Real-time Error Control for Surgical Simulation

TL;DR

This paper introduces a real-time, error-driven adaptive finite element method for surgical simulation, enabling precise control of errors and faster computations during needle insertion procedures.

Contribution

It presents the first real-time a posteriori error-driven adaptive finite element approach for surgical simulation, demonstrated on needle insertion in liver tissue.

Findings

Controlled local and global error levels during simulation.

Convergence demonstrated on academic examples.

Adaptive refinement accelerates simulation speed.

Abstract

Objective: To present the first real-time 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. The refinement strategy relies upon a hexahedron-based finite element method, combined with a posteriori error estimation driven local $h$-refinement, for simulating soft tissue deformation. 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.