94 HANDBOOK OF PHYSIOLOGY ^^ CIRCULATION I 



160. 



120. 



TRYPSIN 



FRESH 



'100 



120 



INIT 



140 ' 160 



CIRCUMFERENCE 



180 



FIG. 1 1 . Tension-length diagrams for the wall of human iliac 

 arteries, after selective digestion of elastin fibers (trypsin), of 

 collagen fibers (acid). [From Roach & Burton (23).] 



ID. THE REASON FOR THE SHAPE OF ELASTIC 

 DIAGRAMS OF BLOOD VESSELS 



Unttretched length 



termi of eiongotion. e. 



FIG. 12. A: the first diflferential of the elastic diagram, 

 giving the "elastance" at each degree of stretch. B: the second 

 diflferential of the elastic diagram (first differential of .-1 ) giving 

 the histogram of number of collagen fibers vs. degree of stretch. 

 [From Roach & Burton (23).] 



Why does the vessel wall resist stretch more strongly 

 the greater its stretch? In the case of human iliac 

 arteries (from autopsy), the reason for this behavior 

 has been proved to be a result of the heterogeneity 

 of the wall, and is evidence of the separate roles of 

 elastin and collagenous fibers (23). When the col- 

 lagenous fibers are removed by digestion with crude 

 formic acid (fig. 1 1 ) the remaining elastin fibers obey 

 Hooke's law over a wide range. When, in contrast, 

 the elastin fibers are selectively digested (by crude 

 trypsin) the remaining collagenous fibers also obey 

 Hooke's law over a wide range except for the start 

 of the curve. The much steeper slope is equal to the 

 final slope of the original graph. The final slope of 

 the elastic diagram of the artery denotes that all of 

 the collagenous fibers have reached their unstretched 

 length, whereas the low initial slope, for very small 

 stretch, represents the elasticity of the elastin fibers 

 plus a few of the collagenous fibers that are "tightly 

 strung" in the wall. The upturning of the curve thus 

 is an indication of successive "recruitment" of strong 

 collagen fibers, as they successively reach their 

 respective unstretched length. Indeed, by plotting 

 the second differential of the elastic diagram (i.e., 

 (PT/dP) vs. degree of elongation e (fig. 12) we can 

 derive a histogram of the number of collagenous 



fibers, vs. the degree of elongation in the wall before 

 their unstretched length is reached (24). The changes 

 in this diagram with age of the arteries are most 

 illuminating, showing that the process of aging is 

 accompanied, not only by an increase in the total 

 number of collagen fibers in the wall, but even more 

 importantly by a tightening up of these fibers so 

 that they are brought into action by a much smaller 

 degree of stretch of the wall. Full explanation of the 

 analysis is given in the papers cited. 



I I . GR.'^PHICAL METHOD FOR THE EQUILIBRIU.M 

 UNDER ELASTIC TENSION ALONE 



Since we can confidently assume the shape of the 

 tension-length diagram of the blood vessel wall, i.e., 

 that the slope increases as the stretch is increased, 

 we can examine the stability of the equilibrium of 

 the vessel under the transmural pressure (fig. 13). 

 The curved line represents the relation between 

 elastic tension and stretch (i.e., the elastic diagram). 

 For equilibrium we must have the law of Laplace 

 (equation 6, 7" = Ptm X r), which is represented by a 

 straight line through the origin, the slope of which 



