ELECTROCARDIOGRAPHY 333 





 RESULTANT 



FIG. 1 1. Vectorial addition of two fiber dipoles showing complete cancellation of the potentials. 

 FIG. 12. The same as fig. 1 1, but with a resultant emf larger than the single component. 



The heart \-ector can be characterized by its magni- 

 tude, direction, and position. The magnitude depends 

 upon the number of simuhaneously active fibers, 

 their individual electric moments (including the 

 magnitude of their cross section, which influences M), 

 and the degree of divergence of the individual fibers. 

 If, in an extreme case, all fillers were to start from a 

 central point symmetrically in all directions, the 

 fields of these fibers would cancel each other com- 

 pletely and no electric field would occur, in spite of a 

 great activity of the muscle mass of the heart. This 

 cancellation of fields takes place in every heart. As 

 will be shown later, the fibers diverge to a consider- 

 able degree, and, in some hearts, diverge so strongly 

 that nearly no QRS complex remains This phenom- 

 enon of cancellation may be called "physiological low 

 voltage" (410). 



The direction of the heart vector is determined by 

 the result of this cancellation as well, because some 

 fibers do not find a canceling counterpart, so that 

 these alone in the total pattern of individual vectors 

 remain as components of the resultant heart vector. 

 Its direction therefore corresponds to the average 

 direction of the uncanceled fibers. Every disturbance 

 in the spread of excitation during the \'entricular 

 activation will immediately disturb this balance of 

 vectorial addition, and thereby change the direction 

 and magnitude of the vector. The direction of the 

 heart vector can be completely described only in a 

 three-dimensional space, by determining the angles 

 in zenith (elevation) and azimuth on the sphere. In 

 practice, these data are replaced by the angles which 

 the projections of the vector on the three planes form 

 with the horizontal or the transverse line. The sense in 



which the angles are counted may be seen in figure 58. 

 The classical derivations of Einthoven's extremity 

 leads record only the frontal projection of the vector. 

 The angle which the frontal projection of vector forms 

 with the horizontal line is the Einthoven angle a. 

 The "position" of the vector is irrelevant in the 

 ideal case of a parallel lead field. If this condition is 

 not realized, the position has to be determined by 

 methods which will be discussed later. 



5. LIMITS OF APPLICABILITY OF SIMPLE 

 VECTORIAL CONCEPT 



The vectorial composition of the heart vector, 

 according to figures 11, 12, and its projection on a 

 lead line are correct in the ideal case, in which the 

 medium has a homogeneous conductivity, the field 

 has a boundary of simple configuration (sphere), 

 the heart is centered in the sphere (all surface elec- 

 trodes having the same distance from it), and the 

 dimensions of the heart are small compared with the 

 dimensions of the field, so that all myocardial fibers 

 may be assumed to be concentrated in the central 

 point of the sphere. Inasmuch as these assumptions 

 are invalid, for exact application the vectorial con- 

 cepts need corrections for which, in most cases, the 

 mathematics are extremely difficult. 



Two problems arise out of this difficulty. The 

 first one is: if and how far the cardiac potentials can 

 be represented by one single resultant vector of fixed 

 location, the changes of direction and magnitude of 

 which interpret changes in the interior of the heart. 

 The second problem is; how the heart vector projects 



