METHODS OF MEASURING BLOOD FLOW 



>3>9 



difference procedure. Cylindric ceramic "trans- 

 ducers" are placed about i inch apart around the 

 vessel wall. They are arranged to transmit and receive 

 ultrasound (/ = 400 kc sec) alternately upstream and 

 downstream at a rate of 75 per sec. The phase differ- 

 ences between the signals received upstream and 

 downstream are detected by phase meters and used as 

 a measure of the differences (A/) between the upstream 

 and downstream sound transit times: 



*"*■& 



c+v 



l_) ~ 2Lv 



(18) 



where L = distance between the transducers. Since 

 the phase angle A<i> = 2irf-At, we get: 



A<t> 



4irfLv 



radians. 



(19) 



In the present design (31, 59) where/ = .l-io 5 cps 

 and L = 2.5 cm, a blood velocity of 1 cm per sec will 

 cause a phase angle of about 5- io~ 4 radians or 0.03°. 

 The output signal of the apparatus is proportional 

 to A4>. Due to undesired phase differences, assessment 

 of the base line remains a difficult problem. An im- 

 provement was achieved by introducing an automatic 

 phase-shift control. The authors succeeded in con- 

 structing a reliable recorder of extracorporeal blood 

 flow. Preliminary findings indicate that satisfactory 

 results may ultimately be attained on vessels in vivo. 

 For this purpose, the switching rate of the transducers 

 has to be increased, and the time constants of some 

 of the circuits have to be reduced (59). 



Franklin et al. (43-45) made use of the pulse tech- 

 nique in detecting and evaluating the differences in 

 upstream and downstream sound-transit times. As 

 seen in figure 32, their flow-sensing element consists 

 of a short (1-3 cm) Lucite cylinder which is split 

 longitudinally and mounted snugly about the vessel. 

 The sound is transmitted and received by two barium 

 titanate crystals placed on the vessel wall diagonally 

 from each other across the vessel lumen. The crystals 

 are set to function alternately 800 times per sec as 

 transmitter and receiver. The respective transmitter 

 crystal is pulse-excited at a repetition rate of 12,000 

 per sec so that it will, during each switching period of 

 1/800 sec, give off a train of ultrasound bursts at 

 its resonant frequency of 3 mc per sec. These waves 

 travel through the adjacent vessel wall, the blood, and 

 the opposite vessel wall to reach the receiver crystal. 

 In the next switching period, the functions of both 

 crystals are exchanged so that in every 1 400th sec a 

 train of upstream and a train of downstream transits 

 are available for determination of At. Equation 18 is 



applicable to this device if L is replaced by d-cos 9 

 where d = length of diagonal between the crystals 

 and 9 = angle between diagonal and vessel axis. 

 The transit-time voltage converter generates a ramp 

 voltage showing a strictly constant slope of 40 volts 

 per ^sec. This ramp voltage is started at the beginning 

 of every sound transmission, and its ascent is abruptly 

 stopped when the respective receiver crystal begins to 

 be excited by the sound, so that the amplitude of the 

 ramp voltage is proportional to the sound-transit 

 time. It is obvious that, due to the blood flow, the up- 

 stream ramp-voltage amplitude is greater than the 

 downstream one. This difference amounts to 4 mv per 

 io -10 sec and is detected by the voltage comparator 

 which delivers a 400 cps square-wave voltage with an 

 amplitude proportional to the difference between the 

 upstream and downstream ramp-voltage amplitudes. 

 Finally, a synchronized detector converts the square 

 wave into a d-c voltage, which indicates the instanta- 

 neous magnitude and direction of the blood velocity. 

 The device possesses satisfactory sensitivity to flow 

 and high stability of the base line. The stability is 

 achieved mainly by using whenever possible, only one 

 functional unit or channel for detecting differences in 

 time or voltage of consecutive events. Due to the 

 carrier frequency of 400 cps, the apparatus is capable 

 of an excellent frequency response to pulsatile blood 

 flow. As far as seen from the tracings published in 

 reduced scale, the flow patterns recorded on blood 

 vessels of different sizes in vivo are very similar to 

 those obtained by the electromagnetic method. In 

 addition, the simultaneous application of several or 

 many ultrasonic meters is possible without any 

 mutual interaction (44). One is inclined to predict 

 that this kind of versatile flowmeter is on its way 

 toward becoming a favorite instrument in cardio- 

 vascular research. The same may happen regarding 

 the application of ultrasound to the recording of 

 instantaneous dimensional changes of organs [Keidel 

 (74); Edler & Hertz (27); Rushmer et al. (1 15)]. 



However, it seems that the possible dependence of 

 the calibration of the ultrasonic flowmeters on the 

 velocity profile has not yet been duly considered. The 

 sound passes from the transmitter to the receiver 

 crystal on a diagonal path which crosses the stream- 

 lines of moving fluid at the angle 9 (see fig. 32). It 

 may be assumed that only the streamlines crossing 

 this diagonal will cause flow-related changes of the 

 sound-transit times. Furthermore, the relative velocity 

 distribution taken over the diagonal may be con- 

 sidered to equal that taken over the vessel's diameter 

 or radius. This means that the device will indicate the 



