Symmetry and Asymmetry of the Antegonial Notch

Abstract

The symmetry of a human organism’s structure is an expression of the general law of development regarding organic life. Assessing the symmetry of the face and its individual components is one of the most important factors when it comes to the overall assessment of a patient’s stomatognathic system and is essential in the planning of orthodontic and prosthetic treatment. The aim of this study is to assess the symmetry of the occurrence and the measurement parameters of the pre-angular notch of the mandible. The study included computed tomography scans of 187 patients who all exhibited a visible pre-angular notch in the mandible. There was a noticeable and measurable asymmetry in the length of the angle of the notches as well as in the area of the notch angles. The differentiation of the right- and left-side measurements points to the existence of a fluctuating asymmetry. Other measurements which describe the pre-angular notch of the lower jaw do not show asymmetry.

1. Introduction

The symmetry of the structure of the human organism is an expression of the general law of development regarding organic life. This not only applies to the external parts of the body, but also to some internal organs such as the kidneys [1] and the brain [2]. In addition, many basic activities are performed in a symmetrical way: walking involves symmetrical, albeit alternating, movements of the lower limbs [3]. Having said that, this model is by no means perfect, and the deviations from it manifest themselves internally and externally, in structure and functions, both in ontogenesis and phylogenesis. Asymmetry can be observed both at the biochemical level and in the organs and the body as a whole [4]. Taking some simplifications as read, two groups of deviations from the two-sided symmetry model can be distinguished [5]:

(a)

deviations of an internal nature, concerning the asymmetry of internal organs, both even and odd. These are morphological asymmetries: size, shape, position, structure (e.g., two and three lobes of the lungs) and in the case of paired organs-asymmetries regarding function (e.g., the ovaries) [6];

(b)

deviations of an external nature, mainly concerning the asymmetry of the limbs and paired sense organs, as well as other phenomena related to them. Among humans, this group of deviations is strongly related to the dominance of one hemisphere of the brain [2].

Ludwig proposed one of the most universal systems for the classification of forms of asymmetry in living organisms. It distinguishes the following types of morphological asymmetry: directional asymmetry, fluctuating and antisymmetry [7].

Directional asymmetry (DA) occurs when the differences between the features on the right-hand and left-hand sides of the body exhibit a constant direction and when their distribution is skewed. It is possible to predict which side will be bigger [8].

Fluctuating asymmetry (FA) occurs when the mean of the distribution of differences is statistically equal to normal and the distribution itself is also close to normal [9]. The condition for diagnosing this is the exclusion of DA and antisymmetry. In the case of FA, bilateral features show slight, random deviations from two-sided symmetry without any specific direction. FA is caused by environmental stress (diet, climate, toxins), developmental problems caused by genetics (aneuploidy, heterozygosity, inbreeding) and developmental instability, especially in the early stages of growth. An organism that is less able to cope with developmental stress is more asymmetric. The stimuli of the environment that weaken the organism evoke a number of responses, one of which is FA [5,10,11].

Antisymmetry occurs when the frequency distribution of the differences is bimodal or platykurtic. In antisymmetry a stronger development of the trait occurs on one side. However, in the population it is impossible to predict which side of the structure under investigation is the one that will reach the higher value [5].

The causes of morphological asymmetry may be congenital, developmental or acquired; it varies between different organisms, organs and different types of asymmetry which has been reviewed comprehensively elsewhere [12]. In humans, morphological symmetry is regarded as one of the factors that determines attractiveness: symmetry studied by means of measurement methods as well as assessed subjectively has a positive correlation with attractiveness rating [13]. Asymmetrical faces tend to be rated as less attractive than symmetric ones, although perfect symmetry is not necessary; subjective estimation of facial-trait symmetry with the naked eye does not recognize canting and differences less than 3°–4° and 3–4 mm, respectively, as an asymmetry [14].

Sensitivity to the symmetry of morphological structures may be a result of evolutionary adaptation in order to recognize individuals that are well adapted to their environment and are resistant to stress factors. Symmetry may be considered as an indicator of an individual’s genetic and phenotypic quality [13]. Some conditions resulting in extreme facial asymmetry include laterogenia (malocclusion type in which chin is shifted toward one side) or craniofacial clefts (including most common palate cleft) which may be indeed caused by teratogenic factors or genetic defects [15,16,17].

Apart from the attractiveness evaluation, the assessment of facial symmetry and its individual components is an important factor in the overall assessment of a patient’s stomatognathic system and is essential when planning orthodontic and prosthetic treatments [18,19,20,21]. Mandibular-symmetry disorders are also associated with SAPHO syndrome (Synovitis, Acne, Pustulosis, Hyperostosis and Osteitis), which limits the movement of the temporomandibular joint, causes swelling and pain, and can lead to complete ankylosis of the temporomandibular joint [22,23,24]. In the evaluation of facial asymmetry for research or diagnostic purposes, a number of diagnostic tools may be used, including clinical examination, 2D and 3D radiographs as well as intraoral scanners [25,26].

