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Bertram, John E. A.
1
; Swartz, Sharon M.
2
The “law of bone transformation”: a case of crying Wolff?
Biol Rev
. August 1991;66(3):245-273
Affiliations
1
Department of Biology,
Dalhousie University
, Halifax, Nova Scotia, Canada
2
Department of Cell, Molecular, and Structural Biology,
Northwestern University
, Chicago, Illinois, U.S.A.
Links
DOI:
10.1111/j.1469-185X.1991.tb01142.x
PubMed:
1932466
WoS:
A1991GE86700001
History
Received: 1990-05-31
Revised: 1991-01-12
Accepted: 1991-02-21
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1983
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1980
Lanyon LE. The influence of function on the development of bone curvature: an experimental study on the rat tibia.
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1982
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1984
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1968
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1988
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1986
Jaworski ZFG, Uhthoff HK. Reversibility of nontraumatic disuse osteoporosis during its active phase.
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1982
Rubin CT, Lanyon LE. Limb mechanics as a function of speed and gait: a study of functional strains in the radius and tibia of horse and dog.
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1985
Rubin CT, Lanyon LE. Regulation of bone mass by mechanical strain magnitude.
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1970
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1980
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1981
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1983
Biewener AA, Thomason J, Lanyon LE. Mechanics of locomotion and jumping in the forelimb of the horse (
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1984
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1988
Skerry TM, Bitensky L, Chayen J, Lanyon LE. Loading-related reorientation of bone proteoglycan in vivo: strain memory in bone tissue?
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1978
Morey ER, Baylink DJ. Inhibition of bone formation during space flight.
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1989
Weinreb M, Rodan GA, Thompson DD. Osteopenia in the immobilized rat hind limb is associated with increased bone resorption and decreased bone formation.
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1984
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1987
Carter DR. Mechanical loading history and skeletal biology.
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1977
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1983
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1984
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1979
Starkebaum W, Pollack SR, Korostoff E. Midroelectrode studies of stress-generated potentials in four-point bending of bone.
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1984
Rubin CT, Lanyon LE. Dynamic strain similarity in vertebrates: an alternative to allometric limb bone scaling.
J Theo Biol
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1988
Meunier PJ. Assessment of bone turnover by histomorphometry in osteoporosis. In: Riggs BL, Melton LJ III, eds.
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. New York, NY: Raven Press; 1988:317-332.
1984
Rubin CT, Lanyon LE. Regulation of bone formation by applied dynamic loads.
J Bone Joint Surg
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Cited By (53)
Year
Entry
1992
Hall BK. Historical overview of studies on bone growth and repair. In: Hall BK, ed.
Bone. Volume 6: Bone Growth — A
. Boca Raton, FL: Inc., CRC Press; 1992:1-19.
2001
Cowin SC. The false premise of Wolff's Law. In: Cowin SC, ed.
Bone Mechanics Handbook
. 2nd ed. Boca Raton, FL: CRC Press; 2001:30-1–30-15.
2025
Skedros JG. Biomechanical foundations of histological analysis in limb bones: the crucial role of load-complexity categorization and collagen fiber orientation analysis when interpreting bone adaptation. In: Stout SD, Crowder C, eds.
Bone Histology: A Biological Anthropological Perspective
. 2nd ed. Boca Raton, FL: CRC Press; 2025:150-224.
2002
Currey JD.
Bones: Structure and Mechanics
. Princeton, NJ: Princeton University Press; 2002.
1998
Martin RB, Burr DB, Sharkey NA.
Skeletal Tissue Mechanics
. New York, NY: Springer-Verlag; 1998.
2006
Ruff C, Holt B, Trinkaus E. Who's afraid of the big bad Wolff? “Wolff's law” and bone functional adaptation.
Am J Phys Anthropol
. April 2006;129(4):484-498.
2020
Mulder B, Stock JT, Saers JPP, Inskip SA, Cessford C, Robb JE. Intrapopulation variation in lower limb trabecular architecture.
Am J Phys Anthropol
. September 2020;173(1):112-129.
1996
Yaszemski MJ, Payne RG, Hayes WC, Langer R, Mikos AG. Evolution of bone transplantation: molecular, cellular and tissue strategies to engineer human bone.
Biomaterials
. January 1996;17(2):175-185.
1994
Forwood MR, Turner CH. The response of rat tibiae to incremental bouts of mechanical loading: a quantum concept for bone formation.
Bone
. November–December 1994;15(6):603.
1995
Forwood MR, Turner CH. Skeletal adaptations to mechanical usage: results from tibial loading studies in rats.
