The validity of the equilateral tetrahedron as a spatial reference system.

The error involved in the use of the equilateral tetrahedron reference system for electrocardiographic or vectorcardiographic studies has been investigated by means of an electrical dipole placed in the esophagus. Vectors plotted from the potential differences between electrodes defining the reference system were found to correspond fairly closely to the actual position of the dipole, indicating that the error is small. T HE STUDY of spatial vectorcardi-ography in progress in this laboratory prompted an examination of the equi-lateral tetrahedron, which is the reference system employed. In this system the shoulders, the pubis, and a point on the back represent the apices of the figure, and the assumption of the Einthoven hypothesis that shoulders and pubis are sufficiently removed electrically from the heart to be considered equidistant must also be applied to the electrode position on the back. On a purely anatomic basis, this seems justified , since in a study of 30 normal subjects this point on the back was found to be of equal distance from the heart as the left shoulder or even more distant.' It must also be assumed, as in the Einthoven hypothesis, that the body acts as an essentially homogeneous conducting medium. It is generally agreed that these assumptions are approximations only, but are useful in frontal plane electrocardiography. If they can be applied with similar accuracy to a volu-metric reference system, three dimensional vec-torcardiography may provide new and valuable information. In the report suggesting the use of the tetra-hedron reference system, Wilson and co-workers2 presented the results of an experiment designed to test its validity. An electric field was produced in a cadaver by means of electrodes inserted in various positions in the region of the heart. The potentials at the points representing the apices of the tetrahedron were then compared with those predicted on the basis of the known dipole position. As the authors pointed out, the results were inconclusive because of the special conditions of the experiment. The effect of death on tissue resistance and the effects of accumulation of fluid in the dependent portions of the body made the data difficult to interpret. In the experiments reported herein, the potential differences between limb electrodes and limb and back electrodes produced by a "dipole" placed in the esophagus of living subjects have been determined. It is recognized that a dipole so located is not entirely comparable to the heart in relation to …