1 INTRODUCTION

Immature bone is subjected to continuous modeling due to variations in functional and biomechanical stresses that occur during ontogeny (Lieberman et al., 2001, 2003; Raab et al., 1990; Steinberg & Trueta, 1981). However, long bone diaphyseal shape and size variation during growth is influenced by the combined action of nutritional, hormonal, and genetic factors, that may modulate the mechanical forces acting upon growing individuals as they progressively acquire a mature gait (Gosman et al., 2011). Many studies have investigated how growth trajectories of long bones diaphyseal shape vary in relation to different locomotor behaviors and biomechanical requirements on subadult individuals (Cowgill et al., 2010; Cowgill & Johnston, 2018; Goldman et al., 2009; Gosman et al., 2011, 2013; Macdonald et al., 2006; Ruff, 1994, 2003a, 2003b; Ruff et al., 1994; Sumner, 1984; Sumner & Andriacchi, 1996).

Mechanical and structural properties of the femoral diaphysis in subadults revealed the influence of loading regimens during mobility on ontogenetic trajectories (Cowgill et al., 2010; Cowgill & Johnston, 2018). In particular, the authors analyzing ground reaction forces and diaphyseal cross-sectional geometric (CSG) evidence in subadults individuals showed that femoral midshaft shape is correlated to load changes that happen during bipedal development during infancy: from a more rounded femoral midshaft produced by the higher mediolateral loads in the early stages of infancy to a more anteroposteriorly elongated one due to the progressively more anteroposterior-oriented loads to which the femur is subjected as bipedal locomotion develops. Similar results have been obtained by Goldman et al. (2009), who analyzed both femoral midshaft CSG and histological properties. The authors also argued that the histological manifestations of cortical bone resorption and formation play a key role in diaphyseal shape changes, as cortical drift patterns emerge before any measurable change in the biomechanical properties of the midshaft femoral cross section. Other studies (Ruff, 2003a, 2003b) found early changes in the femoral and humeral strength proportions in subadults and interpreted them as the effect of the initiation of upright walking. In particular, comparing femoral and humeral growth patterns, Ruff (2003a) found a peak in growth velocity at mean age of 1.4 years, corresponding to the initiation of bipedal walking. A similar peak was found slightly earlier with a subsequent steep decline interpreted as the result of the shift from crawling to independent walking and therefore changing the humeral loading regimen (Ruff, 2003b).

Regarding the leg, while the body of evidence on the structural and biomechanical properties on the tibiofibular complex in adults is progressively increasing (Auerbach et al., 2017; Marchi & Shaw, 2011; Rantalainen et al., 2010, 2014; Tümer et al., 2019), scarce information is available for subadult individuals, with analyses focusing mostly on the tibia (Gosman et al., 2013; Hubbell et al., 2011). The importance of considering leg bones together (and not the tibia alone) to better understand load distribution in the distal segment of the lower limb has been previously stressed in anthropological and biomechanical studies (Funk et al., 2004, 2007; McNeil et al., 2009; Scott et al., 2007). In particular, some studies brought attention to the functional role of the fibula in transmitting to the foot a portion of the mechanical load encountered during gait by the leg, which varies between 5% and 19% depending on ankle position (Funk et al., 2004; Goh et al., 1992; Lambert, 1971; Takebe et al., 1984). Moreover, recent research on the diaphyseal CSG properties of the fibula allowed the association of fibular structure to diverse mobility patterns in modern humans (Auerbach et al., 2017; Hagihara & Nara, 2016; Lüscher et al., 2019; Marchi et al., 2011; Marchi & Shaw, 2011; Sparacello et al., 2014), great apes (Marchi, 2005, 2007), and non-hominoid primates (Marchi, 2015b), with further application in paleoanthropology and the origins of bipedal locomotion (Marchi, 2015a; Marchi et al., 2019).

The role of the tibia during growth and the onset of bipedal walking has been investigated by Ireland et al. (2014), who found an association between the timing of unsupported walking (~15 months) and tibiae greater bone mass, cortical bone area, pericortical circumference and polar moment of inertia, even when sex and body size were taken into account. Other studies observed a shift of midshaft cross-sectional shape from relatively circular in early childhood to more anteroposteriorly orientated in early puberty (Gosman et al., 2013; Hubbell et al., 2011). Finally, Cowgill and Johnston (2018) proposed an evaluation of humeral to tibial, and femoral to tibial strength ratio to identify a “walking peak” in a large Holocene subadult skeletal sample. The authors found a more defined peak of humeral to tibial strength at the age corresponding to children shifting from crawling to walking and interpreted the result as the effect of the limited load to which the tibia is subjected during crawling compared to the femur and to the more dramatic biomechanical transition experienced by the tibia during this walking pattern transition.

