Fast Update Procedures for Finite Element Based Suturing, Tissue Cutting and Skin Undermining in a Haptic Environment

This research presents formulations and fast numerical procedures for supporting a real-time finite element-based haptic simulator that can handle the tasks of cutting, undermining, removing and suturing soft tissue, as is typical in suturing procedures. The continuum soft-tissue is discretized and modeled by a constrained set of equilibrium equations. The coefficient of the equilibrium equations is the stiffness matrix of the system, and topological changes, due to cutting and suture placement, are represented by displacement constraint addition and removal. We show how this formulation allows us to obtain real-time solutions through low-rank updates of the inverse of the Schur complement of the stiffness matrix. Operation count and timing tests show that the update frequencies are well within an acceptable range for haptic feedback, even for reasonably-sized models. A prototype simulator using these techniques has been developed to allow users to haptically perform bi-manual soft-tissue cutting, skin undermining, and suturing.