8l6 HANDBOOK OF PHYSIOLOGY ^ CIRCULATION II 



fig. 5. A reconstruction of the arterial reservoir of the dog. [From Remington (94).] For 

 description, see text. 



no longer produce a constant pressure in the upper 

 end. The lower part of the tube will require less fluid 

 to construct the same pressure rise. Hence the pressure 

 in the pump will continue to rise as the wave front 

 moves through the tube, the pressure rise being a 

 function of the distensibility of the lower part of the 

 funnel. This increased pressure at the upper end will 

 also be propagated, so that we are now creating a 

 whole pressure wave. 



Quantitation of Fluid Displacement and ]Vall 

 Distensibility Relationships 



The propagation of the wave front is really the 

 same as the initial displacement of fluid from segment 

 to segment in the tube. The rate of this displacement 

 should be a function of wall distensibility, and it 

 should be possible to formulate the relationship in 

 quantitative terms. This is another case where the 

 textbooks have such a formula so well established 

 that it has assumed the nature of a physiological law. 

 The supporting evidence is far from adequate. 

 Discounting all friction and other resistance factors, 

 Korteweg presented a theoretical formula, and Moens 

 (see 46), working independently, arrived at almost 

 the same formula on the basis of experiments done 

 with various distensible tubes. The latter used arti- 

 ficial waves which were relatively slow in their rate of 

 pressure rise, and he used not the first part of the 

 pressure wave for his measurements of wave velocity, 

 but the time interval between successive peaks as the 

 whole wave was propagated back and forth through 

 his closed end system. His formula differs from that 

 of Korteweg in that he had a constant of 0.9. We 

 have shown (46) that the velocity of the peak of such 



artificial wave is less than that of the start, by a 

 factor not greatly different from Moens' constant. 

 Using the Korteweg formula, then, the velocity of the 

 wave foot (v) is related to an "elastic modulus" (E) 

 of the tube, and the density of the contained fluid 

 (p), thus: 



. g_Ea_ 

 2r/> 



where g is the gravitational constant and a is the wall 

 thickness. Neglecting hysteresis, E would be the same 

 as Sd of equation 4 derived above. Hence by sub- 

 stitution: 



,2 - 



gadTr d gadT 

 2t ■ />dr ' 2/>dr 



(15) 



If p is regarded as a constant, and given the value of 

 1 .055 for blood, and a is taken as unity, then 



2 . 9.3dT ' _ 4.65 dT ' 

 ' 2dr dr 



where T' is the tension per unit length of tube. 

 Similarly, from equation 8: 



s _ godPrf 4.65 d Pr d 



and from equation 1 2 : 



(16) 



dr 



(17) 



.2 = 



ga2dPV d r d _ 9.3dPV d 

 2r d/ >adV dV 



(18) 



This equation 18 is the same as that derived by 

 Bramwell & Hill (15) and has since borne their 

 name. They further corrected the constant by multi- 

 plying it by the weight of mercury, so that pressure 



