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. 2019 Apr 26;235(1):34–44. doi: 10.1111/joa.12997

Maturation of the human foetal basioccipital: quantifying shape changes in second and third trimesters using elliptic Fourier analysis

Mélissa Niel 1,✉, Kathia Chaumoître 1,2, Julien Corny 1, Loïc Lalys 1, Pascal Adalian 1
PMCID: PMC6579950  PMID: 31025333

Abstract

During prenatal development, the brain is considered the best maturation criterion for the estimation of foetal physiological age, regardless of the conditions of pregnancy. Unfortunately, the brain lyses very quickly after death, but fortunately, the brain also has a major influence over osseous structures of the cranial base during development. Therefore, we considered the osseous structures of the cranial base potential indirect maturation indicators of foetal age. Because of its early formation and robustness, the basioccipital is a cranial base bone that is often used for studies in biological anthropology. Studies generally use conventional morphometry and bone size ratio to highlight morphological changes occurring during the foetal period and to create age estimation methods. These methods usually define thresholds beyond which the morphology of the basioccipital changes, but do not fully consider the form that might be valuable precisely to visualize its development or improve age estimation methods. Using geometric morphometric methods, the present study aims to analyse the development of the basioccipital during the second and third trimesters of foetal life by quantifying and visualizing shape changes in the inferior view. Basioccipital shapes are used as direct indicators of the maturation of the cranial base and as indirect indicators of the maturation of the brain and, by extension, the whole body. A sample of 221 anonymized computed tomographic (CT) scans of normal foetuses, ranging from 18 to 41 gestational weeks (GW), was used. Elliptic Fourier analysis (EFA) was used to quantify the basioccipital outline, and maturation stages were established to visualize shape changes with a principal component analysis. Our study allowed us precisely to quantify and continuously visualize shape changes occurring during prenatal life. Additionally, this study provides the first evidence of two distinct linear shape trajectories of the basioccipital. Foetuses aged between 18 and 26 GW have a rapid shape change with well‐individualized stages, whereas shape changes are less visible in the second trajectory (27–41 GW). Furthermore, intra‐stage shape variation is higher for the basioccipital at the beginning of the second and third trimesters than at the first trimester. By using geometric morphometric methods and EFA, this study shows that it was possible to go beyond classical methods. Indeed, the developed methodology enabled the first quantification of the overall shape changes of the basioccipital between gestational ages. The morphological shape changes throughout the foetal period can be useful for anthropological studies and provide new perspectives for immature age estimation methods.

Keywords: age estimation, geometric morphometrics, occipital bone, skull base, stage

Introduction

During prenatal development, brain maturation is considered the best criterion for the estimation of foetal physiological age, regardless of the environmental or socio‐economic conditions, and even in cases of foetal or maternal pathologies (Feess‐Higgins & Larroche, 1987; Piercecchi‐Marti et al. 2000; Scheuer et al. 2000). Certainly, the brain will be affected by unfavourable growth conditions and may, for instance, be of a smaller size, but its maturation will be best preserved. Unfortunately, the brain lyses very quickly after death, but it has an influence on osseous structures of the cranial base during development (Grossman & Zuckerman, 1955; Ford, 1956; Trenouth, 1984; Mandarim de lacerda & Alves, 1992; Lieberman et al. 2000; Jeffery & Spoor, 2002; Morimoto et al. 2008; Captier et al. 2013). Therefore, the osseous structures of the cranial base are considered indirect and stable maturation indicators of foetal age.

