Subject-specific finite element models of long bones: An in vitro evaluation of the overall accuracy

https://doi.org/10.1016/j.jbiomech.2005.07.018Get rights and content

Abstract

The determination of the mechanical stresses induced in human bones is of great importance in both research and clinical practice. Since the stresses in bones cannot be measured non-invasively in vivo, the only way to estimate them is through subject-specific finite element modelling. Several methods exist for the automatic generation of these models from CT data, but before bringing them in the clinical practice it is necessary to assess their accuracy in the predictions of the bone stresses. Particular attention should be paid to those regions, like the epiphyseal and metaphyseal parts of long bones, where the automatic methods are typically less accurate. Aim of the present study was to implement a general procedure to automatically generate subject-specific finite element models of bones from CT data and estimate the accuracy of this general procedure by applying it to one real femur. This femur was tested in vitro under five different loading scenarios and the results of these tests were used to verify how the adoption of a simplified two-material homogeneous model would change the accuracy with respect to the density-based inhomogeneous one, with special attention paid to the epiphyseal and metaphyseal proximal regions of the bone. The results showed that the density-based inhomogeneous model predicts with a very good accuracy the measured stresses (R2=0.91, RMSE=8.6%, peak error=27%), while the two-material model was less accurate (R2=0.89, RMSE=9.6%, peak error=35%). The results showed that it is possible to automatically generate accurate finite element models of bones from CT data and that the strategy of material properties mapping has a significant influence on its accuracy.

Introduction

The determination of the mechanical stresses that physiological activities induce in human bones is of great importance in both research and clinical practice. For example, in research it is essential to investigate any mechano-biological phenomenon (Ruimerman et al., 2005); while in the clinical practice it could be extremely useful to plan the individual rehabilitation after subject-specific limb-salvage procedures (Taddei et al., 2003). Unfortunately, the mechanical stress in bones cannot be measured in living subjects without the use of an invasive surgical procedure (Aamodt et al., 1997), which, in general, is not ethically permissible. The only way to estimate bone stresses non-invasively in vivo is “subject-specific” finite element modelling. This procedure allows the creation of a numerical model of the bone segment from computed tomography (CT) images of that segment (Viceconti and Taddei, 2003); at present this represents the best source of information on bone morphology and mechanical properties applicable in vivo. As for any other mathematical model, subject-specific finite element models predict physical reality with an accuracy that is undetermined a priori.

Many methods have been proposed in the literature that are characterized by different levels of automation. The adoption of an automatic mesh generator is a forced choice when the finite element method is to be compatible with the times of the clinical practice or when it should be used to perform the analysis on a large population, since the manual generation of a mapped finite element model requires an intensive effort and is a time consuming procedure. One fully automatic approach allows the direct generation of Cartesian meshes (also known as voxel meshes) from the CT data (Keyak et al., 1990, Keyak et al., 1998; Keyak and Skinner, 1992). While this method is widely used to investigate small volumes of trabecular bones as imagined by micro-CT scanners (Hollister and Riemer, 1993; Jacobs et al., 1999), its application to whole bones has been criticized (Viceconti et al., 1998), and it is currently avoided in favour of a two steps process. This procedure requires the extraction of the bone geometry, that can be defined from CT images with good accuracy (Testi et al., 2001), followed by its automatic meshing with various well-established algorithms that are also implemented in commercial finite element programs (Viceconti and Taddei, 2003). Although some of these methods were found to provide enough automation, intrinsic accuracy, robustness and generality to be used in clinical applications (Viceconti et al., 2004), still the overall accuracy of these subject-specific finite element models is unclear. This is especially true for those anatomical regions, such as the epiphysis of long bones, where the morphological complexity increases. Those regions, that are often of great interest (e.g. in the studies of resurfacing prosthesis, to estimate the calcar stresses in total hip replacements or to investigate intramedullary and gamma nails, etc.), are usually characterized by a bulk of spongious bone surrounded by a thin layer of cortical tissue, which represents a very fine feature that is almost impossible to capture with an automatic mesh generation strategy. In addition, those regions present higher curvatures, e.g. in the femoral neck, that give rise to lower image quality due to the increase of partial volume artefacts in the CT images (Testi et al., 2001). The full validation of this modelling technique is a necessary step before its adoption for routine use in clinical practice.

