Micromechanical Modeling of Hydroxyapatite Whisker Reinforced Polymer Composites and Cortical Bone Tissue

A new micromechanical model was developed to predict the elastic moduli of hydroxyapatite (HA) whisker reinforced polymer biocomposites based upon the elastic properties of each phase and the reinforcement volume fraction, morphology and preferred orientation. The effects of the HA whisker volume fraction, morphology and orientation distribution were investigated by comparing two and three-dimensional model predictions with experimentally measured elastic moduli or stiffness coefficients, respectively, for HA whisker reinforced high density polyethylene (HDPE) composites. Predictions using experimental measurements of the HA whisker aspect ratio distribution and orientation distribution were also compared to common idealized assumptions. The best model predictions were obtained using the experimentally measured HA whisker aspect ratio distribution and orientation distribution. The same micromechanical model developed and validated for HA whisker reinforced composites was also applied to the elastic properties of human cortical bone tissue. The orientation distribution of apatite crystals in bone was measured and statistically correlated to the elastic anisotropy of bone tissue. The relationship was further investigated using the micromechanical model. The orientation distribution of apatite crystals was shown to be a significant factor contributing to the elastic anisotropy of cortical bone tissue.

Year	Entry
1986	Weiner S, Price PA. Disaggregation of bone into crystals. Calcif Tiss Int. November 1986;39(6):365-375.
1988	Schaffler MB, Burr DB. Stiffness of compact bone: effects of porosity and density. J Biomech. 1988;21(1):13-16.
1979	Cusack S, Miller A. Determination of the elastic constants of collagen by Brillouin light scattering. J Mol Biol. 1979;135(1):39-51.
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.
1993	Mammone JF, Hudson SM. Micromechanics of bone strength and fracture. J Biomech. April–May 1993;26(4-5):439-446.
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.
1999	Wenk H-R, Heidelbach F. Crystal alignment of carbonated apatite in bone and calcified tendon: results from quantitative texture analysis. Bone. April 1999;24(4):361-369.
2001	Hernandez CJ, Beaupré GS, Keller TS, Carter DR. The influence of bone volume fraction and ash fraction on bone strength and modulus. Bone. July 2001;29(1):74-78.
1996	Aoubiza B, Crolet JM, Meunier A. On the mechanical characterization of compact bone structure using the homogenization theory. J Biomech. December 1996;29(12):1539-1547.
1989	Sasaki N, Matsushima N, Ikawa T, Yamamura H, Fukuda A. Orientation of bone mineral and its role in the anisotropic mechanical properties of bone: transverse anisotropy. J Biomech. 1989;22(2):157-164.
1999	Cowin SC. Bone poroelasticity. J Biomech. March 1999;32(3):217-238.
1992	Weiner S, Traub W. Bone structure: from ȧngstroms to microns. FASEB J. February 1992;6(3):879-885.
1973	Piekarski K. Analysis of bone as a composite material. Int J Eng Sci. June 1973;11(6):557-565.
1971	Katz JL, Ukraincik K. On the anisotropic elastic properties of hydroxyapatite. J Biomech. May 1971;4(3):221-227.
1981	Katz JL. Composite material models for cortical 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; 1981:171-184.
1998	Akiva U, Wagner HD, Weiner S. Modelling the three-dimensional elastic constants of parallel-fibred and lamellar bone. J Mater Sci. March 15, 1998;33(6):1497-1509.
1996	Pidaparti RMV, Chandran A, Takano Y, Turner CH. Bone mineral lies mainly outside collagen fibrils: predictions of a composite model for osternal bone. J Biomech. July 1996;29(7):909-916.
1999	Turner CH, Rho J, Takano Y, Tsui TY, Pharr GM. The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. J Biomech. April 1999;32(4):437-441.
1990	Keller TS, Mao Z, Spengler DM. Young's modulus, bending strength, and tissue physical properties of human compact bone. J Orthop Res. 1990;8(4):592-603.
2004	Dong XN, Guo XE. The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity. J Biomech. August 2004;37(8):1281-1287.
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.
1976	Ascenzi A, Bonucci E. Mechanical similarities between alternate osteons and cross-ply laminates. J Biomech. 1976;9(2):65-71.
1967	Bonfield W, Li CH. Anisotropy of nonelastic flow in bone. J Appl Phys. May 1967;38(6):2450-2455.
1976	Yoon HS, Katz JL. Ultrasonic wave propagation in human cortical bone, II: measurements of elastic properties and microhardness. J Biomech. 1976;9(7):459-464.
1993	Crolet JM, Aoubiza B, Meunier A. Compact bone: numerical simulation of mechanical characteristics. J Biomech. June 1993;26(6):677-687.
1996	Takano Y, Turner CH, Burr DB. Mineral anisotropy in mineralized tissues is similar among species and mineral growth occurs independently of collagen orientation in rats: results from acoustic velocity measurements. J Bone Miner Res. September 1996;11(9):1292-1301.
1994	Hasegawa K, Turner CH, Burr DB. Contribution of collagen and mineral to the elastic anisotropy of bone. Calcif Tiss Int. November 1994;55(5):381-386.
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.
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.
1962	Currey JD. Strength of bone. Nature. August 4, 1962;195:513-514.
1998	Rho J-Y, Kuhn-Spearing L, Zioupos P. Mechanical properties and the hierarchical structure of bone. Med Eng Phys. 1998;20(2):92-102.

