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Image-based mass-spring model of mitral valve closure for surgical planning

Surgical repair of the mitral valve is preferred in most cases over valve replacement, but replacement is often performed instead due to the technical difficulty of repair. A surgical planning system based on patient-specific medical images that allows surgeons to simulate and compare potential repair strategies could greatly improve surgical outcomes. In such a surgical simulator, the mathematical model of mechanics used to close the valve must be able to compute the closed state quickly and to handle the complex boundary conditions imposed by the chords that tether the valve leaflets. We have developed a system for generating a triangulated mesh of the valve surface from volumetric image data of the opened valve. We then compute the closed position of the mesh using a mass-spring model of dynamics. The triangulated mesh is produced by fitting an isosurface to the volumetric image data, and boundary conditions, including the valve annulus and chord endpoints, are identified in the image data using a graphical user interface. In the mass-spring model, triangle sides are treated as linear springs, and sides shared by two triangles are treated as bending springs. Chords are treated as nonlinear springs, and self-collisions are detected and resolved. Equations of motion are solved using implicit numerical integration. Accuracy was assessed by comparison of model results with an image of the same valve taken in the closed state. The model exhibited rapid valve closure and was able to reproduce important features of the closed valve.