Investigation of Bone Mechanical Properties At the Microscopic Level Using Ultrasonic Methods and Numerical Simulation

Osteoporosis related fracture is a growing health care problem in the United States, with a predicted annual cost by the year 2020 of over 30 billion dollars. In order to better diagnose osteoporosis and predict osteoporosis-related fracture risk, an understanding of the failure mechanisms of bone at the microscopic level is needed.

Scanning acoustic microscopy (SAM) was used to measure bone properties down to the individual lamellar level (with a resolution of 10 microns). A relationship between the acoustic reflection coefficient and elastic modulus was obtained (R² = 0:942;p < 0:001) to make it possible to measure the elastic modulus of bone at the lamellar level directly using SAM images. 52 vertebrae from 12 cadavers were measured under SAM. The results showed that, thickness of both the cortical shell and endplate significantly decreased with age ( p < 0:05); the anterior curvature of vertebrae from elder specimens increased 50.6% compared with younger specimens; the trabecular volume fraction of younger specimens was 0.153 ±0.019, while that of elder specimens was 0.0948±0.0165; the degree of trabecular anisotropy of elder specimens was significantly greater than that of younger specimens ( p < 0:05); the elastic modulus of individual trabeculae of younger specimens was 7.47±0.97 GPa which was significantly greater ( p < 0:05) than that of elder specimens (5.90±1.97 GPa). The elastic modulus of the cortical shell and endplate were found to be same as that of adjacent individual trabeculae. The data set was insufficient to conclude any significant difference between gender for these measured properties.

Representative volume element (RVE) models were developed for individual lamellae and trabecular bone, to investigate the microscopic level mechanical properties of bone. The predicted modulus of individual trabeculae ranged from 3.9 GPa to 21.1 GPa, which bounded most of the available experimental data including that of the present study. The model also showed that brittle fracture of the mineral phase is the failure mechanism of bone under global tensile stress. The elastic buckling behavior of trabecular bone was modeled and the critical buckling stress of the model was predicted. The results showed that under low volume fractions (less than 0.1) the predicted critical elastic buckling stress can match the trabecular strength. But under higher volume fractions, the predicted critical elastic buckling stress overestimates the strength of trabecular bone. Finally, the predicted critical buckling stress for elder specimen decreased 84% compared with that of younger specimens, according to the models developed based on the microstructural parameters measured using SAM.

