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Research Papers

Effect of Specimen-Specific Anisotropic Material Properties in Quantitative Computed Tomography-Based Finite Element Analysis of the Vertebra

[+] Author and Article Information
Ginu U. Unnikrishnan, 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

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received November 19, 2012; final manuscript received July 27, 2013; accepted manuscript posted August 5, 2013; published online September 20, 2013. Assoc. Editor: Tammy Haut Donahue.

J Biomech Eng 135(10), 101007 (Sep 20, 2013) (11 pages) Paper No: BIO-12-1575; doi: 10.1115/1.4025179 History: Received November 19, 2012; Revised July 27, 2013; Accepted August 05, 2013

Intra- and inter-specimen variations in trabecular anisotropy are often ignored in quantitative computed tomography (QCT)-based finite element (FE) models of the vertebra. The material properties are typically estimated solely from local variations in bone mineral density (BMD), and a fixed representation of elastic anisotropy (“generic anisotropy”) is assumed. This study evaluated the effect of incorporating specimen-specific, trabecular anisotropy on QCT-based FE predictions of vertebral stiffness and deformation patterns. Orthotropic material properties estimated from microcomputed tomography data (“specimen-specific anisotropy”), were assigned to a large, columnar region of the L1 centrum (n = 12), and generic-anisotropic material properties were assigned to the remainder of the vertebral body. Results were compared to FE analyses in which generic-anisotropic properties were used throughout. FE analyses were also performed on only the columnar regions. For the columnar regions, the axial stiffnesses obtained from the two categories of material properties were uncorrelated with each other (p = 0.604), and the distributions of minimum principal strain were distinctly different (p ≤ 0.022). In contrast, for the whole vertebral bodies in both axial and flexural loading, the stiffnesses obtained using the two categories of material properties were highly correlated (R2 > 0.82, p < 0.001) with, and were no different (p > 0.359) from, each other. Only moderate variations in strain distributions were observed between the two categories of material properties. The contrasting results for the columns versus vertebrae indicate a large contribution of the peripheral regions of the vertebral body to the mechanical behavior of this bone. In companion analyses on the effect of the degree of anisotropy (DA), the axial stiffnesses of the trabecular column (p < 0.001) and vertebra (p = 0.007) increased with increasing DA. These findings demonstrate the need for accurate modeling of the peripheral regions of the vertebral body in analyses of the mechanical behavior of the vertebra.

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Figures

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Fig. 1

List of the FE analyses conducted to evaluate the effect of incorporating specimen-specific, trabecular anisotropy on QCT-based FE predictions of vertebral stiffness and deformation patterns: For each combination of type of model, type of material property, and loading condition, 12 simulations were performed (one per vertebra), for a total of 336 FE simulations performed in this study

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Fig. 2

(a) Development of the finite element model of vertebra and (b) mapping of material properties into the FE model using the generic-anisotropic and specimen-specific, anisotropic material properties (vertebral geometry is shown in gray in the top row). As with the specimen-specific anisotropic material properties, the DA-based material properties are also mapped for only the regions covered by the μCT block model.

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Fig. 3

(a) Depicted for one of the 12 vertebrae is the finite element mesh of the columnar region of trabecular bone, shown within the vertebral body for the purpose of demonstrating the column's location within the centrum. (b) the QCT blocks used for mapping of the generic-anisotropic material properties; (c) the μCT blocks used for mapping of the specimen-specific, anisotropic material properties.

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Fig. 4

Finite element model of (a) a column of trabecular bone and (b) vertebra with the rigid plate attached to the superior surface of the vertebra showing the force and boundary conditions applied to the reference point for axial compression (AC) and anterior bending (AB). The reference point was constrained to move only in the vertical direction under AC. For both types of loading, the inferior surfaces of the column and the vertebra were constrained in all directions.

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Fig. 5

Axial stiffness obtained from finite element analyses of the column using generic-anisotropic and specimen-specific, anisotropic material properties

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Fig. 6

Distribution of minimum principal strain for the columnar region of trabecular bone with the generic-anisotropic and specimen-specific, anisotropic material properties

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Fig. 7

(a) Direction of the primary Young's modulus and (b) Orientation of minimum principal strain in the midsagittal plane for a representative column model with generic-anisotropic and specimen-specific, anisotropic material properties. Each line represents the orientation for one element in the midsagittal plane.

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Fig. 8

Mean (n = 12) (a) axial stiffness of the column and (b) axial stiffness normalized with the average of the SI Young's modulus of the column of trabecular bone for varying DA. The axial stiffness of the column increased with increasing DA (p < 0.001). The error bars represent standard deviations.

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Fig. 9

(a) Axial stiffness (kN/mm) and (b) bending stiffness (MNmm/rad) obtained from finite element analyses using generic-anisotropic and specimen-specific, anisotropic material properties for 12 vertebrae. The dashed line represents 1:1 relationship.

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Fig. 10

Distribution of minimum principal strain in one of the 12 vertebrae under axial compression, anterior bending, and combined loading obtained using the generic-anisotropy and specimen-specific, anisotropy based material properties

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Fig. 11

(a) Direction of the primary Young's modulus and (b) orientation of minimum principal strain (axial compression) at the midsagittal plane of one of the 12 vertebrae for generic-anisotropic and specimen-specific, anisotropic material properties. The lines are obtained for each element in the midsagittal plane of the vertebra.

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Fig. 12

Mean (n = 12) (a) axial stiffness and (b) bending stiffness obtained from finite element analyses in which the degree of anisotropy (DA) was varied parametrically (* indicates a pairwise difference between the indicated groups (p < 0.05)). The error bars represent standard deviations.

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Fig. 13

Distribution of minimum principal strain under (a) axial compression, (b) anterior bending, and (c) combined loading in one of the 12 vertebrae modeled with different values of DA (shown above each column)

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