Mesh Simplification Research Articles

Management of post-iliac crest bone harvesting hernias: Insights from a case series and systematic review

IntroductionHernias following iliac bone grafting are a rare but significant complication, with the earliest case reported in 1945. Repairing these hernias is challenging. Appropriate repair techniques are needed to minimise morbidity and recurrence. We present our experience with three cases of post-iliac graft hernia repair with mesh anchored to titanium mini-plates and a systematic review of current literature. MethodWe conducted a systematic review of the literature in February 2024 on two online databases, PubMed®/MEDLINE and EMBASE, in accordance with PRISMA guidelines. Keywords used were “Hernia,” “Iliac,” and “Graft.” Data on demographics, initial pathology, time to presentation, type of hernia repair, and outcome were collected. Studies not in English and related to other types of hernia were excluded. ResultsWe included 30 studies out of 751 results, spanning from 1975 to 2023. There were 40 reported cases of hernias post iliac bone grafting. The age distribution ranged from 37 to 88 years, with a median age of 60. The majority of patients (40 %) presented within one year. Fracture management, accounting for 19 cases (47.5 %), was the main indication for bone grafting. Mesh repair was performed in 31 cases (77.5 %). Seven cases (17.5 %) of recurrence were reported. ConclusionRecurrence is a common complication in patients with post-iliac graft hernias. Open mesh repair is the most frequently performed surgery and involves various techniques. While titanium mini-plates as anchors enable a pre-peritoneal plane mesh repair, long-term follow-up and comparative studies are needed to evaluate its efficacy compared to simple mesh.

Algorithms and data structures for Cs-smooth RMB-splines of degree 2s + 1

The simple mesh refinement algorithm of Groiss et al. (2023) generates T-meshes admitting Reachable Minimally supported (RM) B-splines that possess the property of local linear independence and form a non-negative partition of unity. The construction was first presented for the bilinear case and has later been extended to Cs-smooth splines of degree p=2s+1. The present paper is devoted to algorithms and data structures for RMB-splines. We prove that the memory consumption of the data structures for representing a T-mesh and the associated RMB-splines is linear with respect to the mesh size, and we describe the details of the underlying refinement algorithm. Moreover, we introduce a novel evaluation algorithm for RMB-spline surfaces, which is based solely on repeated convex combinations of the control points, thereby generalizing de Boor's algorithm for tensor-product splines. Numerical experiments are included to demonstrate the advantageous behavior of the proposed data structures and algorithms with respect to their efficiency. We observe that the total computational time (which includes also error estimation and spline coefficient computation) scales roughly linearly with the number of degrees of freedom for the meshes considered.

Policy and practice review consensus statements and clinical guidelines on managing pediatric trauma and orthopedics during the COVID-19 pandemic: a systematic review on the global response for future pandemics and public health crises.

The COVID-19 pandemic has been recognized as an unprecedented global health crisis. Over 7 million mortalities have been documented with many paediatric fatalities. Trauma and orthopaedic care, much like other specialities, were marginalized due to resource allocation during the pandemic which affected paediatric care. This is the first systematic review to centralise and compile the recommended published guidelines from professional bodies in principally English speaking countries on managing paediatric trauma and orthopaedic care. These guidelines will be required to be implemented sooner and more effectively in case of future pandemics with similar impact. A search was conducted on PubMed/MedLine, Cochrane Library and Embase using terms including p(a)ediatric or child* and/or COVID* or coronavirus or SARS-CoV-2 and/or trauma and/or orthop(a)edic* with a simplified MeSH heading [mh] in order to make the search as comprehensive as possible. General terminology was utilized to make the search as exhaustive as possible for this systematic review. Another search was conducted on resources available in the public domain from professional bodies publishing on consensus statements and clinical practice guidelines in countries where English is the principal language managing pediatric trauma and orthopedics. The review adhered to PRISMA guidance. The search revealed a total of 62 results from both databases and professional bodies. Duplicates were removed. This was then reviewed to identify a total of 21 results which fit the inclusion criteria and included within the main analysis. The guidelines from professional bodies were outlined and categorized into aspects of clinical care. The impact of COVID-19 pandemic has compelled for changes in clinical practice and pediatric management. The systematic review highlights the relevant guidelines on service provision for pediatric patients including indications for urgent referrals, surgical prioritization, reasons for follow-up and trauma guidelines. The rationale for care during the unpredictable evolution of the COVID-19 pandemic may have the potential to be translated and replicated in future pandemics of similar significance.

