3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques

Parallel 3-D marine controlled-source electromagnetic modelling using high-order tetrahedral Nédélec elements

We present a parallel and high-order Nédélec finite element solution for the marine controlled-source electromagnetic (CSEM) forward problem in 3-D media with isotropic conductivity. Our parallel Python code is implemented on unstructured tetrahedral meshes, which support multiple-scale structures and bathymetry for general marine 3-D CSEM modelling applications. Based on a primary/secondary field approach, we solve the diffusive form of Maxwell’s equations in the low-frequency domain. We investigate the accuracy and performance advantages of our new high-order algorithm against a low-order implementation proposed in our previous work. The numerical precision of our high-order method has been successfully verified by comparisons against previously published results that are relevant in terms of scale and geological properties. A convergence study confirms that high-order polynomials offer a better trade-off between accuracy and computation time. However, the optimum choice of the polynomial order depends on both the input model and the required accuracy as revealed by our tests. Also, we extend our adaptive-meshing strategy to high-order tetrahedral elements. Using adapted meshes to both physical parameters and high-order schemes, we are able to achieve a significant reduction in computational cost without sacrificing accuracy in the modelling. Furthermore, we demonstrate the excellent performance and quasi-linear scaling of our implementation in a state-of-the-art high-performance computing architecture.This project has received funding from the European Union's Horizon 2020 programme under the Marie Sklodowska-Curie grant agreement No. 777778. Furthermore, the research leading to these results has received funding from the European Union's Horizon 2020 programme under the ChEESE Project (https://cheese-coe.eu/ ), grant agreement No. 823844. In addition, the authors would also like to thank the support of the Ministerio de Educación y Ciencia (Spain) under Projects TEC2016-80386-P and TIN2016-80957-P. The authors would like to thank the Editors-in-Chief and to both reviewers, Dr. Martin Cuma and Dr. Raphael Rochlitz, for their valuable comments and suggestions which helped to improve the quality of the manuscript. This work benefited from the valuable suggestions, comments, and proofreading of Dr. Otilio Rojas (BSC). Last but not least, Octavio Castillo-Reyes thanks Natalia Gutierrez (BSC) for her support in CSEM modeling with BSIT.Peer ReviewedPostprint (author's final draft

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

High-resolution 3D weld toe stress analysis and ACPD method for weld toe fatigue crack initiation

Weld toe fatigue crack initiation is highly dependent on the local weld toe stress-concentrating geometry including any inherent flaws. These flaws are responsible for premature fatigue crack initiation (FCI) and must be minimised to maximise the fatigue life of a welded joint. In this work, a data-rich methodology has been developed to capture the true weld toe geometry and resulting local weld toe stress-field and relate this to the FCI life of a steel arc-welded joint. To obtain FCI lives, interrupted fatigue test was performed on the welded joint monitored by a novel multi-probe array of alternating current potential drop (ACPD) probes across the weld toe. This setup enabled the FCI sites to be located and the FCI life to be determined and gave an indication of early fatigue crack propagation rates. To understand fully the local weld toe stress-field, high-resolution (5 mu m) 3D linear-elastic finite element (FE) models were generated from X-ray micro-computed tomography (mu-CT) of each weld toe after fatigue testing. From these models, approximately 202 stress concentration factors (SCFs) were computed for every 1 mm of weld toe. These two novel methodologies successfully link to provide an assessment of the weld quality and this is correlated with the fatigue performance

Feature-sensitive and Adaptive Image Triangulation: A Super-pixel-based Scheme for Image Segmentation and Mesh Generation

With increasing utilization of various imaging techniques (such as CT, MRI and PET) in medical fields, it is often in great need to computationally extract the boundaries of objects of interest, a process commonly known as image segmentation. While numerous approaches have been proposed in literature on automatic/semi-automatic image segmentation, most of these approaches are based on image pixels. The number of pixels in an image can be huge, especially for 3D imaging volumes, which renders the pixel-based image segmentation process inevitably slow. On the other hand, 3D mesh generation from imaging data has become important not only for visualization and quantification but more critically for finite element based numerical simulation. Traditionally image-based mesh generation follows such a procedure as: (1) image boundary segmentation, (2) surface mesh generation from segmented boundaries, and (3) volumetric (e.g., tetrahedral) mesh generation from surface meshes. These three majors steps have been commonly treated as separate algorithms/steps and hence image information, once segmented, is not considered any more in mesh generation. In this thesis, we investigate a super-pixel based scheme that integrates both image segmentation and mesh generation into a single method, making mesh generation truly an image-incorporated approach. Our method, called image content-aware mesh generation, consists of several main steps. First, we generate a set of feature-sensitive, and adaptively distributed points from 2D grayscale images or 3D volumes. A novel image edge enhancement method via randomized shortest paths is introduced to be an optional choice to generate the features’ boundary map in mesh node generation step. Second, a Delaunay-triangulation generator (2D) or tetrahedral mesh generator (3D) is then utilized to generate a 2D triangulation or 3D tetrahedral mesh. The generated triangulation (or tetrahedralization) provides an adaptive partitioning of a given image (or volume). Each cluster of pixels within a triangle (or voxels within a tetrahedron) is called a super-pixel, which forms one of the nodes of a graph and adjacent super-pixels give an edge of the graph. A graph-cut method is then applied to the graph to define the boundary between two subsets of the graph, resulting in good boundary segmentations with high quality meshes. Thanks to the significantly reduced number of elements (super-pixels) as compared to that of pixels in an image, the super-pixel based segmentation method has tremendously improved the segmentation speed, making it feasible for real-time feature detection. In addition, the incorporation of image segmentation into mesh generation makes the generated mesh well adapted to image features, a desired property known as feature-preserving mesh generation

