Predicting Local Cell Deformations in Engineered Tissue Constructs: A Multilevel Finite Element Approach

[+] Author and Article Information
Roel G. M. Breuls, Bram G. Sengers, Cees W. J. Oomens, Carlijn V. C. Bouten, Frank P. T. Baaijens

Eindhoven University of Technology, Department of Biomedical Engineering, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

J Biomech Eng 124(2), 198-207 (Mar 29, 2002) (10 pages) doi:10.1115/1.1449492 History: Received May 31, 2001; Revised December 05, 2001; Online March 29, 2002
Copyright © 2002 by ASME
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Two-dimensional RVE with boundaries Γij and vertex points 1, 2, 3, and 4, which can be thought of as surrounded by identically shaped RVEs
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Flow chart of the Multilevel Finite Element approach. The macroscopic deformation tensors Fmacro,ip are transferred to the corresponding microscopic FE models. The macroscopic stresses σmacro and tangent stiffness matrices 4Smacro are returned from the microscopic models to the macroscopic integration points.
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Macroscopic Finite Element mesh consisting of 14 quadratic elements. The arrows indicate the nodal points to which the compressive load is applied.
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Microstructural meshes A and B consisting of cells embedded in matrix material: (a) microstructure A represents randomly dispersed spherical myoblasts; and (b) microstructure B represents a cross section of mature muscle tissue.
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Results of the simulation with microstructure A. The deformed macroscopic geometry (center) is shown, surrounded with four selected RVEs. The gray-scale bar next to the macroscopic mesh represents the macroscopic SED (in N/m2). The gray-scale bars next to the RVEs represent the SED, averaged over the cell area.
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Results of the simulation with microstructure B (see caption of Fig. 5 for further explanation of the gray-scale bars)
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(a) Detailed SED contour plot for RVE 1 (microstructure B); and (b) magnification of an individual cell. The gray-scale bar denotes the SED in N/m2.



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