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

Parallel Anisotropic Unstructured Grid Adaptation

Computational Fluid Dynamics (CFD) has become critical to the design and analysis of aerospace vehicles. Parallel grid adaptation that resolves multiple scales with anisotropy is identified as one of the challenges in the CFD Vision 2030 Study to increase the capacity and capability of CFD simulation. The Study also cautions that computer architectures are undergoing a radical change and dramatic increases in algorithm concurrency will be required to exploit full performance. This paper reviews four different methods to parallel anisotropic grid generation. They cover both ends of the spectrum: (i) using existing state-of-the-art software optimized for a single core and modifying it for parallel platforms and (ii) designing and implementing scalable software with incomplete, but rapidly maturating functionality. A brief overview for each grid adaptation system is presented in the context of a telescopic approach for multilevel concurrency. These methods employ different approaches to enable parallel execution, which provides a unique opportunity to illustrate the relative behavior of each approach. Qualitative and quantitative metric evaluations are used to draw lessons for future developments in this critical area for parallel CFD simulation

Active Image-based Modeling with a Toy Drone

Image-based modeling techniques can now generate photo-realistic 3D models from images. But it is up to users to provide high quality images with good coverage and view overlap, which makes the data capturing process tedious and time consuming. We seek to automate data capturing for image-based modeling. The core of our system is an iterative linear method to solve the multi-view stereo (MVS) problem quickly and plan the Next-Best-View (NBV) effectively. Our fast MVS algorithm enables online model reconstruction and quality assessment to determine the NBVs on the fly. We test our system with a toy unmanned aerial vehicle (UAV) in simulated, indoor and outdoor experiments. Results show that our system improves the efficiency of data acquisition and ensures the completeness of the final model.Comment: To be published on International Conference on Robotics and Automation 2018, Brisbane, Australia. Project Page: https://huangrui815.github.io/active-image-based-modeling/ The author's personal page: http://www.sfu.ca/~rha55

Tetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and RBF surface reconstruction

Given a tetrahedral mesh and objective functionals measuring the mesh quality which take into account the shape, size, and orientation of the mesh elements, our aim is to improve the mesh quality as much as possible. In this paper, we combine the moving mesh smoothing, based on the integration of an ordinary differential equation coming from a given functional, with the lazy flip technique, a reversible edge removal algorithm to modify the mesh connectivity. Moreover, we utilize radial basis function (RBF) surface reconstruction to improve tetrahedral meshes with curved boundary surfaces. Numerical tests show that the combination of these techniques into a mesh improvement framework achieves results which are comparable and even better than the previously reported ones.Comment: Revised and improved versio

Wind field simulation with isogeometric analysis

[EN]For wind field simulation with isogeometric analysis, firstly it is necessary to generate a spline parameterization of the computational domain, which is an air layer above the terrain surface. This parameterization is created with the meccano method from a digital terrain model. The main steps of the meccano method for tetrahedral mesh generation were introduced in [1, 2]. Based on the volume parameterization obtained by the method, we can generate a mapping from the parametric T-mesh to the physical space [3, 4]. Then, this volumetric parameterization is used to generate a cubic spline representation of the physical domain for the application of isogeometric analysis. We consider a mass-consistent model [5] to compute the wind field simulation in the three-dimensional domain from wind measurements or a wind forecasted by a meteorological model (for example, WRF or HARMONIE). From these data, an interpolated wind field is constructed. The mass-consistent model obtains a new wind field approaching the interpolated one, but verifying the continuity equation (mass conservation) for constant density and the impermeabilitycondition on the terrain. This adjusting problem is solved by introducing a Lagrange multiplier, that is the solution of a Poisson problem. The resulting field is obtained from the interpolated one and the gradient of the Lagrange multiplier. It is well known that if we use classical Lagrange finite elements, the gradient of the numerical solution is discontinuous over the element boundary. The advantage of using isogeometric analysis with cubic polynomial basis functions [6, 7] is that we obtain a C2 continuity for the Lagrange multiplier in the whole domain. In consequence, the resulting wind field is better approximated. Applications of the proposed technique are presented.Ministerio de Economía y Competitividad del Gobierno de España; Fondos FEDER; CONACYT-SENE

An Alternating Mesh Quality Metric Scheme for Efficient Mesh Quality Improvement

AbstractIn the numerical solution of partial differential equations (PDEs), high-quality meshes are crucial for the stability, accuracy, and convergence of the associated PDE solver. Mesh quality improvement is often performed to improve the quality of meshes before use in numerical solution of the PDE. Mesh smoothing (performed via optimization) is one popular technique for improving the mesh quality; it does so by making adjustments to the vertex locations. When an inefficient mesh quality metric is used to design the optimization problem, and hence also to measure the mesh quality within the optimization procedure, convergence of the optimization method can be much slower than desired. However, for many applications, the choice of mesh quality metric and the optimization problem should be considered fixed. In this paper, we propose a simple mesh quality metric alternation scheme for use in the mesh optimization process. The idea is to alternate the use of the original inefficient mesh quality metric with a more efficient mesh quality metric on alternate iterations of the mesh optimization procedure in order to reduce the time to convergence, while solving the original mesh quality improvement problem. Typical results of using our application scheme to solve mesh quality improvement problems yield approximately 40-55% improvement in comparison to the original mesh optimization procedure. More frequent use of the efficient metric results in greater speed-ups

Bayesian nonparametric multivariate convex regression

In many applications, such as economics, operations research and reinforcement learning, one often needs to estimate a multivariate regression function f subject to a convexity constraint. For example, in sequential decision processes the value of a state under optimal subsequent decisions may be known to be convex or concave. We propose a new Bayesian nonparametric multivariate approach based on characterizing the unknown regression function as the max of a random collection of unknown hyperplanes. This specification induces a prior with large support in a Kullback-Leibler sense on the space of convex functions, while also leading to strong posterior consistency. Although we assume that f is defined over R^p, we show that this model has a convergence rate of log(n)^{-1} n^{-1/(d+2)} under the empirical L2 norm when f actually maps a d dimensional linear subspace to R. We design an efficient reversible jump MCMC algorithm for posterior computation and demonstrate the methods through application to value function approximation