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Research Papers

Inverse Finite Element Modeling for Characterization of Local Elastic Properties in Image-Guided Failure Assessment of Human Trabecular Bone

[+] Author and Article Information
Alexander Zwahlen

Institute for Biomechanics,
ETH Zurich,
Vladimir-Prelog-Weg 3,
Zurich CH-8093, Switzerland
e-mail: azwahlen@ethz.ch

David Christen

Institute for Biomechanics,
ETH Zurich,
Vladimir-Prelog-Weg 3,
Zurich CH-8093, Switzerland
e-mail: davidchristen@gmail.com

Davide Ruffoni

Institute for Biomechanics,
ETH Zurich,
Vladimir-Prelog-Weg 3,
Zurich CH-8093, Switzerland
e-mail: druffoni@ulg.ac.be

Philipp Schneider

Institute for Biomechanics,
ETH Zurich,
Vladimir-Prelog-Weg 3,
Zurich CH-8093, Switzerland
e-mail: p.schneider@soton.ac.uk

Werner Schmölz

Department of Trauma Surgery,
Medical University Innsbruck,
Anichstrasse 35,
Innsbruck A-6020, Austria
e-mail: Werner.schmoelz@uki.at

Ralph Müller

Institute for Biomechanics,
ETH Zurich,
Vladimir-Prelog-Weg 3,
Zurich CH-8093, Switzerland
e-mail: ram@ethz.ch

1Corresponding author.

Manuscript received September 5, 2014; final manuscript received October 21, 2014; accepted manuscript posted November 5, 2014; published online December 10, 2014. Assoc. Editor: Blaine Christiansen.

J Biomech Eng 137(1), 011012 (Jan 01, 2015) (9 pages) Paper No: BIO-14-1439; doi: 10.1115/1.4028991 History: Received September 05, 2014; Revised October 21, 2014; Accepted November 05, 2014; Online December 10, 2014

The local interpretation of microfinite element (μFE) simulations plays a pivotal role for studying bone structure–function relationships such as failure processes and bone remodeling. In the past μFE simulations have been successfully validated on the apparent level, however, at the tissue level validations are sparse and less promising. Furthermore, intratrabecular heterogeneity of the material properties has been shown by experimental studies. We proposed an inverse μFE algorithm that iteratively changes the tissue level Young’s moduli such that the μFE simulation matches the experimental strain measurements. The algorithm is setup as a feedback loop where the modulus is iteratively adapted until the simulated strain matches the experimental strain. The experimental strain of human trabecular bone specimens was calculated from time-lapsed images that were gained by combining mechanical testing and synchrotron radiation microcomputed tomography (SRμCT). The inverse μFE algorithm was able to iterate the heterogeneous distribution of moduli such that the resulting μFE simulations matched artificially generated and experimentally measured strains.

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Figures

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Fig. 1

(a) Visual verification of deformable image registration. Red arrows show displacement from undeformed (white) to deformed (green) image of a single trabecular; (b) Experimentally measured von Mises effective strain; (c) μFE von Mises effective strain with experimental boundary conditions; (d) μFE von Mises effective strain with standard boundary conditions.

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Fig. 2

(a) Schematic of inverse μFE algorithm; (right) verification study 1 (2D), using random modulus (b) and μFE to generate a “virtual” experimental strain map (c). Iterated strain and modulus after 0, 1 and 10 iterations ((e)–(g)).

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Fig. 3

Verification study 2, random 3D: single trabecula with a random modulus (a) for creating “virtual” experimental strain map (b), iterated modulus (c), and strain (d) for 0, 1, and 99 iterations. Correlation between “virtual” experimental strain and iterated strain pattern (e). Correlation between randomly generated modulus and iterated modulus (f). Iterated modulus from attenuation based initial condition (g).

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Fig. 4

Verification study 3: Single trabecular with attenuation based modulus (a) for creating “virtual” experimental strain map (b), iterated modulus (c), and strain (d) for 0, 1, and 99 iterations. Correlation between “virtual” experimental strain and iterated strain pattern (e). Correlation between attenuation based modulus and iterated modulus (f). Iterated modulus from 10% and 30% noise added to the initial condition (g).

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Fig. 5

Verification study 4, experimental strain 3D: Single trabecula with real experimental strainmap (b), iterated strain pattern and modulus for 0–18 iterations (d), correlation between experimental strain and iterated strain (e). Correlation between modulus at iteration (i) and (i+1) (f).

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Fig. 6

Verification study 4, strain pattern (a), iterated modulus with homogeneous initial condition (b), and attenuation based initial condition (c). (b) and (c) show similar pattern which however does not correlate with experimentally measured density (d).

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