by Keyword: Micromechanics

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Blanchard, R., Morin, C., Malandrino, A., Vella, A., Sant, Z., Hellmich, C., (2016). Patient-specific fracture risk assessment of vertebrae: A multiscale approach coupling X-ray physics and continuum micromechanics International Journal for Numerical Methods in Biomedical Engineering , 32, (9), e02760

Summary: While in clinical settings, bone mineral density measured by computed tomography (CT) remains the key indicator for bone fracture risk, there is an ongoing quest for more engineering mechanics-based approaches for safety analyses of the skeleton. This calls for determination of suitable material properties from respective CT data, where the traditional approach consists of regression analyses between attenuation-related grey values and mechanical properties. We here present a physics-oriented approach, considering that elasticity and strength of bone tissue originate from the material microstructure and the mechanical properties of its elementary components. Firstly, we reconstruct the linear relation between the clinically accessible grey values making up a CT, and the X-ray attenuation coefficients quantifying the intensity losses from which the image is actually reconstructed. Therefore, we combine X-ray attenuation averaging at different length scales and over different tissues, with recently identified 'universal' composition characteristics of the latter. This gives access to both the normally non-disclosed X-ray energy employed in the CT-device and to in vivo patient-specific and location-specific bone composition variables, such as voxel-specific mass density, as well as collagen and mineral contents. The latter feed an experimentally validated multiscale elastoplastic model based on the hierarchical organization of bone. Corresponding elasticity maps across the organ enter a finite element simulation of a typical load case, and the resulting stress states are increased in a proportional fashion, so as to check the safety against ultimate material failure. In the young patient investigated, even normal physiological loading is probable to already imply plastic events associated with the hydrated mineral crystals in the bone ultrastructure, while the safety factor against failure is still as high as five.

Keywords: Bone, Bone mass density, Continuum micromechanics, Elastoplasticity, Spine, Strength, X-ray physics

Malandrino, A., Fritsch, A., Lahayne, O., Kropik, K., Redl, H., Noailly, J., Lacroix, D., Hellmich, C., (2012). Anisotropic tissue elasticity in human lumbar vertebra, by means of a coupled ultrasound-micromechanics approach Materials Letters , 78, 154-158

The extremely fine structure of vertebral cortex challenges reliable determination of the tissue's anisotropic elasticity, which is important for the spine's load carrying patterns often causing pain in patients. As a potential remedy, we here propose a combined experimental (ultrasonic) and modeling (micromechanics) approach. Longitudinal acoustic waves are sent in longitudinal (superior-inferior, axial) as well as transverse (circumferential) direction through millimeter-sized samples containing this vertebral cortex, and corresponding wave velocities agree very well with recently identified 'universal' compositional and acoustic characteristics (J Theor Biol 287:115, 2011), which are valid for a large data base comprising different bones from different species and different organs. This provides evidence that the 'universal' organization patterns inherent to all the bone tissues of the aforementioned data base also hold for vertebral bone. Consequently, an experimentally validated model covering the mechanical effects of this organization patterns (J Theor Biol 244:597, 2007, J Theor Biol 260:230, 2009) gives access to the complete elasticity tensor of human lumbar vertebral bone tissue, as a valuable input for structural analyses aiming at patient-specific fracture risk assessment, e.g. based on the Finite Element Method.

Keywords: Human vertebra, Micromechanics, Tissue elasticity, Ultrasonics