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. 2016 Apr;10(4):334-47.
doi: 10.1002/term.1751. Epub 2013 Jun 20.

Computational model for the analysis of cartilage and cartilage tissue constructs

David W Smith  1 , Bruce S Gardiner  1 , John B Davidson  1 , Alan J Grodzinsky  2
Affiliations

Computational model for the analysis of cartilage and cartilage tissue constructs

David W Smith et al. J Tissue Eng Regen Med. 2016 Apr.

Abstract

We propose a new non-linear poroelastic model that is suited to the analysis of soft tissues. In this paper the model is tailored to the analysis of cartilage and the engineering design of cartilage constructs. The proposed continuum formulation of the governing equations enables the strain of the individual material components within the extracellular matrix (ECM) to be followed over time, as the individual material components are synthesized, assembled and incorporated within the ECM or lost through passive transport or degradation. The material component analysis developed here naturally captures the effect of time-dependent changes of ECM composition on the deformation and internal stress states of the ECM. For example, it is shown that increased synthesis of aggrecan by chondrocytes embedded within a decellularized cartilage matrix initially devoid of aggrecan results in osmotic expansion of the newly synthesized proteoglycan matrix and tension within the structural collagen network. Specifically, we predict that the collagen network experiences a tensile strain, with a maximum of ~2% at the fixed base of the cartilage. The analysis of an example problem demonstrates the temporal and spatial evolution of the stresses and strains in each component of a self-equilibrating composite tissue construct, and the role played by the flux of water through the tissue.

Keywords: cartilage; depth-dependent; mathematical model; multi-phase; osmotic swelling; tissue construct.

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Figures

Figure 1
Figure 1
Simulation geometry
Figure 2
Figure 2
Aggrecan concentration
Figure 3
Figure 3
Osmotic pressure
Figure 4
Figure 4
Collagen stress
Figure 5
Figure 5
Collagen strain
Figure 6
Figure 6
Excess water pressure. This pressure arises from the drag force created from the exit of aggrecan from the tissue (refer to Discussion)
Figure 7
Figure 7
Osmotic modulus
Figure 8
Figure 8
Comparison between the osmotic modulus predicted in the model and the best fit to the aggregate modulus data of Klein et al. (2007)
See this image and copyright information in PMC

References

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