92 HANDBOOK OF PHYSIOLOGY "^ CIRCULATION I 



F/A 



ML 



FIG. 7. Illustration of Hooke's law. F/A — Elastic force per 

 unit area of cross section; Lo — unstretched length. Homoge- 

 neous materials eventually reach a "yield point" and give 

 completely when a "breaking stress" is reached. 



9. ELASTIC TENSION IN THE WALL 



Elasticity is the property of matter by which it 

 dev^elops a force resisting deformation. For simple 

 homogeneous substances the relation between the 

 force and the amount of deformation is linear, obeying 

 Hooke's law. This law is that the force F per unit 

 cross section area (as of a steel wire) is proportional 

 to the elongation (lit tenso, sic vis), i.e., the difference 

 between the stretched length, /, and the "unstretched 

 length," /o. The relation is, in modern terms: 





 160-1 



120- 



ao- 



40- 



2 



z 



n 



o 



z 



z 

 o 



(A 



z 



80 



AORTA 



VENA CAVA 



Pressure in cms h^o 

 I I ■ ' ' ' 



160 



200 



16 



20 



2 3 4 5 



Radius or vessel 



FIG. 8. A: volume-pressure curves of aorta and vena cava 

 (after Green). B: the same data transformed to give the elastic 

 diagrams. [From Burton (5).] 



(■7) 



Y is the Young's modulus of elasticity. The linear 

 law of Hooke is only appro.ximate, even for such 

 materials as steel or rubber, since as the material is 

 stretched in one direction the cross-sectional area is 

 necessarily reduced (fig. 7). Its application is also 

 limited, for if the stretched length exceeds a certain 

 point, called the "yield point," the material "yields" 

 or "flows" and will not return to its original un- 

 stretched length when the elongating force is re- 

 moved. For details any physics text on elasticity 

 may be consulted, as also for the connection between 

 Young's modulus and the two fundamental moduli, 

 namely the "bulk modulus," resisting change of 

 volume of the material, and the "shear modulus," 

 resisting change of shape. 



As early as 1880, Roy (22) investigated the elastic 

 behavior of the wall of arteries, and there have been 

 many measurements of this since. Roy used the direct 

 method of cutting a strip from the wall and measuring 

 its length under different loads. Better methods are 

 to use circular rings of arteries or to deduce the 

 tension vs radius from the volume-pressure rela- 

 tions of a segment of artery or \cin, by the use of 



the law of Laplace (equation 6). Details have been 

 discussed elsewhere (21), but the principle is simply 

 that from the volume, T, in a given length of tissue, 

 the mean radius can be calculated {V = vr-l). The 

 total tension in the wall can then be calculated as 

 equal to the product of the pressure, P, and the 

 radius, r, i.e., T = P X r. Figure 8 is an example of 

 such a transformation from volume-pressure curves 

 to tension-length diagrams, for the aorta and the 

 vena cava from classical data of Hallock and Benson. 

 Though the volume-pressure curves may have very 

 different shapes, as for aortas of different ages (fig. 9), 

 the tension-length diagrams are all of the same char- 

 acter, agreeing with what Roy found. There are 

 also more indirect methods, such as that of measure- 

 ment of pulse-wave velocity in long arteries, which 

 can estimate the elastic constants of arterial walls, 

 using the relation between pulse-wave velocity and 

 distensibility developed by Bramwell et al. (3). 

 All these methods thus give the same result, that 

 the resistance to stretch of the vessel wall (Young's 

 modulus) increases markedly the inore the wall is 

 stretched. The elastic diagratn (e.g., fig. 8) shows a 

 curve that turns upward instead of obeying Hooke's 

 law which, as explained already, is a straight line. 



