IV. SINGLE CHANNEL ANALYSIS

1 Introduction

fig 4.1: Autopowerspectrum of intramural electrogram during VF in a healthy dog with artificial respiration and coronary perfusion. Sampling freq. 800 Hz, filter freq. 200 Hz.

fig. 4.2: example of VF recording after AD conversion from an intra mural needle electrode

1. in the time domain by calculation of the amplitude histogram in order to check the stationarity and the type of the probability distribution of the amplitudes of the signal;
2. in the frequency domain by Fourier transformation of 20 consecutive blocks of 2 sec's each and estimating from the ensemble averages the autopower spectra, the autocorrelation function and the auto bicoherency spectra.

Although in general all possible care was taken to keep the heart in a good condition, in some cases deliberate changes were made by suddenly changing the mean systemic pressure or by resetting the automatic pump control from constant flow mode to constant systemic pressure mode or to the mode of constant oxygenator weight. These changes in the pumping mode did not really effect the classification of the signals.

No difference has been found between types of electrodes or leads with respect to the classification. The unipolar leads however seem more suitable for an understanding of the results of signal analysis during ventricular fibrillation than the bipolar ones, see the previous chapter. For a meaningful analysis of signals these should be stationary and although Oppenheim and Schafer (1975) state: "In practice, it is common to assume that a given sequence is a sample sequence of an ergodic random process", attempts have been made to check the assumptions of stationarity and ergodicity; the results are reported in the paragraphs upon histograms, autocorrelation function and auto power spectra. In total 888 signals were analyzed. A summary of this chapter has been published already (Herbschleb 1979).

2 Amplitude histograms

2.1 results

type	figure	percentage
unimodal symmetric		40%
	fig.4.3: normal amplitude distribution during VF (ch. 5 of fig. 4.19) power spectrum in fig. 4.26
	fig.4.4: symmetrical, not normal amplitude distribution during VF (ch. 2 of fig. 4.19)
unimodal skewed		40%
	fig.4.5: asymmetrical amplitude distribution during VF (ch. 6 of fig. 4.19) power spectrum in fig. 4.12
multimodal or uniform		11%
	fig.4.6: uniform or rectangular amplitude distribution during VF (intramural needle electrode)
two-peaked		9%
	fig.4.7: 2-peaked amplitude distribution during VF from intramural needle electrode

2.2 discussion

All 888 histograms have been classified without reference to other information like spectra, histograms of neighbouring electrodes or previous histograms of the same electrode. The numbers in table 4.1 may be considered an indication of consistent histogram classification.

Maybe the whole classification is lacking any significance, as will be explained in chapter VI.

The procedure of recording the signals upon analog tape and replaying them on different recorders for analog-digital conversion has introduced some DC offset, so the mean of the histograms will differ somewhat from zero.

3 Autocorrelation function

3.1 results

The next table indicates the distribution of the estimated autocorrelations after 2 seconds over 4 classes:

classification of autocorrelation functions

r after 2 s	number	perc.	examples	references
r = 0	472	53
			fig. 4.8: ECG II in a dog during VF with artificial coronary perfusion An example of a completely damped function.
0< r <=0.75	325	37		amplitude histogram in fig. 4.5 power spectrum in fig. 4.12
			fig.4.9: bipolar epicardial electrogram channel 6 of fig. 4.19 incompletely damped: r=0.71 after 2 s
0.75< r <=0.9	45	5		amplitude histogram in fig. 4.6
			fig.4.10: unipolar electrogram from an intramural needle electrode incompletely damped; r=0.79 after 2 s
r >0.9	46	5
			fig.4.11: unipolar electrogram from an intramural electrode during VF undamped function (r=0.94 after 2 s) note typical asymmetry

3.2 discussion

Three remarks should be made about the appearance of the estimated autocorrelation function.

