PHYSIOLOGY OF AORTA AND MAJOR ARTERIES 



would be in terms of mm Hg. Hence their formula 

 reads : 



# 12.7 VdP 

 dV 



Bramwell and Hill did not use the first slope to 

 determine dP and dV, but appreciable increments in 

 pressure and volume instead. Commonly the pressure 

 increment is taken to be the pulse pressure, which 

 strains the use of even AP. Because our methodology 

 is not adequate to give dP and dV values, we have 

 no right to use the above equations. If, instead, the 

 formula is derived from equation 1 1 : 



e gaAPvj2r d + 3Ar + %. ) 

 2r d/ ,aAV 



. 12.7 AP V d (r d + 1.5 Ar + 0.57T ) 



AV 



(19) 



Actually, Ar z /rd is so small it can be practically- 

 neglected, so that 



.i - 



Ar 

 12.7 APV d (l + l.5~) 



AV 



(20) 



Validation of these formulas has centered on the 

 Bramwell and Hill equation. The earlier results, 

 which have been reviewed (46), offer no clear evi- 

 dence that the velocity of artificially generated or 

 natural pressure waves shows either a quantitative or 

 qualitative agreement with values predicted by the 

 formula, when it is applied to stretch data taken from 

 isolated vessels. The solid line of figure 6 shows an 

 average relation of pulse wave velocity to diastolic 

 pressure for some 200 pulses of a living dog, taken 

 from the aortic arch to the diaphragm. The broken 

 line shows the velocity calculated, using equation 

 19, from the continuous second stretch curve given 

 in figure 3. Agreement is certainly not good. If the 

 mean slope for each loop given in figure 3 is used 

 instead, then, as shown by the dotted lines, agreement 

 with the actual becomes qualitatively better, with 

 equation 20 giving a better fit than ig. But the mean 

 slope can have little significance as far as the propaga- 

 tion velocities of the parts of a wave are concerned. 

 The speed of the wave front should be dictated by 

 the slope taken at the beginning of the stretch phase 

 of the loop. Calculation from these initial slopes, 

 using equation 19 (which is here valid), gives the 



125- 



100' 



50 



Pulse wave velocity, M / Sec 

 1 r 



5 6 7 8 



fig. 6. Relation of pulse wave velocity to diastolic pressure. 

 Solid line, actual values from a living dog. Broken line, calcu- 

 lated (eq. 19) from continuous stretch curves of fig. 3 Dotted 

 line, closed circles, calculated (eq. 19) from mean slopes of 

 loops shown in fig. 3. Dotted line, open circles, calculated (eq. 

 20) from mean slopes of loops of fig. 3. Crosses, calculated (eq. 

 19) from initial slopes of stretch phase of loops of fig. 3. 



unconnected crosses of figure 6. These velocities are 

 greater than the actual by 10 to 20 per cent. 



In our earlier study (103), in which we compared 

 a curve such as the broken line of figure 6 (based, 

 however, upon a careful compilation of the stretch 

 curves of all rings, taken in sequence, from the aorta 

 being studied) with the actual, we believed that the 

 underestimation would be correctable by using the 

 slopes resulting from a hysteresis steepening of the 

 first part of the stretch curve. The loops obtained in 

 this earlier study were not numerous, and we did not 

 attempt any quantitative verification of this belief. 

 Further, and unfortunately, in this study we used 

 both a rubber tube and the excised aorta, leaving the 

 implication (although it very definitely was never 

 stated) that the two behaved similarly. With rubber, 

 the initial slope of the stretch phase of a loop proved 

 clearly dependent on the rate of stretch. In keeping, 

 the propagation velocity of artificial pulses through a 

 rubber tube was found to be directly related to the 

 rate of initial pressure rise. But with the aorta, using 

 either artificial or natural pulses, there was no similar 

 relation between the rate of pressure rise and the 

 wave velocity. My more recent evidence (96) that a 

 dependency of the aortic stretch curve upon the rate 

 of stretch is minor is quite compatible with this 

 finding. 



A calculated velocity for the wave start, in excess 

 of the actual velocity, may be explained by four 



