Mesh Modification Research Articles

Zometool shape approximation

We present an algorithm that approximates 2-manifold surfaces with Zometool models while preserving their topology. Zometool is a popular hands-on mathematical modeling system used in teaching, research and for recreational model assemblies at home. This construction system relies on a single node type with a small, fixed set of directions and only 9 different edge types in its basic form. While being naturally well suited for modeling symmetries, various polytopes or visualizing molecular structures, the inherent discreteness of the system poses difficult constraints on any algorithmic approach to support the modeling of freeform shapes. We contribute a set of local, topology preserving Zome mesh modification operators enabling the efficient exploration of the space of 2-manifold Zome models around a given input shape. Starting from a rough initial approximation, the operators are iteratively selected within a stochastic framework guided by an energy functional measuring the quality of the approximation. We demonstrate our approach on a number of designs and also describe parameters which are used to explore different complexities and enable coarse approximations.

Coating of mesh grafts for prolapse and urinary incontinence repair with autologous plasma: exploration stage of a surgical innovation.

Purpose. Optimized biocompatibility is a major requirement for alloplastic materials currently applied for stress urinary incontinence (SUI) and pelvic organ prolapse (POP) repair. In the preliminary studies the mesh modification by coating with autologous plasma resulted in the increased adherence score in vitro and improved biocompatibility in an animal model. The first use of plasma coated meshes in human is presented. Materials and Methods. Between 04/2013 and 05/2014, 20 patients with the indication for SUI and POP repair were selected in a single institution. The applied meshes were modified by autologous plasma coating prior to implantation. A retrospective chart review for peri- and early postoperative complications was performed. Functional outcome and QoL were evaluated pre- and postoperatively. Results. The functional outcome and QoL improved significantly in all groups. Two reoperations (Grade IIIB) with the release of TVT-mesh in anesthesia due to the obstruction were needed. No other severe complications were registered. Conclusion. For the first time we applied a mesh modification in a human setting according to IDEAL criteria of surgical innovations. The procedure of mesh coating with autologous plasma is safe and a prospective randomized trial proving a positive effect of plasma coating on the biocompatibility and morbidity outcome with long-term registry is planned.

Metric-orthogonal Anisotropic Mesh Generation

We introduce a procedure to generate metric-orthogonal anisotropic volume meshes. These meshes are obtained when most of the edges are aligned with the eigenvectors of a provided input metric field. The goal is to generate locally structured meshes in an anisotropic context and in the presence of complex geometries. The algorithm relies on two local mesh modification operators. The first one is used to quickly coarsen volume meshes. From a coarse volume mesh, the second operator is used to insert iteratively points in a frontal manner. The local alignment and orthogonality are naturally inherited from the eigenvectors and eigenvalues of an input metric field. We show on several 3D numerical examples that this procedure is robust and can generate anisotropic locally structured meshes.

三次元非構造メッシュ修正システムへの要素細分化手法の導入とシステム適用性の向上研究

本論文は，三次元非構造メッシュをバーチャルリアリティ空間において立体可視化して，メッシュの品質の評価および修正を対話的に行うことが可能なシステムの構築を行うものである．メッシュの修正方法としては，節点移動法に加えて要素細分化法の実装を行うとともに，任意形状の表面メッシュに対して節点移動制御を行うことを可能とし，システムの適用性の向上を実現した．また，要素のオーバーラップを検出する手法の構築とそれらを修正するための機能の実装を行った，本システムの妥当性と有効性の検証行うために，固体解析の例題に適用を行った．

A Modification of the Shishkin Discretization Mesh

AbstractIn this paper we consider a modification of the Shishkin discretization mesh designed for the numerical solution of one‐dimensional linear convection‐diffusion singularly perturbed problems. The modification consists of a slightly different choice of the transition point between the fine and coarse parts of the mesh. This leads to a better layer‐resolving mesh and to an improvement in the accuracy of the computed solution although the convergence order remains the same. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

An error analysis of some higher order space-time moving finite elements

This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a method of lines approach coupled with mesh modification to solve linear partial differential equations. Mesh modification can be both continuous (moving meshes) and discrete (static rezone). These methods can lead to significant savings in computation costs for problems having solutions that develop steep moving fronts or other localized time-dependent features of interest. Our main result is a symmetric a priori error estimate for the finite element solution computed in this setting.