Patterns of sex and age variations in relation to diaphyseal lengths and breadths in subadults have been explored by traditional morphometric studies on tibial and fibular diaphyses. In general, no sex-related difference is found for tibial length and breadth until 15 years of age (Cardoso et al., 2014; López-Costas et al., 2012). On the other hand, Humphrey (1998) found that tibial and fibular breadths may slightly diverge between sexes since earlier in childhood (4.2–5.3 years for tibial diameters; 2.3–11.2 years for fibular diameters). Regarding age variations, the positive relationship between age and long bone diaphyseal length, epiphyseal and metaphyseal widths and breadths has been observed in many different populations and used to provide specific standards for age estimation in subadult individuals (Black & Scheuer, 1996; Cardoso et al., 2014, 2017; López-Costas et al., 2012; Maresh, 1943, 1955, 1970; Primeau et al., 2012, 2016; Rissech et al., 2008, 2013; Stull et al., 2014, 2017; Tsai et al., 2016).

In this work, we perform a quantitative traditional morphometrics study of tibia and fibula diaphyses of subadult individuals (n = 68) aging 0–6 years, belonging to the Human Identified Skeletal Collection of the University of Bologna (Belcastro et al., 2017). The aim of this research is to better characterize linear and geometric changes in the diaphyses of tibia and fibula during growth in relation to biological sex and age, providing new research data and contributing to the understanding of the developmental patterns concerning sex and age. Based on previous literature, we will test the following hypotheses: We hypothesize for both tibia and fibula a shift from subcircular symmetric outline of the diaphysis (i.e., similar sagittal and transverse diameters along the whole shaft) in younger individuals toward a more anteroposterior-oriented outline (i.e., relatively greater anteroposterior diameters along the whole shaft) in older individuals in relation to the onset of bipedal locomotion (Cowgill et al., 2010; Cowgill & Johnston, 2018; Goldman et al., 2009; Gosman et al., 2011, 2013). Moreover, we expect to find a similar longitudinal growth pace (i.e., diaphyseal length) for both bone diaphyses and a positive correlation among tibial and fibular metrics, given the two bone proportionate interaction that is crucial for the normal development of the lower leg (Beals & Skyhar, 1984). We hypothesize little to no sex dimorphism in diaphyseal size and shape and a strong relationship with age for all measurements for the two bones, which may proceed according to growth spurts (Cardoso et al., 2014; López-Costas et al., 2012) 2 MATERIALS AND METHODS

The sample analyzed in this study refers to right and left tibiae and fibulae of 68 subadult individuals belonging to the Human Identified Skeletal Collection of the University of Bologna. This collection, housed at the Museum of Anthropology of University of Bologna, was put together by Fabio Frassetto (1876–1953) and Elsa Graffi Benassi (1901–2000) in the first half of the 20th century, consisting of cemetery exhumations carried out between the late 19th and early 20th centuries (Belcastro et al., 2017). The analyzed sample includes both males and females spanning 0–6 years of age (Table 1; Figures 1 and 2).

TABLE 1. Sample composition by sex and age classes Age class Females Males Total Age class 1 15 29 44 Age class 2 4 10 14 Age class 3 7 3 10 Total 26 42 68 Note: Age class 1 = 0–1 years of age; age class 2 = 1.1–3 years of age; age class 3 = 3.1–6 years of age.

Right tibiae and fibulae belonging to three individuals from the human-identified skeletal collection of the University of Bologna, representing different age classes. Tibiae are displayed in anterior view, while fibulae are displayed in anterolateral view. (a) Age class 1: BO25, female, 9 days old; (b) age class 2: BO11, male, 1 year and 3 months old; (c) age class 3: BO6, female, 5 years and 10 months old

Barplot representing sample composition, with subdivision by sex and age classes 1 (from 0 to 1 year of age), 2 (from 1.1 to 3 years of age), and 3 (from 3.1 to 6 years of age)

This identified skeletal collection, with a total of 126 subadult individuals, includes information on the sex, age-at-death, and social status of each individual, ensuring exhaustive and punctual biological parameters on each individual profile. Sources for these parameters include cemetery and hospital records, as well as anagraphic data (e.g., birth certificates and residence certificates from public archives). All specimens had unfused proximal and distal epiphyses on both tibia and fibula. Individuals with documented skeletal pathologies such as metabolic disease or trauma were not included in this study (Tanganelli, n.d.). Moreover, tibiae and fibulae with postmortem damage or other taphonomic alterations were excluded from analysis.

