ELECTROCARDIOGRAPHY 



329 



> 5000 n 



> 5000 Q. 



,^^-— Kw 



/ > 5000 a 



/ , — VW 



FIG. 5. The commonly used network to gain a zero potential 

 electrode, called central terminal (CT). 



of more than 5000 ohms to one point (fig. 5). This 

 point has the mid-dipole potential if the field is homo- 

 geneous and if the dipole lies exactly in the center of 

 an equilateral triangle, the angles of which are formed 

 by the three electrode points R, L, F. This follows 

 from the original concept of the Einthoven triangle 

 (528). It has been proved all too often that this con- 

 cept introduces errors of considerable magnitude 

 into the ECG. [Examples of a much broader literature 

 (99, 147).] Nevertheless, there are general solutions 

 possible, by replacing the resistances in the network 

 of figure 5 by resistance values calculated for certain 

 electrode positions and certain thorax configurations. 

 Such networks, however, are not interchangeable, 

 neither from one electrode combination to another 

 one nor from one patient to the next (335)- They 

 are therefore, practically speaking, inapplicable to 

 clinical electrocardiography. Here, the simple pro- 

 cedure of Wilson (fig. 5) is still in use, in spite of its 

 errors. The zero point is called the "central terminal" 

 (CT). 



3. VECTOR THEORY OF THE ELECTROCARDIOGRAM 



In the production of the ECG very many individual 

 fibers are involved. The activation time, anatomical 

 site, and direction of their excitation waves can 

 scarcely be analyzed in detail. Every theory of the 

 ECG is therefore based on simplifications. Analysis 

 of the excitation process going on in the heart may be 

 performed in two different ways : one is to gain as 

 much detailed information as possible about the 

 various parts of the heart, their interaction, and their 

 local electrical events. We may call data of this kind 

 "partial or local derivations" of the excitation proc- 



ess. The second way is to represent the totality of the 

 heart's excitation by one single measurement ("total 

 derivation" — see section 6). Which of the two types a 

 specific derivation really represents depends merely 

 upon the position of the electrodes. 



An ECG is thus the potential difference recorded 

 by unipolar or bipolar leads put on the body surface. 

 Under ideal conditions these potential differences 

 can be calculated or graphically constructed by the 

 projection laws of the dipole vectors, but simple 

 equations or constructions are only possible if the 

 body is replaced by a spherical conductor of homo- 

 geneous conductivity, with the dipole lying in the 

 center of the sphere. Even for a cylindrical model of 

 the thorax the mathematics are very complicated and 

 completely inapplicable to practical electrocardiog- 

 raphy using realistic thoracic models. We neverthe- 

 less have had to develop the simple equations, partly 

 for historical reasons, and partly because modern and 

 exact solutions are based on the theoretical under- 

 standing of the ideal case. The simplified concept is 

 indicated in figure 6. If one considers a cross section 

 through the sphere, going through the center, we 

 may put three electrodes on the spherical boundary, 

 all electrodes being equidistant from each other and 

 lying in the same plane of this cross section. They 

 form an equilateral triangle. Under these, and only 

 under these conditions, the well-known projection 

 laws of Einthoven will be observed: the relative 

 magnitude of the bipolar derivations of the ECG, 

 named I, II, and III, respectively, are proportional 

 to the cosine of the angle between the instantaneous 

 dipole moment and the line connecting the electrodes 

 of each derivation. The simple derivation of these 

 projection laws from equations 2.2 and 2.5 may be 

 omitted here. The construction of figure 6 gives only 

 the relative magnitude of the derived potentials. The 

 absolute values depend mostly upon the distance 

 between electrodes and dipole or, in other words, 

 upon the radius of the sphere. They may be calculated 

 as the differences between the unipolar potentials of 

 each electrode, as they are given in equation 2.5a. 



The Einthoven concept (183) started from the 

 assumption that the electromotive forces of the heart 

 could be represented by one single vector centered in 

 an equilateral triangle (fig. 7). The figure, however, 

 shows clearly that not even the geometrical assump- 

 tions of the triangle concept are valid for the ana- 

 tomical properties of the human body. Several correc- 

 tions have been made, but there is only one correct 

 solution of the problem, the Burger triangle (see 

 section 6, fig. 18). 



