Data-driven image mechanics (D2IM): a deep learning approach to predict displacement and strain fields from undeformed X-ray tomography images - Evaluation of bone mechanics.

Abstract

Experimental measurement of displacement and strain fields using techniques such as digital volume correlation (DVC) from in situ X-ray computed tomography (XCT) has notably advanced the understanding of bone mechanics from organ to tissue level. Being experimental in nature, DVC output has been often employed to validate finite element (FE) models of bone improving their predictive ability. Despite the excellent results achieved, these techniques are complex, time consuming, potentially affecting tissue mechanical properties, and their predictive ability requiring prior knowledge of material properties. The recent advent of deep learning (DL) has enabled data-driven models, paving the way for the full exploitation of rich image datasets from which physics can be learnt and retained. Here we propose a novel data-driven image mechanics (D2IM) approach based on feed forward convolutional neural network (CNN) that learns from DVC displacement fields of vertebrae, predicting displacement and strain fields for undeformed XCT images. D2IM successfully predicted all displacement fields, particularly the one for the z loading axis (w), where high correlation (R2=0.93) and minimal error (as low as less than 1m) were found when comparing measured against predicted displacements. The predicted axial strain field in z ({varepsilon}zz) was also consistent in distribution with the measured one, displaying generally reduced errors (as low as few tens of {varepsilon}) in the regions within the vertebral body where the effect of border outliers was minimal. This is the first study using experimental full-field measurements on bone structures from DVC to inform DL-based model such as D2IM, which represents a major contribution in the prediction of displacement and strain fields only based on the greyscale content of undeformed XCT images. The future development of D2IM will incorporate a wider range of structures and loading scenarios for accurate prediction of physical fields in both hard and soft tissues, aiming at clinical translation for improved diagnostics.