Monte Carlo multiphysics simulation on adaptive unstructured mesh geometry

Monte Carlo simulation based on Constructive Solid Geometry (CSG) brings unique challenges for multiphysics simulation, including establishing field transfers with mesh-based physics codes, the combination of stochastic and deterministic solvers, and high computational expense. In this work, an adaptive, on-the-fly mesh-based Monte Carlo geometry algorithm is implemented in Cardinal to reduce the barrier-to-entry for high-fidelity multiphysics by (i) eliminating ambiguity in defining CSG cells for temperature and density feedback, (ii) enabling simple mesh convergence studies, and (iii) more closely integrating Computer Aided Design (CAD) workflows with Monte Carlo methods. During Picard iterations, an OpenMC mesh geometry is adaptively refined or coarsened by contouring temperature and/or density fields from a thermal-fluid solver. This algorithm is applied to a full-core Molten Salt Fast Reactor (MSFR) geometry with NekRS Large Eddy Simulation (LES) coupled to OpenMC neutron transport. A performance study indicates a net speedup of 2.3× in the OpenMC solver when using an adaptive geometry for cell sizes chosen intermediate to the as-built CAD geometry versus 1:1 element tracking, which points to future algorithmic research in accelerated Monte Carlo mesh tracking.

A parallel coupling framework for DEM-MBD: Model verification and application

Bulk material handling equipment can be numerically studied using the DEM-MBD method, where the particulate dynamics are solved by DEM (Discrete Element Method) and the motion characteristics of the mechanical components are modeled by MBD (Multi-Body Dynamics). In this work, a two-way coupling framework is proposed for the co-simulation of our self-developed DEM solver (DEMSLab) with the commercial MBD software (RecurDyn) using a parallel staggered coupling approach. To verify the proposed coupling method, the simulation result of a torsional spring damper system is compared with the corresponding analytical solution. After that, to assess the feasibility of this method in industrial-scale applications, a series of simulations involving a wheel loader is carried out. Different simulation conditions are adopted to reveal their impact on computational efficiency and simulation accuracy. These conditions include the mesh representation of the equipment geometry, the MBD time step size, and the coupling interval. An improved mesh simplification algorithm is proposed and used to reasonably simplify the surface mesh of the wheel loader, thus lowering the computational intensity of particle-wall interactions in DEM. The comparison results indicate that the computational time can be largely saved while the simulation accuracy remains considerably high. The MBD step size and coupling interval are crucial for numerical stability and should be selected carefully.

Necessary and sufficient conditions for avoiding Babuška’s paradox on simplicial meshes

Abstract It is shown that discretizations based on variational or weak formulations of the plate bending problem with simple support boundary conditions do not lead to the failure of convergence when polygonal domain approximations are used and the imposed boundary conditions are compatible with the nodal interpolation of the restriction of certain regular functions to approximating domains. It is further shown that this is optimal in the sense that a full realization of the boundary conditions leads to failure of convergence for conforming methods. The abstract conditions imply that standard nonconforming and discontinuous Galerkin methods converge correctly while conforming methods require a suitable relaxation of the boundary condition. The results are confirmed by numerical experiments.

Weights for moments’ geometrical localization: a canonical isomorphism

This paper deals with high order Whitney forms. We define a canonical isomorphism between two sets of degrees of freedom. This allows to geometrically localize the classical degrees of freedom, the moments, over the elements of a simplicial mesh. With such a localization, it is thus possible to associate, even with moments, a graph structure relating a field with its potential.

