INTRODUCTION

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A DOMINANT RHYTHM IS OBSERVED in electrocardiograms (ECGs) during ventricular fibrillation (VF). Cycle periods and amplitudes of the dominant rhythm, however, vary with time. Mechanisms of VF, hypothesized by other investigators (11, 12, 28), propose that nonstationary activation within the myocardium produces cycle period changes or frequency modulation. Recently, experimental data have shown that periods of reentrant activation during VF, mapped epicardially with the use of optical techniques, correlate with the dominant frequency within ECG (18). Results of this (18) and another study (29) show that drugs that change cellular conduction and repolarization properties change the periods of reentrant activation and, therefore, dominant frequencies within ECG. A correlation between local cycle periods measured during atrial fibrillation (AF), VF, and effective refractory periods has also been observed in several studies (16, 21, 22, 30). Collectively, results of these studies suggest that assessment of changes in dominant frequencies, or their reciprocal cycle periods, as VF evolves may provide an assessment of temporal changes in the properties of cellular substrate during VF. Assessment of temporal changes in cycle periods obtained from spatially different recordings, such as from body surface or epicardium, may be used to investigate spatio-temporal variation in these properties such as spatio-temporal dispersion of refractoriness (16). The generally recognized role of spatio-temporal variation in properties of cellular conduction and refractoriness in genesis of VF is further supported by the results of two recent studies (4, 23).

Our objective in the present study was to develop an analysis technique that provides assessment of time-varying changes in dominant frequencies during VF. The technique for assessment of changes in dominant frequencies does not require an often difficult process of detection of activation times. We demonstrate the application of the technique with the use of three orthogonal body surface ECGs. The technique can be easily applied, however, to recordings from multiple sites, from either the body surface, the epicardium, or the endocardium, and used to construct spatio-temporal cycle period maps. As discussed above, experimental evidence shows that dominant frequencies contain information about important physiological processes. Time-varying assessment of dominant frequencies, obtained from different spatial locations, can therefore be used to study dynamic spatio-temporal variation in these physiological processes.

	METHODS

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Data collection. Data were collected from 19 adult mongrel dogs of either sex weighing between 24 and 31 kg. All studies were approved by the Institutional Animal Care and Use Committee at the University of Kentucky. Anesthesia was induced with the use of Pentothal Sodium (25 mg/kg iv) and maintained with isoflurane (0.5/l vol%). Animals were intubated and ventilated. Normal blood gas and electrolyte levels were maintained. A defibrillation catheter (Endotak, CPI) was placed from the right jugular vein at the right ventricular apex. Defibrillation shocks were delivered between the apical coil electrode and a 14-cm² patch electrode (L67, CPI) placed subcutaneously on the left side of the thorax over the apical impulse.

View larger version (28K): [in this window] [in a new window]   Fig. 1.   Typical electrocardiograms (ECGs) recorded during ventricular fibrillation (VF). Data shown are from 1 10-s trial in 1 dog. First 2 s of VF are not shown. Time-frequency estimates were computed from last 8 s of VF before defibrillation shock. Large change in voltage at end of VF that was due to defibrillation shock was excluded from analysis. X, Y, and Z are sagittal, transverse, and longitudinal directions, respectively.

