Voxel size dependency, reproducibility and sensitivity of an in vivo bone loading estimation algorithm

Abstract

A bone loading estimation algorithm was previously developed that provides in vivo loading conditions required for in vivo bone remodelling simulations. The algorithm derives a bone's loading history from its microstructure as assessed by high-resolution (HR) computed tomography (CT). This reverse engineering approach showed accurate and realistic results based on micro-CT and HR-peripheral quantitative CT images. However, its voxel size dependency, reproducibility and sensitivity still need to be investigated, which is the purpose of this study. Voxel size dependency was tested on cadaveric distal radii with micro-CT images scanned at 25 µm and downscaled to 50, 61, 75, 82, 100, 125 and 150 µm. Reproducibility was calculated with repeated in vitro as well as in vivo HR-pQCT measurements at 82 µm. Sensitivity was defined using HR-pQCT images from women with fracture versus non-fracture, and low versus high bone volume fraction, expecting similar and different loading histories, respectively. Our results indicate that the algorithm is voxel size independent within an average (maximum) error of 8.2% (32.9%) at 61 µm, but that the dependency increases considerably at voxel sizes bigger than 82 µm. In vitro and in vivo reproducibility are up to 4.5% and 10.2%, respectively, which is comparable to other in vitro studies and slightly higher than in other in vivo studies. Subjects with different bone volume fraction were clearly distinguished but not subjects with and without fracture. This is in agreement with bone adapting to customary loading but not to fall loads. We conclude that the in vivo bone loading estimation algorithm provides reproducible, sensitive and fairly voxel size independent results at up to 82 µm, but that smaller voxel sizes would be advantageous.

Keywords: HR-pQCT; bone loading estimation; human distal radius; reproducibility; sensitivity; voxel size dependency.

Figure 1.

Overview of the bone loading estimation algorithm. The bone microstructure is first assessed with high-resolution CT, and the greyscale images are segmented. Micro-FE models are then created, and unit load cases covering the physiologically possible loading directions are defined. Micro-FE analyses are subsequently run to calculate the tissue loading for each of these load cases. Finally, the unit loads are scaled using optimization to achieve a homogeneous tissue loading if the results of all scaled load cases are combined together. (Online version in colour.)

Figure 2.

Cross-sectional slice of the segmented micro-CT image of the human distal radius at the original voxel size of 25 µm and its downscaled versions as indicated in the top left corner to test the voxel size dependency of the bone loading estimation algorithm.

Figure 3.

Voxel size dependency of the bone loading estimation algorithm for the three load cases in the human distal radius. Each subject is represented with a single line.

Figure 4.

In vitro and in vivo reproducibility of the bone loading estimation algorithm for the three load cases in the human distal radius. Estimated loading is correlated with bone volume fraction, showing that the variation in estimated loading and bone volume fraction is much smaller within the three repeated measurements compared to the variation between subjects and thus within the population. For each subject, the three estimates are plotted using the same symbol whereas the symbols are different for each subject.