Patient-specific fracture risk assessment of vertebrae: A multiscale approach coupling X-ray physics and continuum micromechanics.

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. Copyright © 2016 John Wiley & Sons, Ltd.

Placement of trans-sternal wires according to an ellipsoid pressure vessel model of sternal forces.

Dehiscence of median sternotomy wounds remains a clinical problem. Wall forces in thin-walled pressure vessels can be calculated by membrane stress theory. An ellipsoid pressure vessel model of sternal forces is presented together with its application for optimal wire placement in the sternum. Sternal forces were calculated by computational simulation using an ellipsoid chest wall model. Sternal forces were correlated with different sternal thicknesses and radio-density as measured by computerized tomography (CT) scans of the sternum. A comparison of alternative placement of trans-sternal wires located either at the levels of the costal cartilages or the intercostal spaces was made. The ellipsoid pressure vessel model shows that higher levels of stress are operative at increasing chest diameter (P < 0.001). CT scans show that the thickness of the sternal body is on average 3 mm and 30% thicker (P < 0.001) and 53% more radio-dense (P < 0.001) at the costal cartilage levels when compared with adjacent intercostal spaces. This results in a decrease of average sternal stress from 438 kPa at the intercostal space level to 338 kPa at the costal cartilage level (P = 0.003). Biomechanical modelling suggests that placement of trans-sternal wires at the thicker bone and more radio-dense level of the costal cartilages will result in reduced stress.