96 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



human iliac arteries found a value for the maximum 

 Young's Modulus (from the final slope of elastic 

 diagrams) of 7 X 10" dynes per cm- per 100 per 

 cent stretch, for vessels of age 30, and 1.8 X 10' for 

 age 80. The thickness of the wall was 0.7 mm, the 

 radius 3.5 mm. Taking the smaller value for the 

 modulus, blowout would occur at a pressure given 

 by: 



7 X io« X 0.07 

 0-35 



= 1.4 X 10" dynes/cm^ 



Since 1.3 X 10' dynes per cm- equals a pressure of 

 I mm Hg, this is equivalent to over 1000 mm Hg. 

 It must be concluded that blowout in normal arteries 

 would never occur except at blood pressures at least 

 10 times the normal values (it was actually found 

 that pressures of 900 mm Hg did not burst these 

 iliac arteries). However, when disease has weakened 

 the wall, blowout may occur at lower pressures. 



Laplacian line intersects the horizontal line, repre- 

 senting the constant "active tension" at point .4, 

 which represents a possible equilibrium at radius r 

 for the vessel. However, it is easily seen that this is a 

 completely unstable equilibrium. If the radius were 

 to increase to r + \r, the tension required for equi- 

 librium would be the ordinate of point B, i.e., greater 

 than the tension existing in the wall. The pressure 

 would then continue to increase the radius indefinitely. 

 Similarly, a decrease in radius would result in the 

 active tension exceeding the tension required for 

 equilibrium (point C) and the radius would further 

 decrease. Such complete instability is easily shown 

 in soap bubbles if the pressure within them is kept 

 constant. (A closed, isolated soap bubble is rendered 

 stable because the pressure within automatically 

 falls as its radius increases, by Boyle's law.) If the 

 bubble is connected to a large reservoir of air under 

 pressure, so that the pressure remains practically 

 constant, or if the pressure is otherwise kept constant, 

 a soap bubble is unstable. 



13. EQLriLIBRIUM UNDER ACTIVE TENSION ALONE 



This is a hypothetical situation, where a vessel 

 wall possessed negligible elasticity, but due to active 

 contraction of smooth muscle had an active tension 

 that was independent of the degree of stretch. The 

 sphincters of the gut, and probably the "glomus- 

 bodies" controlling flow through the arterial-venous 

 anastomoses of the stomach vessels, and of the skin 

 of the fingers and toes, possess very little elastic tissue 

 but much smooth muscle. They would approach this 

 case, but of course have some elasticity. (The surface 

 tension in a soap film is the extreme situation of a 

 tension that is independent of stretch of the surface.) 

 Figure 14 shows this situation graphically. The 



I 4. EqUlLIBRIUM UNDER ELASTIC TENSION PLUS 

 ACTIVE TENSION 



When, as in the real situation of a blood vessel 

 wall, both elastic tension, a function of stretch, and 

 an active tension independent of stretch are present, 

 the situation is shown by figures 15 and 16. These are 

 alternative ways of showing the conditions for equi- 

 librium graphically, of which figure 15 is perhaps 

 more enlightening. As in figure 13, the curve for 

 the elastic tension only is shown, with the Laplacian 

 line drawn for the particular transmural pressure of 

 the vessels. The intersection, at point A, represents 

 the equilibrium under elastic tension alone, with 



Radius r-^ "2 Ri 



FIG. 15. Equilibrium under both active and elastic tensions. First method. [From Burton (5).] 

 FIG. 16. Equilibrium under both active and elastic tensions. Second method. [From Burton (5).] 



Radius r- 