Assessment of frequency modulation. We used the smoothed pseudo-Wigner distributions (SPWD) to estimate dominant frequencies as VF progressed. As shown by Pola et al. (27), compared with short-time Fourier transforms and parametric (autoregressive) approaches, the SPWD has excellent time resolution and good frequency resolution at the expense of having artifactual cross terms in the spectra. The ECGs recorded in dogs during VF are primarily monocomponent within a frequency region of ~5-15 Hz (1-3, 5, 6, 8, 9, 13). Therefore, problems associated with cross terms were not likely to affect the estimates of dominant frequencies, and we could take advantage of the good time and frequency localization permitted by the SPWD. The discrete SPWD is given by (17)
where k and f are the time and frequency indexes, respectively, h and w are the time and frequency smoothening windows, respectively, x is the time series and * indicates conjugate. For time and frequency smoothening we selected Blackman and Hanning windows. Time frequencies were estimated at 40-ms intervals [k = 0.04 s]. The frequency F(k) of the maximum of the SPWD surface within limits f_low (f_l), f_high (f_h) was used to estimate instantaneous dominant frequency: F(k) = f_m, where f_m is such that
This time-frequency analysis can be illustrated with a simulated signal. Figure 2A shows a frequency-modulated signal x(t) that was created with a 9-Hz sinusoid as carrier, modulated by a 0.8-Hz sinusoid: x(t) = a(t)cos(29t + sin2 0.8t). Such signal may be produced, for example, by a rotating spiral with a circular core movement, as in the simulation results in previous studies (11, 28). The carrier frequency was selected as 9 Hz so as to be similar to the average dominant frequency during VF in some dogs, and the modulating frequency was selected to be 0.8 Hz, which gave a velocity ratio between the two frequencies (analogous to the ratio between spiral rotation and the core velocity) to be comparable with those reported by Gray et al. (11, 12). The scaling factor  was selected to produce a maximum (max) change in frequency of 1.5 Hz. A sinusoidal amplitude modulation function a(t) was used to change the amplitude of the frequency-modulated signal, as changes in amplitude in ECGs are also observed during VF. Figure 2A shows the changes in cycle periods and amplitudes in 5 s of simulated signal, x(t). Figure 2, B and C, shows the time-frequency surface estimated by the SPWD and the contour plot of the time-frequency surface. The estimated dominant frequency, F(k) (thick line going through the contours in Fig. 2C), shows that, as expected, the instantaneous frequency within series x(t) oscillated between 10.5 and 7.5 Hz, around a mean of 9 Hz.

View larger version (38K): [in this window] [in a new window]   Fig. 2.   An example of the use of smoothed pseudo-Wigner distributions (SPWD) for tracking of dominant frequency. A: simulated time series with both frequency and amplitude modulation. B: time-frequency surface from estimated SPWD shows curving and undulations due to frequency and amplitude modulation. By localization of maximum of time-frequency surface, dominant frequency can be tracked, as shown by solid line overlaid on contour plots of time-frequency surface (C).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

A sample of ECG recorded during a 10-s trial in one dog (Fig. 3A) shows that during the last 8 s of VF, the amplitudes and cycle periods change considerably as VF evolves. The time-frequency surface and the contour plots computed from this ECG (Fig. 3, B and C) show how the SPWD can be used to track changes in dominant frequency. The dominant frequency is shown as a thick solid line overlaid on the contours in Fig. 3C. To show changes in dominant frequency in detail without the presence of other contours, the dominant frequencies are plotted in Fig. 3D. Figure 3D shows that in this trial of VF, the dominant frequency changed from 7 to ~11 Hz, around a mean value of ~9 Hz. A gradual trend toward increasing mean frequency is also evident in Fig. 3D.

View larger version (36K): [in this window] [in a new window]   Fig. 3.   A: 8 s of ECGs recorded in direction X during 1 trial in a dog. SPWD surface (B) and contours (C) show amplitude and frequency changes similar to those seen in Fig. 2. Dominant frequency during VF is very nonstationary and changes from as low as 7 to as high as 10.5 Hz (D).

Figure 4A shows the average maximum, minimum, and mean dominant frequencies from 10 dogs within one ECG (X) recorded during 10-s VF trials. The maximum, minimum, and mean frequencies from all trials within each animal were averaged to obtain one estimate of maximum, minimum, and mean frequencies per animal. Variability in these frequencies within each animal are shown in Fig. 4A as the standard deviation plotted on the top of the average maximum, mean, and minimum frequencies for each animal. Figure 4A shows that during 10 s of VF, the difference between slow and fast periods was as large as 40-50% (for example, in a dog, a change from a minimum of 7 to a maximum of 10.5 Hz). The standard deviations in Fig. 4A also show that although the mean frequencies during multiple trials within each animal were fairly similar (small standard deviations in the middle, note different scale), there was considerable variation in maximum and minimum dominant frequencies during VF (top and bottom panels). Figure 4B shows the average change in dominant frequencies expressed as percent change from mean dominant frequency for 10 dogs. Two standard deviations of the dominant frequency estimates F(k) (computed over the entire 8 s) were averaged within each animal to obtain an estimate of average variation in frequencies. Figure 4B shows that for the 10 dogs, average change in dominant frequency was considerable, between ±12 and 18%. Similar changes in dominant frequencies were observed for the other two ECGs and also during 30 s of VF. To determine how the frequencies were distributed above and below the mean frequency, we estimated probability distribution functions with the use of smoothed histograms. Shown in Fig. 5 are the average probability distributions for all three ECGs from one dog during 10-s VF trials. Figure 5 shows that the frequencies were distributed symmetrically above and below the mean frequency in a shape almost like a normal distribution.

