Although the current EKG data acquisition system has only a single channel of input, 2d cross-plots of one input with respect to another are easy to perform by extracting a single waveform from each lead, shifting and synchronizing them in time with respect to a common feature shared between them, and then using the two extracted and shifted waveforms as the input to a single 2d plot.
Here is an example of cross-plotting a waveform from each of the lead pairs V1/V6, V2/V5, and V3/V4 taken from a previously acquired set of 12 lead EKG data:
In this case, the 3 pairs of inputs were selected under the assumption that the two outer most leads (V1 and V6) would show the greatest left-right asymmetry, while the two inner most (septal) leads (V3 and V4) would show the most similarity. This does appear to be true, as can be seen by the shapes of the 3 cross-plots. In each plot, the range of the curve is dominated by the RS strokes in each lead. As predicted, the V1 and V6 leads show the greatest independence in RS subsegments, having almost complete (circular) independence in the lower left quadrant of the plot. In this part of the trace there is a 90 degree phase difference between the two signals, suggesting a conduction timing difference between the left and right ventricles as observed by the two different electrode locations.
The V2 and V5 leads show more dependence between RS subsegments, while the V3 and V4 leads are almost completely dependent on one another. Thus, as one moves toward the septal leads, there is less left-right asymmetry between inputs, and as one moves outward from the septal leads, there is increased independence between signals.
In order to create the 2d plots, a single 1 second waveform is extracted from each recorded lead. Here are the waveforms used to create the V1/V6 plot. Both waveforms are shifted and manually positioned so that the peak of the R stroke is synchronized at the same point in time, here 1/4 second (64 points) into the trace. Eventually, extraction and synchronization will be automated by the software.
Note that the synchronization of the two waveforms is critical, although it is usually easy to accomplish. In the examples below, the V3 waveform has been shifted one point forward and then one point back of its proper location, and there is a significant effect on the RS subsegment of the corresponding 2d plots. Because the V3 and V4 waveforms are very similar in shape (since they are close to one another in physical electrode location), proper synchronization is achieved (a) when the area swept out by the RS subsegment is smallest, and (b) when the locus of the RS subsegment approaches a line segment through diagonally opposed quadrants (1 and 3, 2 and 4), indicating that the two signals are in phase.
One point out of phase:
One point out of phase:
Although the range of the 2d plots is dominated by the RS stroke of the EKG, other features of the waveform may be discernable near to the origin at higher magnifications. This is obviously a topic for further study. Here are two details of the V1/V6 plot shown above near to the origin at increasing magnifications. The left detail shows the T "wave" subsegment of the two waveforms. The right detail shows everything else. Both endpoints of the trace are visible in the upper half of the right detail near the Y axis. While it is currently difficult to discern individual features of the various waveforms, color-coding the trace as to the relative time of each point, and using arrows to show the direction of motion (time), would considerably improve the information available from the plot.
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