Despite the abundant literature on blood vessel mechanical properties, blood vessel constitutive models are far less common. Blood vessels are nonlinear, anisotropic and viscoelastic, heterogeneous in the unloaded state and compressible when studying macroscopic characteristic and they behave differently in different temperatures. Despite the long list of attributes, constitutive equations generally account for only a subset of these characteristics.
In general, blood vessels can be treated as pseudoelastic, randomly elastic, poroelastic or viscoelastic . Pseudoelasticity assumes that a material can be modeled using separate equations describing the loading and unloading behavior. Random elasticity, however, assumes that the strain response for a given load is rendered around a definite value that lies on a well defined curve, such that data from both the loading and unloading curves can be included simultaneously. Poroelastic formulations treat a material as a fluid-saturated porous medium and are well suited to model wall transport. Viscoelastic formulations include time-dependent responses in the constitutive equation and are useful for modeling creep, stress relaxation, and hysteresis. Useful reviews are available, concerning the biomechanics of soft biological tissues :
Vito, R.P. and S.A. Dixon, Blood vessel constitutive models-1995-2002. Annual Review Of Biomedical Engineering, 2003. 5: p. 413-439.
Humphrey, J.D., Continuum biomechanics of soft biological tissues. Proceedings: Mathematical, Physical and Engineering Sciences (Series A), 2003. 459(2029): p. 3-46.
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