Research Papers

Patient-Specific Finite-Element Analyses of the Proximal Femur with Orthotropic Material Properties Validated by Experiments

[+] Author and Article Information
Nir Trabelsi

Department of Mechanical Engineering,  Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel

Zohar Yosibash

Department of Mechanical Engineering,  Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israelzohary@bgu.ac.il

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J Biomech Eng 133(6), 061001 (Jun 14, 2011) (11 pages) doi:10.1115/1.4004180 History: Received November 29, 2010; Revised March 30, 2011; Posted May 06, 2011; Published June 14, 2011; Online June 14, 2011

Patient-specific high order finite-element (FE) models of human femurs based on quantitative computer tomography (QCT) with inhomogeneous orthotropic and isotropic material properties are addressed. The point-wise orthotropic properties are determined by a micromechanics (MM) based approach in conjunction with experimental observations at the osteon level, and two methods for determining the material trajectories are proposed (along organs outer surface, or along principal strains). QCT scans on four fresh-frozen human femurs were performed and high-order FE models were generated with either inhomogeneous MM-based orthotropic or empirically determined isotropic properties. In vitro experiments were conducted on the femurs by applying a simple stance position load on their head, recording strains on femurs’ surface and head’s displacements. After verifying the FE linear elastic analyses that mimic the experimental setting for numerical accuracy, we compared the FE results to the experimental observations to identify the influence of material properties on models’ predictions. The strains and displacements computed by FE models having MM-based inhomogeneous orthotropic properties match the FE-results having empirically based isotropic properties well, and both are in close agreement with the experimental results. When only the strains in the femoral neck are being compared a more pronounced difference is noticed between the isotropic and orthotropic FE result. These results lay the foundation for applying more realistic inhomogeneous orthotropic material properties in FEA of femurs.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Schematic flow chart describing the generation of the p-FE model from QCT scans: (a) typical CT-slice, (b) contour identification, (c) smoothing boundary points, (d1) points cloud representing the bone surface, (d2) close splines for all slices, (e) bone surface, (f) p-FE mesh, and (g) material evaluation from CT data

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Figure 2

(a) closest point (CP) on the bone outer surface to a specific POI. (b) Tangent (circumferential) direction.

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Figure 3

Axial material trajectories throughout a femur, zoomed portion in the trabecular area and femoral neck (left) and zoomed portion in cortical area and shaft (right)

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Figure 4

Typical experiments on fresh-frozen bones (FF3 and FF4) at different inclination angles. Right: Strain gauges location at the neck and shaft regions.

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Figure 5

(a) E(HU) relation for orthotropic MM-based and isotropic empirical-based models [(34),47]. (b) Ratio of Young’s modulus in different directions. (c) Poisson ratio dependence on HU for MM-based model (ν=0.3 for empirically based model). (d) Shear moduli relation to HU for MM-based and empirically based models.

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Figure 6

FF3-FE model and locations at which displacements and strains were computed and measured in the experiment

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Figure 7

Comparison of the computed strains + and displacements ⊕ to the experimental observations. Material properties assigned by two different strategies in the FE models: (a) empirical-based, (b) MM-based.

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Figure 8

Young’s modulus in different directions versus HU or apparent density for cortical bone. EIsoKey represents the isotropic Young’s modulus in Ref. [36], EaxialMM and EtransverseMM are the axial and the transversal Young’s modulus computed by the micro-mechanics model, EaxialWirtz and EtransverseWirtz are the axial and transversal Young’s modulus according to Eqs. 2,2, and EaxialRho and EtranseverseRho is the axial and transversal Young’s modulus according to Eqs. 9,9.

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Figure 9

Young’s modulus in different directions versus HU or apparent density for trabecular bone



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