Frequency Analysis of Ventricular Fibrillation in Swine Ventricles

The experimental model has been previously described.¹⁶ The hearts of 15 farm pigs of either sex (purchased from S&S Farms, Ranchita, Calif) were removed via thoracotomy, the RV wall was excised and placed in a tissue bath, and the right coronary artery was perfused. In 12 tissues, the endocardium faced upward, an oblique cut was then performed at the distal edge, exposing the transmural surface¹³ and including the papillary muscle (PM). Optical mapping during VF was performed in the cut transmural surface as well as the adjacent endocardial surface. For comparison of transmural versus epicardial or endocardial reentry, 3 RVs were mapped in the epicardium and 3 in the endocardium. The research protocol was approved by the Institutional Animal Care and Use Committee of Cedars-Sinai Medical Center and followed guidelines of the American Heart Association.

Our LV wedge preparation has been previously described.^13,17 In 9 tissues, a rim of tissue surrounding the left circumflex and the second obtuse marginal artery was excised, leaving an inverted L-shaped preparation that always contained at least part of the posteromedial PM. The tissue was placed in the bath with the transmural cut surface facing upward. In 3 tissues, the left circumflex artery was ligated proximally and a wedge of tissue surrounding the left anterior descending artery was cut, exposing the transmural surface of the interventricular septum.

Tissues were stained for 20 minutes with 1 to 2 μmol/L di-4-ANEPPS and were illuminated with either quasimonochromatic (500±30 nm) or laser (532 nm) light. The fluorescence was collected with a CCD camera, at either 279 or 435 frames per second, for either 4.3 or 2.3 seconds (1200 and 1000 frames, respectively). To test the short-term time dependency of frequency domains, several 5000-frame (11.5 seconds) recordings were performed in 3 tissues.

One-minute recordings of single-cell transmembrane potentials (TMPs) were performed in 6 RV endocardial tissues, using a standard glass microelectrode, digitized at an acquisition rate of 5000 Hz.

Optical signals were processed to reduce noise as described previously.¹³ Wavelets were identified using our previously described depolarization and repolarization detection algorithm.¹³ Points where depolarization and repolarization met were defined as wavebreak points. Reentry was defined as wavefront rotation around a wavebreak point completing a 360° cycle (although a stationary center of rotation was not required). The fraction of reentrant wavelets was determined as the ratio of the number of wavelets participating in a reentrant circuit over the total number of wavelets in the mapping field. Isochronal maps were generated based on the location of wavefronts in each frame, coded to different colors over time.

FFT, STPs, and pseudo-ECGs were derived from optical recordings as described elsewhere.³ STP sampling lines were generated both vertically and horizontally, dividing the maps into two halves (see Figure 1). Wenckebach-like conduction was defined to occur when the number of activations across one domain exceeded the number across the neighboring domain with a consistent ratio or with apparent decremental conduction.

Data are presented as mean±SD. χ² test was used to compare proportions of reentrant wavelets. Kruskal-Wallis ANOVA was used to compare wavelet descriptors.

We simulated cardiac arrhythmias using the following partial differential equation^8,18:

where V is the transmembrane potential and C_m the membrane capacitance. I_ion is the total ionic current density of the membrane, which was generated from phase I of the Luo and Rudy (LR1) action potential model.¹⁵

is the diffusion tensor, where ς∼ is the conductivity tensor and S_v the surface-to-volume ratio of the cell.

In the 3D simulation, the only heterogeneity was the fiber rotation. Details of incorporating fiber rotation into Equation 1 are described in our previous study.¹⁸

In the 2D simulation, we assumed that diffusion in Equation 1 was isotropic. However, we incorporated electrophysiological heterogeneities into the tissue as previously described.¹⁹ Methods for detection of reentry, FFT analysis, and pseudo-ECG generation were the same as in the experiments.

An expanded Materials and Methods section can be found in the online data supplement available at http://www.circresaha.org.

The Table summarizes the number of wavelets per mapped area, the mean wavelet lifetime, the incidence of complete reentry, and the mean number of reentry cycles per reentry episode. The combined (RV and LV) incidence of full-loop reentry was 11.9% (of all activation pathways), with a mean number of reentry cycles of 6.5±5.7 per reentry episode. The shortest stable rotor from 83 epochs of VF in 12 LV and 15 RV preparations lasted 69 ms (1 cycle) and the longest lasted 3423 ms (54 cycles). The incidence of transmural reentry in both LV and RV was similar to that of the endocardium but higher than that of the epicardium.

