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TECHNICAL PAPERS: Bone/Orthopedic

Micromechanically Based Poroelastic Modeling of Fluid Flow in Haversian Bone

[+] Author and Article Information
C. C. Swan

Civil and Environmental Engineering, University of Iowa, Iowa City, IA 52242

R. S. Lakes

Engineering Physics, University of Wisconsin-Madison

R. A. Brand

Orthopaedic Surgery, University of Iowa, Iowa City, IA 52242

K. J. Stewart

Civil & Environmental Engineering, University of Iowa, Iowa City, IA 52242

J Biomech Eng 125(1), 25-37 (Feb 14, 2003) (13 pages) doi:10.1115/1.1535191 History: Received February 01, 2002; Revised September 01, 2002; Online February 14, 2003
Copyright © 2003 by American Institute of Physics
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References

Figures

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Three-dimensional idealizations of Haversian bone. a) transverse section with square-packed non-overlapping osteons; b) transverse section with hexagonally packed, overlapping osteons; c) unit cell for non-overlapping osteons; d) unit cell for overlapping osteons.
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a) Idealized transverse section through Haversian bone with lamellar structure neglected and bone matrix treated as linear, isotropic, homogeneous elastic medium; b) finite element mesh of unit cell model with 4% Haversian porosity. To estimate poroelastic model coefficients, five strain-controlled tests were performed on this model: (1) undrained ε̄11≠0; (2) undrained ε̄33≠0; (3) undrained γ̄12≠0; (4) undrained γ̄13≠0; and (5) drained ε̄11≠0.
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a) Finite element model of prismatic cortical bone specimen; b) Haversian canals oriented in alignment with longitudinal axis of specimen; c) Haversian canals oriented transverse to longitudinal axis of bone specimen.
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Computed fluid pressure relaxation responses in the model of cortical bone specimens for both sets of poroelastic properties, and for both longitudinal and transverse orientation of the Haversian canals. A uniaxial stress of 1 MPa was applied to the bone model. When the Haversian canals are oriented longitudinally in the prismatic bone specimen, initial fluid pressures are smaller but pressure relaxation takes longer.
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Computed peak Haversian fluid pressures versus frequency for material assumptions A and B, and both transverse and longitudinal orientation of the osteonal bone in the prismatic specimen model. At each frequency, the computed fluid pressures have been normalized by the peak bone pressure in the corresponding model at that same frequency.
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Computed peak Haversian shear stresses versus frequency for material assumptions A and B, and both transverse and longitudinal orientation of the osteonal bone in the prismatic specimen model. At each frequency, the computed fluid shear stresses have been normalized by the peak bone pressure in the corresponding model at that same frequency.
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Computed peak bone pressures versus frequency for material assumptions A and B, and both longitudinal and transverse orientation of osteonal bone within the prismatic specimen model. For each model, the computed dynamic peak bone pressures have been normalized by the static peak bone pressure for that same model.
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Computed tan δ versus frequency for material assumptions A and B, and both longitudinal and transverse orientation of osteonal bone within the prismatic specimen model. The computed values are compared with experimentally measured tan δ by Garner et al. (2000).

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