Accuracy of Individual Trabecula Segmentation Based Plate and Rod Finite Element Models in Idealized Trabecular Bone Microstructure

Abstract

Currently, specimen-specific micro finite element (lFE) analysis based micro computed tomography (lCT) images have become a major computational tool for the assessment of the mechanical properties of human trabecular bone. Despite the fine characterization of the three-dimensional (3D) trabecular microstructure based on high-resolution lCT images, conventional lFE models with each voxel converted to an element are not efficient in predicting the nonlinear failure behavior of bone due to a prohibitive computational cost. Recently, a highly efficient individual trabecula segmentation (ITS)-based plate and rod (PR) modeling technique has been developed by substituting individual plates and rods with shell and beam elements, respectively. In this technical brief, the accuracy of novel PR lFE models was examined in idealized microstructure models over a broad range of trabecular thicknesses. The Young's modulus and yield strength predicted by simplified PR models strongly correlated with those of voxel models at various voxel sizes. The conversion from voxel models to PR models resulted in an $762-fold reduction in the largest model size and significantly accelerated the nonlinear FE analysis. The excellent predictive power of the PR lFE models, demonstrated in an idealized trabecular microstructure, provided a quantitative mechanical basis for this promising tool for an accurate and efficient assessment of trabecular bone mechanics and fracture risk.

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

“…(27,33,57,58) Therefore, the modeling strategy of including the trabecular plate as a major element type is critical for accurate assessment of mechanical parameters of trabecular bone with a broad range of BV/TV values from severely osteoporotic to healthy. The feasibility of the PR modeling strategy was tested in our recent studies in both idealized structure (59) and high-resolution µCT images of human trabecular bone (34) and there was excellent agreement between model predictions and mechanical testing results. Independent from our work, a different approach was proposed by Vanderoost and colleagues (60) to simplify the voxel FE model to a combination of shell and beam elements and linear elastic analysis was implemented in their models for assessing apparent Young's modulus.…”

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

“…The feasibility of our PR μFE modeling approach has been quantified in idealized plate and rod microstructural models, which were made of either a combination of two plates and four rods or purely eight interconnected rods in a unit cell [38]. Excellent agreement was found between the mechanical properties calculated from PR models and the corresponding voxel models, such as elastic modulus and yield strength.…”

“…Alternatively, specimen specific, voxel-based μFE models do not make any assumption regarding trabecular types but fully represent the original 3D trabecular microarchitecture. 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].…”

Biomechanics and Mechanobiology of Trabecular Bone: A Review

“…They decomposed the trabecular bone into its volu metric elements using skeletonization, optimization, and multi color dilation algorithms (Fig. Wang et al [149] examined the accuracy of this conversion by constructing idealized pla te-rod and rod-rod microstructures at typical //CT resolution. The advantage of ITS is that it reduces the computational effort for finite element analysis and also examines the contribution of each component to the mechani cal properties of trabecular bone.…”