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Research Papers

Large-Scale Finite Element Analysis of Human Cancellous Bone Tissue Micro Computer Tomography Data: A Convergence Study

[+] Author and Article Information
Yuan Chen

Department of Mechanical Engineering,
University of Sheffield,
Sheffield S1 3JD, UK
INSIGNEO Institute for in Silico Medicine,
Engineering Graduate School,
University of Sheffield,
Pam Liversidge Building, Mappin Street,
Sheffield S1 3JD, UK
e-mail: Ychen48@sheffield.ac.uk

Martino Pani

Laboratorio di Tecnologia Medica,
Istituto Ortopedico Rizzoli,
Via di barbiano 1/10,
Bologna 40136, Italy
e-mail: pani@tecno.ior.it

Fulvia Taddei

Laboratorio di Tecnologia Medica,
Istituto Ortopedico Rizzoli,
Via di barbiano 1/10,
Bologna 40136, Italy
e-mail: taddei@tecno.ior.it

Claudia Mazzà

Department of Mechanical Engineering,
University of Sheffield,
Sheffield S1 3JD, UK
INSIGNEO Institute for in Silico Medicine,
Engineering Graduate School,
University of Sheffield,
Pam Liversidge Building, Mappin Street,
Sheffield S1 3JD, UK
e-mail: c.mazza@sheffield.ac.uk

Xinshan Li

Department of Mechanical Engineering,
University of Sheffield,
Sheffield S1 3JD, UK
INSIGNEO Institute for in Silico Medicine,
Engineering Graduate School,
University of Sheffield,
Pam Liversidge Building, Mappin Street,
Sheffield S1 3JD, UK
e-mail: xinshan.li@sheffield.ac.uk

Marco Viceconti

Department of Mechanical Engineering,
University of Sheffield,
Sheffield S1 3JD, UK
INSIGNEO Institute for in Silico Medicine,
Engineering Graduate School,
University of Sheffield,
Pam Liversidge Building, Mappin Street,
Sheffield S1 3JD, UK
e-mail: m.viceconti@sheffield.ac.uk

Defined as the most negative stain at that point in a certain direction, where there is no shear. Fung, Y. C., and Tong, P., 2001, Classical and computational solid mechanics, World Scientific, Singapore.

Manuscript received January 25, 2014; final manuscript received July 16, 2014; accepted manuscript posted January July 30, 2014; published online August 14, 2014. Assoc. Editor: Brian D. Stemper.

J Biomech Eng 136(10), 101013 (Aug 14, 2014) (7 pages) Paper No: BIO-14-1047; doi: 10.1115/1.4028106 History: Received January 25, 2014; Revised July 16, 2014; Accepted July 30, 2014

The complex geometry of cancellous bone tissue makes it difficult to generate finite element (FE) models. Only a few studies investigated the convergence behavior at the tissue scale using Cartesian meshes. However, these studies were not conducted according to an ideal patch test and the postelastic convergence behavior was not reported. In this study, the third principal strain and stress, and the displacement obtained from human micro finite element (microFE) models of lower resolutions were compared against the model of 19.5 μm as a reference, representing the original spatial resolution of microCT data. Uni-axial compression simulations using both linear-elastic and nonlinear constitutive equations were performed. The results showed a decrease in percentage difference in all three values as the element size decreased, with the displacement converging the fastest among the three. Simulations carried out using a nonlinear constitutive equation however, failed to show convergence for the third principal strains and stresses. It was concluded that at the tissue level, Cartesian meshes of human cancellous bone tissue were able to reach a converged solution in all three parameters investigated for linear simulation and only in displacement for nonlinear simulation. These parameters can be used as references in the future for studies in local biomechanical behavior of human cancellous bone tissues with linear simulation. The convergence behavior for human cancellous bone tissue using nonlinear constitutive equations needs further investigation.

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Figures

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Fig. 1

Radiograph of the proximal femur where the cylindrical sample is taken (Reprinted with permission from Ref. [26] Copyright 2007 by Elsevier)

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Fig. 2

3D presentation of cancellous bone specimen obtained by microCT at 19.5 μm (Reprinted with permission from Ref. [26] Copyright 2007 by Elsevier.)

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Fig. 3

Cross section view of Cartesian mesh models with a resolution of 312 μm, 156 μm, and 39 μm (from left to right)

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Fig. 4

Third principal strain plotted against NDOFs for linear elastic models

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Fig. 5

Third principal stress plotted against NDOFs for linear elastic models

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Fig. 6

Displacement plotted against NDOFs for linear elastic models (dot) and nonlinear models (square)

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