# Life Span of Ventricular Fibrillation Frequencies

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## Abstract

The nature and organization of electrical activity during ventricular fibrillation (VF) are important and controversial subjects dominated by 2 competing theories: the wavebreak and the dominant mother rotor hypothesis. To investigate spatiotemporal characteristics of ventricular fibrillation (VF), transmembrane potentials (V_{m}) were recorded from multiple sites of perfused rabbit hearts using a voltage-sensitive dye and a photodiode array or a CCD camera, and the time-frequency characteristics of V_{m} were analyzed by short-time fast Fourier transform (FFT) or generalized time-frequency representation with a cone-shaped kernel. The analysis was applied to all pixels to track VF frequencies in time and space. VF consisted of blobs, which are groups of contiguous pixels with a common frequency and an ill-defined shape. At any time *t*, several VF frequency blobs coexisted in the field of view, and the number of coexisting blobs was on average 5.9±2.1 (n=8 hearts) as they appeared and disappeared discontinuously with time and were not fixed in space. The life span of frequency blobs from birth to either annihilation or breakup to another frequency had a half-life of 0.39±0.13 second (n=4 hearts). The Ca^{2+} channel blocker nifedipine increased the stability of VF frequencies and reduced the number of frequency blobs progressing to a single frequency. In conclusion, VF consists of dynamically changing frequency blobs, which have a short life span and can be modified by pharmacological interventions, suggesting that VF is maintained by dynamically changing multiple wavelets.

- ventricular fibrillation
- ventricular tachycardia
- time-frequency analysis
- optical mapping
- L-type Ca
^{2+}channel

Ventricular fibrillation (VF) has been linked to the development of vortex-like reentry or spiral waves that have been studied in computer simulations,^{1,2}⇓ tissue slices, and perfused hearts.^{3,4}⇓ In this context, nonstationary (meandering or drifting) spiral waves and/or their turbulence could account for the complex morphology of electrocardiograms (ECGs) in VF. Experimental studies mapped electrical activation using multiple electrodes or optical probes of membrane potential to investigate the mechanisms underlying ECG signals seen in VF. VF has been traditionally investigated by analyzing activation maps, but the complex waveforms recorded in VF and the algorithms used to derive activation maps have made it difficult to interpret the underlying mechanisms. Another approach is to analyze voltage oscillations in the frequency domain using fast Fourier transforms (FFT) and to represent reentrant circuits as sources of periodic wave formation.^{5–7}⇓⇓ However, FFT spectra must be interpreted with caution because they measure the averaged contribution of each frequency component with no information on their time of occurrence. For instance, simple FFT spectra with a single dominant peak can be generated from continuously appearing and disappearing frequency sources; conversely, complex FFT spectra can be obtained from a single source with an increasing and/or decreasing frequency.

To overcome the limitations of frequency analysis, this study applied time-frequency analysis where membrane potential oscillations from different regions of the heart are transferred to time and frequency domains to visualize the creation and annihilation of each frequency component in VF in time and space.

## Materials and Methods

### Heart Preparations

New Zealand White rabbits (female, 1.6 to 2.5 kg, n=8; Myrtle’s Rabbitry, Thompson Station, Tenn) were injected with pentobarbital (35 mg/kg, IV) plus heparin (200 U/kg), and the heart was excised and retrogradely perfused through the aorta with (in mmol/L) NaCl 130, NaHCO_{3} 24, MgCl_{2} 1.0, KCl 4.0, NaH_{2}PO_{4} 1.2, dextrose 20, and CaCl_{2} 1.5, at pH 7.4, and gassed with 95% O_{2} and 5% CO_{2}. In 5 of the 8 rabbit hearts, the L-type Ca^{2+} blocker nifedipine (2 μmol/L) was perfused during VF, and the electrical activity was monitored continuously to track changes in the structure of VF caused by nifedipine. This investigation conformed to the current *Guide for the Care and Use of Laboratory Animals* published by the National Institutes of Health (NIH publication No. 85-23, revised 1996).

