Controlling the error on target motion through real-time mesh adaptation: Applications to deep brain stimulation.

An error-controlled mesh refinement procedure for needle insertion simulations is presented. As an example, the procedure is applied for simulations of electrode implantation for deep brain stimulation. We take into account the brain shift phenomena occurring when a craniotomy is performed. We observe that the error in the computation of the displacement and stress fields is localised around the needle tip and the needle shaft during needle insertion simulation. By suitably and adaptively refining the mesh in this region, our approach enables to control, and thus to reduce, the error whilst maintaining a coarser mesh in other parts of the domain. Through academic and practical examples we demonstrate that our adaptive approach, as compared with a uniform coarse mesh, increases the accuracy of the displacement and stress fields around the needle shaft and, while for a given accuracy, saves computational time with respect to a uniform finer mesh. This facilitates real-time simulations. The proposed methodology has direct implications in increasing the accuracy, and controlling the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anaesthesia, or cryotherapy. Moreover, the proposed approach can be helpful in the development of robotic surgeries because the simulation taking place in the control loop of a robot needs to be accurate, and to occur in real time.

Real-Time Error Control for Surgical Simulation.

OBJECTIVE: To present the first a posteriori error-driven adaptive finite element approach for real-time simulation, and to demonstrate the method on a needle insertion problem. METHODS: We use corotational elasticity and a frictional needle/tissue interaction model. The problem is solved using finite elements within SOFA.1 For simulating soft tissue deformation, the refinement strategy relies upon a hexahedron-based finite element method, combined with a posteriori error estimation driven local -refinement. RESULTS: We control the local and global error level in the mechanical fields (e.g., displacement or stresses) during the simulation. We show the convergence of the algorithm on academic examples, and demonstrate its practical usability on a percutaneous procedure involving needle insertion in a liver. For the latter case, we compare the force-displacement curves obtained from the proposed adaptive algorithm with that obtained from a uniform refinement approach. CONCLUSIONS: Error control guarantees that a tolerable error level is not exceeded during the simulations. Local mesh refinement accelerates simulations. SIGNIFICANCE: Our work provides a first step to discriminate between discretization error and modeling error by providing a robust quantification of discretization error during simulations.