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TECHNICAL PAPERS: Bone/Orthopedic

# Effects of Intracortical Porosity on Fracture Toughness in Aging Human Bone: A $μCT$-Based Cohesive Finite Element Study

[+] Author and Article Information
Ani Ural

Department of Biomedical Engineering, Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180

Deepak Vashishth1

Department of Biomedical Engineering, Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180

1

Corresponding author.

J Biomech Eng 129(5), 625-631 (Feb 09, 2007) (7 pages) doi:10.1115/1.2768377 History: Received August 03, 2006; Revised February 09, 2007

## Abstract

The extent to which increased intracortical porosity affects the fracture properties of aging and osteoporotic bone is unknown. Here, we report the development and application of a microcomputed tomography based finite element approach that allows determining the effects of intracortical porosity on bone fracture by blocking all other age-related changes in bone. Previously tested compact tension specimens from human tibiae were scanned using microcomputed tomography and converted to finite element meshes containing three-dimensional cohesive finite elements in the direction of the crack growth. Simulations were run incorporating age-related increase in intracortical porosity but keeping cohesive parameters representing other age-related effects constant. Additional simulations were performed with reduced cohesive parameters. The results showed a 6% decrease in initiation toughness and a 62% decrease in propagation toughness with a 4% increase in porosity. The reduction in toughnesses became even more pronounced when other age-related effects in addition to porosity were introduced. The initiation and propagation toughness decreased by 51% and 83%, respectively, with the combined effect of 4% increase in porosity and decrease in the cohesive properties reflecting other age-related changes in bone. These results show that intracortical porosity is a significant contributor to the fracture toughness of the cortical bone and that the combination of computational modeling with advanced imaging improves the prediction of the fracture properties of the aged and the osteoporotic cortical bone.

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Copyright © 2007 by American Society of Mechanical Engineers
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## Figures

Figure 1

(a) μCT scans of the compact tension specimens from 19- and 81-year-old donors. (b) Finite element meshes generated from μCT scans of 19- and 81-year-old specimens. Note that the arrows indicate the locations of the loading. The loading is applied in the form of incremental displacement. The white triangles indicate the fixed boundary conditions in directions 1 and 2. The black triangles indicate the location of fixed boundary conditions in all three directions along a line on the far surface of the specimen. (c) Deformed meshes at the end of the crack growth simulations showing the crack opening for the 19- and 81-year-old specimens.

Figure 2

(a) Traction-displacement relationship defining the cohesive zone model. (b) Schematics of 3D, eight-noded cohesive element and its compatibility with solid elements.

Figure 3

μCT images of the cross sections of (a) 19-year-old specimen and (b) 81-year-old specimen. The images also show cross-sectional views of the compact tension specimens at the marked sections. Note that the scale corresponds to the dimensions of the cross-sectional views. (c) Close-up views of the regions marked by boxes in (a) and (b) showing the intracortical porosity variation between two specimens. (d) Finite element meshes of the crack planes defined by cohesive elements for 19- and 81-year-old specimens. Compared to 19-year-old specimen, note the extended porosity in both the μCT images and the finite element mesh for the 81-year-old specimen.

Figure 4

FEM simulation results for crack propagation in compact tension specimens. (a) Stress intensity factor versus crack growth for 19- and 81-year-old specimens with the same and reduced cohesive properties. (b) Percentage change in initiation toughness due to the increased intracortical porosity and due to changes in both intracortical porosity and material properties. (c) Percentage change in propagation toughness due to the increased intracortical porosity and due to changes in both intracortical porosity and material properties. Note that percentage change reflects the change in values corresponding to the specimen from the 19-year-old donor.

Figure 5

Comparison of intracortical porosity on the crack plane with different finite element mesh sizes for the 81-year-old specimen: (a) 210μm and (b) 105μm. Porosity is measured as 10% and 8% at the crack planes for 210μm and 105μm resolutions, respectively. This discrepancy is caused by the two-dimensional evaluation of the three-dimensional porosity distribution and by the slight variation in the coordinates of the planes shown in both figures.

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