Experimental study of the tension forming model of a long-span string-supported spoke-type truss structure

This paper investigates the structural response of the long-span string-supported spoke-type (LSSS) truss structure during the tension forming process, as well as the influences of the errors caused by initial defects of the structure. A 1:10 scaled test model was designed and fabricated with reference to the main hall structure of the Northwest University gymnasium. The mesh simplification and scaling-down of the design of the prototype were performed to obtain a test model with good similarity to the prototype. Subsequently, after the comparative analysis of different tensioning batches, numbers of tensioning stages, and tensioning sequences, a radial-cable-forming scheme of three-stage, five-batch, clockwise tensioning for each ring cables was determined to be superior for this type of system. The cable force, node vertical displacement, and rod stress were monitored during the test. SAP2000 finite element software was employed to establish a numerical model, which was then verified by the test results. The test results were found to be in good agreement with the simulation results. The outer-ring cables withstood a larger share of the load, which could provide more stiffness support for the structure. During the tensioning process, the tensioning of the inner-ring cables would further increase the vertical displacement of the outer-ring roof nodes, which increased the compressive stress of the upper-chord-rods near the outer-ring. After the tensioning was completed, the lower-chord-rods in the mid-span and at the ends of the truss were in tension. Comparative analyses of the variations of the position and geometry, as well as the cable force, in each ring of cables during the construction process demonstrated that initial defects in the installation of the upper roof will lead to the uneven distribution of the radial cable forces, and that the errors will gradually accumulate with the advancement of the tensioning stage. However, after the structure was formed, the verticality deviation of most struts was close to or less than 1/150, and the error between the measured value and the simulated value of the rod stress was basically kept below 10 %, which proved the rationality of the tension scheme adopted in the test.

CWF: Consolidating Weak Features in High-quality Mesh Simplification

In mesh simplification, common requirements like accuracy, triangle quality, and feature alignment are often considered as a trade-off. Existing algorithms concentrate on just one or a few specific aspects of these requirements. For example, the well-known Quadric Error Metrics (QEM) approach [Garland and Heckbert 1997] prioritizes accuracy and can preserve strong feature lines/points as well, but falls short in ensuring high triangle quality and may degrade weak features that are not as distinctive as strong ones. In this paper, we propose a smooth functional that simultaneously considers all of these requirements. The functional comprises a normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) [Du et al. 1999] energy term, with the variables being a set of movable points lying on the surface. The former inherits the spirit of QEM but operates in a continuous setting, while the latter encourages even point distribution, allowing various surface metrics. We further introduce a decaying weight to automatically balance the two terms. We selected 100 CAD models from the ABC dataset [Koch et al. 2019], along with 21 organic models, to compare the existing mesh simplification algorithms with ours. Experimental results reveal an important observation: the introduction of a decaying weight effectively reduces the conflict between the two terms and enables the alignment of weak features. This distinctive feature sets our approach apart from most existing mesh simplification methods and demonstrates significant potential in shape understanding. Please refer to the teaser figure for illustration.

Binary Opacity Grids: Capturing Fine Geometric Detail for Mesh-Based View Synthesis

While surface-based view synthesis algorithms are appealing due to their low computational requirements, they often struggle to reproduce thin structures. In contrast, more expensive methods that model the scene's geometry as a volumetric density field (e.g. NeRF) excel at reconstructing fine geometric detail. However, density fields often represent geometry in a "fuzzy" manner, which hinders exact localization of the surface. In this work, we modify density fields to encourage them to converge towards surfaces, without compromising their ability to reconstruct thin structures. First, we employ a discrete opacity grid representation instead of a continuous density field, which allows opacity values to discontinuously transition from zero to one at the surface. Second, we anti-alias by casting multiple rays per pixel, which allows occlusion boundaries and subpixel structures to be modelled without using semi-transparent voxels. Third, we minimize the binary entropy of the opacity values, which facilitates the extraction of surface geometry by encouraging opacity values to binarize towards the end of training. Lastly, we develop a fusion-based meshing strategy followed by mesh simplification and appearance model fitting. The compact meshes produced by our model can be rendered in real-time on mobile devices and achieve significantly higher view synthesis quality compared to existing mesh-based approaches. Our interactive webdemo is available at https://binary-opacity-grid.github.io.

