Modeling in cardiovascular biomechanics

In this review, we briefly summarize some of Professor K.R. Rajagopal’s contributions to the field of cardiovascular mechanics and highlight some applications that have employed his theories and have expanded the ability to model the complex behaviors that characterize biological tissues. His contributions, spawning directly from the classical nonlinear theories of mechanics, have had general impact in diverse fields of engineering. Within biomechanics per se, Rajagopal’s efforts have provided state-of-the-art modeling tools not only to characterize tissues, such as blood vessels, cerebral aneurysms, or blood, but also to characterize their evolution, i.e. vessel growth and remodeling or blood clotting. Our review lists some contributions to model the mechanical behavior of cardiovascular tissues and blood rheology and follows with some modeling strategies suited for the interaction between solids and fluids, e.g. the theory of “small on large” or applications of mixture theory. We conclude with the theory of bodies who possess multiple natural configurations that evolve maximizing the rate of dissipation, which for biological tissues in particular, has yet to be employed to its full potential.