Original ResearchAccuracy Quantification of the Reverse Engineering and High-Order Finite Element Analysis of Equine MC3 Forelimb
Introduction
Bones are mainly responsible for withstanding and absorbing applied loads. To predict bone fracture and failure, and to investigate reasons for such incidents, comprehensive insight into the responses of bones to loading is crucial. Identifying the strains and stresses to which bones are exposed will assist in elucidating the reasons for fractures and locating their most likely sites. Bones are complex both in their material characteristics and their shape but respond in similar ways to external loads throughout the animal kingdom [1]. Clearly, a large bone that shows a relatively restricted range of normal movements would provide the best chance to develop a model to investigate the normal responses of bones to loading. Horses are large animals with large, elongated, and simplified forelimb bones that are apparently well-adapted for exercise at high speeds. Hence, considerable forces can be exerted on their forelimb bones. These forces are believed to be involved in different kinds of injuries and incidents, and most disastrous injuries in racing horses worldwide are associated with forelimb injuries, especially failures of the third metacarpal bone (MC3) [2], [3], [4], [5], [6], [7], [8]. The third metacarpal bone forms an essential part of the lower forelimb in withstanding loads [9]. Furthermore, due to its large size, minimal muscle attachments, and relatively simple movements, the MC3 is a unique long bone that can assist in investigating the responses of bones when they are exposed to forces. Surface strains on the MC3 midshaft bone can be related to exercise speed [10], locomotion type [11], [12], and, more significantly, the shape of the bone [13], [14]. The shape of the midshaft dorsal cortex (DC) of MC3 alters (expands and thickens) when it undergoes increasing applied forces during racing and training [15], [16]. Many investigations into human bone fatigue, for example, are heavily reliant on the outcome of equine bone research [9].
Computer-aided design (CAD) and finite element analysis (FEA) are indispensable tools in attempts to model and analyze bones and to replicate experimental data. Using different CAD methodologies in biomedical and tissue engineering practices demands considerable effort and diligence to appreciate the value and significance of different methods [17], [18]. Finite element analysis may still be unfamiliar to the readers of equine-related journals, yet it has the potential to provide tremendous benefits [19]. As Erdemir et al. reported, “There has been a 6,000% increase in the number of finite element articles published between 1980 and 2009” [20]. However, mesh quality, model validation, and appropriate energy balance have not been adequately addressed in these studies [21]. Generating a three-dimensional model, which has been done by various methods such as geometry-based and voxel-based [22], [23], [24], [25], is an initial step before performing FEA. In many biomechanical engineering activities [26], [27], [28], alternative methods such as reverse engineering via CAD are frequently required to produce the 3D models of bones. Examples of times when alternative methods are required include when computed tomography (CT)/magnetic resonance imaging (MRI) images are not available, if the images possess poor or bad quality, if bones are shattered, or when modifications are required to the 3D model of bones before implant design or conducting FEA. Furthermore, CT/MRI imaging has drawbacks, being expensive and difficult to perform on live animals [29], and causing a relatively high radiation exposure [30], [31], [32], so CT scanning may not be ethically justified [25]. Neither is it advisable for it to be regularly used in scanning healthy bone volunteers [33]. Reverse engineering techniques can be used either to reconstruct an incomplete or damaged bone or to make a duplicate model from an existing one [34]. In addition, 3D voxel-based surface extraction (CT/MRI-based modeling) requires a substantial computational power, and although they can describe anatomical morphology, a CAD-based solid modeling (vector-based) environment is needed to design, analyze, and simulate anatomical models [25]. This emphasizes the utility of CAD-based solid modeling. Irrespective of many influential factors that alter the mechanical behavior of bones, the importance of shape has been overly neglected in the literature. However, the significance of shape variation in the diaphysis of MC3 has been highlighted in some research [15], [29]. The DC of MC3 midshaft enlarges when the horses are exposed to fast exercise speed [10], [13], [35], [36], and compressive strains exceeding 3000 and 5670 microstrains have been recorded in this region [37], [38]. These findings define bone as a smart material that is able to adjust its mass and structure according to the loads it experiences [39]. The midshaft of MC3 is a region of considerable interest to investigate its response under load and to comprehend the shape-dependent mechanical behavior of bones. To commence addressing such inquiries, reverse engineering and determining accuracy of the 3D models are required to shape the fundamental grounding. Afterward, investigating the relationship among size, shape, and mechanical properties is feasible. The 6 cm segment of the MC3 midshaft which was investigated in this study has thick cortical bone, and this bone material redistributes toward either ends to become predominantly trabecular. The MC3 has variable directions of loads at either ends, which need to focus onto the central shaft (the segment being studied here). Not only does the elliptical cross-sectional shape of MC3 prevent and equalize directional loading but also it serves to enhance the sagittal bending once a horse is racing [9], [40]. In addition, having unique length and cross-sectional properties, MC3 can support relatively large compressive loads without experiencing substantial strains [41]. The objective is to comprehend the importance of different sizes and shapes in this piece of MC3 and to investigate how those shapes change with loads and strains. To accomplish this, reliable 3D models of the MC3 in this region and accurate FEA are essential.
