Homogenization Analysis of Trabecular Bone and Prediction Ofbone Ingrowth Using Topology Optimization

Year	Entry
1964	Hashin Z, Rosen BW. The elastic moduli of fiber-reinforced materials. J Appl Mech. June 1964;31(2):223-232.
1987	Parfitt AM. Bone remodeling and bone loss: understanding the pathophysiology of osteoporosis. Clin Obstet Gynecol. December 1987;30(4):789-811.
1990	Beaupré GS, Orr TE, Carter DR. An approach for time‐dependent bone modeling and remodeling: theoretical development. J Orthop Res. September 1990;8(5):651-661.
1985	Gibson LJ. The mechanical behaviour of cancellous bone. J Biomech. 1985;18(5):317-328.
1988	Ashman RB, Rho JY. Elastic modulus of trabecular bone material. J Biomech. 1988;21(3):177-181.
1984	Parfitt AM. The cellular basis of bone remodeling: the quantum concept reexamined in light of recent advances in the cell biology of bone. Calcif Tiss Int. March 1984;36(suppl 1):S37-S45.
1966	Arnold JS, Bartley MH, Tont SA, Jenkins DP. Skeletal changes in aging and disease. Clin Orthop Relat Res. December 1966;49:17-38.
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.
1978	Singh I. The architecture of cancellous bone. J Anat. October 1978;127(2):305-310.
1990	Fyhrie DP, Carter DR. Femoral head apparent density distribution predicted from bone stresses. J Biomech. 1990;23(1):1-10.
1963	Hashin Z, Shtrikman S. A variational approach to the theory of the elastic behaviour of multiphase materials. J Mech Phys Solids. March–April 1963;11(2):127-140.
1892	Wolff J. Das Gesetz der Transformation der Knochen. Berlin: Hirschwald; 1892.
1964	Frost HM. Mathematical Elements of Lamellar Bone Remodelling. Springfield, IL: Charles C. Thomas; 1964.
1982	Gibson LJ, Ashby MF. The mechanics of three-dimensional cellular materialsthe mechanics of three-dimensional cellular materials. Proc R Soc Lon Ser-A. July 8, 1982;382(1782):43-59.
1975	Townsend PR, Rose RM, Radin EL. Buckling studies of single human trabeculae. J Biomech. July 1975;8(3-4):199-200.
1989	Burr DB, Schaffler MB, Yang KH, Lukoschek M, Sivaneri N, Blaha JD, Radin EL. Skeletal change in response to altered strain environments: is woven bone a response to elevated strain? Bone. 1989;10(3):223-233.
1971	Whitehouse WJ, Dyson ED, Jackson CK. The scanning electron microscope in studies of trabecular bone from a human vertebral body. J Anat. April 1971;108(3):481-496.
1974	Whitehouse WJ. The quantitative morphology of anisotropic trabecular bone. J Microsc (Oxford). July 1974;101:153-168.
1989	Kuhn JL, Goldstein SA, Choi K, London M, Feldkamp LA, Matthews LS. Comparison of the trabecular and cortical tissue moduli from human iliac crests. J Orthop Res. November 1989;7(6):876-884.
1987	Carter DR, Fyhrie DP, Whalen RT. Trabecular bone density and loading history: regulation of connective tissue biology by mechanical energy. J Biomech. 1987;20(8):785-794.
1987	Kuhn JL. Trabecular Bone Structure and Mechanical Properties [PhD thesis]. University of Michigan; 1987.
1985	Beaupre GS, Hayes WC. Finite element analysis of a three-dimensional open-celled model for trabecular bone. J Biomech Eng. August 1985;107(3):249-256.
1977	Carter DR, Hayes WC. The compressive behavior of bone as a two-phase porous structure. J Bone Joint Surg. 1977;59A(7):954-962.
1986	Frost HM. Intermediary Organization of the Skeleton. Vols. 1-2. Boca Raton, FL: CRC Press; 1986.
1990	Choi K, Kuhn JL, Ciarelli MJ, Goldstein SA. The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus. J Biomech. 1990;23(11):1103-1113.
1984	Harrigan TP, Mann RW. Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J Mater Sci. March 1984;19(3):761-767.
1987	Goldstein SA. The mechanical properties of trabecular bone: dependence on anatomic location and function. J Biomech. 1987;20(11-12):1055-1061.
1988	Harrigan TP, Jasty M, Mann RW, Harris WH. Limitations of the continuum assumption in cancellous bone. J Biomech. 1988;21(4):269-275.
1989	Mente PL, Lewis JL. Experimental method for the measurement of the elastic modulus of trabecular bone tissue. J Orthop Res. 1989;7(3):456-461.
1982	Williams JL, Lewis JL. Properties and an anisotropic model of cancellous bone from the proximal tibial epiphysis. J Biomech Eng. February 1982;104(1):50-56.
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.
1989	Feldkamp LA, Goldstein SA, Parfitt MA, Jesion G, Kleerekoper M. The direct examination of three‐dimensional bone architecture in vitro by computed tomography. J Bone Miner Res. 1989;4(1):3-11.
1986	Fyhrie DP, Carter DR. A unifying principle relating stress to trabecular bone morphology. J Orthop Res. 1986;4(3):304-317.
1963	Hill R. Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids. September 1963;11(5):357-372.
1988	Skerry TM, Bitensky L, Chayen J, Lanyon LE. Loading-related reorientation of bone proteoglycan in vivo: strain memory in bone tissue? J Orthop Res. July 1988;6(4):547-551.
1973	Pugh JW, Rose RM, Radin EL. A structural model for the mechanical behavior of trabecular bone. J Biomech. 1973;6(6):657-670.
1989	Martin RB, Burr DB. Structure, Function, and Adaptation of Compact Bone. New York, NY: Raven Press; 1989.
1990	Beaupré GS, Orr TE, Carter DR. An approach for time‐dependent bone modeling and remodeling—application: a preliminary remodeling simulation. J Orthop Res. September 1990;8(5):662-670.
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.
1974	Whitehouse WJ, Dyson ED. Scanning electron microscope studies of trabecular bone in the proximal end of the human femur. J Anat. 1974;118(pt 3):417-444.
1983	Huiskes R, Chao EYS. A survey of finite element analysis in orthopedic biomechanics: the first decade. J Biomech. 1983;16(6):385-409.
1990	Orr TE, Beaupré GS, Carter DR, Schurman DJ. Computer predictions of bone remodeling around porous-coated implants. J Arthoplast. September 1990;5(3):191-200.
1983	Parfitt AM, Mathews CH, Villanueva AR, Kleerekoper M, Frame B, Rao DS. Relationships between surface, volume, and thickness of iliac trabecular bone in aging and in osteoporosis: implications for the microanatomic and cellular mechanisms of bone loss. J Clin Invest. October 1983;72(4):1396-1409.
1987	Cheal EJ, Snyder BD, Nunamaker DM, Hayes WC. Trabecular bone remodeling around smooth and porous implants in an equine patellar model. J Biomech. 1987;20(11-12):1121-1134.
1970	McElhaney J, Alem N, Roberts V. A porous block model for cancellous bones. Winter Annual Meeting of the American Society of Mechanical Engineers; November 29–December 3, 1970; New York, NY.1-9. ASME Publication 70-WA/BHF-2.