DFs, defined as the largest peak in the FFT spectra of the optical voltage signal at each pixel, were detected in all VF episodes and were spatially localized in well-circumscribed domains.¹² However, these DF domains were not stationary over time, and, except at gross anatomical structures (see below), shifted their location continuously. This instability was present not only in different VF acquisitions but also within segments of a prolonged VF recording. Figure 1 shows a typical example of a 9.2-second (4000 frames) epoch of VF recorded from RV epicardium. Figure 1A shows 5 to 10 spatially discrete domains with DFs ranging from 11.9 to 14.0 Hz, which did not remain stationary over time. In fact, the spatial patterns of DF domains, when analyzed in consecutive segments, not only differed from each other, but also differed from the pattern obtained when the corresponding segments were analyzed as a whole (Figure 1A, compare panels a and b versus panel c, and panels d and e versus panel f). Subtraction maps, cross-correlation, and statistical analysis of the frequency distributions confirmed the differences between consecutive DF maps (see the online data supplement available at http://www.circresaha.org). Figure 2A shows another example.

Only at locations corresponding to gross anatomical structures such as PM insertions and endocardial trabeculae in the RV were boundaries between DF domains relatively stable. However, the DF values on either side of the boundary often changed, and the direction of DF gradients across such boundaries was variable. Figures 2A and 3A show examples: despite generally shifting DF domain boundaries, there was one location (black dotted line in Figure 2A, red arrows in Figure 3A) that consistently showed a domain boundary, regardless of the frequencies it separated. Moreover, the high-DF region could be either above or below the boundary. Of all VF acquisitions, 73% exhibited one boundary in a stable location (defined as present in at least 4 of 5 frequency maps). The mechanism of boundary formation at this location was due to the increased incidence of reentry at these locations, leading to double potentials (a characteristic of the core of reentry)^2,20 generating shifts in DFs (see next section).

Local DF instability underlay frequency domain instability. Figures 1A and 2B illustrate this finding. Figure 1A shows representative FFT spectra from three pixels (labeled 1, 2, and 3) obtained from different segments of the acquisition. In Figure 1A, at the pixel labeled 1, the FFT spectrum had a DF of 11.9 Hz during the first 4.6 seconds of VF (Figure 1Ac) that shifted to 13.0 Hz during the next 4.6 seconds (Figure 1Af). This pixel had shown other DFs during other segments of the VF episode (13.2 Hz in Figures 1Aa and Figure 1Ad, 12.3 Hz in Figure 1Ab, and 12.7 Hz in Figure 1Ad). However, when all 9.2 seconds were analyzed together, the resulting DF was 13.3 Hz (Figure 1C). Figure 2B, left, shows, in a different tissue, FFT spectra of a single pixel calculated at 2.3-second intervals throughout 11.5 seconds of VF. Five different DFs are present. DF was unstable consistently in all tissues. Figure 2B, right, shows the DF time course of single pixels for 5 different tissues. To show that the changing DF was not due to filtering of the optical signal, we also analyzed the FFT of prolonged single-cell TMP recordings, which revealed a similar second-to-second variability in DF (Figure 2C).

Although a largest peak (DF) could always be identified, the FFT spectra were multipeaked and exhibited significant broadband power. This was especially true when long intervals were analyzed, as illustrated by the comparison of FFT spectra of 2.3-second intervals (0.4-Hz resolution, Figure 1A, panels a, b, d, and e) with those of 4.6-second intervals (0.2-Hz resolution, Figure 1A, panels c and f), 9.2-second intervals (0.1-Hz resolution, Figure 1C), and finally, 1-minute recordings from TMPs (0.019-Hz resolution, Figure 2C).

Figures 3 and 4 illustrate the most common form of apparent conduction block observed in the STP. Between 150 and 400 ms, the STP (Figures 3C and 4B) shows a discontinuity in activation sequence with branching bands in the lower third. The DF corresponding to these regions (pixels 3 through 5 in Figure 4) was 11.04 Hz, with the adjacent sites on either side having lower values of 9.77 to 10.19 Hz. One possible interpretation, consistent with the mother rotor hypothesis, is that reentry (or breakthrough activation arising from a rotor underneath the mapped surface) with a frequency of 11.04 Hz was driving the adjacent domains with 11:10 conduction block occurring on either side. However, optical activation maps did not reveal such a pattern. As shown in Figure 3, no stable rotor was visualized on the transmural surface. Instead, two colliding wavefronts (Figure 3B, at arrows in a and b) resulted in the formation of a reentrant circuit (Figure 3B, c through i). The core of this reentrant circuit was located in the 11.04-Hz DF domain (sites 3 through 5 in Figure 4A). There was no evidence of conduction block in the surrounding domains with lower DF. Figure 4 illustrates that the shift to higher DF at the core compared with surrounding sites could be attributed to double potentials^2,20 in the core of the scroll wave (as seen in the voltage traces at sites 3 through 5 in Figure 4C). In addition, there was a small (nondominant) peak in the FFT spectra at 22 Hz, corresponding to the double-potential frequency, which coincided with the DF harmonic. As described previously,³ this pattern of branching bands in the STP (Figures 3C and 4B) is characteristic of the core of a rotating scroll wave. This reentry was unstable both spatially (note the subtle core displacement to the right in the isochronal maps, Figure 3B, c through e) and temporally, as it was successively interrupted (Figure 3B, g and i) and resumed (Figure 3B, h and j). In Figure 3B, k through l, another wavelet invaded this area and the reentrant circuit was terminated and the branches in the STP fused together. Note that the DF in the region where this core formed was only 11.04 Hz, not double the DF of the adjacent regions (9.77 to 10.19 Hz). This reflects the fact that the segment during which double potentials were present in the voltage traces (150 to 400 ms) was only part of the total segment (0 to 2300 ms) from which the FFT spectrum was obtained and thus did not have sufficient power to become the DF. However, the high-frequency segment was sufficient to alter the relative powers of the multiple peaks in the FFT spectrum near 10 Hz so that the DF was shifted to a higher value. We confirmed this explanation by simulating the sequence with sine waves of mixed frequencies and examining the FFT spectra (data not shown).

