9 : 7/ Mechanical and Electrical Character of the Heartbeat 175 



This is clearly only an approximation but is useful in describing the 

 electrocardiogram. 



Equation 10 may be applied directly to the standard ekg leads. If 

 the line to the foot makes an angle a with the heart vector, then the right 

 arm is located at 6 = a + 120° and the left at 6 = a — 120° as shown in 

 Figure 9. Therefore, the three voltages, V L , V R , and V F , should be 



3P cos(a - 120°) 

 L ~ y R 2 



3P cos (a + 120°) 

 R ~ y R 2 



3P cos a 



Vf = ~~w 



The three lead voltages may be found by the appropriate differences, 

 and the validity of Equations 8 and 9 can be noted. Thus, the Einthoven 

 triangle is as valid as the spherical approximation with a dipole current 

 source. 



Clearly, the representation as a dipole is misleading and at best an 

 approximation. The standard ekg leads are not necessarily the best 

 ones. Various attempts to improve these are discussed in Section 8. 

 Nonetheless, the four or five leads (including both chest and back) have 

 been used for most clinical and diagnostic purposes. 



7. Vector Electrocardiography 



In attempts to increase the information obtained from the electro- 

 cardiogram, various schemes have been developed. The most success- 

 ful, called vectorcardiography, records the magnitude, location, and spatial 

 orientation of the equivalent heart dipole as a function of time. As 

 has been pointed out, the physical relationship between the equivalent 

 dipole and the cellular events in the heart is not in any way obvious. 

 The abnormalities producing a given change in the heart potentials 

 cannot be logically related to the change in many instances. In spite 

 of the inability to logically interpret the vector electrocardiogram, it 

 can still form a powerful diagnostic tool for clinical work. The equiva- 

 lent dipole is referred to as the heart vector. The rationale behind these 

 systems is presented in this section. 



Calculations, confirmed by model experiments, show that the use of 

 the four standard ekg leads could give rise to very erroneous interpreta- 

 tions of the location and orientation of the heart vector for hearts as 



