2.5.2. Growth Criterion: Femoral Lengths

Femoral diaphysis lengths were measured (in millimeters) on Avizo Standard Edition®. Percentiles were calculated from sample A according to each maturation stage of the *pars basilaris* and used as growth criteria (Table 1). To include a greater range, a margin of ten percentiles was added at each extreme, calculated as the difference between 0 and 10 percentiles and between 100 and 90 percentiles, thus providing 0–10 percentiles and 100 + 10 percentiles, respectively (Table 1).

#### *2.6. Statistical and Morphometric Analyses*

#### 2.6.1. Bilateral Femoral Asymmetry and Sex Effect on the Variables

Between-sex comparisons of the *pars basilaris* shapes were explored using nonparametric multivariate ANOVA (MANOVA) [59], and the between-sex comparison of the femoral lengths was performed using Kruskal–Wallis rank sum testing. The bilateral femoral asymmetry was explored using a *t*-test.

#### 2.6.2. Application of the Coupling Method in Samples B and C

Each *pars basilaris* of samples B and C was tested, one at a time, by comparison with the 19 stages representing the maturation consensus shapes. Once the outlines were quantified with EFA after the GPA procedure, assigning a maturation stage to the tested *pars basilaris* was realized by calculating the Euclidian distance (or Procrustes distance) between the centroids of the 19 consensus stages and the tested (compared) shape [60,61]. The minimal distance between the centroid of the tested *pars basilaris* and one of the 19 consensus shapes allowed for the assignation of a stage to the *pars basilaris*.

For growth, the measurement of the tested individual femoral length was compared to the range expected for the defined maturation stage (Table 1). If this measurement was found to be within the expected range, we considered that growth corresponded to the maturation stage values and there was "coupling". Then, it could be concluded that growth was "normal" (i.e., nonpathological). On the contrary, if growth did not correspond to the maturation stage values, then "uncoupling" had occurred.

Analyses were performed using *RStudio* (developed for R software—Version 1.1.383— ® 2009–2017 RStudio, Inc., Boston, United States) and the software packages *Momocs* [62], *Morpho* [63], *geomorph* [64], *car* [65], *gap* [66], *efourier*, and *iefourier* functions [56]. *Biology* **2022**, *10*, x FOR PEER REVIEW 8 of 20

#### **3. Results 3. Results**

#### *3.1. Quantification of Pars Basilaris Shapes 3.1. Quantification of Pars Basilaris Shapes*

#### 3.1.1. Number of Harmonics 3.1.1. Number of Harmonics

The percentage of measurement error was inferior to the threshold defined at 10% for the first 14 harmonics, corresponding to 56 Fourier coefficients per individual. This allowed us to faithfully reconstruct the outline of the *pars basilaris* (Figure 2). The percentage of measurement error was inferior to the threshold defined at 10% for the first 14 harmonics, corresponding to 56 Fourier coefficients per individual. This allowed us to faithfully reconstruct the outline of the *pars basilaris* (Figure 3).

**Figure 3.** Outline reconstructions of the *pars basilaris* (dark outline): harmonics 1, 5, 10, and 14. Gray shapes represent the reconstruction of the *pars basilaris* with the maximum number of harmonics (74 in this study). **Figure 2.** Outline reconstructions of the *pars basilaris* (dark outline): harmonics 1, 5, 10, and 14. Gray shapes represent the reconstruction of the *pars basilaris* with the maximum number of harmonics (74 in this study).

#### 3.1.2. Measurement Error 3.1.2. Measurement Error

The percentage of measurement error for the outline protocol is 1.13% for repeatability and 1.96% for reproducibility for the selected first 14 harmonics. This protocol is reliable and reproducible. The percentage of measurement error for the outline protocol is 1.13% for repeatability and 1.96% for reproducibility for the selected first 14 harmonics. This protocol is reliable and reproducible.

#### *3.2. Between-Sex Differences and Femoral Length 3.2. Between-Sex Differences and Femoral Length*

The nonparametric MANOVA showed that there were no significant shape differences between sex groups (*F* = 1.503, d*f* = 2, *p* = 0.199) and the femoral lengths were not The nonparametric MANOVA showed that there were no significant shape differences between sex groups (*F* = 1.503, d*f* = 2, *p* = 0.199) and the femoral lengths were not sig-

significantly different between sex groups (*p* = 0.706). Additionally, there was no bilateral

The maturation and growth criteria are summarized in Figure 4. Each maturation stage corresponds to a range of femur lengths defined by the lower bound (0 − 10 percentiles) and the upper bound (100 + 10 percentiles), corresponding to the extremes.

asymmetry (*p* = 0.239) between the right and left femoral diaphysis.

