Constitutive modeling of the mechanical response of arterial tissues

Despite the tremendous impact that a good constitutive relation for the response of arterial tissues can have with regard to advances in cardiovascular science and medicine, and notwithstanding the intense effort to put a felicitous constitutive relation into place, no reliable constitutive relation is available in the literature. In this review article, we provide a brief survey and assessment of the evolution of constitutive relations that have been developed to describe the response of arterial tissues, their inadequacies, and the various quintessential aspects of the response that need to be taken into consideration. We then fashion a nonlinear constitutive relation to describe an inhomogeneous anisotropic compressible viscoelastic solid, which while being grossly inadequate to describe the tissue in its entirety, makes it evident that what one ought to strive for is not in capturing the complexity of tissues, but rather the development of a simple global measure that can be a reliable predictor of the onset of tissue disease, and tissue damage and failure.