Automatic generation of accurate subject-specific bone finite element models to be used in clinical studies
Introduction
In 1972 Brekelmans first used a finite element (FE) model to investigate the stresses acting in a human bone under the action of physiological loads (Brekelmans et al., 1972). Since then, the use of finite element analysis in orthopaedic biomechanics constantly expanded. Most of the studies are focused on general biomechanical considerations regarding the physiological or pathological stress fields induced in intact or surgically treated bones. In these cases, the finite element model is generated with reference to a generic or average anatomy, which is used to draw generic or average conclusions.
Although this approach is perfectly valid to answer to many scientific questions, there is an increasing interest in bringing this method closer to the clinical application. As an example, in the design of orthopaedic implants the significant inter-subject variability, increased by ageing and anatomical deformities, should be accounted in biomechanics studies (Noble et al (1988), Noble et al (1995); Bloebaum et al., 1993; Hicks et al., 1995; Sugano et al., 1998). In particular, it would be interesting to generate a separate finite element model for each subject of a study group, to account for the inter-subject differences. Early applications along these lines are subject-specific FE models to investigate the risk of femoral neck fracture (Testi et al., 1999; Keyak and Rossi, 2000), to account for the inter-subject variability of biomechanical factors in animal studies (Weinans et al., 2000), but also to support the interpretation of clinical results in follow-up studies (Gardner et al., 2000). Other possible and promising applications are patient-specific identification of the appropriate load regime after skeletal surgery (Sutherland et al., 1999; Taddei et al., 2002), or support in pre-operative planning (Kopperdahl et al., 1999). It is of extreme importance to assess the accuracy of the methods used to generate such models, since it is not possible to directly verify the results predicted by such models. Even neglecting the inherent accuracy with which the finite element model is solved numerically, a subject-specific finite element model may be affected by various potential sources of inaccuracy:
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The boundary conditions applied to the model may not accurately reproduce the joint, ligaments and muscle forces acting on a bone segment (Cristofolini et al., 1995; Stolk et al., 2001; Bergmann et al., 2001; Duda et al., 1998);
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The constitutive laws used to model the mechanical behaviour of the bone tissues may not be adequate or their parameters accurately identified (Pattijn et al., 2001; Zannoni et al., 1998; Kopperdahl et al., 2002; Keller, 1994; Carter and Hayes, 1977);
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The finite element mesh may be topologically inaccurate, in the sense that geometry of the bone is inaccurately derived from the CT data (Helterbrand et al., 1997; Prevrhal et al., 1999; Viceconti et al (1999a), Viceconti et al (1999b); Testi et al., 2001);
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The finite element mesh may be topologically ill conditioned, i.e. the shape of the elements is so distorted that the numerical accuracy of the model is reduced (Hart et al., 1992; Villarraga et al., 1999; Polgar et al., 2001; Viceconti et al., 1998; Viceconti et al (1999a), Viceconti et al (1999b)).
While the first two aspects have been investigated extensively in previous studies, the latter source of error has been investigated only in vitro, and with reference to a particular bone segment.
Subject-specific finite element analysis requires the generation of three-dimensional finite element meshes of the bone segments from diagnostic data (collected using Computerized Tomography). Such procedure must be:
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Automatic, because in most cases subject-specific models are useful if they can be created for fairly large population of subjects, which is feasible only if the mesh generation is automatic;
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Accurate, because in some cases diagnostic (Testi et al., 1999; Keyak and Rossi, 2000; Gardner et al. 2000; Nightingale et al., 2000), or treatment decisions (Sutherland et al., 1999; Taddei et al., 2002; (Kopperdahl et al., 1999) would be based also on the results of the finite element models;
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Robust, i.e. able to generate a mesh of almost every data set, because in many cases the diagnostic data provide a description of the organ anatomy which is partial, inaccurate, and difficult to process;
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General, i.e. able to provide well-conditioned meshes for all bones, independently from their geometric complexity.
In a recent study a hexahedral mesh generator, based on a grid projection algorithm, was found to be superior to any other method in terms of accuracy and automation (Viceconti et al (1998), Viceconti et al (1999a), Viceconti et al (1999b)). However, so far the use of this method has been documented only on data collected in vitro and only for long bones. The aim of the present study is to verify if this innovative procedure for the generation of finite element models of human bones from data collected in vivo present all the requirements (robustness, accuracy, automation and generality) for clinical applications.
Section snippets
Attributes metrics
The method for automatic mesh generation (AMG) under study had been already proven to be automatic and accurate when used on data collected in vitro (Viceconti et al (1998), Viceconti et al (1999a), Viceconti et al (1999b)). Thus, the present study must verify if the method is also general and robust. At the same time, it is necessary to ensure that the levels of automation and accuracy observed when using data collected in vitro do not degrade significantly when the method is used to process
Results
In order to achieve a well-conditioned mesh, the femur models generated from CT data collected in vivo required a mesh refinement slightly higher than that used in the previous study for the model created with CT data collected in vitro.
This moderate increase of the models’ size was overshadowed by the better performance of the computers used in this study, with respect to those used to process the data collected in vitro in the previous study. In fact, the computational weight, measured by the
Discussion
The method for the automatic generation of finite element meshes from CT data here described, based on a grid-projection algorithm, was found in a previous study very effective in terms of accuracy and automation, when used to process data collected in vitro and only for long bones (Viceconti et al., 1998). The present study was aimed to verify if this method represents a procedure for the generation of finite element models of human bones from data collected in vivo automatic, accurate robust,
Acknowledgements
The authors would like to thank Luigi Lena for the illustrations and Mauro Ansaloni and Roberta Fognani for the support during the experiments.
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