Sex- and age-related variations in the three-dimensional orientations and curvatures of the articular surfaces of the human talus

The high prevalence of foot pathologies in women and the elderly could be associated with gender and age difference in the morphology of the foot, particularly the morphology of the keystone of the foot, the talus. The present study investigated the orientation and curvature of the three articular surfaces of the talus in relation to sex and age based on computer tomography (CT), to identify possible morphological factors of the higher prevalence of foot disorders in women and elderly. Fifty-six participants were included in this study. The orientations of the talocrural, subtalar, and talonavicular joints were quantified three-dimensionally by calculating normal and principal axes of the articular surfaces defined by planar approximation. The curvature radii of the articular surfaces were quantified by cylindrical and spherical approximations. The talonavicular surface was significantly more twisted in the frontal plane and less adducted in the transverse plane in females than in males. With aging, the subtalar articular surface was significantly facing more posteriorly. Moreover, it was found that the curvature radii of the trochlea and navicular articular surfaces significantly increased with aging, indicating a flattening of these surfaces. The identified changes in the talar morphology with aging could potentially lead to a higher prevalence of foot disorders in the elderly.


Introduction
The talus is articulated superiorly with the tibia and fibula at the talocrural joint, inferiorly with the calcaneus at the subtalar joint, and anteriorly with the navicular at the talonavicular joint. Thus, the talus acts as a mechanical linkage between the foot and the leg, and the orientations of the articular surfaces of the talus determine relative positions and movements of the calcaneus and navicular with respect to the tibia during locomotion.
There is a widely held perception that foot disorders such as the hallux valgus and flatfoot deformity are more frequent in women than men (Holmes and Mann 1992;Dufour et al. 2014;Nix et al. 2010;Cho et al. 2009;Coughlin and Jones 2007;Nguyen et al. 2010) and increases with age (Nix et al. 2010). The mechanism underlying this sex-and age-associated differences in the higher prevalence of foot disorders in women and the elderly is not well documented in current literature, but this could possibly be associated with gender and age difference in the morphology of the foot (Nozaki et al. 2019;Nozaki et al. 2020b). The foot morphology basically determines how the foot makes contact with the ground and how the ground reaction force is transmitted to the upper part of the body during walking. Since the talus is the keystone of the foot that connects the calcaneus with the remaining upper part of the body, it is expected that there exists sex-and age-related differences of the articular morphology of the talus that possibly explains the sex-and age-associated differences in the higher prevalence of the foot disorders in women and the elderly.
Sex differences in the articular morphology of the talus have been reported (Ferrari et al. 2004;Moore et al. 2019;Tumer et al. 2019). For examples, the female navicular articular surface of the talus was more twisted in the frontal plane and more curved than that in males (Ferrari et al. 2004), the female talar head was relatively larger than that of the male (Moore et al. 2019), and the female talus had a smaller posterior calcaneal facet contour than the male talus (Tumer et al. 2019). In contrast, a recent geometric morphometric study has not detected sex differences in the three articular surfaces of the talus (Sorrentino et al. 2020a). Hence, the sex-related differences in the articular morphology of the talus are still under debate. On the other hand, age-related differences in the articular morphology of the talus have not been well investigated at present, although it has been recognized that prevalence of bony spur formation on the superior surface of the talar neck increases with aging (Talbot et al. 2018).
Under this circumstance, we previously investigated the morphological differences of the talus between sexes and genders using geometric morphometrics (Nozaki et al. 2020a). However, in our previous study, some landmarks were defined on the circumference of the three articular surfaces of the talus, but not on the articular surfaces themselves to represent detailed surface contours, because the main focus of the previous study was to investigate the overall shape differences of the entire talus. Therefore, differences in the orientations and curvatures of the articular surfaces were not necessarily well represented and quantified in the previous study. Much more research on the sex-and age-related differences in the orientation and curvature of the articular surfaces of the talus are certainly essential to identify the possible cause of the higher prevalence of foot disorders in women and the elderly.
The present study aimed to compare the orientations and curvatures of the articular surfaces of the human talus between males and females, and to explore the correlations between the talar articular morphology and age using threedimensional computed tomography (CT) images. To extend our knowledge of sex-and age-related differences in the articular morphology of the talus is essential to explain the mechanism underlying the foot disorders, which are more prevalent in women and the elderly.

