The laws of bone architecture

Koch, John C.

Year	Entry
2007	Cowin SC, Doty SB. Bone tissue adaptation. In: Tissue Mechanics. Boca Raton, FL: Springer; 2007:385-424.
1957	Evans FG. Stress and Strain in Bones: Their Relation to Fractures and Osteogenesis. Springfield, IL: Charles C. Thomas; 1957.
1981	Hayes WC, Snyder B. Toward a quantitative formulation of Wolff's Law in trabecular bone. In: Cowin SC, ed. Mechanical Properties of Bone. The Joint ASME-ASCE Applied Mechnics, Fluids Engineering and Bioengineering Conference; June 22-24, 1981; Boulder, CO. New York, NY: American Society of Mechical Engineers; 1981:43-68.
1981	Lanyon LE. The measurement and biological significance of bone strain in vivo. In: Cowin SC, ed. Mechanical Properties of Bone. The Joint ASME-ASCE Applied Mechnics, Fluids Engineering and Bioengineering Conference; June 22-24, 1981; Boulder, CO. New York, NY: American Society of Mechical Engineers; 1981:93-105.
1981	Huiskes R, Janssen JD, Slooff TJ. A detailed comparison of experimental and theoretical stress-analyses of a human femur. In: Cowin SC, ed. Mechanical Properties of Bone. The Joint ASME-ASCE Applied Mechnics, Fluids Engineering and Bioengineering Conference; June 22-24, 1981; Boulder, CO. New York, NY: American Society of Mechical Engineers; 1981:211-234.
1963	Frost HM. Bone Remodelling Dynamics. Springfield, IL: Charles C. Thomas; 1963.
1964	Frost HM. The Laws of Bone Structure. Springfield, IL: Charles C. Thomas; 1964.
1986	Frost HM. Intermediary Organization of the Skeleton. Vols. 1-2. Boca Raton, FL: CRC Press; 1986.
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.
2001	Villarraga ML, Ford CM. Applications of bone mechanics. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:33-1–33-33.
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.
1965	Zarek JM, Edwards J. Dynamic considerations of the human skeletal system. In: Kenedi RM, ed. Biomechanics and Related Bio-Engineering Topics: Proceedings of a Symposium Held in Glasgow, September 1964. Oxford, UK: Pergamon Press; 1965:187-203.
1988	Genant HK, Volger JB, Block JE. Radiology of osteoporosis. In: Riggs BL, Melton LJ III, eds. Osteoporosis: Etiology, Diagnosis, and Management. New York, NY: Raven Press; 1988:181-220.
1990	Goldstein SA, Hollister SJ, Kuhn JL, Kikuchi N. The mechanical and remodeling properties of trabecular bone. In: Mow VC, Ratcliffe A, Woo SL-Y, eds. Biomechanics of Diarthrodial Joints. Vol 2. New York, NY: Springer-Verlag; 1990:61-81.
1998	Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.
1958	Evans FG. Relations between the microscopic structure and tensile strength of human bone. Acta Anat. 1958;35(4):285-301.
1964	Ascenzi A, Bonucci E. The ultimate tensile strength of single osteons. Acta Anat. 1964;58(1-2):160-183.
1965	Sedlin ED. A rheologic model for cortical bone: a study of physical properties of human femoral samples. Acta Orthop Scand. 1965;(suppl 83):1-77.
1989	Benaissa R, Uhthoff HK, Mercier P. Repair of trabecular fatigue fractures: cadaver studies of the upper femur. Acta Orthop Scand. October 1989;60(5):585-589.
1952	Dempster WT, Liddicoat RT. Compact bone as a non-isotropic material. Am J Anat. 1952;91(3):331-362.
1983	Ruff CB, Hayes WC. Cross‐sectional geometry of Pecos Pueblo femora and tibiae: a biomechanical investigation, I: method and general patterns of variation. Am J Phys Anthropol. 1983;60(3):359-381.