Nonetheless, there is no current evidence of reverse engineering (CAD-based) through an extrapolation process of slices in the literature for reconstructing MC3. Neither has dimensional error analysis been performed in most of the previous studies to verify and assess the accuracy of reconstructed models [29], [42], [43], [44]. In CT imaging (voxel-based representation), a 3D model of an object is reconstructed from a 3D region growing from a series of cross-sectional slices (2D segmentations). In extrapolation via CAD systems, on the other hand, inner and outer cortices (contours) of slices are detected independently for each slice. A multisection surface will then be generated by sweeping the contours (cortex or curves) of each slice along an automatically defined long axis of the bone. This process is separately performed to generate internal and external surfaces. A similar process was discussed as an application of reverse engineering methods to reconstruct the human femur [26].
Several studies have been conducted on 3D modeling and stress distribution in the equine MC3 and surrounding structures [45], [46], [47], [48], [49], [50]. An essential part of an FEA should be dedicated to convergence and error analysis before publishing the results. A limitation to most of these previous studies is the lack of evidence in terms of quantifying dimensional error of reconstructed geometries, performing mesh quality assessment, determining the error of FEA, or assigning linear tetrahedron meshes to the models, which would all potentially lead to misleading stress and strain results. A summary of considerations in FEA error analysis reported in the literature is presented in Table 1. In addition, orthotropic material identification is one of the most crucial contributions toward a reliable FEA. To the best knowledge of the authors, finite element error analysis, as conducted in the present study, has never been discussed in the equine literature. Even in human studies, literature similar to what has formerly been conducted on the computer simulations of human feet [56] is limited in determining proper elements and methods for FEA. The purpose of this study is to present dimensional error analysis of reverse engineering through an extrapolation process of cross-sectional slices. In addition, the relations of stress and strain convergence and the displacement-based error estimation are presented that can be used to evaluate the accuracy of FEA and to minimize the associated errors.
Section snippets
Reconstructed Surface Error Analysis
Fifteen equine MC3 bones were extracted from forelimbs of cadavers of Thoroughbred and Standardbred horses that were more than 2 years old. The horses died for reasons unrelated to the locomotory system or this study and cadavers were sourced from a local slaughterhouse or specifically donated for use in teaching and research. The bones were taken for CT imaging using a SIEMENS CT scanner machine (Fig. 1). The DICOM images (slice thickness of 0.75 mm) were imported into 3D slicer software and
Reconstructed Bone Samples
Table 3 and Fig. 5 present the calculated error analysis of the reconstructed MC3 obtained through the extrapolation process. Design rules could be implemented that enabled the extrapolated CAD model (3E) to achieve a minimum error of +0.135 and −0.185 mm when compared with the equivalent CT-based CAD model (reference model). These minimum errors were further reduced to +0.01 and −0.009 mm when more cross-sectional slices (11E) within the diaphysis of the bones were included. By eliminating the
Discussion
Reverse engineering is an approach for constructing a CAD model from a physical part through surface modeling and 3D measurements. A critical issue for rapid product development is to efficiently create and modify a CAD model from the existing components of a desired object. Apart from the wide applications of CAD in mechanical engineering, it has been receiving considerable attention in medical engineering to gain a successful design. This requires a detailed knowledge of surrounding areas of
Conclusion
This article presented a consideration of reverse engineering through extrapolated cross-sectional slices and an FEA study with a focus on solid mechanics of long bones. A basic explanation of the mesh discretization error has been provided, and ANSYS error estimation tools were used to evaluate the accuracy of the finite element solution. Although FEA errors of 3%–5% have been shown to be acceptable in previously published articles, design rules presented in our study reduced the FEA error to
Acknowledgments
The authors would like to thank Dr. Marcus Volz for proofreading of the article.
