330 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



FIG. 6. The Einthoven triangle. The resultant vector of all heart fiber potentials, lying at the 

 center of an equilateral triangle, is recorded by the three standard leads with potential differences 

 proportional to the projections of the vector on the electrode lines. R, L and F : right and left arms 

 and left leg as electrode sites; a is the angle of the vector with the horizontal. 



FIG. 7. Demonstration of the invalidity of the Einthoven triangle Even if one assumes the dipole 

 to be centered in the chest, the electrode at the left leg does not form an equilateral triangle with 

 the electrodes at the arms. The projections indicated in the figure therefore cannot be valid. [From 

 Schaefer (58).] 



We are never able to record the heart vector directly 

 except by means of vectorcardiography, which will 

 be discussed later. In classical electrocardiography 

 derivations are recorded, i.e., potential differences 

 between two electrodes. These derivations may be 

 regarded as the projections of the heart vector on the 

 lead line. In the reverse sense, if the lead lines and 

 their projections are known, we may reconstruct 

 the heart vector. Under the conditions of the spherical 

 thorax model of figure 6, the lead lines of Einthoven 

 electrodes are identical with the line connecting the 

 electrodes. When a unipolar system is used, the lead 

 line is identical with the connection between elec- 

 trode and dipole center. All derivations are pro- 

 portional to the projection of the heart vector on 

 these lead lines. For comparing bipolar and unipolar 

 leads, however, a constant factor must be used to 

 convert one kind of derivation into the other. If the 

 Einthoven derivation I (horizontal) is compared with 

 a unipolar horizontal lead, the latter records a 

 potential difference V^ which is compared with the 

 magnitude of the dcri\ation I V'l 



Vu = V,/3"2 



Details can be found in the literature (150). 



The assumptions basic to the use of the Einthoven 

 triangle are not actually realized. It therefore seems 

 necessary to derive generally acceptable solutions 

 which describe the potential differences and their 

 correct interpretation even under the extremely 

 complicated anatomical conditions existing in the 

 human body. All modern solutions are based on the 

 Helmholtz theorem (253, 472). The meaning of this 

 theorem is symbolized in figure 8. In the interior of 

 the thorax a charged surface (double layer) Q may be 

 a.ssumed, which produces a current through a record- 

 ing instrument connected with the thorax by two 

 surface electrodes. The electromotive force (emf) of 

 Q is called V, and the current going through the 

 instrument is called j. If we now replace the galvanom- 

 eter by a battery with the same emf as that of the 

 intrathoracic surface Q, the battery will produce the 

 same current strength i through Q, which Q itself 

 actually produces in tlie circuit with the galvanometer. 