Quality-preserving multilevel mesh generation for building models

ABSTRACT Three-dimensional (3D) high-fidelity building models are crucial for digital twin cities. Multi-scale modeling is crucial for accurately capturing the complexity of urban environments; however, existing methods often lack the flexibility required to satisfy the varied demands of diverse applications. In this paper, we propose a framework to continuously simplify 3D building models, it dynamically adjusts mesh accuracy to meet diverse needs, enabling seamless transitions from high-poly to medium and low-poly meshes. Our method contains three main stages: First, in the mesh repair stage, we introduce a novel mesh repair framework based on an advanced Marching Cubes 33 algorithm to ensure a watertight and clean topology mesh. Then, for generating medium-poly meshes, we employ a feature-preserving mesh simplification algorithm that combines curvature and area-weighted quadratic error metrics to achieve a high-fidelity simplified mesh. For generating low-poly meshes, we use the concept of carving visual hull to generate low-poly mesh with high visual similarity. Our method has been evaluated on building subsets of the Free3D and Thingi10 K datasets, as well as on various building models generated from different observation scales, and its superiority has been validated through extensive comparisons with state-of-the-art techniques.

Evaluating Entropy of Geometric Accuracy in 3D Objects During Mesh Simplification

Evaluating Entropy of Geometric Accuracy in 3D Objects During Mesh Simplification

Industry Foundation Class-Based Building Information Modeling Lightweight Visualization Method for Steel Structures

The efficient extraction, storage, and visualization of geometric and semantic information is a key foundation for the operation of the building information modeling (BIM) platform. This study aims to develop a lightweight BIM system and optimize the system’s performance according to the specific characteristics of steel structures. This study proposes several novel techniques for extracting and decoupling the geometric and semantic information of components from industry foundation class (IFC) files. A redundancy removal approach combining the principal content analysis (PCA) algorithm and the Hausdorff-based comparison algorithm is proposed to identify standardized steel components, and a lightweight visualization method on Web3D for redundant instances is also presented. A loading mechanism of the level of detail (LOD) model based on a mesh simplification algorithm is presented to optimize the display efficiency. The developed system is evaluated by three steel structural models. Using the redundancy removal approach, the number of instances is decreased by 96.46% in less than 30 s and over 30 FPS (frame per second) is kept when rendering. Using the LOD loading mechanism, 95.38% of vertices and 98.46% of patches are eliminated under 50 mm precision. The experiment results indicate that users can quickly load large BIM models and fetch sufficient information from the website.

Laparoscopic repair for a recurrent epigastric incisional hernia following xiphoidectomy: A case report

Introduction: Xiphodynia is a rare musculoskeletal disorder characterized by epigastric or anterior chest pain, for which xiphoidectomy is considered as a definitive treatment. This procedure and its complications are not well researched, particularly within Australasian populations. We describe the novel laparoscopic incisional hernia repair from a xiphoidectomy complicated by recurrent epigastric hernias. Case Report: A 49-year-old female presented with chronic epigastric pain post-xiphoidectomy for xiphoidynia. The patient previously underwent open mesh repair for an incisional epigastric hernia, complicated by infection and subsequent removal of the mesh. A vacuum-assisted closure device was then utilized, followed by delayed primary closure. However, she experienced ongoing pain, a recurrent mass, and hypertrophic scarring, confirmed by abdominal computed tomography (CT) scan. Our laparoscopic approach involved a standard supine position with three ports and preperitoneal dissection similar to transabdominal preperitoneal (TAPP) hernia repair. The defect was 5 × 8 cm in size. A simple prolene mesh (9 × 12 cm) was secured with AsorbaTack and Glubran 2, followed by peritoneal closure with a 3/0 V-Loc suture. At two months follow-up, the patient had no evidence of recurrent hernia, no ongoing pain, and satisfactory wound healing. Conclusion: Laparoscopic surgical repair using a TAPP approach is a safe alternative to open repair of an incisional recurrent epigastric hernia post-xiphoidectomy.

