9 : 6/ Mechanical and Electrical Character of the Heartbeat 



171 



spread of the spike potential over the ventricle takes about 60 msec. As 

 it starts down the interventricular septum, the Q-wave appears on the 

 electrocardiogram recorded at the surface of the body. The R-wave 

 coincides roughly with the spike reaching the bottom (apex) of the heart 

 and starting up the outer ventricular walls. The S-wave appears as the 

 spike potential reaches the top of the ventricle. 



6. Physics of Dipoles 



Einthoven stated that if the three lead voltages given in Equation 7 

 were represented as vectors directed along the sides of an equilateral 

 triangle, all three could be represented as the projections of a single 

 vector on this triangle. As is seen in Figure 7, 

 this follows for any set of voltages. 



Although this procedure can be carried out 

 for any three points, it has significance only if 

 the resulting vector V indicates or is related 

 to the axis of the heart. The use of an equi- 

 lateral triangle is based on the assumption 

 that the three points chosen are electrically 

 equidistant from the heart. If this is the case, 

 one should find that 



Figure 7. Einthoven's tri- 

 angle. From the figure it 

 can be shown that V x = V 

 cos0;F„= V cos (60° - d) 

 = ^Vcosd + i\/2Vsin0; 

 V m = F~cos (120° - d) = 

 -£Fcos 6 + JvTFsin 9; 

 .-. V u = V m + V v 



V c = Wl + V B + V,) = (9) 



Albeit this is hard to test because "neutral" 

 electrodes are never truly neutral, the pre- 

 ceding condition is approximately satisfied. 

 However, it is far from exact. 



To obtain three-dimensional information, 

 a fourth electrode is placed on the back or 

 chest. Its voltage, relative to a neutral electrode, is designated by V B . 

 The ekg "lead" voltage V 1V is given by 



v IV = v B - v c 



where V c is an approximately neutral lead formed as above. V 1V 

 tends to show up heart abnormalities in front or back of the midline of 

 the heart, whereas the first three ekg leads tend to de-emphasize this 

 type of abnormality. 



To develop a more precise picture of the basis of the electrocardio- 

 gram, it is helpful to be familiar with electrical theory of a more advanced 

 nature. This theory of current sources in a conducting medium is 

 presented in this section. Those whose mathematical background does 



