ADVANCES IN GEOMETRY INDEPENDENT APPROXIMATIONS

We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no-longer has to be identical to the approximation used to describe the geometry of the domain. As such, the geometry can be described using usual CAD representations, e.g. NURBS, which are the most common in the CAD area, whilst local refinement and meshes approximations can be used to describe the field variables, enabling local adaptivity. We show in which cases the approach passes the patch test and present applications to various mechanics, fracture and multi-physics problems

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

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

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

Biomechanical modelling of probe to tissue interaction during ultrasound scanning

Purpose: Biomechanical simulation of anatomical deformations caused by ultrasound probe pressure is of outstanding importance for several applications, from the testing of robotic acquisition systems to multi-modal image fusion and development of ultrasound training platforms. Different approaches can be exploited for modelling the probe-tissue interaction, each achieving different trade-offs among accuracy, computation time and stability. Methods: We assess the performances of different strategies based on the finite element method for modelling the interaction between the rigid probe and soft tissues. Probe\u2013tissue contact is modelled using (i) penalty forces, (ii) constraint forces, and (iii) by prescribing the displacement of the mesh surface nodes. These methods are tested in the challenging context of ultrasound scanning of the breast, an organ undergoing large nonlinear deformations during the procedure. Results: The obtained results are evaluated against those of a non-physically based method. While all methods achieve similar accuracy, performance in terms of stability and speed shows high variability, especially for those methods modelling the contacts explicitly. Overall, prescribing surface displacements is the approach with best performances, but it requires prior knowledge of the contact area and probe trajectory. Conclusions: In this work, we present different strategies for modelling probe\u2013tissue interaction, each able to achieve different compromises among accuracy, speed and stability. The choice of the preferred approach highly depends on the requirements of the specific clinical application. Since the presented methodologies can be applied to describe general tool\u2013tissue interactions, this work can be seen as a reference for researchers seeking the most appropriate strategy to model anatomical deformation induced by the interaction with medical tools

Strain smoothing for compressible and nearly-incompressible finite elasticity

We present a robust and efficient form of the smoothed finite element method (S-FEM) to simulate hyperelastic bodies with compressible and nearly-incompressible neo-Hookean behaviour. The resulting method is stable, free from volumetric locking and robust on highly distorted meshes. To ensure inf-sup stability of our method we add a cubic bubble function to each element. The weak form for the smoothed hyperelastic problem is derived analogously to that of smoothed linear elastic problem. Smoothed strains and smoothed deformation gradients are evaluated on sub-domains selected by either edge information (edge-based S-FEM, ES-FEM) or nodal information (node-based S-FEM, NS-FEM). Numerical examples are shown that demonstrate the efficiency and reliability of the proposed approach in the nearly-incompressible limit and on highly distorted meshes. We conclude that, strain smoothing is at least as accurate and stable, as the MINI element, for an equivalent problem size

Beam-inside-beam contact: Mechanical simulations of slender medical instruments inside the human body

Background and Objective This contribution presents a rapid computational framework to mechanically simulate the insertion of a slender medical instrument in a tubular structure such as an artery, the cochlea or another slender instrument. Methods Beams are employed to rapidly simulate the mechanical behaviour of the medical instrument and the tubular structure. However, the framework’s novelty is its capability to handle the mechanical contact between an inner beam (representing the medical instrument) embedded in a hollow outer beam (representing the tubular structure). This “beam-inside-beam” contact framework, which forces two beams to remain embedded, is the first of its kind since existing contact frameworks for beams are “beam-to-beam” approaches, i.e. they repel beams from each other. Furthermore, we propose contact kinematics such that not only instruments and tubes with circular cross-sections can be considered, but also those with elliptical cross-sections. This provides flexibility for the optimization of patient-specific instruments. Results The results demonstrate that the framework’s robustness is substantial, because only a few increments per simulation and a few iterations per increment are required, even though large deformations, large rotations and large curvature changes of both the instrument and tubular structure occur. The stability of the framework remains high even if the modulus of the inner tube is thousand times larger than that of the outer tube. A mesh convergence study furthermore exposes that a relatively small number of elements is required to accurately approach the reference solution. Conclusions The framework’s high simulation speed originates from the exploitation of the rigidity of the beams’ cross-sections to quantify the exclusion between the inner and the hollow outer beam. This rigidity limits the accuracy of the framework at the same time, but this is unavoidable since simulation accuracy and simulation speed are two competing interests. Hence, the framework is particularly attractive if simulation speed is preferred over accuracy

Vessel-based brain-shift compensation using elastic registration driven by a patient-specific finite element model

International audienceDuring brain tumor surgery, planning and guidance are based on pre-operative images which do not account for brain-shift.However, this shift is a major source of error in neuro-navigation systems and affects the accuracy of the procedure. The vascular tree is extracted from pre-operative Magnetic Resonance Angiography and from intra-operative Doppler ultrasound images, which provides sparse information on brain deformations.The pre-operative images are then updated based on an elastic registration of the blood vessels, driven by a patient-specific biomechanical model.This biomechanical model is used to extrapolate the deformation to the surrounding soft tissues.Quantitative results on a single surgical case are provided, with an evaluation of the execution time for each processing step.Our method is proved to be efficient to compensate for brain deformation while being compatible with a surgical process

Silhouette-based Pose Estimation for Deformable Organs Application to Surgical Augmented Reality

International audience— In this paper we introduce a method for semi-automatic registration of 3D deformable models using 2D shape outlines (silhouettes) extracted from a monocular camera view. Our framework is based on the combination of a biomechanical model of the organ with a set of projective constraints influencing the deformation of the model. To enforce convergence towards a global minimum for this ill-posed problem we interactively provide a rough (rigid) estimation of the pose. We show that our approach allows for the estimation of the non-rigid 3D pose while relying only on 2D information. The method is evaluated experimentally on a soft silicone gel model of a liver, as well as on real surgical data, providing augmented reality of the liver and the kidney using a monocular laparoscopic camera. Results show that the final elastic registration can be obtained in just a few seconds, thus remaining compatible with clinical constraints. We also evaluate the sensitivity of our approach according to both the initial alignment of the model and the silhouette length and shape