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Subject-specific finite element modelling of canine long bones up to fracture ab
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C. Laurent , B. Bohme , V. d'Otreppe , M. Balligand & J.-P. Ponthot a
Department of Aerospace and Mechanics, University of Liège, Liège, Belgium
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Department of Clinical Sciences, Faculty of Veterinary Medicine, University of Liège, Liège, Belgium Published online: 07 Aug 2013.
To cite this article: C. Laurent, B. Bohme, V. d'Otreppe, M. Balligand & J.-P. Ponthot (2013) Subject-specific finite element modelling of canine long bones up to fracture, Computer Methods in Biomechanics and Biomedical Engineering, 16:sup1, 270-271, DOI: 10.1080/10255842.2013.815843 To link to this article: http://dx.doi.org/10.1080/10255842.2013.815843
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Computer Methods in Biomechanics and Biomedical Engineering, 2013 Vol. 16, No. S1, 270–271, http://dx.doi.org/10.1080/10255842.2013.815843
Subject-specific finite element modelling of canine long bones up to fracture C. Laurenta,b*, B. Bohmeb, V. d’Otreppea, M. Balligandb and J.-P. Ponthota a
Department of Aerospace and Mechanics, University of Lie`ge, Lie`ge, Belgium; bDepartment of Clinical Sciences, Faculty of Veterinary Medicine, University of Lie`ge, Lie`ge, Belgium Keywords: canine long bone; finite element method; bone fracture; bending tests
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1.
Introduction
Long bone fracture constitutes a common reason for medical consultation within veterinary orthopaedic services. Owing to the specificities of the veterinary field, post-operative complications after a fracture osteosynthesis are usually more numerous than those in human medicine, and therefore, there is a need to better understand which orthopaedic device(s) should be preferred for a given fracture. The interest of subjectspecific finite element (FE) simulations in the understanding of long bone mechanics has been largely emphasised (Helgason et al. 2008; Schileo et al. 2008). However, available studies are often limited by the many assumptions made throughout the procedure of creating a validated subject-specific FE model of a long bone, including geometry acquisition and modelling, assignment of realistic material properties and accurate validation of FE results based on ex vivo experiments. Particularly, fracture prediction has often been limited to the fracture onset prediction based on arbitrary criteria. Based on these previous studies, the objective of the present contribution is to propose and compare different subject-specific FE models of long bones that could accurately predict long bone response and failure.
2. Methods We chose to simulate bending tests on canine humeri, as this type of loading has been widely used to study the mechanical behaviour of long bones (Varghese et al. 2011). Eight pairs of canine humeri were harvested from adult dogs euthanised for reasons unrelated to this study. Bone epiphyses were embedded in resin moulds (Figure 1(a)) in order to properly control the boundary conditions. Embedded humeri were then scanned, and multi-label geometries were reconstructed using an inhouse algorithm (d’Otreppe et al. 2012). FE simulations were carried out using an in-house nonlinear FE code (Ponthot 2002). The material mapping was based on
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calibrated CT information (Figure 1(b)), and both isotropic and transversely isotropic material properties were assigned and compared using reported density – elasticity relationships (Wirtz et al. 2000) for the elastic part. The post-yield behaviour was modelled using an elastoplastic material model with linear isotropic hardening. In the case of transverse isotropy, privileged direction was taken as the computed least square line of the bone diaphysis. A maximum principal strain criterion (Schileo et al. 2008) with tensile/compressive asymmetry was used to model bone failure (Figure 1(c)) based on reported data concerning cortical bone failure (Pithioux et al. 2004), and using a killing element technique. In order to mimic experimental boundary conditions, resin plots were modelled as single hexahedrons whose corners were linked to bone surface with artificial spring elements. The bending tool and the stand were modelled as rigid geometrical halfcylinders with unilateral and bilateral contact, respectively, with regions of bone and resin blocks (Figure 1(c)) with sticking contact conditions. An increasing vertical displacement was imposed to the tool. Boundary condition locations were determined from the coordinates of resin moulds, both experimentally and numerically.