Population
Participants were recruited from the previous retrospective study, which investigated the calcaneal morphology (Nozaki et al. 2019). A total of 56 tali of the Japanese healthy participants were analyzed in the present study. Thirty-one participants were male and 25 participants were female (mean age of men, 49.2 years [20-82 years]; mean age of women, 52.6 years [17-87 years]). This study was approved by the ethics committee of our institution. The CT scanning were performed using an Aquilion Multi-detector CT scanner (Toshiba Medical Systems, Otawara, Japan). The CT image parameters were: tube voltage 120 kV, current 10-500 mA, and slice thickness 0.5-1.00 mm. Cross-sectional images were reconstructed at 0.5-1.00 mm intervals with pixel size ≤ 0.470 mm. All tali were segmented from the CT images using a commercial software (Mimics Version 9.0; Materialise Inc., Leuven, Belgium). The threshold values were determined by visual inspection. A 3-D bone model of the talus was then reconstructed in this software. The left side specimens were treated as right side specimens by creating mirror image models of left-side specimens using the Geomagic Design X (3-D Systems Inc., Rock Hill, SC, USA), because no asymmetry has been detected on the talus (Islam et al. 2014).

Articular surface analysis
To quantify the orientations of the articular surfaces (i.e., the directions to which the articular surfaces are facing with respect to the talar body), a body-fixed coordinate system was defined for the talus. For this, we used the human talus specimen designated as the most typical in Kanamoto et al.
(2011) (a dry bone specimen of a modern Japanese housed at the Laboratory of Physical Anthropology, Kyoto University) as a standard specimen and defined a body-fixed orthogonal coordinate system with the X-, Y-, and Z-axes the representing the mediolateral, anteroposterior, and dorsoplantar axes, respectively ( Fig. 1) based on a previous report (Lisowski et al. 1974). The median sagittal talar plane and the trochlea-head plane were perpendicular to the X-and Z-axes, respectively. The origin of the coordinate system was defined as an average of 37 landmarks coordinates on the surface of the talus (Nozaki et al. 2020a). All specimens were superimposed on this standard specimen based on the 37 landmark coordinates (Nozaki et al. 2020a) using the Generalized Procrustes Analysis method (Goodall 1991;Rohlf and Slice 1990;Gower 1975) to place them in the same coordinate system.
Three regions of the articular surfaces in the talus, i.e., the superior surface of the trochlea, calcaneal articular surfaces, and navicular articular surface, were manually extracted by outlining the visible borders of the corresponding subchondral bone surfaces. To quantify the orientation of the three articular surfaces, the planes were fitted to each articular surface using the least-squares method, and the normal vector of each plane was calculated using custom-made software ( Fig. 2). Furthermore, the first principal axis of each articular surface was calculated ( Fig. 2) using the same custommade software.
For the trochlea and subtalar articular surfaces ( Fig. 2a, b), the angle between the normal vector and the Y-axis projected on the sagittal (YZ-) plane was defined as the superoinferior angle, whereas the angle between the normal vector and the Z-axis projected on the frontal (XZ-) plane was defined as the mediolateral angle. The angle between the principal axis and the Y-axis projected on the horizontal (XY-) plane was defined as the rotational angle. For the navicular surface (Fig. 2c), the angles between the normal vector and the Y-axis projected on the sagittal plane, between the normal vector and the Y-axis projected on the horizontal plane, and between the principal axis and the Z-axis projected on the frontal plane were defined as the superoinferior, mediolateral, and rotational angles, respectively. The angles were positive if the surfaces were oriented superiorly, laterally, and internally rotating directions, respectively.
To assess the radii of curvatures of the articular surfaces, the superior trochlea and the posterior calcaneal articular surface were approximated by a cylindrical surface, and the navicular surface were approximated by a spherical surface, using the least-squares minimization (Solid Primitive command in Geomagic Design X, 3D Systems, Rock Hill, SC, USA) (Fig. 3). The subtalar articular facet consisting of the anterior, middle, and posterior calcaneal articular surfaces is essentially a plane joint on which the calcaneus slightly translates and rotates. However, the posterior calcaneal surface is cylindrical. Therefore, a cylinder was fitted only to the posterior calcaneal facet. The calculated radii of curvatures were normalized by the talar length which is a measurement for the allover size of the talus (Koshy et al. 2002), defined as the distance between the most distomedial point on the posterior calcaneal articular surface and the center of the navicular articular surface (landmark points of 23 and 36 described in Nozaki et al. 2020b) for comparisons.

