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Research Papers

Quantification of Age-Related Tissue-Level Failure Strains of Rat Femoral Cortical Bones Using an Approach Combining Macrocompressive Test and Microfinite Element Analysis

[+] Author and Article Information
Ruoxun Fan

State Key Laboratory of Automotive
Simulation and Control,
Jilin University,
Changchun 130025, China;
Department of Engineering Mechanics,
Jilin University,
Nanling Campus,
Changchun 130025, China
e-mail: 76232696@qq.com

He Gong

Professor
State Key Laboratory of Automotive
Simulation and Control,
Jilin University,
Changchun 130025, China;
Department of Engineering Mechanics,
Jilin University,
Nanling Campus,
Changchun 130025, China
e-mail: gonghe@jlu.edu.cn

Rui Zhang

Department of Engineering Mechanics,
Jilin University,
Nanling Campus,
Changchun 130025, China;
Key Laboratory for Biomechanics and
Mechanobiology of Ministry of Education,
School of Biological Science and
Medical Engineering,
Beihang University,
Beijing 10000, China
e-mail: 425035587@qq.com

Jiazi Gao

Department of Engineering Mechanics,
Jilin University,
Nanling Campus,
Changchun 130025, China
e-mail: 544218588@qq.com

Zhengbin Jia

Department of Engineering Mechanics,
Jilin University,
Nanling Campus,
Changchun 130025, China
e-mail: 491457836@qq.com

Yanjuan Hu

School of Mechatronic Engineering,
Changchun University of Technology,
Changchun 130025, China
e-mail: yanjuan_hu@126.com

1Corresponding author.

Manuscript received July 30, 2015; final manuscript received January 25, 2016; published online March 4, 2016. Assoc. Editor: Brian D. Stemper.

J Biomech Eng 138(4), 041006 (Mar 04, 2016) (13 pages) Paper No: BIO-15-1374; doi: 10.1115/1.4032798 History: Received July 30, 2015; Revised January 25, 2016

Bone mechanical properties vary with age; meanwhile, a close relationship exists among bone mechanical properties at different levels. Therefore, conducting multilevel analyses for bone structures with different ages are necessary to elucidate the effects of aging on bone mechanical properties at different levels. In this study, an approach that combined microfinite element (micro-FE) analysis and macrocompressive test was established to simulate the failure of male rat femoral cortical bone. Micro-FE analyses were primarily performed for rat cortical bones with different ages to simulate their failure processes under compressive load. Tissue-level failure strains in tension and compression of these cortical bones were then back-calculated by fitting the experimental stress–strain curves. Thus, tissue-level failure strains of rat femoral cortical bones with different ages were quantified. The tissue-level failure strain exhibited a biphasic behavior with age: in the period of skeletal maturity (1–7 months of age), the failure strain gradually increased; when the rat exceeded 7 months of age, the failure strain sharply decreased. In the period of skeletal maturity, both the macro- and tissue-levels mechanical properties showed a large promotion. In the period of skeletal aging (9–15 months of age), the tissue-level mechanical properties sharply deteriorated; however, the macromechanical properties only slightly deteriorated. The age-related changes in tissue-level failure strain were revealed through the analysis of male rat femoral cortical bones with different ages, which provided a theoretical basis to understand the relationship between rat cortical bone mechanical properties at macro- and tissue-levels and decrease of bone strength with age.

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Figures

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Fig. 1

Overview of the boundary and loading conditions in compressive mechanical test and micro-FE analysis: (a) the specimen positioned in the mechanical testing machine and (b) the same boundary condition was applied to the micro-FE model

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Fig. 2

Flowchart for determining the tissue-level failure strain of rat femoral cortical bone

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Fig. 3

Longitudinal elastic moduli of rat femoral cortical bones with different ages obtained by nanoindentation test [11]. Box plot showed the median and quartile for longitudinal elastic moduli of rat femoral cortical bone materials.

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Fig. 4

Mesh sensitivity analysis for a rat cortical bone specimen in 1 month of age. The average edge lengths of element were 10, 20, and 30 μm. The apparent stress–strain curves from the micro-FE models with three average edge lengths of element were compared with the corresponding experimental curve.

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Fig. 5

Comparison of the effects of variations in ratio between tissue-level tensile and compressive failure strains on rat cortical bone specimens with different ages: (a) a specimen in 1 month of age, (b) a specimen in 3 months of age, (c) a specimen in 5 months of age, (d) a specimen in 7 months of age, (e) a specimen in 9 months of age, (f) a specimen in 11 months of age, and (g) a specimen in 15 months of age

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Fig. 6

Comparison of the apparent stress–strain curves simulated by the micro-FE model assigning with isotropic (solid line) and anisotropic (dashed line) cortical bone materials

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Fig. 7

The simulated apparent stress–strain curves from micro-FE analyses (dashed lines) and experimental ones (solid lines) for rat cortical bone specimens with different ages: (a) specimens in 1 month of age, (b) specimens in 3 months of age, (c) specimens in 5 months of age, (d) specimens in 7 months of age, (e) specimens in 9 months of age, (f) specimens in 11 months of age, and (g) specimens in 15 months of age

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Fig. 8

The correlations between the experimental and micro-FE analysis predicted results: (a) apparent fracture strain and (b) apparent ultimate stress

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Fig. 9

Comparison of the failure contour plot between the micro-FE simulation and compressive experiment for a rat cortical bone specimen in 7 months of age. The arrows represented the fracture direction.

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Fig. 10

Tissue-level failure strains of rat femoral cortical bones with different rat ages. The failure strains in tension and compression gradually increased in the period of skeletal maturity (1–7 months of age) and reached the peak values at 7 months of age, then significantly decreased with age. Box plot showed the median and quartile for tissue-level failure strains in tension and compression. (a) Tissue-level failure strains in tension and (b) tissue-level failure strains in compression.

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Fig. 11

Visualization of the complete failed micro-FE models. (a) Micro-FE model of a 1 month of age rat femoral cortical bone, in which failure elements accounted for 2.01% of all the elements when complete failure occurs. (b) Micro-FE model of a 7 months of age rat femoral cortical bone, in which failure elements accounted for 6.75% of all the elements when complete failure occurs.

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