1. the clear periodicity in the autocorrelation function corresponds to the first peak in the auto spectrum. Compare fig. 4.9 with fig. 4.12. This periodicity has already been noted by Angelakos and Shepherd in 1957. (Angelakos 1957) In contrast Aubert et al (Aubert 1982) conclude that the ECG during ventricular fibrillation is from a mathematical point of view random, because their autocorrelation function discloses no periodicity. These authors , however, did not analyze purely ventricular fibrillation, but the transition from tachycardia to fibrillation, so their conclusion about the character of ventricular fibrillation is ill-based.
2. the autocorrelation function is considered as damped, if the function remains between the indicated 95% confidence lines. The fact that the function still shows a periodic component, is caused by the strong correlations between the autocovariances of a series with moderately strong correlations between the elements of that series (Jenkins and Watts, 1968 p. 185).
3. the clear asymmetry in the plotted autocorrelation function - the positive values are higher than the absolute values of the negative r's - especially in the undamped functions, is explained by the fact that in most cases the autocorrelation function can be thought of as the sum of three cosines:

     r(t')=F(t')·(A·cos(f·t')+B·cos(2f·t')+C·cos(3f·t'))
   
     where A+B+C=1; A,B,C>0
   
     F(0)=1; F(t') monotone not-increasing
   

   for the autocorrelation function and the autospectrum form a Fourier transform pair and the auto spectrum contains in these cases mostly two higher harmonics of the basic fibrillation frequency (see the following paragraphs). The above equation can be rewritten as:

    r(t')=F(t')·((A-3C)·cos(f·t')+2B·cos2(f·t')+4C·cos3(f·t')-B)

   This function reaches its maximum at cos(f·t')=1: rmax=F(t')·(A+B+C); the minimum is reached at cos(f·t')=-1: rmin=F(t')·(-A+B-C). In the case that F(t') does not decrease too quickly a maximum is always higher than the absolute value of the neigbouring minima.

4 Autopower spectra

4.1 results

Characteristic for ventricular fibrillation is a high, relatively narrow peak around 12 Hz (range: 9-13 Hz) in the dog and around 6 Hz in man, followed by peaks at frequencies two, three, four etc times higher than the first one. Mostly three clear peaks were seen.

fig.4.12: sharp, equidistant peaks from bipolar epicardial electrogram during VF
peaks at 11.5, 23.5 & 35 Hz

channel 6 in fig. 4.19 correlation in fig. 4.9 histogram in fig. 4.5 zoomed spectrum in fig. 4.31

In about 25% of all signals analyzed low peaks were seen at the half frequencies in between the high peaks. In chapter VI the possible significance of these peaks will be discussed. Only 35 cases (4%) have been found with just one narrow peak in the auto spectrum.

fig. 4.13: bipolar epicardial electrogram during VF
1 peak at 11 Hz

In only 14 cases (2%) autopower spectra have been found without narrow peaks, but with a broad peak like e.g. low-pass filtered white noise.

4.2 discussion

The auto spectrum of an electro(cardio)gram during ventricular fibrillation differs from such a spectrum during other rhythms in having most of the power concentrated in a few more or less equidistant peaks, see: Nygårds 1977, Hulting 1979, Martín 1981, Forster 1982, Cosín 1982 and Herbschleb 1980a. The spectra published by Nygårds & Hulting (1977) and Hulting (1979) of ventricular fibrillation in patients agree in general with the most common type of spectrum in this study. These authors diagnose ventricular fibrillation if the spectrum contains above 4 Hz a frequency peak with 85% of all power. The spectra published by Martín et al (1981), Forster and Weaver (1982) and Cosín et al (1982) do mostly show just one peak, as they use a linear vertical scale. None of these authors applied ensemble averaging, so the variability in their spectra is much higher than the variability in the spectra used for this study.

Contrary to accepted views (e.g. Scher 1976 or Zipes 1975) on the random nature of the ECG during ventricular fibrillation, the spectra mentioned above indicate a very high regularity. In chapter VI, par. 5 a method to estimate the degree of regularity will be given.

The following authors seem to support the hypothesis of randomness of ventricular fibrillation by their experimental results. Agizim et al. (1976) published a spectrum of the ECG during ventricular fibrillation in a dog looking like the spectrum of white noise; no explanation could be found for this controversy. (Agizim 1976). Tabak et al (1980) analyzed the spectrum of the ECG during ventricular fibrillation in dogs without coronary perfusion. In the first stadium they saw a peak at 12 Hz and as they estimated the spectra up to 25 Hz, no higher harmonics could be found. In later stadia they saw 2 peaks at 4.5 and 9 Hz, but as the hearts of their animals must have been already greatly anoxic, these results cannot be compared with the spectra described in this chapter. (Tabak 1980).