View larger version (26K): [in this window] [in a new window]   Fig. 4.   A: maximum (max), mean, and minimum (min) dominant frequencies in ECG (X) during 10 s of VF in 10 animals. All trials within each animal were averaged to obtain 1 estimate of maximum, minimum, and mean frequencies per animal. Variation in maximum, mean, and minimum frequencies within each animal is shown as 1 standard deviation bar plotted on top of maximum, mean, and minimum average frequencies. B: for 10 animals, average change (in time) in dominant frequency expressed as percent change from mean dominant frequency. Standard deviation of each estimate of dominant frequency during each 8-s trial of VF was computed. Changes in dominant frequencies were quantified as 2 standard deviations of dominant frequency estimates for each trial and were averaged within each animal. Similar changes were observed for other 2 ECGs.

View larger version (10K): [in this window] [in a new window]   Fig. 5.   Probability distribution of dominant frequencies within 3 ECGs (X, solid line; Y, dashed line; and Z, dotted line) during 10 s of VF in 1 dog. Distribution shows that likelihood of frequencies being higher and lower than mean frequency was similar. Distributions also show that in time-averaged sense (these distributions do not contain information regarding temporal location), variation in frequencies in 3 ECGs was similar.

Although the frequency distribution was similar for all three ECGs, within any time interval during a VF episode, the dominant frequencies within the three spatially different ECGs were not always similar. We quantified the differences in dominant frequencies between the ECGs as the square root of the squares of the differences between frequencies from different ECGs, i.e., for ECGs X and Y
Figure 6A shows the difference_XY(k) during one 10-s VF trial in one dog. Figure 6A shows that during the last 8 s of VF, frequencies recorded in ECGs X and Y were sometimes similar to each other (small difference), whereas at other times the frequencies within these ECGs were quite different from each other. Figure 6B shows the average and standard deviation of the differences in dominant frequencies in 10 dogs during 8 s of VF among the three ECGs (X-Y, X-Z, and Y-Z). The absolute differences in frequencies during 8 s of VF were averaged in time for each trial to obtain one estimate of difference between the frequencies. Shown in Fig. 6B are the average and the standard deviation of the time-averaged differences in frequencies in each animal. We observed that the differences in frequencies between the ECGs were similar during the entire VF duration, i.e., we did not see a pattern that showed small (or large) differences in frequencies between ECGs early in VF and large (or small) differences late in VF. Because the differences were uniformly distributed in time during VF, we averaged the absolute differences over time to obtain one estimate of difference in the frequencies in a pair of ECGs per trial. Results in Fig. 6B show that the dominant frequencies estimated from spatially different (in our case 3 orthogonal body surface) ECGs can be substantially different. Similar results were observed in the nine dogs during 30 s of VF.

View larger version (20K): [in this window] [in a new window]   Fig. 6.   A: absolute value of differences between dominant frequencies within a pair of ECGs (X and Y) in 1 dog during 1 10-s VF trial. These differences show that at many time instances, for example at ~4.1 s after onset of VF (i.e., 2-s transition period + 2.1-s location in plot), frequencies registered in ECGs X and Y were different by ~1.5 Hz. There were also many instances during which ECGs recorded similar frequencies. B: differences between dominant frequencies within pairs of ECGs (X-Y, X-Z, and Y-Z) in 10 dogs. Absolute differences between frequencies within each trial were averaged over time to obtain 1 value of differences in frequencies per trial. Shown are the average of these differences within each animal. Variation within each animal in differences is shown as 1 standard deviation plotted as a bar on top of average value bars. Frequencies registered in different ECGs could be considerably different from each other.

Figure 7 shows the average dominant frequencies during 30 s of VF from nine animals. Figure 7A shows the dominant frequencies in three ECGs during the last 28 s of the 30-s VF trials. In Fig. 7B, corresponding to panels in Fig. 7A, are shown probability of error values (i.e., the P value) for comparisons between instantaneous frequencies and the "time-averaged initial frequency" from the first 8 s of VF. Dominant frequencies for the first 8 s were averaged to obtain one initial frequency in each of the 335 trials; subsequent estimates of frequency F(k) at each time step k in each trial were compared with the initial frequency with the use of one-way analysis of variance. Figure 7B shows that after ~11 s from onset of VF, the increase in frequencies seen in Fig. 7A was significant (P < 0.05). A regression analysis on these frequencies showed average slopes (and standard deviations) to be 0.021 (0.014), 0.022 (0.016), and 0.021 (0.016) Hz/s and the r² values (all significant at P < 0.0005) to be 0.92, 0.93, and 0.93 for the three ECGs.

