Framework for a low-cost intra-operative image-guided neuronavigator including brain shift compensation

In this paper we present a methodology to address the problem of brain tissue deformation referred to as 'brain-shift'. This deformation occurs throughout a neurosurgery intervention and strongly alters the accuracy of the neuronavigation systems used to date in clinical routine which rely solely on pre-operative patient imaging to locate the surgical target, such as a tumour or a functional area. After a general description of the framework of our intra-operative image-guided system, we describe a procedure to generate patient specific finite element meshes of the brain and propose a biomechanical model which can take into account tissue deformations and surgical procedures that modify the brain structure, like tumour or tissue resection

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

A New Transition Technique for the Combination of Meshfree Methods with other Numerical Methods from Macro- to Nano-Scales

Coupling the meshfree methods with othe numerical methods has good potential in computational mechanics. In this paper, to ensure the compatibility conditions for not only displacements but also its gradients, a new transition technique is proposed based on the penalty method and the transition particles. The bridge regions are used to connect the domains of different methods. The high-order compatibility conditions are satisfied through some regularly distributed transition particles. The new transition technique has several advantages: 1) through the use of the transition particles, the nodes (or atoms) in the transition region are totally independent, which will reduce significantly the cost for the node generation in the transition region; 2) the compatibility conditions in the transition region can be conveniently controlled through the adjustment of the number and distribution of the transition particles; 3) the compatibility of higher order derivatives can be easily satisfied. Several problems of fracture mechanics and multiscale analyses for solids are simulated by the newly developed coupled methods. Some key parameters used in the transition technique have been thoroughly studied and recommended. It has been demonstrated that the new transition technique is very accurate and stable, and it has very good potential to become a practical modeling and simulation tool for engineering

A mesh adaptivity scheme on the Landau-de Gennes functional minimization case in 3D, and its driving efficiency

This paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral meshes by a posteriori error estimates based on metrics, studied on the case of a nonlinear finite element minimization scheme for the Landau-de Gennes free energy functional of nematic liquid crystals. Newton's iteration for tensor fields is employed with steepest descent method possibly stepping in. Aspects relating the driving of mesh adaptivity within the nonlinear scheme are considered. The algorithmic performance is found to depend on at least two factors: when to trigger each single mesh adaptation, and the precision of the correlated remeshing. Each factor is represented by a parameter, with its values possibly varying for every new mesh adaptation. We empirically show that the time of the overall algorithm convergence can vary considerably when different sequences of parameters are used, thus posing a question about optimality. The extensive testings and debugging done within this work on the simulation of systems of nematic colloids substantially contributed to the upgrade of an open source finite element-oriented programming language to its 3D meshing possibilities, as also to an outer 3D remeshing module

Adaptive grid methods for Q-tensor theory of liquid crystals : a one-dimensional feasibility study

This paper illustrates the use of moving mesh methods for solving partial differential equation (PDE) problems in Q-tensor theory of liquid crystals. We present the results of an initial study using a simple one-dimensional test problem which illustrates the feasibility of applying adaptive grid techniques in such situations. We describe how the grids are computed using an equidistribution principle, and investigate the comparative accuracy of adaptive and uniform grid strategies, both theoretically and via numerical examples

A fast and robust patient specific Finite Element mesh registration technique: application to 60 clinical cases

Finite Element mesh generation remains an important issue for patient specific biomechanical modeling. While some techniques make automatic mesh generation possible, in most cases, manual mesh generation is preferred for better control over the sub-domain representation, element type, layout and refinement that it provides. Yet, this option is time consuming and not suited for intraoperative situations where model generation and computation time is critical. To overcome this problem we propose a fast and automatic mesh generation technique based on the elastic registration of a generic mesh to the specific target organ in conjunction with element regularity and quality correction. This Mesh-Match-and-Repair (MMRep) approach combines control over the mesh structure along with fast and robust meshing capabilities, even in situations where only partial organ geometry is available. The technique was successfully tested on a database of 5 pre-operatively acquired complete femora CT scans, 5 femoral heads partially digitized at intraoperative stage, and 50 CT volumes of patients' heads. The MMRep algorithm succeeded in all 60 cases, yielding for each patient a hex-dominant, Atlas based, Finite Element mesh with submillimetric surface representation accuracy, directly exploitable within a commercial FE software

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

Parallel semiconductor device simulation: from power to 'atomistic' devices

This paper discusses various aspects of the parallel simulation of semiconductor devices on mesh connected MIMD platforms with distributed memory and a message passing programming paradigm. We describe the spatial domain decomposition approach adopted in the simulation of various devices, the generation of structured topologically rectangular 2D and 3D finite element grids and the optimisation of their partitioning using simulated annealing techniques. The development of efficient and scalable parallel solvers is a central issue of parallel simulations and the design of parallel SOR, conjugate gradient and multigrid solvers is discussed. The domain decomposition approach is illustrated in examples ranging from `atomistic' simulation of decanano MOSFETs to simulation of power IGBTs rated for 1000 V