Finite Element formulation of Triphasic Mechano-electrochemical Theory for Charged, Hydrated Biological Soft Tissues

Research Category: 
ITS and FEA of skeletons

In collaboration with the Orthopaedic Research Laboratory at Columbia University, we are developing a mixed finite element formulation for triphasic mechano-electrochemical theory for charged, hydrated biological soft tissues, such as cartilage and cells. The finite element formulation is developed using the standard Galerkin weighted residual method. The finite element formulation has been used to investigate a triphasic stress relaxation problem in the confined compression configuration and a triphasic free swelling problem. The formulation accuracy and convergence were examined with independent finite difference methods. The FEM results are in excellent agreement with those obtained from the other methods. We are currently extending the formulation to axisymmetric and three-dimensional cases.

Related Publications
1. Lu, X. L., Sun, D. D., Chen, F. H., Guo, X. E., Lai, M. W., and Mow, V. C., Correlations of Indentation Determined Mechano-Electrochemical Properties of Articular Cartilage with Fixed Charge Density, 50th Orthopaedic Research Society Annual Meeting, 29, San Francisco, Ca, March 7-10, 2004. Download
2. Likhitpanichkul, M., Guo, X. E., Lai, M. W., and Mow, V. C., Tension-Compression Nonlinearity Influences the Mechano-Electrochemical Environment of Chondrocytes in Cartilage Under Confined Compression, 50th Orthopaedic Research Society Annual Meeting, 29, San Francisco, Ca, March 7-10, 2004. Download
3. Wan, L. Q., Miller, C., Guo, X. E., and Mow, V. C., 2004, " An Exact Theoretical Solution for Predicting the Apparent Poisson's Ratio of Articular Cartilage -- a Charged-Hydrated Biological Tissues: The Triphasic Paradigm ," IMECE2004-60961, Anaheim, California, USA.
4. Wan, L.Q., Miller, C., Guo, X. E., and Mow, V. C., 2004, '' An Exact Solution for a Nonlinear Triphasic CLE Model of Articular Cartilage Under Unconfined Compression ," BMES, Philadelphia, PA, USA
5. Wan, L. Q., Miller, C., Guo, X. E., and Mow, V. C., 2004, " Fixed Electrical Charges and Mobile Ions Affect the Measurable Mechano -Electrochemical Properties of Charged-Hydrated Biological Tissues: The Articular Cartilage Paradigm ," Mechanics & Chemistry of Biosystems , 1(1), pp.81-99.
6. Lu, X.L., Sun, D. D. ,Guo, X. E., Chen, F. H., Lai, W. M., Mow, V. C., Indentation determined mechanoelectrochemical properties and fixed charge density of articular cartilage. Ann Biomed Eng, 2004. 32(3): p. 370-9.
7. Lu, X. L., Miller, C, Chen, F. H., Guo, X. E., Mow, V. C., Using correspondence of elastic and triphisic materials to determine both fixed charge density and porosity of articular cartilage. Trans Orthop Res Soc, 2005.
8. Wan, L. Q., Miller, C., Guo, X. E., and Mow, V. C., 2005, " A Three-layer Orthotropic Model for Swelling and Curling of Articular Cartilage ," ASME2005, Vail, Colorado, USA.
9. Lu, X.L., Miller, C., Guo, X. E., Mow, V. C., The influence of the fixed negative charges on mechanical behavior of articular cartilage under indentation, ASME2005, Vail, Colorado, USA.
10. Lu, X.L., Miller, C., Guo, X. E., Mow, V. C., A new correspondence principle for triphasic materials: determination of fixed charge density and porosity of articular cartilage by indentation, ASME2005, Vail, Colorado, USA.
11. Likhitpanichkul, M., Miller C., Lu, X.L., Guo, X. E., Mow, V. C., A triphasic model of cell under micropipette aspiration: the osmotic effect on cell mechanical properties, ASME2005, Vail, Colorado, USA.
12. Wan, L.Q., Miller, C., Guo, X. E., and Mow, V. C., 2005, '' The Origin of Residual stress and Curling Behavior in Biological Tissues," BMES, Baltimore, MD, USA
13. Lu, X.L., Guo, X. E., Miller, C., Mow, V. C., Electrical Phenomena inside Articular Cartilage under Indentation, BMES, Baltimore, MD, USA

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