes back in step by chance. Consider the case that the ARs in each interval are drawn from a random distribution. Then, choosing the optimal period for AR_cons will result in an error that will be close to the minimal error possible for this particular random sequence. In other words, randomly shuffling this sequence will result in errors that are mostly larger that the error from the original, unshuffled sequence. This would erroneously suggest that the clinical spiral wave was more in step than would have been expected based on random sequences.

For this reason, for each clinical spiral wave, we compared the error to a probability distribution obtained by taking linearly progressing ARs for every intermittency interval with a period T_opt and a random starting value (Methods). This probability distribution depends on the number of intervals, N_int, with its mean getting closer to $\mathrm{\pi }/\sqrt{3}$ and becoming narrower as the number of intervals increases (Fig. 6B). We then compared the clinical error to the resulting cumulative probability distribution and determined the probability that the clinical error is smaller than a certain fraction p of this distribution. For a probability value of p=0.05, we found that 68% of all spiral waves were identified as coming back in step while for p=0.01 this value was still 48% (Fig. 6C, dashed and dotted lines). This error was not correlated with duration (correlation coefficient of −0.04, p>0.1). It is unclear if substrate complexity affected stability in our patient cohort, and this will require further studies that correlate indices of structural remodeling, such as from MRI or biopsy, or features of electrical remodeling such as action potential duration. In conclusion, in the majority of patients, the rotational activation comes back in step, suggesting that it is a spatially and temporally conserved spiral wave that is intermittently obscured during the recording.

To determine whether intermittency intervals reflected lower signal quality or amplitude, we first computed, for each electrogram, the average amplitude of the recomposed electrogram signal during intervals where the spiral wave was and was not present (Methods). We then compared the resulting two distributions for each patient. Note that this amplitude is proportional to the maximum value of the negative time derivative of the electrogram, which is widely used to mark local activation times ^{24, 25}. Thus, larger amplitudes correspond to signals that are more easily interpretable and degraded signals should have, on average, smaller amplitudes. Nevertheless, we found that the two resulting distributions did not change in a statistically significant manner for any patient (Fig. S5). This suggests that periods when the spiral wave was not detectable did not reflect lower electrogram quality as indicated by lower amplitude (such as may occur from poor electrode contact or at regions bordering scar).

Discussion

In this study, we developed algorithms to investigate whether intermittent spiral waves, such as those observed in patients with AF, represent stable patterns obscured intermittently from various causes or are truly intermittent phenomena. We studied clinical recordings of patients in AF and developed computer approaches to track spiral wave tips with great accuracy. In computational models of AF, spiral waves were continuously annihilated and created such that each spiral wave tip trajectory ended when it collided with another tip or with a non-conducting boundary and were only present during intermittent intervals. In sharp contrast, we found that the majority of intermittent rotational activity in patients with AF resumed while maintaining phase. In these patients, a new trajectory starting in the same domain was associated with the same spiral wave. In other words, rotational activity was a manifestation of a stable spiral wave that came back in step.

Relevance to AF recorded directly from patients

The application of our studies to clinical data considered the most prominent CW and CCW rotating spiral waves, determined by computing a spiral tip density map (Fig. 4C). Only spiral waves that were present for at least 10%, i.e. 6s, of the recording time were considered. We found that the majority of patients displayed a spiral wave that came back in step. This is evident from the folded-time presentation of the AR, which shows that the clinical data did not fill the entire folded-time space but was concentrated in a narrow band along the constantly progressing solution AR_cons (Fig. 5 and Fig. S4). Furthermore, shuffling the sequence of intermittent intervals resulted in a probability distribution that had non-zero values for much larger errors than found in the clinical data (Fig. 5 and Fig. S4). To avoid overestimating the likelihood that the spiral wave came back in step, we performed a probability analysis in which the clinical data is compared to data with the same number of intermittent intervals in which the AR is linearly progressing and starting with a random initial value. This analysis showed that, at a 5% probability level, 68% of the spiral wave analyzed came back in step.

