dc.description.abstract
Introduction
Inverse bone remodelling (IBR) is a method to estimate the in vivo loading conditions based on the bone microstructure, depicted, for example, by computed tomography (CT). Briefly, IBR uses finite element (FE) models and a set of unit load cases, which are scaled by coefficients to get the most homogeneous loading of the bone [1]. Recently, IBR was translated from micro-FE to homogenized-FE models to increase the computational speed and enable its use with clinical CT data [2]. However, the dependency on CT image resolution has only been analyzed for micro-FE-based IBR [3]. Therefore, the aim of this study was to investigate the effect of image resolution on the prediction of homogenized-FE-based IBR.
Methods
A set of 20 proximal femora was used for which micro-CT images were available from a previous study [4]. The micro-CT images were resampled from 0.03mm to 0.09mm voxel size, and a reference model was established using smooth homogenized-FE models, with a material mapping based on bone volume fraction (BV/TV) and a separate cortex model [4]. The images were then resampled to voxel sizes of 0.18mm (×2 the reference size), 0.36mm (×4), 0.72mm (×8), and 1.44mm (×16). FE meshes, without a separate cortex, were created for all bones and each image resolution, and an inhomogeneous material based on bone mineral density was applied, as BV/TV cannot be reliably measured in these low-resolution images. Twelve unit load cases were applied to the femoral head and IBR was applied by only using the elements in the femoral head, as described in the literature [4]. The predicted magnitudes for each unit load case were collected and compared to the reference model.
Results
The reference models identified the physiological peak load near the “stance” position and additional high loads in the anterior region around the peak load. For lower resolution, the load estimations diverged from the reference; however, the predicted peak load showed only low variability for all resolutions. The overall pattern, i.e., how high and low loads are distributed spatially, was similar for all tested resolutions. However, with lower image resolution, the loads tended to be more evenly distributed, i.e., high loads were reduced while previously predicted small loads increased.
Discussion
This study provides a systematic analysis of voxel size dependency for homogenized-FE-based IBR, which has so far only been performed for micro-FE-based IBR [3]. A similar trend of reduced precision with lower resolution was observed. However, reasonable results were achieved even for low image resolutions in the mm-range, lower than currently available with clinical CT. Although, the peak load was accurately identified with any resolution, the exact distribution of the loads was not. The tendency that the peak loads were distributed to surrounding loads was already observed when comparing micro-FE-based to homogenized-FE-based IBR [4]. This effect can be explained by the averaging effect on the BMD distribution with lower resolutions. Therefore, the dominant microstructural details are “washed out” and lead to a distributed load prediction. A limitation of this study is that only resampled images were used as no real CT images with different resolutions were available.
References
1. Christen et al, Biomech Model Mechanobiol, 2011
2. Bachmann et al, Ann Biomed Eng, 2022
3. Christen et al, J. R. Soc. Interface, 2016
4. Bachmann et al, Comput Methods Programs Biomed, 2023
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