Year	Entry
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.
1994	Kanis JA, Melton LJ III, Christiansen C, Johnston CC, Khaltaev N. The diagnosis of osteoporosis. J Bone Miner Res. August 1994;9(8):1137-1141.
1988	Ashman RB, Rho JY. Elastic modulus of trabecular bone material. J Biomech. 1988;21(3):177-181.
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.
1995	Grimm MJ. Ultrasound Propagation Through the Calcaneus: Dependence on “Bone Quality” and Prediction by Biot's Theory [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 1995.
1984	Ashman RB, Cowin SC, Van Buskirk WC, Rice JC. A continuous wave technique for the measurement of the elastic properties of cortical bone. J Biomech. 1984;17(5):349-361.
1999	Roy ME, Rho J-Y, Tsui TY, Evans ND, Pharr GM. Mechanical and morphological variation of the human lumbar vertebral cortical and trabecular bone. J Biomed Mater Res. February 1999;A44(2):191-197.
1987	Ashman RB, Corin JD, Turner CH. Elastic properties of cancellous bone: measurement by an ultrasonic technique. J Biomech. 1987;20(10):979-986.
1994	Zioupos P, Currey JD, Sedman AJ. An examination of the micromechanics of failure of bone and antler by acoustic emission tests and laser scanning confocal microscopy. Med Eng Phys. May 1994;16(3):203-212.
1994	Silva MJ, Wang C, Keaveny TM, Hayes WC. Direct and computed tomography thickness measurements of the human, lumbar vertebral shell and endplate. Bone. July 8, 1994;15(4):409-414.
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.
1988	Ruff CB, Hayes WC. Sex differences in age‐related remodeling of the femur and tibia. J Orthop Res. November 1988;6(6):886-896.
1999	Zysset PK, Guo XE, Hoffler CE, Moore KE, Goldstein SA. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J Biomech. October 1999;32(10):1005-1012.
1994	Goulet RW, Goldstein SA, Ciarelli MJ, Kuhn JL, Brown MB, Feldkamp LA. The relationship between the structural and orthogonal compressive properties of trabecular bone. J Biomech. April 1994;27(4):375-389.
1975	Townsend PR, Rose RM, Radin EL. Buckling studies of single human trabeculae. J Biomech. July 1975;8(3-4):199-200.
1989	Turner CH. Yield behavior of bovine cancellous bone [published correction appears in J Biomech Eng. 1989;111(4):335]. J Biomech Eng. August 1989;111(3):256-260.
1976	Carter DR, Hayes WC. Bone compressive strength: the influence of density and strain rate. Science. September 10, 1976;194(4270):1174-1176.
1992	Wagner HD, Weiner S. On the relationship between the microstructure of bone and its mechanical stiffness. J Biomech. November 1992;25(11):1311-1320.
1993	Marotti G. A new theory of bone lamellation. Calcif Tiss Int. February 1993;53(suppl 1):S47-S56.
1993	Faulkner KG, Cummings SR, Black D, Palermo L, Glüer C, Genant HK. Simple measurement of femoral geometry predicts hip fracture: the study of osteoporotic fractures. J Bone Miner Res. September 1993;8(10):1211-1217.
1989	Mosekilde L. Sex differences in age-related loss of vertebral trabecular bone mass and structure—biomechanical consequences. Bone. 1989;10(6):425-432.
1996	Jepsen KJ, Goldstein SA, Kuhn JL, Schaffler MB, Bonadio J. Type‐I collagen mutation compromises the post‐yield behavior of Mov13 long bone. J Orthop Res. May 1996;14(3):493-499.
1993	Fung YC. Biomechanics: Mechanical Properties of Living Tissues. 2nd ed. New York, NY: Springer-Verlag; 1993.
1997	Jepsen KJ, Schaffler MB, Kuhn JL, Goulet RW, Bonadio J, Goldstein SA. Type I collagen mutation alters the strength and fatigue behavior of Mov13 cortical tissue. J Biomech. November–December 1997;30(11-12):1141-1147.
1988	Melton LJ III, Chao EYS, Lane J. Biomechanical aspects of fractures. In: Riggs BL, Melton LJ III, eds. Osteoporosis: Etiology, Diagnosis, and Management. New York, NY: Raven Press; 1988:111-131.
1995	Grote HJ, Amling M, Vogel M, Hahn M, Pösl M, Delling G. Intervertebral variation in trabecular microarchitecture throughout the normal spine in relation to age. Bone. March 1995;16(3):301-308.
