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Research Papers

Experimental Determination of the Permeability in the Lacunar-Canalicular Porosity of Bone

[+] Author and Article Information
Gaffar Gailani

Mechanical Engineering Department at Graduate Center and City College of the City, University of New York (CUNY), New York, NY 10016; Department of Mechanical Engineering Technology and Industrial Design, New York City College of Technology, Brooklyn, NY 11201

Mohammed Benalla

Biomedical Engineering Department at Graduate Center and City College of the City, University of New York (CUNY), New York, NY 10016

Rashal Mahamud

Mechanical Engineering Department, City College of New York, New York, NY 10031

Stephen C. Cowin1

New York Center for Biomedical Engineering, Mechanical and Biomedical Engineering Department, City College of New York, New York, NY 10031scowin@earthlink.net

Luis Cardoso

New York Center for Biomedical Engineering, Mechanical and Biomedical Engineering Department, City College of New York, New York, NY 10031

1

Corresponding author.

J Biomech Eng 131(10), 101007 (Sep 02, 2009) (7 pages) doi:10.1115/1.3200908 History: Received November 15, 2008; Revised June 04, 2009; Published September 02, 2009

Permeability of the mineralized bone tissue is a critical element in understanding fluid flow occurring in the lacunar-canalicular porosity (PLC) compartment of bone and its role in bone nutrition and mechanotransduction. However, the estimation of bone permeability at the tissue level is affected by the influence of the vascular porosity in macroscopic samples containing several osteons. In this communication, both analytical and experimental approaches are proposed to estimate the lacunar-canalicular permeability in a single osteon. Data from an experimental stress-relaxation test in a single osteon are used to derive the PLC permeability by curve fitting to theoretical results from a compressible transverse isotropic poroelastic model of a porous annular disk under a ramp loading history (2007, “Compressible and Incompressible Constituents in Anisotropic Poroelasticity: The Problem of Unconfined Compression of a Disk,” J. Mech. Phys. Solids, 55, pp. 161–193; 2008, “The Unconfined Compression of a Poroelastic Annular Cylindrical Disk,” Mech. Mater., 40(6), pp. 507–523). The PLC tissue intrinsic permeability in the radial direction of the osteon was found to be dependent on the strain rate used and within the range of O(1024)O(1025). The reported values of PLC permeability are in reasonable agreement with previously reported values derived using finite element analysis (FEA) and nanoindentation approaches.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Osteon isolation process. A thick section was cut from the mid-diaphysis of the bone, and a cubical sample was prepared. Cylindrical rods of about 1.5 mm diameter were extracted from this bone cube and analyzed using a Micro-CT to identify the samples with Haversian canals approximately concentrical and parallel to the axis of the cylindrical rod. Selected samples were processed in a Micro-Lathe to reduce the diameter of the sample to 300 mm, resulting in samples containing a single osteon. All cutting procedures are performed under continuous irrigation and low speed.

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Figure 2

Micro-CT image of a bone sample (diameter is 1.5 mm approximately) prior osteon isolation. The figure showing few Haversian canals with one that is approximately in the center. The diameters of the Haversian canals can be measured from these images.

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Figure 3

A uniaxial micromechanical testing device was constructed based on a small piezoelectric motor. The motor was integrated to a custom compression loading stage and axially aligned to a load cell. The position, speed, and acceleration of the motor were controlled from a computer via a network driver controller using a custom LABVIEW application. Load cell measurements were amplified and digitized using a USB interface, and displayed in real time during the test and recorded for offline data analysis.

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Figure 4

Photograph of the material testing stage which consists of (a) micrometer, (b) load cell (10 g, 0.05% FOM), (c) steel platens, (d) osteon sample, (e) sample stage, and (f) picomotor linear actuator (30 nm displacement/step)

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Figure 5

Stress relaxation curve for a sample made of steel and for one of the isolated osteons in response to a ramp displacement with constant strain rate (ε̇≈100 με s−1). The load intensity and loading time in both curves were normalized by the peak load intensity and t0, respectively.

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Figure 6

Stress relaxation response of a representative osteon loaded at three different strain rates: ε̇≈10 με s−1, 100 με s−1, and 1000 με s−1. The axes display the nondimensional load intensity versus the nondimensional time t/t0.

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Figure 7

Curve fitting of the theoretical and experimental results of stress-relaxation tests to estimate the intrinsic permeability Krr. The curve fitting results have shown a good agreement in the loading period and some deviations in the relaxation period.

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