2.1 Age classes

Age class subdivision was designed with reference to medical literature, considering different stages of locomotor behavior in growing children progressively acquiring bipedal locomotion according to specific patterns and timing. Age class 1 includes individuals from 0 to 1 year of age: by the end of this stage, children normally develop an immature toddling gait. Starting from birth, children usually progress to toddling through an early phase (up to 6 months of age), in which weight-bearing on lower limbs is absent, characterized by precursory locomotor movements such as supine kicking and supported sitting (Thelen et al., 1984; Thelen & Fisher, 1982), as well as postural control in pronation, including chin and torso holding and rolling with upper limb support (Adolph & Joh, 2007; Bly, 1994; Swan et al., 2020). Following a brief phase (up to 8 months of age) of dependent/independent crawling and scooting, infants usually acquire a standing position and begin cruising toward the end of first year of age, at first while holding on to objects or caregivers for support and ultimately to independent toddling (Adolph et al., 1998; Bly, 1994).

Age class 2 includes individuals from 1.1 to 3 years of age: during this phase, independent toddling is at its early stages, as the product of a gradual maturation of the locomotor pattern during the period of supported locomotion, ultimately leading to unsupported plantigrade walking at a slow, irregular pace (Hallemans, De Clercq, & Aerts, 2006). At this stage the flexed position of the hip and knee lead to a dominance of plantarflexing movements at the ankle, while the upper limbs are abducted with a slightly flexed forearm (Forssberg, 1985; Hallemans et al., 2003; Hallemans, De Clercq, & Aerts, 2006; Hallemans, De Clercq, Dongen, & Aerts, 2006; McGraw, 1940, 1945; Stout, 2004; Swan et al., 2020). As the torso leans forward, the pelvis is forced to tilt mediolaterally during the swing phase of the stride, since the flexed hip contralateral to the standing leg induces the swinging leg to elevate (Hallemans et al., 2004). By the end of this phase, children usually engage in a more mature toddling pattern, with improved gait, longer steps, and a loading pattern of an initial heel-strike (Adolph et al., 2003; Hallemans, De Clercq, Dongen, & Aerts, 2006; Ivanenko et al., 2004; Swan et al., 2020; Zeininger et al., 2018).

Age class 3 includes individuals from 3.1 to 6 years of age: this phase spans late toddling to mature bipedal gait. At the beginning of this phase, children usually begin their stride with the center of pressure under the calcaneus, consistent with the pattern of initial heel-strike seen in adults (Zeininger et al., 2018). Afterwards, mature bipedal gait is progressively acquired: steps become longer, narrower, straighter, and more consistent with an adult walking gait, as the result of an increased stability produced by elevated femoral bicondylar angle that adducts the knee (Swan et al., 2020; Tardieu & Trinkaus, 1994).

2.2 Skeletal leg development during growth (0–6 years of age) 2.2.1 Age class 1 (0–1 year)

Primary ossification centers for tibial shaft appear at 7–8 weeks in utero. At birth, tibial shaft is arched posteriorly in the proximal third and straight in the distal two-thirds, while borders are usually blunt and less marked, with an evident nutrient foramen posteriorly. The perinatal fibula appears straight and slender, with rounded or angled outline in the proximal half and flattened mediolaterally in the distal half (Figure 1a). Its primary ossification center usually appears around 8 weeks in utero but does not begin ossification until the end of fetal period (O'Rahilly & Gardner, 1975). Posterolaterally, the subcutaneous triangular surface (STS) is often porotic-looking, while at the distal end of the medial surface, where the inferior transverse part of the posterior tibiofibular ligament inserts, appears as a roughened triangle.

By 6 weeks after birth, tibial proximal secondary center appears. During the first few months after birth, the tuberosity develops distally to the main proximal tibial growth plate, followed by tibial distal secondary centers around 3–10 months of age (Schaefer et al., 2009; Scheuer & Black, 2000). Around the age of 1, when toddlers normally start to walk, the foot skeleton is formed by partially ossified centers, connected by soft tissue, with no visible longitudinal arch, whose bony structure only starts developing approximately at the end of this phase (Hallemans, De Clercq, Dongen, & Aerts, 2006). In the meantime, tibial shaft, despite certain variations, usually rotates 5° laterally (tibial shaft rotates another 10° by mid-childhood and in older children and adult lateral torsion degree may reach 14°, Staheli & Engel, 1972). Tibial distal epiphysis starts to ossify, in parallel to the appearance and consequent ossification of the fibular distal epiphysis (Hoerr et al., 1962; Schaefer et al., 2009; Scheuer & Black, 2000).

