Articular Cartilage Constitutive Modeling: A Polyconvex Strain Energy Function for Proteoglycan and Validation of a Growth Mixture Model With Collagen Remodeling

The scope of this work is composed of two objectives: First, to develop a continuum level proteoglycan (PG) Cauchy stress constitutive equation suitable for FEA implementation. Second, to perform a validation study of an articular cartilage (AC) growth mixture model with collagen (COL) remodeling. A PG swelling stress model suitable for bovine calf AC was determined, and a PG Cauchy stress fit equation was selected. Results indicate possible swelling stress overprediction by several commonly used models, and that PG Cauchy stress can be modeled with adequate accuracy over a range of bovine AC biochemical content as a function of PG density only. Growth and remodeling were implemented to successfully predict grown tissue mechanical properties. The majority of the tested remodeling parameters were correlated to pyridinoline content. Growth functions for both PG and COL were not correlated to tissue cell content.

Year	Entry
1977	Mow VC, Mansour JM. The nonlinear interaction between cartilage deformation and interstitial fluid flow. J Biomech. 1977;10(1):31-39.
1999	Soulhat J, Buschmann MD, Shirazi-Adl A. A fibril-network-reinforced biphasic model of cartilage in unconfined compression. J Biomech Eng. June 1999;121(3):340-347.
1998	Basser PJ, Schneiderman R, Bank RA, Wachtel E, Maroudas A. Mechanical properties of the collagen network in human articular cartilage as measured by osmotic stress technique. Arch Biochem Biophys. March 15, 1998;351(2):207-219.
2001	Williamson AK, Chen AC, Sah RL. Compressive properties and function—composition relationships of developing bovine articular cartilage. J Orthop Res. November 2001;19(6):1113-1121.
1980	Mow VC, Kuei SC, Lai WM, Armstrong CG. Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments. J Biomech Eng. February 1980;102(1):73-84.
1995	Buschmann MD, Grodzinsky AJ. A molecular model of proteoglycan-associated electrostatic forces in cartilage mechanics. J Biomech Eng. May 1995;117(2):179-192.
1976	Woo SL-Y, Akeson WH, Jemmott GF. Measurements of nonhomogeneous, directional mechanical properties of articular cartilage in tension. J Biomech. 1976;9(12):785-791.
2002	Mow VC, Guo XE. Mechano-electrochemical properties of articular cartilage: their inhomogeneities and anisotropies. Annu Rev Biomed Eng. 2002;4:175-209.
2001	Chen AC, Bae WC, Schinagl RM, Sah RL. Depth- and strain-dependent mechanical and electromechanical properties of full-thickness bovine articular cartilage in confined compression. J Biomech. January 2001;34(1):1-12.
2004	Chahine NO, Wang CC-B, Hung CT, Ateshian GA. Anisotropic strain-dependent material properties of bovine articular cartilage in the transitional range from tension to compression. J Biomech. August 2004;37(8):1251-1261.
1990	Williams RPW, Cooper WD. Osmotic flow caused by polyelectrolytes. Biophys Chem. August 15, 1990;36(3):223-234.
2007	Ficklin TP. Application of a Cartilage Growth Finite Element Model: Simulation of Steady-State Fluid Permeation Experiments [Master's thesis]. California Polytechnic State University; July 31, 2007.
2002	Hunziker EB. Articular cartilage repair: basic science and clinical progress. a review of the current status and prospects. Osteoarthritis Cartilage. June 2002;10(6):432-463.
1979	Maroudas A. Physicochemical properties of articular cartilage. In: Freeman MAR, ed. Adult Articular Cartilage. 2nd ed. Kent, England: Pitman Medical; 1979:215-290.
2004	Hung CT, Mauck RL, Wang CC-B, Lima EG, Ateshian GA. A paradigm for functional tissue engineering of articular cartilage via applied physiologic deformational loading. Ann Biomed Eng. January 2004;32(1):35-49.

Year

Entry

1977

Mow VC, Mansour JM. The nonlinear interaction between cartilage deformation and interstitial fluid flow. J Biomech. 1977;10(1):31-39.