The occipital bone, situated at the posterior part of the cranial base, comprises four separate elements in foetuses: the pars squama, two pars laterales and the pars basilaris or basioccipital (Fig. 1). Because of its early formation and robustness, the basioccipital is often used for studies in biological anthropology. A single centre of ossification appears between the 10th and 14th gestational weeks (GW; Fazekas & Kósa, 1978; Jeffery & Spoor, 2004; Macklin, 1921; Nemzek et al. 2000; Noback, 1944; Noback & Robertson, 1951; Redfield, 1970) from the embryonic parachordal cartilage. Ossification occurs from the anterior part of the cartilage to the posterior part (Nemzek et al. 2000). The basioccipital articulates anteriorly with the sphenoid bone at the spheno‐occipital synchondrosis, with a fusion between 11 and 16 years in girls and 13 and 18 years in boys (Scheuer et al. 2000). Posteriorly, the basioccipital articulates with the pars lateralis at the anterior intra‐occipitalis suture, with a fusion between the 4th and 7th year (Kamina & Martinet, 2009; Schaefer et al. 2009; Scheuer et al. 2000; Fig. 1). The basioccipital is particularly dense and compact (Redfield, 1970; Fazekas & Kósa, 1978; Scheuer & Black, 2004) and is generally found intact in forensic and archaeological contexts (Fazekas & Kósa, 1978; Lewis, 2006).

Figure 1.

Figure 1

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3D CT scan reconstruction of the occipital bone in inferior view of a foetus aged 28 gestational weeks (GW).

In biological anthropology, studies on the basioccipital generally use conventional morphometry [maximum length (ML), sagittal length (SL), maximal width (MW)] and bone size ratio to highlight morphological changes occurring during foetal development and for age estimation methods (Redfield, 1970; Fazekas & Kósa, 1978; Scheuer & MacLaughlin‐Black, 1994; Nagaoka et al. 2012; Olivares & Aguilera, 2017). These methods have defined thresholds beyond which the morphology of the basioccipital changes, but do not consider the form which might be valuable to highlight its ontogenetic development or to improve age estimation methods.

Geometric morphometric methods enable the quantification and visualization of precise morphological variation through powerful statistical and visualization tools (Slice, 2007; Mitteroecker & Gunz, 2009). In geometrical morphometrics, the form of an object is defined by both its shape and size (Needham equation: form = shape + size; Needham, 1950). The shape is defined as the geometric properties of an object that are invariant to scale, rotation and translation (Mitteroecker & Gunz, 2009). In biological anthropology, the shape corresponds to bone maturation, whereas the size corresponds to growth. Based on geometric morphometric methods, previous studies have described the development of the foetal cranial base as a whole (Jeffery, 2002; Jeffery & Spoor, 2004; Morimoto et al. 2008; Herlin et al. 2011), but the basioccipital has never been analysed alone in detail.

Using computed tomographic (CT) scan imaging of non‐pathological foetuses, the purpose of the present study is to analyse the maturation of the human basioccipital during the second and third trimesters of foetal life by (1) quantifying shape changes and variation and (2) accurately identifying which aspects of shape differ between gestational ages using geometric morphometric methods. Finally, to determine the potential of our approach for age estimation purposes, we will test whether it is possible to assign a shape to a gestational age with a validation sample.

Methods

Dataset

The studied population included 221 foetuses with no pathological growth (75 girls, 110 boys, 36 of unknown sex), ranging from 18 to 41 GW (mean age: 29.4 GW). The antemortem and postmortem CT scans were collected from the Picture Archiving and Communication System (PACS) in the hospital services of Marseilles (AP‐HM, France). The foetuses were scanned with a helical CT scanner (Somatom Sensation Cardiac 64; Siemens, Erlangen, Germany). The scanning parameters were as follows: voltage 100–140 kVp, amperage 50–150 mA, and thickness 0.75–1 mm. These high‐resolution native slices recorded in the Digital Imaging and Communications in Medicine (DICOM) format were anonymized before being used in our study.

Non‐pathological development was established by the medical records after antemortem (CT scan in utero) or postmortem examinations (complete visceral examination, histological study, foetal karyotype, placenta examination, description of external and visceral abnormalities, front and profile radiography) conducted by a panel of experts. Indeed, since the advent of prenatal diagnosis centres (Decree 97‐578 of 28 May 1997, consolidated on 11 May 2018, France), foetuses are systematically examined in case of medical interruption of pregnancy or for foetuses that die spontaneously (miscarriages and in utero death). These examinations enable the identification of malformations (bone or visceral) or chromosomal abnormalities, or even the precise determination of the cause of death (Adalian et al. 2001, 2002).

