Osteoporosis is a bone disease in which the bone mineral density (BMD) is reduced, bone microarchitecture is disrupted, and the amount and variety of non-collagenous proteins in bone is altered. However, as bone is a hierarchal complex 3D material system and its properties and functions are intrinsically linked to its underlying morphological and compositional details over a range of spatial scales, BMD is not an informative and reliable indicator of osteoporosis. In this project, we use camera, micro-CT scanner and digital image analyses to measure the bone micro-architecture and to carry out micromechanical testing of bone to refine and validate material models on bone damage and fracture due to osteoporosis.
In this thesis, a general formulation and subsequently selected algorithms are presented for high-accuracy 1D, 2D and 3D deformation measurements by correlation of a digital image pair. The new algorithm for 3D digital image correlation use higher order local deformation mapping functions and solve for the local deformation mapping parameters by an iterative Newton-Raphson method so that a perfect or nearly perfect correlation can be achieved for every subset region of an image pair. Besides, a MATLAB-based digital image correlation program for analyzing 3D micro-CT data is described. The program applies a local deformation mapping function, trilinear interpolation, and iterative nonlinear optimization to match subsets of a bone before and after deformation. The program computes a total of 12 parameters, including 3 displacement and their 9 gradient components, from which various 3D rigid body motion and deformation measures can be obtained. The developed program will be used to measure the mechanical properties of bone in the on-going bone mechanics research project.