A Critique of Einthoven's Law in Electrocardiography. ∗

Abstract

It is stated in authoritative books on electrocardiography that Einthoven's Law is mathematically exactly true. I wish to discuss this statement and to show that it is not correct. It is true that Einthoven's Law is approximately correct, 1 and that its practical usefulness is unimpaired; the authoritative misstatement quoted above should nevertheless be refuted for the sake of scientific accuracy. I shall first define Einthoven's triangle and develop Einthoven's Law, and shall then show its inaccuracies.

It is considered that an electrocardiographic lead records the projection on a single line, called the line of the lead, of the cardiac potential vector; this vector is the sum of all the individual vectors of the heart muscle fibers. The 3 lines of the 3 ordinary leads of clinical electrocardiography are considered as lying all in one plane, so that they determine a triangle A₁A₂A₃ (Fig. 1); this is Einthoven's triangle. In developing Einthoven's Law, it has been assumed that this triangle is equilateral; we gain something, however, by not making this assumption. Let the angles of the triangle be a₁, a₂, a₃. Let the projection of the cardiac potential on this plane be E; for convenience we represent E as directed from the point A₃, which may be done by shifting E parallel to itself, an operation which leaves unaltered its 2 properties, namely length and direction. Let e represent the length of E, and let α be the angle in a clockwise direction between A₃A₂ and E. It may be mentioned that whereas ordinarily E is spoken of as the electrical axis and α as the angle of this axis, this is not correct, since E is only the projection of the true electrical axis on this plane.