Simulation of hyperelastic materials in real-time using Deep Learning

The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition, parallel computing, adaptive meshing, and model order reduction. In this paper we present U-Mesh: a data-driven method based on a U-Net architecture that approximates the non-linear relation between a contact force and the displacement field computed by a FEM algorithm. We show that deep learning, one of the latest machine learning methods based on artificial neural networks, can enhance computational mechanics through its ability to encode highly non-linear models in a compact form. Our method is applied to two benchmark examples: a cantilever beam and an L-shape subject to moving punctual loads. A comparison between our method and proper orthogonal decomposition (POD) is done through the paper. The results show that U-Mesh can perform very fast simulations on various geometries, mesh resolutions and number of input forces with very small errors

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

A Shell Model for Real-time Simulation of intra-ocular Implant Deployment

International audienceWith 30 million interventions a year worldwide, cataract surgery is one of the most frequently performed procedures. Yet, no tool currently allows teaching all steps of the procedure without putting pa- tients at risk. A particularly challenging stage of this surgery deals with the injection and deployment of the intra-ocular lens implant. In this paper we propose to rely on shell theory to accurately describe the com- plex deformations of the implant. Our approach extends the co-rotational method used in finite element analysis of in-plane deformations to incor- porate a bending energy. This results in a relatively simple and compu- tationally efficient approach which was applied to the simulation of the lens deployment. This simulation also accounts for the complex contacts that take place during the injection phase

Augmented Reality for Cryoablation Procedures

International audienceCryotherapy is a rapidly growing minimally invasive technique for the treatment of different kinds of tumors, such as breast cancer, renal and prostate cancer. Several hollow needles are percutaneously inserted in the target area under image guidance and a gas (usually argon) is then decompressed inside the needles. Based on the Thompson-Joule principle, the temperature drops drown and a ball of ice crystals forms around the tip of each needle. Radiologists rely on the geometry of this iceball (273K), visible on computer tomographic (CT) or magnetic resonance (MR) images, to assess the status of the ablation. However, cellular death only occurs when the temperature falls below 233K. The complexity of the procedure therefore resides in planning the optimal number, position and orientation of the needles required to treat the tumor, while avoiding any damage to the surrounding healthy tissues.This planning is currently done qualitatively, based on experience, and can take several hours, with a result that is often different from the expected one. To solve this important limitation of cryotherapy, a few planning systems have been proposed in the literature. Currently, commercial systems are nearly non existent, and emerging tools are limited to a visualization of the isotherms obtained for each needle in ideal conditions (usually in a gel). They do not account for any influence of the soft tissue properties, the presence of blood vessels, or the combined effect of multiple needles. As a consequence, large safety margins over 5mm are defined.To address this challenge, our method extracts information from medical images (CT or MR) and allows to assess different strategies with an augmented visualization of the resulting iceball and the associated isotherms

Computation and Visualization of Risk Assessment in Deep Brain Stimulation

International audienceDeep Brain Stimulation is a neurosurgical approach for the treatment of pathologies such as Parkinson's disease. The basic principle consists in placing a thin electrode in a deep part of the brain. To safely reach the target of interest, careful planning must be performed to ensure that no vital structure (e.g. blood vessel) will be damaged during the insertion of the electrode. Currently this planning phase is done without considering the brain shift, which occurs during the surgery once the skull is open, leading to increased risks of complications. In this paper, we propose a method to compute the motion of anatomical structures induced by the brain shift. This computation is based on a biomechanical model of the brain and the cerebro-spinal fluid. We then visualize in a intuitive way the risk of damaging vital structures with the electrode.La stimulation cérébrale profonde est une procédure neurochirurgicale pour le traitement de pathologies comme la maladie de Parkinson. La procédure consiste à implanter une électrode dans une région profonde du cerveau. Pour atteindre la cible sans risque, le chirurgien procède à une plannification minutieuse pour s'assurer qu'aucune structure vitale (vaisseaux sanguins, ventricules) ne se retrouve sur le chemin de l'électrode. Actuellement, la plannification ne considère pas les déformations intra-opératoires, qui se produisent une fois que le crâne est ouvert. Cela peut entraîner des compolications. Dans ce papier, nous proposons une méthode pour calculer le risque de mouvement des structures anatomiques causés par ces déformations. Le calcul s'appuie sur un modèle biomécanique du cerveau et du fluide céphalo-rachidien. Nous visualisons ensuite intuitivement le risque d'endommager une structure vitale avec l'électrode

