Efficient parallelization strategy for real-time FE simulations

This paper introduces an efficient and generic framework for finite-element simulations under an implicit time integration scheme. Being compatible with generic constitutive models, a fast matrix assembly method exploits the fact that system matrices are created in a deterministic way as long as the mesh topology remains constant. Using the sparsity pattern of the assembled system brings about significant optimizations on the assembly stage. As a result, developed techniques of GPU-based parallelization can be directly applied with the assembled system. Moreover, an asynchronous Cholesky precondition scheme is used to improve the convergence of the system solver. On this basis, a GPU-based Cholesky preconditioner is developed, significantly reducing the data transfer between the CPU/GPU during the solving stage. We evaluate the performance of our method with different mesh elements and hyperelastic models and compare it with typical approaches on the CPU and the GPU

Nouvelles architectures parallèles pour simulations interactives médicales

This thesis provides solutions to effectively exploit the new highly parallel architectures, in the context of simulations of deformable objects in real time. The first contributions of this paper focus on calculating the deformation of objects. For that purpose, we will propose solutions of parallelization of linear solvers, coupled with asynchronous preconditioning techniques. The second set of contributions relies on the graphics processor to produce a new collision detection method, based on intersection volumes between deformable objects. Then the last works provide solutions to produce an accurate response to contacts and is compatible with real time. We will discuss issues related to the organs cutting, and the recognition of the mechanical coupling between the contacts. Finally, we will illustrate our contributions in a range of medical applications which make the most of the contributions of this paper.Cette thèse apporte des solutions pour exploiter efficacement les nouvelles architectures hautement parallèles, dans le contexte des simulations d'objets déformables en temps réel. Les premières contributions de ce document, se concentrent sur le calcul de la déformation des objets. Pour cela nous proposerons des solutions de parallélisations de solveurs linéaires, couplées à des techniques de preconditionnement asynchrone. Le second ensemble de contributions, repose sur le processeur graphique pour produire une nouvelle méthode de détection des collisions, basée sur le volume d'intersection entre les objets déformables. Enfin les derniers travaux apportent des solutions pour produire une réponse précise aux contacts, et compatible avec le temps réel. Nous aborderons notamment les problèmes liés à la découpe des organes, et à la prise en compte du couplage mécanique entre les contacts. Pour terminer, nous illustrerons nos contributions dans un ensemble d'applications médicales, qui tirent parti des contributions de ce document

Implicit FEM and Fluid Coupling on GPU for Interactive Multiphysics Simulation

International audienceWe present a method to implement on the GPU an implicit FEM solver which is fast and stable enough to handle interactions and collisions. We combine this method with GPU-based fluids and collision detection to achieve interactive multiphysics simulations entirely running on the GPU

Calipso: Physics-based Image and Video Editing through CAD Model Proxies

We present Calipso, an interactive method for editing images and videos in a physically-coherent manner. Our main idea is to realize physics-based manipulations by running a full physics simulation on proxy geometries given by non-rigidly aligned CAD models. Running these simulations allows us to apply new, unseen forces to move or deform selected objects, change physical parameters such as mass or elasticity, or even add entire new objects that interact with the rest of the underlying scene. In Calipso, the user makes edits directly in 3D; these edits are processed by the simulation and then transfered to the target 2D content using shape-to-image correspondences in a photo-realistic rendering process. To align the CAD models, we introduce an efficient CAD-to-image alignment procedure that jointly minimizes for rigid and non-rigid alignment while preserving the high-level structure of the input shape. Moreover, the user can choose to exploit image flow to estimate scene motion, producing coherent physical behavior with ambient dynamics. We demonstrate Calipso's physics-based editing on a wide range of examples producing myriad physical behavior while preserving geometric and visual consistency.Comment: 11 page

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

Haptic Rendering of Hyperelastic Models with Friction

International audience— This paper presents an original method for inter-actions' haptic rendering when treating hyperelastic materials. Such simulations are known to be difficult due to the non-linear behavior of hyperelastic bodies; furthermore, haptic constraints enjoin contact forces to be refreshed at least at 1000 updates per second. To enforce the stability of simulations of generic objects of any range of stiffness, this method relies on implicit time integration. Soft tissues dynamics is simulated in real time (20 to 100 Hz) using the Multiplicative Jacobian Energy Decomposition (MJED) method. An asynchronous preconditioner, updated at low rates (1 to 10 Hz), is used to obtain a close approximation of the mechanical coupling of interactions. Finally, the contact problem is linearized and, using a specific-loop, it is updated at typical haptic rates (around 1000 Hz) allowing this way new simulations of prompt stiff-contacts and providing a continuous haptic feedback as well

Asynchronous Preconditioners for Efficient Solving of Non-linear Deformations

International audienceIn this paper, we present a set of methods to improve numerical solvers, as used in real-time non-linear deformable models based on implicit integration schemes. The proposed approach is particularly beneficial to simulate nonhomogeneous objects or ill-conditioned problem at high frequency. The first contribution is to desynchronize the computation of a preconditioner from the simulation loop.We also exploit today's heterogeneous parallel architectures: the graphic processor performs the mechanical computations whereas the CPU produces efficient preconditioners for the simulation. Moreover, we propose to take advantage of a warping method to limit the divergence of the preconditioner over time. Finally, we validate our work with several preconditioners on different deformable models. In typical scenarios, our method improves significantly the performances of the perconditioned version of the conjugate gradient

FEM-based confidence assessment of non-rigid registration

International audienceNon-rigid registration is often used for 3D representations during surgical procedures. It needs to provide good precision in order to guide the surgeon properly. We propose here a method that allows the computation of a local upper bound of the registration confidence over the whole organ volume. Using a bio-mechanical model, we apply tearing forces over the whole organ to compute the upper bound of the degrees of freedom left by the registrations constraints. Confrontation of our method with experimental data shows promising results to estimate the registration confidence. Indeed, the computed maximum error appears to be a real upper bound

Model-Based Identification of Anatomical Boundary Conditions in Living Tissues

International audienceIn this paper, we present a novel method dealing with the identification of boundary conditions of a deformable organ, a particularly important step for the creation of patient-specific biomechani-cal models of the anatomy. As an input, the method requires a set of scans acquired in different body positions. Using constraint-based finite element simulation, the method registers the two data sets by solving an optimization problem minimizing the energy of the deformable body while satisfying the constraints located on the surface of the registered organ. Once the equilibrium of the simulation is attained (i.e. the organ registration is computed), the surface forces needed to satisfy the constraints provide a reliable estimation of location, direction and magnitude of boundary conditions applied to the object in the deformed position. The method is evaluated on two abdominal CT scans of a pig acquired in flank and supine positions. We demonstrate that while computing a physically admissible registration of the liver, the resulting constraint forces applied to the surface of the liver strongly correlate with the location of the anatomical boundary conditions (such as contacts with bones and other organs) that are visually identified in the CT images

Controlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation

We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our approach enables to control the error in the computation of the displacement and stress fields around the needle tip and needle shaft by suitably refining the mesh, whilst maintaining a coarser mesh in other parts of the domain. We demonstrate through academic and practical examples that our approach increases the accuracy of the displacement and stress fields around the needle without increasing the computational expense. This enables real-time simulations. The proposed methodology has direct implications to increase the accuracy and control the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anesthesia, or cryotherapy and can be essential to the development of robotic guidance.Comment: 21 pages, 14 figure