Digital image correlation of bone sequential microscopic observations

Abstract

A method of image correlation is presented to study sequential microscopic observations of human Haversian cortical bone. Imaging biological tissues is sometimes challenging owing to their complex microstructures in particular when microcracks appear. Bone microfractures can be studied in micro compression tests where the progressive growth of small cracks is imaged by light microscopy. The two-dimensional displacement field on the sample surface is then tracked by various digital image correlation methods based on cross-correlation formulation. Because of the potential high number of sequential observations, the method calculates the displacements at given growth steps obtained either by direct comparison of the studied step and the undeformed initial state, called 'direct correlation', or by iterative comparisons of successive pairs of observations, called 'gradual correlation'. In the gradual procedure, two cases are studied, referred to as 'invariant gradual correlation' and 'varying gradual correlation', when the correlation domain is transferred till the last observation or reinitialised for each image pairs. As bone is highly heterogeneous, two types of correlation procedures are considered with or without domain partition (WDP or WODP) delimiting material and strong discontinuities. The precision of the methods is specifically evaluated for experimental observations.

Displacement Discontinuity or Complex Shape of Sample: Assessment of Accuracy and Adaptation of Local DIC Approach

“…Two DIC approaches exist: global DIC or local DIC. In this article, we consider only local DIC process . In this case, the determination of displacement at a point is performed on a subset D , usually squared, surrounding this point.…”

“…In this case, the determination of displacement at a point is performed on a subset D , usually squared, surrounding this point. Other shapes of D (circular or any shape) are used for particular applications . The subset D is selected in the reference image and used to find its location in the deformed image assuming a homogeneous material transformation ϕ inside D .…”

“…The use of a mask permits to directly exclude some subsets or to make a new adapted DIC process by suppressing only some pixels of the subset. This method is similar to a local DIC process with any geometry of the subset . This technique is principally employed for brittle fracture mechanics and remains to be tested in other cases.…”

Analysis of micro fracture in human Haversian cortical bone under compression

“…In the experimental setting, human cortical bone millimetric samples of about 2 × 2 × 5 mm 3 are subjected to a horizontal micro compression applied by a miniaturised device that fits under a light microscope shown in Figure (a). The thickness of the displayed sample is t = 2.37 mm.…”

“…In the presented micro compression test performed on human Haversian cortical bone, the sample morphology and local mechanics are first described in Section 2. The surface displacements within the Haversian microstructure can be observed in the anti‐plane longitudinal direction by image correlation and then included into a physical imaging analysis . Section 3 details the finite element formulation for microcracks under compression, where the non‐interpenetration is enforced by penalty constraints, and the tearing of the collagen fibres is modelled by a cohesive law.…”