### Optical Apparatus

Optical action potentials (APs) were recorded from Langendorff-perfused rabbit hearts stained with di4-ANEPPS. Hearts were mounted in a chamber to image the anterior surface with either a photodiode array (16×16 matrix, 1000 frames per second; Hamamatsu, Bridgewater, NJ) or a 14-bit digital CCD camera (72×78 pixels, 1000 frames per second; FastOne, PixelVision, Tigard, Oreg). The optical apparatus, chamber, computer interface, and software were previously described.^{7} Each diode viewed a 1.1×1.1-mm^{2} area, and each pixel on the CCD camera viewed a 0.055×0.055-mm^{2} area. The integration time of CCD camera was set to 0.2 ms to reduce possible motion blurring caused by rapid wave propagation. VF was induced by burst stimulation for 2 seconds; voltage recordings were taken continuously for 5 minutes with the photodiode array after the onset of VF (n=8). The recordings of the CCD camera were taken for 8-second intervals from different hearts (n=4). In the subgroup of experiments with nifedipine (n=5), electrical activity was continuously mapped for 5 minutes after the addition of the drug.

### Time-Frequency Analysis

To analyze V_{m} signals during VF in time and frequency domains, a spectrogram (short-time Fourier transform) was generated for each pixel by calculating the FFT spectrum for a brief gaussian window of 1.5 to 2.0 seconds, then shifting the window stepwise in time (Δ*t*=1 ms) and remeasuring the FFT spectrum at successive *t* intervals. The frequency resolution is 0.5 to 0.66 Hz and is inversely related to the window size. Transmembrane potential oscillations during VF events are thus transformed to time and frequency domains to visualize the evolution of VF frequencies.

The spectral peaks in time-frequency representations can be enhanced using Cohen’s bilinear class,^{8} convolution of the Wigner distribution with a smoothing kernel. A generalized time-frequency representation *C*(*t*, *f*;Φ) of the signal *x*(*t*) with the kernel Φ(*t*, τ) is as follows^{8}:

where *t* is time, τ is the delay in the autocorrelation function,

and the asterisk (*) denotes complex conjugation. This study applied a cone-shaped kernel, ^{9} as follows:

The cone-shaped kernel has a constraint on a cone-shaped nonzero region in *t* and τ domains to maintain good resolution for fast-changing spectral peaks and to preserve the onset of time at which the signals arise.^{9} An efficient algorithm to calculate discrete data was previously reported.^{9} The cone-shaped smoothing kernel resulted in considerably sharper frequency resolution compared with the standard spectrogram, as previously applied to ECG recordings.^{10}

The time-frequency distribution is represented as a contour map where the horizontal axis represents time and the vertical axis represents frequency. The corresponding optical traces are shown on top of the frequency distribution and overall power spectra of optical traces are shown on the left. The contour lines are drawn every 12.5% of maximum, and the higher the intensity the darker the color. The time-frequency representation with the cone-shaped kernel was filtered further in the time domain to reduce small high-frequency noise using a low-pass Butterworth filter (cutoff <60 Hz).

### Segmentation of VF Frequency Blobs

Time-frequency analysis was extended to all 252 channels (256−4 channels at each corner), and the distribution of VF frequencies was analyzed in 4 dimensions, space (*x*, *y*), frequency (Hz), and time (*t*). Because of the massive computational and memory requirements, time-frequency analysis for all pixels was subdivided into 2-minute intervals. The distribution of VF frequencies *P*(*x,y, f*) at time *t* is visualized as an isosurface plot in space (*x*, *y*) and frequency (*z*) axis where *P*(*x, y,f*) is above an arbitrary threshold (see Figure 1A). The threshold (≈12.5%) was chosen from the histogram of time-frequency distribution so that only the background noise can be eliminated without losing small-frequency peaks.

