Solute transport in cartilage undergoing cyclic deformation

Computer Methods in Biomechanics and Biomedical Engineering

Volumn 10, Issue 4, 2007, Pages 265-278

  Gardiner, Bruce ^a   Smith, David ^a   Pivonka, Peter ^a   Grodzinsky, Alan ^b   Frank, Eliot ^b   Zhang, Lihai ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b USA   (United States)

Author keywords

Cartilage; Cyclic deformation; Insulin like growth factor I (IGF I); Timescale; Transport

Indexed keywords

AXIAL DEFORMATIONS; AXISYMMETRIC; CARTILAGE GROWTH; CHONDROCYTES; CYCLIC DEFORMATIONS; CYCLIC LOADINGS; DYNAMIC LOADINGS; DYNAMIC STRAIN; FIXED BOUNDARIES; GROWTH FACTOR; INSULIN-LIKE GROWTH FACTOR-I; LOADING FREQUENCIES; STEADY STATE; TIME-SCALES; TRANSPORT;

BLOOD VESSELS; BODY FLUIDS; CARTILAGE; DEFORMATION; DYNAMIC LOADS; MATHEMATICAL MODELS; SOLUTE TRANSPORT;

LOADING;

SOMATOMEDIN C;

ANIMAL; ARTICLE; ARTICULAR CARTILAGE; CARTILAGE CELL; HUMAN; METABOLISM; PHYSIOLOGY; THEORETICAL MODEL; TRANSPORT AT THE CELLULAR LEVEL;

ANIMALS; BIOLOGICAL TRANSPORT; CARTILAGE, ARTICULAR; CHONDROCYTES; HUMANS; INSULIN-LIKE GROWTH FACTOR I; MODELS, THEORETICAL;

EID: 34848842406     PISSN: 10255842     EISSN: 14768259     Source Type: Journal    
DOI: 10.1080/10255840701309163     Document Type: Article

References (40)