Parallel mesh adaptation for high-order finite element methods with curved element geometry

This paper presents a parallel adaptive mesh control procedure designed to operate with high-order finite element analysis packages to enable large-scale automated simulations on massively parallel computers. The curved mesh adaptation procedure uses curved entity mesh modification operations that explicitly consider the influence of the curved mesh entities on element shape. Applications of the curved mesh adaptation procedure have been developed to support the parallel automated adaptive accelerator simulations at SLAC National Accelerator Laboratory.

Geometry seam carving

We present a novel approach to feature-aware mesh deformation. Previous mesh editing methods are based on an elastic deformation model and thus tend to uniformly distribute the distortion in a least-squares sense over the entire deformation region. Recent results from image resizing, however, show that discrete local modifications such as deleting or adding connected seams of image pixels in regions with low saliency lead to far superior preservation of local features compared to uniform scaling — the image retargeting analog to least-squares mesh deformation. Hence, we propose a discrete mesh editing scheme that combines elastic as well as plastic deformation (in regions with little geometric detail) by transferring the concept of seam carving from image retargeting to the mesh deformation scenario. A geometry seam consists of a connected strip of triangles within the mesh’s deformation region. By collapsing or splitting the interior edges of this strip, we perform a deletion or insertion operation that is equivalent to image seam carving and can be interpreted as a local plastic deformation. We use a feature measure to rate the geometric saliency of each triangle in the mesh and a well-adjusted distortion measure to determine where the current mesh distortion asks for plastic deformations, i.e., for deletion or insertion of geometry seams. Precomputing a fixed set of low-saliency seams in the deformation region allows us to perform fast seam deletion and insertion operations in a predetermined order such that the local mesh modifications are properly restored when a mesh editing operation is (partially) undone. Geometry seam carving hence enables the deformation of a given mesh in a way that causes stronger distortion in homogeneous mesh regions while salient features are preserved much better.

A modification of the Shishkin discretization mesh for one-dimensional reaction–diffusion problems

In this paper we consider a modification of the Shishkin discretization mesh designed for the numerical solution of one-dimensional singularly perturbed reaction–diffusion problems. The modification consists of a slightly different choice of the transition points between the fine and coarse parts of the mesh. We prove that this change does not affect the order of convergence of the numerical solution obtained by using the central finite-difference scheme. However, due to a better layer-resolving mesh, numerical results show an improvement in the accuracy of the computed solution when compared to the results on the standard Shishkin mesh.

Triangular element partition method with consideration of crack tip

In fracture simulation, how to model the pre-existing cracks and simulate their propagation without remeshing is an important topic. The newly developed triangular element partition method (TEPM) provides an efficient approach to this problem. It firstly meshes the cracked body regardless of the geometry integrity of the interesting object with triangular elements. After the meshing procedure is completed, some elements are intersected by cracks. For the element intersected by a crack, the TEPM takes the element partition technique to incorporate the discontinuity into the numerical model without any interpolation enrichment. By this approach, the TEPM can simulate fracture without mesh modification. In the TEPM, all the cracked elements are treated as the usual partitioned elements in which the crack runs through. The virtual node pairs (the intersection points of crack faces and elements) at the opposite faces of the crack move independently. Their displacements are respectively determined by their neighbor real nodes (nodes formatted in the original mesh scheme) at the same side of the crack. However, among these cracked elements, the element containing a crack tip, referred to as the crack tip element thereafter, behaves differently from those cut through by the crack. Its influence on the singular field at the vicinity of the fracture tip becomes increasingly significant with the element size increasing. In the crack tip element, the virtual node pair at the crack tip move consistently before fracture occurs while the virtual node pair separate and each virtual node moves independently after the fracture propagates. Accordingly, the crack tip element is automatically transformed into the usual partitioned element. In the present paper, the crack tip element is introduced into the TEPM to account for the effect of the crack tip. Validation examples indicate that the present method is almost free from the element size effect. It can reach the same precision as the conventional finite element method under the same meshing scheme. But the TEPM is much more efficient and convenient than the conventional finite element method because the TEPM avoids the troubles that the conventional finite element method suffers, e.g., the meshing problem of cracked body, modification of mesh scheme, etc. Though the extended finite element method can also avoid these troubles, it introduces extra degrees of freedom due to node interpolation enrichment. Due to the simplicity of the present TEPM, it is believed that its perspective should be highly inspiring.