Bone
. October 1995;17(4)(suppl):197S-205S.
2011
Barak MM, Lieberman DE, Hublin J-J. A Wolff in sheep's clothing: trabecular bone adaptation in response to changes in joint loading orientation.
Bone
. December 2011;49(6):1141-1151.
1993
Forwood MR, Burr DB. Physical activity and bone mass: exercises in futility?
Bone Miner
. May 1993;21(2):89-112.
2019
Liu P, Liang X, Li Z, Zhu X, Zhang Z, Cai L. Decoupled effects of bone mass, microarchitecture and tissue property on the mechanical deterioration of osteoporotic bones.
Compos Pt B-Eng
. November 15, 2019;177:107436.
1994
Turner CH, Forwood MR, Otter MW. Mechanotransduction in bone: do bone cells act as sensors of fluid flow?
FASEB J
. August 1994;8(11):875-878.
1995
Klein-Nulend J, van der Plas A, Semeins CM, Ajubi NE, Frangos JA, Nijweide PJ, Burger EH. Sensitivity of osteocytes to biomechanical stress in vitro.
FASEB J
. March 1995;9(5):441-445.
1997
Turner CH, Annet V, Pidaparti RMV. A uniform strain criterion for trabecular bone adaptation: do continuum-level strain gradients drive adaptation?
J Biomech
. June 1997;30(6):555-563.
2005
Ruimerman R, Hilbers P, van Rietbergen B, Huiskes R. A theoretical framework for strain-related trabecular bone maintenance and adaptation.
J Biomech
. April 2005;38(4):931-941.
2019
Yang H, Xu X, Bullock W, Main RP. Adaptive changes in micromechanical environments of cancellous and cortical bone in response to in vivo loading and disuse.
J Biomech
. May 24, 2019;89:85-94.
1997
Guldberg RE, Caldwell NJ, Guo XE, Goulet RW, Hollister SJ, Goldstein SA. Mechanical stimulation of tissue repair in the hydraulic bone chamber.
J Bone Miner Res
. August 1997;12(8):1295-1302.
2003
Lieberman DE, Pearson OM, Polk JD, Demes B, Crompton AW. Optimization of bone growth and remodeling in response to loading in tapered mammalian limbs.
J Exp Biol
. September 15, 2003;206(18):3125-3138.
2006
Pontzer H, Lieberman DE, Momin E, Devlin MJ, Polk JD, Hallgrímsson B, Cooper DML. Trabecular bone in the bird knee responds with high sensitivity to changes in load orientation.
J Exp Biol
. January 2006;209(1):57-65.
2007
Skedros JG, Baucomb SL. Mathematical analysis of trabecular “trajectories” in apparent trajectorial structures: the unfortunate historical emphasis on the human proximal femur.
J Theo Biol
. January 7, 2007;244(1):15-45.
2014
Christen P, Ito K, Ellouz R, Boutroy S, Sornay-Rendu E, Chapurlat RD, van Rietbergen B. Bone remodelling in humans is load-driven but not lazy.
Nat Commun
. September 2014;5:4855.
1994
Parfitt AM. The two faces of growth: benefits and risks to bone integrity.
Osteoporos Int
. November 1994;4(6):382-398.
2007
Fratzl P, Weinkamer R. Nature’s hierarchical materials.
Prog Mater Sci
. November 2007;52(8):1263-1334.
2004
Pearson OM, Lieberman DE. The aging of Wolff's “law”: ontogeny and responses to mechanical loading in cortical bone.
Yearb Phys Anthropol
. 2004;47:63-99.
1998
Bateman TA.
Cytokine Therapies for Short-Term Disuse Osteopenia Models in Murines
[PhD thesis]. University of Colorado; 1998.
1993
Lieberman DE.
Mobility and Strain: The Biology of Cementogenesis and Its Application to the Evolution of Hunter-Gatherer Seasonal Mobility During the Late Quaternary in the Southern Levant
[PhD thesis]. Cambridge, MA: Harvard University; January 1993.
2006
Main RP.
Skeletal Mechanics, Bone Histomorphology, and Growth in Tetrapods
[PhD thesis]. Cambridge, MA: Harvard University; September 2006.
2007
Devlin MJ.
Interactions of Estrogen, Strain, and Bone Growth: Implications for Human Skeletal Robusticity
[PhD thesis]. Cambridge, MA: Harvard University; September 2007.
2005
Zumwalt AC.
