The EKG signals shown in the previous examples are all "unipolar", in the sense that they have been acquired from a single electrode placed against the surface of the chest (although the electrical return path for this electrode is provided by the three limb electrodes which can be considered to be at "infinity"). It is also possible to acquire "bipolar" signals from the precordial leads by using two electrodes which are both connnected to the surface of the chest in various orientations, and which provide the complete conduction path for the recorded signal, without the use of electrodes attached to the limbs. However, it is possible to synthesize different bipolar lead configurations by simply subtracting one unipolar lead signal from another, without the need to perform additional experiments.
In the following examples, the 25 unipolar EKG signals acquired previously have been used to synthesize bipolar signals by subtracting the average V(3, 3) signal from each of the 24 other signals. In the following image, each average precordial signal in the 5x5 grid has had the average V(3, 3) signal subtracted from it to produce a bipolar signal, as if that signal had been recorded using two electrodes, one (-) located at the V(3, 3) gridpoint, the other (+) oriented radially outward from the center of the grid.
(Click for larger image)
The resulting radially oriented bipolar signals can then be used to visualize the orientation of the cardiac axis on the surface of the chest. Here are two frames from an animation of the grid of signals shown above. The first image shows the R peak of the grid (in this case all other signals are below the level of the V(3, 3) signal). The cardiac axis can be seen as an asymmetry in the grid which is oriented at about 30 degrees clockwise from horizontal.
Here is an image showing the S peak of the bipolar grid, again showing the cardiac axis as an asymmetry oriented about 30 degrees clockwise of horizontal.
According to theory, the shape of an EKG waveform is related to the orientation of the two bipolar electrodes used to acquire it. An electrical potential which is moving toward the more positive of two electrodes generates an upswing in the recorded EKG signal, while a potential moving away from the positive electrode generates a downswing in the recorded signal. A potential which is moving at right angles to the orientation of the bipolar electrodes generates both an upswing and a downswing of equal magnitiude (actually, of equal areas) in the recorded signal.
Thus, it is possible to estimate and visualize the electrical depolarization axis of the heart (the cardiac axis) by looking at the relative areas of the upswing and downswing of the RS "wave" as recorded by different bipolar electrode configurations having different angular orientations. Those configurations in which the integral of the RS "wave" is most nearly zero are oriented perpendicular to the direction of the depolarization axis.
Here is an example of using the component sofware to integrate those subsets of the bipolar signals shown above which contain the RS "wave". To begin, the RS subset of the average V(3, 3) EKG signal is identified. An integration component can perform trapezoid summation of the area under a curve either for the entire signal in question, or for only a subset of the signal defined by two limits of integration.
Integration was performed on all 25 bipolar signals using the same limits of integration (in this case points 56 to 77 out of 256). The resulting integrals were then combined into another 5x5 grid, and are displayed below as a surface and as two images. In these plots, grid points whose vectors from the center of the grid are oriented perpendicular to the cardiac axis should have integral values which are close to zero (i.e. they have equal areas in the RS upswing and downswing part of the signal). This occurs for grid points which are located on a diagonal of the grid from the lower left corner to the upper right corner.
The surface shown below has been oriented so that its projection crossing the XY plane along the line of sight has been minimized. This happens when one is looking along the zero diagonal of the grid, perpendicular to the cardiac axis, which is again seen to be at an orientation of about 30 degrees. The two images shown below have been scaled so that their maximum or minimum value is at zero, showing the boundary between positive and negative values of the RS integral. Again, the line of zero integrals is oriented perpendicular to the cardiac axis.
Finally, the gradient of the integral surface (a vector field showing the X and Y derivatives of the grid) can be calculated and displayed as a set of 2d vectors having different lengths and orientations. In the image below, the first plot has been drawn so that the magnitude of the gradient at each grid point is shown by the length of the corresponding arrow, while the arrow points in the direction of steepest ascent. In the second plot, all arrows are draw the same length, showing only the direction of the gradient at each grid point. Those arrows which lie along the RS zero integral line (the diagonal from lower left to upper right in each image) point in the direction of the cardiac axis.
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