3. Results and discussion The proposed approach enables efficient and repeatable nonlinear simulation of long bones bending tests up to failure. Owing to the automation of the subject-specific FE model procedure (except CT volume segmentation), the approach is suitable for extended validation using a large sample of canine humeri. With the adopted constitutive laws, the consideration of anisotropy increased by around 20% the bending stiffness and to significantly affect the fracture pattern. Similarly, we found that modelling the diaphysis as filled versus tubular significantly affects the bending stiffness by around 10% (higher stiffness for tubular model due to partial volume effect correction). The adopted rupture criterion enabled to obtain realistic failure patterns. Ex vivo
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The present contribution, however, suffers from some limitations: first, the direction of anisotropy was not assigned locally but globally, which does not represent real bone structure. However, it is thought that the direction of anisotropy is rather constant in long bone diaphysis, which is the segment of interest in the case of bending tests. Second, density – elasticity relationships were chosen from human data which may, therefore, not be suitable for canine bone modelling, and a single constitutive law was used independently of dogs breed or age. Moreover, the adopted constitutive law did not take into account reported tension – compression asymmetry of bone material properties, and post-yield behaviour was based on a von Mises yield surface, whereas other criteria have been recently suggested: these points will be encompassed in further improvements of the current procedure.
4.
Figure 1. (a) Canine humerus embedded in rectangular resin moulds. (b) Multi-labelled geometry extracted from CT scans of embedded humerus. Material mapping strategy is used to assign local properties from the CT information. (c) Simulation of a bending test including bone failure computed from a strain-based rupture criterion.
experimental tests were carried out which corroborate the obtained load–deflection responses and fracture onset location. Particularly, bending stiffness is predicted with a mean error of 20%, which is smaller than similar reported studies. The elastoplastic constitutive law was able to reproduce the nonlinear patterns obtained experimentally, and adjustments were currently carried out to best fit observed behaviour. FE models of canine humeri along with resin moulds were semi-automatically generated, which ensures consistence between experimental and numerical boundary conditions. Particularly, although failure onset has often been located at the maximum von Mises stress (which is not thought to be representative of bone behaviour), our simulations enable to model bone behaviour up to and beyond failure. This was carried out both by using a realistic rupture criterion and by implementing it within a nonlinear FE code dealing with large displacements.
Conclusions
This work significantly contributes to the understanding of how and to what extent common modelling assumptions affect FE-predicted long bone behaviour. It also shows that realistic fracture patterns and load –deflection curves may be obtained using strain-based rupture criterion and nonlinear elastoplastic constitutive laws. The next step of this work is to further validate and adjust the presented model based on experiments carried out on a large sample of canine humeri. The long-term objective is to use this validated model to compare the effect of various orthopaedic materials on bone mechanical properties, helping veterinary surgeons in choosing the most suitable implant for a given bone failure.
References d’Otreppe V, Boman R, Ponthot J.-P. 2012. Generating smooth surface meshes from multi-region medical images. Int J Numer Methods Biomed Eng. 28:642 – 660. Helgason B, Taddei F, Palsson H, Schileo E, Cristofolini L, Viceconti M, Brynjolfsson S. 2008. A modified method for assigning material properties to FE models of bones. Med Eng Phys. 30:444 – 453. Pithioux M, Subit D, Chabrand P. 2004. Comparison of compact bone failure under two different loading rates: experimental and modelling approaches. Med Eng Phys. 26:647– 653. Ponthot J.-P. 2002. Unified stress update algorithms for the numerical simulation of large deformation elasto-plastic and elasto-viscoplastic processes. Int J Plasticity. 18:91– 126. Schileo E, Taddei F, Cristofolini L, Viceconti M. 2008. Subjectspecific finite element models implementing a maximum principal strain criterion are able to estimate failure risk and fracture location on human femurs tested in vitro. J Biomech. 41:356 – 367. Wirtz DC, Schiffers N, Pandorf T, Radermacher K, Weichert D, Forst R. 2000. Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur. J Biomech. 33:1325 – 1330.
