The spatial angle between the long axis of the QRS loop and the longitudinal axis of the ventricles

Abstract

The positional relationship between the spatial QRS loop and the longitudinal axis of the cardiac ventricles is of interest in studies relating anatomic and electrical heart position. Although the spatial angle between the mean spatial QRS vector (SÂ QRS) and the longitudinal axis of the cardiac ventricles (H) has been estimated by Ashman and associates, 1 the relationship has not, to our knowledge, been calculated mathematically. We, therefore, decided to determine the spatial angle, hereafter called θ, between H and the long axis of the QRS loop which is employed instead of the mean QRS vector as a matter of convenience. The derivation of trigonometric formulae for the determination of the spatial angle between two vectors, given the projection of the vectors upon any two of three mutually perpendicular planes, provided the opportunity to calculate this value. It was believed that such a calculation might be of interest for several reasons. In addition to the magnitude and range of the normal angle, some idea of the relationship between the anatomic and electrical position of the heart could be obtained. Further, the use of more than one system for estimating the long axis of the QRS loop would give a basis for comparison between the different systems. Finally, it was hoped that some information could be obtained with regard to the validity of the lead used for the sagittal component of the spatial vectorcardiogram. For these reasons, the following study was undertaken.