326 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 





f=r^/ 



■^^* 



[/■ 



(3) ®+ + + + + 



FIG. I . Model of an elementary dipole ; a myocardial fiber. The right part of the fiber is at rest, 

 the left maximally excited. Both parts of the fiber may be reduced to electrical ineffectiveness by 

 adding charged discs, i and 4, having the same potential difference across their surfaces as the 

 membrane of the fiber. The two now completely closed, though oppositely charged, parts of the 

 fiber no longer develop an electric field. The addition of discs i and 4 is neutralized, however, by 

 the addition of two more discs, 2 and 3. of opposite polarity but the same potential difference as 

 disc I or 4. These two discs, 2 and 3, now produce the same electric field as the action potential. 

 The area between the discs is disregarded here, but it may be analyzed in the same manner, with 

 the same result, by cutting it into infinitesimally small .slices. V and V" are the respective membrane 

 potentials of the resting and the excited membrane. The potential recorded is determined according 

 to fig. 2. [From Schaefer (58).] 



one part (the left) already completely activated, we 

 may perform the following theoretical operation. Let 

 the membrane potential of the resting fiber be V, of 

 the activated fiber V", in l^oth cases as viewed from 

 the inside to the outside of the fiber. The resting po- 

 tential V appears to be positive, the activated mem- 

 brane potential V" ("overshoot") negative. The rest- 

 ing as well as the activated part of the fiijer may be 

 completed to an over-all closed surface of constant 

 membrane potential by inserting a disc (i and 4 in 

 fig. i), so that these parts of tiie fiber become elec- 

 trically inactive. The introduction of the closing 

 disc (i) must be compensated for electrically by a 

 second disc, (2), of equal area but opposite charge. 

 This disc 2 is thus the only charge acting to produce 

 an electrical field. The same procedure is utilized with 

 the resting part of the fiber, which opens toward the 

 active portion. It is closed by disc 4, the charge of 

 which is electrically compensated for by the charge 

 of disc 3. The result is that the electrical disturbance 

 at the region of activation may be represented by two 

 discoid charges. Each of these two discs represents a 

 dipole, which is composed of two surfaces carrying 

 opposite charges. A dipole of this type is characterized 

 by the magnitude of the area and the dipole moment 

 m per unit area, which is defined as 



V 



4ir 



(2.1) 



when V is the potential difference between the two 

 surfaces of each disc. The potential difference of these 

 discs is measured in the direction of the tra%eling 



excitation wave, i.e., in figure i from left to right. 

 Under these circumstances the potential differences 

 of the disc i to 4, \\ to V4, are 



V, = V"; V... = -Vi; V3 = -V4; V4 = -V 



This moment m introduces the real membrane poten- 

 tial V into the calculation, its magnitude being well 

 known from experimentation. This is important, be- 

 cause all electrocardiographic records are made using 

 electrodes that lie far away from the heart on the 

 conductive medium that surrounds the electrically 

 active fibers. If we consider the distribution in such a 

 homogeneously resistive medium of the potential 

 originated by discoid charges like those of figure i , 

 and their dipole moments per unit area, a very sim- 

 ple equation can lie written, which describes the 

 local potential V,, at any point p of the field (without 

 regarding the sign) : 



V„ = m ■ fJ (2.2) 



where fi is the solid angle under which the charged 

 discs appear, looking from the electrode (fig. 2). The 

 surface q of the disc determines, to a great extent, 

 the local field potential; it is, however, contained in 

 the value of the solid angle fi, which is directly pro- 

 portional to the surface q of the dipole. 



In figure i, the two discs 2 and 3 develop two 

 different moments m2 and m^, which may be added 

 without appreciable error, if the exploring electrode 

 is sufficientK- remote from the fif)er.- In this case the 



^ "Sufficiently remote" mecms that the distance between the 

 exploring electrode and the center of the disc is great com- 

 pared with the dimensions of the myocardial liber. 



