METHODS OF MEASURING BLOOD FLOW 



1311 



linearizing circuit has to be adjustable to correct the 

 calibration curves in the range from about v 1 ' 2 to v 2 - . 

 In case of large flow pulsations, the recording of the 

 mean flow by integrating circuits must be preceded 

 by linearization. Obviously, some of these properties 

 concern other flowmeters as well (particularly differ- 

 ential-pressure flowmeters). As to flowmeters which 

 are equipped with the transducer tube, the temper- 

 ature of material surrounding the tube should be kept 

 constant, and the heater current should be stabilized. 

 Furthermore, some 5734 tubes show "pressure 

 artifacts," i.e., changes in plate current when the 

 pressure exerted on the tube's diaphragm is altered. 

 According to Brecher, very few new factory-delivered 

 tubes respond to pressure; however, careless handling 

 of a tube, especially anything causing deflections of 

 the plate shaft beyond 30 min of arc, can effect 

 permanent distortion of the diaphragm which will 

 give rise to such artifacts. 



Muller (96) showed theoretically that at present, 

 exact mathematical calculation of the forces exerted 

 on a body immersed in the streaming fluid is im- 

 possible even in the case of steady flow. Only in the 

 range of very small Reynolds numbers will forces 

 be fully calculable as the sum of a term proportional 

 to v and another term proportional to ;»' 2 (cf equation 

 10). Also, in the range of high Reynolds numbers, 

 friction cannot be ignored. For the force exerted on 

 the body is due to a thin boundary layer of fluid 

 around its surface (Prandtl's theory). Within this 

 layer, the velocity gradient perpendicular to the body 

 surface is very high. The lower the fluid's velocity, 

 the thinner will be the boundary layer and the greater 

 the velocity gradient. Muller's experimental data 

 show that the boundary layer around a streamlined 

 bristle is stable up to Reynolds numbers of about 900; 

 above this, disturbances of the layer and hence 

 irregularities of the force exerted on the bristle are 

 observed, even if the flow is laminar. As to pulsatile 

 flow in blood vessels, the conditions are still more 

 complicated as the blood is nonhomogeneous and 

 a very large range of Reynolds numbers (from up to 

 several thousand) may occur within one pulse cycle. 

 According to Muller's experimental findings as well 

 as to Womersley's theory, the fluid laminae moving 

 at various distances from the vessel axis are oscillating 

 out of phase with each other. Thus, one must consent 

 to Muller's conclusion that, from a theoretical point 

 of view, this type of flowmeter type is far from having 

 a clear theoretical and mathematical basis. 



Taylor (127) simplified some of the physical 

 presumptions and presented a valuable theoretical 



study of the recording properties of bristle and 

 pendulum flowmeters. Considering the velocity 

 profile at various frequencies (fundamental and higher 

 Fourier harmonics) of oscillatory flow according to 

 Womersley's theory, he found that simple bristles 

 (see fig. 1 7a, b and c) give relatively true records of 

 the oscillatory flow. Compared with their response to 

 steady laminar flow, these instruments progressively 

 underestimate the average velocity as the flow 

 oscillations increase in frequency. The error in 

 amplitude approaches 25 per cent at higher fre- 

 quencies, and the maximum phase lag is about 7 . 

 Taylor also compared an actual femoral-artery flow 

 curve [recorded by McDonald (g2) with gas-bubble 

 high-speed cinematography] to the record which a 

 bristle would give according to his calculation. He 

 showed that the errors which are mainly due to the 

 higher harmonic components have no great distorting 

 effect because of their small amplitude. In Taylor's 

 words, "the final "recording' is a quite acceptable 

 reproduction of the flow." Attaching a paddle to the 

 bristle (fig. 1 yd and e) gives rise to greater errors in 

 amplitude and phase while the recording by a 

 coaxial cylinder (fig. 1 7/) shows small errors in 

 amplitude, but an enormous phase lead at higher 

 frequencies. In case of an almost flat velocity profile, 

 as in the great arteries near the heart, bristles and 

 even paddle-mounted pendulums will give still more 

 satisfactory results. 



METHODS BASED ON THE 

 ELECTROMAGNETIC-INDUCTION PRINCIPLE 



This type of flow measurement is notable in several 

 respects. It furnishes direct transformation of the 

 mechanical magnitude into an electrical signal. Its 

 interference with the blood flow is so small that it 

 can be completely neglected. It delivers strictly linear 

 calibration curves and equal sensitivities with opposite 

 signal directions to forward and backward flow so 

 that the assessment of mean flow by integrating 

 circuits can be easily achieved. Its calibration in 

 terms of average velocity or flow rate is independent 

 of the velocity profile and of the density, viscosity, 

 and temperature of the fluid. Its range of frequency 

 response is theoretically unlimited and depends in 

 practice on the electrical equipment used. It is 

 applicable to all fluids having electrical conductivity 

 equal to or higher than that of tap water, e.g., saline 

 solutions, blood, mercury. 



In addition to these physically inherent character- 