Physiological Interpretation

Our clinical results are consistent with a scenario in which the same spiral is responsible for rotational activity seen in intermittent intervals. This scenario is distinct from the spiral defect chaos scenario shown in Fig. 3A where spiral waves are constantly created de-novo. How is it then possible to observe this single spiral in an intermittent fashion rather than continuously throughout the entire recording? One possibility is that the spiral wave is pinned or lodged to a particular tissue area but is temporarily unpinned and dislodged. Pinning of spiral waves have been investigated in computer simulations, which have demonstrated that large enough tissue heterogeneities can anchor spiral waves ^26–28. Furthermore, additional simulations have shown that under certain conditions it is possible for the spiral wave to be intermittently trapped ²³. It would be unlikely, however, that an intermittently trapped spiral wave comes back in step. After all, it will migrate through tissue with different characteristics, which will alter its rotational frequency and thus the phase of the AR. Indeed, our simulations demonstrate that an intermittently trapped spiral wave comes back out-of-step (Fig. 3), suggesting that this scenario is not responsible for our clinical observations.

Alternatively, it has been proposed that competition between multiple driving sites in AF may result in an alternation between, for example, multiple rotational sites, or between sites with rotational and focal activity ¹⁸. In this scenario, however, the spiral wave would have to form anew after the disappearance due to the competing site. Therefore, this re-formed spiral wave will have an AR that is uncorrelated with the one from previous intermittent intervals and will not come back in step.

In a third scenario, spiral waves may be intermittently obscured due to recording challenges and may reflect inherent methodology limitations. In particular, it is possible that motion artifacts interfere with the recordings by changing the relative orientation of the basket of by significantly reducing the quality of the electrograms. For example, the motion of the atrial wall during the heart’s contraction will alter the distance between electrodes and tissue, which can significantly affect the electrogram quality ^{29, 30}. In addition, the breathing of patients can also influence the quality of electrograms or can change the location of the basket. These imaging challenges would not, of course, affect spiral wave dynamics, but could explain their intermittent appearance and disappearance. Importantly, when we determined the average amplitude of the recomposed signal, a measure of electrogram quality, we did not find significant differences between intervals with and without an observable spiral wave. Therefore, it is unlikely that a reduction in electrogram amplitude or quality explains clinically observed intermittency, although a repeated reorientation of the basket can not be ruled out.

Our finding that spiral waves can be spatially conserved in some patients may have clinical significance. AF patients in which spiral waves are not conserved may be challenging to treat by spatially-directed ablation. Conversely, patients in whom AF is more organized, with spatially conserved spiral waves, may have different prognosis and better response to medications or pulmonary vein isolation through ablation ³¹. In patients in whom pulmonary vein isolation does not eliminate AF, spatially conserved spiral waves could be targets for ablation to destroy tissue close to the spiral wave tip, as demonstrated in computational analyses ^{32, 33}, in explanted hearts ³⁴, and in some clinical studies ^{11, 12}. In such cases, removing spatially conserved spiral waves can result in wave dynamics with a finite termination time ^{22, 35, 36} as shown in subsets of patients ^{12, 37}. In addition, our finding that a spiral wave come back in step and are thus manifestations of a temporally stable, spatially conserved wave may also explain why a recording interval that is much shorter than 60s can be sufficient to determine the location of AF drivers ^{10, 12}.

Limitations

The number of spiral waves examined in this paper (N=69) is modest. Furthermore, although our recording time of 60s is longer compared to previous studies, it does not allow for the analysis of spiral wave activity that is more intermittent. In particular, while our study quantifies spatial conservation of spiral waves in recordings for periods of 1–2 minutes, they do not address conservation over tens of minutes or hours that would require patient consent for extended intracardiac recordings with no intervention.

What Is Known?

• Atrial fibrillation (AF) is associated with spiral wave activation, focal activity, collision or partial versions of these spatial patterns.

• It is unclear why clinical recordings often show only intermittent spiral wave activity and if this represents a conserved spiral wave that is intermittently obscured or newly created spiral waves.

What The Study Adds

• In N=34 AF patients, spiral waves were intermittently observed at a spatially conserved location for at least 10% of 60s recordings.

• The spatially conserved spiral waves in the patients returned “in-step” in the majority (68%) of patients, indicating that spiral wave activity was a manifestation of stable spiral waves and not of newly created ones.

Nonstandard Abbreviations and Acronyms

AF

Atrial Fibrillation

AR

Angle of Rotation

CW

Clockwise

CCW

Counterclockwise

DF

Dominant Frequency

LA

left atrium

RMS

Root Mean Square