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Technical Brief

Elastic Anisotropy of Trabecular Bone in the Elderly Human Vertebra

[+] Author and Article Information
Ginu U. Unnikrishnan, John A. Gallagher, Amira I. Hussein

Orthopaedic and Developmental Biomechanics Laboratory,
Department of Mechanical Engineering,
Boston University,
Boston, MA 02215

Glenn D. Barest

Department of Radiology,
Boston University,
Boston, MA 02118

Elise F. Morgan

Orthopaedic and Developmental Biomechanics Laboratory,
Department of Mechanical Engineering,
Boston University,
Boston, MA 02215;
Department of Biomedical Engineering,
Boston University,
Boston, MA 02215;
Orthopaedic Surgery,
Boston University,
Boston, MA 02118
e-mail: efmorgan@bu.edu

Manuscript received October 9, 2014; final manuscript received July 31, 2015; published online October 1, 2015. Assoc. Editor: Joel D Stitzel.

J Biomech Eng 137(11), 114503 (Oct 01, 2015) (6 pages) Paper No: BIO-14-1504; doi: 10.1115/1.4031415 History: Received October 09, 2014; Revised July 31, 2015

Knowledge of the nature of the elastic symmetry of trabecular bone is fundamental to the study of bone adaptation and failure. Previous studies have classified human vertebral trabecular bone as orthotropic or transversely isotropic but have typically obtained samples from only selected regions of the centrum. In this study, the elastic symmetry of human vertebral trabecular bone was characterized using microfinite element (μFE) analyses performed on 1019 cubic regions of side length equal to 5 mm, obtained via thorough sampling of the centrums of 18 human L1 vertebrae (age = 81.17 ± 7.7 yr; eight males and ten females). An optimization procedure was used to find the closest orthotropic representation of the resulting stiffness tensor for each cube. The orthotropic elastic constants and orientation of the principal elastic axes were then recorded for each cube and were compared to the constants predicted from Cowin's fabric-based constitutive model (Cowin, 1985, “The Relationship Between the Elasticity Tensor and the Fabric Tensor,” Mech. Mater., 4(2), pp. 137–147.) and the orientation of the principal axes of the fabric tensor, respectively. Deviations from orthotropy were quantified by the “orthotropic error” (van Rietbergen et al., 1996, “Direct Mechanics Assessment of Elastic Symmetries and Properties of Trabecular Bone Architecture,” J. Biomech., 29(12), pp. 1653–1657), and deviations from transverse isotropy were determined by statistical comparison of the secondary and tertiary elastic moduli. The orthotropic error was greater than 50% for nearly half of the cubes, and the secondary and tertiary moduli differed from one another (p < 0.0001). Both the orthotropic error and the difference between secondary and tertiary moduli decreased with increasing bone volume fraction (BV/TV; p ≤ 0.007). Considering only the cubes with an orthotropic error less than 50%, only moderate correlations were observed between the fabric-based and the μFE-computed elastic moduli (R2 ≥ 0.337; p < 0.0001). These results indicate that when using a criterion of 5 mm for a representative volume element (RVE), transverse isotropy or orthotropy cannot be assumed for elderly human vertebral trabecular bone. Particularly at low values of BV/TV, this criterion does not ensure applicability of theories of continuous media. In light of the very sparse and inhomogeneous microstructure found in the specimens analyzed in this study, further work is needed to establish guidelines for selecting a RVE within the aged vertebral centrum.

