3D boundary recovery by constrained Delaunay tetrahedralization

Si, Hang; Gärtner, Klaus

doi:10.1002/nme.3016

Cited by 54 publications

(39 citation statements)

References 55 publications

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“…This deforming process involved in finite element simulations [i.e., finite elements for biomechanics, FEBio (Ref. 23 26 The nontrivial integration of these open-source packages was described below as a multiple step process.…”

Section: Methodsmentioning

confidence: 99%

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Building a virtual simulation platform for quasistatic breast ultrasound elastography using open source software: A preliminary investigation

2015

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Purpose: Quasistatic ultrasound elastography (QUE) is being used to augment in vivo characterization of breast lesions. Results from early clinical trials indicated that there was a lack of confidence in image interpretation. Such confidence can only be gained through rigorous imaging tests using complex, heterogeneous but known media. The objective of this study is to build a virtual breast QUE simulation platform in the public domain that can be used not only for innovative QUE research but also for rigorous imaging tests. Methods: The main thrust of this work is to streamline biomedical ultrasound simulations by leveraging existing open source software packages including Field II (ultrasound simulator), VTK (geometrical visualization and processing), FEBio [finite element (FE) analysis], and Tetgen (mesh generator). However, integration of these open source packages is nontrivial and requires interdisciplinary knowledge. In the first step, a virtual breast model containing complex anatomical geometries was created through a novel combination of image-based landmark structures and randomly distributed (small) structures. Image-based landmark structures were based on data from the NIH Visible Human Project. Subsequently, an unstructured FE-mesh was created by Tetgen. In the second step, randomly positioned point scatterers were placed within the meshed breast model through an octree-based algorithm to make a virtual breast ultrasound phantom. In the third step, an ultrasound simulator (Field II) was used to interrogate the virtual breast phantom to obtain simulated ultrasound echo data. Of note, tissue deformation generated using a FE-simulator (FEBio) was the basis of deforming the original virtual breast phantom in order to obtain the postdeformation breast phantom for subsequent ultrasound simulations. Using the procedures described above, a full cycle of QUE simulations involving complex and highly heterogeneous virtual breast phantoms can be accomplished for the first time. Results: Representative examples were used to demonstrate capabilities of this virtual simulation platform. In the first set of three ultrasound simulation examples, three heterogeneous volumes of interest were selected from a virtual breast ultrasound phantom to perform sophisticated ultrasound simulations. These resultant B-mode images realistically represented the underlying complex but known media. In the second set of three QUE examples, advanced applications in QUE were simulated. The first QUE example was to show breast tumors with complex shapes and/or compositions. The resultant strain images showed complex patterns that were normally seen in freehand clinical ultrasound data. The second and third QUE examples demonstrated (deformation-dependent) nonlinear strain imaging and time-dependent strain imaging, respectively. Conclusions: The proposed virtual QUE platform was implemented and successfully tested in this study. Through show-case examples, the proposed work has demonstrated its capabilities of creating sophisticated QUE ...

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Section: Methodsmentioning

confidence: 99%

“…Once a geometric breast model (i.e., multiple 3D complex triangulated surfaces) is obtained, an open-source mesh generator Tetgen 26 (version 1.4.2; WIAS, Berlin, Germany) was used to generate high quality tetrahedral meshes as shown in Fig. 1(b).…”

Section: B Mesh Generationmentioning

confidence: 99%

Building a virtual simulation platform for quasistatic breast ultrasound elastography using open source software: A preliminary investigation

2015

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“…With respect to another type of mainstream unstructured meshing algorithm, i.e., the Delaunay triangulation algorithm, its termination problem for arbitrary complex geometries has been theoretically resolved. Despite this key achievement, the boundary recovery (BR) procedure (Chen, Zhao, Huang, Zheng, & Gao, 2011;Du & Wang, 2004;Si & Gärtner, 2011) is still the main practical challenge of developing a robust Delaunay mesher, particularly in the context of local remeshing, where the grid faces can be greatly stretched during the grid deformation process, and some stretched faces may appear on the boundaries of the holes. In this study, an improved Delaunay mesher for local remeshing is presented.…”

Section: Introductionmentioning

confidence: 99%

An improved local remeshing algorithm for moving boundary problems

Zheng

Chen

Zheng

et al. 2016

Engineering Applications of Computational Fluid Mechanics

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Three issues are tackled in this study to improve the robustness of local remeshing techniques. Firstly, the local remeshing region (hereafter referred to as 'hole') is initialized by removing low-quality elements and then continuously expanded until a certain element quality is reached after remeshing. The effect of the number of the expansion cycle on the hole size and element quality after remeshing is experimentally analyzed. Secondly, the grid sources for element size control are attached to moving bodies and will move along with their host bodies to ensure reasonable grid resolution inside the hole. Thirdly, the boundary recovery procedure of a Delaunay grid generation approach is enhanced by a new grid topology transformation technique (namely shell transformation) so that the new grid created inside the hole is therefore free of elements of extremely deformed/skewed shape, whilst also respecting the hole boundary. The proposed local remeshing algorithm has been integrated with an in-house unstructured grid-based simulation system for solving moving boundary problems. The robustness and accuracy of the developed local remeshing technique are successfully demonstrated via industry-scale applications for complex flow simulations. ARTICLE HISTORY

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“…The right illustration is the constrained Delaunay tetrahedralization of the PLC. rithm [22]. We propose solutions to several issues that have been ignored in more theoretical papers, particularly the fact that vertices inserted on a common line are not always perfectly collinear, and the vertices of a polygonal facet are not always perfectly coplanar.…”

Section: Figurementioning

confidence: 99%

“…Their ability to conform to domain boundaries makes them valuable for applications such as finite element simulation, computer graphics, and geographic information systems. Several algorithms for constructing CDTs have been proposed [17,18,19,21,22]. Some of them operate by constructing an ordinary Delaunay triangulation and then inserting polygonal boundaries one by one.…”

Section: Introductionmentioning

confidence: 99%

Incrementally constructing and updating constrained Delaunay tetrahedralizations with finite-precision coordinates

Shewchuk

2013

Engineering with Computers

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Summary. Constrained Delaunay tetrahedralizations (CDTs) are valuable for generating meshes of nonconvex domains and domains with internal boundaries, but they are difficult to maintain robustly when finite-precision coordinates yield vertices on a line that are not perfectly collinear and polygonal facets that are not perfectly flat. We experimentally compare two recent algorithms for inserting a polygonal facet into a CDT: a bistellar flip algorithm of Shewchuk (Proc. 19th Annual Symposium on Computational Geometry, June 2003) and a cavity retriangulation algorithm of Si and Gärtner (Proc. Fourteenth International Meshing Roundtable, September 2005). We modify these algorithms to succeed in practice for polygons whose vertices deviate from exact coplanarity.

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3D boundary recovery by constrained Delaunay tetrahedralization

Cited by 54 publications

References 55 publications

Building a virtual simulation platform for quasistatic breast ultrasound elastography using open source software: A preliminary investigation

Building a virtual simulation platform for quasistatic breast ultrasound elastography using open source software: A preliminary investigation

An improved local remeshing algorithm for moving boundary problems

Incrementally constructing and updating constrained Delaunay tetrahedralizations with finite-precision coordinates

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