The accuracy of the vectorial interpretation of electrocardiographic tracings

Abstract

Starting from the principle that the accuracy of the vectorial interpretation of the electrocardiographic tracings must be ascertained in each individual and is only established when the vectors may be constructed, the conditions of this construction were logically determined. It is shown that all the points for the leads (more than one point is obviously necessary) must be located on a continuous convex region of the surface of the body with a spherical electrical symmetry. In such a region, first, the difference of potential between a point P on the thorax and points P i equidistant from P is a sinusoidal function of the angle defining the position of the points P i and, second, the difference of potential between the point P and a conducting ring including all the points P i is proportional to the potential at P. The degree with which the first condition is verified may be measured by a correlation coefficient, and the second condition implies that the tracing so obtained must be similar to the unipolar at P, and the quotient of the amplitudes of the two tracings at each instant is a function of the distance of the dipole to the point P. It is supposed that the vectorial interpretation is valid when that correlation coefficient is approximately equal to 1 (or, more practically, when a sinusoidal curve is approximately obtained with the differences of potential measured as referred to in the first condition), and the calculated distances are the same for the dipoles of a cardiac cycle. Methods are given for the calculation of the vectors and the construction of the vectorcardiogram in this case. When the calculated distances are different during the cardiac cycle, they still may determine the spatial localization of the successive dipoles. As the limb leads do not satisfy the conditions of applicability of the methods proposed, it is not possible for them to offer new proofs of their vectorial nature in this way. But it is shown that, particularly the kind of nonvectorial interpretation of the limb unipolars which is associated with the usual definitions of the electrical positions of the heart, is not necessary. These definitions are compatible with the vectorial interpretation; the similarity of the patterns of the precordials and those of the limb leads are probably in relation to the fact that the vectorcardiogram is normally approximately a plane. When a vectorial interpretation of the tracings is valid for all the current leads, the ideal sphere equivalent to the human body may be determined. Finally, we justify the opinion that the points for the precordial leads must be chosen in accordance with the electrical position, and a new principle for an indifferent electrode is presented.