Hp-Multigrid Preconditioner for a Divergence-Conforming HDG Scheme for the Incompressible Flow Problems

In this study, we present an hp-multigrid preconditioner for a divergence-conforming HDG scheme for the generalized Stokes and the Navier–Stokes equations using an augmented Lagrangian formulation. Our method relies on conforming simplicial meshes in two- and three-dimensions. The hp-multigrid algorithm is a multiplicative auxiliary space preconditioner that employs the lowest-order space as the auxiliary space, and we develop a geometric multigrid method as the auxiliary space solver. For the generalized Stokes problem, the crucial ingredient of the geometric multigrid method is the equivalence between the condensed lowest-order divergence-conforming HDG scheme and a Crouzeix–Raviart discretization with a pressure-robust treatment as introduced in Linke and Merdon (Comput Methods Appl Mech Engrg 311:304–326, 2022), which allows for the direct application of geometric multigrid theory on the Crouzeix–Raviart discretization. The numerical experiments demonstrate the robustness of the proposed hp-multigrid preconditioner with respect to mesh size and augmented Lagrangian parameter, with iteration counts insensitivity to polynomial order increase. Inspired by the works by Benzi and Olshanskii (SIAM J Sci Comput 28:2095–2113, 2006) and Farrell et al. (SIAM J Sci Comput 41:A3073–A3096, 2019), we further test the proposed preconditioner on the divergence-conforming HDG scheme for the Navier–Stokes equations. Numerical experiments show a mild increase in the iteration counts of the preconditioned GMRes solver with the rise in Reynolds number up to 103\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^3$$\\end{document}.

Bony reconstruction after internal hemipelvectomy: A retrospective analysis of 44 patients undergoing femoro-pelvic pseudoarthrosis.

e23509 Background: After acetabular resection for sarcomas, achieving a bony femoro-pelvic fusion is very difficult, and prosthetic reconstructions have very high complication rates. We reconstructed the defects with a simple polypropylene mesh between the femoral head and the remaining part of the pelvis thereby aiming at a pseudo-arthrosis and analyzed its functional outcome. Methods: Between 2013 and 2022, 44 patients having bone tumors of the pelvis underwent acetabular resections and femoro-pelvic pseudoarthrosis. Commonest Histology was chondrosarcoma (23). According to Enneking’s classification, type II (3), type I+II (9) , type II+III (24), type I+II+IV (5), and type I+II+III (3) resections were carried out. A 30 x 30 cm polypropylene mesh was tied to the remains of the capsule around the head and was then turned on itself to make a strong braided rope-like structure. It was passed through the remaining ilium/ ischium/ sacrum and was tied to itself in proper rotation with heavy ethibond suture. In 4 cases, a proximal femur megaprosthesis and in 2, a nail cement spacer was implanted in femur to reduce shortening. Functional limb results were reported according to MSTS functional scores. Results: 37/44 patients attained independent ambulation. The mean time to full weight bearing was 4.7 months (3-9 months). There were 6 flap necrosis, 3 infections, 1 nerve injury, and 1 vascular injury. Local recurrence occurred in 6 (13%) and Systemic metastasis developed in 20 patients (47% of malignant tumors). At an average follow-up of 56 months ( 24 – 127 months), 26 are alive without any signs of disease. The average MSTS score was 22 (range 13–27). The best MSTS scores were with type II or II+III IH where ilium was left to support the femur while the worst was with type I+II+III resection patients. Patients with higher BMI have poorer functional outcomes with meshplasty. Conclusions: Mesh-pseudoarthrosis is a very simple reconstruction option that has an excellent functional outcome. It reduces surgical time and eliminates uncertainties about fusion/joint replacement. This should be strongly recommended as a method of reconstruction for patients undergoing acetabular resections.

Space-time CutFEM on overlapping meshes II: simple discontinuous mesh evolution

We present a cut finite element method for the heat equation on two overlapping meshes: a stationary background mesh and an overlapping mesh that evolves inside/“on top” of it. Here the overlapping mesh is prescribed by a simple discontinuous evolution, meaning that its location, size, and shape as functions of time are discontinuous and piecewise constant. For the discrete function space, we use continuous Galerkin in space and discontinuous Galerkin in time, with the addition of a discontinuity on the boundary between the two meshes. The finite element formulation is based on Nitsche’s method. The simple discontinuous mesh evolution results in a space-time discretization with a slabwise product structure between space and time which allows for existing analysis methodologies to be applied with only minor modifications. We follow the analysis methodology presented by Eriksson and Johnson (SIAM J Numer Anal 28(1):43–77, 1991; SIAM J Numer Anal 32(3):706–740, 1995). The greatest modification is the introduction of a Ritz-like “shift operator” that is used to obtain the discrete strong stability needed for the error analysis. The shift operator generalizes the original analysis to some methods for which the discrete subspace at one time does not lie in the space of the stiffness form at the subsequent time. The error analysis consists of an a priori error estimate that is of optimal order with respect to both time step and mesh size. We also present numerical results for a problem in one spatial dimension that verify the analytic error convergence orders.

