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Technical Briefs

# Strain-Dependent Oxygen Diffusivity in Bovine Annulus Fibrosus

[+] Author and Article Information
T.-Y. Yuan, A. R. Jackson

Department of Biomedical Engineering, Tissue Biomechanics Laboratory, University of Miami, Coral Gables, FL 33146

C.-Y. Huang

Department of Biomedical Engineering, Stem Cell and Orthopaedic Bioengineering Laboratory, University of Miami, Coral Gables, FL 33146

W. Y. Gu1

Tissue Biomechanics Laboratory, Department of Biomedical Engineering, University of Miami, Coral Gables, FL 33146wgu@miami.edu

1

Corresponding author.

J Biomech Eng 131(7), 074503 (Jun 04, 2009) (4 pages) doi:10.1115/1.3127254 History: Received August 27, 2008; Revised February 02, 2009; Published June 04, 2009

## Abstract

The intervertebral disk (IVD) is the largest avascular structure in the human body. Transport of small molecules in IVD is mainly through diffusion from the endplates and the peripheral blood vessels surrounding IVD. Studies have investigated the structure, chemical components, and water content in IVD, but to our knowledge no study has investigated the effect of mechanical loading on oxygen transport in IVD. The objective of this study was to determine the strain-dependent behavior of oxygen diffusivity in IVD tissue. A one-dimensional steady-state diffusion experiment was designed and performed to determine the oxygen diffusivity in bovine annulus fibrosus (AF). The oxygen diffusivity was calculated using equation derived from Fick’s law. A total of 20 AF specimens ($d=6 mm$, $h∼0.5 mm$) from bovine coccygeal IVD were used to determine oxygen diffusivity at three levels of compressive strain. The average oxygen diffusivity $(mean±SD)$ of bovine AF in the axial direction was $1.43±0.242×10−5 cm2/s$$(n=20)$ at $4.68±1.67%$ compressive strain level, $1.05±0.282×10−5 cm2/s$$(n=20)$ at $14.2±1.50%$ strain level, and $7.71±1.63×10−6 cm2/s$$(n=20)$ at $23.7±1.34%$ strain level. There was a significant decrease in oxygen diffusivity with increasing level of compressive strain (ANOVA, $p<0.05$). Oxygen diffusivity of bovine AF in the axial direction has been determined. The mechanical loading has a significant effect on oxygen transport in IVD tissues. This study is important in understanding nutritional transport in IVD tissues and related disk degeneration.

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## Figures

Figure 1

Schematic of the custom-designed diffusion apparatus. Oxygen diffusion occurs from upstream chamber (right), across the tissue specimen, and into the downstream chamber (left), where the oxygen concentration is measured using an oxygen sensor.

Figure 2

An example of raw experimental data showing the change in the oxygen concentration in the downstream chamber with elapsed time. For this particular specimen, the actual levels of compression were 1.4%, 11.2%, and 21.1%. The diffusivity was calculated using Eq. 2. Note the decrease in the slope with increasing compressive strain, indicating the strain-dependent behavior of oxygen diffusivity.

Figure 3

Variation in diffusivity of oxygen with applied strain at room temperature (22.2°C±0.45°C). A linear regression (R2=0.562, n=60) was used to estimate the diffusivity at zero stain. In the linear regression, D is the diffusivity and ε is the applied compression (%). From this, the oxygen diffusivity in bovine AF at 0% compression (i.e., ε=0) was determined to be 1.56×10−5 cm2/s.

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