356 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



/ 



FIG. 40. The microelectrodes are inserted into a ventricular 

 fiber, and the difference of the membrane potentials at the 

 two points recorded. The two monophasic action potentials, 

 as they would have been recorded between each of the elec- 

 trodes and an indifferent external electrode, are drawn sepa- 

 rately. Their difference, changing with time, is Mi. The time 

 course of M, is represented by the curve enveloping the shaded 

 areas ("Differenzkonstrulction"' of Schiitz). The total sum of 

 all shaded areas is zero, if the polarity is taken into account. 

 (This assumes no ventricular gradient, and that repolarization 

 is homogeneous all over the fiber.) 



in building up a resultant electric field by spatial 

 and temporal superposition of the individual com- 

 ponents. The moment Mi as defined above has the 

 nature of a vector. The addition of these vectors Mi 

 then leads to a resultant vector, the well-known 

 "heart vector" M (see section 4): 



M = ^Mi 



(9-3) 



where this sum is a vectorial sum, for a given instance. 

 For this resultant vector, the time-voltage integral 

 is governed by the same laws as govern the individual 

 vector Mi, i.e., the time-voltage area 



/ M dt = / YM> cit = X! / M, dt (9.4) 



or in analogy to our previous formulation: 



M 



ZM: 



(95) 



The value of M is commonly known as the "ven- 

 tricular gradient." Under the above-mentioned 

 conditions (homogeneous behavior of the monophasic 

 action current), the value of M equals zero. This 

 means: as M is a vector entitv, M can be divided 



into three components Mx, My, and Mz, corre- 

 sponding to the three axes of figure 19. If therefore 



M (the time-voltage integral of M) disappears, 

 every component of M forms a time-voltage integral 

 (or area) Mx, My, and M^, equaling zero. This 

 form of an analysis may be called the "integrated 

 electrocardiogram" (125). 



Every individual dipole Mi builds up an electric 

 field, the form of which can never be determined 

 exactly, as has been shown in the preceding sections. 

 The total field of the heart, possibly recorded b\- the 

 electrocardiographic leads, is formed by the super- 

 position of all individual fields. Now the following 

 general statement can be made. If one records the 

 potential difference U between arbitrarily chosen 

 points of this field, U is the algebraic sum of all 

 individual voltages Ui generated from the individual 

 fibers with their dipoles Mi (U = ^ Ui). Cor- 

 respondingly, the time-voltage integral is U = JZ 

 Ui. We now make the following assumptions: /) The 

 monophasic action potential should be homogeneous 

 all over the heart. 2) The form (e.g., the cross section) 

 of the fiber should be constant, j) The anatomical 

 (spatial) orientation and position of the fiber should 

 remain unchanged. ^) The relationship between 

 source and field should be linear, e.g., a doubling 

 of source voltage should lead to a doubling of flow 

 lines and local potentials. Under these conditions, 

 every individual voltage Ui is proportional to Mi 

 with a fixed factor of proportionality. In the same 

 way, Ui is proportional to Mi, and equals therefore 

 zero. Furthermore, U, as the time-voltage area of U 

 and the algebraic sum of Ui, equals zero as well 



(233)- 



To summarize, the following relations are \alid. 



If we suppose the individual events in the heart to 

 be homogeneous, and assume the other three con- 

 ditions mentioned, every record with every lead 

 system would give a time-voltage area of exactly 

 zero. This would be true for every lead, every pro- 

 jection of the heart vector in case of a lead field with 

 parallel flow lines, and every local (e.g., precordial) 

 lead. It would remain true regardless of how dis- 

 torted the potential field and how peculiar the 

 conditions of derivations might iae. Now, it is well 

 known that in fact the time-voltage area generally 

 differs considerably from zero. Therefore one or more 

 of the above-mentioned conditions must not be 

 realized. Since condition 4 (the linearity condition) 

 is at least approximately fulfilled, the deviation from 

 the ideal points to the inxalidits' of conditions i to 3. 