The studied population was divided into two samples: a learning sample (A) on which the shape was quantified (Fig. 2) and a validation sample (B) on which to assess whether a given maturation is correctly assigned to its own gestational age (Fig. 2).

Figure 2.

Figure 2

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Age and sex distribution of both samples: a learning sample (A) comprising 191 foetuses and a validation sample (B) comprising 30 foetuses.

Data analysis

Segmentation and bone surface reconstructions

For the segmentation step, a grey‐scale value representing Hounsfield units and corresponding to the separation between bone and soft tissue, was calculated from DICOM slices on imagej® v1.51 software (National Institutes of Health, USA). The threshold value was obtained by calculating a threshold mean value (TMV; Coleman & Colbert, 2007), which is an average of the half‐maximum height (HMH; Spoor et al. 1993) values. The TMV was reported in avizo Standard Edition software (v.7.0.0®, Visualization Sciences Group, SAS) to reconstruct the three‐dimensional (3D) surface of the basioccipital.

Analysis of shape: elliptic Fourier analysis

The shapes of the basioccipital, corresponding to the maturation process, were analysed using geometric morphometric methods with elliptic Fourier analysis (EFA; Caple et al. 2017; Kuhl & Giardina, 1982; Lestrel, 1982; Rohlf, 1990; Lestrel, 2008), where the outline shape variation was quantified in the inferior view.

Definition of a reference plane

Before analysing the shape of the basioccipital, it was necessary to define a homologous reference plane that gives the same orientation to all of the basioccipital. Three type II and III landmarks were digitized on a 3D reconstructed surface (Table 1) using avizo v.7.0.0® software. The plane passing through these three points made it possible to obtain all 3D reconstructions in the same 2D plane. The resulting 2D representations of the basioccipital in the inferior view were used for morphometric procedures (Fig. 3).

Table 1.

Landmark definitions and types, according to Bookstein's classification (Bookstein, 1991), which were used to define the 2D plane of the basioccipital

Landmark Definition Type
A The most posterior point of the left horn II
B The most posterior point of the right horn II
C Central point of the anterior surface III
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Figure 3.

Figure 3

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2D plane of the basioccipital obtained with landmarks A, B and C. The basioccipital is represented in the inferior view, anterior view downward and posterior view upward.

Outline digitization and normalization

The 2D representations of the basioccipital were contrasted to automate the outline. The shapes were quantified by 150 equally linearly spaced points digitized along the contour with the tpsdig2 v.2.17® digitization programme (Rohlf, 2013).

Before comparison, the contour data for the basioccipital must be normalized to be invariant to location, size, orientation and starting point, as elliptical Fourier coefficients belong to a coordinate system (Rohlf & Archie, 1984; Lestrel, 1989; Rohlf, 1990). The normalization was based on a generalized Procrustes analysis (GPA; Friess & Baylac, 2003). The GPA normalization on EFA is based on homologous landmarks called control points. The latter are superimposed in the GPA (Gower, 1975; Rohlf and Slice, 1990; Rohlf, 2000). This normalization involves the superimposition of the control points by extracting their position, size and orientation parameters (Lestrel, 2008). Thus, the GPA generated a corresponding outline to follow and normalize these points (Friess & Baylac, 2003).

Four type II and III landmarks (Bookstein, 1991; Table 2) were used to superimpose the basioccipital outlines (Fig. 4). EFA must begin with a single landmark to initiate the shape approximation, so the starting point of the outline corresponds to landmark 1 (Table 2).

Table 2.

2D landmarks or control points used to normalize basioccipital outlines and types according to Bookstein's classification (Bookstein, 1991)

Landmark Definition Type
1 Extreme end of the left horn II
2 Basion II
3 Extreme end of the right horn II
4 Midpoint of the spheno‐occipital synchondrosis III
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Figure 4.