**Figure 4.** Maturation and growth criteria by stage and age group (in weeks).

nificantly different between sex groups (*p* = 0.706). Additionally, there was no bilateral asymmetry (*p* = 0.239) between the right and left femoral diaphysis. significantly different between sex groups (*p* = 0.706). Additionally, there was no bilateral asymmetry (*p* = 0.239) between the right and left femoral diaphysis.

**Figure 3.** Outline reconstructions of the *pars basilaris* (dark outline): harmonics 1, 5, 10, and 14. Gray shapes represent the reconstruction of the *pars basilaris* with the maximum number of harmonics

The percentage of measurement error for the outline protocol is 1.13% for repeatability and 1.96% for reproducibility for the selected first 14 harmonics. This protocol is

The nonparametric MANOVA showed that there were no significant shape differences between sex groups (*F* = 1.503, d*f* = 2, *p* = 0.199) and the femoral lengths were not

The percentage of measurement error was inferior to the threshold defined at 10% for the first 14 harmonics, corresponding to 56 Fourier coefficients per individual. This

allowed us to faithfully reconstruct the outline of the *pars basilaris* (Figure 3).

#### *3.3. Coupling between Maturation and Growth 3.3. Coupling between Maturation and Growth*

*3.2. Between-Sex Differences and Femoral Length*

The maturation and growth criteria are summarized in Figure 3. Each maturation stage corresponds to a range of femur lengths defined by the lower bound (0–10 percentiles) and the upper bound (100 + 10 percentiles), corresponding to the extremes. The maturation and growth criteria are summarized in Figure 4. Each maturation stage corresponds to a range of femur lengths defined by the lower bound (0 − 10 percentiles) and the upper bound (100 + 10 percentiles), corresponding to the extremes.

*Biology* **2022**, *10*, x FOR PEER REVIEW 8 of 20

*3.1. Quantification of Pars Basilaris Shapes*

3.1.1. Number of Harmonics

**3. Results**

(74 in this study).

3.1.2. Measurement Error

reliable and reproducible.

**Figure 4.** Maturation and growth criteria by stage and age group (in weeks). **Figure 3.** Maturation and growth criteria by stage and age group (in weeks).

Method Application

The method was applied to the validation sample B and the pathological sample C to verify whether growth and maturation were coupled or, in other words, whether the individual's growth corresponded to the values expected by their maturation stage (Figure 3).

In sample B, we observed coupling in 90.48% of samples. The four cases where uncoupling was detected correspond to two growth delays (−4.82 and −1.70 mm) and two growth advancements (+1.26 and +13.13 mm). These values were calculated by subtracting the femoral length of the tested individual (*X T* ) at the upper (*I s* ) or lower (*I i* ) values of the expected interval for the maturation stage, depending on whether individual measurement was inferior or superior to the interval.

For a measurement inferior to the interval:

*X <sup>T</sup>* <sup>−</sup> *<sup>I</sup> <sup>i</sup>* <sup>=</sup> <sup>−</sup>*<sup>x</sup>* or growth delay,

For a measurement superior to the interval:

*X <sup>T</sup>* <sup>−</sup> *<sup>I</sup> <sup>s</sup>* = *+x* or growth advancement.

In sample C, 26 individuals (22.81% of the sample) showed uncoupling. Most of them were girls (61.5%). Uncoupling in these cases corresponded to 14 cases of growth delay (from −23.02 to −1 mm) and 12 cases of growth advancement (from +0.43 to +6.61 mm).

Regarding the subgroups of pathological conditions for uncoupling, LA was the most represented (29%), followed by CBD (26%) and GD (26%) in equal parts; CA was the least represented (19%). More precisely, individuals in the LA subgroup who were most likely to have uncoupling were those presenting a cranial anomaly (45%), followed by polymalformative syndromes (33%) and limb anomalies (11%). In the GD subgroup, IUGR was the most common pathology (50%), followed by macrosomia/diabetes (37%). Then, among individuals with CBD, uncoupling was more frequently observed for the

*Biology* **2022**, *10*, x FOR PEER REVIEW 9 of 20

ing the femoral length of the tested individual (*XT*) at the upper (*I*

*X<sup>T</sup>* − *I*

urement was inferior or superior to the interval. For a measurement inferior to the interval:

For a measurement superior to the interval:

*X<sup>T</sup>* − *I*

3.3.1 Method Application

(Figure 4).

mm).

thanatophoric dysplasia cases (25%) and in relatively equal parts for the other diseases. Finally, CA was the least frequent in uncoupled individuals (19%) (Figure 4). thanatophoric dysplasia cases (25%) and in relatively equal parts for the other diseases. Finally, CA was the least frequent in uncoupled individuals (19%) (Figure 5).