The isosurface plots show that frequency peaks are not uniformly distributed but that certain frequencies appear in small contiguous regions of ill-defined shape. We define this contiguous object in space and frequency domains as a VF frequency blob, because a common approach to identify such objects uses a blob-coloring algorithm. Individual VF frequency blobs at time *t* are given a unique identification number (region index) as follows. The function describing the distribution of VF frequencies, *P*(*x,y,f*), is set to 0 when the pixel value *P*(*x,y,f*) is below threshold. For pixels above threshold, each pixel is assigned the same unique identification number as its neighboring pixels when the neighboring pixels are also above threshold (nonzero). VF frequency blobs are then formed by the pixels that are contiguous in space and frequency, with the same identification number (see Figure 1A).

### Life Span of VF Frequency Blobs

A similar algorithm can be applied to calculate the life span of VF frequency blobs but now in 4 dimensions to include *x*, *y*, frequency, and time *t*. Blobs connected in *x*, *y*, *f*, and *t* dimensions are given the same identification number, and each blob was tested to determine whether it subdivided into several blobs in space and frequency domains. Therefore, the life span of VF frequency blobs can be measured until they either split or disappear (see Figure 1B). The life span of VF frequency blobs was calculated from 4 rabbit hearts (2-minute interval of VF) such that >500 VF frequency blobs were identified, tracked in time and space to calculate their life span. A histogram of life span was generated and fitted to the first-order exponential decay curve (*y*=*Ae*^{−t/τ}) by nonlinear least-squares fitting using Microcal Origin 6.0 (Microcal Software, Inc, Northampton, Mass), and half-life was calculated from the exponential decay constant.

## Results

### FFT Spectra From Photodiode Array and CCD Camera

Electrical activity measured during VF was found to have complex multiple component FFT spectra when recorded optically with a photodiode array.^{7,11}⇓ The interpretation of multiple-component FFT spectra was challenged because of the lower spatial resolution of the photodiode array compared with the CCD sensors.^{12} Figure 2A illustrates the field of view of the 16×16 photodiode array and the image (72×78) recorded by the CCD camera. Figure 2B compares the optical recording from a diode from an array (top) to a pixel recording from the CCD camera (bottom) and their FFT spectra (Figure 2C). Voltage transients and FFT spectra from a 0.8×0.8-mm^{2} area of the heart (top trace) were equally complex as those recorded at a higher spatial resolution from a 50×50-μm^{2} area (bottom trace) from a single CCD pixel.

### Time-Frequency Representation of VF Signals

To determine the time when individual FFT peaks occurred, voltage oscillations were represented in time and frequency domains by generating a standard spectrogram (see Materials and Methods). Transmembrane potential oscillations during VF are thus transformed to time and frequency domains to visualize the evolution of VF frequencies. Figure 3A illustrates a spectrogram from a single photodiode where the frequency peaks tend to appear and disappear rapidly in time. Note that the bands of VF frequencies are broad and lack sharp boundaries. The poor resolution is due to an inherent trade-off between time and frequency in the spectrogram algorithm that is best suited for slowly varying frequencies.

In Figure 3B, the frequency peaks in the spectrogram were enhanced by applying the general time-frequency distribution analysis with a cone-shaped kernel^{9} (see Materials and Methods for detail). The cone-shaped kernel (Figure 3B) was applied to the same signal to produce a contour map with similar general features but considerably sharper frequency resolution compared with the standard spectrogram (Figure 3A), as previously described. ^{10} Enhanced time-frequency representation shows separate discontinuous bands, suggesting that VF frequency peaks appeared and disappeared abruptly.

A contour map of time-frequency representation in Figure 3C is obtained from a CCD signal after applying the cone-shaped kernel and shows the same general features as from a photodiode, indicating that the multicomponents in the time-frequency domain were not due to lower spatial resolution of the photodiode array.

### Spatial and Temporal Characteristics of VF Frequencies

In many intervals of VF (see Figure 3), VF frequencies were not stable but appeared and disappeared, forming discrete bands. To study the dynamics of VF frequencies along the surface of the heart, time-frequency analysis was extended to all the pixels and reconstructed in space, time, and frequency domains. Figure 4A shows snapshots of VF frequency distribution as isosurface plots (see Materials and Methods) by plotting frequencies (*z*-axis) against position on the heart (*x*-, *y*-axis). The results show that at any given time *t*, several frequencies coexisted, occupying different regions. It should be noted that successive isosurface plots (Figure 4A) are significantly different from each other.

