9 : 8/ Mechanical and Electrical Character of the Heartbeat 177 



fitted very well by an equivalent dipole for a variety of different sets of 

 points. The P- and T-waves of the ekg definitely cannot be described 

 by the same dipole. Moreover, although the error in fitting F 4 with a 

 linear combination of V x , V 2 , and V 3 is small, it is definitely larger than 

 experimental error. 



Another test of the dipole approximation is that of mirror images. 

 For the central dipole in a sphere, discussed in Section 7, the equator 

 of the sphere is a zero potential line. Any two points equidistant from 

 the equator will have potentials which are equal in magnitude but 

 opposite in sign. They are called mirror points. For the human torso 

 (or indeed even for a cylinder with an eccentric dipole), the zero potential 

 line is not an anatomically or geometrically obvious feature. Nonethe- 

 less, it could be located by finding mirror images if (and only if) the 

 dipole approximation is a good one. Experiments have revealed the 

 existence of a mirror point for the QR§-complex at any arbitrary point 

 on the torso. This also confirms the validity of the dipole approxima- 

 tion. The data are good enough to show the best mirror points are not 

 perfect mirror points. However, the errors are too small to compute a 

 meaningful quadrupole moment. 



In practice, the heart vector can be found by two different methods. 

 If one wishes to determine the position of the heart vector in an indivi- 

 dual, a lengthy series of determinations of mirror points is sufficient. 

 The other alternative is to use a combination of a series of leads that 

 allows one to compute magnitude and direction of the heart vector 

 without knowing its location. Only the latter seems practical for any 

 clinical purpose. 



Several persons have set up systems of linear combinations of five to 

 16 points of contact with the torso. The aim is to arrive at a set of 

 points which is independent of the exact body shape or the location of 

 the heart but which reveals the direction and magnitude of the heart 

 vector. These "orthogonal" systems have been increasingly successful 

 in recent years. 



The success of an equivalent dipole representation of the QRS- 

 complex seems both fortuitous and unfortunate. It implies that the 

 ekg information obtainable from separate parts of the heart is very 

 slight. The validity of the dipole approximation implies that one can 

 measure an average which reflects solely the properties of the heart, but 

 one cannot distinguish individual regions within the heart. 



8. Summary 



The heart is a large mass of muscle which pumps blood through the 