We examined STPs for evidence of conduction block. No consistent direction of propagation gradient was present (Figures 1B and 2)A. Although rare, we occasionally identified Wenckebach-like conduction patterns in the STP (11 of 166 STPs). Figure 5 shows an example. Wenckebach-like conduction occurred once at ≈400 ms and then again at 550 ms on the STP (Figure 5B). Figure 5A shows the corresponding isochronal activation maps, and Figure 5D the optical voltage traces from sites 1 through 3 as indicated. In Figure 5Aa, a wavelet spread downward from the left upper portion of the tissue in a planar fashion, with wide isochrones across the STP line, reflecting rapid conduction. In the following activation (Figure 5Ab), this wavelet formed a reentrant circuit, whose core was near the vertical STP line. This reentry persisted for two additional rotations (Figure 5A, c and d), and then was interrupted by a wavelet spreading downward from the top (Figure 5A, e and f). The subsequent activation, also from the top (Figure 5Ag), blocked between site 1 and sites 2 and 3 (Figure 5Bg), causing a 7:6 Wenckebach-like cycle. Later, a second Wenckebach-like block occurred by a similar mechanism, but this time was due to an upward planar wave (Figure 5Ak).

Therefore, a 7:6 Wenckebach-like conduction pattern was followed by a 4:3 Wenckebach-like cycle. Of note, the apparent block occurred in both directions (from top-to-bottom in the first case and from bottom-to-top in the second), which is inconsistent with the concept of one stable domain driving the neighboring regions. However, in both episodes, the apparent block occurred during propagation from a region of low DF (10.61 Hz at sites 1 and 3) to a region of high DF (11.46 at site 2), as shown in the accompanying FFT spectra (Figure 5C). This does not support the idea that high-DF domains correspond to regions that are better able to sustain 1:1 conduction, as postulated by the mother rotor hypothesis.

We performed computer simulations to examine the relative importance of tissue heterogeneities and APD restitution steepness. In simulated 3D tissue with a physiological degree of fiber rotation but otherwise homogeneous conditions, steep APD restitution slope in the cardiac action potential model caused spontaneous scroll wave breakup, with multiple wavelets coursing through the tissue similar to VF. The Table summarizes the average number of wavelets per mapped area, the mean lifetime of wavelets, the incidence of completed reentry, and the mean number of reentry cycles per reentry episode. The incidences of reentry on the epicardial/endocardial surfaces were similar and matched the incidence on the endocardial surface in the biological tissue experiments. In contrast, the incidence of transmural reentry was lower than on the surfaces in simulated tissue, which contrasts with the similar incidence in biological tissue. This discrepancy is probably due to the heterogeneities such as PM attachments and trabeculae in the biological experiments, which our previous mapping studies showed acted as transient anchoring points for reentry.¹³ These findings also indicate that the lack of morphologically identifiable scroll waves on the tissue surface does not reliably exclude scroll wave dynamics as the underlying mechanism.

We performed frequency analysis in 2D simulated tissue (due to the computational intractability for 3D tissue). In heterogeneous tissue with physiological APD restitution (slope >1) (Figure 6), we obtained similar findings as in the tissue experiments, with spatially discrete DF domains that shifted rapidly over time and space (Figure 6A). STPs across the boundaries of these domains commonly showed the branching 2:1 patterns characteristic of spiral wave cores, and patterns resembling Wenckebach-like conduction were also observed (Figure 6B). Homogeneous tissue gave similar results, except that the DF domains were smaller in size and varied over a smaller range (data not shown).

To reproduce DF domains whose boundaries and DF values remained stationary required heterogeneous simulated tissue with flattened APD restitution slope (Figure 7). Under these conditions, DF domains were well-defined and remained stationary in time and space (Figure 7A). STPs across these boundaries often showed clear Wenckebach-like conduction patterns as impulses propagated from a region of high-to-low DF (Figure 7B). The most rapid spiral wave, the mother rotor, was fairly stationary and located in a region with the highest DF (at the lower left corner in the spatial DF maps in Figure 7A).