Experimental validation is without doubt the best tool to assess the overall accuracy of finite element model predictions. Unfortunately, this validation has not been carried out extensively in the past, mostly due to the difficulty and tediousness of the procedure, and only a limited number of studies are available in the literature. The majority of these studies also lack the necessary generality to be applied to other models. One historic group of studies addressed the accuracy of “voxel-meshes” for predicting strain in long bones (Keyak et al., 1993; Les et al., 1997). This meshing strategy, although fully automatic, generates jagged edges on the bone surface that are known to lower the accuracy of the predicted stresses, especially on the bone surface (Keyak et al., 1990). This is the main reason for the reported very poor agreement between predicted and measured strains in the cited works. Considering other meshing strategies, the most recent and complete validation study reports the accuracy obtained with a CT-derived 3D model of a human scapula (Gupta et al., 2004). Although this work provides acceptably good results, the peculiarity of the bone segment studied led the authors to adopt an innovative but extremely specific meshing strategy. This meshing strategy is not applicable to other bony segments and thus limits the generality of the reported agreement. This lack of generality is common to other works where very specialized and non-automatic meshing strategies were adopted (Dalstra et al., 1995) or where the material properties of the bone tissue were tailored to meet the experimental results (Couteau et al., 2001) or derived from literature with no correlation to the CT numbers (Lengsfeld et al., 1998). To the authors’ knowledge only one paper has been published that investigates the accuracy of an automatically generated finite element model of a human femur, particularly addressing the extreme epiphyseal region of the bone (Ota et al., 1999). In that paper, however, the authors reported a really low accuracy that was probably due to the meshing strategy adopted and may be significantly improved.

Not only is the morphology of long bone epiphysis and metaphysis difficult to model correctly, but also in these regions the definition of the distribution of material properties presents a critical issue in the automatic generation of these models. The most recently published studies consider bone as an inhomogeneous material and derive its mechanical properties from the CT dataset, averaging the CT scalar field over each element volume using various algorithms (Huiskes et al., 1998; Keaveny and Bartel, 1993; Perillo-Marcone et al., 2003; Taddei et al., 2003). Until quite recently the majority of studies described bone as a homogeneous two phase material, deriving the mechanical properties of cortical and spongious bone from the literature (Spears et al., 2001; Verdonschot et al., 1993; Villarraga et al., 1999), a simplistic approach that has not been still completely abandoned (Cegonino et al., 2004). It is true that the adoption of an inhomogeneous model, often characterized by dozens, if not hundreds, of different material properties, may induce a large computational effort, particularly when performing non-linear simulations. However, it should be verified that the adoption of a two-material model does not compromise the accuracy of a simulation to a non-acceptable level. Other authors have addressed this question, but either lacked the experimental validation (Cattaneo et al., 2001) or limited their comparison to the maximum stress predicted on the surface of the bone without investigating the differences in the stress field distribution in the whole bone (Dalstra et al., 1995). In both cases, the authors came to the conclusion that adopting a two-material model does change the stress field distribution, however the point is to quantitatively evaluate how much it lowers the accuracy of the predicted results.

The aim of the present study was to implement a general procedure to automatically generate subject-specific finite element models of bones from CT data and estimate the accuracy of this general procedure by applying it to one real femur. This femur was tested in vitro under different loading scenarios. The results from these tests were used to verify how the adoption of a simplified two-material model would change the obtained accuracy with respect to the density-based inhomogeneous model. Special attention was paid to the epiphyseal and metaphyseal proximal regions of the bone.

Section snippets

Femur specimen

The right femur of a 51-year-old male donor, weight 75 kg, height 175 cm, deceased because of cerebral haemorrhage, was used for this study (Fig. 1). The donor had no reported history of muscle–skeletal disease. The anatomical appearance of the femur was normal, with no signs of osteoarthritis at the cartilages and no deformities. In a radiographic examination, the bone showed a normal trabecular density.

The specimen was preserved wrapped in a cloth soaked with physiological saline solution and

Experimental measurements

All strain measurements were successfully performed. Linearity was checked for each individual grid, each load replication, and each loading configuration. Linearity was excellent:

  • R20.99 for 88% of the cases where strains reached a value of 50 micro-strain or larger. Only in six cases a value of R2 lower than 0.90 was found. This confirmed that the bone could reasonably be assumed to behave linearly.

  • In no case was R2 lower than 0.70. Additionally, no grid had a consistently non-linear

Discussion

In the past few years, several methods have been proposed for the generation of subject-specific finite element models of bones from CT data. These new techniques usually rely on automatic mesh generators to reduce the time necessary to build the model, making it possible to apply the finite element modelling to study real clinical cases or large populations. Before bringing this method in the clinical practice, however, it is necessary to assess the accuracy of these finite element models in

Acknowledgements

The authors would like to thank Luigi Lena for the illustrations, Mauro Ansaloni for the support during the experiments and Barbara Bordini for the statistical analyses.

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