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| − | ==1 Title, abstract and keywords<!-- Your document should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations and formulae where possible. Capitalize the first word of the title. | + | ==Abstract== |
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| − | Provide a maximum of 6 keywords, and avoiding general and plural terms and multiple concepts (avoid, for example, 'and', 'of'). Be sparing with abbreviations: only abbreviations firmly established in the field should be used. These keywords will be used for indexing purposes.
| + | There are numerous challenges in generating high-quality meshes of cardiac anatomies due to |
| | + | the complex geometry of the heart, its curvature, and its motion. More generally, computational |
| | + | modeling of anatomical models bounded by curved surfaces can benefit from the use of high-order |
| | + | curved meshes. Using such meshes ensures that the curvature is captured correctly in the corresponding |
| | + | mesh. In addition, for a fixed level of accuracy, pairing a high-order mesh with a high-order PDE solver |
| | + | requires fewer mesh elements hence making the mesh generation and PDE solve much less |
| | + | computationally expensive. The use of high-order meshes in dynamic simulations helps prevent |
| | + | instabilities.<br> |
| | + | In this talk, we first present our advancing front-based high-order tetrahedral mesh generation method |
| | + | for finite element meshes. While most existing high-order mesh generation methods employ a |
| | + | computer-aided design (CAD) model to represent the boundary surface, our method requires only the |
| | + | element vertices and connectivities. Thus, it can employ a high-order surface mesh which was |
| | + | generated from medical image segmentation masks or a CAD model. Our method then directly |
| | + | generates a high-order volume mesh and applies mesh optimization to utilize the higher degrees of |
| | + | freedom and further improve the mesh quality.<br> |
| | + | Second, we present our high-order mesh warping algorithm for tetrahedral meshes, which allows us to |
| | + | perform time-dependent deformations present in biomedical applications. Our method is based on a |
| | + | finite element formulation for hyperelastic materials. We employ the two-parameter incompressible |
| | + | Mooney-Rivlin model with appropriate material properties to represent the continuum model. We use |
| | + | Newton iteration to solve the nonlinear elasticity equations obtained from the Mooney-Rivlin model and |
| | + | equilibrium conditions; the solution to the nonlinear elasticity equations then yields the deformed |
| | + | mesh.<br> |
| | + | Finally, we use our methods to generate several second-order tetrahedral meshes of anatomical models |
| | + | obtained from medical images and CAD models and apply several time-dependent deformations. We |
| | + | conclude with a vision for research in mesh generation for biomedical simulation.<br> |
| | + | This talk represents joint work with Fariba Mohammadi, University of Michigan, and Cristian Linte, |
| | + | Rochester Institute of Technology |
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| − | An abstract is required for every document; it should succinctly summarize the reason for the work, the main findings, and the conclusions of the study. Abstract is often presented separately from the article, so it must be able to stand alone. For this reason, references and hyperlinks should be avoided. If references are essential, then cite the author(s) and year(s). Also, non-standard or uncommon abbreviations should be avoided, but if essential they must be defined at their first mention in the abstract itself. -->==
| + | ==Video== |
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| − | ==2 The main text<!-- You can enter and format the text of this document by selecting the ‘Edit’ option in the menu at the top of this frame or next to the title of every section of the document. This will give access to the visual editor. Alternatively, you can edit the source of this document (Wiki markup format) by selecting the ‘Edit source’ option.
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| − | 2.1 Subsections
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| − | 2.2 General guidelines
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| − | 1. The first entry in this list
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| − | 2.4 Supplementary material
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| − | ==3 Bibliography<!--
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| − | ==4 Acknowledgments<!-- Acknowledgments should be inserted at the end of the document, before the references section. -->==
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| − | ==5 References<!--[1] Author, A. and Author, B. (Year) Title of the article. Title of the Publication. Article code. Available: http://www.scipedia.com/ucode.
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| − | [2] Author, A. and Author, B. (Year) Title of the article. Title of the Publication. Volume number, first page-last page.
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| − | [3] Author, C. (Year). Title of work: Subtitle (edition.). Volume(s). Place of publication: Publisher.
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| − | [5] Author, E. (Year, Month date). Title of the article. In A. Editor, B. Editor, and C. Editor. Title of published proceedings. Paper presented at title of conference, Volume number, first page-last page. Place of publication.
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| − | [6] Institution or author. Title of the document. Year. [Online] (Date consulted: day, month and year). Available: http://www.scipedia.com/document.pdf.
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There are numerous challenges in generating high-quality meshes of cardiac anatomies due to
the complex geometry of the heart, its curvature, and its motion. More generally, computational
modeling of anatomical models bounded by curved surfaces can benefit from the use of high-order
curved meshes. Using such meshes ensures that the curvature is captured correctly in the corresponding
mesh. In addition, for a fixed level of accuracy, pairing a high-order mesh with a high-order PDE solver
requires fewer mesh elements hence making the mesh generation and PDE solve much less
computationally expensive. The use of high-order meshes in dynamic simulations helps prevent
instabilities.
In this talk, we first present our advancing front-based high-order tetrahedral mesh generation method
for finite element meshes. While most existing high-order mesh generation methods employ a
computer-aided design (CAD) model to represent the boundary surface, our method requires only the
element vertices and connectivities. Thus, it can employ a high-order surface mesh which was
generated from medical image segmentation masks or a CAD model. Our method then directly
generates a high-order volume mesh and applies mesh optimization to utilize the higher degrees of
freedom and further improve the mesh quality.
Second, we present our high-order mesh warping algorithm for tetrahedral meshes, which allows us to
perform time-dependent deformations present in biomedical applications. Our method is based on a
finite element formulation for hyperelastic materials. We employ the two-parameter incompressible
Mooney-Rivlin model with appropriate material properties to represent the continuum model. We use
Newton iteration to solve the nonlinear elasticity equations obtained from the Mooney-Rivlin model and
equilibrium conditions; the solution to the nonlinear elasticity equations then yields the deformed
mesh.
Finally, we use our methods to generate several second-order tetrahedral meshes of anatomical models
obtained from medical images and CAD models and apply several time-dependent deformations. We
conclude with a vision for research in mesh generation for biomedical simulation.
This talk represents joint work with Fariba Mohammadi, University of Michigan, and Cristian Linte,
Rochester Institute of Technology
