PHYSIOLOGY OF AORTA AND MAJOR ARTERIES 



833 



existing pressure level does not remain constant during 

 a prolonged diastolic period (25). It is difficult to 

 generalize about the factors which contribute to the 

 height of the diastolic oscillations. When the pressure 

 is raised to hypertensive levels, the postincisural 

 hump of the central pulse is usually much less con- 

 spicuous. This is due in part to the fact that it is 

 then superimposed upon a part of the pressure curve 

 which falls much more steeply, since the vessel 

 distensibility is decreased in the high pressure range. 

 It is much more probable that the relatively small 

 size of the hump is a result of the fact that it starts 

 near the time of the incisura (or even before), because 

 the propagation velocity of the returning wave is 

 more rapid. Conversely, at low aortic pressures, the 

 postincisural hump of the central pulse may be quite 

 conspicuous. This is partly because the basic diastolic 

 slope is so shallow that any pressure increase is 

 clearly evident, and partly because the frequency of 

 the "'resonant" oscillations is decreased, so that the 

 swell comes later in diastole; also, it may be due partly 

 to an actual augmentation of the swell itself. 



Calculation of the Stroke Volume From 

 the Central Pressure Pulse 



On the theory that the aorta achieved immediate 

 resonance, which means that the time interval be- 

 tween two successive pressure oscillations on all 

 peripheral pulses would be the same and would be 

 an index to the length and distensibility charac- 

 teristics of the aortic reservoir, Frank (30) regrouped 

 a formula similar to that of Bramwell and Hill to 

 have it express the total distensibility of the whole 

 resonant system. Hence where v is the pulse wave 

 velocity, --1 the cross-sectional area of the bed, L 

 its length, p the specific gravity of blood, and AP/AV 

 the slope characterizing the system distensibility : 



ALAP 

 AV 



(21) 



With the simplifying assumption that AP AV remains 

 constant throughout the range covered by a given 

 pulse, we can, with extreme reservations, take AP to 

 be the recorded pulse pressure, and AV the cor- 

 responding volume change. This assumes that the V 

 for a given vessel would have a fixed relationship to 

 the volume gain by the whole arterial bed. Re- 

 arrangement of the formula gives: 



Since the time interval between successive pressure 

 peaks is assumed to be that required for the pulse 

 wave to make a round trip through the system, T = 

 1 L/v, or L = Tv/2. Substituting in the formula 

 then gives: 



AV -" 



ATvAP 



2/>v' 



ATAP 

 2pv 



(22) 



AV 



ALAP 



pv* 



German workers have continued to use the Frank 

 formula, or modifications of it. These formulas have 

 received only restricted support in this country (124). 

 While they may, perhaps, predict in reasonable 

 degree the volume input into a rubber tube where 

 the distensibility is uniform through the tube length, 

 their use with the complicated arterial bed requires 

 very large assumptions. First, there is the inference 

 given above that the AP/AV relation for any single 

 vessel is indicative of the relation for the whole 

 reservoir system. Second, A does not represent the 

 area of any single vessel, but rather that of a hy- 

 pothetical tube which happens to have the same 

 dimensions as the mean of the whole reservoir net- 

 work. Attempts have been made to take values for 

 A from autopsy data, using the upper aorta, which 

 certainly would not have the same dimensions as 

 this mean. Further, autopsy data give a diameter at 

 near zero pressure and not that at a physiological 

 pressure. Third, since AV is the volume stored in the 

 Windkessel during systole, it is not directly measur- 

 able. If a calculation is made for the drainage loss 

 during systole (and various formulas have been pro- 

 posed for calculating this loss), then the stored volume 

 plus the calculated drainage loss would equal the 

 stroke volume, which can be measured directly only 

 under restricted conditions, but which is usually 

 taken from a cardiac output determination. Fourth, 

 L, the length of the reservoir network, cannot be 

 directlv measured. As described earlier, it has instead 

 been calculated from the length of the resonant 

 wave, as indicated by the time interval between 

 successive pressure peaks of a peripheral pulse. This, 

 of course, assumes that the reflecting end of the 

 system is also the end of the Windkessel. The estima- 

 tion of wave velocity and of the time interval between 

 pressure peaks, by the techniques employed, leaves 

 room for doubt as to the validity of any strict quan- 

 titation. 



If the stroke volume could be directly measured, 

 it might be that the various unknowns could be 

 combined into a single constant. Its value, however, 

 would apply only at the diastolic pressure for which 

 it was derived, only if neither A nor L was subject 



