Surface spherical encoding and contrastive learning for virtual bone shape aging

Bone shape changes are considered a relevant biomarker in understanding the onset and progression of knee osteoarthritis (OA). This study used a novel deep learning pipeline to predict longitudinal bone shape changes in the femur four years in advance, using bone surfaces that were extracted in knee MRIs from the OA initiative study, via a segmentation procedure and encoded as shape maps using spherical coordinates. Given a sequence of three consecutive shape maps (collected in a time window of 24 months), a fully convolutional network was trained to predict the whole bone surface 48 months after the last observed time point, and a classifier to diagnose OA in the predicted maps. For this, a novel multi-term loss function, based on contrastive learning was designed. Experimental results show that the model predicted shape changes with an L₁ error comparable to the MRI slice thickness (0.7mm). Next, an ablation study demonstrated that the introduction of a contrastive term in the loss improved sensitivity of the OA classifier, increasing sensitivity from 0.537 to 0.709, just shy of the upper bound of 0.740 computed on the ground truth bone shape maps. Our approach provides a promising tool, suitable for patient specific OA trajectory analysis.