Figure 4

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Outline defined at 150 points and homologous control points (1–4) used for the generalized Procrustes analysis.

Measurement error and harmonics number

In our protocol, measurement error can come from the definition of the reference plane and the digitization of landmarks and outlines of the basioccipital. To validate the whole protocol, we performed repeatability (intra‐observer error) and reproducibility tests (inter‐observer error) on 30 randomly selected individuals in our sample. Repeatability was tested by the same observer repeating the protocol twice, several weeks apart (sessions 1 and 2); for reproducibility, a second observer applied the protocol once (session 3).

Using EFA, the number of harmonics determines the accuracy outline. According to the Nyquist theorem (Shannon, 1949), the harmonic number must be less than half the number of sampled outline points. Consequently, on the 150 points sampled for EFA, only the first 74 harmonics were retained for analysis. Given that we cannot retain all the Fourier coefficients for our analysis because the measurement error is expected to increase with harmonic ranks, the percentage of error on harmonic coefficients was calculated using a similar approach as the Procrustes anova on the three sessions (Claude, 2013). This procedure calculated the mean sums of squares for the four coefficients of each harmonic to observe the evolution of error according to the rank of harmonics (in percentage). Only the first harmonics, showing an acceptable digitization error rate, were retained for further analyses. An error rate under 35% is considered to be reasonable in an outline tooth analysis using EFA (Claude, 2013).

The assessment of the total percentage of measurement error was then performed using a Procrustes anova (Goodall, 1991; Klingenberg & McIntyre, 1998; Claude et al. 2003; Debat et al. 2008; Claude, 2013) adapted to elliptic Fourier coefficients. The Fourier coefficients of the coupled series (sessions 1 and 2, and sessions 1 and 3) are used in the Procrustes anova with the number of harmonics previously defined. The intra‐ and inter‐individual variances were calculated directly from the means of the sums of squares and crossed products corresponding to individuals and residual sources of variation. These residuals, representing the variability between the two sessions, correspond to the measurement error (Klingenberg & McIntyre, 1998).

Creation of maturation stages

To visualize chronologically the morphological changes during the second and third trimesters of foetal development, maturation stages were established based on the basioccipital shapes. Consensus shapes, comprising four GW with overlap every 2 weeks, were created to obtain a continuous vision of the maturation process from 18 to 41 GW. Eleven stages of consensus shapes, defined by the mean of 9–52 shapes depending on stages, were obtained (Table 3). To visualize and compare the morphology of each consensus shape, the basioccipital outlines were reconstructed from Fourier coefficients with the inverse Fourier transform (Rohlf & Archie, 1984; Monti et al. 2001; Claude, 2008).

Table 3.

Age groups (GW: gestational weeks) and number of individuals according to the 11 stages of maturation of the basioccipital

Stage Age group (GW) Number in group
1 18–21 9
2 20–23 34
3 22–25 52
4 24–27 36
5 26–29 30
6 28–31 39
7 30–33 50
8 32–35 51
9 34–37 37
10 36–39 24
11 38–41 13
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Principal components analysis of shape variation and intra‐stage shape variability

To explore the morphological changes and quantify the variability between stages during the foetal development of the basioccipital, a principal components analysis (PCA; Wold et al. 1987) was performed on the consensus shapes of the 11 stages of maturation. The reconstruction of extreme morphologies along each principal component (PC) was obtained for elliptic Fourier data to understand and visualize which shape features were involved in the variation observed along the two axes.

The quality of projection of the stages on the PCA plot was calculated with the squared cosine (cos²). This corresponds to the square of the cosine of the angle from the right triangle made with the origin, the stage, and its projection on the component (Abdi & Williams, 2010). This value is calculated for each axis, and the closer it is to 1, the better projected the stage is on the plane (Abdi & Williams, 2010; Husson et al. 2016). Proximity between individuals that are well projected can be interpreted. Also, the contribution of each stage to the first two PC was obtained by the ratio of the squared factor score of the stage by the eigenvalue associated with that component (Abdi & Williams, 2010). This value is expressed as a percentage, and the sum of the contributions of all stages for a given component is equal to 100%. The larger the value of the contribution, the more the stage contributes to the component (Abdi & Williams, 2010; Husson et al. 2016).

