The effect of cyclic deformation and solute binding on solute transport in cartilage
Section snippets
Methods
The proposed model will be based on an upscaled porous media theory, in which the heterogeneity of the material on the micro-scale is ignored and only the relative volume ratios of the various phases are taken into account, along with a general form of their interactions [23], [24], [25]. The use of porous media theory to model cartilage mechanical behavior (and other biological tissues) is not a recent idea [26], [27], [28], however its use to model the transport nutrients through a cyclically
Radial solute transport in cartilage
Consider the case of a homogenous cylindrical disc of cartilage undergoing axisymmetric unconfined loading by an impermeable, frictionless barrier as shown in Fig. 1. Under this geometry we may assume the following.
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The axial strain is independent of the radial coordinate.
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There is no gradient of solute concentration (and therefore diffusion) in the axial direction.
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Due to symmetry, and furthermore we can assume uθ = 0.
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The strain in the axial direction is homogeneous—a condition only
Results and discussion
Before presenting model results, it is useful to first define the total solute uptake ratio (Ru), the free solute uptake ratio (RF) and the bound solute uptake ratio (RB). These parameters provide a measure of the solute concentration in the cartilage compared to the bath concentration. Simply stated the total solute uptake ratio is the sum of free solute uptake ratio (RF) and bound solute uptake ratio (RB), viz,whereand c0 is the solute bath concentration.
Since the
Conclusion
This paper describes solute transport through articular cartilage under cyclic loading and with solute binding to the extra-cellular matrix. A quantitative model was developed based on porous media theory, and it was used to describe the coupled solute transport and the mechanical behavior of cartilage. The model was used to explore the system behaviour for solute transport with free diffusion and advective-diffusion, and particular attention was given to the role of bath concentration, applied
Acknowledgments
The authors thank The Australian Research Council (DP50192) and The University of Melbourne for their support.
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