Measurement reproducibility assessment
The intra-rater reproducibility for the measurements in each of the 56 tali (two independent measurements per talus) was assessed using the intraclass correlation coefficient with one-way random effects, absolute agreement, single rater/ single measurement (ICC, model 1, 1), and 95% confidence intervals. The standard error of measurement (SEM) was calculated to represent the consistency of the results within individuals in the same unit as the original measurement. The 95% minimal detectable change (MDC 95 ) was also determined for assuming the amount of change required to represent a true change (i.e., exceeding measurement error). (Vincent and Weir 1994) Repeated measurements were conducted by one observer with a 4-week interval. Calculation of the ICC was performed using the SPSS statistics (version 25.0, IBM, Armonk, NY, USA).

Statistical analyses
Multivariate analysis of variance (MANOVA) was individually conducted for each three articular surfaces to investigate sex-related differences in the orientation angles and curvatures as well. Age-related differences in the orientation angles and curvatures of the articular surfaces were also analyzed using the Pearson's correlation coefficient. The statistical significance level was set at P < 0.05. All statistical analyses were performed in the open source R software, version 3.5.2 (R Core Team 2016).

Results
The value of ICC, model 1, 1 for reproducibility of repeated measurements exceeded 0.94, and MDC 95 was less than 2.3° and 0.8 mm for the orientation angles and curvature radii, respectively (Table 1).
MANOVA did not detect statistically significant sex differences in the orientations at the superior trochlea (Wilks' lambda = 0.976, F = 0.43, P = 0.73) and calcaneal articular surfaces (Wilks' lambda = 0.983, F = 0.29, P = 0.83), but there was statistically significant overall difference in the orientation angles at the navicular articular surface (Wilks' lambda = 0.846, F = 3.16, P = 0.03). Particularly, the navicular articular surface in the female talus exhibited significantly lower mediolateral angle (mean differences of 2.5°, P = 0.03) and lower rotational angle (mean differences of 5.2°, P < 0.01) compared with that of males (Table 2, Fig. 4). There were no significant sex differences in the curvatures of the three articular surfaces (Table 3).
There was a significant negative correlation between the superoinferior angle of the calcaneal articular surfaces and age (R = − 0.357, P < 0.01, Fig. 5a), indicating that the articular surface is more posteriorly oriented with increasing age. However, there were no significant age-related differences in the other orientation angles. The curvatures of the superior trochlea and navicular articular surface were significantly correlated with age (R = − 0.436, P < 0.001; R = − 0.476, P < 0.001, respectively) (Fig. 5b), indicating a flattening of these surfaces with aging. In contrast,

