The aim of the current study was to develop quantitative computed-tomography (QCT)-based bone-strength indicators that highly correlate with finite-element (FE)-based strength. We perform a combined numerical-experimental study, comparing FE-predicted surface strains with strain gauge measurements, to validate the FE models of 36 long bones (humerus, radius, femur and tibia) under three-point bending and torsion. The FE models were constructed from trans-axial volumetric CT scans, and the segmented bone images were corrected for partial-volume effects. The material properties (Young's modulus for cortex, density-modulus relationship for trabecular bone and Poisson's ratio) were calibrated by minimizing the error between experiments and simulations among all bones. The resultant R2 values of the measured strains versus load under three-point bending and torsion were 0.96-0.99 and 0.61-0.99, respectively, for all bones in our data set. The errors of the calculated FE strains in comparison to those measured using strain gauges in the mechanical tests ranged from -6% to 7% under bending and from -37% to 19% under torsion. The observation of comparatively low errors and high correlations between the FE-predicted strains and the experimental strains, across the various types of bones and loading conditions (bending and torsion), validates our approach to bone segmentation and our choice of material properties.
Based on the analysis of the various FE models of the long bones, the location of the CT slice on the bone that showed the highest propensity to fracture was identified for four loading conditions (compression, three-point bending, cantilever bending and torsion). The identified CT slice was then used to derive novel and improved bone-strength indicators. We evaluated the performance of area-weighted (AW), density-weighted (DW) and modulus-weighted (MW) rigidity measures as well as popular strength indicators like section modulus and stress-strain index. We have also developed a novel strength metric, the centroid deviation, which takes into consideration the spatial distribution of the centroids. Here, we observed that the MW polar moment of inertia and the MW moment of inertia were the two top-performers (average r < 0.87) for all bones and loading conditions. The MW centroid deviations correlated highly with the load to fracture for all bones under compression (r <0.83), except for the humerus (r = 0.67).
To test the power of the bone-strength indicators, a receiver operating characteristic (ROC) analysis of the MW rigidity measures that showed the two highest correlations in the femur under compression and three-point bending was performed. QCT scans of a subset of 10 white and 10 black males, who were subjects of a larger study, which reported ethnic differences in bone strength, were used. Results from this small pilot study indicated that the MW section modulus and the MW stress-strain index are the two top performing indicators (area under the ROC curve < 0.79).
Consistently DW or MW rigidity measures produced a statistically significant improvement in capturing bone strength compared to AW rigidity measures. The improvement in MW over DW rigidity measures was small yet statistically significant.