Finally, the morphological disparity among stages was also calculated with the individual.disparity function (Polly, 2008). Disparity is calculated as the mean squares distance among the 11 stages.

Assigning a shape to a maturation stage

The final aim of this study follows an age estimation perspective: is it possible to assign a given shape to a maturation stage? The protocol of the previously described outline analysis (definition of a 2D reference plane, outline and landmark digitization) was applied to the basioccipital of validation sample B to verify whether a given shape was correctly attributed to its maturation stage. The protocol was applied to each of the 30 tested basioccipital samples and the resulting outline was added to the 11 outlines representing the consensus shapes. Once the 12 outlines are quantified with EFA after the GPA procedure, assigning a maturation stage to the tested basioccipital is realized by calculating the Euclidian distance (or Procrustes distance) between the sets of Procrustes shape coordinates (the square root of the sum of the squared distances). The minimal distance between the centroid of the tested basioccipital and one of the 11 consensus shapes allowed us to assign a stage to the pars basilaris.

Analyses were performed with RStudio (developed for R software–Version 0.99.893 – ® 2009‐2016 RStudio, Inc.) using the software packages Momocs (Bonhomme & Claude, 2017), Morpho (Schlager & Jefferis, 2017), Geomorph (Adams et al. 2017), factoextra (Kassambara & Mundt, [Link]), efourier and iefourier functions (Claude, 2008), and individual.disparity function (Polly, 2008).

Results

Quantification of basioccipital shapes

Number of harmonics

The percentage of measurement error is inferior to the threshold that we defined at 10% for the first 14 harmonics (Supporting Information Fig. S1). Beyond the 14th harmonic, the measurement error per harmonic increases almost continuously because the higher the harmonic ranks are, the smaller the details on the outline shape. Thus, the first 14 harmonics corresponding to 56 Fourier coefficients per individual were chosen for analyses, allowing us faithfully to reconstruct the outline of the basioccipital (Supporting Information Fig. S2).

Measurement error

The percentage of measurement error for our protocol is 1.13% for repeatability and 1.96% for reproducibility for the selected first 14 harmonics. These results show that the impact of measurement error is very low, indicating that our protocol is reliable and reproducible.

Morphological description

Shape of the basioccipital

The PCA results for the 11 consensus stages of maturation are shown in Fig. 5. The first two principal components account for 99.41% of the total shape variation (PC1: 93.76%, PC2: 5.65%). The shape changes associated with the first two PCs are provided in Fig. 5.

Figure 5.

Figure 5

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Principal component analysis (PCA) of the shape data for the 11 stages (S) of the basioccipital with the quality of representation for each stage (squared cosines), and variation along PC1 and PC2; the grey shape corresponds to minimal scores and the black outline corresponds to maximal scores.

Before describing the morphological variation, the quality of projection of the stages on the PCA plot was calculated with the squared cosine (cos²). In Fig. 5, the squared cosine values of each stage are all very close to 1 (cos² > 0.90), meaning that they are well projected on the plane with the first two PCs (Fig. 5). Therefore, the increasing order of the stages and the two shape trajectories visible on the PCA plot are a biological reality.

