Three-dimensional analysis of shape variations and symmetry of the fibula, tibia, calcaneus and talus

The bones forming the talocrural joint (TCJ) and subtalar joint (STJ) are often assumed to be bilaterally symmetric. Therefore, the contralateral limb (i.e. the fibula, tibia, calcaneus and talus) is used as a template or an intra-subject control in clinical and research practice. However, the validity of the symmetry assumption is controversial, because insufficient information is available on the shape variations and bilateral (a)symmetry of the fibula, tibia, calcaneus and talus. Using three-dimensional spatially dense sampled representations of bone shapes extracted from bilateral computed tomography scans of 66 individuals (55 male, mean age: 61 ± 10 years; 11 female, mean age: 53 ± 15 years), we analyzed whether: (i) similar shape patterns exist in the left and right bones of the same type; (ii) gender has an effect on bone shape variations; (iii) intra-subject shape variation is smaller than that of inter-subject for a given shape variance direction. For the first set of analyses, all left and right instances of the same type of bone were considered as two separate groups, and statistically compared with each other on multiple aspects including group location (central tendency), variance-covariance scale (dispersion) and orientation (covariance structure) using distance-based permutational tests. For the second and third sets of analyses, all left and right bones of the same type were pooled into one group, and shape variations in the TCJ and STJ bones were extracted using principal component analysis. The effects of gender on age-adjusted bone shape differences were assessed using an analysis of covariance. Moreover, intra-class correlation was employed to evaluate intra- and inter-subject bone shape variations. For each bone type, both sides had similar shape patterns (P_{permutational} -values > 0.05). After Bonferroni adjustment, gender led to shape differences, which were mainly in the lateral and medial condyles of the tibia (P = 0.003), the length and height of the calcaneus (P < 0.001), the posterior and anterior talar articular surfaces of the calcaneus (P = 0.001), and in the posterior aspect of the talus (P = 0.001). Intra-subject shape variations in the tibial tuberosity together with the diameter of the tibia, and the curvature of the fibula shaft and the diameter of the fibula were as high as those of inter-subject. This result suggests that the shape symmetry assumption could be violated for some specific shape variations in the fibula and tibia.