Mechanical Properties and Active Remodeling of Blood Vessels

Abstract

Blood vessels belong to the class of soft tissues discussed in Chapter 7. They do not obey Hooke's law. Figure 7.5:1 in Chapter 7, Sec. 7.5 demonstrates the nonlinearity of the stress---strain relationship and the existence of hysteresis. They also creep under constant stress and relax under constant strain. These mechanical properties have a structural basis. In Sec. 8.2 we consider the structure of the blood vessel wall. From Sec. 8.3 on, however, our attention will be concentrated on the mathematical description of the mechanical properties. In seeking simplification whenever it is justifiable, we take advantage of the fact that most blood vessels are thin-walled tubes deforming axisymmetrically (including inflation, longitudinal stretching, and torsion), and that as far as hemodynamics is concerned, we need to know only the relationship between the blood pressure and the inner diameter of the tube. In this situation we may treat the vessel wall as a membrane. The stresses of concern are circumferential and longitudinal, the principal strains are also circumferential and longitudinal. The vessel wall may be treated as a two-dimensional body, the constitutive equation is biaxial. In Secs. 8.3--8.5, we formulate a two-dimensional quasi-linear viscoelastic constitutive equation for blood vessels, using the pseudo-elasticity concept introduced in Chapter 7. In Secs. 8.7 and 8.8, we treat the blood vessel wall as a three-dimensional body, and study the differences between the mechanical properties of the intima-media layer and those of the adventitia. The results can then be applied to general three-dimensional problems such as bifurcation, aneurysm, surgery, etc. In Secs. 8.9--8.11, we consider the mechanical properties of arterioles, capillary blood vessels, and veins.