SOniCS: Develop intuition on biomechanical systems through interactive error controlled simulations

E-print/Working paper (2022)

This new approach allows the user to experiment with model choices easily and quickly without requiring in-depth expertise, as constitutive models can be modified by one line of code only. This ease in ... [more ▼]

This new approach allows the user to experiment with model choices easily and quickly without requiring in-depth expertise, as constitutive models can be modified by one line of code only. This ease in building new models makes SOniCS ideal to develop surrogate, reduced order mod- els and to train machine learning algorithms for uncertainty quantification or to enable patient-specific simulations. SOniCS is thus not only a tool that facilitates the development of surgical training simulations but also, and perhaps more importantly, paves the way to increase the intuition of users or otherwise non-intuitive behaviors of (bio)mechanical systems. The plugin uses new developments of the FEniCSx project enabling au- tomatic generation with FFCx of finite element tensors such as the local residual vector and Jacobian matrix. We validate our approach with nu- merical simulations such as manufactured solutions, cantilever beams, and benchmarks provided by FEBio. We reach machine precision accuracy and demonstrate the use of the plugin for a real-time haptic simulation involv- ing a surgical tool controlled by the user in contact with a hyperelastic liver. We include complete examples showing the use of our plugin for sim- ulations involving Saint Venant-Kirchhoff, Neo-Hookean, Mooney-Rivlin, and Holzapfel Ogden anisotropic models as supplementary material. [less ▲]

Real-time Error Control for Surgical Simulation

in IEEE Transactions on Biomedical Engineering (2017)

To present the first real-time a posteriori error-driven adaptive finite element approach for realtime simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational ... [more ▼]

To present the first real-time a posteriori error-driven adaptive finite element approach for realtime 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. [less ▲]

Fracture in augmented reality

Poster (2015, August)

Real-time error controlled adaptive mesh refinement in surgical simulation: Application to needle insertion simulation

in IEEE Transactions on Biomedical Engineering (n.d.)

This paper presents the first real-time discretisation-error-driven adaptive finite element approach for corotational elasticity problems involving strain localisation. We propose a hexahedron-based ... [more ▼]

This paper presents the first real-time discretisation-error-driven adaptive finite element approach for corotational elasticity problems involving strain localisation. We propose a hexahedron-based finite element method combined with local oct-tree $h$-refinement, driven by a posteriori error estimation, for simulating soft tissue deformation. This enables to control the local error and global error level in the mechanical fields during the simulation. The local error level is used to refine the mesh only where it is needed, while maintaining a coarser mesh elsewhere. We investigate 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. [less ▲]