Compromise in vectorcardiography II. Alterations of coefficients as a means of adapting one lead system to another : Subjective and mathematical comparison of four systems of VCG

Abstract

If it were assumed that the electrical action of the heart could be described as that of a stationary dipole, one could show that a VCG system L could be transformed into another system K by means of a set of three linear equations. In these equations, each coordinate of a general point of K is expressed in all three coordinates of its corresponding (i.e., isophasic) point of L:

XK=pxXL+qxYL+rxZL

, YK=pyXL+qyYL+ryZL

, ZK=pzXL+qzYL+rzZL The values XK, YK, ZK and XL, YL, ZL can be found by measuring the coordinates of a pair of isophasic points of a loop K and a loop L in a single individual. To be able to calculate the nine unknown coefficients px … … … … rz, two more sets of three equations are required, which can be obtained by measuring the coordinates of a second and third pair of points. Individual transformations of this kind have been calculated in a limited number of patients for the following four systems: Frank (F), Schmitt III (S), McFee (M), and Burger (B). In this way, good adaptation was possible, showing that in the individual case the assumption of a stationary dipole is a good working hypothesis. However, in order to obtain a single transformation that ensures for each individual case, on the average, the best possible adaptation, an average transformation must be determined. This may be calculated from a sufficiently large number of individual transformations. It is easier, however, to pool all equations which pertain to each vector component from all experimental subjects, and then to carry out a single calculation, using the method of least squares. In 169 individuals, transformations were calculated in this manner for the relations B-M, B-F, M-F, and M-S. The formulas are presented in the paper. With the help of the transformations it is also possible to quantitatively formulate the degree to which two systems disagree. These values were found to be in reasonable agreement with the ratings assigned by means of subjective evaluation to the degree of correspondence shown by each pair of systems. The M, S, and F systems satisfactorily resemble each other. The B system shows a lack of agreement with this group, possibly because of the postulation of electrical heterogeneity of the human trunk in this system. The validity of the transformation method was subsequently tested in 139 persons from whom vectorcardiograms were obtained according to systems B, M, and B-transformed-to-M. Owing to the transformation a marked improvement in agreement was gained: the B system now lay within the limits of the M,S,F group. Any wellfounded VCG system might in this manner, while maintaining its characteristic electrode arrangement, be adapted to any other system desired.