The continuous technological improvements of medical instruments and devices make minimally-invasive approaches a real and valid alternative to standard open surgery in more and more cases. Recent developments in cardiovascular surgery, in particular, have led to the success of thoracic endovascular repair (TEVAR) and transcatheter aortic valve implantation (TAVI). If, on the one hand, minimally-invasive interventions induce shorter hospital stays, faster recovery, and thus reduced costs, on the other hand, since, for obvious reasons, the direct control of the operator on the procedure is much more limited, operation planning and decision-making steps cover a crucial importance. In this context, computational tools have demonstrated to play a remarkable role, providing the surgeon with predictive information regarding the potential optimality of the treatment strategy. In the present chapter, we aim at describing recent developments of TEVAR and TAVI modeling, from both the structural and fluid-dynamic point of view.
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