1968	Ascenzi A, Bonucci E. The compressive properties of single osteons. Anat Rec. July 1968;161(3):377-392.
1990	Frost HM. Skeletal structural adaptations to mechanical usage (SATMU), I: redefining Wolff's law: the bone modeling problem. Anat Rec. 1990;226(4):403-413.
2003	Frost HM. Bone's mechanostat: a 2003 update. Anat Rec. 2003;275A(2):1081-1101.
2000	Fyhrie DP, Hoshaw SJ, Hamid MS, Hou FJ. Shear stress distribution in the trabeculae of human vertebral bone. Ann Biomed Eng. October 2000;28(10):1194-1199.
1993	Odgaard A, Gundersen HJG. Quantification of connectivity in cancellous bone, with special emphasis on 3-D reconstructions. Bone. March–April 1993;14(2):173-182.
1994	Fyhrie DP, Schaffler MB. Failure mechanisms in human vertebral cancellous bone. Bone. 1994;15(1):105-109.
1994	Heřt J, Fiala P, Petrtýl M. Osteon orientation of the diaphysis of the long bones in man. Bone. May–June 1994;15(3):269-277.
1996	Biewener AA, Fazzalari NL, Konieczynski DD, Baudinette RV. Adaptive changes in trabecular architecture in relation to functional strain patterns and disuse. Bone. July 1996;19(1):1-8.
1997	Odgaard A. Three-dimensional methods for quantification of cancellous bone architecture. Bone. 1997;20(4):315-328.
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.
2013	Carter Y, Thomas CDL, Clement JG, Peele AG, Hannah K, Cooper DM. Variation in osteocyte lacunar morphology and density in the human femur: a synchrotron radiation micro-CT study. Bone. January 2013;52(1):126-132.
2020	Oh Y, Yamamoto K, Hashimoto J, Fujita K, Yoshii T, Fukushima K, Kurosa Y, Wakabayashi Y, Kitagawa M, Okawa A. Biological activity is not suppressed in mid-shaft stress fracture of the bowed femoral shaft unlike in “typical” atypical subtrochanteric femoral fracture: a proposed theory of atypical femoral fracture subtypes. Bone. August 2020;137:115453.
1993	Goldstein SA, Goulet R, McCubbrey D. Measurement and significance of three-dimensional architecture to the mechanical integrity of trabecular bone. Calcif Tiss Int. February 1993;53(suppl 1):S127-S133.
1972	Rybicki EF, Simonen FA, Weis EB Jr. On the mathematical analysis of stress in the human femur. J Biomech. March 1972;5(2):203-215.
1974	Behrens JC, Walker PS, Shoji H. Variations in strength and structure of cancellous bone at the knee. J Biomech. 1974;7(3):201-207.
1978	Hayes WC, Swenson LW Jr, Schurman DJ. Axisymmetric finite element analysis of the lateral tibial plateau. J Biomech. 1978;11(1-2):21-33.
1980	Viano DC, Stalnaker RL. Mechanisms of femoral fracture. J Biomech. 1980;13(8):701-715.
1983	Huiskes R, Chao EYS. A survey of finite element analysis in orthopedic biomechanics: the first decade. J Biomech. 1983;16(6):385-409.
1983	Goldstein SA, Wilson DL, Sonstegard DA, Matthews LS. The mechanical properties of human tibial trabecular bone as a function of metaphyseal location. J Biomech. 1983;16(12):965-969.
1987	Bentzen SM, Hvid I, Jorgensen J. Mechanical strength of tibial trabecular bone evaluated by X-ray computed tomography. J Biomech. 1987;20(8):743-752.
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.
1992	Turner CH. On Wolff's law of trabecular architecture. J Biomech. January 1992;25(1):1-9.
1992	Gross TS, McLeod KJ, Rubin CT. Characterizing bone strain distributions in vivo using three triple rosette strain gages. J Biomech. September 1992;25(9):1081-1087.
1994	Prendergast P, Taylor D. Prediction of bone adaptation using damage accumulation. J Biomech. August 1994;27(8):1067-1076.