1993	Dempster DW, Ferguson-Pell MW, Mellish RWE, Cochran GVB, Xie F, Fey C, Horbert W, Parisien M, Lindsay R. Relationships between bone structure in the iliac crest and bone structure and strength in the lumbar spine. Osteoporos Int. March 1993;3(2):90-96.
2000	Hoffler CE, Moore KE, Kozloff K, Zysset PK, Brown MB, Goldstein SA. Heterogeneity of bone lamellar-level elastic moduli. Bone. June 2000;26(6):603-609.
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.
1997	Ray NF, Chan JK, Thamer M, Melton LJ III. Medical expenditures for the treatment of osteoporotic fractures in the United States in 1995: report from the National Osteoporosis Foundation. J Bone Miner Res. January 1997;12(1):24-35.
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.
1981	Van Buskirk WC, Cowin SC, Ward RN. Ultrasonic measurement of orthotropic elastic constants of bovine femoral bone. J Biomech Eng. May 1981;103(2):67-72.
1970	Lang SB. Ultrasonic method for measuring elastic coefficients of bone and results on fresh and dried bovine bones. IEEE Trans Biomed Eng. April 1970;17(2):101-105.
1991	Sasaki N, Ikawa T, Fukuda A. Orientation of mineral in bovine bone and the anisotropic mechanical properties of plexiform bone. J Biomech. 1991;24(1):57-61.
1999	Rho JY, Zioupos P, Currey JD, Pharr GM. Variations in the individual thick lamellar properties within osteons by nanoindentation. Bone. September 1999;25(3):295-300.
1983	Burris CL Sr. A Correlation of Quasistatic and Ultrasonic Measurements of the Elastic Properties of Cortical Bone [PhD thesis]. New Orleans, LA: Tulane University; 1983.
1991	Hollister SJ, Fyhrie DP, Jepsen KJ, Goldstein SA. Application of homogenization theory to the study of trabecular bone mechanics. J Biomech. 1991;24(9):825-839.
1994	Hollister SJ, Brennan JM, Kikuchi N. A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stres. J Biomech. 1994;27(4):433-444.
1993	Katz JL, Meunier A. Scanning acoustic microscope studies of the elastic properties of osteons and osteon lamellae. J Biomech Eng. November 1993;115(4B):543-548.
1988	Phillips S, Fox N, Jacobs J, Wright WE. The direct medical costs of osteoporosis for american women aged 45 and older, 1986. Bone. 1988;9(5):271-279.
1993	Crolet JM, Aoubiza B, Meunier A. Compact bone: numerical simulation of mechanical characteristics. J Biomech. June 1993;26(6):677-687.
1999	Cody DD, Gross GJ, Hou FJ, Spencer HJ, Goldstein SA, Fyhrie DP. Femoral strength is better predicted by finite element models than QCT and DXA. J Biomech. October 1999;32(10):1013-1020.
1986	Wolff J. The Law of Bone Remodelling. Maquet P, Furlong R, trans. New York, NY: Springer; 1986.
1991	Eastell R, Cedel SL, Wahner HW, Riggs BL, Melton LJ III. Classification of vertebral fractures. J Bone Miner Res. March 1991;6(3):207-215.
1994	Fyhrie DP, Schaffler MB. Failure mechanisms in human vertebral cancellous bone. Bone. 1994;15(1):105-109.
1986	Cowin SC. Wolff’s law of trabecular architecture at remodeling equilibrium. J Biomech Eng. February 1986;108(1):83-88.
1993	Rho JY, Ashman RB, Turner CH. Young's modulus of trabecular and cortical bone material: ultrasonic and microtensile measurements. J Biomech. February 1993;26(2):111-119.
1994	Currey JD, Brear K, Zioupos P. Dependence of mechanical properties on fibre angle in narwhal tusk, a highly oriented biological composite. J Biomech. July 1994;27(7):885-897.
1993	Fyhrie DP, Fazzalari NL, Goulet R, Goldstein SA. Direct calculation of the surface-to-volume ratio for human cancellous bone. J Biomech. August 1993;26(8):955-967.
1989	Ryan SD, Williams JL. Tensile testing of rodlike trabeculae excised from bovine femoral bone. J Biomech. 1989;22(4):351-355.
1975	Runkle JC, Pugh J. The micro-mechanics of cancellous bone, II: determination of the elastic modulus of individual trabeculae by a buckling analysis. Bull Hosp Joint Dis. April 1975;36(1):2-10.

