I04 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION 



It is obvious that results from these three methods 

 cannot all be linearly related to active tension, for a 

 plot of change of resistance vs. concentration of 

 drug is of very different shape according to whether 

 constant pressure or constant flow is used. It was 

 shown by the experiments that the method of constant 

 flow gave results that were remarkably linear, except 

 near the origin (fig. 20), with the active tension 

 measurements (by the null method). In contrast, 

 measurements of changes of resistance with constant 

 pressure perfusion were completely nonlinear (in- 

 deed, when the active tension reaches the critical 

 value, the increase of resistance becomes infinite). 

 Theoretical justification for this astonishing and 

 convenient result is given in the original publication 

 (g), which should be consulted for details. 



It seems therefore (though other vascular beds 

 might be different from the rabbit ear) that to obtain 

 a practical measure of the degree of active tension in 

 vascular smooth muscle, the method of constant 

 flow perfusion should be used, where this is possible. 

 On the other hand, where the greatest sensitivity 

 for qualitative assay of vasoactive drugs is desired, 

 the method of constant pressure perfusion is much 

 to be preferred, particularly if the conditions can 

 be such that the vessels are close to their critical 

 closing state, when the sensitivity to vasoactive 

 agents is very high indeed. 



muscle might approach this case, though the elasticity of the 

 smooth muscle itself could not be ignored. The ventricular wall 

 of the heart, during systolic contraction, might also approach 

 this case, though, as Rushmer et al. (25) have shown, the con- 

 siderable elasticity of the fibers between the layers of muscle is 

 of great importance in the heart's action. 



Considering the tension T' , to be constant through the 

 wall equal to T\ we have : 



P = 



!'■ 



■ T'lm + c 



(2) 



where C is the constant of integration. Inserting into this 

 equation the boundary conditions, i.e., that for r = Ti , P = 

 Piv , and for r = r„ , P = P, , yields the relation for the pres- 

 sure Pr at radius r. 



Piv 



log r„/ri 



log r/r,-. 



(3) 



The pressure through the wall thus falls off in a logarithmic 

 curve. Actually the gradient will not be very far from linear, 

 even where the artery is very thick-walled, as in arterioles 

 (thickness of wall equal to half the radius of lumen). Here we 

 have : 



log r/r, = 0.1761 X 



Pr 



(4) 



This shows that for the pressure to have fallen to three-fourths 

 of the intravascular pressure (P,,. — P,)IPtm = 0.25, rln 

 will be I.I I, i.e., the pressure falls by 25 per cent of its value 

 in the innermost 22 per cent of the wall. Similarly it falls to 

 50 per cent in the inner 45 per cent, and by 75 per cent in the 

 inner 71 per cent of the thickness of the wall (fig. 21). If the 



APPENDIX 



PRESSURE GRADIENT THROUGH THE VESSEL WALL 



As explained in section 6, the law of Laplace applies across 

 each successive coaxial shell of the wall, and integration of the 

 equation: 



dPIdr 



T,'/r 



(l) 



will give the way in which the pressure falls through the thick- 

 ness of the wall. The integration is easily made for idealized 

 cases, but the actual case has so many complications that only 

 understanding of the general trends in the solution is worth 

 while. Details of the mathematical solutions are given else- 

 where. Only the general result is important. 



Case i: Active Tension Only in the Wall 



This is a purely hypothetical case, since, as has been shown, 

 without automatic adjustment of tension to stretch, a cylindri- 

 cal vessel is completely unstable. However, a very muscular 

 small artery maintained in strong contraction of the smooth 



20 



40 



60 



80 



100 



FIG. 2 1 . Calculated fall of pressure in the wall of an artery, 

 with a transmural pressure of 100 mm Hg. For all curves it is 

 assumed that the elasticity is uniformly distributed through 

 the wall, ^-l.- on the basis of Hooke's law. B: on the basis of the 

 experimentally determined nonlinear elasticity of young arteries 

 (20-40 years). C: for old arteries (60-80 years). 



