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.

Bilateral symmetry of the subtalar joint facets and the relationship between the morphology and osteoarthritic changes

“…The high degree of symmetry is in line with earlier studies that have demonstrated a high degree of symmetry in the lower extremity (Latimer and Lowrance, 1965). Specifically for the hindfoot, a strong degree of symmetry was demonstrated for the whole talus (Islam et al, 2014), the calcaneus (Stephan et al, 2014) and tibia, fibula, talus, and calcaneus (Tümer et al, 2018). A clear cause for the asymmetry in type 12100% 80The diagonal with bold numbers represent the corresponding classifications between the two observers.…”

“…Despite the known variation only two studies analyzed the degree of bilateral symmetry of the facet joints: one describing the pattern of calcaneal facets (Ragab et al, 2003), and another one describing the surface area and three-dimensional (3D) orientation of the calcaneal facets (Stephan et al, 2014). In general, literature describing the bilateral symmetry of the hindfoot is scarce (Shultz and Nguyen, 2007;Islam et al, 2014;Tümer et al, 2018). This is remarkable since many surgeons use the contralateral noninjured side as reference for anatomical reduction in case of a fractured bone (Pierre et al, 2010;Dobbe et al, 2011;Young et al, 2013;Ten Berg et al, 2016).…”

Investigation of the Average Shape and Principal Variations of the Human Talus Bone Using Statistic Shape Model

“…Zhao et al (2019)'s study supports the current study's findings around the deviation contour of PC2 in the area of the talar dome ( Figure 5). In addition, Tümer et al (2019) revealed that the principal FIGURE 5 | The percentage of points with the deviation >1 mm in the first five PCA eigenvectors scaled by +3σ and its mean shape for male and female.…”

Typical Shape Differences in the Subtalar Joint Bones Between Subjects with Chronic Ankle Instability and Controls

“…In the alignment procedure (Fig. , step 3), each bone sample was first translated to the origin of a common coordinate system and was then scaled to the unit centroid size . Then, an evolving mean shape was fit to each bone sample described by a point cloud (i.e., a set of points sampled across all the surfaces of the bone sample).…”

“…Then, an evolving mean shape was fit to each bone sample described by a point cloud (i.e., a set of points sampled across all the surfaces of the bone sample). The registration parameters that needed to be input by the user (i.e., the scaling parameter for the mixture of Gaussians, σ , the number of points in the mean cloud, n m , and the trade‐off parameter, λ ) were retrieved from our previously published studies for the tali ( σ = 3 mm, n m = 2,000, λ = 10 −6 ) and calcanei ( σ = 3 mm, n m = 2,000, λ = 5 × 10 −4 ) …”