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

Abstract

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.

Keywords: bilateral symmetry; calcaneus; fibula; subtalar joint; talocrural joint; talus; tibia.

Figure 1

(a) A flow diagram of the study. Bilateral computed tomography (CT) scans were collected from 66 subjects. Left and right fibulae, tibiae, calcanei and tali were segmented from each CT scan. All bone samples of the same type were aligned into a common coordinate frame using an unbiased registration algorithm. For each bone type, shape variations and (a)symmetry were evaluated. (b–d) Multiple aspect analysis: group location, variance‐covariance scale and orientation. Two groups that show a difference in (b) their locations, (c) variance‐covariance scale and (d) variance‐covariance orientation only. In the group location, variance‐covariance scale and orientation tests, the features to concentrate on are (b) the sample mean, (c) the sample dispersion from the centroid, and (d) the sample subspace described using eigenvectors and the principal angles between them, respectively.

Figure 2

The scree plots with parallel analyses (PAs) are given for (a) left fibulae, (b) right fibulae, (c) left tibiae, (d) right tibiae, (e) left calcanei, (f) right calcanei, (g) left tali and (h) right tali. Blue and dark gold markers stand for observed and simulated data, respectively. All the principal components (PCs) up to the one found at the intersection of two lines (lines represented with blue and dark gold colors) were retained and used in the variance‐covariance orientation test and description of bone shape variations within a studied population. Accordingly, the number of PCs kept is (a, b) 8 for left and right fibulae, (c, d) 8 for left and right tibiae, (e, f) 15 for left and right calcanei, and (g, h) 14 for left and right tali.

Figure 3

The first three rows display deviations (mm) of the fibula and tibia from the mean fibula shape (left column) and the mean tibia shape (right column) in the positive (+3 SD) and negative (−3 SD) directions of the first three principal components (PCs) of the fibula and tibia, respectively. Shape variations of the fibula and tibia explained by PC 6 of the fibula and PC 8 of the tibia, respectively, are shown in the fourth row. The shape variance directions that expressed significantly different shape variations between females and males are marked with ‘*’. The marker ‘§’ is used to indicate shape variance directions for which intra‐ and inter‐subject shape variations were comparable to each other.

Figure 4

The first three rows display deviations (mm) of the talus and calcaneus from the mean talus shape (left column) and the mean calcaneus shape (right column) in the positive (+3 SD) and negative (−3 SD) directions of the first three principal components (PCs) of the talus and calcaneus, respectively. Shape variations in the talus and calcaneus explained by PC 8 of the talus and PC 7 of the calcaneus are shown in the fourth row. Shape variance directions that expressed significantly different shape variations between females and males are marked with ‘*’.

Figure 5

(a) Box plots showing the distributions of shape parameters observed along principal component (PC) 1 of the tibia, PC 1 and PC 7 of the calcaneus, and PC 8 of the talus. These PCs described statistically significant shape variations between males (blue color) and females (dark gold color). (b) Point‐to‐surface distances (mm) calculated between female and male (i) tibiae deviating from each other the most along PC 1 of the tibia, (ii) calcanei deviating from each other the most along PC 1 of the calcaneus, (iii) PC 7 of the calcaneus, and (iv) tali deviating from each other the most along PC 8 of the talus. (c) The distributions of shape parameters observed for the left (blue color) and right (dark gold color) sides along PC 8 of the tibia, PC 3 and PC 6 of the fibula. Intra‐subject shape variations in the tibia and fibula described by these PCs were similar to those of inter‐subject. (d) Point‐to‐surface distances (mm) calculated between left and right (i) tibiae deviating from each other the most along PC 8 of the tibia, (ii) fibulae deviating from each other the most along PC 3 of the fibula, and (iii) PC 6 of the fibula.