A parallel adaptive mesh method for the numerical simulation of multiphase flows

Methodology for performing large scale parallel numerical simulations of two-phase flow is presented that uses a three-dimensional (3-D) finite element method (FEM) solver, PHASTA, to perform the simulation and a parallel mesh adaptation code, phParAdapt, to iteratively refine and coarsen regions of the solution domain. This version of PHASTA uses a stabilized FEM to discretize the 3-D Incompressible Navier–Stokes (INS) equations plus a level set method to capture the two-phase interface. The phParAdapt code takes the current parallel mesh along with the PHASTA flow solution and, using various user-specified correction indicators as input, performs a parallel mesh refinement/coarsening procedure. Utilizing local mesh modification operators, element sizes are adjusted to equally distribute the errors across the distributed mesh during the mesh refinement/coarsening procedure. Numerical simulations ranging from simple canonical test problems up to an experimental annular steam/water flow condition were performed to illustrate this methodology. The annular flow simulation captured the instabilities that generate both the ripple and roll wave like structures on the steam/water interface and the droplet entrainment mechanisms expected in annular two-phase flows.

Underlay mesh repair for spontaneous lumbar hernia

INTRODUCTIONLumbar hernia is a rare condition with fewer than 300 cases reported in the literature. It arises through posterolateral abdominal wall defects, named the inferior triangle (Petit) and superior triangle (Grynfelt). It can be congenital or acquired, primary or secondary, peritoneal or extraperitoneal, reducible or complicated. PRESENTATION OF CASEWe report a 63 year old female patient who presented to our hospital with a reducible right superior lumbar hernia. She underwent repair with underlay mesh after inversion of the sac and had a smooth postoperative course. DISCUSSIONIn contrast to the classical procedure the underlay mesh modification saved us from enlarging the defect, and was quick and associated with minimal tissue injury. CONCLUSIONUnderlay mesh repair for spontaneous lumbar hernia is feasible when the defect is small.

Dynamic Analysis of Latch-in Relay Using 3-D Finite Element Method with Mesh Modification Method Employing Multi-Mesh and the Interpolation

Dynamic Analysis of Latch-in Relay Using 3-D Finite Element Method with Mesh Modification Method Employing Multi-Mesh and the Interpolation

Does pelvic mesh treated with phosphorylcholine improve outcomes? An early experience

Implantable devices treated with phosphorylcholine (PC) have been successfully used in cardiac, ophthalmic, and other applications. This surface modification has resulted in a reduction in the host inflammatory responses. This pilot study tested the safety and efficacy of PC treated polypropylene mesh grafts implanted for the treatment of pelvic organ prolapse. Surgeons from five U.S. sites collected data on subjects implanted with Perigee IntePro Lite+PC. Pre-procedure data collected included demographics and prolapse severity. At follow-up, subjects were assessed for anatomical outcomes (success≤stage I POPQ or Baden Walker), symptomatic improvement, and complications, particularly mesh exposure. A total of 40 subjects were enrolled with 80% (32/40) of them completing at least 5-7 months of follow-up. Mean patient age was 60 years (range 36-78 years) and the mean BMI was 28 (range 20-40). There were no cases of mesh exposure/extrusion or granuloma formation. The anatomical success rate was 100% at 5-7 months (32/32). This is the first publication on pelvic mesh treated with PC. There were no adverse events attributed to this surface modification. However, as the numbers are small, the results are not statistically significant. PC surface modification of pelvic mesh shows promise in its application for the reduction of mesh related complications.

