Real-time Error Control for Surgical Simulation

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.Comment: 12 pages, 16 figures, change of the title, submitted to IEEE TBM

TetSplat: Real-time Rendering and Volume Clipping of Large Unstructured Tetrahedral Meshes

We present a novel approach to interactive visualization and exploration of large unstructured tetrahedral meshes. These massive 3D meshes are used in mission-critical CFD and structural mechanics simulations, and typically sample multiple field values on several millions of unstructured grid points. Our method relies on the pre-processing of the tetrahedral mesh to partition it into non-convex boundaries and internal fragments that are subsequently encoded into compressed multi-resolution data representations. These compact hierarchical data structures are then adaptively rendered and probed in real-time on a commodity PC. Our point-based rendering algorithm, which is inspired by QSplat, employs a simple but highly efficient splatting technique that guarantees interactive frame-rates regardless of the size of the input mesh and the available rendering hardware. It furthermore allows for real-time probing of the volumetric data-set through constructive solid geometry operations as well as interactive editing of color transfer functions for an arbitrary number of field values. Thus, the presented visualization technique allows end-users for the first time to interactively render and explore very large unstructured tetrahedral meshes on relatively inexpensive hardware

Robust interactive cutting based on an adaptive octree simulation mesh

We present an adaptive octree based approach for interactive cutting of deformable objects. Our technique relies on efficient refine- and node split-operations. These are sufficient to robustly represent cuts in the mechanical simulation mesh. A high-resolution surface embedded into the octree is employed to represent a cut visually. Model modification is performed in the rest state of the object, which is accomplished by back-transformation of the blade geometry. This results in an improved robustness of our approach. Further, an efficient update of the correspondences between simulation elements and surface vertices is proposed. The robustness and efficiency of our approach is underlined in test examples as well as by integrating it into a prototype surgical simulato

Adaptive Resolution for Topology Modifications in Physically-based Animation

This paper shows the interest of basing a mechanical mesh upon an efficient topological model in order to give any simulation the ability to refine this mesh locally and apply topological modifications such as cutting, tear and matter destruction.Refinement and modifications can indeed be combined in order to get a more precise result.The powerful combinatorial map model provides the mathematical background which ensures that the quasi-manifold property is guaranteed for the mesh after any topological modification.The obtained results offer the versatility and time efficiency that are expected in applications such as surgical simulation

Finite element analysis of forward extrusion of 1010 steel

Reliability of FE simulation of metal forming processes depends critically on the proper definition of material properties, the friction boundary conditions and details of the FE approach. To address these issues, the room temperature strain hardening behaviour of 1010 steel was established by performing a uniaxial compression test for the true strain of up to 1.5. Friction was evaluated using a ring test, with the two faces of the ring coated with a phosphate conversion layer and soap; the friction experimental results were matched with the FE established reference curves. The experimentally obtained material and friction input data were used in FE simulation, employing Arbitrary Lagrangian Eulerian adaptive meshing, to provide a valuable insight into the process of forward extrusion of an industrial component

VoroCrust: Voronoi Meshing Without Clipping

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrarily curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably-correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples, while preserving all sharp features in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf. Supplemental materials available on https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd

Parallel software tool for decomposing and meshing of 3d structures

An algorithm for automatic parallel generation of three-dimensional unstructured computational meshes based on geometrical domain decomposition is proposed in this paper. Software package build upon proposed algorithm is described. Several practical examples of mesh generation on multiprocessor computational systems are given. It is shown that developed parallel algorithm enables us to reduce mesh generation time significantly (dozens of times). Moreover, it easily produces meshes with number of elements of order 5 · 107, construction of those on a single CPU is problematic. Questions of time consumption, efficiency of computations and quality of generated meshes are also considered

A Framework for Fast Computation of Hyper-Elastic Materials Deformations in Real-Time Simulation of Surgery

International audienceReal-time simulation of surgery requires fast and realistic modeling of deformable objects. However today, few models are available, they are still time costly and limited in number of tetrahedra by algorithm complexity. We present here a framework to design algorithms adapted to any kind of hypere-lastic models, which include Saint Venant-Kirchhoff, Neo-Hookean and Mooney-Rivlin, handling large deformations and large displacements. Moreover , the algorithm complexity is linear in the number of tetrahedra; a comparison in number of operations performed with an existing algorithm on a similar case shows a gain of more than 40 times faster

Real-time hybrid cutting with dynamic fluid visualization for virtual surgery

It is widely accepted that a reform in medical teaching must be made to meet today's high volume training requirements. Virtual simulation offers a potential method of providing such trainings and some current medical training simulations integrate haptic and visual feedback to enhance procedure learning. The purpose of this project is to explore the capability of Virtual Reality (VR) technology to develop a training simulator for surgical cutting and bleeding in a general surgery