PHYSIOLOGY OF AORTA AND MAJOR ARTERIES 



8o 9 



tion of the stress used and the time over which it 

 acted. This has seldom been done. A derived slope 

 obtained by the use of a conveniently large stress, 

 because of the nonlinearity of the stretch curve, often 

 has no counterpart in this curve — the modulus 

 represents a mathematical figure only. 



Evidence presented above leaves room for doubt 

 that the internal structure of a vascular tissue is 

 necessarily the same, just because the unloaded 

 diameter might be restored. This restoration might 

 involve muscle contraction, or it might be due to a 

 passive creep recovery. Even in the latter case, an 

 architectural rearrangement conditioned by the 

 stretch might still be present. We have seen that, with 

 enough load, the contracted ring may start from a 

 smaller diameter but reach the same stretched value 

 as an unstimulated one. Shall we, from the calculated 

 modulus value, deduce that the tissue has been 

 weakened because of the muscle contraction? We 

 have seen that with aging the unloaded diameter 

 tends to increase — an increase which may or may not 

 be at the expense of the elements which condition the 

 major portion of wall extensibility. Here, a calculated 

 modulus value might seem to be evidence for a wall 

 stiffening, which may or may not have developed. 

 In those cases where the slope of the pressure-volume 

 curve remains unchanged, we may seriously doubt 

 that the increased modulus value is an overly mean- 

 ingful index to wall stiffness. 



The claim is often made that the increase in 

 diameter is a way of compensating for a wall stiffening 

 with age. This statement arose from the modulus 

 formula itself. If the ratio of AP/AV remains constant, 

 the volume uptake for a unit length of vessel remains 

 constant, and the change in initial diameter can 

 hardly be said to be a compensation at all. Actually, 

 as will be discussed later, the diameter change will 

 affect the propagation velocity of the pulse wave, 

 which will affect the length of vessel that is receiving 

 volume at any given time interval. Thus, indirectly, 

 some compensation for a wall stiffening might be 

 effected, but it is questionable that this effect can be 

 stated in quantitative terms, and any such formulation 

 certainly would not use the same equation as is used 

 for a modulus calculation. For the time being, it 

 appears essential that before we can talk in meaning- 

 ful fashion about changes in stiffness of the wall, a 

 change in the actual slope of the pressure-diameter or 

 pressure-volume curve alone must be shown. It is on 

 this last point that the evidence on the effect of aging 

 seems to be weakest. 



Since, when one is working with a vessel during 

 life, the stretch does not start from an unloaded size, 

 another modulus has often been substituted, in which 

 the diameter change is related to the real size seen 

 just before the new increment in stress was applied, 

 i.e., the diastolic diameter. This modulus is just as 

 justifiable as that given above, but its value must be 

 quite different. One can be converted to the other 

 arithmetically only if the tension-length relation is 

 linear. Unfortunately, the two moduli have too often 

 been treated as interchangeable. Finally, since 

 changes in pressure and volume are usually the 

 primary data in the living aorta, a modulus based on 

 the pressure-volume relation has been substituted. 

 Conversion of this modulus to that using tension and 

 length is quite complicated. Perhaps the interrelations 

 could be best expressed in terms of their derivations: 



Young's modulus (length) is the applied force per 

 unit area divided by the proportionate length change. 

 For a circumference increase, the area over which a 

 given load is applied will be the length of the ring 

 (/) times the wall thickness (a). The strain will then 

 be the relative increase in circumference, i.e., 2irAr/ 

 2irr, or Ar/r. Since the material is being stretched 

 from an unloaded state, the applied tension will be 

 AT, and r will be r a . 



Thus 



AT 

 Ar 



*Tr 

 Ar 



:d 



If the change in radius and in tension are small 

 enough that they lie on the actual stretch curve, the 

 equation can be written as 



S.OIr*- 



dr 



(2) 



This derivation assumes that there will be no signifi- 

 cant change in length or in wall thickness accompany- 

 ing the radial stretch, which, with large diameter 

 changes at least, is certainly not true, as will be 

 discussed later. 



Now let us suppose that the initial radius is not the 

 unloaded value, but is taken when the tissue is 

 already under stretch. The basic equation would not 

 be altered: 



S -^ 

 ** Ar 



(3) 