The morphological variation across PC1 corresponds to important shape changes in the outline of the basioccipital. The shape variability represented by the extreme negative scores of PC1 corresponds to foetuses aged between 18 and 27 GW (stage 1–4) and a narrow anteroposteriorly elongated basioccipital with a curved anterior base. Posterior horns and lateral reliefs are not developed, and the anterior edge of the foramen magnum is not pronounced. On the extreme positive scores of PC1 for foetuses over 27 GW (stage 5–11), the basioccipital is wide, with developed lateral reliefs and posterior horns. The anterior edge of the foramen magnum is deep, allowing the individualization of the curved posterior horns. The anterior surface base is enlarged and angular, forming an angle of approximately 120° with lateral relief. Not much information about shape variation is provided by the basioccipital outline on PC2. The basioccipitales located in the negative scores of PC2, corresponding to foetuses aged from 22 to 35 GW, have a slightly less pronounced width than those located in positive values (foetuses from 18 to 23 GW to 34‐41 GW). PC2 mainly shows more developed lateral relief in the positive scores.

Moreover, stages 1–4 and 5–11 show two different linear shape trajectories (Fig. 5), with a break point of approximately 26–27 GW. During the second and third trimesters, there is continuous and progressive logic in the different stages of maturation along PC1 (Fig. 5). The first shape trajectory (stage 1–4) is defined by important and rapid shape changes (Fig. 5) on the negative values of PC1, whereas on the positive values, there is a slowdown in shape changes (Figs 5 and 6) from stages 5–11. Furthermore, in the first linear shape trajectory, stage 1 is separate from stages 2–4. For the second linear trajectory, stages 6–8 are near each other and stages 10 and 11 are apart from the other stages. All stages are well individualized, with their own shapes, except for stages 6–8 and 10–11, which have a relatively closed shape (Fig. 5).

Figure 6.

Figure 6

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Consensus shapes of the 11 stages of maturation.

The contribution of each stage to the first two PCs is expressed as a percentage (Fig. 7). On the graph, the dashed line indicates the expected average contribution value if each stage was homogeneous, around 9.09% (100/11 stages). The maturation stages with a contribution greater than this threshold (stages 1, 2, 10 and 11) indicate that they strongly contribute to PC1 and PC2 and are the most important to explain the shape variability during the foetal development. Stages 5–8 are those that contribute the least (Fig. 7).

Figure 7.

Figure 7

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Contribution (in percentage) of the maturation stages to the first two principal components. The dashed line indicates the expected average contribution value if each stage was homogeneous.

Intra‐stage shape variability

Intra‐stage shape variability is not linear (Fig. 8). The youngest foetuses (stage 1: 18–21 GW) have the highest intra‐stage shape variation. Foetuses of stage 9, aged between 34 and 37 GW, also have a high intra‐shape variation. Variation is lower for other stages (stages 2–8: 20–35 GW, and 10–11: 36–41 GW), particularly for stage 3 (Fig. 8).

Figure 8.

Figure 8

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Variability within each stage of the consensus shape of the basioccipital.

Assessment of a maturation stage

Among the individuals of sample B, 24 (80%) have shapes that are well assigned to maturation stages. For five of these individuals (16.66%), the assigned maturation stage was shifted by one stage (inferior or superior). When the stages are transformed into gestational age, the shift between expected and assigned stages represents only one or two GW. Finally, for one individual, the assigned stage was shifted by two stages, corresponding to a minimal difference of three GW between the expected and assigned stages (Table 4).

Table 4.

Assessment of the maturation stage for sample B individuals (GW: gestational week). Italic and bold lines represent incorrect assignment

Individual Age (GW) Sex Expected stage Assigned stage
43 31 F 6 or 7 8
65 30 F 6 or 7 7
81 20 F 1 or 2 1
84 41 M 11 11
100 22 M 2 or 3 1
122 24 M 3 or 4 4
124 31 M 6 or 7 7
89 38 M 10 or 11 10
108 22 M 2 or 3 2
112 22 F 2 or 3 2
121 23 M 2 or 3 3
127 33 F 7 or 8 7
137 23 F 2 or 3 3
150 24 M 3 or 4 4
158 25 F 3 or 4 2
161 26 M 4 or 5 5
167 24 M 3 or 4 4
186 25 M 3 or 4 3
204 33 M 7 or 8 9
243 28 M 5 or 6 6
257 28 I 5 or 6 6
288 31 F 6 or 7 5
356 29 M 5 or 6 5
1017 34 F 8 or 9 6
1046 32 F 7 or 8 8
1048 35 M 8 or 9 8
1055 37 F 9 or 10 9
1063 36 I 9 or 10 9
1124 35 M 8 or 9 9
1132 33 I 7 or 8 8
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Discussion

