Optimum Design of an Anchoring System for Percutaneous Mitral Valve Repair

In a novel procedure for percutaneous mitral valve repair, inter-related hook-shaped anchors are inserted around the annulus to replace the surgeon’s suturing in open-heart ring annuloplasty. To properly attach to the tissue, the anchors should withstand large deformation applied during the delivery process and recover their original shape when released into the heart tissue. To this end, stress concentration is avoided along the anchors, which are fabricated of a super-elastic material, by means of shape optimization. Shape optimization consists in finding the smoothest anchor mid-curve possible, which minimizes the von Mises stresses applied during the delivery process. An optimization algorithm aimed at minimizing the weighted rms value of the curvature is introduced. A geometrically optimum shape is obtained by equally weighting the curvature values. Further reduction in the stress values is possible by weighting the curvature values along the anchor in an iterative procedure that yields a structurally optimum anchor. The weights at each iteration are defined proportional to the stress distribution along the anchor obtained in the previous iteration.