VF frequency distribution consisted of separate blobs occupying contiguous regions of epicardium, and these were assigned a unique identifier using a blob-coloring algorithm, as described in Materials and Methods. We further investigated how many VF frequency blobs coexist during VF and how long the frequency blobs exist. A plot of the number of frequency blobs versus time (Figure 4B) shows the dynamic nature of VF frequencies and that 2 to 12 blobs (average 5.9±2.1, n=8) coexist at any given time in the field of view. Each blob was traced in time to investigate its life span, as described in Materials and Methods. The life span of individual VF frequencies from their time of birth to either their death or subdivision to several VF frequency blobs was measured and the number of VF blobs with a life span ≥ time *t* was displayed as a histogram (Figure 4C). The majority of VF frequencies lasted <1 second, with the longest time of 8 seconds in this episode of VF. The life span plot was curve-fitted to a single-exponential decay function with a time constant τ=0.57±0.19 second (n=4, half-life=0.39 second). VF frequencies were spread over an area of 32±34 mm^{2} during their life time, where the larger the area occupied by a frequency blob, the longer the lifetime of the frequency blob with correlation coefficient of 0.59 (*P*<0.0001).

### Effect of L-Type Ca^{2+} Channel Blocker on VF Frequencies

L-type Ca^{2+} channel blockers such as verapamil have been shown to change VF to ventricular tachycardia (VT).^{13,14}⇓ Time-frequency analysis was applied to better understand and visualize how a Ca^{2+} channel blocker influences the behavior of VF dynamics in time and space. Nifedipine (2 μmol/L) was added during VF, and transmembrane potentials were recorded continuously for 5 minutes for time-frequency analysis. Figure 5A shows snapshots of VF frequency isosurface plots recorded during perfusion of the heart with nifedipine. The complex spatial distribution of VF frequencies was consistently converted to a large stable frequency blob by nifedipine (n=5 of 5 hearts). In this experiment, nifedipine converted VF to VT, which appeared at steady state, as a stable doughnut. The activation map of corresponding isosurface plots is shown in Figure 5B. Time-frequency plots from a single pixel in Figure 5C also showed that the complex dynamics of VF were converted to a single frequency on the addition of nifedipine. Figure 5D shows that the number of frequency blobs was gradually reduced by nifedipine, showing that the shift from VF to VT was due to a reduction of the number of VF frequencies that coexisted in the field of view.

## Discussion

Technological advances now provide high-resolution maps of electrical activity that have been used to investigate the structure of VF using frequency analysis to correlate a particular frequency with a source of reentry.^{5,6}⇓ However, FFT analysis does not provide information regarding time-varying frequencies, which is essential to understand the life and death of VF frequencies in time and space. To overcome this limitation, we analyzed signals in time, frequency, and space at high spatial and temporal resolution, making it possible to track VF dynamics in great detail. Major findings are that VF is composed of several VF frequency blobs that have ill-defined shapes, are unstable in space and time, and are created, subdivided, and destroyed with a brief life span. The dynamics of VF frequency blobs can be modified by a blocker of voltage-gated Ca^{2+} channel, suggesting that VF is maintained by the continuous creation and annihilation of periodic sources.

Reentrant wave propagation has been thought to be the major mechanism underlying complex transmembrane oscillations during VF, but the maintenance of VF is still under debate. As early as 1914, Garrey ^{15,16}⇓ suggested that atrial fibrillation (AF) is caused by reentry and that the multiple waves maintain AF. However, Lewis^{17} proposed that AF is caused by a single, rapidly rotating central wave, and its rapid activation causes an irregular impulse propagation across partially refractory tissue (see review^{18}). Nearly 80 years later, the hypotheses first proposed by Garrey and Lewis are still controversial and have been expanded to multiple wavelets and mother rotor hypotheses (see reviews^{19,20}⇓). According to the multiple wavelets hypothesis, continuous wavebreaks create meandering fragmented wavelets that cause complex meandering, annihilation, and creation of new wavelets.