Quantification of shape

Because the foetal basioccipital is anteroposteriorly elongated and thin, a 2D analysis provides a quantification of the major pattern of shape variation of this bone, and the inferior surface is more regular. The curved morphology of the basioccipital does not enable the positioning of the homologous type I landmark (Bookstein, 1991); only type II and III landmarks can be positioned. Furthermore, the aim of this study was to analyse the global shape of the basioccipital.

Outline analysis provides complex and detailed information on the shape. The choice of the outline analysis method tended towards Fourier descriptors frequently used to quantify morphological differences or discriminate biological forms (Rohlf & Archie, 1984; Friess & Baylac, 2003; Lestrel, 2008; Claude, 2013; Corny & Detroit, 2014). This method allows the mathematical quantification of the global characteristics of a complex form, which are not dependent on homologous points (Lestrel, 2008). As ellipses are used, the shape description in EFA is global and helpful for describing bones with curved edges (Caple et al. 2017). Thus, EFA provides a powerful geometric morphometric method to analyse, both visually and quantitatively, the shape changes of the basioccipital.

The few landmarks available (type II and III, Bookstein, 1991) were used to define the reference plane and normalize the Fourier descriptors. The normalization method using GPA on the control point (Friess & Baylac, 2003) prevents the homology problems encountered by specimen alignment on the major axis of the first ellipse, which is conventionally used for Fourier descriptor normalization (Kuhl & Giardina, 1982). Indeed, this method is not adapted to the basioccipital because the ratio between length and width changes during foetal development (Redfield, 1970; Fazekas & Kósa, 1978; Scheuer & MacLaughlin‐Black, 1994; Tocheri & Molto, 2002; Nagaoka et al. 2012). It was also shown that normalization with GPA is the most appropriate method to use for almost circular contours (Corny & Detroit, 2014), such as the basioccipital contour.

Morphology and variability of the basioccipital

Several authors have shown with traditional morphometry that basioccipital dimensions evolve during foetal development (Scheuer & MacLaughlin‐Black, 1994; Scheuer et al. 2000; Tocheri & Molto, 2002; Nagaoka et al. 2012) and its characteristics intensify with age (Scheuer et al. 2000). Morphological characteristics of the basioccipital are used not only in anatomy but also in biological anthropology, as they can give an idea about the foetal age. Indeed, the ratio between width and length has often been used (Redfield, 1970; Fazekas & Kósa, 1978; Scheuer & MacLaughlin‐Black, 1994; Tocheri & Molto, 2002; Nagaoka et al. 2012). According to Redfield (1970), the youngest foetuses have a longer than wide basioccipital, which usually remains this way or becomes squared in older foetuses. In the Fazekas & Kósa (1978) study, the basioccipital thickens gradually, and from 8.5 lunar months, the width exceeds the length due to lateral relief development. According to Scheuer & MacLaughlin‐Black (1994), if the MW is inferior to the SL, then the foetus is probably less than 28 weeks in utero. If the MW is larger than the maximal length, then the individual must be older than 5 months postnatal. For Tocheri & Molto (2002), if the SL is greater than the MW, then the individual is probably less than 32 weeks or 8 lunar months pregnant. Finally, according to Nagaoka et al. (2012), the SL is greater than the maximum width before 7 months, whereas after 7 months, this ratio is reversed. Our analysis using geometric morphometric methods confirmed this increase in morphological changes from 18 to 41 GW.

