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1. Automated hexahedral meshing of knee cartilage structures – application to data from the osteoarthritis initiative

   https://doi.org/10.1080/10255842.2017.1383984  

   Rodriguez-Vila, B. ; Sánchez-González, P. ; Oropesa, I. ; Gomez, E. J. ; Pierce, D. M. ( October 2017 , Computer Methods in Biomechanics and Biomedical Engineering)
2. Feature Preserving Octree‐Based Hexahedral Meshing

   https://doi.org/10.1111/cgf.13795  

   Gao, Xifeng ; Shen, Hanxiao ; Panozzo, Daniele ( August 2019 , Computer Graphics Forum)
3. FULLY AUTOMATED, HEXAHEDRAL MESHING OF PATIENT-SPECIFIC CARTILAGE STRUCTURES: DATA FROM THE OSTEOARTHRITIS INITIATIVE

   Borja Rodriguez‑Vila, David M. ( July 2017 , SB3C2017 Summer Biomechanics, Bioengineering and Biotransport Conference June 21 – 24, Tucson, AZ, USA)
4. Robust automatic hexahedral cartilage meshing framework enables population-based computational studies of the knee

   https://doi.org/10.3389/fbioe.2022.1059003  

   Gibbons, Kalin D. ; Malbouby, Vahid ; Alvarez, Oliver ; Fitzpatrick, Clare K. ( December 2022 , Frontiers in Bioengineering and Biotechnology)

   Osteoarthritis of the knee is increasingly prevalent as our population ages, representing an increasing financial burden, and severely impacting quality of life. The invasiveness of in vivo procedures and the high cost of cadaveric studies has left computational tools uniquely suited to study knee biomechanics. Developments in deep learning have great potential for efficiently generating large-scale datasets to enable researchers to perform population-sized investigations, but the time and effort associated with producing robust hexahedral meshes has been a limiting factor in expanding finite element studies to encompass a population. Here we developed a fully automated pipeline capable of taking magnetic resonance knee images and producing a working finite element simulation. We trained an encoder-decoder convolutional neural network to perform semantic image segmentation on the Imorphics dataset provided through the Osteoarthritis Initiative. The Imorphics dataset contained 176 image sequences with varying levels of cartilage degradation. Starting from an open-source swept-extrusion meshing algorithm, we further developed this algorithm until it could produce high quality meshes for every sequence and we applied a template-mapping procedure to automatically place soft-tissue attachment points. The meshing algorithm produced simulation-ready meshes for all 176 sequences, regardless of the use of provided (manually reconstructed) or predicted (automatically generated)more »segmentation labels. The average time to mesh all bones and cartilage tissues was less than 2 min per knee on an AMD Ryzen 5600X processor, using a parallel pool of three workers for bone meshing, followed by a pool of four workers meshing the four cartilage tissues. Of the 176 sequences with provided segmentation labels, 86% of the resulting meshes completed a simulated flexion-extension activity. We used a reserved testing dataset of 28 sequences unseen during network training to produce simulations derived from predicted labels. We compared tibiofemoral contact mechanics between manual and automated reconstructions for the 24 pairs of successful finite element simulations from this set, resulting in mean root-mean-squared differences under 20% of their respective min-max norms. In combination with further advancements in deep learning, this framework represents a feasible pipeline to produce population sized finite element studies of the natural knee from subject-specific models.« less
5. A Large-Scale Comparison of Tetrahedral and Hexahedral Elements for Solving Elliptic PDEs with the Finite Element Method

   https://doi.org/10.1145/3508372  

   Schneider, Teseo ; Hu, Yixin ; Gao, Xifeng ; Dumas, Jérémie ; Zorin, Denis ; Panozzo, Daniele ( June 2022 , ACM Transactions on Graphics)

   The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which require a tetrahedral or hexahedral mesh to construct the basis. While the theoretical properties of FEM basis (such as convergence rate, stability, etc.) are well understood under specific assumptions on the mesh quality, their practical performance, influenced both by the choice of the basis construction and quality of mesh generation, have not been systematically documented for large collections of automatically meshed 3D geometries. We introduce a set of benchmark problems involving most commonly solved elliptic PDEs, starting from simple cases with an analytical solution, moving to commonly used test problem setups, and using manufactured solutions for thousands of real-world, automatically meshed geometries. For all these cases, we use state-of-the-art meshing tools to create both tetrahedral and hexahedral meshes, and compare the performance of different element types for common elliptic PDEs. The goal of this benchmark is to enable comparison of complete FEM pipelines, from mesh generation to algebraic solver, and exploration of relative impact of different factors on the overall system performance. Asmore »a specific application of our geometry and benchmark dataset, we explore the question of relative advantages of unstructured (triangular/ tetrahedral) and structured (quadrilateral/hexahedral) discretizations. We observe that for Lagrange-type elements, while linear tetrahedral elements perform poorly, quadratic tetrahedral elements perform equally well or outperform hexahedral elements for our set of problems and currently available mesh generation algorithms. This observation suggests that for common problems in structural analysis, thermal analysis, and low Reynolds number flows, high-quality results can be obtained with unstructured tetrahedral meshes, which can be created robustly and automatically. We release the description of the benchmark problems, meshes, and reference implementation of our testing infrastructure to enable statistically significant comparisons between different FE methods, which we hope will be helpful in the development of new meshing and FEA techniques.« less