PHYSIOLOGY OF AORTA AND MAJOR ARTERIES 



8l 5 



Matching with the resonant characteristics of the 

 fluid-filled tube could be either with the fundamental 

 wave or one of the prominent harmonics. 



Use of the same pump coupled to a distensible tube 

 of uniform bore and wall extensibility will present a 

 somewhat different pattern. Because the wall can 

 yield, a large part of the energy imparted by the 

 piston can cause an increased tension in the tube wall. 

 It is no longer necessary to construct a pressure 

 sufficient to overcome the resistance of the whole 

 fluid column, for as soon as the fluid resistance to 

 displacement in the first small segment of tube is 

 overcome, piston movement can displace volume 

 into this segment. The pressure energy of this fluid 

 will go into a stretching of the walls of the segment. 

 If the wall extensibility is great (as with condom 

 rubber), the first segment could accomodate all the 

 fluid displaced from the pump, and there would be 

 no appreciable pressure rise in the tube and no flow- 

 through its length. It might be pointed out that the 

 molecular movements in this wall stretching are 

 directed toward the side of the tube, so that the 

 displacement pattern is more like that of turbulent 

 flow in a rigid pipe than that of streamline flow. 



If the tube is less distensible, only part of the fluid 

 compression transmitted to the first segment will 

 go to produce wall extension, for the fluid must 

 retain enough pressure to prevent the elastic recoil of 

 the stretched walls. This erects a pressure differential 

 between the first and next segment of tube, a differ- 

 ential related to wall elasticity (which need not be 

 identical with wall extensibility) and the fluid re- 

 sistance of the second segment. When the differential 

 becomes larger than the resistance, fluid displacement 

 will follow. In a tube of uniform distensibility, then, 

 except for the frictional energy dissipation, the same 

 volume will be accepted, per unit length of time, by 

 each successive tube segment as the first part or front 

 of the wave moves through the tube. Hence, if the 

 piston displacement is linear against time, the pressure 

 in the pump and the upper part of the tube will 

 simply remain constant, since all the pump outflow 

 will be taken to establish the wave front as it moves 

 from segment to segment through the tube. This 

 pattern of a constant pressure can be demonstrated 

 in a rubber-tube model. As the pressure front moves, 

 flow through the stretched segments behind it will 

 be streamlined. While the frictional cost of such 

 movement will be small, the further the wave pro- 

 gresses the greater will be the cumulative energy- 

 dissipation. This analysis also means that once fluid 

 displacement into the first tube segment occurs, the 



first part of a pressure wave has been created. This 

 wave will continue to move through the tube whether 

 piston movement continues or not. Further piston 

 movement does act to support the later parts of the 

 wave, or to broaden it in time. 



A sinusoidal piston movement leads to a rising and 

 falling pressure in the upper end of the tube. This 

 produces a pressure wave, positive or negative, which 

 is propagated back and forth through the tube. No 

 matter in which direction waves may be traveling 

 through the tube, the pressure in any one tube segment 

 at a given time simply reflects the balance between 

 the amount of fluid entering it and that leaving it. 

 The extensible tube should show a phase lag, too, 

 but since only tiny segments of tube, acting more or 

 less independently, presumably are involved, the 

 resistance to fluid movement out of the pump should 

 be very small. Hence a phase lag should also be 

 small. It is well to note here that the loss in pressure 

 in the aorta, due to frictional dissipation, is within 

 the error of recording. 



Our model of a tube with uniform distensibility has 

 no counterpart in the arterial bed. Figure 5 shows 

 four drawings taken from an earlier analysis of this 

 problem (04), based primarily on the extensibility 

 values given by isolated rings. That on the upper 

 left depicts a part of the arterial bed of a dog, drawn 

 to scale in respect to anatomical length and cross- 

 sectional area at a pressure of 100 mm Hg. But in 

 describing fluid displacements, we are more concerned 

 with the propagation time of the pulse wave through 

 a region than we are with actual length. The natural 

 pulse wave moves slowly in the upper aorta, more 

 rapidly in the lower aorta, and faster yet in the 

 large arteries (10, 24). Suppose we redraw the figure 

 so that the length now represents the distance tra- 

 versed by the wave in a unit length of time (lower 

 left). Next, since the pressure rise in the parts of the 

 bed will be set by the segmental distensibility (ne- 

 glecting wall hysteresis), let us redraw the figure 

 (upper right) letting the assigned width represent the 

 distensibility, expressed as AF/AP, rather than the 

 cross-sectional area. Lastly, if frictional resistance is to 

 be discounted as of small amount, we can neglect the 

 effect of tube diameter per se, and group together 

 into a single composite tube all vessels which might 

 lie at the same time distance from the heart (lower 

 right). Such a theoretical tube has a funnel shape, 

 distensibility being great in the top (ascending aorta) 

 and tapering down gradually to the stiff vessels that 

 are farthest from the heart, those of the hind legs. 



A linear piston displacement into such a tube will 