Nolle et al. (1980) estimated the power spectrum of the ECG during ventricular fibrillation in patients of episodes with a duration of maximal 4.096 seconds (1024 samples). When there were not enough data, the samples were augmented with zero's; a very questionable procedure, see appendix A. Moreover, no averaging or smoothing had been performed, so their results in ventricular fibrillation/tachycardia (sic) do not look very useful. (Nolle 1980). The ill-based conclusion of Aubert et al (1982) about the random character of the ECG during ventricular fibrillation has already been dealt with in the preceding paragraph.

Most of these results seem to indicate a very rapid, repetitive phenomenon during ventricular fibrillation, viz. 12 Hz or 720 "beats" per minute in dogs and 6 Hz or 360 "beats" per minute in men. These frequencies are much higher than can be reached by a beating heart, (in chapter 6, par. 3 an explanation will be attempted) but are in accordance with the emphasis in the older literature put upon the high, rather regular, repetititon rate of "beats" during ventricular fibrillation. In 1850 Hoffa & Ludwig mention 84 "heartbeats" in 8.34 seconds (10.1 Hz) in fibrillating rabbit hearts. Hoffa 1850. McWilliam (1887), Rothberger & Winterberg (1914,1916) and Kisch (1921) also drew attention to this high repetititon rate (McWilliam 1887, Rothberger 1914, Rothberger 1916 and Kisch 1921).

In order to get an idea of the stability of the heart during ventricular fibrillation the mean fibrillation frequency in long lasting experiments has been plotted in the next figure.

fig. 4.14: bipolar epicardial electrogram during VF
a spectrum without a clear, narrow peak

fig. 4.15: mean peak frequency during VF in 5 dogs
hor. axis in minutes after start of VF

No trends in fibrillation frequency have been found in these experiments, although prominent shifts have been found in several experiments described in chapter XI.
The various mean systemic blood pressures do not affect the fibrillation frequency, see the next figure.

fig. 4.16: mean peak frequency during VF in 2 dogs versus mean systemic blood pressure
arrows indicate flow of time

line color and type correspond to those in fig. 4.15

5 Auto bicoherency spectrum

Only those equidistant peaks in the auto power spectrum were considered as true harmonics of each other if their autobicoherency rose above a confidence level of 0.999 for white noise. Of the 888 analyzed electro(cardio)grams 839 showed narrow, equidistant peaks in their power spectrum, see the previous paragraph. Of these 839 signals 251 or 30% did not show any autobicoherency above the significance level. The peaks in the spectrum of the remaining 588 signals were true harmonics of each other. In the separate bicoherency page examples are given of autobicoherency spectra, where only the values above the significance level of 0.5687 have been plotted (see also appendix D).

Figure 4.17 shows that, albeit low, there is a coherency between 11.5, 12 and 23.5 Hz and between 11.5, 23,5 and 35 Hz, which means that the peaks in the power spectrum fig. 4.25 of 11.5, 23.5 and 35 Hz are harmonics of each other. In fig. 4.18 an example is given of high autobicoherencies. The peaks in the power spectrum fig. 4.12 of 23.5, 35 and 47 Hz are clearly higher harmonics of 11.5 Hz.

As could be expected, the majority of the signals without significant autobicoherencies are in the class of symmetric histograms with a damped autocorrelation function. In paragraph 8 a summary of the results of the paragraphs 2, 3, 4 and 5 is given in the form of a table.

6 Diversity of signals from one fibrillating heart

fig. 4.19: detail of fig. 3.3 shows place of epicardial electrodes and channel nr in experiment 24056

electrode in fig. 3.2 analysis of experiment in tabular form

The bewildering diversity can be studied through the following table.

table 4.4: diversity of signals from one small area of a fibrillating dog heart.

type of analysis	channels
	2	4	5	6	ECG
TV-raster plot			fig. 3.5	fig. 3.6	fig. 3.7
amplitude histogram	fig. 4.4	fig. 4.20	fig. 4.3	fig. 4.5	fig. 4.21
auto power spectrum		fig. 4.25	fig. 4.26	fig. 4.12	fig. 4.27
auto correlation		fig. 4.22	fig. 4.23	fig. 4.9	fig. 4.24
auto bicoherency		fig. 4.17	fig. 4.29	fig. 4.18	fig. 4.28
zoom FT			fig. 4.31	fig. 4.31	fig. 4.31
signal plot			fig. 4.30	fig. 4.30	fig. 4.30

