Computational finite element bone mechanics accurately predicts mechanical competence in the human radius of an elderly population
Research highlights
► Accurate estimation of radius bone strength as assessed by μFE analyses. ► Distal volumes of interest better predict bone strength than more proximal ones. ► Most relevant VOI to determine bone strength is located below the subchondral plate. ► New parameter settings using the strain-based failure criterion are presented. ► HR-pQCT derived μFE analysis is a promising way to assess bone strength.
Introduction
Osteoporosis is recognized as a major public health problem worldwide, leading to reduced bone strength and an increase in fractures. Fractures in the region of the distal radius are among the most common in humans and their incidence is increasing due to the aging population. Osteoporosis reduces bone strength through a loss of bone mass and diminished structural integrity. Bone loss can be assessed easily and accurately with dual-energy X-ray absorptiometry (DXA) and was shown to correlate with mechanical strength and bone fracture risk [1], [2]. For this reason, estimates of bone strength are nowadays typically based on areal bone mineral density (aBMD) measurements. However, aBMD is not a direct measure of bone strength and is not sufficient to predict bone strength in individual patients. It has been shown that predicting trabecular bone strength can be improved by including microarchitectural parameters in the analysis [3], [4]. Indeed, the decrease in bone mass and the removal of structural elements have been shown to result in an increased fracture incidence [5], [6]. Furthermore, distal radius volumetric BMD (vBMD) and microstructural indices better discriminated 35 postmenopausal women with mixed fractures from 78 postmenopausal women without fractures than aBMD of the hip or spine [7].
With the introduction of a new generation of high-resolution 3D peripheral quantitative computed tomography (HR-pQCT) systems, direct quantification of structural bone parameters has become possible in living patients. In addition, it is now possible to estimate bone strength directly using micro-finite element (μFE) analysis [8]. It was recently found that estimated load/strength ratios as assessed by μFE analysis at the ultradistal radius more closely simulated patterns of wrist fractures occurring in the same population than did measurements of vBMD [9]. Furthermore, in human cadaveric forearms good agreement was demonstrated between estimated bone strength as assessed by μFE analyses and those measured using mechanical testing [10]. The μFE estimated bone strength predicted the measured bone strength significantly better than bone densitometry [11]. The good predictive capability of μFE estimated bone strength was confirmed for more recent HR-pQCT systems that provide an improved nominal resolution of 82 μm. MacNeil and Boyd have also shown that both the experimentally and computationally determined bone stiffness are excellent predictors of bone strength [12]. Furthermore, the potential of HR-pQCT based μFE to identify people at risk of distal radius fracture has been demonstrated [13]. In addition, it has been shown that bone geometry, microstructure and strength contribute to forearm fractures in postmenopausal women, as does BMD, and that these additional determinants of risk promise greater insight into fracture pathogenesis [14]. Consequently, HR-pQCT provides a non-invasive and clinically useful measure of 3D micro-architecture at the distal radius, and these data are adequate to estimate bone strength using patient-specific finite element models.
Yet, images from only a relatively small part of the radius are acquired (9.02 mm field of view in axial direction) as recommended by the manufacturer for clinical measurements of the forearm. So far, no studies are available assessing bone strength in different measurement volumes of interest in a larger patient population. Furthermore, μFE bone strength estimates of former clinical studies were assessed using a failure criterion developed by Pistoia et al. [10]. Specifically, this criterion defines bone strength as the force at which 2% of the bone volume is strained above 0.7% effective strain. Due to improvements in image resolution and differences in the clinically measured volume of interest it is questionable if this criterion is still valid. Even more so, the dependency of the criterion on the measured bone volume is debatable. Therefore, two hypotheses were tested in this study. First, we hypothesized that regions with thinner cortices, hence, regions closer to the subchondral plate than currently recommended, would improve the bone strength prediction at the distal radius. We tested this hypothesis by using μFE predictions of estimated bone strength as well as by a visualization of the failure behavior using image-guided failure analysis (IGFA). Second, we hypothesized that the estimated bone strength would be improved when the criterion would be independent of the measured volume of interest. Acceptance of these hypotheses might influence future clinical studies, by which human radius bone strength estimations will be performed, a focus which has been developing quickly over the last years.
Section snippets
Specimens
A sample group of 163 embalmed human cadavers was investigated, from which results have been presented in different studies up to this date [2], [15], [16], [17], [18]. In line with German legislative requirements, the donors had dedicated their bodies to the Institute of Anatomy of the Ludwig-Maximilians-University (LMU) Munich prior to death. The intact forearms were detached at the distal humerus. Based on different exclusion criteria, as previously reported [18], the final sample included
Results
The tissue-level stresses and strains were calculated for all VOIs. Marked differences in strain distribution were found when going from the most distal VOI to more proximal ones (Fig. 2). RMSE values depended strongly on Vcrit (Fig. 3). For all VOIs an optimal Vcrit could be found that minimized RMSE. Smallest RMSE values were found for VOI FB, and were closely followed by the distal VOIs. The minimal RMSE values, either expressed in absolute or relative terms, differed strongly for the
Discussion
The first hypothesis that regions closer to the subchondral plate would improve the bone strength prediction at the distal radius compared to the recommended measurement region was accepted. When investigating the strengths of the associations between the estimated and the measured bone strength, VOI 1 best predicted measured bone strength (RMSE = 511 N) with RMSE increasing and correlation coefficients decreasing towards more proximal VOIs (Table 1). VOI 1B, recommended by the manufacturer,
Acknowledgments
This work was supported in part by the AO Foundation (network grant CPP1) and Swiss National Science Foundation (FP 620-58097.99). Computational time was granted by the Swiss National Supercomputing Centre (CSCS).
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