VII MULTI CHANNEL ANALYSIS

1 Introduction

2 Methods used: a justification

2.1 Number of analyzed electrode pairs

2.2 Squared coherency spectrum

The coherencies discussed in this chapter are based upon a division of the signals in 20 consecutive blocks, so the critical value is 0.2113. For illustrative purposes the coherencies have been classified into three classes:

Table 7.2: coherency classes

1	0.2113 < K² <= 0.5322
2	0.5322 < K² <= 0.8161
3	0.8161 < K² <= 1.

An area will be called a coherent area if all electrodes within that area are coherent. By adding the coherency class numbers an impression can be given of the strength of the coherence between electrode sites in such an area.

2.3 Cross phase spectra

2.4 Unipolar versus bipolar electrodes

In a particular experiment (18116) both the unipolar and the bipolar cardiac electrograms from three epicardial electrodes spaced 1 mm apart have been recorded.

fig 7.1: multi terminal disc electrode
a, b & c: electrodes used in unipolar - bipolar comparison

If the electrodes, the amplifiers, the recording sites and the contacts between electrode and tissue are equal, the bipolar electrogram can be reconstructed from the unipolar electrograms. As explained in chapter III, par. 3 no good calibration was possible, but - assuming equalness and just a shift in time between the measured signals - the bipolar phase was calculated from the unipolar phases at the fibrillation frequency and compared with the actually measured bipolar phase. From the difference between these two a factor expressing the assumed unequal amplitudes was calculated for all three electrode sites. This factor could be calculated for one site in two different ways and so the accurateness of the method could be estimated. The results are put in table 7.3.

table 7.3: changes of relative amplitudes at three different sites during VF.

minutes after start of VF	A{ab}	A{bc}	A{ac}	A{ab}/A{bc}	%	comments
0	0.878	0.878	0.980	1.000	-2	See fig. 7.1 and appendix C. The last column expresses the percentage difference between column 4 and 5. The electrodes and amplifiers are stable, VF is unstable.
2.3	0.848	0.823	1.029	1.030	0
3.2	0.837	0.817	1.037	1.024	1
126.0	0.902	0.819	1.049	1.101	-5
127.1	1.019	0.913	1.085	1.116	-3
128.4	1.094	0.975	1.102	1.122	-2
200.0	0.404	0.879	0.440	0.460	-4
201.1	1.257	0.158	-	7.956	-
326.0	1.096	0.868	1.209	1.263	-4
327.1	1.057	0.871	1.194	1.214	-2
328.5	1.520	1.113	1.403	1.367	3

The amplification and filter settings of the amplifiers had not been changed during the experiment and the electrode had been fixed to the epicardium, so the differences seen in course of time likely reflect changes in the electrical behaviour of the myocardium at the recording sites. The last column clearly indicates the reliability of the methods used.

The rest of this chapter will be devoted to unipolar cardiac electrograms for the reasons given above.

3. Size of coherent areas

• The basic fibrillation frequency is the frequency with the highest peak in the autopowerspectrum.
• Two electrodes will be called coherent, if the coherency between their signals at the basic fibrillation frequency is so high that the critical value associated with this level is surpassed.
• An area will be called a coherent area if all electrodes within that area are coherent.

3.1 Largest coherent area

fig. 7.2: placement of epicardial and intramural electrodes

3.2 Change in size of coherent area

fig. 7.3: coherent areas during VF

see fig. 3.1 for the electrode needle

3.3 Discussion

4 Wavefront propagation in coherent areas

4.1 Introduction

4.2 Travelling wavefronts

fig. 7.4: wavefront passing through 2 electrodes a & b, a distance D apart

Of seven dogs all apparent velocities between adjacent unipolar terminals on the intramural needle or the epicardial electrode are shown in the form of a histogram in the next figure.

fig. 7.5: histogram of apparent conduction velocities v' between adjacent unipolar leads in 7 dogs during ventricular fibrillation

The few velocities lower than 0.1 m/s will for the moment be left out of the discussion. If the travelling wavefront concept during ventricular fibrillation is correct and if a constant and uniform velocity of propagation of that front is assumed, than that velocity during ventricular fibrillation is about 0.1 m/s. This figure is not too far away from the normal conduction velocity in the ventricle of 0.4 m/s as given in literature (Scher 1976). The second horizontal axis in fig. 7.5 indicates the angle the wavefront must make with the line between two electrodes to result in the apparent velocity of the first axis.

4.3 Velocities

For v=0.1 m/s this theoretical distribution density has been indicated with a broken line in fig. 7.5.

No systematic differences have been found between the 7 dogs, so the fact that the apparent velocities do not follow this theoretical density must be explained either by assuming a non-uniform conduction velocity over the ventricle or by rejecting the homogeneous distribution of , i.e. by assuming a preference for the wavefront to hit the line between two electrodes at small angles.

4.4 Travelling wavefront reconstruction

fig. 7.6: travelling wavefront reconstruction along an intramural needle electrode (fig. 3.1) during VF in a dog at several moments (in minutes) after start of VF.

arrows indicate direction of front.

