On Identification Methodology of Three-dimensional Displacement Field in Inhomogeneous Body by X-Ray CT Images

A material test system combined with X-ray computed tomography (CT) is newly developed for material characterization of biological tissue in non-invasive manner. An identification method is investigated for internal displacement field of inhomogeneous body through the CT images from the system. Two voxel models are constituted by laying up thicken pixels of the cross-sectional tomograms taken under unloaded and loaded conditions. Representing the displacement field in terms of the Fourier series, we pose an inverse problem to identify unknown Fourier coefficients by using unloaded and actually loaded voxel models. A virtually deformed voxel model is embodied through an image processing technique to transform the unloaded voxel model via the tentative Fourier series. An error function between actually loaded and virtually deformed voxel model is defined by the voxel values, which indicate brightness of voxels. The error is minimized with respect to unknown coefficients by means of the SCE-UA method (Shuffled Complex Evolution Method Developed at the University of Arizona). The validity of the proposed method is demonstrated through an experimental example.