Anisotropic Structure-Property Relations for Trabecular Bone: An Analysis of the Morphological and Constitutive Properties of Trabecular Bone from the Human Proximal Femur and Lumbar Spine

Trabecular bone is an open-celled, porous material which plays a major role in load transmission in normal and osteoporotic joints, influences fracture processes in high fracture risk regions such as the hip and spine and governs the porous ingrowth fixation of endoprostheses. Changes in trabecular morphology accompanying pathologic conditions such as osteoporosis and metastatic cancer profoundly affect its properties. Non-invasive predictions of the structural integrity of high risk regions of the skeleton by CT and MRI depend on accurate constitutive data for trabecular bone as a function of local trabecular morphology. Quantitative microscopic techniques for describing the 3-D structural morphology of trabecular bone were developed and verified. Stereological analyses of human proximal femora and L1 vertebral bodies, predominantly from elderly females, demonstrated that both the number and thickness of the trabeculae decreased with density while the effective length of the remaining trabeculae reciprocally increased, thereby posing a triple threat to the strength and stability of the bone. Bone volume fraction varied as the square root of trabecular thickness divided by the effective trabecular length determined from intertrabecular spacing. While it is widely assumed that density provides first order approximations of the stiffness and strength for trabecular bone, the relative importance of trabecular anisotropy is far less certain. Power-law functions of density describe only isotropic material behavior. The orthotropic compliance matrix has not been previously measured for trabecular bone since multiple modes of testing are difficult to apply to the same specimen and the principal trabecular directions are not aligned with the specimen. The independent compliances were calculated by seeking the least-square solution to a system of tensor transformation equations generated from non-destructive compression tests conducted in each of two cube configurations extracted from the same mass of bone relative to the principal trabecular directions. Power functions of bone volume fraction accounted for 47% of the variance in the compressive compliances and 44% of the variance in the shear compliances. Tensorial functions relating the trabecular morphology to the independent compliances accounted for 69% of the variance in the compressive compliances and 66% of the variance in the shear compliances.

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Year	Entry
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.
1997	Silva MJ, Gibson LJ. Modeling the mechanical behavior of vertebral trabecular bone: effects of age-related changes in microstructure. Bone. 1997;21(2):191-199.
1993	Snyder BD, Piazza S, Edwards WT, Hayes WC. Role of trabecular morphology in the etiology of age-related vertebral fractures. Calcif Tiss Int. February 1993;53(suppl 1):S14-S22.
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.
1993	Keaveny TM, Borchers RE, Gibson LJ, Hayes WC. Theoretical analysis of the experimental artifact in trabecular bone compressive modulus [published correction appears in J Biomech. 1993;26(9):1143]. J Biomech. April–May 1993;26(4-5):599-607.
1993	Keaveny TM, Hayes WC. A 20-year perspective on the mechanical properties of trabecular bone. J Biomech Eng. November 1993;115(4B):534-542.
2000	Ciarelli TE, Fyhrie DP, Schaffler MB, Goldstein SA. Variations in three‐dimensional cancellous bone architecture of the proximal femur in female hip fractures and in controls. J Bone Miner Res. 2000;15(1):32-40.
1997	Silva MJ, Keaveny TM, Hayes WC. Load sharing between the shell and centrum in the lumbar vertebral body. Spine. January 1997;22(2):140-150.
2003	Bredbenner TL. Damage Modeling of Vertebral Trabecular Bone [PhD thesis]. Cleveland, OH: Case Western Reserve University; January 2003.
1999	Yang G. Averaging and Bounding of Anisotropic Elastic Constants [PhD thesis]. New York, NY: The City University of New York; 1999.
1996	Silva MJ. Predicting the Failure Behavior of the Human Vertebral Body [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; February 1996.
1993	Goulet RW. The Quantification of the Structure and Mechanical Properties of Trabecular Bone [PhD thesis]. University of Michigan; 1993.
1998	Ciarelli TE. Architectural and Material Contributions to Fracture of the Spine and Proximal Femur [PhD thesis]. University of Michigan; 1998.

Year

Entry

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.

1997

Silva MJ, Gibson LJ. Modeling the mechanical behavior of vertebral trabecular bone: effects of age-related changes in microstructure. Bone. 1997;21(2):191-199.

1993

Snyder BD, Piazza S, Edwards WT, Hayes WC. Role of trabecular morphology in the etiology of age-related vertebral fractures. Calcif Tiss Int. February 1993;53(suppl 1):S14-S22.

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.

1993

Keaveny TM, Borchers RE, Gibson LJ, Hayes WC. Theoretical analysis of the experimental artifact in trabecular bone compressive modulus [published correction appears in J Biomech. 1993;26(9):1143]. J Biomech. April–May 1993;26(4-5):599-607.