Stamatina Moraiti ^1,2 Vee San Cheong ^1,2,3 Enrico Dall'Ara ^2,4 Visakan Kadirkamanathan ^2,5 Pinaki Bhattacharya ^1,2*

• ¹ Department of Mechanical Engineering, Faculty of Engineering, The University of Sheffield, Sheffield, United Kingdom
• ² Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield, United Kingdom
• ³ Singapore ETH Centre, ETH Zürich, Singapore, Singapore
• ⁴ Division of Clinical Medicine, University of Sheffield, Sheffield, United Kingdom
• ⁵ Department of Automatic Control and Systems Engineering, Faculty of Engineering, The University of Sheffield, Sheffield, England, United Kingdom

Murine models are used to test the effect of anti-osteoporosis treatments as they replicate some of the bone phenotypes observed in osteoporotic (OP) patients. The effect of disease and treatment is typically described as changes in bone geometry and microstructure over time. Conventional assessment of geometric changes relies on morphometric scalar parameters. However, being correlated with each other, these parameters do not describe separate fractions of variations and offer only a moderate insight into temporal changes. The current study proposes a novel image-based framework that employs deformable image registration on in vivo longitudinal images of bones and Principal Component Analysis (PCA) for improved quantification of geometric effects of OP treatments. This PCA-based model and a novel post-processing of score changes provide orthogonal modes of shape variations temporally induced by a course of treatment (specifically in vivo mechanical loading). Errors associated with the proposed framework are rigorously quantified and it is shown that the accuracy of deformable image registration in capturing the bone shapes (~1 voxel = 10.4 μm) is of the same order of magnitude as the relevant state-of-the-art evaluation studies. Applying the framework to longitudinal image data from the midshaft section of ovariectomized mouse tibia, two mutually orthogonal mode shapes are reliably identified to be an effect of treatment. The mode shapes captured changes of the tibia geometry due to the treatment at the anterior crest (maximum of 0.103 mm) and across the tibia midshaft section and the posterior (0.030 mm) and medial (0.024 mm) aspects. These changes agree with those reported previously but are now described in a compact fashion, as a vector field of displacements on the bone surface. The proposed framework enables a more detailed investigation of the effect of disease and treatment on bones in preclinical studies and boosts the precision of such assessments.