Year

Entry

1986

Weiner S, Price PA. Disaggregation of bone into crystals. Calcif Tiss Int. November 1986;39(6):365-375.

1988

Schaffler MB, Burr DB. Stiffness of compact bone: effects of porosity and density. J Biomech. 1988;21(1):13-16.

1979

Cusack S, Miller A. Determination of the elastic constants of collagen by Brillouin light scattering. J Mol Biol. 1979;135(1):39-51.

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.

1993

Mammone JF, Hudson SM. Micromechanics of bone strength and fracture. J Biomech. April–May 1993;26(4-5):439-446.

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.

1999

Wenk H-R, Heidelbach F. Crystal alignment of carbonated apatite in bone and calcified tendon: results from quantitative texture analysis. Bone. April 1999;24(4):361-369.

2001

Hernandez CJ, Beaupré GS, Keller TS, Carter DR. The influence of bone volume fraction and ash fraction on bone strength and modulus. Bone. July 2001;29(1):74-78.

1996

Aoubiza B, Crolet JM, Meunier A. On the mechanical characterization of compact bone structure using the homogenization theory. J Biomech. December 1996;29(12):1539-1547.

1989

Sasaki N, Matsushima N, Ikawa T, Yamamura H, Fukuda A. Orientation of bone mineral and its role in the anisotropic mechanical properties of bone: transverse anisotropy. J Biomech. 1989;22(2):157-164.

1999

Cowin SC. Bone poroelasticity. J Biomech. March 1999;32(3):217-238.

1992

Weiner S, Traub W. Bone structure: from ȧngstroms to microns. FASEB J. February 1992;6(3):879-885.

1973

Piekarski K. Analysis of bone as a composite material. Int J Eng Sci. June 1973;11(6):557-565.

1971

Katz JL, Ukraincik K. On the anisotropic elastic properties of hydroxyapatite. J Biomech. May 1971;4(3):221-227.

1981

Katz JL. Composite material models for cortical 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; 1981:171-184.

1998

Akiva U, Wagner HD, Weiner S. Modelling the three-dimensional elastic constants of parallel-fibred and lamellar bone. J Mater Sci. March 15, 1998;33(6):1497-1509.

1996

Pidaparti RMV, Chandran A, Takano Y, Turner CH. Bone mineral lies mainly outside collagen fibrils: predictions of a composite model for osternal bone. J Biomech. July 1996;29(7):909-916.

1999

Turner CH, Rho J, Takano Y, Tsui TY, Pharr GM. The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. J Biomech. April 1999;32(4):437-441.

1990

Keller TS, Mao Z, Spengler DM. Young's modulus, bending strength, and tissue physical properties of human compact bone. J Orthop Res. 1990;8(4):592-603.

2004

Dong XN, Guo XE. The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity. J Biomech. August 2004;37(8):1281-1287.

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.

1976

Ascenzi A, Bonucci E. Mechanical similarities between alternate osteons and cross-ply laminates. J Biomech. 1976;9(2):65-71.

1967

Bonfield W, Li CH. Anisotropy of nonelastic flow in bone. J Appl Phys. May 1967;38(6):2450-2455.

1976

Yoon HS, Katz JL. Ultrasonic wave propagation in human cortical bone, II: measurements of elastic properties and microhardness. J Biomech. 1976;9(7):459-464.

1993

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

1996

Takano Y, Turner CH, Burr DB. Mineral anisotropy in mineralized tissues is similar among species and mineral growth occurs independently of collagen orientation in rats: results from acoustic velocity measurements. J Bone Miner Res. September 1996;11(9):1292-1301.

1994

Hasegawa K, Turner CH, Burr DB. Contribution of collagen and mineral to the elastic anisotropy of bone. Calcif Tiss Int. November 1994;55(5):381-386.

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.

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.

1962

Currey JD. Strength of bone. Nature. August 4, 1962;195:513-514.

1998

Rho J-Y, Kuhn-Spearing L, Zioupos P. Mechanical properties and the hierarchical structure of bone. Med Eng Phys. 1998;20(2):92-102.

Year	Entry
2008	Converse GL. Processing and Properties of Hydroxyapaptite Whisker Reinforced Polyaryletherketones for Orthopaedic Applications [PhD thesis]. University of Notre Dame; April 2008.
2010	Deuerling JM. Effects of Ultrastructural Organization on the Mechanical Properties and Anisotropy of Human Cortical Bone [PhD thesis]. University of Notre Dame; December 2010.

Year

Entry

2008

Converse GL. Processing and Properties of Hydroxyapaptite Whisker Reinforced Polyaryletherketones for Orthopaedic Applications [PhD thesis]. University of Notre Dame; April 2008.

2010

Deuerling JM. Effects of Ultrastructural Organization on the Mechanical Properties and Anisotropy of Human Cortical Bone [PhD thesis]. University of Notre Dame; December 2010.