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Research Papers

On the Two-Dimensional Simplification of Three-Dimensional Cementless Hip Stem Numerical Models

[+] Author and Article Information
Fernando J. Quevedo González

Département de Génie de la
Production Automatisée,
Laboratoire de Recherche en
Imagerie et Orthopédie,
École de Technologie Supérieure,
1100 Rue Notre-Dame Ouest,
Montréal, QC H3C 1K3, Canada
e-mail: fernandojquevedo@gmail.com

Michael Reimeringer

Département de Génie de la
Production Automatisée,
Laboratoire de Recherche en
Imagerie et Orthopédie,
École de Technologie Supérieure,
1100 Rue Notre-Dame Ouest,
Montréal, QC H3C 1K3, Canada
e-mail: mickareim@gmail.com

Natalia Nuño

Département de Génie de la
Production Automatisée,
Laboratoire de Recherche en
Imagerie et Orthopédie,
École de Technologie Supérieure,
1100 Rue Notre-Dame Ouest,
Montréal, QC H3C 1K3, Canada
e-mail: natalia.nuno@etsmtl.ca

1Corresponding author.

Manuscript received January 22, 2016; final manuscript received November 25, 2016; published online January 24, 2017. Assoc. Editor: Michael Detamore.

J Biomech Eng 139(3), 031011 (Jan 24, 2017) (7 pages) Paper No: BIO-16-1030; doi: 10.1115/1.4035368 History: Received January 22, 2016; Revised November 25, 2016

Three-dimensional (3D) finite element (FE) models are commonly used to analyze the mechanical behavior of the bone under different conditions (i.e., before and after arthroplasty). They can provide detailed information but they are numerically expensive and this limits their use in cases where large or numerous simulations are required. On the other hand, 2D models show less computational cost, but the precision of results depends on the approach used for the simplification. Two main questions arise: Are the 3D results adequately represented by a 2D section of the model? Which approach should be used to build a 2D model that provides reliable results compared to the 3D model? In this paper, we first evaluate if the stem symmetry plane used for generating the 2D models of bone-implant systems adequately represents the results of the full 3D model for stair climbing activity. Then, we explore three different approaches that have been used in the past for creating 2D models: (1) without side-plate (WOSP), (2) with variable thickness side-plate and constant cortical thickness (SPCT), and (3) with variable thickness side-plate and variable cortical thickness (SPVT). From the different approaches investigated, a 2D model including a side-plate best represents the results obtained with the full 3D model with much less computational cost. The side-plate needs to have variable thickness, while the cortical bone thickness can be kept constant.

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References

Figures

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Fig. 1

Stair climbing loading conditions based on Heller et al. [16] for the (a) 3D reference model and (b) the 2D models. For the latter, only in-plane forces were considered.

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Fig. 2

Transversal cuts in (a) the 3D model, (b) shape of the side-plate, and (c) 2D schematization of the element thickness and the side-plate in a transversal cut

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Fig. 3

Maximum value in the lateral cortex for (a) σVM, (b) U, and (c) τ for the 3D model (solid line) and for the 2D plane (dashed line). Distributions of σVM, U and τ in the 3D model (d)–(f) and in the stem symmetry plane (g)–(i). Maximum values of σVM, U, and τ in the medial cortex (j)–(l) for the 3D model (blue) and in the 2D plane (dashed line).

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Fig. 4

Cumulative distribution of σVM, U, and τ differences between the 3D model and the values in the stem symmetry plane used for the 2D models

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Fig. 5

Von Mises stress (σVM) distribution for (a) the reference 3D model, (b) the WOSP, (c) SPCT, and (d) SPVT 2D models

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Fig. 6

Cumulative distribution of the 2D–3D σVM differences and their distribution for the WOSP, SPCT, and SPVT 2D models

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Fig. 7

Strain energy density (U) distribution for (a) the reference 3D model, (b) the WOSP, (c) SPCT, and (d) SPVT 2D models

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Fig. 8

Cumulative distribution of the 2D–3D U differences and their distribution for the WOSP, SPCT, and SPVT 2D models

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Fig. 9

Interfacial shear stresses (τ) for (a) the reference 3D model, (b) the WOSP, (c) SPCT, and (d) SPVT 2D models

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Fig. 10

Cumulative distribution of the 2D–3D τ differences and their distribution for the WOSP, SPCT, and SPVT 2D models

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