View larger version (15K): [in this window] [in a new window]   Fig. 7.   Average dominant frequencies (from 9 dogs) in 3 ECGs during last 28 s of 30-s VF trials are shown in A. Dominant frequency estimates for first 8 s were averaged in time to obtain 1 initial frequency estimate per trial; each subsequent (in time) frequency estimate from individual trials was compared with initial frequency by use of a 1-way analysis of variance. P values corresponding to each of these comparisons are plotted in B (each below its respective plot in A). Frequencies increased during 28 s of VF in an almost linear fashion; increase was significant from as early as 11 s into VF (2-s transient + 9-s location in plots). Regression analysis on frequencies showed slopes of 0.021, 0.022, and 0.021 Hz/s with R2 values of 0.92, 0.93, and 0.93, respectively (all significant at P < 0.0005).

To validate the observed increase in frequencies during 30 s of VF, calculated by the use of nonstationary SPWD analysis in our study, we computed frequencies from these ECGs by using Fourier analysis (6, 8, 9, 30). We computed the dominant frequencies from blocks of 4 s of ECGs with the use of the Fourier transform, a stationary analysis technique used previously by others (6, 8, 9, 30). We computed dominant frequencies starting at 2, 10, and 26 s from the onset of VF. Comparison of frequencies, in three ECGs in all trials, computed at 10 and 26 s with those computed from the initial VF (starting at 2 s) showed a significant increase from 2 to 10 and 26 s (P < 0.02 and < 0.001). The magnitude of increases in frequencies at these two times were consistent with those shown in Fig. 7.

We explored whether the distribution of frequencies (above and below the mean) changed with increasing duration of VF. First, we subtracted the linear trend, estimated with the use of a linear regression, from frequencies estimated from each trial. After removing the trend, we estimated probability distribution with the use of smoothed histograms from the first and the last 14 s of VF. Figure 8 shows the average probability distributions of frequencies in the three ECGs in one dog. Because the nonstationary mean frequency was removed before estimation of the distributions, the distributions in Fig. 8 are centered at 0 Hz. Figure 8 shows that during the last part of the 30-s VF trial (dashed curves), the variation in frequencies above and below the mean frequency was very similar qualitatively and quantitatively with that observed during the first part of VF (solid curves).

View larger version (11K): [in this window] [in a new window]   Fig. 8.   Probability distribution estimates from early (solid lines) and late (dashed lines) VF in 1 dog. Estimates for 3 ECGs were obtained from dominant frequencies estimated from early, or first 14 s of, VF (after 2-s transition period) and late, or last 14 s of, VF. Linear trends were removed from frequency (freq) estimates from each trial to eliminate effects of nonstationary means. After removal of a linear increase in mean frequency, these plots show that variation in frequencies was symmetrical and unchanged between early and late VF. These results also show that in time-averaged sense, variation in frequencies among 3 ECGs was similar.

To verify that expected alteration in cellular repolarization properties related changes in cycle periods can be estimated by using our technique, we compared dominant frequencies between VF trials before and after administration of amiodarone in four dogs. Results of 79 trials in these animals showed that during 10 s of VF, in all three ECGs, the dominant frequencies decreased from means of 6.5, 7.4, and 7.0 to 6.1, 6.4, and 6.3 Hz, respectively, after amiodarone (P < 0.005). Furthermore, the variations in dominant frequencies (i.e., 2 times the standard deviation) also decreased from 1.18, 1.38, and 1.19 to 0.98, 1.11, and 1.02 Hz, respectively. All differences were significant at a level of P < 0.02.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Time-frequency analysis has been used previously by other investigators (1, 2) to assess changes in the dominant frequency during VF. In these studies, assessment of dominant frequencies was made over a longer time scale relative to our study and with time resolution in tens of seconds or more. The focus of these earlier studies was on characterization of changes in dominant frequencies as a function of prolonged duration of VF (300 s or more) to predict duration of VF (1, 2) or to study effects of ischemia or anti-arrhythmic drugs on average dominant rhythm (8, 9). Assessment of dominant frequencies with the use of time-frequency analysis over shorter time scales of 10-30 s, with the finer time resolution that we used (40 ms), has not been previously reported. Investigation of the dynamics of activation pattern and cellular properties over time scales of 10-30 s may be particularly important because of the expected increase in the use of implantable defibrillators that typically deliver therapy within this time window. In addition, as evidence from several recent studies indicates, dynamic or time-varying assessment of cycle periods or dominant frequencies during VF may be useful to study the organization of VF in terms of spatio-temporal changes in activation and excitable gap and spatial and temporal variation in cellular properties such as effective refractory periods.

