Neural shape models encode bone shape features not captured by statistical shape models

The recently proposed B-Score uses statistical shape models (SSM) to represent femur shape as a scalar value similar to the osteoporosis T-score. The B-Score quantifies OA bone shape and is defined as the distance from the mean healthy bone shape (B-Score=0) to the mean OA bone shape, where 1-unit is equal to the standard deviation of the healthy B-Scores [Bowes et al. 2021]. However, SSMs require finding matching points between subjects’ femurs, and learn linear features, potentially limiting their ability to capture physiologic shape. Neural Shape Models (NSM) have been shown to represent object surfaces without requiring matching points between subjects using non-linear neural networks. Here, we use NSMs to reconstruct bone shapes and use these features to encode information about OA. To compare B-Scores learned from a NSM and a SSM. Data from the 24 and 48-month visit of the right knee of 562 participants enrolled in the OAI were included (335 females, mean age 63.5(8.9) years, BMI 30.8(4.8) kg/m2, and KLG counts of 0=35, 1=79, 2=269, 3=167, 4=12). Fig 1 depicts the data analysis pipeline; sagittal DESS MRIs were segmented using a CNN and femur surfaces were extracted using marching cubes. The NSM and SSM models were fit to the 24-month data of half the subjects. The NSM and SSM learned feature spaces were 256 and 90 dimensions, respectively. Fitted models were used to obtain shape features from the 48-month data of all subjects. Finally, NSM and SSM B-scores were computed to assess how the NSM and SSM feature spaces affect the learned B-scores. To determine whether each model has the capacity to represent the other's B-Score, the amount of variance in the B-Score explained by the feature space of the other model was calculated using linear regression. Since the B-Score produces a range of scores within each KL grade, the distribution of B-Scores per KLG were plotted. The odds ratios (OR) for knee pain and TKA were computed between B-Score quartiles (1 vs 2, 3, 4) in OA knees (KLG >=2). Pain was defined using previous criteria [Morales et al. 2021]. The NSM explained 82% of the variance in SSM B-score, yet the SSM only explained 55% of the variance in NSM B-score (Fig 2). Fig 3 shows the distribution of B-Scores per KLG demonstrating that within a KLG there is a range of B-Scores providing more specific shape information. Table 1 includes ORs for pain and TKA between quartile 1 and all other quartiles for both B-scores. The NSM learned non-linear shape features that encode clinically relevant information about OA without a need to find matching points between subjects. The NSM and SSM performed similarly for predicting clinical outcomes. The NSM had a broader range of B-scores between KLGs primarily driven by a large difference between KLG 0 and 1, potentially indicating greater expressivity for the NSM. The SSM did a poor job predicting the NSM B-score, which was particularly evident in KLG 0 knees where the SSM was unable to reproduce NSM B-Scores in the healthy range (Fig 2). Small samples of KLG 0 and 4 knees likely limit both SSM and NSM B-Scores. More data from the OAI will likely enable the more flexible NSM to learn more expressive representations particularly in under-represented sub-samples, like KLG 4 knees. Results from this study indicate that the NSM captures novel bone shape information that cannot be learned by the SSM.