A novel approach to estimate trabecular bone anisotropy from stress tensors

Abstract

Continuum finite element (FE) models of bones and bone-implant configurations are usually based on clinical CT scans. In virtually all of these models, material properties assigned to the bone elements are chosen as isotropic. It has been shown, however, that cancellous bone can be highly anisotropic and that its elastic behavior is best described as orthotropic. Material models have been proposed to derive the orthotropic elastic constants from measurements of density and a fabric tensor. The use of such relationships in FE models derived from CT scans, however, is hampered by the fact that the measurement of such a fabric tensor is not possible from clinical CT images since the resolution of such images is not good enough to resolve the trabecular micro-architecture. In this study, we explore an alternative approach that is based on the paradigm that bone adapts its micro-architecture to the loading conditions, hence that fabric and stress tensors should be aligned and correlated. With this approach, the eigenvectors and eigenvalues of the element continuum-level stress tensor are used as an estimate of the element fabric tensor, from which the orthotropic material properties then are derived. Using an iterative procedure, element orthotropic material properties and fabric tensors are updated until a converged situation is reached. The goals of this study were to investigate the feasibility and accuracy of such an iterative approach to derive orthotropic material properties for a human proximal femur and to investigate whether models derived in this way can provide more accurate results than isotropic models. Results were com- pared to those obtained from models of the same femurs for which the fabric was measured from micro-CT scans. It was found that the iterative approach could well estimate the orientation of the fabric principal directions. When comparing the stress/damage values in the models with material properties based on estimated and measured fabric tensors, the differences were not significant, suggesting that the material properties based on the estimated fabric tensor well reflected those based on the measured fabric tensor. Errors were less than those obtained when using isotropic models. It is concluded that this novel approach can provide a reasonable estimate of anisotropic material properties of cancellous bone. We expect that this approach can lead to more accurate results in particular for models used to study implants, which are usually anchored in highly anisotropic cancellous bone regions.

Statistical analysis of the inter-individual variations of the bone shape, volume fraction and fabric and their correlations in the proximal femur

“…However, this prediction error corresponds to previous studies [7][8][9]11,37]. Two alternative techniques were tested to improve the prediction of fabric orientation compared to the global alignment obtained by Procrustes; first bone fabric was aligned based on the local orientation of the elements.…”

“…However, since it is not possible to obtain images of the bone micro-structure in vivo, several methods have been proposed to determine the most probable bone fabric from clinical resolution scans of the patient's bone. Some authors proposed to estimate the local anisotropy based on the outer shape of the bone [3,4] or based on the principal directions obtained from FE calculations, either from the principal strains of a homogenous model [5] or during an iterative approach progressively refining the anisotropic directions based on the principle stresses [6,7].…”

Bone Volume Fraction and Fabric Anisotropy Are Better Determinants of Trabecular Bone Stiffness Than Other Morphological Variables

“…(43) Finally, research now focuses on deriving fabric anisotropy tensors from conventional CT imaging, either via gradient-based methods or mapping of mCT information. (44)(45)(46)(47) Nevertheless, morphological variables are still combined into multiple linear models to predict the mechanical properties of cancellous bone, (14)(15)(16)(17)21,45) but never compared to a combination BV/TV-fabric anisotropy. In this study, a systematic analysis of the stiffness and morphology of 743 samples extracted from femur, radius, iliac crest, and vertebral body was performed to determine the relevant predictors of the bone elastic properties.…”

A novel in silico method to quantify primary stability of screws in trabecular bone

“…Continuum FE models offer a great variety of interface modeling options ranging from perfect bonding to the inclusion of friction, cohesive forces between materials, detachment at predetermined thresholds as well as other non‐linear mechanical behaviors . However, in a typical continuum FE model, the trabecular bone micro‐architecture is modeled as a continuous material without any local porous characteristics . Continuum FE models usually account for density variations in the bone by assuming a relationship between the local CT Hounsfield numbers and the local mechanical properties.…”