Discussion
The present study demonstrated that the navicular surface of the talus was significantly more twisted and less internally oriented in females than in males, as previously suggested (Nozaki et al. 2020a, Ferrari et al. 2004) although such sex-associated differences in the orientations of the articular surfaces were not observed in the superior trochlea and calcaneal articular surfaces. The biomechanical effect of the greater torsion angle in the female talus is obscure, but a recent morphometric study indicated that the navicular articular surface significantly exhibits greater torsion angle in patients with flatfoot than that of neutral foot (Louie et al. 2014). Based on the study by Louie et al. (2014), the greater torsion angle of the navicular surface of the talus may predispose women to developing flatfoot (Louie et al. 2014). However, in the field of evolutionary studies, the greater torsion angle of the navicular surface has been believed to be linked to the restricted range of motion at the talonavicular joint (Day and Wood 1968, Kidd et al. 1996, Sorrentino et al. 2020b, possibly leading to the higher medial longitudinal arch in females. Further studies are certainly needed to investigate the effect of the torsion angle of the navicular articular surface of the talus on the foot kinematics and the pathogenetic mechanism of the flatfoot deformity. The present study demonstrated that there are considerable age-associated changes in the articular surface morphology of the talus. Firstly, the calcaneal articular surface was found to be significantly more posteriorly oriented with increasing age. If the articular surface is more posteriorly oriented, it means that the surface is more steeply sloping in the anteroposterior direction. Recent morphological study reported that the talar articular surface of the female calcaneus flattens with aging (Nozaki et al. 2020b). Therefore, the calcaneus should easily move in the superoposterior direction with respect to the talus during weight-bearing, possibly leading to the larger excessive mobility of the subtalar joint with increasing age. It is suggested that the excessive mobility of the subtalar joint during weight-bearing is linked to foot disorders such as flatfoot deformity (Kido et al. 2013;Kido et al. 2011). Several studies actually demonstrated that the medial longitudinal arch tends to lower and flatten with aging (Redmond et al. 2008;Scott et al. 2007;Staheli et al. 1987). Consequently, the change in the orientation of the calcaneal articular surface with aging could be a morphological factor for the higher prevalence of flatfoot with aging (Redmond et al. 2008;Scott et al. 2007;Staheli et al. 1987).
The present study also revealed that the curvatures of the superior talar trochlea and navicular articular surfaces significantly decreased with age, indicating that the articular surfaces flattened as the age increased. This is possibly due to joint surface remodeling caused by loading accumulation over a long period of time. In fact, a large compressive force is applied to the talocrural joint in a weight-bearing situation (Kimizuka et al. 1980, Manter 1946. Therefore, such accumulation of the large compressive force applied to the superior trochlea and navicular articular surfaces over the years may cause talus remodeling. This result is consistent with the fact that the trochlea is generally flattened particularly in the medial border in ankle osteoarthritis patients (Seki et al. 2019).
This study identified the changes in the articular morphology of the talocrural and subtalar joints with aging, but such the age-related changes were not extracted by our previous study based on geometric morphometrics (Nozaki et al. 2020a). This is owing to the fact that the surface orientations and curvatures were more precisely quantified in the present study by approximating the articular surfaces  by planar, cylindrical or spherical surfaces using hundreds of vertices composing the surfaces, whereas only a small number of landmark coordinates were used to represent the articular surfaces in our previous study. Both holistic analysis of the entire bone and partial but detailed quantification of articular surfaces of the bone were suggested necessary, in a mutually complementary manner, for comprehensive investigation of the sex-and age-related bony morphological differences. There are several limitations in the present study. First, we investigated the age-related changes in the articular morphology by cross-sectional design. Therefore, true agerelated morphological changes were not tested in the same participants. Second, the threshold values for extracting the contour of the talus on the CT scans were determined by visual inspection, which may affect the results in this study. Third, the regions of the articular surfaces were manually selected and this might affect the validity of our results. However, the intra-rater reproducibility of all measurements was excellent; thus, this manual selection did not change the main conclusion of this study. Finally, the present study did not examine other factors which cause the differences in the talar morphology including, body mass index, allometry, footwear and mobility strategy (Parr et al. 2011;Sorrentino et al. 2020a;Sorrentino et al. 2020c).

Conclusions
The sex-related differences of the articular morphology of the talus were found only at the navicular articular surface. The calcaneal articular surfaces significantly oriented more posteriorly with aging, which could consequently cause posterior sliding motion of the calcaneus respective to the talus, possibly leading to the medial longitudinal arch flattening. Furthermore, the superior trochlea and the navicular articular surfaces significantly flattened with aging. In the future, biomechanical studies will be needed to clarify the effect of greater torsion angle of the talar head in females on the height of the medial longitudinal arch and the kinematics of the talonavicular joint. In addition, the biomechanical effect of the age-related morphological change of the posterior calcaneal facet should be investigated in future studies for better understanding of the pathogenesis of foot disorders, which are prevalent in the elderly.  5 Bivariate plots of the superoinferior angle of the calcaneal articular surfaces a and size-normalized curvatures at the superior trochlea and navicular articular surface b relative to age. Age is significantly correlated with the superoinferior angle (R = − 0.357, P < 0.01) and curvatures at the superior trochlea (R = − 0.436, P < 0.001) and navicular articular surface (R = − 0.476, P < 0.001)