Robust RANSAC-based blood vessel segmentation

International audienceMany vascular clinical applications require a vessel segmentation process that is able to both extract the centerline and the surface of the blood vessels. However, noise and topology issues (such as kissing vessels) prevent existing algorithms from being able to easily retrieve such a complex system as the brain vasculature. We propose here a new blood vessel tracking algorithm that 1) detect the vessel centerline; 2) provide a local radius estimate; and 3) extracts a dense set of points at the blood vessel surface. This algorithm is based on a RANSAC-based robust fitting of successive cylinders along the vessel. Our method was validated against the Multiple Hypothesis Testing (MHT) algorithm on 10 3DRA patient data of the brain vasculature. Over 30 blood vessels of various sizes were considered for each patient. Our results demonstrated a greater ability of our algorithm to track small, tortuous and touching vessels (96% success rate), compared to MHT (65% success rate). The computed centerline precision was below 1 voxel when compared to MHT. Moreover, our results were obtained with the same set of parameters for all patients and all blood vessels, except for the seed point for each vessel, also necessary for MHT. The proposed algorithm is thereafter able to extract the full intracranial vasculature with little user interaction

Asynchronous haptic simulation of contacting deformable objects with variable stiffness

International audienceAbstract--This paper presents a new asynchronous approach for haptic rendering of deformable objects. When stiff nonlinear deformations take place, they introduce important and rapid variations of the force sent to the user. This problem is similar to the stiff virtual wall for which a high refresh rate is required to obtain a stable haptic feedback. However, when dealing with several interacting deformable objects, it is usually impossible to simulate all objects at high rates. To address this problem we propose a quasi-static framework that allows for stable interactions of asynchronously computed deformable objects. In the proposed approach, a deformable object can be computed at high refresh rates, while the remaining deformable virtual objects remain computed at low refresh rates. Moreover, contacts and other constraints between the different objects of the virtual environment are accurately solved using a shared Linear Complementarity Problem (LCP). Finally, we demonstrate our method on two test cases: a snap-in example involving non-linear deformations and a virtual thread interacting with a deformable object

Connective Tissues Simulation on GPU

International audienceRecent work in the field of medical simulation have led to real advances in the mechanical simulation of organs. However, it is important to notice that, despite the major role they may have in the interaction between organs, the connective tissues are often left out of these simulations. In this paper, we propose a model which can rely on either a mesh based or a meshless methods. To provide a realistic simulation of these tissues, our work is based on the weak form of continuum mechanics equations for hyperelastic soft materials. Furthermore, the stability of deformable objects simulation is ensured by an implicit temporal integration scheme. Our method allows to model these tissues without prior assumption on the dimension of their of their geometry (curve, surface or volume), and enables mechanical coupling between organs. To obtain an interactive frame rate, we develop a parallel version suitable for to GPU computation. Finally we demonstrate the proper convergence of our finite element scheme

Constrained Stochastic State Estimation of Deformable 1D Objects: Application to Single-view 3D Reconstruction of Catheters with Radio-opaque Markers

International audienceMinimally invasive fluoroscopy-based procedures are the gold standard for diagnosis and treatment of various pathologies of the cardiovascular system. This kind of procedures imply for the clinicians to infer the 3D shape of the device from 2D images, which is known to be an ill-posed 10 problem. In this paper we present a method to reconstruct the 3D shape of the interventional device, with the aim of improving the navigation. The method combines a physics-based simulation with non-linear Bayesian filter. Whereas the physics-based model provides a prediction of the shape of the device navigating within the blood vessels (taking into account non-linear interactions be-15 tween the catheter and the surrounding anatomy), an Unscented Kalman Filter is used to correct the navigation model using 2D image features as external observations. The proposed framework has been evaluated on both synthetic and real data, under different model parameterizations, filter parameters tuning and external observations data-sets. Comparing the reconstructed 3D shape with a known ground truth, for the synthetic data-set, we obtained average values for 3D Hausdorff Distance of $0.81 ± 0.53 mm$, for the 3D mean distance at the segment of $0.37 ± 0.17$ mm and an average 3D tip error of $0.24 ± 0.13 mm$. For the real data-set,we obtained an average 3D Hausdorff distance of $1.74 ± 0.77 mm$, a average 3D mean distance at the distal segment of 0.91 ± 0.14 mm, an average 3D error on the tip of $0.53 ± 0.09 mm$. These results show the ability of our method to retrieve the 3D shape of the device, under a variety of filter parameterizations and challenging conditions: uncertainties on model parameterization, ambiguous views and non-linear complex phenomena such as stick and slip motions