Results of a recent study (18) show that the period of rotation of reentrant activation, mapped with the use of optical measurement of transmembrane voltage, correlates with the dominant frequency within the surface ECG. Results of several studies (21, 22, 30) showed that local cycle periods during VF and AF correlate with effective refractory periods. The changes in frequencies that we estimated can be grouped into those that occur over a short time (of order of 500-1,000 ms) and those that occur over a long time (over 10 s). We observed that over the long time, the dominant frequencies increased or cycle periods decreased, whereas for short time, there was considerable local variation above and below the mean frequencies. We believe, as discussed in detail below, that the long-term changes in frequencies may reflect changes in cellular repolarization properties. Although it is possible that cellular conduction and repolarization properties may change dynamically to affect short-term variation in frequencies also, a more likely cause for the short-term variation may be activation patterns. The symmetrical variation in dominant frequencies above and below the mean, as shown in Figs. 5 and 8, supports the above possibility and also explains the two apparently contradictory observations from previous studies by others: that the effective refractory period correlates with AF and VF cycle length, which would suggest that there is no excitable gap or a constant fixed excitable gap during AF and VF (14, 21, 22), and evidence of an excitable gap (15, 23). Some investigators observed a presence of diastolic potential and thus an excitable gap during VF (7, 23), whereas others observed no diastolic potential during VF (14, 22). Our results suggest that the average (in time) dominant frequency period may correlate (but not necessarily be equal) with the effective refractory period, and short-time changes in frequencies may result because cells within a specific site are stimulated as soon as they are repolarized (no excitable gap present at that site at that time resulting in higher-than-mean dominant frequency, with cycle periods equal to refractory periods; Ref. 16) or are stimulated at intervals longer than their refractory periods (excitable gap present at that site at that time, which would lead to lower-than-mean dominant frequencies). Our results are based on measurements of ECG that are global in a spatial sense; however, the electrical activity recorded at each electrode site can be approximated as the sum of contribution from all myocardial cells, each weighted inversely by the distance of the cell from the electrode. Therefore, changes in frequencies that we observed would be influenced by the integrated effect of activity within a relatively large group of cells.

Results of a study by Mandapati et al. (18) and of previous studies by others (7, 12, 28, 29) have suggested that multiple rotors may coexist within different regions of the heart, and nonstationarity of these rotors may lead to polymorphism in VF. Mandapati et al. (18) discussed the possibility that, because there was a strong correlation between periods of single rotors, mapped within a local region, and dominant frequency within global ECG, multiple spiral waves or rotors will have a narrow range of rotation periods. Our results provide further information regarding this issue. Figure 6 shows that at any time instant, the ECGs recorded from different spatial locations often register different frequencies. Although these data do not provide information regarding existence of multiple rotors or their synchronicity, they do suggest that considerable spatial heterogeneity exists during VF. It is possible that distinct activations within different regions have different rotation periods because of differences in either core size, shape, or conduction velocity. Activations may drift from one region to another or activation pattern within a region may change; these changes would produce temporal variation in the differences in the frequencies between ECGs, i.e., sometimes the frequencies within different ECGs will be similar, and at other times they will be different. Under such conditions, similarity of frequencies between spatially different ECGs, within a given time window, would indicate uniform activation pattern or properties of cellular substrate during that time. We have previously shown that similarity of frequencies within the X and Y ECGs from the 10-s VF trials was correlated with successful defibrillation shock outcome (24). Although we observed short time differences in frequencies between spatially different ECGs, frequencies averaged in time were similar for all three ECGs. The similarity of time-averaged frequencies among the ECGs provides an explanation for the observations of Chorro et al. (8), who reported no differences in frequencies estimated from different electrodes. They (8) used a block of 2.4 s of VF to estimate frequencies, which would be analogous to an averaging in time of our data. To assess whether the frequencies registered within different ECGs were just phase shifted relative to each other, we calculated cross correlations between the dominant frequencies in the X-Y, X-Z, and Y-Z ECG pairs. The cross correlations (which compare 2 signals for similarity at different relative time shifts between them) did not show any consistent peaks, which indicated that the dominant frequencies among the three ECGs were indeed different temporally, not just shifted in time. A delay or time shift in dominant frequencies among ECGs could result from a single, large, nonstationary (in cycle length) activation drifting from one region of the heart to another; our results are not consistent with the existence of such a single large-drifting activation pattern.