Year

Entry

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.

1994

Kanis JA, Melton LJ III, Christiansen C, Johnston CC, Khaltaev N. The diagnosis of osteoporosis. J Bone Miner Res. August 1994;9(8):1137-1141.

1988

Ashman RB, Rho JY. Elastic modulus of trabecular bone material. J Biomech. 1988;21(3):177-181.

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.

1995

Grimm MJ. Ultrasound Propagation Through the Calcaneus: Dependence on “Bone Quality” and Prediction by Biot's Theory [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 1995.

1984

Ashman RB, Cowin SC, Van Buskirk WC, Rice JC. A continuous wave technique for the measurement of the elastic properties of cortical bone. J Biomech. 1984;17(5):349-361.

1999

Roy ME, Rho J-Y, Tsui TY, Evans ND, Pharr GM. Mechanical and morphological variation of the human lumbar vertebral cortical and trabecular bone. J Biomed Mater Res. February 1999;A44(2):191-197.

1987

Ashman RB, Corin JD, Turner CH. Elastic properties of cancellous bone: measurement by an ultrasonic technique. J Biomech. 1987;20(10):979-986.

1994

Zioupos P, Currey JD, Sedman AJ. An examination of the micromechanics of failure of bone and antler by acoustic emission tests and laser scanning confocal microscopy. Med Eng Phys. May 1994;16(3):203-212.

1994

Silva MJ, Wang C, Keaveny TM, Hayes WC. Direct and computed tomography thickness measurements of the human, lumbar vertebral shell and endplate. Bone. July 8, 1994;15(4):409-414.

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.

1988

Ruff CB, Hayes WC. Sex differences in age‐related remodeling of the femur and tibia. J Orthop Res. November 1988;6(6):886-896.

1999

Zysset PK, Guo XE, Hoffler CE, Moore KE, Goldstein SA. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J Biomech. October 1999;32(10):1005-1012.

1994

Goulet RW, Goldstein SA, Ciarelli MJ, Kuhn JL, Brown MB, Feldkamp LA. The relationship between the structural and orthogonal compressive properties of trabecular bone. J Biomech. April 1994;27(4):375-389.

1975

Townsend PR, Rose RM, Radin EL. Buckling studies of single human trabeculae. J Biomech. July 1975;8(3-4):199-200.

1989

Turner CH. Yield behavior of bovine cancellous bone [published correction appears in J Biomech Eng. 1989;111(4):335]. J Biomech Eng. August 1989;111(3):256-260.

1976

Carter DR, Hayes WC. Bone compressive strength: the influence of density and strain rate. Science. September 10, 1976;194(4270):1174-1176.

1992

Wagner HD, Weiner S. On the relationship between the microstructure of bone and its mechanical stiffness. J Biomech. November 1992;25(11):1311-1320.

1993

Marotti G. A new theory of bone lamellation. Calcif Tiss Int. February 1993;53(suppl 1):S47-S56.

1993

Faulkner KG, Cummings SR, Black D, Palermo L, Glüer C, Genant HK. Simple measurement of femoral geometry predicts hip fracture: the study of osteoporotic fractures. J Bone Miner Res. September 1993;8(10):1211-1217.

1989

Mosekilde L. Sex differences in age-related loss of vertebral trabecular bone mass and structure—biomechanical consequences. Bone. 1989;10(6):425-432.

1996

Jepsen KJ, Goldstein SA, Kuhn JL, Schaffler MB, Bonadio J. Type‐I collagen mutation compromises the post‐yield behavior of Mov13 long bone. J Orthop Res. May 1996;14(3):493-499.

1993

Fung YC. Biomechanics: Mechanical Properties of Living Tissues. 2nd ed. New York, NY: Springer-Verlag; 1993.

1997

Jepsen KJ, Schaffler MB, Kuhn JL, Goulet RW, Bonadio J, Goldstein SA. Type I collagen mutation alters the strength and fatigue behavior of Mov13 cortical tissue. J Biomech. November–December 1997;30(11-12):1141-1147.

1988

Melton LJ III, Chao EYS, Lane J. Biomechanical aspects of fractures. In: Riggs BL, Melton LJ III, eds. Osteoporosis: Etiology, Diagnosis, and Management. New York, NY: Raven Press; 1988:111-131.

1995

Grote HJ, Amling M, Vogel M, Hahn M, Pösl M, Delling G. Intervertebral variation in trabecular microarchitecture throughout the normal spine in relation to age. Bone. March 1995;16(3):301-308.

1993

Dempster DW, Ferguson-Pell MW, Mellish RWE, Cochran GVB, Xie F, Fey C, Horbert W, Parisien M, Lindsay R. Relationships between bone structure in the iliac crest and bone structure and strength in the lumbar spine. Osteoporos Int. March 1993;3(2):90-96.

2000

Hoffler CE, Moore KE, Kozloff K, Zysset PK, Brown MB, Goldstein SA. Heterogeneity of bone lamellar-level elastic moduli. Bone. June 2000;26(6):603-609.

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.

1997

Ray NF, Chan JK, Thamer M, Melton LJ III. Medical expenditures for the treatment of osteoporotic fractures in the United States in 1995: report from the National Osteoporosis Foundation. J Bone Miner Res. January 1997;12(1):24-35.

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.

