Meshless Mechanics and Point-Based Visualization Methods for Surgical Simulations

Computer-based modeling and simulation practices have become an integral part of the medical education field. For surgical simulation applications, realistic constitutive modeling of soft tissue is considered to be one of the most challenging aspects of the problem, because biomechanical soft-tissue models need to reflect the correct elastic response, have to be efficient in order to run at interactive simulation rates, and be able to support operations such as cuts and sutures. Mesh-based solutions, where the connections between the individual degrees of freedom (DoF) are defined explicitly, have been the traditional choice to approach these problems. However, when the problem under investigation contains a discontinuity that disrupts the connectivity between the DoFs, the underlying mesh structure has to be reconfigured in order to handle the newly introduced discontinuity correctly. This reconfiguration for mesh-based techniques is typically called dynamic remeshing, and most of the time it causes the performance bottleneck in the simulation. In this dissertation, the efficiency of point-based meshless methods is investigated for both constitutive modeling of elastic soft tissues and visualization of simulation objects, where arbitrary discontinuities/cuts are applied to the objects in the context of surgical simulation. The point-based deformable object modeling problem is examined in three functional aspects: modeling continuous elastic deformations with, handling discontinuities in, and visualizing a point-based object. Algorithmic and implementation details of the presented techniques are discussed in the dissertation. The presented point-based techniques are implemented as separate components and integrated into the open-source software framework SOFA. The presented meshless continuum mechanics model of elastic tissue were verified by comparing it to the Hertzian non-adhesive frictionless contact theory. Virtual experiments were setup with a point-based deformable block and a rigid indenter, and force-displacement curves obtained from the virtual experiments were compared to the theoretical solutions. The meshless mechanics model of soft tissue and the integrated novel discontinuity treatment technique discussed in this dissertation allows handling cuts of arbitrary shape. The implemented enrichment technique not only modifies the internal mechanics of the soft tissue model, but also updates the point-based visual representation in an efficient way preventing the use of costly dynamic remeshing operations

Modeling of Free Surface Flows with Elastic Bodies Interactions

In this paper, a series of new fluid and structure interactions test cases with strong free surface effects are presented and computations of such flows with the Particle Finite Element Method (PFEM) (Idelsohn, Oiiate, Del Pin and Calvo, 2006) are documented. The structures object of study are elastic cantilever bars clamped inside sloshing tanks subjected ro roll motion. The possibilities of PFEM for the coupled simulation of moderately violent free surface flows interacting with elastic bodies are investigated. The problem can be described as the coupling of a sloshing flow with an easily deformable elastic body. A series of experiments designed and executed specifically for these tests are also described. The experiments comprise cases with different liquid height and liquids of different viscosity. The aim is to identify canonical benchmark problems in FSI (Fluid and Structure Interactions), including free surfaces, for future comparisons between different numerical approaches

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

Meshless deformable models for LV motion analysis

We propose a novel meshless deformable model for in vivo cardiac left ventricle (LV) 3D motion estimation. As a relatively new technology, tagged MRI (tMRI) provides a direct and noninvasive way to reveal local deformation of the myocardium, which creates a large amount of heart motion data which requiring quantitative analysis. In our study, we sample the heart motion sparsely at intersections of three sets of orthogonal tagging planes and then use a new meshless deformable model to recover the dense 3D motion of the myocardium temporally during the cardiac cycle. We compute external forces at tag intersections based on tracked local motion and redistribute the force to meshless particles throughout the myocardium. Internal constraint forces at particles are derived from local strain energy using a Moving Least Squares (MLS) method. The dense 3D motion field is then computed and updated using the Lagrange equation. The new model avoids the singularity problem of mesh-based models and is capable of tracking large deformation with high efficiency and accuracy. In particular, the model performs well even when the control points (tag intersections) are relatively sparse. We tested the performance of the meshless model on a numerical phantom, as well as in vivo heart data of healthy subjects and patients. The experimental results show that the meshless deformable model can fully recover the myocardium motion in 3D. 1