References (69)
- et al.
Bio-CAD modeling and its applications in computer-aided tissue engineering
Comput Aided Des
(2005) - et al.
Considerations for reporting finite element analysis studies in biomechanics
J Biomech
(2012) - et al.
Finite element modeling mesh quality, energy balance and validation methods: a review with recommendations associated with the modeling of bone tissue
J Biomech
(2013) - et al.
Comparison of geometry-based and CT voxel-based finite element modelling and experimental validation
Med Eng Phys
(1998) - et al.
Recent development on computer aided tissue engineering — a review
Comput Methods Programs Biomed
(2002) - et al.
TRI2SOLID: an application of reverse engineering methods to the creation of CAD models of bone segments
Comput Methods Programs Biomed
(1998) Three-dimensional surface reconstruction of human bone using a B-spline based interpolation approach
Comput Aided Des
(2011)- et al.
Quantification of the accuracy of MRI generated 3D models of long bones compared to CT generated 3D models
Med Eng Phys
(2012) - et al.
Effects of treadmill exercise on cortical bone in the third metacarpus of young horses
Res Vet Sci
(1992) - et al.
The distribution of material properties in the equine third metacarpal bone serves to enhance sagittal bending
J Biomech
(1997)
Three-dimensional geometrical modelling of wild boar head by reverse engineering technology
J Bionic Eng
Evaluation of a subject-specific finite-element model of the equine metacarpophalangeal joint under physiological load
J Biomech
Development and validation of a series of three-dimensional finite element models of the equine metacarpus
J Biomech
Equine subchondral bone failure threshold under impact compression applied through articular cartilage
J Biomech
A finite element model of an equine Hoof
J Equine Vet Sci
Finite element prediction of surface strain and fracture strength at the distal radius
Med Eng Phys
A modified method for assigning material properties to FE models of bones
Med Eng Phys
Design factors of lumbar pedicle screws under bending load: a finite element analysis
Biocybernetics Biomed Eng
Comparison of hexahedral and tetrahedral elements in finite element analysis of the foot and footwear
J Biomech
Size dependent free vibration analysis of multicrystalline nanoplates by considering surface effects as well as interface region
Int J Mech Sci
Size-dependent static characteristics of multicrystalline nanoplates by considering surface effects
Int J Mech Sci
Geometric properties of equine metacarpi
J Biomech
Segmentation accuracy of long bones
Med Eng Phys
Bones: structure and mechanics
An update on racing fatalities in the UK
Equine Vet Educ
Horse-level risk factors for fatal distal limb fracture in racing Thoroughbreds in the UK
Equine Vet J
Risk of fatality and causes of death of Thoroughbred horses associated with racing in Victoria, Australia: 1989–2004
Equine Vet J
California racehorse postmortem program: a 4-year overview
Epidemiology of racing injuries in Thoroughbred racehorses with special reference to bone fractures: Japanese experience from the 1980s to 2000s
J Equine Sci
The effect of the sagittal ridge angle on cartilage stress in the equine metacarpo-phalangeal (fetlock) joint
Comput Methods Biomech Biomed Engin
Qualitative assessment of bone density at the distal articulating surface of the third metacarpal in Thoroughbred racehorses with and without condylar fracture
Equine Vet J
A review of dorsal metacarpal disease (bucked shins) in the flat racing horse: prevalence, diagnosis, pathogenesis, and associated factors
J Dairy Vet Anim Res
The timing and distribution of strains around the surface of the midshaft of the third metacarpal bone during treadmill exercise in one Thoroughbred racehorse
Aust Vet J
Surface strains around the midshaft of the third metacarpal bone during turning
Equine Vet J
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Animal welfare/ethical statement: No ethical permission was sought as no animal was euthanised for the purposes of this study.
Conflict of interest statement: The authors have no conflict of interest to declare.