METHODS OF MEASURING BLOOD FLOW 



I3 ! 3 



(128) found that, due to this effect, the resulting 

 voltage picked up by the electrodes is, in case of a 

 parabolic velocity profile, just as high as £,„,, would 

 be if all the fluid layers were to move uniformly at the 

 velocity v A averaged over the cross-sectional area. 

 This means that the method delivers a flow-signal 

 voltage which is linearly proportional to the in- 

 stantaneous velocity v A or to the instantaneous flow 

 rate. The only conditions required are that the 

 magnetic field be homogeneous, that the fluid be 

 homogeneous with respect to its electrical con- 

 ductivity, and that the velocity distribution be sym- 

 metrical in relation to the tube axis (79). It follows 

 that the flow-signal voltage E f which is picked up by 

 the electrodes differs from the originally induced 

 voltage E ind (except the extreme case of a completely 

 flat velocity profile where both are equal) so that 

 for fluid flow, equation 12, has to be modified to: 



E. = BDv.-IO' 8 volts, 

 f 



(13) 



As Kolin (78-80) stated, equation 13 is valid also 

 in case of any other velocity profile and even in the 

 idealized case of a central and coaxial fluid jet which 

 is moving through a tube while the annular fluid 

 cylinder around this jet is quiescent. From this Kolin 

 concluded that the electrically conducting vessel 

 wall may be regarded as representing such a quiescent 

 fluid cylinder surrounding the streaming blood and 

 that, therefore, no error is caused if the voltage E s 

 is picked up by electrodes placed at the outer surface 

 of the vessel wall. Thus the application of the method 

 on unopened blood vessels, which had been carried 

 out earlier as an experimentallv proved procedure by 

 Kolin and other workers, was also justified on a 

 theoretical basis. Any inaccuracy due to the differ- 

 ence in specific conductivities of blood and wall 

 tissue is of minor significance (80, 82). 



If, instead of v,,, the instantaneous flow rate Q, 

 (cm 3 /sec) is used in equation 1 3, we get with D = 

 2Randv A = Q,/(/x 2 tt): 



E f 



2BQ 



-8 



■ 10 volts 



(14) 



It is obvious that, according to the aforementioned 

 considerations, R is the vessel radius including the 

 wall thickness. Equation 14 shows that the sensitivity 

 £//Q, is inversely proportional to R or to the distance 

 between the electrode tips and is independent of the 

 wall thickness (80, 82), provided that B is fixed and 

 that the vessel is surrounded by insulating material. 



The history of electromagnetic flow measurement 

 [see notes in (78, 84, 123)] shows that several authors 

 found the principle independently of each other. 

 Faraday demonstrated electromagnetic induction in 

 solid as well as in liquid conductors. But he did not 

 conceive the idea of measuring fluid flow which in- 

 volves recognition of velocity distribution. His ex- 

 periment at the Waterloo Bridge, in which he tried to 

 detect an induced electromotive force (emf) in the 

 River Thames due to the water's motion through the 

 earth's magnetic field, simply represented his search 

 for an induction phenomenon on a terrestrial scale. 

 This experiment was unsuccessful, probably due to 

 electrode-polarization difficulties. Young et al., in 

 1920, were able to record such an emf. Williams, in 

 1 930, performed the first electromagnetic measure- 

 ments of the velocity distribution in copper sulfate 

 solutions, but made no measurement of flow rate. In 

 1932, Fabre (30) suggested, in a short note, electro- 

 magnetic recording of variations in blood flow in can- 

 nulated vessels [see also (84)]. Kolin [1936 (5)] is to be 

 regarded as the real founder of electromagnetic blood- 

 flow measurement. He was the first to recognize the 

 applicability of the method to unopened vessels and to 

 obtain successful records from dogs. In the following 

 years and decades, he also made the major contribu- 

 tions to further development of the procedure, espe- 

 cially by introducing and refining the a-c modification 

 instead of the d-c type which was employed earlier. 

 The d-c method was also described by Wetterer [1937 

 (133)] and was particularly used for recording flow in 

 the unopened ascending aorta. Valuable contributions 

 were further made by Einhorn (28) concerning the a-c 

 method and by Thurlemann (128) whose findings 

 have already been mentioned. In 1953, the square- 

 wave modification was initiated by Denison (see 125) 

 and, since then, has been undergoing considerable 

 development by the work of Denison and Spencer. 

 It combines, at least theoretically, the advantages of 

 the d-c type with those of the a-c sine-wave type. 



The d-c procedure (68, 69, 72, 75, 84, 133) is the 

 simplest approach to the electromagnetic flowmeter 

 technique (see fig. 26). A constant magnetic field is 

 used from either an electromagnet or a permanent 

 magnet. The pole pieces of the magnet should be con- 

 structed in such a way that the gap can be adapted to 

 the vessel size and the pole faces are large enough to 

 insure a uniform magnetic field across the entire 

 vessel segment. The field strength should be as high as 

 possible, e.g., 1000 to more than 10,000 gauss. In case 

 of 10,000 gauss and a vessel diameter of 0.5 cm, a flow 



