How morphology predicts mechanical properties of trabecular structures depends on intra-specimen trabecular thickness variations

Two observations underlie this work. First, that the architecture of trabecular bone can accurately predict the mechanical stiffness characteristics of bone specimens when considering the combination of volume fraction and fabric, which is a measure of architectural anisotropy. Second, that the same morphological measures could not accurately predict the mechanical properties of porous structures in general. We hypothesize that this discrepancy can be explained by the special nature of trabecular bone as a structure in remodeling equilibrium relative to the external loads. We tested this hypothesis using a generic model of trabecular bone. Five series of 153 different architectures were created with this model. Each architecture was subjected to morphological analysis, and four different fabric measures were calculated to evaluate their effectiveness in characterizing the architecture. Relationships were determined relating morphology to the elastic constants. The quality of these relationships was tested by correlating the predicted elastic constants with those determined from finite element analysis. We found that the four fabric measures used could estimate the mechanical properties almost equally well. So the suggestion that fabric measures based on trabecular bone volume better represent the architecture than mean intercept length could not be affirmed. We conclude that for structures with equally sized elliptical voids the mechanical properties can be predicted well only if trabecular thickness variations within each structure are limited. These structures closely resemble previously developed models of trabecular bone. Furthermore, they are stiff in the principal fabric direction, hence, according to Cowin (J. Biomech. Eng. (108) (1986) 83), they are in remodeling equilibrium. These structures are also stiff over a large range of loading orientations, hence, are relatively insensitive to deviations in direction of loading

Effects of mechanical forces on maintenance and adaptation of form in trabecular bone

The architecture of trabecular bone, the porous bone found in the spine and at articulating joints, provides the requirements for optimal load transfer, by pairing suitable strength and stiffness to minimal weight according to rules of mathematical design. But, as it is unlikely that the architecture is fully pre-programmed in the genes, how are the bone cells informed about these rules, which so obviously dictate architecture? A relationship exists between bone architecture and mechanical usage while strenuous exercise increases bone mass9, disuse, as in microgravity and inactivity, reduces it. Bone resorption cells (osteoclasts) and bone formation cells (osteoblasts) normally balance bone mass in a coupled homeostatic process of remodelling, which renews some 25% of trabecular bone volume per year. Here we present a computational model of the metabolic process in bone that confirms that cell coupling is governed by feedback from mechanical load transfer.This model can explain the emergence and maintenance of trabecular architecture as an optimal mechanical structure, as well as its adaptation to alternative external loads

Subject-specific bone loading estimation in the human distal radius

High-resolution in vivo bone micro-architecture assessment, as possible now for the distal forearm, in combination with bone remodelling simulation algorithms could, eventually, predict patient-specific bone morphology changes. To simulate load-adaptive bone remodelling, however, physiological loading conditions must be defined. In this paper we test a previously developed algorithm to estimate such physiological loading conditions from the bone micro-architecture. The aims of this study were to investigate if realistic boundary forces and moments are predicted for the scanned distal radius section and how these predicted forces and moments should be distributed to the scanned section in order to obtain a load transfer similar to that in situ. Images at in vivo resolution were generated for the clinically measured section of nine distal radius cadaver bones, converted to micro-finite element models and used for load estimation. Models of the full distal radius were created to analyse tissue loading distributions of the sections in situ. It was found that predicted forces and moments at the boundaries of the scanned region varied considerably but, when translated to equivalent radiocarpal joint forces, agreed well with values reported in the literature. Bone tissue loading distribution was in best agreement with in situ distributions when loading was applied to an extra layer of material at both ends of the clinical scan region. The agreement of the predicted loading to previous studies and the wide range of predicted loading values indicate that subject-specific bone loading estimation is possible and necessary

Technical note: cortical thickness and density estimation from clinical CT using a prior thickness-density relationship

\u3cp\u3ePurpose: Cortical thickness and density are critical components in determining the strength of bony structures. Computed tomography (CT) is one possible modality for analyzing the cortex in 3D. In this paper, a model-based approach for measuring the cortical bone thickness and density from clinical CT images is proposed. Methods: Density variations across the cortex were modeled as a function of the cortical thickness and density, location of the cortex, density of surrounding tissues, and imaging blur. High resolution micro-CT data of cadaver proximal femurs were analyzed to determine a relationship between cortical thickness and density. This thickness-density relationship was used as prior information to be incorporated in the model to obtain accurate measurements of cortical thickness and density from clinical CT volumes. The method was validated using micro-CT scans of 23 cadaver proximal femurs. Simulated clinical CT images with different voxel sizes were generated from the micro-CT data. Cortical thickness and density were estimated from the simulated images using the proposed method and compared with measurements obtained using the micro-CT images to evaluate the effect of voxel size on the accuracy of the method. Then, 19 of the 23 specimens were imaged using a clinical CT scanner. Cortical thickness and density were estimated from the clinical CT images using the proposed method and compared with the micro-CT measurements. Finally, a case-control study including 20 patients with osteoporosis and 20 age-matched controls with normal bone density was performed to evaluate the proposed method in a clinical context. Results: Cortical thickness (density) estimation errors were 0.07 ± 0.19 mm (-18 ± 92 mg/cm\u3csup\u3e3\u3c/sup\u3e) using the simulated clinical CT volumes with the smallest voxel size (0.33 × 0.33 × 0.5 mm\u3csup\u3e3\u3c/sup\u3e), and 0.10 ± 0.24 mm (-10 ± 115 mg/cm\u3csup\u3e3\u3c/sup\u3e) using the volumes with the largest voxel size (1.0 × 1.0 × 3.0 mm\u3csup\u3e3\u3c/sup\u3e). A trend for the cortical thickness and density estimation errors to increase with voxel size was observed and was more pronounced for thin cortices. Using clinical CT data for 19 of the 23 samples, mean errors of 0.18 ± 0.24 mm for the cortical thickness and 15 ± 106 mg/cm\u3csup\u3e3\u3c/sup\u3e for the density were found. The case-control study showed that osteoporotic patients had a thinner cortex and a lower cortical density, with average differences of -0.8 mm and -58.6 mg/cm\u3csup\u3e3\u3c/sup\u3e at the proximal femur in comparison with age-matched controls (p-value <0.001). Conclusions: This method might be a promising approach for the quantification of cortical bone thickness and density using clinical routine imaging techniques. Future work will concentrate on investigating how this approach can improve the estimation of mechanical strength of bony structures, the prevention of fracture, and the management of osteoporosis.\u3c/p\u3

Correlation between pre-operative periprosthetic bone density and post-operative bone loss in THA can be explained by strain-adaptive remodelling

Periprosthetic adaptive bone remodelling after total hip arthroplasty can be simulated in computer models, combining bone remodelling theory with finite element analysis. Patient specific three-dimensional finite element models of retrieved bone specimens from an earlier bone densitometry (DEXA) study were constructed and bone remodelling simulations performed. Results of the simulations were analysed both qualitatively and quantitatively. Patterns of predicted bone loss corresponded very well with the DEXA measurements on the retrievals. The amount of predicted bone loss, measured quantitatively by simulating DEXA on finite element models, was found to be inversely correlated with the initial bone mineral content. It was concluded that the same clinically observed correlation can therefore be explained by mechanically induced remodelling. This finding extends the applicability of numerical pre-clinical testing to the analysis of interaction between implant design and initial state of the bone