Development and validation of statistical shape models of the primary functional bone segments of the foot
Authors: Grant Tamara M. , Diamond Laura E. , Pizzolato Claudio , Killen Bryce A. , Devaprakash Daniel , Kelly Luke , Maharaj Jayishni N. , Saxby David J. 
Published: February 2020

Introduction
Musculoskeletal models are important tools for studying movement patterns, tissue loading, and neuromechanics. Personalising bone anatomy within models improves analysis accuracy. Few studies have focused on personalising foot bone anatomy, potentially incorrectly estimating the foot’s contribution to locomotion. Statistical shape models have been created for a subset of foot-ankle bones, but have not been validated. This study aimed to develop and validate statistical shape models of the functional segments in the foot: first metatarsal, midfoot (second-to-fifth metatarsals, cuneiforms, cuboid, and navicular), calcaneus, and talus; then, to assess reconstruction accuracy of these shape models using sparse anatomical data.

Methods
Magnetic resonance images of 24 individuals feet (age = 28 ± 6 years, 52% female, height = 1.73 ± 0.8 m, mass = 66.6 ± 13.8 kg) were manually segmented to generate three-dimensional point clouds. Point clouds were registered and analysed using principal component analysis. For each bone segment, a statistical shape model and principal components were created, describing population shape variation. Statistical shape models were validated by assessing reconstruction accuracy in a leave-one-out cross validation. Statistical shape models were created by excluding a participant’s bone segment and used to reconstruct that same excluded bone using full segmentations and sparse anatomical data (i.e. three discrete points on each segment), for all combinations in the dataset. Tali were not reconstructed using sparse anatomical data due to a lack of externally accessible landmarks. Reconstruction accuracy was assessed using Jaccard index, root mean square error (mm), and Hausdorff distance (mm).

Results
Reconstructions generated using full segmentations had mean Jaccard indices between 0.77 ± 0.04 and 0.89 ± 0.02, mean root mean square errors between 0.88 ± 0.19 and 1.17 ± 0.18 mm, and mean Hausdorff distances between 2.99 ± 0.98 mm and 6.63 ± 3.68 mm. Reconstructions generated using sparse anatomical data had mean Jaccard indices between 0.67 ± 0.06 and 0.83 ± 0.05, mean root mean square error between 1.21 ± 0.54 mm and 1.66 ± 0.41 mm, and mean Hausdorff distances between 3.21 ± 0.94 mm and 7.19 ± 3.54 mm. Jaccard index was higher (P < 0.01) and root mean square error was lower (P < 0.01) in reconstructions from full segmentations compared to sparse anatomical data. Hausdorff distance was lower (P < 0.01) for midfoot and calcaneus reconstructions using full segmentations compared to sparse anatomical data.

Conclusion
For the first time, statistical shape models of the primary functional segments of the foot were developed and validated. Foot segments can be reconstructed with minimal error using full segmentations and sparse anatomical landmarks. In future, larger training datasets could increase statistical shape model robustness, extending use to paediatric or pathological populations.