Space-time CutFEM on overlapping meshes I: simple continuous mesh motion

We present a cut finite element method for the heat equation on two overlapping meshes: a stationary background mesh and an overlapping mesh that moves around inside/“on top” of it. Here the overlapping mesh is prescribed by a simple continuous motion, meaning that its location as a function of time is continuous and piecewise linear. For the discrete function space, we use continuous Galerkin in space and discontinuous Galerkin in time, with the addition of a discontinuity on the boundary between the two meshes. The finite element formulation is based on Nitsche’s method and also includes an integral term over the space-time boundary between the two meshes that mimics the standard discontinuous Galerkin time-jump term. The simple continuous mesh motion results in a space-time discretization for which standard analysis methodologies either fail or are unsuitable. We therefore employ what seems to be a relatively uncommon energy analysis framework for finite element methods for parabolic problems that is general and robust enough to be applicable to the current setting. The energy analysis consists of a stability estimate that is slightly stronger than the standard basic one and an a priori error estimate that is of optimal order with respect to both time step and mesh size. We also present numerical results for a problem in one spatial dimension that verify the analytic error convergence orders.

Parallel Topology-aware Mesh Simplification on Terrain Trees

We address the problem of performing a topology-aware simplification algorithm on a compact and distributed data structure for triangle meshes, the Terrain trees. Topology-aware operators have been defined to coarsen a Triangulated Irregular Network (TIN) without affecting the topology of its underlying terrain, i.e., without modifying critical features of the terrain, such as pits, saddles, peaks, and their connectivity. However, their scalability is limited for large-scale meshes. Our proposed algorithm uses a batched processing strategy to reduce both the memory and time requirements of the simplification process, and thanks to the spatial decomposition on the basis of Terrain trees, it can be easily parallelized. Also, since a Terrain tree after the simplification process becomes less compact and efficient, we propose an efficient post-processing step for updating hierarchical spatial decomposition. Our experiments on real-world TINs, derived from topographic and bathymetric LiDAR data, demonstrate the scalability and efficiency of our approach. Specifically, topology-aware simplification on Terrain trees uses 40% less memory and half the time compared to the most compact and efficient connectivity-based data structure for TINs. Furthermore, the parallel simplification algorithm on the Terrain trees exhibits a 12× speedup with an OpenMP implementation. The quality of the output mesh is not significantly affected by the distributed and parallel simplification strategy of Terrain trees, and we obtain similar quality levels compared to the global baseline method.

Mass lumping of stable generalized finite element methods for parabolic interface problems

Stable generalized finite element method (SGFEM) for interface problem is based on simple mesh independent of interface curves and possesses merits of optimal convergence rates, conditioning of same order as that of finite element method (FEM), robustness, and freedom from any penalty parameters or stability schemes. This paper investigates mass lumping of SGFEM for parabolic interface problems. The mass lumping is important for computational reduction and maximum principle preserving. The difficulty in the mass lumping of conventional generalized FEM (GFEM) and SGFEM consists in their incorporation of extra enriched functions. The existing mass lumping methods of GFEM cannot work properly due to features of SGFEM that enriched shape functions vanish on mesh nodes, and the nodes are enriched partially rather than totally. In this study, we propose two mass lumping schemes for the SGFEM. The first one is to only lump the FEM part, and enriched parts are kept fixed. This scheme enables us to execute a rigorous optimal convergence analysis. It is noted that a theoretical analysis on the mass lumping of GFEM has not been available yet in the GFEM field. The second scheme is to further compress the enriched part and intersection part of mass matrix separately. The lumped mass matrix is almost diagonal, and there is only a line of nonzero entries in the intersection part of mass matrix. Numerical experiments indicate that two schemes both produce the optimal convergence rates; their errors are almost the same as those of SGFEM without using the mass lumping.