Testing Two Predictions for Fracture Load Using Computer Models of Trabecular Bone

Abstract

Aging induces several types of architectural changes in trabecular bone including thinning, increased levels of anisotropy, and perforation. It has been determined, on the basis of analysis of mathematical models, that reduction in fracture load caused by perforation is significantly higher than those due to equivalent levels of thinning or anisotropy. The analysis has also provided an expression which relates the fractional reduction of strength tau to the fraction of elements nu that have been removed from a network. Further, it was proposed that the ratio Gamma of the elastic constant of a sample and its linear response at resonance can be used as a surrogate for tau. Experimental validation of these predictions requires following architectural changes in a given sample of trabecular bone; techniques to study such changes using microcomputed tomography are only beginning to be available. In the present study, we use anatomically accurate computer models constructed from digitized images of bone samples for the purpose. Images of healthy bone are subjected to successive levels of synthetic degradation via surface erosion. Computer models constructed from these images are used to calculate their fracture load and other mechanical properties. Results from these computations are shown to be consistent with predictions derived from the analysis of mathematical models. Although the form of tau(nu) is known, parameters in the expression are expected to be sample-specific, and hence nu is not a reliable predictor of strength. We provide an example to demonstrate this. In contrast, analysis of model networks shows that the linear part of tau(Gamma) depends only on the structure of trabecular bone. Computations on models constructed from samples of iliac crest trabecular bone are shown to be in agreement with this assertion. Since Gamma can be computed from a vibrational assessment of bone, we argue that the latter can be used to introduce new surrogates for bone strength and hence diagnostic tools for osteoporosis.

Vertebral Osteoporosis and Trabecular Bone Quality

“…Alternative diagnostic strategies, such as digital X-ray radiogrammetry (DXR), 17 vibrational testing 78 and determining the genetic regulation of trabecular bone traits 18 are currently being investigated. Regardless of which diagnostic techniques become successful, it is clear that improvements on the current DXA and QCT methods are required if the important contribution of all aspects of bone quality to the fracture resistance of vertebral bone is to be taken into account.…”

“…47,48 Liebschner et al further developed this model and applied it to 3-D models of vertebral and iliac crest trabecular bone derived from lCT scans. 78 They demonstrated the potential for this technique to be used as a direct, non-destructive diagnostic tool for determining the mechanical integrity of trabecular structures. However, the technique has yet to be verified experimentally and issues such as the skin/tissue interface and distinguishing between cortical and trabecular bone have still to be addressed.…”

“…Finite element studies by Liebschner et al have shown that some vertical trabeculae are no longer part of the load transmission pathway as bone loss progresses and are therefore subjected to lower strains under normal loading conditions. 78 Such redundant vertical trabeculae would be subject to higher levels of resorption by adaptive remodelling.…”

“…42,131 The loss of complete trabeculae results in a significantly greater deterioration in mechanical properties than an equivalent bone reduction where trabeculae are thinned but not lost altogether. 33,48,49,78 In a finite element analysis study of human vertebral trabecular bone, Silva et al found that the modulus and strength values were at least twice as sensitive to reductions in the number of trabeculae as compared to uniform reductions in the thickness of trabeculae for the equivalent bone volume. 123 They found that bending was the predominant mode of deformation in the vertebral trabecular network, indicating that buckling due to loss of transverse trabecular cross-braces could have a significant effect.…”

Investigation of the mechanical interaction of the trabecular core with an external shell using rapid prototype and finite element models

“…The morphological and mechanical properties of trabecular bone cores have been extensively studied, using both finite element modelling (Eswaran et al, 2007a;Follet et al, 2007;Harrison et al, 2008;Homminga et al, 2003Homminga et al, , 2001Keaveny et al, 1994;Liebschner et al, 2005;Muller and Ruegsegger, 1995;Nazarian et al, 2006;Niebur et al, 2000;Verhulp et al, 2008;Yeni and Fyhrie, 2001) and experimental testing techniques (Arthur Moore and Gibson, 2002;Hulme et al, 2007;Keaveny, 1997;Nagaraja et al, 2005;Ohman et al, 2007;Perilli et al, 2008;Sran et al, 2007;Thomsen et al, 2002a), with the ultimate goal of improving fracture risk prediction. However, for vertebral bone it is widely acknowledged that the cortical shell also provides an important contribution to the load bearing ability of the whole bone (Andresen et al, 1998;Ito et al, 2002) and finite element studies have indicated that there is a mechanical interaction between the shell and the trabecular core which enhances the overall strength and stiffness properties of the whole vertebra Eswaran et al, 2007b).…”