A novel approach to estimate trabecular bone anisotropy using a database approach

Abstract

Continuum finite element (FE) models of bones have become a standard pre-clinical tool to estimate bone strength. These models are usually based on clinical CT scans and material properties assigned are chosen as isotropic based only on the density distribution. It has been shown, however, that trabecular bone elastic behavior is best described as orthotropic. Unfortunately, the use of orthotropic models in FE analysis derived from CT scans is hampered by the fact that the measurement of a trabecular orientation (fabric) is not possible from clinical CT images due to the low resolution of such images. In this study, we explore the concept of using a database (DB) of high-resolution bone models to derive the fabric information that is missing in clinical images. The goal of this study was to investigate if models with fabric derived from a relatively small database can already produce more accurate results than isotropic models. A DB of 33 human proximal femurs was generated from micro-CT scans with a nominal isotropic resolution of 82 µm. Continuum FE models were generated from the images using a pre-defined mesh template in combination with an iso-anatomic mesh morphing tool. Each element within the mesh template is at a specific anatomical location. For each element within the cancellous bone, a spherical region around the element centroid with a radius of 2mm was defined. Bone volume fraction and the mean-intercept-length fabric tensor were analyzed for that region. Ten femurs were used as test cases. For each test femur, four different models were generated: (1) an orthotropic model based on micro-CT fabric measurements (gold standard), (2) an orthotropic model based on the fabric derived from the best-matched database model, (3) an isotropic-I model in which the fabric tensor was set to the identity tensor, and (4) a second isotropic-II model with its total bone stiffness fitted to the gold standard. An elastic-plastic damage model was used to simulate failure and post failure behavior during a fall to the side. The results show that all models produce a similar stress distribution. However, compared to the gold standard, both isotropic-I and II models underestimated the stress/damage distributions significantly. We found no significant difference between DB-derived and gold standard models. Compared to the gold standard, the isotropic-I models further underestimated whole bone stiffness by 26.3% and ultimate load by 14.5%, while these differences for the DB-derived orthotropic models were only 4.9% and 3.1% respectively. The results indicate that the concept of using a DB to estimate patient-specific anisotropic material properties can considerably improve the results. We expect that this approach can lead to more accurate results in particular for cases where bone anisotropy plays an important role, such as in osteoporotic patients and around implants.

Prediction of apparent trabecular bone stiffness through fourth-order fabric tensors

“…Moreover, fabric tensors estimated through machine learning approaches will be considered (Lekadir et al 2015;Hazrati Marangalou et al 2013). In addition, we plan to apply the proposed model to trabecular bone from different skeletal sites and with different degrees of osteoporosis.…”

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements

“…Microcomputed tomography (μCT) images (37μm voxel size) performed on femoral heads and vertebral bodies were obtained from two previous studies (Lochmüller et al 2008, Marangalou et al 2013 Seven trabecular biopsies were extracted from the vertebral scans (4 male and 2 female donors, 70 ± 6.5 yrs) and thirteen from the femoral ones (2 female donors, 81 and 95 years).…”

Importance of trabecular anisotropy in finite element predictions of patellar strain after Total Knee Arthroplasty

“…Therefore, patellar isotropic models should be used with caution and account for possible inaccuracy. Alternatively, when bone anisotropy cannot be measured directly, a generic or statistical map of anisotropy could be applied to the patella [23] or it can be obtained with template registration approach [24] .…”