1999

Soulhat J, Buschmann MD, Shirazi-Adl A. A fibril-network-reinforced biphasic model of cartilage in unconfined compression. J Biomech Eng. June 1999;121(3):340-347.

1998

Basser PJ, Schneiderman R, Bank RA, Wachtel E, Maroudas A. Mechanical properties of the collagen network in human articular cartilage as measured by osmotic stress technique. Arch Biochem Biophys. March 15, 1998;351(2):207-219.

2001

Williamson AK, Chen AC, Sah RL. Compressive properties and function—composition relationships of developing bovine articular cartilage. J Orthop Res. November 2001;19(6):1113-1121.

1980

Mow VC, Kuei SC, Lai WM, Armstrong CG. Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments. J Biomech Eng. February 1980;102(1):73-84.

1995

Buschmann MD, Grodzinsky AJ. A molecular model of proteoglycan-associated electrostatic forces in cartilage mechanics. J Biomech Eng. May 1995;117(2):179-192.

1976

Woo SL-Y, Akeson WH, Jemmott GF. Measurements of nonhomogeneous, directional mechanical properties of articular cartilage in tension. J Biomech. 1976;9(12):785-791.

2002

Mow VC, Guo XE. Mechano-electrochemical properties of articular cartilage: their inhomogeneities and anisotropies. Annu Rev Biomed Eng. 2002;4:175-209.

2001

Chen AC, Bae WC, Schinagl RM, Sah RL. Depth- and strain-dependent mechanical and electromechanical properties of full-thickness bovine articular cartilage in confined compression. J Biomech. January 2001;34(1):1-12.

2004

Chahine NO, Wang CC-B, Hung CT, Ateshian GA. Anisotropic strain-dependent material properties of bovine articular cartilage in the transitional range from tension to compression. J Biomech. August 2004;37(8):1251-1261.

1990

Williams RPW, Cooper WD. Osmotic flow caused by polyelectrolytes. Biophys Chem. August 15, 1990;36(3):223-234.

2007

Ficklin TP. Application of a Cartilage Growth Finite Element Model: Simulation of Steady-State Fluid Permeation Experiments [Master's thesis]. California Polytechnic State University; July 31, 2007.

2002

Hunziker EB. Articular cartilage repair: basic science and clinical progress. a review of the current status and prospects. Osteoarthritis Cartilage. June 2002;10(6):432-463.

1979

Maroudas A. Physicochemical properties of articular cartilage. In: Freeman MAR, ed. Adult Articular Cartilage. 2nd ed. Kent, England: Pitman Medical; 1979:215-290.

2004

Hung CT, Mauck RL, Wang CC-B, Lima EG, Ateshian GA. A paradigm for functional tissue engineering of articular cartilage via applied physiologic deformational loading. Ann Biomed Eng. January 2004;32(1):35-49.

Year	Entry
2011	Stender ME. Predicting Articular Cartilage Constituent Material Properties Following in Vitro Growth Using a Proteoglycan-Collagen Mixture Model [Master's thesis]. California Polytechnic State University; March 2011.
2012	Griebel MA. Viscoelastic Anisotropic Finite Element Mixture Model of Articular Cartilage Using Viscoelastic Collagen Fibers and Validation With Stress Relaxation Data [Master's thesis]. California Polytechnic State University; June 2012.
2015	Stender ME. Osteochondral Tissue Modeling of Damage, Poroelasticity, and Remodeling in Osteoarthritis [PhD thesis]. University of Colorado; 2015.

Year

Entry

2011

Stender ME. Predicting Articular Cartilage Constituent Material Properties Following in Vitro Growth Using a Proteoglycan-Collagen Mixture Model [Master's thesis]. California Polytechnic State University; March 2011.

2012

Griebel MA. Viscoelastic Anisotropic Finite Element Mixture Model of Articular Cartilage Using Viscoelastic Collagen Fibers and Validation With Stress Relaxation Data [Master's thesis]. California Polytechnic State University; June 2012.

2015

Stender ME. Osteochondral Tissue Modeling of Damage, Poroelasticity, and Remodeling in Osteoarthritis [PhD thesis]. University of Colorado; 2015.