ANATOMY AND PHYSIOLOGY OF THE VASCULAR WALL 



867 



material can maintain a constant tension at any given 

 length for an indefinite time. 



Thus, the term visco-elasticity applies to materials 

 having the combined properties of elasticity and vis- 

 cosity, the elastic action being damped by a viscous 

 one. Such a system is most easily illustrated by a spring 

 which has a brake disc at the top and moves in a 

 viscous fluid. The tension of such a system depends 

 not only on the length but also on the velocity with 

 which it is extended. The tension will be higher the 

 faster it is stretched, and also lower, the faster the 

 stretch is released. When the extension-release cycle 

 of such a system is plotted with tension on the ordinate 

 and length on the abscissa, the graph forms what is 

 called a ''hysteresis loop.'' Two such cycles are shown 

 in figure 2b. The large loop results from a quick 

 stretch cycle, with immediate release, the small loop 

 from a slow stretch cycle. The area between the exten- 

 sion curve and the abscissa is always larger than the 

 area below the release curve. This behavior indicates 

 loss of energy increasing with the velocity of the 

 stretch. More energy is required to stretch such a 

 visco-elastic material than can be recovered during 

 release. The area within the hysteresis loop can be 

 expressed as percentage of the area under the exten- 

 sion curve. It depends only on the velocity with which 

 the system is stretched. Rapid cyclic stretches are 

 called "dynamic stretches," and the shape of the 

 extension-release curves depends on the frequency of 

 the cycles. The hysteresis loop of a pure visco-elastic 

 element will be larger in area, the more frequent the 

 cycles. The hysteresis should vanish if the stretch is 

 made slowly enough, and this is called "static stretch." 

 If the stretched material is purely visco-elastic, it 

 returns, after an extension-release cycle, to its original 

 length. But if it is kept at a constant stretched length, 

 the tension will decrease with time in a hyperbolic 

 manner until it reaches an equilibrium. This process 

 is similar to that shown in the two curves in figure 5. 



A material is called plastic when it shows the tend- 

 ency to retain its new shape after deformation. Plas- 

 ticity is usually understood as the quality of a material 

 which allows it to withstand stresses of less than a 

 critical or yield magnitude without suffering a per- 

 manent set, but which will then allow a viscous 

 deformation with stress above this yield value. The 

 appearance of plastic yield is not time-dependent. 



Viscous or plastic behavior is illustrated in figure 

 ic by a disk which is moved in a viscous fluid. The 

 force required depends upon the velocity with which 

 the disc is moved. The top curve in figure 2c is derived 

 by a quick movement of the disc, the bottom curve by 



a slow movement. As long as the velocity remains 

 constant, the stress will be constant too. If the applied 

 force is removed, the stress decreases without reducing 

 the length. In contrast to the behavior of a visco- 

 elastic element, a viscous or plastic element will never 

 go back to its original shape by itself. 



The systems shown in figure 2a, b, and c are very 

 much simplified models to describe the physical defini- 

 tions of elastic, visco-elastic, and plastic properties. 

 These properties reflect, in organic materials, their 

 complicated molecular structure. In organic materials 

 there is usually a combination of the three qualities 

 described, with elastic, visco-elastic, and plastic prop- 

 erties behaving as though arranged in series, and 

 present in different amount. Such a combination is 

 described by the term "elastic incompleteness." 



For instance, if an elastic and a visco-elastic element 

 are in series, then the element which offers the smaller 

 resistance to extension will dominate the stretch 

 behavior. Since the resistance of the visco-elastic 

 element is greater at high rates of stretch, the prop- 

 erties of this series combination is determined more 

 by the elastic element. The more frequent are the 

 stretch cycles, the less is the hysteresis. If there is also 

 a purely viscous or a plastic element in series, after 

 every stretch cycle the material assumes a greater 

 length. There is also the possibility that many visco- 

 elastic and viscous elements may be in series, each 

 having a different rate- and time-dependency. Such 

 combinations of elastic, visco-elastic, and plastic 

 elements can show a very slight rate-dependency, if, 

 for instance, the elastic element offers the smallest 

 resistance to stretch when compared with the other 

 elements present. Because of the visco-elastic or plastic 

 units, the system may show a great time-dependency, 

 which occurs as an elastic aftereffect or a relaxation 

 when the material is kept on a constant stress or 

 length. 



The viscosity of organic materials may not only 

 derive from a viscous flow within the tissue, but also 

 from an architectural reanangement involving the 

 uncoiling or slippage of twisted elements. Such proc- 

 esses may be involved in the phenomenon of the 

 "stable loop" seen in elastic arteries after a number of 

 stretches, which does not show any rate or time- 

 dependency but does depend on the existing tension 

 level [Remington (73); see also Chapter 24]. The so- 

 called viscosity or plasticity of organic materials may 

 be complicated, and thus not follow the physical 

 definitions. Further, there is usually a certain polarity 

 to these tissues in that tension-length relations are 

 different in various directions. Most organic materials 