1997	Duda GN, Schneider E, Chao EY. Internal forces and moments in the femur during walking. J Biomech. September 1997;30(9):933-941.
1987	Roesler H. The history of some fundamental concepts in bone biomechanics. J Biomech. 1987;20(11-12):1025-1034.
2020	Li T, Chen Z, Gao Y, Zhu L, Yang R, Leng H, Huo B. Fluid–solid coupling numerical simulation of trabecular bone under cyclic loading in different directions. J Biomech. August 26, 2020;109:109912.
1986	Cowin SC. Wolff’s law of trabecular architecture at remodeling equilibrium. J Biomech Eng. February 1986;108(1):83-88.
1952	Robinson RA. An electron-microscopic study of the crystalline inorganic component of bone and its relationship to the organic matrix. J Bone Joint Surg. April 1952;34A(2):389-435, 476.
1970	Singh M, Nagrath AR, Maini PS. Changes in trabecular pattern of the upper end of the femur as an index of osteoporosis. J Bone Joint Surg. April 1970;52A(3):457-467.
1974	Lanyon LE. Experimental support for the trajectorial theory of bone structure. J Bone Joint Surg. 1974;56B(1):160-166.
2021	Farlay D, Rizzo S, Ste-Marie L-G, Michou L, Morin SN, Qiu S, Chavassieux P, Chapurlat RD, Rao SD, Brown JP, Boivin G. Duration-dependent increase of human bone matrix mineralization in long-term bisphosphonate users with atypical femur fracture. J Bone Miner Res. June 2021;36(6):1031-1041.
1976	Cowin SC, Hegedus DH. Bone remodeling, I: theory of adaptive elasticity. J Elast. 1976;6(3):313-326.
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. J Exp Biol. December 1982;101:187-211.
1990	Kuhn JL, Goldstein SA, Feldkamp LA, Goulet RW, Jesion G. Evaluation of a microcomputed tomography system to study trabecular bone structure. J Orthop Res. 1990;8(6):833-842.
2003	Patel V, Issever AS, Burghardt A, Laib A, Ries M, Majumdar S. MicroCT evaluation of normal and osteoarthritic bone structure in human knee specimens. J Orthop Res. 2003;21(1):6-13.
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.
1964	Walker LB Jr, Harris EH, Benedict JV. Stress-strain relationship in human cadaveric plantaris tendon: a preliminary study. Med Electron Biol Eng. March 1964;2:31-38.
1982	Frost HM. Review article mechanical determinants of bone modeling. Metab Bone Dis Rel Res. 1982;4(4):217-229.
2010	Cristofolini L, Schileo E, Juszczyk M, Taddei F, Martelli S, Viceconti M. Mechanical testing of bones: the positive synergy of finite–element models and in vitro experiments. Philos Trans R Soc A-Math Phys Eng Sci. June 13, 2010;368(1920):2725-2763.
1996	Hillam RA. Response of Bone to Mechanical Load and Alterations in Circulating Hormones [PhD thesis]. Bristol, UK: University of Bristol; October 1996.
2016	Guang Y. Characterization of Bone and Bone Marrow Lesions in the Osteoarthritic Hip [Master's thesis]. Boston University; 2016.
1989	Fondrk MT. An Experimental and Analytical Investigation Into the Nonlinear Constitutive Equations of Cortical Bone [PhD thesis]. Cleveland, OH: Case Western Reserve University; May 1989.
1997	Zhang D. Electromechanical Mechanisms of Bone Remodeling [PhD thesis]. New York, NY: The City University of New York; 1997.
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.
2005	Day JS. Bone Quality: The Mechanical Effects of Microarchitecture and Matrix Properties [PhD thesis]. Erasmus University Rotterdam; 2005.
2007	Ali M. Study of a Compact Energy Absorber [PhD thesis]. University of Toronto; 2007.
2009	Edwards WB. Internal Structural Loading of the Lower Extremity During Running: Implications for Skeletal Injury [PhD thesis]. Iowa State University; 2009.