2.2.2 Age class 2 (1.1–3 years)

During the second year of age, the proximal portion of the fibular shaft is more flared and consequently the neck also becomes more evident (Figure 1b). The STS is also well marked, with a flat distal metaphyseal surface. The proximal tibial epiphysis progresses its osseous expansion and appears flattened inferiorly and extended superiorly toward the tibial spines (Schaefer et al., 2009; Scheuer & Black, 2000).

2.2.3 Age class 3 (3.1–6 years)

Around 3–4 years of age, the tibial proximal epiphysis is shaped as an elongated nodule, rounded superiorly, with a pitted surface. The metaphyseal surface is flattened, with a roughly oval outline. Ossification of the tibial proximal epiphysis extends into the intercondylar region and the tubercles by 6–7 years of age. The relative articular surface is smooth, and the condyles have reached their characteristic adult morphology. Regarding the fibula, at 4 years of age in girls and 5 in boys, ossification of the fibular proximal epiphysis begins, but the timing is variable (Hoerr et al., 1962). Proximal fibular epiphysis has completed ossification and presents a rounded superior border, in level with the tibial growth plate, but does not assume adult appearance until late childhood (Scheuer & Black, 2000; Schaefer et al., 2009; Figure 1c).

The tibial distal epiphysis becomes recognizable at 3–4 years of age, shaped as an oval disc, with a projecting beak on the anteromedial aspect of the metaphyseal surface. By 3–5 years of age, the tibial medial malleolus starts to ossify. Growth is rapid, in keeping with that of the foot and by 5 years in girls and 6.5 years in boys the distal epiphyseal and metaphyseal widths are equal. Parallelly, at around 3 years of age the growth plate of the fibular distal epiphysis is at level with the tibiotalar articular surface, as a further response to the biomechanical necessities of bipedal walking. The bony fibular distal epiphysis is usually recognizable by this time and is an irregular nodule of bone with a flat metaphyseal surface (Schaefer et al., 2009; Scheuer & Black, 2000). By 6–7 years of age, the shaft of the fibula, similarly to the shaft of the tibia whose soleal line usually appears by this time as a well-distinguishable porotic fossa or ridge (Belcastro et al., 2020), has achieved adult morphology and the main borders and surfaces can usually be identified, while the distal fibular epiphysis is almost completely ossified, with a well-defined malleolar fossa (Schaefer et al., 2009; Scheuer & Black, 2000).

2.3 Anthropometric measurements

Anthropometric measurements were acquired using an osteometric board, a sliding digital caliper (Mitutoyo Digimatic caliper; resolution: 0.01 mm) and an anthropometric tape measure (Holtain LTD Harpenden Anthropometric tape). Table 2 and Figure 3 present the anthropometric measurements on the tibiae selected for this study. Table 3 and Figure 3 show the anthropometric measurements on the fibulae selected for this study.