If one has to assume locally and temporally varying conduction velocities maybe it is easier to assume there is no conduction at all (see the next chapter). In the remainder of this paragraph some reasons will be given to reject the idea of conduction during ventricular fibrillation.

In table 7.3 is indicated that 201.1 minutes after the start of ventricular fibrillation not all phases could be estimated because of lack of coherency. That block of 20x2 seconds was analyzed in detail. Assuming orderly travelling wavefronts over small distances, 5 ms isochrones have been sketched between electrodes a, b and c (fig. 7.1 at intervals of 2 s.

fig.7.7: assuming orderly travelling wavefronts during VF 5 ms isochrones have been sketched between 3 epicardial electrodes.
topnumbers indicate 2 s intervals

The first 26 seconds a rather regular 'front' seems to travel from b to a and c at a speed of circa 0.05 m/s; see the first 13 blocks in fig. 7.7. Suddenly the 'speed' increases to 0.1 m/s and the direction of the 'front' changes 90°; then the 'speed' returns to 0.05 m/s, thereafter the direction changes 90° back and the 'front' slows down to 0.02 m/s (the next 3 blocks in fig. 7.7). The next 3 episodes of 2 seconds the 'front' stays stable and then suddenly dissolves into a circular movement with a 'speed' varying between 0.025 and 0.05 m/s.

5 Phase and antiphase

5.1 Circular histograms

Table 7.5: coherency classes and circular histograms

class	K²		circular histogram
	lower limit	upper limit
1	0.2113	0.5322
2	0.5322	0.8161
3	0.8161	1.0

5.2 Instable phase shifts

fig.7.9: phase shifts in milliseconds of bipolar leads from two perpendicular intramural needles, relative to the first lead on needle A

Some electrode pairs on needle B however show drastic changes in phase which are hard to reconcile with the concept of travelling wavefronts. The other stable phase shifts are even more difficult to explain within that concept.

As already stated in this paragraph "phase" means the cross phase spectral value at a certain frequency band averaged over 20 consecutive blocks of 2 seconds.

fig. 7.10: change in cross phase at fibrillation frequency in course of time between terminals 12 & 13
shift from anti-phase to in-phase

coherency block 10-12 in fig. 7.3 power spectra fig. 7.12 cross phase fig. 7.23 phase shift? fig. 7.14 action potential fig. 7.15

In fig. 7.10 is illustrated how the cross phase per such block at 12.5 Hz between two adjacent terminals on an intramural needle changes in course of time. At the start of the measurement (83.7 min. after the start of ventricular fibrillation, coherency block 10 of fig. 7.3) the two sites are in anti-phase, but gradually this changes to a constant much smaller phase difference. Not surprisingly this resulted for the first group of 20 blocks in a middle type of coherency and for the other two in a strong coherency. The averaged phases were resp. -0.63 p, -0.29 p and -0.26 p .
gradual loss of coherency

fig. 7.11: change in cross phase at fibrillation frequency in course of time between terminals 6 & 7

coherency block 10-12 in fig. 7.3 simultaneous coherency in fig. 7.10

Figure 7.11 illustrates the behaviour of this instantaneous phase if the coherency between two adjacent terminals is weak (group 1 and 2) or absent (group 3). These measurements came from the same needle at the same time as those of fig. 7.10.

5.3 Phase and form

fig. 7.12: two unipolar adjacent terminals on an intramural needle

coherency block 12 in fig. 7.3 in-phase fig. 7.10 cross phase fig. 7.13 non-linear phase difference fig. 7.14

fig. 7.13: 95% confidence intervals of cross phase spectrum between unipolar leads

power spectra in fig. 7.12 non-linear phase difference fig. 7.14

fig. 7.14: phase differences and 95% confidence intervals at peak freq.

linear phase shifts: continuous line: 12.5 Hz dashed line: 25 Hz auto spectrum in fig. 7.12 action potential in fig. 7.15

Both lines deviate strongly from the other confidence interval, so in this case the whole concept of a travelling wave has to be suspected. This has been indicated in the next figure maybe even more clearly.

fig. 7.15: reconstruction of action potentials from the spectra

see the spectra in fig. 7.12

Here a reconstruction has been attempted like in chapter 4 of the extracellularly measured action potential giving rise to a spectrum as in figure 6.7. The curves have been aligned in such a way that they cross the zero level in at least one point simultaneously. The top of T13 clearly comes later than the top of T12, but then T13 advances in respect to T12, so it makes no sense to talk about a time shift as both curves are so much different.

5.4 Discussion

6 Conclusion

Some evidence has been given in this chapter that even at distances of 2 mm the amplitude and the form of the extracellularly measured action potential might differ so much, that the bipolar electrograms during ventricular fibrillation do not carry the same information as in the case of a regularly beating heart. The unipolar electrograms are of course comparable to those made in a beating heart, but the cross phase spectrum (and necessarily the crosscorrelation function ) is not only dependent upon eventual time lags between electrode sites but also upon those form changes. Moreover, the strong predominance of small phase differences - specially in the strongly coherent areas independent of electrode distance - makes the assumption of conducted wavefronts during ventricular fibrillation highly improbable.