Tetrahedral Image-to-Mesh Conversion Software for Anatomic Modeling of Arteriovenous Malformations

We describe a new implementation of an adaptive multi-tissue tetrahedral mesh generator targeting anatomic modeling of Arteriovenous Malformation (AVM) for surgical simulations. Our method, initially constructs an adaptive Body-Centered Cubic (BCC) mesh of high quality elements. Then, it deforms the mesh surfaces to their corresponding physical image boundaries, hence, improving the mesh fidelity and smoothness. Our deformation scheme, which builds upon the ITK toolkit, is based on the concept of energy minimization, and relies on a multi-material point-based registration. It uses non-connectivity patterns to implicitly control the number of the extracted feature points needed for the registration, and thus, adjusts the trade-off between the achieved mesh fidelity and the deformation speed. While many medical imaging applications require robust mesh generation, there are few codes available to the public. We compare our implementation with two similar open-source image-to-mesh conversion codes: (1) Cleaver from US, and (2) CGAL from EU. Our evaluation is based on five isotropic/anisotropic segmented images, and relies on metrics like geometric & topologic fidelity, mesh quality, gradation and smoothness. The implementation we describe is open- source and it will be available within: (i) the 3D Slicer package for visualization and image analysis from Harvard Medical School, and (ii) an interactive simulator for neurosurgical procedures involving vasculature using SOFA, a framework for real-time medical simulation developed by INRIA

3D Scanning System for Automatic High-Resolution Plant Phenotyping

Thin leaves, fine stems, self-occlusion, non-rigid and slowly changing structures make plants difficult for three-dimensional (3D) scanning and reconstruction -- two critical steps in automated visual phenotyping. Many current solutions such as laser scanning, structured light, and multiview stereo can struggle to acquire usable 3D models because of limitations in scanning resolution and calibration accuracy. In response, we have developed a fast, low-cost, 3D scanning platform to image plants on a rotating stage with two tilting DSLR cameras centred on the plant. This uses new methods of camera calibration and background removal to achieve high-accuracy 3D reconstruction. We assessed the system's accuracy using a 3D visual hull reconstruction algorithm applied on 2 plastic models of dicotyledonous plants, 2 sorghum plants and 2 wheat plants across different sets of tilt angles. Scan times ranged from 3 minutes (to capture 72 images using 2 tilt angles), to 30 minutes (to capture 360 images using 10 tilt angles). The leaf lengths, widths, areas and perimeters of the plastic models were measured manually and compared to measurements from the scanning system: results were within 3-4% of each other. The 3D reconstructions obtained with the scanning system show excellent geometric agreement with all six plant specimens, even plants with thin leaves and fine stems.Comment: 8 papes, DICTA 201

Patient-specific anisotropic model of human trunk based on MR data

There are many ways to generate geometrical models for numerical simulation, and most of them start with a segmentation step to extract the boundaries of the regions of interest. This paper presents an algorithm to generate a patient-specific three-dimensional geometric model, based on a tetrahedral mesh, without an initial extraction of contours from the volumetric data. Using the information directly available in the data, such as gray levels, we built a metric to drive a mesh adaptation process. The metric is used to specify the size and orientation of the tetrahedral elements everywhere in the mesh. Our method, which produces anisotropic meshes, gives good results with synthetic and real MRI data. The resulting model quality has been evaluated qualitatively and quantitatively by comparing it with an analytical solution and with a segmentation made by an expert. Results show that our method gives, in 90% of the cases, as good or better meshes as a similar isotropic method, based on the accuracy of the volume reconstruction for a given mesh size. Moreover, a comparison of the Hausdorff distances between adapted meshes of both methods and ground-truth volumes shows that our method decreases reconstruction errors faster. Copyright © 2015 John Wiley & Sons, Ltd.Natural Sciences and Engineering Research Council (NSERC) of Canada and the MEDITIS training program (´Ecole Polytechnique de Montreal and NSERC)