The Effect of Endurance Exercise on the Morphology of Muscle Attachment Sites: An Experimental Study in Sheep (
Ovis Aries
)
[PhD thesis]. Johns Hopkins University; March 2005.
2007
Organ JM.
The Functional Anatomy of Prehensile and Nonprehensile Tails of the Platyrrhini (primates) and Procyonidae (carnivora)
[PhD thesis]. Johns Hopkins University; September 2007.
2020
Bennison MBL.
The Role of Cancellous Bone Architecture in Misalignment and Side Effect Errors
[Master's thesis]. Sudbury, ON: Laurentian University; 2020.
2019
Du J.
Mechanical Adaptation of Human Trabecular Bone: Experimental and Computational Study
[PhD thesis]. Loughborough University; 2019.
1995
Yaszemski MJ.
The Design, Synthesis, Characterization, and Mechanical Testing of a Novel Degradable Polymeric Biomaterial for Use as a Bone Substitute
[PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; June 1995.
1992
Bloomfield SA.
Site-Specific Changes in Bone Mass and Alterations in Calciotropic Hormones With Electrical Stimulation Exercise in Individuals With Chronic Spinal Cord Injury
[PhD thesis]. The Ohio State University; 1992.
2001
Tanck EJM.
Mechanical Regulation of Bone Development
[PhD thesis]. Nijmegen, Netherlands: Katholieke Universiteit Nijmegen; June 2001.
2001
Kim DG.
Micromechanical Analysis of Bone At a Bone-Implant Interface
[PhD thesis]. Troy, NY: Rensselaer Polytechnic Institute; April 2001.
2005
Ruimerman R.
Modeling and Remodeling in Bone Tissue
[PhD thesis]. Eindhoven University of Technology; 2005.
2006
Macdonald HM.
Effectiveness of a School-Based Physical Activity Intervention for Increasing Bone Strength in Children: Action Schools! British Columbia
[PhD thesis]. Vancouver, BC: University of British Columbia; July 2006.
1999
Judex S.
The Effect of Exercise-Induced Mechanical Stimuli on Cortical Bone
[PhD thesis]. Calgary, AB: University of Calgary; 1999.
2021
Besler BAA.
Bone as an Orientable, Smooth Surface: Distance Transforms, Morphometry, and Adaptation
[PhD thesis]. Calgary, AB: University of Calgary; August 2021.
2021
Kemp TD.
An Inverse Interface Evolution Problem to Identify Participant-Specific Bone Microarchitecture Adaptation
[Master's thesis]. Calgary, AB: University of Calgary; May 2021.
2019
Nguyen C.
Multiscale Network Characterization of the Strength and Robustness of Trabecular Bone
[PhD thesis]. Santa Barbara, CA: Santa Barbara, University of California; September 2019.
1995
Waanders NA.
A Distraction Osteogenesis Model to Investigate the Influence of the Mechanical Environment on Bone Formation
[PhD thesis]. University of Michigan; 1995.
1996
Lerner AL.
Influence of Mechanical Stresses on Normal Bone Growth in the Developing Femur
[PhD thesis]. University of Michigan; 1996.
1997
Richards M.
Strain Environment Effects on New Bone Formation and Precursor Tissue Differentiation During Distraction
[PhD thesis]. University of Michigan; 1997.
2023
Cosman MN.
Trabecular and Cortical Skeletal Correlates of Locomotor Ontogeny in
Pan
With Comparisonsto Skeletal Variation and Adaptation in
Gorilla
and
Pongo
[PhD thesis]. University of Michigan; 2023.
2012
Hennig C.
Determinants of Osteon Geometric Parameters and Their Relation With Age in Cortical Bone
[Master's thesis]. University of Saskatchewan; December 2012.
2002
Wang M-Y.
Quantifying Musculoskeletal Load and Adaptation: Biomechanical Consideration
[PhD thesis]. University of Southern California (USC); August 2002.
2010
Beckstrom AB.
Histologic and Geometric Data Challenge the Assumption of Habitual Superior-Inferior (tension-Compression) Bending Across the Chimpanzee Proximal Femur
[Master's thesis]. University of Utah; August 2010.
2013
Eleazer CD.
The Interaction of Mechanical Loading and Metabolic Stress on Human Cortical Bone: Testing Anthropological Assumptions Using Cross-Sectional Geometry and Histomorphology
[PhD thesis]. Knoxville, University of Tennessee; August 2013.
1996
Kim Y.
A Finite-Element Study of Intervertebral Cages and Spinal Bone Remodeling
[PhD thesis]. University of Wisconsin – Madison; 1996.