1981

Van Buskirk WC, Cowin SC, Ward RN. Ultrasonic measurement of orthotropic elastic constants of bovine femoral bone. J Biomech Eng. May 1981;103(2):67-72.

1970

Lang SB. Ultrasonic method for measuring elastic coefficients of bone and results on fresh and dried bovine bones. IEEE Trans Biomed Eng. April 1970;17(2):101-105.

1991

Sasaki N, Ikawa T, Fukuda A. Orientation of mineral in bovine bone and the anisotropic mechanical properties of plexiform bone. J Biomech. 1991;24(1):57-61.

1999

Rho JY, Zioupos P, Currey JD, Pharr GM. Variations in the individual thick lamellar properties within osteons by nanoindentation. Bone. September 1999;25(3):295-300.

1983

Burris CL Sr. A Correlation of Quasistatic and Ultrasonic Measurements of the Elastic Properties of Cortical Bone [PhD thesis]. New Orleans, LA: Tulane University; 1983.

1991

Hollister SJ, Fyhrie DP, Jepsen KJ, Goldstein SA. Application of homogenization theory to the study of trabecular bone mechanics. J Biomech. 1991;24(9):825-839.

1994

Hollister SJ, Brennan JM, Kikuchi N. A homogenization sampling procedure for calculating trabecular bone effective stiffness and tissue level stres. J Biomech. 1994;27(4):433-444.

1993

Katz JL, Meunier A. Scanning acoustic microscope studies of the elastic properties of osteons and osteon lamellae. J Biomech Eng. November 1993;115(4B):543-548.

1988

Phillips S, Fox N, Jacobs J, Wright WE. The direct medical costs of osteoporosis for american women aged 45 and older, 1986. Bone. 1988;9(5):271-279.

1993

Crolet JM, Aoubiza B, Meunier A. Compact bone: numerical simulation of mechanical characteristics. J Biomech. June 1993;26(6):677-687.

1999

Cody DD, Gross GJ, Hou FJ, Spencer HJ, Goldstein SA, Fyhrie DP. Femoral strength is better predicted by finite element models than QCT and DXA. J Biomech. October 1999;32(10):1013-1020.

1986

Wolff J. The Law of Bone Remodelling. Maquet P, Furlong R, trans. New York, NY: Springer; 1986.

1991

Eastell R, Cedel SL, Wahner HW, Riggs BL, Melton LJ III. Classification of vertebral fractures. J Bone Miner Res. March 1991;6(3):207-215.

1994

Fyhrie DP, Schaffler MB. Failure mechanisms in human vertebral cancellous bone. Bone. 1994;15(1):105-109.

1986

Cowin SC. Wolff’s law of trabecular architecture at remodeling equilibrium. J Biomech Eng. February 1986;108(1):83-88.

1993

Rho JY, Ashman RB, Turner CH. Young's modulus of trabecular and cortical bone material: ultrasonic and microtensile measurements. J Biomech. February 1993;26(2):111-119.

1994

Currey JD, Brear K, Zioupos P. Dependence of mechanical properties on fibre angle in narwhal tusk, a highly oriented biological composite. J Biomech. July 1994;27(7):885-897.

1993

Fyhrie DP, Fazzalari NL, Goulet R, Goldstein SA. Direct calculation of the surface-to-volume ratio for human cancellous bone. J Biomech. August 1993;26(8):955-967.

1989

Ryan SD, Williams JL. Tensile testing of rodlike trabeculae excised from bovine femoral bone. J Biomech. 1989;22(4):351-355.

1975

Runkle JC, Pugh J. The micro-mechanics of cancellous bone, II: determination of the elastic modulus of individual trabeculae by a buckling analysis. Bull Hosp Joint Dis. April 1975;36(1):2-10.

Year	Entry
2005	Cao KD. Development of a 4-Vertebrae, Detailed Finite Element Model of Thoracolumbar Spine [PhD thesis]. Detroit, MI: Wayne State University; August 2005.

Year

Entry

2005

Cao KD. Development of a 4-Vertebrae, Detailed Finite Element Model of Thoracolumbar Spine [PhD thesis]. Detroit, MI: Wayne State University; August 2005.