However, the mother rotor hypothesis suggests that a high-frequency stable rotor generates fragmented conduction or fibrillatory conduction. The mother rotor hypothesis was based on the observation that electrical activity during VF recorded optically with a CCD camera exhibited dominant frequency peaks that were relatively stable and distributed in discrete regions of the heart.^{5,6}⇓ In smaller rabbit and guinea pig hearts, a single peak frequency was found to cover the entire left ventricle, supporting the mother rotor hypothesis. In contrast, Wiggers^{21} reported a considerably more complex frequency distribution in hearts under VF with marked instabilities and heterogeneities of frequencies across the epicardium. Several groups^{22–24}⇓⇓ have reproduced these results and demonstrated that frequencies are spatially heterogeneous and unstable in time, which is opposite to the premise of the mother rotor hypothesis. Furthermore, FFT spectra were more complex, showing multiple peaks instead of an FFT with a single peak and a narrow bandwidth. It is important to emphasize that the detection of multiple frequency peaks requires an analysis with high spectral resolution, which in turn requires longer time intervals of FFT analysis.^{24}

A major limitation of FFT analysis is that it fails to provide temporal information of when a specific FFT peak (or VF source) occurs in time. One possibility is that multiple frequency peaks arise from multiple frequency sources. Alternatively, multiple frequency peaks can arise from a single rotor if the amplitude of the signals oscillates or if frequency signals change gradually, as can occur by the Doppler effect from the drifting of a single rotor. Therefore, VF signals should be investigated in time and frequency domains, and the analysis should be extended to the multiple locations to obtain a complete picture of VF dynamics.

Generalized time-frequency distribution based on Cohen’s bilinear class has been applied to study time-varying biological signals including AF and VF.^{23,25,26}⇓⇓ For example, using grids of extracellular electrodes, Moghe et al^{23} showed that VF frequencies are unstable, varying with time and location, in different regions of the fibrillating heart. Patwardhan et al ^{26} performed a time-frequency analysis on ECG signals and tested the cross correlations between different leads to determine whether the time-frequency distribution in different regions of the heart can be explained by a time shift. They found that after applying a time shift to one ECG lead, they could not improve the cross correlation with respect to another lead, such that the different VF frequencies from different leads could not be attributed to the same frequency source. These findings were not consistent with the existence of a single large, drifting rotor. However, these studies were limited to the number of electrodes that could be simultaneously recorded and by the difficulties of interpreting the surface electrograms during VF.

We applied time-frequency analysis to the surface of hearts with high spatial and temporal resolution. Optical recordings of voltage changes, whose shape is equivalent to intracellular microelectrode measurements, were recorded from the anterior surface of the heart. Signals were analyzed in time, frequency, and space at high spatial and temporal resolution, making it possible to track VF frequency peaks in great detail. It should be noted that signals were recorded for a long period of time (5 minutes). Data analysis was performed in 2-minute segments of VF recordings, owing to a limitation of computing power. Nevertheless, the period of analysis is markedly longer than in previous studies, in which only a few periods of the dominant frequency were analyzed.

Our time-frequency analysis found discrete bands, suggesting that VF frequencies are not fixed but change abruptly in time. It is possible that gradual changes in frequency may appear as step changes in cases with poor spectral resolutions. However, in most cases, the step changes between discrete frequency bands exceeded the frequency resolution (0.5 Hz), and the amplitude of the signals between frequency bands is negligible, such that the discrete bands are most likely due to abrupt changes in VF frequencies. The brief life span and the spatially discontinuous appearance and disappearance of VF frequency blobs suggest that VF is maintained by the seemingly chaotic creation and annihilation of periodic sources.