2015	Noble GJ. Evaluation of a Press Fit, Percutaneous, Skeletally Anchored Endoprosthesis for Prosthetic Limb Attachment: Bone Response and the Effect of Low Intensity Vibration [PhD thesis]. The Ohio State University; 2015.
2003	Peterman MM. A Strain Map of the Human Distal Tibia During the Stance Phase of Walking, from Dynamic Cadaver Experiments and Finite Element Analysis Simulations [PhD thesis]. State College, PA: Pennsylvania State University; August 2003.
2016	Berman AG. Influence of Mechanical Stimulation on the Quantity and Quality of Bone During Modeling [Master's thesis]. Purdue University; August 2016.
1995	DeVries S. A Three-Dimensional Finite Element Stress Analysis of the Glenoid With and Without a Total Shoulder Arthroplasty Component [Master's thesis]. Queen's University; July 1995.
2010	Boyle CH. Computational Study of Wolff's Law Utilizing Design Space Topology Optimization: A New Method for Hip Prosthesis Design [Master's thesis]. Queen's University; August 2010.
1986	Fyhrie DP. Stress Analysis and Design of Proximal Femoral Prostheses [PhD thesis]. Stanford University; January 1986.
1990	Fyhrie PB. Finite Element Analyses of Fracture Healing in Long Bones [PhD thesis]. Stanford University; August 10, 1990.
1990	Orr TE. The Role of Mechanical Stresses in Bone Remodeling [PhD thesis]. Stanford University; September 1990.
1994	Jacobs CR. Numerical Simulation of Bone Adaptation to Mechanical Loading [PhD thesis]. Stanford University; June 1994.
1994	Fritton SP. Computational Simulation of Trabecular Bone Adaptation [PhD thesis]. Tulane University; January 1994.
2006	Rouhi G. Theoretical Aspects of Bone Remodeling and Resorption Processes [PhD thesis]. Calgary, AB: University of Calgary; March 2006.
2002	Morgan EF-i. The Dependence on Anatomic Site of Trabecular Bone Structure-Function Relationships [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2002.
1996	Adams DJ. Mechanical Factors Initiating Appositional Bone Formation [PhD thesis]. University of Iowa; May 1996.
1993	Goulet RW. The Quantification of the Structure and Mechanical Properties of Trabecular Bone [PhD thesis]. University of Michigan; 1993.
1981	Ruff CB. Structural Changes in the Lower Limb Bones With Aging At Pecos Pueblo [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 1981.
2013	Pratt I. In Vivo Imaging of Cortical Porosity by Synchrotron Phase Contrast Micro Computed Tomography [Master's thesis]. University of Saskatchewan; August 2013.
2014	Carter Y. Quantitative Imaging of Sex and Age Differences in Human Cortical Bone Osteocyte Lacunae [PhD thesis]. University of Saskatchewan; July 2014.
1985	Schaffler MB. Stiffness and Fatigue of Compact Bone At Physiological Strains and Strain Rates [PhD thesis]. West Virginia University; 1985.
1984	Ingber DE. Basement Membrane Polarizes Epithelial Cells and Its Loss Can Result in Neoplastic Disorganization [PhD thesis]. Yale University; May 1984.

Year	Entry
1910	Fick R. Handbuch Der Anatomie Und Mechanik Der Gelenke: Unter Berücksichtigung Der Bewegenden Muskeln. Jena: Verlag von Gustav Fischer; 1910.
1876	Rauber AA. Elasticität Und Festigkeit Der Knochen: Anatomisch-Physiologische Studie. Leipzig, Germany: Verlag Von Wilhelm Engelmann; 1876.
1892	Wolff J. Das Gesetz der Transformation der Knochen. Berlin: Hirschwald; 1892.
1880	Messerer O. Über Elasticität und Festigkeit der menschlichen Knochen. Stuttgart, Germany: Cotta; 1880.