METHODS OF MEASURING BLOOD FLOW 



! 303 



eter, in no way represents the time course of the 

 flow velocity v. The magnitude v, however, is con- 

 tained in the linear differential equation which re- 

 mains when term II is removed from equation 8. In 

 order to solve this equation for v continuously, the 

 electrical signal delivered by the differential manom- 

 eter is fed into an analogue computer which has 

 been adjusted according to the magnitudes C\ and C 3 . 

 The output signal of the computer will then follow the 

 actual flow course, provided the coefficients C\ ("veloc- 

 ity resistance") and C 3 ("velocity inductance") are 

 known with sufficient accuracy and the pressure 

 difference is not affected by other physical influences. 

 Difficulties arising from these conditions are discussed 

 by Fry (46) and by McDonald (93). Flow records 

 from the ascending aorta of dog and man demonstrate 

 this method to be promising, while records of the 

 pulmonary artery flow seem to require further 

 clarification. For simplified catheter-tip approaches, 

 consult the papers of Evans (29), Jones et al. (71), and 

 their discussion by McDonald (93). 



Many types of differential manometers have been 

 used to record the pressure differences delivered by 

 the instruments described above. It is obvious that 

 low frequency manometers, particularly water manom- 

 eters, are far from able to follow the rapid fluctua- 

 tions in differential pressure which occur when arterial 

 or central venous flow is recorded. Therefore mem- 

 brane manometers with adequate frequency response 

 are required for recording pulsatile flow. Their 

 sensitivity must be considerably higher than that of 

 common blood pressure recorders because the flow- 

 related pressure differences are relatively small. 



The difficulty of combining high sensitivity and 

 high natural frequency in the same instrument is 

 manifest in the discussions of physical principles by 

 Frank and the models designed by Frank (37, 39), 

 Gregg (54) and Green (50, 51 ). 



The difficult task of recording the very small 

 flow-conditioned pressure differences is made possible 

 by the amplification of electrical signals from rela- 

 tively stiff manometers of high natural frequency. 

 Most important of these are capacitance or inductance 

 manometers as well as resistance manometers of the 

 strain gauge type (6, 50, 51). 



It has been emphasized that, due to term II of 

 equation 8, the calibration curve of most differential- 

 pressure flowmeters is not linear. As in the case of 

 bristle flowmeters, an attempt has been made to avoid 

 the cumbersome graphical correction of records by 

 using linearizing or, especially, square-root extracting 

 devices, some of which a) are employed after registra- 



tion, for evaluation of the records, while others b) are 

 designed to deliver already linearized registrations. 

 For a, Frank (39) proposed a photographic projec- 

 tion method, Broemser (15) and Ranke (108) com- 

 bined the linearizing element with a planimeter. For 

 b, Schroeder (119), as described above, uses optical 

 linearization which works during the registration; 

 Baxter & Pearce (4) connected a linearizing circuit to 

 the electrical differential manometer. See also Green 



(50). 



Finally, the so-called constant-pressure flowmeters 

 or air-expansion systems may be mentioned although 

 they are not differential-pressure meters in the proper 

 sense [see Gregg (54), Green (50)]. If a blood reservoir 

 is connected to a large air chamber, any inflow or 

 outflow of blood will change the air pressure. The 

 rate of volume flow of the blood entering or leaving 

 the reservoir can therefore be determined from the 

 slope of the change in air pressure which is recorded by 

 a sensitive manometer. If the pressure variations are 

 very small as compared to the absolute pressure level, 

 the system delivers a virtually constant pressure for 

 perfusing a vascular bed and acts, at the same time, as 

 a flowmeter. Such systems have been preferentially 

 employed for studies on the coronary circulation 

 [Wiggers & Cotton (137); Green & Gregg (52); Eck- 

 stein et al. (25)]. 



THE ROTAMETER 



The rotameter used in physiological experiments is 

 a device for measuring mean blood flow in cannulated 

 vessels. The prototype instrument was designed for 

 measuring gas flow. In a vertical conic tube a float 

 moves up and down in proportion to the rate of flow, 

 stabilizing its position by fast rotation which results 

 from spiral grooves around the float body. This rota- 

 tion has given the instrument its name. If fluid instead 

 of gas is used, the float does not rotate: stabilization is 

 achieved by other means. Devices in use are based on 

 designs by Gregg et al. (56). The instrument of 

 Shipley & Wilson (121, 122) is shown in figure 16. 

 The conic tube is made of Lucite or plexiglass with 

 various flow capacities from 0.1 to 3.0 liters per min. 

 The movement of the brass float is detected electro- 

 magnetically. An iron rod pierces the middle of the 

 float vertically and is fixed in such a position that it 

 protrudes equally above and below the body of the 

 float. The lower part of the rod is guided by a ring, 

 whereas the upper part enters into the lumen of an 

 electromagnetic coil fed by alternating current. As the 



