Study of mechanical behavior of cancellous bone by Digital Volume Correlation and X-ray Micro-Computed Tomography

This paper presents a study of mechanical behavior of human cancellous bone during a compression loading. Mechanical test is performed inside an X-ray tomography device allowing us to generate a volume image for each loaded step. Digital Volume Correlation (DVC) process has been developed and applied on these volume images. Full 3D displacement field is determined by DVC leading to the calculation of all components of the strain tensor. Then, the evolution of strain repartitions in relation with trabecular structures can be shown. INTRODUCTION We have extended Digital Image Correlation technique (DIC) [1-4] to 3D case in order to measure 3D displacement field within solids [5-8]. This technique, named Digital Volume Correlation (DVC), needs volume images which contain a 3D grey level distribution following displacements of material. To obtain volume data, materials have been probed by X-ray Micro-Computed Tomography (XμCT). However, studied material needs to have variations of density in order to present contrast by X-rays. DVC coupled with XμCT allows us to determine the full 3D strain tensor in order to analyze 3D mechanical phenomena in the core of materials without hypothesis on any strain kinematics formulation and without using numerical simulation. Displacement field between reference and deformed states is determined on a 3D virtual grid by intercorrelation of the grey levels of the neighborhood surrounding a considered point. Several biomaterials, like cancellous bone, present naturally a contrast by X-ray due to density variation involved by its structure made of trabecula and porosities. DVC has already been employed to study trabecular bone for the development of the technique [5,6,9] or to evaluate its accuracy [10]. In this work, DVC and XμCT are used to study a bone sample during a loading test in order to improve the knowledge of mechanical behavior of human cancellous bone. For that, volume images are generated by a laboratory tomography device. The mechanical test is performed inside the tomography device and for each loaded state; we determine 3D displacement field and so all the components of the 3D strain tensor within the sample. These mappings show several strain localizations indicating some different mechanisms of deformation. DIGITAL VOLUME CORRELATION DIC technique which is usually used in mechanics to measure plane or 3D displacements of loading surfaces [14,11,12] has been extended to DVC for full 3D displacement and strain measurement [5-9]. The displacement field between a reference state and a deformed state is measured on a 3D virtual grid. The displacement of each point of this grid is calculated by intercorrelation of the grey levels of the neighborhood D surrounding the considered point in both states. D is composed of several voxels corresponding to a subset of the volume. By noting X and x the coordinates (in voxels) of a same point in the reference and the deformed states, both configurations are linked by the 3D material transformation φ: x = φ(X). For a subset D centered at the point X0 in the reference state, φ is approximated by its expansion at the first order corresponding to a rigid body motion combined with a homogeneous deformation: (1) ) ).( ( ) ( ) ( ) ( 0 0 0 X X X X U X U X X U X X − ∂ ∂ + + = + = φ Proceedings of the XIth International Congress and Exposition June 2-5, 2008 Orlando, Florida USA ©2008 Society for Experimental Mechanics Inc. The displacement U(X0) of the subset center gives the intensity (u,v,w) of the rigid body translation. The value of the local displacement gradient ) ( 0 X X U ∂ ∂ includes the rigid body rotation and the local stretch of the subset volume, it is characterized by 9 parameters:       ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