Results of trials with amiodarone confirmed that alteration in cellular repolarization (although acute administration of amiodarone has other cellular effects as well; Ref. 9) is reflected in changes in dominant frequencies. We observed that amiodarone decreased dominant frequency, likely a result of prolongation of refractory period. These results are consistent with those of Chorro et al. (9), who also observed a decrease in dominant frequencies after amiodarone. The advantage of using time-frequency analysis was that it permitted us to observe that amiodarone also decreased temporal or short-term variation in dominant frequencies, which could not be observed in earlier studies. This decrease in temporal variation in dominant frequencies may contribute to or reflect the mechanisms that result in anti-arrhythmic qualities of this drug.

We observed that the mean dominant frequencies increased linearly during the first 30 s of VF. It is generally known that during minutes after induction of VF (1 min and longer), the dominant frequencies in ECGs decrease (1, 2, 8, 9, 19). Investigation of dominant frequencies during early VF (<1 min after induction) has also been reported by others (2, 5, 8-10); however, except for the study in humans by Clayton et al. (10) and the study in dogs by Martin et al. (19), in the other studies either an increase was not observed or the observed increase was not statistically significant. The analysis techniques employed earlier included estimation of frequencies from blocks of data, thereby resulting in a loss of the temporal aspect of changes in frequencies. For example, Martin et al. used 13-s blocks of data to estimate frequencies; they observed a significant increase in dominant frequencies in the 26- to 39-s block compared with initial frequencies. Relative to the earlier studies, use of time-frequency analysis permitted us to estimate frequencies with a substantially increased time resolution.

Our results in Fig. 7 show a highly significant and almost linear increase in dominant frequencies during the first 30 s of VF in all three ECGs. Although the exact mechanisms for this increase are unclear, one possibility is that the effective refractory period restitution property of myocardial cells may have contributed to this acceleration. It has been shown previously and in a recent study (4) that, up to a limit, the effective refractory periods decrease as the previous pacing cycle lengths are decreased. It has also been shown by several recent studies (21, 22, 30) that the effective refractory periods in both atrial and ventricular myocardium, estimated with the use of extrastimulus technique, correlate with cycle lengths during AF and VF. It is possible, therefore, that although there may be short time variation in activation intervals, over a longer time, subsequent reentrant activations arrive at specific sites at shorter and shorter intervals on average, the faster activation being facilitated by restitution of effective refractory periods. That is, if the shortening of the refractory periods due to faster activations occurred at a faster rate than the lengthening due to slower activations, then the observed acceleration of VF is possible until a point in time when the slowing effects due to ischemia predominate and cycle periods start to increase. It is also possible, as discussed previously by other investigators (8), that factors such as sympathetic activation, because of loss of blood pressure, may also have contributed to the observed acceleration during VF.

The distribution of frequencies was similar between early and late (first and last 14 s of, respectively) VF. These results suggest that the dominant frequencies were equally likely to be higher or lower than the mean frequency, with similar probability either early or late in VF. After the effects of acceleration due to the hypothesized asymmetrical restitution of refractoriness were factored out, the magnitude of change in frequencies from the mean was similar during the 30 s of VF. The similarity of the distributions in Fig. 8, therefore, suggests that the pattern of activation of VF remains stable during 30 s of VF.

In summary, our results show that during VF 1) frequencies within ECGs change substantially and continuously; 2) during the first 30 s, mean frequencies increase linearly; 3) variability in frequency does not change during 30 s of VF; and 4) at any given time, the frequencies within spatially different body surface ECGs can be markedly different.

There are potential applications for our findings. The results of our study and those of others discussed earlier suggest that time-varying assessment of dominant frequencies during VF from multiple recordings, such as those obtained during body surface, epicardial, or endocardial mapping, may be used to study spatio-temporal variation in conduction and repolarization properties. The time-frequency technique used in our study does not require identification of activation times and may be used to construct cycle-period spatio-temporal maps to study spatio-temporal variation in refractory periods over the entire heart. Such spatio-temporal variation in cellular properties is hypothesized to play an important role in genesis of VF (4).