A uniformly stable Fortin operator for the Taylor–Hood element

We construct a new Fortin operator for the lowest order Taylor---Hood element, which is uniformly stable both in $$L^2$$ and $$H^1$$ . The construction, which is restricted to two space dimensions, is based on a tight connection between a subspace of the Taylor---Hood velocity space and the lowest order Nedelec edge element. General shape regular triangulations are allowed for the $$H^1$$ -stability, while some mesh restrictions are imposed to obtain the $$L^2$$ -stability. As a consequence of this construction, a uniform inf---sup condition associated the corresponding discretizations of a parameter dependent Stokes problem is obtained, and we are able to verify uniform bounds for a family of preconditioners for such problems, without relying on any extra regularity ensured by convexity of the domain.

Adaptive mesh refinement and coarsening for cohesive zone modeling of dynamic fracture

SUMMARYAdaptive mesh refinement and coarsening schemes are proposed for efficient computational simulation of dynamic cohesive fracture. The adaptive mesh refinement consists of a sequence of edge‐split operators, whereas the adaptive mesh coarsening is based on a sequence of vertex‐removal (or edge‐collapse) operators. Nodal perturbation and edge‐swap operators are also employed around the crack tip region to improve crack geometry representation, and cohesive surface elements are adaptively inserted whenever and wherever they are needed by means of an extrinsic cohesive zone model approach. Such adaptive mesh modification events are maintained in conjunction with a topological data structure (TopS). The so‐called PPR potential‐based cohesive model (J. Mech. Phys. Solids 2009; 57:891–908) is utilized for the constitutive relationship of the cohesive zone model. The examples investigated include mode I fracture, mixed‐mode fracture and crack branching problems. The computational results using mesh adaptivity (refinement and coarsening) are consistent with the results using uniform mesh refinement. The present approach significantly reduces computational cost while exhibiting a multiscale effect that captures both global macro‐crack and local micro‐cracks. Copyright © 2012 John Wiley & Sons, Ltd.

Altering surface characteristics of polypropylene mesh via sodium hydroxide treatment

Incisional hernias represent a serious and common complication following laparotomy. The use of synthetic (e.g. polypropylene) meshes to aid repair of these hernias has considerably reduced recurrence rates. While polypropylene is biocompatible and has a long successful clinical history in treating hernias and preventing reherniation, this material may suffer some limitations, particularly in challenging patients at risk of wound failure due to, for example, an exaggerated inflammation reaction, delayed wound healing, and infection. Surface modification of the polypropylene mesh without sacrificing its mechanical properties, critical for hernia repair, represents one way to begin to address these clinical complications. Our hypothesis is treatment of a proprietary polypropylene mesh with sodium hydroxide (NaOH) will increase in vitro NIH/3T3 cell attachment, predictive of earlier and improved cell colonization and tissue integration of polypropylene materials. Our goal is to achieve this altered surface functionality via enhanced removal of chemicals/oils used during material synthesis without compromising the mechanical properties of the mesh. We found that NaOH treatment does not appear to compromise the mechanical strength of the material, despite roughly a 10% decrease in fiber diameter. The treatment increases in vitro NIH/3T3 cell attachment within the first 72 h and this effect is sustained up to 7 days in vitro. This research demonstrates that sodium hydroxide treatment is an efficient way to modify the surface of polypropylene hernia meshes without losing the mechanical integrity of the material. This simple procedure could also allow the attachment of a variety of biomolecules to the polypropylene mesh that may aid in reducing the complications associated with polypropylene meshes today.

Dual Contouring for domains with topology ambiguity

This paper describes an automatic and robust approach to generate quality triangular and tetrahedral meshes for complicated domains with topology ambiguity. In previous works, we developed an octree-based Dual Contouring (DC) method to construct surface and volumetric meshes for complicated domains. However, topology ambiguity exists and causes non-conformal meshes. In this study, we discuss all possible topology configurations and develop an extension of DC which guarantees the correct topology. We first generate one base mesh with the previous DC method. Then we analyze all the octree leaf cells and categorize them into 31 topology groups. In order to discriminate these cells, we compute the values of their face and body saddle points based on a tri-linear representation inside the cells. Knowing the correct categorization, we are able to modify the base mesh and introduce more minimizer points within the same cell. With these minimizer points we update the mesh connectivities to preserve the correct topology. This method is further extended to 3D tetrahedral mesh generation via an advancing front technique. Finally we use a Laplacian smoothing technique to improve the mesh quality; for tetrahedral mesh a combination of edge-contraction, smoothing and optimization is also applied. Our main contribution is the topology categorization and mesh modification. We have applied our algorithm to three complicated domains and obtained good results.

