Resumen de Mechanical and morphometric characterization of cancellous bone
Bone fracture is a social health problem of increasing magnitude because of its prevalence in aged population due to osteoporosis. Bone quality is often characterized by bone mineral density (BMD) measured at cancellous bone regions using dual-energy X-ray absorptiometry (DXA). However, BMD alone cannot predict several cases because not only density is important, but also microstructure plays an important role in cancellous bone strength. The mechanical properties can be used as indicators of bone integrity as a function of age, disease or treatment. Therefore, cancellous bone fracture characterization and its relationship to microstructure has not been completely solved in the literature and is relevant to improve fracture prediction.
In this thesis, we aim at characterizing cancellous bone morphometry and mechanical behavior. Morphometry is estimated through the analysis of micro-computed tomography (micro-CT) images of vertebral cancellous bone specimens. With regards to the mechanical behavior, we calculate elastic, yield and failure properties at the apparent and tissue levels. To determine them, we followed different approaches: compression tests, finite element models and micro-CT phantoms.
We have developed finite element models that reproduce the elastic and failure response of cancellous bone under compression conditions. We modeled failure as a combination of continuum damage mechanics and the element deletion technique. The numerical models permitted to estimate elastic and failure properties. Failure properties were consistent with results reported in the literature. Specifically, our results revealed that yield strain is relatively constant (0.7 %) over a range of apparent densities, while failure strain presents a wider range of variation. A single strain parameter (equivalent strain) was found as an accurate descriptor of cancellous bone compression failure.
Image-based numerical models usually need for the action of a technician to segment the images. Therefore, we studied the sensitivity to variations of the segmentation threshold on the morphometry and the elastic properties of vertebral cancellous bone specimens of different bone volume fractions. The apparent modulus is highly sensitive to the segmentation threshold. We report variations between 45 and 120 % for a ± 15 % threshold variation. Other parameters, such as BS/BV, BS/TV, Tb.Sp, Tb.N, Conn.D and fractal dimension were influenced significantly.
Digital image correlation (DIC) was applied to images taken during compression testing to analyze displacement fields at failure and characterize them. Some variables were explored to describe failure and a study is done about how DIC parameters influence the strain field obtained. Facet and step sizes have a relevant effect on the failure strain estimation, and an increment of both parameters reduces the strain estimation up to 40 %. Besides, several parameters combination led to correct failure pattern detection, so values reported in the literature should be referred to the parameters used. Furthermore, we explored if cancellous bone microstructure acts (non-speckle/texture approach) as a proper pattern to calculate displacements using DIC technique.
As regards relationships between microstructure and mechanics, single and multiple parameter analysis were performed to assess the morphometric variables that control the explanation of mechanical properties variation. Bone volume fraction (BV/TV), bone surface to volume ratio (BS/BV), mean trabecular thickness (Tb.Th) and fractal dimension (D) presented the best linear correlations to the elastic properties, while both the yield and failure strains did not show correlation to any morphometric parameter. The regressions obtained permit to estimate those mechanical properties that describe the state of a specimen.
