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Research Papers

The Multi-Axial Failure Response of Porcine Trabecular Skull Bone Estimated Using Microstructural Simulations

[+] Author and Article Information
Ziwen Fang

Mem. ASME
The Penn State Computational
Biomechanics Group,
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
320 Leonhard Building,
University Park, PA 16802

Allison N. Ranslow, Patricia De Tomas

The Penn State Computational
Biomechanics Group,
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
320 Leonhard Building,
University Park, PA 16802

Allan Gunnarsson, Tusit Weerasooriya, Sikhanda Satapathy, Kimberly A. Thompson

United States Army Research Laboratory,
Aberdeen Proving Ground,
Aberdeen, MD 21001

Reuben H. Kraft

Mem. ASME
The Penn State Computational
Biomechanics Group,
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
320 Leonhard Building,
University Park, PA 16802;
Department of Biomedical Engineering,
The Pennsylvania State University,
320 Leonhard Building,
University Park, PA 16802
e-mail: reuben.kraft@psu.edu

1Corresponding author.

Manuscript received March 14, 2017; final manuscript received March 16, 2018; published online June 21, 2018. Assoc. Editor: Beth A. Winkelstein. This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government's contributions.

J Biomech Eng 140(10), 101002 (Jun 21, 2018) (10 pages) Paper No: BIO-17-1107; doi: 10.1115/1.4039895 History: Received March 14, 2017; Revised March 16, 2018

The development of a multi-axial failure criterion for trabecular skull bone has many clinical and biological implications. This failure criterion would allow for modeling of bone under daily loading scenarios that typically are multi-axial in nature. Some yield criteria have been developed to evaluate the failure of trabecular bone, but there is a little consensus among them. To help gain deeper understanding of multi-axial failure response of trabecular skull bone, we developed 30 microstructural finite element models of porous porcine skull bone and subjected them to multi-axial displacement loading simulations that spanned three-dimensional (3D) stress and strain space. High-resolution microcomputed tomography (microCT) scans of porcine trabecular bone were obtained and used to develop the meshes used for finite element simulations. In total, 376 unique multi-axial loading cases were simulated for each of the 30 microstructure models. Then, results from the total of 11,280 simulations (approximately 135,360 central processing unit-hours) were used to develop a mathematical expression, which describes the average three-dimensional yield surface in strain space. Our results indicate that the yield strain of porcine trabecular bone under multi-axial loading is nearly isotropic and despite a spread of yielding points between the 30 different microstructures, no significant relationship between the yield strain and bone volume fraction is observed. The proposed yield equation has simple format and it can be implemented into a macroscopic model for the prediction of failure of whole bones.

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Figures

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Fig. 1

(a) Cross-sectional microCT slice from mini pig skull, showing relative size of cropped sections and (b) binarized microstructure slices after applying bone labels

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Fig. 2

Three-dimensional rendered surfaces of the 30 microstructures with different geometries but similar DA and BV/TV

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Fig. 3

Three mesh densities compared during mesh sensitivity analysis

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Fig. 4

Explanation of boundary conditions for simulations: (a) graphical description of various circles with unique radii and z-coordinate, (b) x and y coordinates are determined from points along the perimeter of each unique circle from (a), and (c) sample BC for microstructure subjected to biaxial loading with z tension and y compression

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Fig. 5

Yield strains from biaxial simulations. Open and filled circles represent points from each of the 30 microstructure models, while the filled-in blue triangles are an average between all microstructures: (a) yield points from simulations with loading in the X- and Y-directions, (b) yield points from simulations with loading in the X- and Z-directions, and (c) yield points from simulations with loading in the Y- and Z-directions.

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Fig. 6

Yield strains for biaxial simulations. Blue points represent average of points between all microstructure models under the same loading conditions. Yellow points are −1 SD from the mean, while orange points are +1 SD from the mean.

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Fig. 7

Two-dimensional views of optimized surface with seven parameters: (a) view from the XY direction, (b) view from the XZ direction, and (c) view from the YZ direction

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Fig. 8

Biaxial yield strains in the XY, YZ, and XZ directions for the averaged point set superimposed on each other (seven-parameter model)

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Fig. 9

Biaxial yield strains in the XY, YZ, and XZ directions for the averaged point set superimposed on each other (three-parameter model)

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Fig. 10

Histogram of the prediction error of the seven-parameter model and three-parameter model

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Fig. 11

Biaxial yield stresses in the XY, YZ, and XZ directions for the averaged point set superimposed on each other, displaying a nearly isotropic response in the XZ and YZ planes, and slight deviations from isotropic in the XY plane

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