9 : 6/ Mechanical and Electrical Character of the Heartbeat 



173 



potential between any two external points will be the sum of the poten- 

 tials due to each of the current sources acting independently. (This 

 superposition theorem is not true for voltage sources.) 



The potential due to a group of current sources in an infinite con- 

 ducting medium can be used to find an approximation to the currents 



Right 



Arm t*--~. 



(a) 



(b) 



Figure 9. (a) Vector relationship for finding potential V t due 

 to current source I t at A. (b) Geometrical relationship 

 between heart dipole along 6 = and arms and foot. This 

 diagram is used in deriving the equations on page 175. 



produced in the body by the heart. For convenience, the two terminals 

 in Figure 8 will be treated as two sources, one positive and the other 

 negative. Let the location of the i th current source be denoted by the 

 vector distance r t from the origin of the coordinate system as shown in 

 Figure 9. Then the current due to this source, considered by itself, 

 will spread throughout the medium giving rise to a potential V t (r) at 

 the point r from the origin. Because there are no net charges in the 

 medium, the potential V t must obey the Laplacian equation 



V 2 Vi = 



(This is shown in any electricity and magnetism text.) 



Because the tissues have a finite conductivity y there will be a current 



density J i throughout the medium originating from the i th current source 