The method was applied to the validation sample B and the pathological sample C to verify whether growth and maturation were coupled or, in other words, whether the individual's growth corresponded to the values expected by their maturation stage

In sample B, we observed coupling in 90.48% of samples. The four cases where uncoupling was detected correspond to two growth delays (−4.82 and −1.70 mm) and two growth advancements (+1.26 and +13.13 mm). These values were calculated by subtract-

*<sup>i</sup>* = −*x* or growth delay,

*<sup>s</sup>* = *+x* or growth advancement.

In sample C, 26 individuals (22.81% of the sample) showed uncoupling. Most of them were girls (61.5%). Uncoupling in these cases corresponded to 14 cases of growth delay (from −23.02 to −1 mm) and 12 cases of growth advancement (from +0.43 to +6.61

Regarding the subgroups of pathological conditions for uncoupling, LA was the most represented (29%), followed by CBD (26%) and GD (26%) in equal parts; CA was the least represented (19%). More precisely, individuals in the LA subgroup who were most likely to have uncoupling were those presenting a cranial anomaly (45%), followed by polymalformative syndromes (33%) and limb anomalies (11%). In the GD subgroup, IUGR was the most common pathology (50%), followed by macrosomia/diabetes (37%). Then, among individuals with CBD, uncoupling was more frequently observed for the

the expected interval for the maturation stage, depending on whether individual meas-

*s*

) or lower (*I*

*i*

) values of

**Figure 5.** Chart summarizing the subgroups and the detailed pathological conditions for individuals in the medical imaging sample with uncoupling. IUGR = intrauterine growth retardation. **Figure 4.** Chart summarizing the subgroups and the detailed pathological conditions for individuals in the medical imaging sample with uncoupling. IUGR = intrauterine growth retardation.

#### **4. Discussion**

#### *4.1. The Fetus and Infant Sample*

In France, since the advent of prenatal diagnosis centers (Decree 97–578 of 28 May 1997, consolidated on 11 May 2018, France), fetuses have been systematically examined in cases of medically interrupted pregnancy or spontaneous death (miscarriages and in utero deaths). A panel of experts' analyses medical records follows ante mortem (CT scan in utero) and post mortem (complete visceral examination, histological study, fetal karyotype, placenta examination, description of external and visceral abnormalities, and front and profile radiography) examinations. After respecting a strict anonymization protocol, we could access these examinations records and be informed about malformations (bone or visceral), chromosomal abnormalities, or even the precise determination of the cause of death.

For sudden and unexpected infant death and forensic cases, CT scans and autopsies are performed only with the written consent of the parents. Not all parents agreed, which is why there were few available exams. Moreover, sudden and unexpected infant death generally occurs before the age of one year according to the High Authority for Health, which stated in its 2007 report that 80% of sudden infant deaths occur before the age of 6 months, with a peak at 2–3 months. This is consistent with the age distribution of our study sample.

For children aged more than 1 year, we could access some rare autopsy reports and some ante mortem CT scans, which are mostly performed for infants who have fallen or have been in a car accident. Cases are rather rare, and when they exist, the whole body is rarely examined to avoid unnecessary radiation. For our analyses, however, we required images that at least included the portion of the body from the skull base to the proximal end of the tibia. All of these elements made it difficult for us to obtain a large sample of fetuses and infants and almost impossible to have homogeneous age groups.

The second difficulty in studying young individuals concerns the CT scan quality. We first sorted the CT scans according to their image quality as excellent, average, or poor. This sorting forced us to rule out many examinations that were not exploitable for our study (due to flowing bone surfaces, incomplete bone, and irregular contours). It should be recalled that fetal X-ray exposure increases the risk of malformation (teratogenic effects) and long-term cancer induction (carcinogenic effects) [67], so the dose of radiation should be as low as possible.

In the case of a postmortem CT scan, the dose of radiation may be higher because the same ethical concerns are no longer relevant. These obtained slices were generally of high or excellent quality and therefore represent the largest part of our studied material.