The histograms of channels 4, 5, 6 and 7 (ECG) show respectively a symmetric (but not Normal), a Normal, and two asymmetrical amplitude distributions simultaneously. The autocorrelation function of channels 4 and 5 is damped after 1000 resp. 1750 ms. the autocorrelation of channel 6 reaches a value of 0.71 after 2 sec's and that of channel 7 is almost damped (0.21) after 2 sec's. Even the basic fibrillation frequency is not the same in this small area. The spectrum of channel 4 consists of peaks at the frequencies 11.5, 23.5, 35 Hz (like channel 6) and - less clearly - at the frequencies 6, 17.5 and 29 Hz. The spectrum of channel 5 however shows a clear peak at a frequency of 10.5 Hz and much less pronounced a peak at 20.5 Hz. In the ECG (channel 7) both frequencies seem present, although the size of the 95% confidence interval as plotted in the right upper corner precludes such a conclusion. The next paragraph will show that this ECG can be considered as the electrical summation of signals with a basic frequency of 10.5 and 11.5 Hz. The bicoherencies indicate that the frequencies of 23.5 and 20.5 Hz are really higher harmonics of the basic frequencies. The conclusion is that different "types" of fibrillation are simultaneously present in one fibrillating heart and that these types are independent of the electrodes used.

fig.4.20: symmetric, but not normal histogram of bipolar epicardial electrogram (ch. 4 of fig.4.19)

power spectrum infig4.25

fig.4.21: asymmetrical histogram of ECG lead II during VF (see fig. 4.19 for related signals)

power spectrum in fig. 4.27

fig.4.22: damped autocorrelation function of channel 4 of fig. 4.19

amplitude histogram in fig4.20 power spectrum in fig. 4.25

fig.4.23: damped autocorrelation function;
bipolar epicardial electrode, channel 5 of fig. 4.19

amplitude histogram in fig4.3 power spectrum in fig. 4.26

fig. 4.24: ECG II during VF; for other signals see fig. 4.19

730 ms corresponds to 1.37 Hz, see fig4.31 amplitude histogram in fig. 4.21 power spectrum in fig. 4.27

fig. 4.25: epicardial bipolar electrogram channel 4 of fig. 4.19
peaks at 6, 11.5, 17.5, 23.5, 29 & 35 Hz

correlation in fig. 4.22 histogram in fig. 4.20

fig.4.26: bipolar epicardial electrode channel 5 in fig. 4.19
peaks at 10.5 & 20.5 Hz

correlation in fig. 4.23 histogram in fig. 4.3 zoomed in fig. 4.31

fig. 4.27: ECG lead II during VF; see fig. 4.19 for other channels
peaks at 10.5, 11.5, 20.5 & 23.5 Hz

correlation in fig. 4.24 histogram in fig. 4.21 zoomed spectrum in fig. 4.31

7 Amplitude pulsation

fig. 4.30: regular amplitude modulation of 730 ms (=1.37 Hz)

see channel numbers in fig. 4.19 zoomed spectrum in fig. 4.31

In fig. 4.30 a part is plotted of the signals from the channels 5, 6 and 7 discussed in the preceding paragraph. The pulsation interval of 0.73 seconds has been indicated in this figure. The autospectrum of the ECG fig. 4.27 did not justify the conclusion of two separate peaks, so a higher resolution of the frequency band of 6 - 14 Hz was necessary. This higher resolution has been reached by a technic known as "ZoomFFT" (see appendix F) and the result is shown in fig. 4.31 for all 3 channels mentioned.

fig. 4.31: combined "zoomed" spectra of ECG II and
2 epicardial electrograms (ch. 5 & 6 of fig. 4.19
peaks at 10.24 & 11.61 Hz; 1.37 Hz difference

Very clearly the ECG can be considered as the sum of two signals with frequencies of 10.24 and 11.61 Hz; the difference of 1.37 Hz leads to a pulsation interval of 0.73 sec's. The much more irregular amplitude variations of channels 5 and 6 could be caused by a mixture of amplitude- and frequency modulation, see chapter VIII and appendix E. This pulsation caused by summation of signals with slightly different frequencies has also been demonstrated in other experiments.

8 General discussion and conclusion

This controversy can be solved by another assumption. In paragraph 4 of this chapter the fact has already been mentioned that in 25% of all spectra subharmonic peaks were seen, which can arise if the measured phenomena alternate in shape and/or size. Maybe the repetition rate of individual cells is lower than the overall rate measured by extracellular electrodes. In order to get some insight in this possibility, model studies have been performed. See the next chapter for the models and chapter 6 for a re-evaluation of this chapter in the light of the results of chapter 5.