Most importantly, this analysis enables the first precise quantification and visualization of the shape changes of the whole basioccipital during prenatal development. The creation of maturation stages with overlapping ages allowed us continuously to follow the development of the basioccipital in inferior view. Analyses highlighted that the basioccipital shape presents two distinct linear trajectories between individuals whose age is inferior and superior to 26–27 GW, with rapid shape changes occurring during the first trajectory (18–26 GW). Shape changes are fast, with well‐individualized shape and marked intra‐stage shape variability for the youngest foetuses. Shape changes slow down for the second trajectory (27–41 GW), with marked intra‐stage shape variability for foetuses near the end of the pregnancy. This increase in shape variability at the beginning of the second and third trimesters of foetal life was not highlighted in previous studies of the basioccipital.

Age estimation perspective

The two linear shape trajectories and the results obtained from sample B were very encouraging for age estimation methods. The developed methodology shows that it is possible to assign a maturation stage correctly to a given basioccipital for 80% of the individuals who have not been used to establish maturation stages. For the remaining 20% of the individuals, the attribution error is one (16.66%) or two stages (3.33%), representing up to 3 weeks of error only. Thus, the assessment of a given basioccipital based on a consensus stage from 18 to 41 GW will allow archeo‐anthropologists and forensic anthropologists visually to distinguish a young foetus from an older foetus and to obtain an age estimation from the shape. As the basioccipital is a robust bone that resists very well to taphonomic changes, when facing a forensic context where no organs are available and the rest of the skeleton is poorly preserved, these morphological shape changes of the basioccipital have a major impact because they can be a useful tool to assess the foetal viability fixed to 22 GW by the World Health Organization.

The maturation process of the basioccipital can also be used to complement bone measurement. For instance, there is close accordance between the stages of maturation of the basioccipital and the length of the humeral bone in foetuses (Kyrkanides et al. 1993). For further analyses, the developed method could be of interest to control the development of foetuses by combining both maturation and growth processes with geometric morphometric analysis. This can be particularly important in forensic contexts. With a few exceptions, most developmental pathologies leading to biometric changes in very young individuals do not leave traces on the bones. Consequently, it is often considered that finding a short bone (say, a femur or a humerus) is synonymous with finding a young individual. Our approach will nuance this interpretation, and if we observe a discrepancy between the size of the bone and the maturation stage of the basioccipital, we may suspect a change in the ontogenetic trajectory, and qualify our conclusions.

Conclusion

This innovative study, developed from a validated protocol, enabled the first step‐by‐step analysis of the two linear trajectories of normal human basioccipital shapes during the second and third trimesters of foetal life. Using geometric morphometric methods and EFA, it was possible to quantify shape changes and intra‐stage shape variability, allowing the precise identification of shape changes between gestational ages. These morphological shape changes throughout 18 and 41 GW can be useful for anthropological studies, especially for immature ageing methods.

Author contributions

M. Niel: conception and design, image selection and treatment, data analysis and interpretation, manuscript writing. K. Chaumoître: CT scan data for human foetuses. J. Corny: data analysis and interpretation, manuscript revision and approval of the article. P. Adalian and L. Lalys: conception and design, data interpretation, manuscript revision and approval of the article.

Supporting information

Fig. S1. Percentage of measurement error based on the harmonic rank (1 to 74). The red line represents the threshold of 10%.

Click here for additional data file. (8.3MB, eps)

Fig. S2. Outline reconstructions of the basioccipital (dark outline): harmonic 1, 5, 10 and 14. Grey shapes represent the reconstruction of the basioccipital, with a total of 74 harmonics.

Click here for additional data file. (2.9MB, eps)

Acknowledgements

The authors would like to thank the anonymous reviewers for their comments and suggestions which helped to improve the quality of the manuscript. We declare no conflict of interest.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Fig. S1. Percentage of measurement error based on the harmonic rank (1 to 74). The red line represents the threshold of 10%.

Click here for additional data file. (8.3MB, eps)

Fig. S2. Outline reconstructions of the basioccipital (dark outline): harmonic 1, 5, 10 and 14. Grey shapes represent the reconstruction of the basioccipital, with a total of 74 harmonics.

Click here for additional data file. (2.9MB, eps)

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