1. J. Bear and Y. Bachmat, Introduction to Modeling of Transport Phenomena in Porous Media, Dordrecht, The Netherlands: Kluwer Academic Publishers, 1991.
2. N.R. Bhakta, A.M. Garcia, E.H. Frank, A.J. Grodzinsky and T.I. Morales, "The insulin-like growth factors (igfs) i and ii bind to articular cartilage via the igf-binding proteins", J. Biol. Chem., 275(8), pp. 5860-5866, 2000.
3. M.A. Biot, "General theory of three dimensional consolidation", J. Appl. Phys., 12, pp. 155-164, 1941.
4. L.J. Bonassar, A.J. Grodzinsky, A. Srinivasan, S.G. Davila and S.B. Trippel, "Mechanical and physiochemical regulation of the action of insulin-like growth factor-i on articular cartilage", Arch. Biochem. Biophys., 379(1), pp. 57-63, 2000.
5. L.J. Bonassar, A.J. Grodzinsky, E.H. Frank, S.G. Davila, N.R. Bhaktav and S.B. Trippel, "The effect of dynamic compression on the response of articular cartilage to the insulin-like growth factor-i", J. Orthop. Res., 19, pp. 11-17, 2001.
6. M.D. Buschmann, Y.J. Kim, M. Wong, E.H. Frank, E.B. Hunziker and A.J. Grodzinsky, "Stimulation of aggrecan synthesis in cartilage explants by cyclic loading is localized to regions of high interstial fluid flow", Arch. Biochem. Biophys., 366(1), pp. 1-7, 1999.
7. E. De Angelis and L. Preziosi, "Advection-diffusion models of solid tumour evolution in vivo and related free boundary problem", Math. Models Methods Appl. Sci., 10, pp. 379-407, 2000.
8. FEMLAB-Multiphysics in MATLAB, MA, USA: COMSOL, Inc., 2003.
9. S.J. Ferguson, K. Ito and L.-P. Nolte, "Fluid flow and convective transport of solutes within the intervertebral disc", J. Biomech., 37, pp. 213-221, 2004.
10. A.J. Grodzinsky, M.E. Levenston, M. Jin and E.H. Frank, "Cartilage tissue remodeling in response to mechanical forces", Annu. Rev. Biomed. Eng., 2, pp. 691-713, 2000.
11. W.Y. Gu, W.M. Lai and V.C. Mow, "A mixture theory for chargedhydrated soft tissues containing multi-electrolytes: passive transport and swelling behaviors", J. Biomech. Eng., 120, pp. 169-180, 1998.
12. W.Y. Gu, H. Yao, C.Y. Huang and H.S. Cheung, "New insight into deformation-dependent hydraulic permeability of gels and cartilage, and dynamic behaviour of agarose gels in confined compression", J. Biomech., 36, pp. 593-598, 2003.
13. Y.J. Kim, R.L.Y. Sah, A.J. Grodzinsky, A.H.K. Plaas and J.D. Sandy, "Mechanical regulation of cartilage biosynthetic behavior: physical stimuli", Arch. Biochem. Biophys., 311(1), pp. 1-12, 1994.
14. S.M. Klisch, S.S. Cheng, R.L. Sah and A. Hoger, "A growth mixture theory for cartilage with application to growth-related experiments on cartilage explants", J. Biomech. Eng., 125, pp. 169-179, 2003.
15. S.M. Klisch, R.L. Sah and A. Hoger, "A cartilage growth mixture model for infinitesimal strains: solutions of boundary-value problems related to in vitro growth experiments", Biomech. Model. Mechanobiol., 3, pp. 209-223, 2005.
16. R. Krishnan, S. Park, F. Eckstein and G.A. Ateshian, "Inhomogeneous cartilage properties enhance superficial interstial fluid support and frictional properties, but do not provide a homogeneous state of stress", J. Biomech. Eng., 125, pp. 569-577, 2003.
17. W.M. Lai, J.S. Hou and V.C. Mow, "A triphasic theory for the swelling and deformation behaviors of articular cartilage", J. Biomech. Eng., 113, pp. 245-258, 1991.
18. G. Lemon, J.R. King, H.M. Byrne, O.E. Jensen and K.M. Shakesheff, "Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory", J. Math. Biol., 52, pp. 571-594, 2006.
19. K.W. Li, Y.H. Falcovitz, J.P. Nagrampa, A.C. Chen, L.M. Lottman, J.Y.-J. Shyy and R.L. Sah, "Mechanical compression of transplanted chondrocytes", J. Orthop. Res., 18, pp. 374-382, 2000.
20. K.W. Li, A.K. Williamson, A.S. Wang and R.L. Sah, "Modulators of cartilage biology: growth response of cartilage to static and dynamics compression", Clin. Orthop. Relat. Res., 391S, pp. S34-S48, 2001.
21. L.P. Li, M.D. Buschmann and A. Shirazi-Adl, "The asymmetry in transient response in compression versus release for cartilage in unconfined compression", J. Biomech. Eng., 123, pp. 519-522, 2001.
22. R.L. Mauck, C.T. Hung and G.A. Ateshian, "Modeling of neutral solute transport in a dynamically loaded porous permeable gel: implications for articular cartilage biosynthesis and tissue engineering", J. Biomech. Eng., 125, pp. 602-614, 2003.
23. V.C. Mow, S.C. Kuei, W.M. Lai and C.G. Armstrong, "Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments", J. Biomech. Eng., 102, pp. 73-84, 1980.
24. B.P. O'Hara, J.P. Urban and A. Maroudas, "Influence of cyclic loading on the nutrition of articular cartilage", Ann. Rheum. Dis., 49, pp. 536-539, 1990.
25. K.D. Osborn, S.B. Trippel and H.J. Mankin, "Growth factor stimulation of adult articular cartilage", J. Orthop. Res., 7(1), pp. 35-42, 1989.
26. G.P. Peters and D.W. Smith, "Solute transport through a deforming porous medium", Int. J. Numer. Anal. Methods Geomech., 26, pp. 683-717, 2002.
27. T.M. Quinn, A.J. Grodzinsky, M.D. Buschmann, Y.-J. Kim and E.B. Hunziker, "Mechanical compression alters proteoglycan deposition and matrix deformation around individual cells in cartilage explants", J. Cell Sci., 111, pp. 573-583, 1998.
28. T.M. Quinn, P. Dierickx and A.J. Grodzinsky, "Glycosaminoglycan network geometry may contribute to anisotropic hydraulic permeability in cartilage under compression", J. Biomech., 34, pp. 1483-1490, 2001.
29. T.M. Quinn, C. Studer, A.J. Grodzinsky and J.J. Meister, "Preservation and analysis of nonequilibrium solute concentration distributions within mechanically compressed cartilage explants", J. Biochem. Biophys. Methods, 52, pp. 83-95, 2002.
30. V.R. Sara and K. Hall, "Insulin-like growth factors and their binding proteins", Physiol. Rev., 70(3), pp. 591-614, 1990.
31. R. Schneiderman, E. Snir, O. Popper, J. Hiss, H. Stein and A. Maroudas, "Insulin-like growth factor-i and its complexes in normal human articular cartilage: studies of partition and diffusion", Arch. Biochem. Biophys., 324(1), pp. 159-172, 1995.
32. A.C. Shieh and K.A. Athanasiou, "Principles of cell mechanics for cartilage tissue engineering", Ann. Biomed. Eng., 31, pp. 1-11, 2003.
33. F.H. Silver and G. Bradica, "Mechanobiology of cartilage: how do internal and external stresses affect mechanochemical transduction and elastic energy storage?", Biomech. Model. Mechanobiol., 1, pp. 219-238, 2002.
34. D.W. Smith, "One-dimensional contaminant transport through a deforming porous medium: theory and a solution for a quasi-steady state problem", Int. J. Numer. Anal. Methods Geomech., 24, pp. 693-722, 2000.
35. K. Terzaghi, Theoretical Soil Mechanics, New York, USA: Wiley, 1943.
36. A. Verruijt, Computational Geomechanics, Dordrecht, The Netherlands: Kluwer Academic Publishers, 1995.
37. A.K. Williamson, A.C. Chen and R.L. Sah, "Compressive properties and function-composition relationships of developing bovine articular cartilage", J. Orthop. Res., 19(6), pp. 1113-1121, 2001.
38. L. Zhang and A.Z. Szeri, "Transport of neutral solute in articular cartilage: effects of loading and particle size", Proc. R. Soc. A, 461, pp. 2021-2042, 2005.
39. O.C. Zienkiewicz and R.L. Taylor, "The finite element method", Fluid Dynamics, 5th ed., Oxford, United Kingdom: Butterworth-Heinemann, 2000, vol. 3.
40. W.B. van den Berg, P.M. van der Kraan, A. Scharstuhl and H.M. van Beuningen, "Tissue engineering, cells, scaffolds, and growth factors: growth factors and cartilage repair", Clin. Orthop. Relat. Res., 391S, pp. S244-S250, 2001.