NDLI: Influence of boundary conditions on computed apparent elastic properties of cancellous bone

Content Provider	Springer Nature Link
Author	Pahr, Dieter H. Zysset, Philippe K.
Copyright Year	2007
Abstract	High-resolution finite element models of trabecular bone can be used to study trabecular structure–function relationships, elasticity, multiaxial strength, and tissue remodelling in more detail than experiments. Beside effects of the model size, scan/analysis resolution, segmentation process, etc., the type of the applied boundary conditions (BCs) have a strong influence on the predicted elastic properties. Appropriate BCs have to be applied on hexahedral digital finite element models in order to obtain effective elastic properties. Homogeneous displacement BCs as proposed by Van Rietbergen et al. (J Biomech 29(12):1653–1657, 1996) lead to “apparent” rather than to “effective” elastic properties. This study provides some answers concerning such differences by comparing various BC types (uniform displacement, mixed BCs, periodic BCs), different volume element definitions (original and mirrored models), and several bone volume fractions (BVTV ranging from 6.5 to 37.6%). First, the mixed BCs formulated by Hazanov (Arch Appl Mech 68(6):385–394, 1998) are theoretically extended to shear loading of a porous media. Second, six human bone samples are analyzed, their orthotropic Young’s moduli, shear moduli, and Poisson’s ratios computed and compared. It is found that the proposed mixed BCs give exactly the same effective elastic properties as periodic BCs if a periodic and orthotropic micro-structured material is used and thus denoted as “periodicity compatible” mixed uniform BCs (PMUBCs). As bone samples were shown to be nearly orthotropic for volume element side lengths ≥5 mm the proposed mixed BCs turn out to be the best choice because they give again essentially the same overall elastic properties as periodic BCs. For bone samples of smaller dimensions ( < 5 mm) with a strong anisotropy (beyond orthotropy) uniform displacement BCs remain applicable but they can significantly overestimate the effective stiffness.
Starting Page	463
Ending Page	476
Page Count	14
File Format	PDF
ISSN	16177959
Journal	Biomechanics and Modeling in Mechanobiology
Volume Number	7
Issue Number	6
e-ISSN	16177940
Language	English
Publisher	Springer-Verlag
Publisher Date	2007-10-31
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Digital finite element model Elastic properties Mixed boundary conditions Periodic boundary conditions Trabecular bone Biophysics/Biomedical Physics Biomedical Engineering Theoretical and Applied Mechanics
Content Type	Text
Resource Type	Article
Subject	Mechanical Engineering Modeling and Simulation Biotechnology

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