TABLE 2. Tibial measurements and indices, obtained by anthropological literature, selected and modified for this study Nr. Definition Description References T1 Maximum tibial length Distance from the most prominent point on the proximal metaphyseal plate to the most prominent point on the distal metaphyseal plate Modified after Martin and Saller (1957), #1 T2 Tibial sagittal shaft diameter at nutrient foramen The greater distance from anterior border to the posterior surface at the level of the nutrient foramen Martin (1928), 1050, #8a; Buikstra e Ubelaker (1994): 83, #72 T3 Tibial transverse shaft diameter at nutrient foramen The maximum mediolateral (i.e., coronal) dimension of the shaft at the level of the nutrient foramen Martin (1928), 1050, #9a; Buikstra e Ubelaker (1994): 83, #73 T4 Tibial sagittal midshaft diameter Anteroposterior diameter at 50% of tibial length, from the anterior crest to the posterior surface Martin (1928), 1050, #8 T5 Tibial transverse midshaft diameter Mediolateral (i.e., coronal) diameter at 50% of tibial length Martin (1928), 1050, #9 T6 Minimum shaft circumference Minimum circumference, usually at the inferior third of tibial length Krogman and Işcan (1986) T7 Tibial midshaft shape index (T5/T4) × 100 Martin and Saller (1957) Tibial and fibular measurements, obtained by anthropological literature selected for this study and specifically designed for this study. See Tables 2 and 3 for measurement explanation TABLE 3. Fibular measurements and indices, both obtained by anthropological literature, and specifically designed for this study Nr. Definition Description References F1 Maximum fibular length Distance from the most prominent point on the proximal metaphyseal plate to the most prominent point on the distal metaphyseal plate Modified after Martin and Saller (1957), #1 F2 Fibular maximum diameter at midshaft The greatest diameter of shaft at 50% of fibular length Martin (1928): 1052, #2; Buikstra e Ubelaker (1994): 84, #76 F3 Fibular minimum diameter at midshaft The minimum diameter of shaft at 50% of fibular length Martin (1928): 1052, #3; Buisktra e Ubelaker (1994): 84, #77 F4 Circumference at midshaft The minimum circumference of shaft at 50% of fibular length Martin (1928): 1053, #4 F5 Sagittal diameter at neck Distance form anterior border to posterior surface at fibular neck Developed by DM F6 Transverse diameter at neck Distance from medial to lateral surfaces at fibular neck (i.e., coronal diameter) Developed by DM F7 Maximum diameter at neck The greatest dimension at neck, usually found along the sagittal plane Developed by DM F8 Minimum diameter at neck The shortest dimension at neck, usually found along the transverse plane Developed by DM F9 Circumference at neck The minimum circumference at fibular neck Developed by DM F10 Fibular neck shape index (F6/F5) × 100 Developed by DM F11 Sagittal diameter at midshaft Distance form anterior border to posterior surface at fibular midshaft Developed by DM F12 Transverse diameter at midshaft Distance from medial to lateral surfaces at fibular midshaft (i.e., coronal diameter) Developed by DM F13 Fibular midshaft shape index (F12/F11) × 100 Developed by DM F14 Distance from neck to STS Linear distance along the anterior border from fibular neck to the most proximal point of the subcutaneous triangular surface (STS) Developed by DM F15 Distance from neck to ILA Linear distance along the medial surface from fibular neck to the most proximal point of the interosseous tibiofibular ligament attachment (ILA) Developed by DM F16 ILA length Linear distance from the most proximal to most distal point of the ILA Developed by DM F17 STS length Maximum distance from the most proximal to the most distal point of the STS Developed by DM F18 Distance from STS to ILA Longitudinal distance from the most proximal point of the STS to the most proximal point of the ILA Developed by DM F19 STS-ILA index (F18/F15) × 100 Developed by DM F20 STS index (F17/F1) × 100 Developed by DM F21 ILA index (F16/F1) × 100 Developed by DM Abbreviations: ILA, interosseous ligament attachment; STS, subcutaneous triangular surface. 2.4 Statistical analyses

All statistical analyses were carried out in RStudio (version 4.0.0 “Arbor Day,” R Core Team, 2020). Missing data were replaced with each variable mean value. To evaluate possible asymmetry between the left and the right side, a subsample (N = 30) was selected and a t-test or a Wilcoxon test (McDonald, 2014) was carried out depending on each variable distribution. Analysis on the whole sample (N = 68) was accordingly performed. Normality distribution was assessed by Shapiro–Wilk normality test (Shapiro & Wilk, 1965). Descriptive statistics (mean, standard deviation, minimum and maximum values, and interquartile range) were then calculated for each variable on the whole sample and by sex and age class. For each variable, we assessed the presence of a linear correlation with age and calculated both a linear regression model and a LOESS fitted polynomial regression, with 95% confidence intervals and a smoothing value set at 0.6 (McDonald, 2014). This smoothing value was selected since it produced the best-fitting curves, whereas lower values tended to excessively capture the random error in the data generated by outliers (Cleveland & Devlin, 1988). The Kruskal–Wallis test (Kruskal & Wallis, 1952) was used to evaluate possible differences among sexes and age classes and pairwise comparisons were performed using the Dunn post-hoc test (Dunn, 1964). The correlation between tibiae and fibulae measurements was assessed by calculating linear regression models between homologous measurements (maximal length, sagittal midshaft diameter, transverse midshaft diameter, midshaft circumference, midshaft shape index) on the two leg bones. Finally, a principal component analysis (PCA) was carried out by computing a variance–covariance matrix, to explore data variance among sexes and age classes, utilizing the function prcomp () that by defaults centers the data.

3 RESULTS

Analyses showed no significant difference (p < 0.05) between left and right side of both the tibia and fibula. Therefore, in the analyses we considered measurements taken on the right side, occasionally replaced by measurements of the left side if the former was absent. The Shapiro–Wilk normality test revealed that data were not normally distributed therefore for the following analyses we adopted nonparametric tests.

Tables 4 and 5 and Figure S1 present descriptive statistics and boxplots of linear measurements and shape indices for the tibia for the whole sample and by sex and age 1 and 2. Tables 6 and 7 and Figure S2 show descriptive statistics and boxplots of linear measurements and shape indices for the fibula for the whole sample and by sex and age.

TABLE 4. Descriptive statistics (mean, standard deviation, max–min values, interquartile ranges) for the tibia, considering the whole sample Mean (SD)