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References

Odgaard, A. , Kabel, J. , van Rietbergen, B. , Dalstra, M. , and Huiskes, R. , 1997, “ Fabric and Elastic Principal Directions of Cancellous Bone are Closely Related,” J. Biomech., 30(5), pp. 487–495. [CrossRef] [PubMed]
Cowin, S. C. , 1985, “ The Relationship Between the Elasticity Tensor and the Fabric Tensor,” Mech. Mater., 4(2), pp. 137–147. [CrossRef]
Zysset, P. K. , and Curnier, A. , 1995, “ An Alternative Model for Anisotropic Elasticity Based on Fabric Tensors,” Mech. Mater., 21(4), pp. 243–250. [CrossRef]
Keller, T. S. , Hansson, T. H. , Abram, A. C. , Spengler, D. M. , and Panjabi, M. M. , 1989, “ Regional Variations in the Compressive Properties of Lumbar Vertebral Trabeculae. Effects of Disc Degeneration,” Spine, 14(9), pp. 1012–1019. [CrossRef] [PubMed]
Morgan, E. F. , and Keaveny, T. M. , 2001, “ Dependence of Yield Strain of Human Trabecular Bone on Anatomic Site,” J. Biomech., 34(5), pp. 569–577. [CrossRef] [PubMed]
Kim, D.-G. , Hunt, C. , Zauel, R. , Fyhrie, D. , and Yeni, Y. , 2007, “ The Effect of Regional Variations of the Trabecular Bone Properties on the Compressive Strength of Human Vertebral Bodies,” Ann. Biomed. Eng., 35(11), pp. 1907–1913. [CrossRef] [PubMed]
van Rietbergen, B. , Odgaard, A. , Kabel, J. , and Huiskes, R. , 1998, “ Relationships Between Bone Morphology and Bone Elastic Properties can be Accurately Quantified Using High-Resolution Computer Reconstructions,” J. Orthop. Res., 16(1), pp. 23–28. [CrossRef] [PubMed]
Kabel, J. , van Rietbergen, B. , Odgaard, A. , and Huiskes, R. , 1999, “ Constitutive Relationships of Fabric, Density, and Elastic Properties in Cancellous Bone Architecture,” Bone, 25(4), pp. 481–486. [CrossRef] [PubMed]
Harrigan, T. P. , Jasty, M. , Mann, R. W. , and Harris, W. H. , 1988, “ Limitations of the Continuum Assumption in Cancellous Bone,” J. Biomech., 21(4), pp. 269–275. [CrossRef] [PubMed]
Ridler, T. W. , and Calvard, S. , 1978, “ Picture Thresholding Using an Iterative Selection Method,” IEEE Trans. Syst., Man Cybern., 8(8), pp. 630–632. [CrossRef]
Hoffler, C. E. , Moore, K. E. , Kozloff, K. , Zysset, P. K. , Brown, M. B. , and Goldstein, S. A. , 2000, “ Heterogeneity of Bone Lamellar-Level Elastic Moduli,” Bone, 26(6), pp. 603–609. [CrossRef] [PubMed]
Hildebrand, T. , and Rüegsegger, P. , 1997, “ A New Method for the Model-Independent Assessment of Thickness in Three-Dimensional Images,” J. Microsc., 185(1), pp. 67–75. [CrossRef]
Whitehouse, W. J. , 1974, “ The Quantitative Morphology of Anisotropic Trabecular Bone,” J. Microsc., 101(2), pp. 153–168. [CrossRef] [PubMed]
Harrigan, T. P. , and Mann, R. W. , 1984, “ Characterization of Microstructural Anisotropy in Orthotropic Materials Using a Second Rank Tensor,” J. Mater. Sci., 19(3), pp. 761–767. [CrossRef]
van Rietbergen, B. , Odgaard, A. , Kabel, J. , and Huiskes, R. , 1996, “ Direct Mechanics Assessment of Elastic Symmetries and Properties of Trabecular Bone Architecture,” J. Biomech., 29(12), pp. 1653–1657. [CrossRef] [PubMed]
Gross, T. , Pahr, D. , and Zysset, P. , 2013, “ Morphology–Elasticity Relationships Using Decreasing Fabric Information of Human Trabecular Bone From Three Major Anatomical Locations,” Biomech. Model. Mechanobiol., 12(4), pp. 793–800. [CrossRef] [PubMed]
Panyasantisuk, J. , Pahr, D. H. , Gross, T. , and Zysset, P. K. , 2015, “ Comparison of Mixed and Kinematic Uniform Boundary Conditions in Homogenized Elasticity of Femoral Trabecular Bone Using Microfinite Element Analyses,” ASME J. Biomech. Eng., 137(1), p. 011002. [CrossRef]
Crawford, R. , Rosenberg, W. S. , and Keaveny, T. M. , 2003, “ Quantitative Computed Tomography-Based Finite Element Models of the Human Lumbar Vertebral Body: Effect of Element Size on Stiffness, Damage, and Fracture Strength Predictions,” ASME J. Biomech. Eng., 125(4), pp. 434–438. [CrossRef]
Chevalier, Y. , Charlebois, M. , Pahr, D. , Varga, P. , Heini, P. , Schneider, E. , and Zysset, P. , 2008, “ A Patient-Specific Finite Element Methodology to Predict Damage Accumulation in Vertebral Bodies Under Axial Compression, Sagittal Flexion and Combined Loads,” Comput. Methods Biomech. Biomed. Eng., 11(5), pp. 477–487. [CrossRef]
Crawford, R. P. , Cann, C. E. , and Keaveny, T. M. , 2003, “ Finite Element Models Predict In Vitro Vertebral Body Compressive Strength Better Than Quantitative Computed Tomography,” Bone, 33(4), pp. 744–750. [CrossRef] [PubMed]
Buckley, J. M. , Loo, K. , and Motherway, J. , 2007, “ Comparison of Quantitative Computed Tomography-Based Measures in Predicting Vertebral Compressive Strength,” Bone, 40(3), pp. 767–774. [CrossRef] [PubMed]
Unnikrishnan, G. U. , Barest, G. D. , Berry, D. B. , Hussein, A. I. , and Morgan, E. F. , 2013, “ Effect of Specimen-Specific Anisotropic Material Properties in Quantitative Computed Tomography-Based Finite Element Analysis of the Vertebra,” ASME J. Biomech. Eng., 135(10), p. 101007. [CrossRef]
Pollintine, P. , Przybyla, A. S. , Dolan, P. , and Adams, M. A. , 2004, “ Neural Arch Load-Bearing in Old and Degenerated Spines,” J. Biomech., 37(2), pp. 197–204. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

Schematic representation of the procedure adopted to find the best orthotropic representation of each cube of trabecular bone: All δij terms in COPT (d) are set to zero to obtain CORT (e); no other changes are made when obtaining CORT from COPT. (a) μCT image of vertebra, (b) micro-FE analyses of the cube, (c) trabecular fabric-Eigenvectors of the cube, (d) nearly orthotropic stiffness matrix after optimization, and (e) orthotropic stiffness matrix after assigning nonorthotropic terms of zero.

Grahic Jump Location
Fig. 2

Histogram of orthotropic error (a) and correlations between orthotropic error and BV/TV (b) and between E2/E1 and BV/TV (c)

Grahic Jump Location
Fig. 3

Correlations of the Young's moduli ((a)–(c)), shear moduli ((d)–(f)), and Poisson's ratio ((g)–(i)) from the μFE model versus the morphology-based model: The correlation coefficients were nearly unchanged when the circled data point was excluded

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