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HANDBOOK OF PHYSIOLOGY 



CIRCULATION II 



is shifted along the tube, the boundary layer is iound 

 to increase in thickness and will finally occupy the 

 whole cross section forming the parabolic profile of 

 laminar flow, provided that the Reynolds number 

 is below the critical value. The so-called inlet length, 

 i.e., the distance between the beginning of the tube 

 and the site where a parabolic profile is just estab- 

 lished, can be calculated [see McDonald (93)]. If the 

 Reynolds number is above the critical value, the inlet 

 length is the distance between the beginning of the 

 tube and the site where turbulence is fully developed; 

 this inlet length, too, is calculable and will be much 

 shorter than for laminar flow. Under both conditions, 

 however, the velocity profiles in the trunks of the 

 aorta and pulmonary artery are almost flat so that 

 the use of flowmeters involves no essential difficulties 

 regarding the velocity profile, unless the flow type is 

 altered by abnormalities such as valvular stenosis. 

 Some flattening of the velocity profile also occurs 

 when the fluid is streaming from a wider into a nar- 

 rower tube segment through a conical intermediate 

 section. This effect may be utilized to improve the 

 performance of some flowmeters regarding the de- 

 pendence on the velocity profile. 



The pulsatile flow in peripheral arteries is charac- 

 terized by phase differences between the layers oscil- 

 lating at various distances from the axis. Generally, 

 the oscillation of the layers near the axis shows a 

 phase lag in relation to the more marginal zones. 

 While at low frequencies of the flow oscillations the 

 phase lag increases continuously from the margin 

 toward the axis, the inner zones will swing closer in 

 phase to each other when the frequency is raised. At 

 high frequencies, a wide central column of fluid will 

 oscillate uniformly, and the profile of oscillation will 

 approach flatness (93). It is obvious that flowmeters 

 which respond to v^ or to v R are showing, in case of 

 pulsatile flow in peripheral arteries, errors not only in 

 amplitude but also in phase, as will be discussed below 

 with special reference to the pendulum and bristle 

 flowmeters. Only flowmeters responding to v A will 

 deliver records free from such distortions. 



Another point of view is the consideration of the 

 frequency characteristics which a flowmeter must 

 possess to obtain adequate recordings of pulsatile 

 flow. The highest frequencies occurring in the central 

 flow pulse of the dog under physiological conditions 

 amount to 50 to 100 cycles per sec (cps). For record- 

 ing the main features of the central pulse a frequency 

 response up to about 50 cps is sufficient (34, 35). 

 In larger animals and in man the upper frequency 

 limit may be somewhat lower, but it is remarkablv 



higher in small animals. In case of mechanical pickup 

 systems capable of vibrating, the natural frequency 

 should be at least double the highest frequency to be 

 recorded when the system is critically damped. In an 

 electrical system based on a carrier-frequency proce- 

 dure, the carrier frequency must be high enough to 

 reach an adequate band width. Further details will 

 be discussed in the description of the various flow- 

 meters. 



The application of flowmeters to the circulation 

 usually involves a local alteration of the flow condi- 

 tions resulting from insertion of a cannula, from 

 placing an obstacle to flow within the streaming 

 fluid, from constriction of the blood vessel from out- 

 side, or at least from surrounding the vessel with a 

 rigid sleeve. A slight constriction extended over a 

 short length generally will not give rise to objection- 

 able changes of the flow conditions. The factional 

 drop of the mean pressure is often used as a measure 

 of the impediment to flow caused by the flowmeter. 

 It is obvious that the pressure drop should be small 

 as compared to the absolute pressure level. This 

 criterion alone, however, is not sufficient, since an 

 arterial segment which contains an obstacle or is 

 made rigid by an inserted cannula or a surrounding 

 sleeve can change the hemodynamic conditions by 

 causing pulse-wave reflections even if there is no 

 remarkable drop of the mean pressure. For this 

 reason, the length of a rigid segment should not exceed 

 1 cm (93). 



FLOWMETERS BASED ON THE REGISTRATION 

 OF PRESSURE DIFFERENCES 



When a liquid flows through a tube, a pressure 

 differerfce between two points along the tube may be 

 generated by friction and by mass inertia. Whereas 

 the influence of friction results in a pressure difference 

 proportional to the flow velocity, the effect of inertia 

 is causally connected with flow acceleration. Two 

 kinds of acceleration, convective and local, have to be 

 considered. Convective acceleration (dv/dx = change 

 in velocity along the axial direction) occurs in steady 

 as well as in pulsatile flow as a result of variation in 

 cross-sectional area of the tube or bv an arrangement 

 which causes a locally circumscribed stagnation of the 

 fluid or a change of the flow direction. According to 

 Bernoulli's theorem, pressure differences due to con- 

 vective acceleration are proportional to the square of 

 flow velocity. Local acceleration (do dt = velocity 

 change in time, observable at a single point, i.e., 



