PHYSICAL EQUILIBRIA OF HEART AND VESSELS 



93 



z 



UJ 



_l 



u 



2 



Z2- 



3 



50 



100 



150 



200 



U-; 



Length of fibers 



30 



40 



50 



60 CMS 70 



FIG. g. A : volume-pressure curves for human aortas of different age groups (after Hallock and 

 Benson). B: same data transformed to give elastic diagrams. [From Burton (5).] 



NCE VS P. 



RADIUS VS P. 



MM, ^*-->>--'^--«.--«i- 



© 



Tm 



.<. -y-y-x- 



I TENSION VS RADIUS 



4- i 



3- 



2- 



40 60 80 



10 20 30 40 10 20 30 40 I 



FIG. 10. A: typical flow-pressure curves of a vascular bed (rabbit leg). Broken curve — without 

 vasomotor tone: solid curve — with tone produced by sympathetic stimulation. B: resistance cal- 

 culated from same data. C: radius, in arbitrary units of a single equivalent vessel giving the re- 

 sistance. D: tension-length diagram, in arbitrary units, for the wall of that single equivalent vessel. 



or eventually turns downward at the yield point 



(fig. 7)- 



There is evidence that the same generalization 



applies to the elastic behavior of the smaller vessels 

 such as the arterioles, which offer the important 

 resistance to flow in the circulation. From the flow- 

 pressure relations of a vascular bed (fig. io.4) a 

 calculation of the resistance to flow, as pressure-to- 

 flow, can be made for different transmural pressures 

 of these vessels, since the pressure in the resistance 

 vessels will be approximately the mean of arterial 

 and venous pressures, if most of the resistance is in 

 these vessels." Thus the resistance may be plotted vs. 

 the transmural pressure (fig. lofi). If now the Poi- 

 seuille formula for the resistance is used and changes 

 in length of the vessels are ignored (the resulting 

 conclusion would not be invalidated if the changes 



- If this "lumped parameter" theory is permissible, the 

 transmural pressure of this single equi\'alent vessel will be 

 AP/2, for venous pressure near zero. 



in length were significant), the relative changes in 

 radius can be deduced (i.e., r cc i //?"'') as in figure 

 loC The tension in the wall of the resistance vessels 

 must be, by Laplace's law, equal to the pressure 

 times this radius {Tc = Ptm X r). Thus from the 

 original flow-pressure curve we can deduce the 

 shape of the tension-length diagram for the wall of a 

 "single equivalent vessel" representing the arterioles 

 (fig. loD). A curve results which turns upwards, 

 i.e., the resistance to stretch increases, as the wall is 

 more stretched. All flow-pressure curves of va.scular 

 beds (with the exception of that of the kidney where 

 there is "autoregulation," probably due to some 

 reflex effect) that have been analyzed by us from 

 data in the literature show the same shape of re- 

 sistance vs. pressure curves, so the generalization 

 about the elasticity of arteries and veins seems to 

 apply also to the small vessels that offer the major 

 part of the resistance to flow. 



