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Remodeling of the bone material containing microcracks: A theoretical analysis

Published online by Cambridge University Press:  15 December 1999

S. Ramtani  and
M. Zidi
S. Ramtani*
Affiliation:
Université Paris Val de Marne, Faculté des Sciences et Technologie, Laboratoire de Mécanique Physique (ESA 7052 du CNRS), 61 avenue du général de Gaulle, 94010 Créteil Cedex, France
M. Zidi
Affiliation:
Université Paris Val de Marne, Faculté des Sciences et Technologie, Laboratoire de Mécanique Physique (ESA 7052 du CNRS), 61 avenue du général de Gaulle, 94010 Créteil Cedex, France
*
[email protected]
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Abstract

The question is, what happens when the bone loses its ability for load-driven adaptation, when damage is no longer repaired as it seems to be the case for bone loss associated with age, medication or disease? In this study, we tempt to show how damage can influence the remodeling process. A thermodynamic theoretical framework is therefore provided as a basis for a consistent formulation of bone remodeling involving a chemical reaction and mass transfer between two constituents in presence of microcracks.

Keywords

Type
Research Article
Information
The European Physical Journal - Applied Physics , Volume 8 , Issue 3 , December 1999 , pp. 257 - 263
Copyright
© EDP Sciences, 1999

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References

Cowin, S.C., Hegedus, D.M., J. Elasticity 6, 313 (1976). CrossRef
Ascenzi, A., J. Biomechanics 26, 95 (1993). CrossRefPubMed
Y.C. Fung, Biomechanics: motions, flow, stress, and growth (Springer, New York, 1990).
Burr, D.B., Milgrom, C., Boyd, R.D., Higgins, W.L., Robin, G., Radin, E.L., J. Bone Joint Surgey B 72, 370 (1990).
Haeney, R.P., Calcified Tissue Intern. 53, S3 (1993). CrossRef
Burr, D.B., Martin, R.B., Schaffler, M.B., Radin, E.L., J. Biomechanics 18, 189 (1985). CrossRef
Martin, R.B., J. Orth. Res. 10, 818 (1992). CrossRef
Mori, S., Burr, D.B., Bone 14, 103 (1993). CrossRefPubMed
Chamay, A., Tschantz, P., J. Biomechanics 5, 173 (1972). CrossRef
Carter, D.R., Hayes, W.C., J. Biomechanics 10, 325 (1977). CrossRef
D. Taylor, Fatigue damage in bone: links to adaptation, in Synthesis in Bio Solid Mechanics, edited by P. Pederson, M.P. Bendsoe (Kluwere Academic Publishers, Dortrecht, 1998).
Prendergast, P.J., Taylor, D., J. Biomechanics 27, 1067 (1994). CrossRef
T.C. Lee, Ph.D. thesis, University of Dublin, 1995.
Frost, H.M., Bull. Henry Ford Hosp. 8, 25 (1960).
McNamara, B.P., Prendegast, P.J., Taylor, D., J. Biomed. Eng. 14, 209 (1992). CrossRef
Martin, R.B., Burr, D.B., J. Biomechanics 15, 137 (1982). CrossRef
Cowin, S.C., Moss-Salentijn, L., Moss, J., J. Biomed. Eng. 113, 191 (1991).
Mullender, M.G., Huiskes, R., Weinans, H.J., J. Biomechanics 27, 1389 (1994). CrossRef
Zidi, M., Ramtani, S., Eur. Phys. J. AP 3, 97 (1998). CrossRef
J.D. Currey, The mechanical adaptations of bones (Princeton University Press, NJ, 1984).
H.M. Frost, The laws of bone Structure (Charles C. Thomas, Springfield, 1964).
Treharne, R.W., Orth. Rev. 10, 35 (1981).
Weinbaum, S., Cowin, S.C., Zeng, Y., J. Biomechanics 27, 339 (1994). CrossRef
Justus, R., Luft, J.H., Calc. Tissue Res. 5, 222 (1970). CrossRef
Lee, T.C., Myers, E.R., Hayes, W.C., J. Anat. 193, 179 (1998). CrossRef
R.B. Martin, D.B. Burr, The structure, function and adaptation of cortical bone (Raven Press, New York, 1989).
T.C. Lee, L. Noelke, G.T. McMahon, J.P. Mulville, D. Taylor, Functional adaptation in bone, in Synthesis in Bio Solid Mechanics, edited by P Pedersen, M.P. Bendsoe (Kluwer Academic Publishers: Dortrecht, 1999), pp. 1-10.
Schaffler, B., Pitchford, W., Choi, K., Riddle, J.M., Bone 15, 483 (1994). CrossRefPubMed
Kachanov, M., J. Engng. Mech. Div. 106, 1039 (1980).
Lemaitre, J., Nucl. Engng. Des. 80, 233 (1984). CrossRef
Krajcinovic, D., Fonseka, G.U., J. Appl. Mech. 48, 809 (1981). CrossRef
Ramtani, S., Berthaud, Y., Mazars, J., Nucl. Engng. Des. 133, 97 (1992). CrossRef
Zioupos, P., Currey, J.D., J. Mat. Sci. 29, 978 (1994). CrossRef
T.C. Lee, M.D. thesis, University of Dublin, 1997.
Pattin, C.A., Caler, W.E., Carter, D.R., J. Biomechanics 29, 69 (1996). CrossRef
Goodman, M.A., Cowin, S.C., Arch. Rat. Mech. Anal. 44, 249 (1972). CrossRef
C. Truesdell, R.A. Toupin, The Classical field theories, in Encyclopedia of Physics, edited by S. Flügge (Springer-Verlag, Berlin, 1960), Vol. 3/1, pp. 226-793.
C. Truesdell, R.W. Noll, The non-linear field theories of mechanics, in Encyclopedia of Physics, edited by S. Flügge (Springer-Verlag, Berlin, 1965), Vol. 3/3, pp. 226-793.
C. Truesdell, The elements on continuum mechanics (Springer Verlag, 1966).
Coleman, B.D., Gurtin, M., J. Chem. Phys. 47, 597 (1967). CrossRef
L.E. Malvern, Introduction to the Mechanics of a Continuum Medium (Englewood Cliffs, N.J.: Prentice-Hall Inc., New Jersey, 1969).
J. Kestin, J.R. Rice, A critical review of thermodynamics (Stuart Ed. Mono book, 1970).
P. Germain, Cours de mécanique des milieux continus (Masson, 1973).
R.M. Bowen, Threory of Mixtures, in Continuum Physics, edited by A.C. Eringen (Academic Press, New York, 1976), Vol. 3, pp. 1-127.
A.E. Green, W. Zerna, Theoretical Elasticity (Oxford University Press, London, 1968).
Prendergast, P.J., Huiskes, R., J. Biomech. Engng. 118, 240 (1996). CrossRef
H.M. Frost, Intermediary Organisation of the Skeleton (CRC Press, Boca Raton, FL, 1986).
Cowin, S.C., van Buskirk, W.C., J. Biomechanics 11, 269 (1978). CrossRef