Bone remodeling of diaphysial surfaces under constant load: theoretical predictions

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Cowin, Stephen C.¹; Firoozbakhsh, Keykhosrow^1,2

Bone remodeling of diaphysial surfaces under constant load: theoretical predictions

J Biomech. 1981;14(7):471-484

©1981 U.S. Government

Affiliations

¹Department of Biomedical Engineering, Tulane University, New Orleans, LA 70118, U.S.A.

²Present address: College of Engineering, Shiraz University, Shiraz, Iran
Abstract

Theoretical predictions of surface bone remodeling in the diaphysis of a long bone under a constant superposed compressive load are made. The bone is modeled as a hollow circular cylinder. The surface remodeling theory due to Cowin and Van Buskirk is employed. It is shown that there is a great variety of solutions to the problem. Both endosteal and periosteal surfaces can move in either direction, in or out, in the same or opposite direction. It is possible for the medullary canal to fill up completely and for the endosteal surface to vanish. The particular type of response that develops depends upon the magnitude of the applied compressive load and the values of the surface remodeling rate coefficients.
Links

DOI: 10.1016/0021-9290(81)90097-X

PubMed: 7276008

WoS: A1981MK28600003
History

Received: 1981-02-10

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1991	Weinans HH. Mechanically Induced Bone Adaptations Around Orthopaedic Implants [PhD thesis]. Nijmegen, The Netherlands: Katholieke Universiteit te Nijmegen; 1991.
2001	Hart RT. Bone modeling and remodeling: theories and computation. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:31-1–31-42.
1990	Fung YC. Biomechanics: Motion, Flow, Stress, and Growth. New York, NY: Springer-Verlag; 1990.
1990	Cowin SC. Properties of cortical bone and theory of bone remodeling. In: Mow VC, Ratcliffe A, Woo SL-Y, eds. Biomechanics of Diarthrodial Joints. Vol 2. New York, NY: Springer-Verlag; 1990:119-153.
1998	Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.
1989	Burr DB, Schaffler MB, Yang KH, Wu DD, Lukoschek M, Kandzari D, Sivaneri N, Blaha JD, Radin EL. The effects of altered strain environments on bone tissue kinetics. Bone. 1989;10(3):215-221.
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.
1987	Cowin SC. Bone remodeling of diaphyseal surfaces by torsional loads: theoretical predictions. J Biomech. 1987;20(11-12):1111-1120.
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.
1990	Fyhrie DP, Carter DR. Femoral head apparent density distribution predicted from bone stresses. J Biomech. 1990;23(1):1-10.
1990	Brown TD, Pedersen DR, Gray ML, Brand RA, Rubin CT. Toward an identification of mechanical parameters initiating periosteal remodeling: a combined experimental and analytic approach. J Biomech. 1990;23(9):893-905.
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1983	Hart RT. Quantitative Response of Bone to Mechanical Stress [PhD thesis]. Cleveland, OH: Case Western Reserve University; January 1983.
2004	Mi LY. Analysis of Avian Bone Response to Mechanical Loading Using a Computational Connected Network [PhD thesis]. New York, NY: The City College of New York; 2004.
2010	Chennimalai Kumar N. Numerical Modeling of Cortical Bone Adaptation Due to Mechanical Loading Using the Finite Element Method [PhD thesis]. University of Illinois at Urbana-Champaign; 2010.
1994	Fischer KJ. Correspondence Between Bone Density Distributions and Mechanical Loading [PhD thesis]. Stanford University; December 1994.
1994	Jacobs CR. Numerical Simulation of Bone Adaptation to Mechanical Loading [PhD thesis]. Stanford University; June 1994.
1994	Levenston ME. Simulation of Functional Adaptation in Trabecular and Cortical Bone [PhD thesis]. Stanford University; September 1994.
1997	Qin Y-X. Fluid Flow, Matrix Strain and Loading Frequency as Interdependent Control Parameters in Skeletal Adaptation [PhD thesis]. Stony Brook, NY: State University of New York at Stony Brook; May 1997.
2008	Mulvihill BMC. Computational Investigation Into the Mechanoregulation of Osteoporosis [PhD thesis]. Trinity College Dublin; December 2008.
2005	Ruimerman R. Modeling and Remodeling in Bone Tissue [PhD thesis]. Eindhoven University of Technology; 2005.
1994	Fritton SP. Computational Simulation of Trabecular Bone Adaptation [PhD thesis]. Tulane University; January 1994.
1994	Oden ZM. Computational Prediction of Functional Adaptation in Canine Radii [PhD thesis]. Tulane University; 1994.
2004	Roberts MD. Adaptation of Bone to Mechanical and Nonmechanical Stimuli: An Integrated Experimental and Computational Study [PhD thesis]. Tulane University; 2004.
2006	Rouhi G. Theoretical Aspects of Bone Remodeling and Resorption Processes [PhD thesis]. Calgary, AB: University of Calgary; March 2006.
2021	Besler BAA. Bone as an Orientable, Smooth Surface: Distance Transforms, Morphometry, and Adaptation [PhD thesis]. Calgary, AB: University of Calgary; August 2021.
2003	Nyman JS. Simulations of Bone Adaptation to Total Knee Arthroplasty and Bisphosphonates Through Remodeling Stimulated by Microdamage and Disuse [PhD thesis]. Davis, University of California; 2003.
1996	Adams DJ. Mechanical Factors Initiating Appositional Bone Formation [PhD thesis]. University of Iowa; May 1996.
1992	Cohen CS. Relationships Among Stability, Bony Ingrowth, and Remodeling for a Porous Coated Hip Endoprosthesis [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 1992.
1995	Marcolongo MS. Bioactive Glass Fiber/polymeric Composite as a Bone Bonding Biomaterial [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 1995.