Fast Trabecular Bone Strength Predictions of HR-pQCT and Individual Trabeculae Segmentation–Based Plate and Rod Finite Element Model Discriminate Postmenopausal Vertebral Fractures

Abstract

While high-resolution peripheral quantitative computed tomography (HR-pQCT) has advanced clinical assessment of trabecular bone microstructure, nonlinear microstructural finite element (μFE) prediction of yield strength by HR-pQCT voxel model is impractical for clinical use due to its prohibitively high computational costs. The goal of this study was to develop an efficient HR-pQCT-based plate and rod (PR) modeling technique to fill the unmet clinical need for fast bone strength estimation. By using individual trabecula segmentation (ITS) technique to segment the trabecular structure into individual plates and rods, a patient-specific PR model was implemented by modeling each trabecular plate with multiple shell elements and each rod with a beam element. To validate this modeling technique, predictions by HR-pQCT PR model were compared with those of the registered high resolution μCT voxel model of 19 trabecular sub-volumes from human cadaveric tibiae samples. Both Young’s modulus and yield strength of HR-pQCT PR models strongly correlated with those of μCT voxel models (r2=0.91 and 0.86). Notably, the HR-pQCT PR models achieved major reductions in element number (>40-fold) and CPU time (>1,200-fold). Then, we applied PR model μFE analysis to HR-pQCT images of 60 postmenopausal women with (n=30) and without (n=30) a history of vertebral fracture. HR-pQCT PR model revealed significantly lower Young’s modulus and yield strength at the radius and tibia in fracture subjects compared to controls. Moreover, these mechanical measurements remained significantly lower in fracture subjects at both sites after adjustment for aBMD T-score at the ultradistal radius or total hip. In conclusion, we validated a novel HR-pQCT PR model of human trabecular bone against μCT voxel models and demonstrated its ability to discriminate vertebral fracture status in postmenopausal women. This accurate nonlinear μFE prediction of HR-pQCT PR model, which requires only seconds of desktop computer time, has tremendous promise for clinical assessment of bone strength.

Trabecular plates and rods determine elastic modulus and yield strength of human trabecular bone

“…This idealized study provided fundamental assessment of PR μFE models in predicting mechanical properties of trabecular bone, independent of biological variations among human bone specimens and image noises existing in the imaging process. We have also applied PR μFE models on clinical HRpQCT images and demonstrated the ability of HRpQCT-based μFE PR models to predict bone strength and discriminate postmenopausal women with and without vertebral fractures [20]. Elastic modulus and yield strength predicted by HRpQCT-based PR models were strongly correlated with those by voxel models.…”

“…Recently, we examined the accuracy and efficiency of the PR modeling strategy in an idealized, synthetic trabecular bone structure model, and demonstrated that the Young's modulus that was predicted by the ITS-based PR model correlated strongly with those by the voxel-based model at various voxel sizes [19]. Additionally, conversion from the voxel model to the PR model resulted in a 47-fold reduction in the number of elements [20]. Independently, Vanderoost et al developed specimen-specific skeleton based beam-shell μFE models for simulating trabecular bone elastic modulus [36].…”

Vertebral deformities and fractures are associated with MRI and pQCT measures obtained at the distal tibia and radius of postmenopausal women

“…These associations are not surprising because vertebral deformities are manifestations of mechanical impairment of the cortical and trabecular network. A recent study by Liu et al also reported that trabecular bone measures derived from distal extremities using HR-pQCT-based finite element analysis discriminate postmenopausal women with and without prevalent vertebral fractures [53]. …”

Modelling of bone fracture and strength at different length scales: a review

“…Next, we will briefly outline several representative studies modelling strength, damage, fracture and softening mechanisms of a single trabecula and trabecular bone. Different approaches have been employed including elastic-plastic constitutive laws and progressive damage evolution by element deletion [187][188][189][190][191][192][193][194][195][196][197][198][199][200][201]. Due to the complex architecture of trabecular bone, many of the models used micro-computed tomography (mCT) based three-dimensional voxel FEM models, which give an accurate representation of trabecular bone geometry [192][193][194][195].…”