Statistical osteoporosis models using composite finite elements: A parameter study

An in silico parametric model of vertebrae trabecular bone based on density and microstructural parameters to assess risk of fracture in osteoporosis

Osteoporosis is a progressive bone disease characterized by deterioration in the quantity and quality of bone, leading to inferior mechanical properties and an increased risk of fracture. Current assessment of osteoporosis is typically based on bone densitometry tools such as Quantitative Computed Tomography (QCT) and Dual Energy X-ray absorptiometry (DEXA). These assessment modalities mainly rely on estimating the bone mineral density (BMD). Hence present densitometry tools describe only the deterioration of the quantity of bone associated with the disease and not the affected morphology or microstructural changes, resulting in potential incomplete assessment, many undetected patients, and unexplained fractures. In this study, an in-silico parametric model of vertebral trabecular bone incorporating both material and microstructural parameters was developed towards the accurate assessment of osteoporosis and the consequent risk of bone fracture. The model confirms that the mechanical properties such as strength and stiffness of vertebral trabecular tissue are highly influenced by material properties as well as morphology characteristics such as connectivity, which reflects the quality of connected inter-trabecular parts. The FE cellular solid model presented here provides a holistic approach that incorporates both material and microstructural elements associated with the degenerative process, and hence has the potential to provide clinical practitioners and researchers with more accurate assessment method for the degenerative changes leading to inferior mechanical properties and increased fracture risk associated with age and/or disease such as Osteoporosis.

Validation of composite finite elements efficiently simulating elasticity of trabecular bone

Patient-specific analyses of the mechanical properties of bones become increasingly important for the management of patients with osteoporosis. The potential of composite finite elements (CFEs), a novel FE technique, to assess the apparent stiffness of vertebral trabecular bone is investigated in this study. Segmented volumes of cylindrical specimens of trabecular bone are compared to measured volumes. Elasticity under uniaxial loading conditions is simulated; apparent stiffnesses are compared to experimentally determined values. Computational efficiency is assessed and recommendations for simulation parameters are given. Validating apparent uniaxial stiffnesses results in concordance correlation coefficients 0.69 ≤ r(c) ≤ 0.92 for resolutions finer than 168 μm, and an average error of 5.8% between experimental and numerical results at 24 μm resolution. As an application, the code was used to compute local, macroscopic stiffness tensors for the trabecular structure of a lumbar vertebra. The presented technique allows for computing stiffness using smooth FE meshes at resolutions that are well achievable in peripheral high resolution quantitative CT. Therefore, CFEs could be a valuable tool for the patient-specific assessment of bone stiffness.

Long range node-strut analysis of trabecular bone microarchitecture

PURPOSE

We present a new morphometric measure of trabecular bone microarchitecture, called mean node strength (NdStr), which is part of a newly developed approach called long range node-strut analysis. Our general aim is to describe and quantify the apparent "latticelike" microarchitecture of the trabecular bone network.

METHODS

Similar in some ways to the topological node-strut analysis introduced by Garrahan et al. [J. Microsc. 142, 341-349 (1986)], our method is distinguished by an emphasis on long-range trabecular connectivity. Thus, while the topological classification of a pixel (after skeletonization) as a node, strut, or terminus, can be determined from the 3 × 3 neighborhood of that pixel, our method, which does not involve skeletonization, takes into account a much larger neighborhood. In addition, rather than giving a discrete classification of each pixel as a node, strut, or terminus, our method produces a continuous variable, node strength. The node strength is averaged over a region of interest to produce the mean node strength of the region.

RESULTS

We have applied our long range node-strut analysis to a set of 26 high-resolution peripheral quantitative computed tomography (pQCT) axial images of human proximal tibiae acquired 17 mm below the tibial plateau. We found that NdStr has a strong positive correlation with trabecular volumetric bone mineral density (BMD). After an exponential transformation, we obtain a Pearson's correlation coefficient of r = 0.97. Qualitative comparison of images with similar BMD but with very different NdStr values suggests that the latter measure has successfully quantified the prevalence of the "latticelike" microarchitecture apparent in the image. Moreover, we found a strong correlation (r = 0.62) between NdStr and the conventional node-terminus ratio (Nd∕Tm) of Garrahan et al. The Nd∕Tm ratios were computed using traditional histomorphometry performed on bone biopsies obtained at the same location as the pQCT scans.

CONCLUSIONS

The newly introduced morphometric measure allows a quantitative assessment of the long-range connectivity of trabecular bone. One advantage of this method is that it is based on pQCT images that can be obtained noninvasively from patients, i.e., without having to obtain a bone biopsy from the patient.