Gentamicin supplemented polyvinylidenfluoride mesh materials enhance tissue integration due to a transcriptionally reduced MMP-2 protein expression

BackgroundA beneficial effect of gentamicin supplemented mesh material on tissue integration is known. To further elucidate the interaction of collagen and MMP-2 in chronic foreign body reaction and to determine the significance of the MMP-2-specific regulatory element (RE-1) that is known to mediate 80% of the MMP-2 promoter activity, the spatial and temporal transcriptional regulation of the MMP-2 gene was analyzed at the cellular level.MethodsA PVDF mesh material was surface modified by plasma-induced graft polymerization of acrylic acid (PVDF+PAAc). Three different gentamicin concentrations were bound to the provided active sites of the grafted mesh surfaces (2, 5 and 8 μg/mg). 75 male transgenic MMP-2/LacZ mice harbouring the LacZ reporter gene under control of MMP-2 regulatory sequence -1241/+423, excluding the RE-1 were randomized to five groups. Bilateral of the abdominal midline one of the five different meshes was implanted subcutaneously in each animal. MMP-2 gene transcription (anti-ß-galactosidase staining) and MMP-2 protein expression (anti-MMP-2 staining) were analyzed semiquantitatively by immunohistochemistry 7, 21 and 90 days after mesh implantation. The collagen type I/III ratio was analyzed by cross polarization microscopy to determine the quality of mesh integration.ResultsThe perifilamentary ß-galactosidase expression as well as the collagen type I/III ratio increased up to the 90th day for all mesh modifications, whereas no significant changes could be observed for MMP-2 protein expression between days 21 and 90. Both the 5 and 8 μg/mg gentamicin group showed significantly reduced levels of ß-galactosidase expression and MMP-2 positive stained cells when compared to the PVDF group on day 7, 21 and 90 respectively (5 μg/mg: p < 0.05 each; 8 μg/mg: p < 0.05 each). Though the type I/III collagen ratio increased over time for all mesh modifications significant differences to the PVDF mesh were only detected for the 8 μg/mg group at all 3 time points (p < 0.05 each).ConclusionsOur current data indicate that lack of RE-1 is correlated with increased mesh induced MMP-2-gene expression for coated as well as for non-coated mesh materials. Gentamicin coating reduced MMP-2 transcription and protein expression. For the 8 μg/mg group this effect is associated with an increased type I/III collagen ratio. These findings suggest that gentamicin is beneficial for tissue integration after mesh implantation, which possibly is mediated via RE-1.

Algorithms and data structures for massively parallel generic adaptive finite element codes

Today's largest supercomputers have 100,000s of processor cores and offer the potential to solve partial differential equations discretized by billions of unknowns. However, the complexity of scaling to such large machines and problem sizes has so far prevented the emergence of generic software libraries that support such computations, although these would lower the threshold of entry and enable many more applications to benefit from large-scale computing. We are concerned with providing this functionality for mesh-adaptive finite element computations. We assume the existence of an “oracle” that implements the generation and modification of an adaptive mesh distributed across many processors, and that responds to queries about its structure. Based on querying the oracle, we develop scalable algorithms and data structures for generic finite element methods. Specifically, we consider the parallel distribution of mesh data, global enumeration of degrees of freedom, constraints, and postprocessing. Our algorithms remove the bottlenecks that typically limit large-scale adaptive finite element analyses. We demonstrate scalability of complete finite element workflows on up to 16,384 processors. An implementation of the proposed algorithms, based on the open source software p4est as mesh oracle, is provided under an open source license through the widely used deal.II finite element software library.