An analytical model of Pauwels’ functional adaptation mechanism in bone

Firoozbakhsh, K.; Cowin, S. C.

Affiliations

¹College of Engineering, Shiraz University, Shiraz, Iran

²Department of Biomedical Engineering, Tulane University, New Orleans, La. 70118

Abstract and keywords

In this paper it is argued and partially demonstrated that the features of Pauwels’ qualitative theory of functional adaptation of bone tissue are expressed mathematically by the cubic approximation to the theory of internal remodeling presented by Cowin and Hegedus. Complete solutions for the steady stress and steady strain situations in the cubic approximation to the theory of internal remodeling are presented. The cubic remodeling rate equation is shown to correspond closely to the remodeling equation suggested by Kummer for the qualitative theory of Pauwels.

Keywords:

Links

DOI: 10.1115/1.3138288

PubMed: 7311490

WoS: A1981MU33100004

History

Received: 1981-02-02

Revised: 1981-06-12

Cited Works (3)

Year	Entry
1976	Cowin SC, Hegedus DH. Bone remodeling, I: theory of adaptive elasticity. J Elast. 1976;6(3):313-326.
1972	Kummer BKF. Biomechanics of bone: mechanical properties, functional structure, functional adaptation. In: Fung YC, Perrone N, Anliker M, eds. Biomechanics: Its Foundations and Objectives. Symposium on Biomechanics, its Foundations and Objectives; July 29-31, 1970. Englewood Cliff, NJ: Inc., Prentice-Hall International; 1972:237-271.
1976	Hegedus DH, Cowin SC. Bone remodeling: small strain adaptive elasticity. J Elast. October 1976;6(4):337-352.

Cited By (17)

Year	Entry
1998	Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.
1984	Cowin SC. Mechanical modeling of the stress adaptation process in bone. Calcif Tiss Int. March 1984;36(suppl 1):S98-S103.
1984	Hart RT, Davy DT, Heiple KG. Mathematical modeling and numerical solutions for functionally dependent bone remodeling. Calcif Tiss Int. March 1984;36(suppl 1):S104-S109.
1985	Cowin SC, Hart RT, Balser JR, Kohn DH. Functional adaptation in long bones: establishing in vivo values for surface remodeling rate coefficients. J Biomech. 1985;18(9):665-684.
1987	Huiskes R, Weinans H, Grootenboer HJ, Dalstra M, Fudala B, Slooff TJ. Adaptive bone-remodeling theory applied to prosthetic-design analysis. J Biomech. 1987;20(11-12):1135-1150.
1989	Carter DR, Orr TE, Fyhrie DP. Relationships between loading history and femoral cancellous bone architecture. J Biomech. 1989;22(3):231-244.
1990	Fyhrie DP, Carter DR. Femoral head apparent density distribution predicted from bone stresses. J Biomech. 1990;23(1):1-10.
1994	Prendergast P, Taylor D. Prediction of bone adaptation using damage accumulation. J Biomech. August 1994;27(8):1067-1076.
1984	Hart RT, Davy DT, Heiple KG. A computational method for stress analysis of adaptive elastic materials with a view toward applications in strain-induced bone remodeling. J Biomech Eng. November 1984;106(4):342-350.
1995	Zioupos P, Currey JD, Mirza MS, Barton DC. Experimentally determined microcracking around a circular hole in a flat plate of bone: comparison with predicted stresses. Philos Trans R Soc Lond B Biol Sci. March 29, 1995;347(1322):383-396.
1983	Hart RT. Quantitative Response of Bone to Mechanical Stress [PhD thesis]. Cleveland, OH: Case Western Reserve University; January 1983.
2019	Du J. Mechanical Adaptation of Human Trabecular Bone: Experimental and Computational Study [PhD thesis]. Loughborough University; 2019.
1994	Jacobs CR. Numerical Simulation of Bone Adaptation to Mechanical Loading [PhD thesis]. Stanford University; June 1994.
2005	Ruimerman R. Modeling and Remodeling in Bone Tissue [PhD thesis]. Eindhoven, The Netherlands: Technische Universiteit Eindhoven; 2005.
2006	Rouhi G. Theoretical Aspects of Bone Remodeling and Resorption Processes [PhD thesis]. Calgary, AB: University of Calgary; March 2006.
1996	Adams DJ. Mechanical Factors Initiating Appositional Bone Formation [PhD thesis]. University of Iowa; May 1996.
1998	Arslanoğlu R. Mathematical Modeling and Experimental Aspects of Cellular Mechanotransduction [PhD thesis]. University of Texas at Austin; December 1998.