The general consensus is that the source of a VF frequency is a reentrant circuit or a rotor; however, the relationship between frequency and its underlying rotor has not been demonstrated rigorously. Computer simulations and mapping studies^{27–32}⇓⇓⇓⇓⇓ found complex activation patterns with wavefronts of varying amplitude and activation intervals. However, complete reentrant circuits are rarely delineated from activation maps. Previous analysis of activation patterns in an open-chest canine model of VF showed reentrant circuits with a short life span (<0.5 second per wavefront).^{33,34}⇓ This study used an array of bipolar electrodes and is in excellent agreement with our life-span measurements based on time-frequency analysis and optical measurements of electrical activity on an isolated rabbit heart. It is reasonable, therefore, to speculate that VF frequency blobs identified by frequency distribution analysis represent reentrant circuits with virtually identical life spans. However, it is possible that single VF frequency blobs are composed of several rotors with the same frequency. Alternatively, frequency blobs can be due to a complex meandering reentrant circuit. Previous studies^{5,7,23,35}⇓⇓⇓ indicated that the action potential duration (APD) and refractory period at each site influences the VF frequencies and activation intervals recorded from the same site. Hence, conditions that reduce the dispersion of APDs are expected to depress the number of VF frequency blobs because either a single dominant rotor is formed or multiple rotors in different location share the same frequency. Further studies may reveal the correlation between wave propagation patterns and VF frequencies using a combination of wave pattern and time-frequency analysis.

Theoretical studies predicted that wave breakup can be caused by spontaneous wavelength oscillations of reentry circuits.^{36,37}⇓ For instance, APDs exhibit a dynamic adaptation to rate changes and diastolic intervals (period from the recovery of the last AP to the onset of the next AP), a phenomenon called restitution kinetics. Experimental studies showed a marked correlation between the complexity of voltage oscillations in VF and the slope of the restitution curve.^{20,34,38,39}⇓⇓⇓ When the slope of the restitution curve is >1, small perturbations in the APD become amplified with successive reentrant cycles, and when the APD or wavelength is too short, conduction fails, resulting in wavebreak. The slope of the restitution curve has therefore been suggested as a major predictor of wave breakup. Of interest would be to look for a correlation between restitution and life span of VF frequencies.

In conclusion, the analysis provides new insights regarding the birth and evolution of periodic sources during VF, which are tracked in space and time. We found that VF frequencies are not anchored to certain regions on the epicardium and are not stable in time, lasting <1 second before being annihilated, suggesting that VF is maintained by multiple wavelets as a result of continuous wave breakups. The visualization of VF dynamics in space, time, and frequency domains in various pathological conditions (heart failure, ischemia, and long-QT-related arrhythmias) can provide new insights of the nature of these arrhythmias and new strategies for their interruption.

### Limitations of the Study

A small change in VF frequency, which is due to changes in several frequency sources, may appear as a single VF frequency blob in cases of poor frequency resolution, causing an overestimation of life span. Although time-frequency representation with a cone-shaped kernel provided a marked improvement of peak resolution, further improvements could be achieved with more sophisticated algorithms. In the future, increasing computer power may make it possible to calculate optimized time-frequency representations for VF in relatively brief computer times.

Optical recordings were limited to the anterior region of the epicardium. Therefore, it is possible that stable frequency sources in time and space can still exist transmurally. Further studies may reveal whether a stable frequency source can exist in different regions.

## Acknowledgments

This work was supported by grant awards from the NIH: R01 HL57929 and HL59614 to G. Salama and a postdoctoral fellowship from the Western Pennsylvania Affiliate of the American Heart Association to Drs B.-R. Choi and T. Liu.

## Footnotes

Original received June 4, 2002; revision received July 17, 2002; accepted July 22, 2002.

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- Life Span of Ventricular Fibrillation FrequenciesBum-Rak Choi, Wonchul Nho, Tong Liu and Guy SalamaCirculation Research. 2002;91:339-345, originally published August 1, 2002https://doi.org/10.1161/01.RES.0000031801.84308.F4
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