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We developed an adaptive boundary and finite element mesher, namely, a Level Set Bounded Interior and Exterior(LBIE)-mesher that produces high quality meshes. This mesher has also been used for studying diffusion in biomolecular systems using continuum mechanics equations. Specifically, finite element methods have been developed to solve the steady-state Smoluchowski equation to calculate ligand binding rate constants for large biomolcules. The approach taken by our LBIE-mesher tetrahedralizes or hexahedralizes the interval volume between the biomolecular surface and an outer boundary sphere which is usually 20-40 times that of the biomolecule. |
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| :Meshes | This collection of images is from an effort to extract adaptive and quality 3D meshes directly from volumetric imaging data. These extracted tetrahedral and hexahedral meshes are extensively used in the Finite Element Method.
Our method generates high quality adaptive 3D meshes without introducing any hanging nodes.
The images show the extracted adaptive tetrahedral mesh of mAChE, which has been used as the geometric model in solving the steady-state Smoluchowski equation to calculate ligand binding rate constants using FEM. The most important part in the geometric structure of the molecule mAChE is the cavity, where fine meshes are required.
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| | Adaptive tetrahedral mesh of the volume between the isosurface at 0.5 and an outer sphere | |
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| | | | | Wireframe of the isosurface at 0.5 and an outer sphere | |
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| | | Adaptive tetrahedral mesh of the volume between the isosurface at 0.5 and an outer sphere | |
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| | | Coarser Mesh Movie | |
| | The isosurface is extracted from the electrodensity data and the color shows the hydrophobicity. The color map for hydrophobicity is as follows: less than -0.1 red, -0.1 to 0.1 white, greater than 0.1 blue |
| | | Finer Mesh | |
| | The isosurface is extracted from the electrodensity data and the color shows the hydrophobicity. The color map for hydrophobicity is as follows: less than -0.1 red, -0.1 to 0.1 white, greater than 0.1 blue |
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Credits
Mache data courtesy Nathan Baker (Washington University St. Louis)
Images created by Yongjie Zhang
Related Publications
Y. Zhang, C. Bajaj, B.-S. Sohn
Adaptive and Quality 3D Meshing from Imaging Data
ACM Symposium on Solid Modeling and Applications. Seattle, WA. pp. 286-291. 2003 (pdf) (abstract)
Y. Song, Y. Zhang, T. Shen, C. Bajaj, J. McCammon, N. Baker
Finite Element Solution of the Steady-state Smolchowski Equation for Rate Constant Calculations
Biophysical Journal, 86(4):2017-2029, 2004. (pdf) (abstract)
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