Some of the traits worth considering for evaluation of facial asymmetry are the measurements of the antegonial (also: “pre-angular”) notch, including its depth, length and shape [27]. The pre-angular notch is a slight elevation of the lower edge of the mandibular body, most often occurring on both sides, which is found forward of the angle of the mandible, and is located at the junction of the mandible’s body and ramus. It is considered to be a source of information on the course of mandibular development and may also be a predictor of mandibular growth [28]. It is acknowledged that the morphology of the pre-angular notch may vary with age, sex and dentition status [29]. Evaluation of the antegonial notch is necessary for maxillofacial surgeons in the treatment of the mandibular deformities [30].

Measurements of the antegonial notch and its asymmetry usually concern solely its depth. There was found statistically significant differences between the indentation depth on the right- and left-hand sides [26,28,29]. The observed difference in mean values for the right- and left-hand sides in Kaczkowski’s studies was 0.3 mm.

The aim of this study is to assess the symmetry of the occurrence and measurement parameters of the pre-angular notch of the mandible and find the parameters most susceptible for asymmetrical development.

2. Materials and Methods

2.1. Study Material

In this study, facial tomograms were used, taken in the Computed Tomography laboratory of Affidea (Wrocław, Poland) from 2015–2017. These photos were taken for diagnostic purposes. The scans used for research have been anonymised and do not contain any information that would enable the identification of patients. All participants had given their written consent for the use of these anonymised scans for research purposes prior to treatment. The present study was approved by the Bioethics Committee of the Medical University of Wrocław, no. KB-1086/2021.

The study included photos of 187 patients, of whom 80 were women (43%) and 107 were men (57%), aged 16 to 93 years. The mean age of the surveyed women was 41.5 years, while that of men was 38.46 years. The tests were conducted with the use of spiral-tomography technology. The side-view photographs were taken with the aid of an OPTIMA CT660 device (GE Healthcare, Chicago, IL, USA), in accordance with manufacturer’s recommendations. All tomograms were obtained in the format of 152 mm × 152 mm × 135 mm, with reconstruction matrices of 512 × 512.

The examination was carried out only on full parts of the face using a CT scan of the skull, with the pre-angular notch of the mandible visible on both sides. Exclusion criteria include fractured craniofacial bones, the lack of a pre-angular notch in the mandible, or the absence of 2 or more adjacent teeth. An example of an angular indentation in a side projection is given in Figure 1B.

2.2. Measurement of the Antegonial Notch

Three landmarks (A, B and C, as shown in Figure 1) were designated and three straight lines were measured corresponding to the respective sides, forming one triangle. For the proposes of calculations and measurements, the indentation area was described as triangle, and the indentation roundness was omitted. These measurements were used to calculate the area of indentation with the aid of the Heron formula, which allows us to determine the triangle’s area based on the lengths of its sides [31].

A and B landmarks were designated at the most posterior and anterior edges of the antegonial notch, respectively. Landmark C was designated at the deepest point of the notch.

Segment AB describes the antegonial notch maximum length. AC—posterior segment, towards the angle of the mandible. BC—anterior segment, towards the mental tubercle. All measurement are given in mm.

Additionally, the height of the triangle (also: the antegonial notch depth) was measured and this was treated as the depth of the indentation; it was defined as the shortest distance between point C and line AB.

All measurements were made for both the left and the right body of the mandible. Points were assigned in the OsiriX MD 9.0 program (Pixmeo SARL, Geneva, Switzerland), to an accuracy of 0.01 mm and saved as coordinates in three-dimensional space. The distance between two distinct landmarks (e.g., A and B) were calculated with the following formula: $\left|\mathrm{AB}\right|=\sqrt{{\left({\mathrm{x}}_2-{\mathrm{x}}_1\right)}^2+{\left({\mathrm{y}}_2-{\mathrm{y}}_1\right)}^2+{\left({\mathrm{z}}_2-{\mathrm{z}}_1\right)}^2}$, where x₁, y₁ and z₁ are the coordinates for the first point and x₂, y₂, z₂ are the coordinates for the second one. All points were set three times by the same person (GM), an orthodontist, experienced in CT scan measurements. The inter-measurement error (calculated as |A − B|/[(A + B)/2] for all measurements pairs) was not in excess of 3%. The average of three measurements was used for the calculations.

2.3. Asymmetry Calculation

The basic asymmetry estimation included relative differences between same measurement on the right and left side (R − L). Histograms showing distributions of R-L differences were used to determine the type of asymmetry, where symmetrical distributions with a mean close to 0 were considered as indication for fluctuating asymmetry. Statistically significant differences between both sides were considered directional asymmetry.

Unsigned fluctuating asymmetry was calculated with equations |R − L| and correction for individual (|R − L|)/[(R + L)/2)]; in Palmers classification these indices are referred to as FA1 and FA2, respectively [32].

2.4. Statistical Methods

The Kolmogorov–Smirnov test was used as a way of establishing the normality of the distributions. The existence of statistically significant differences in the test for dependent (correlated) variables was assumed to indicate the asymmetry of the examined features. In instances where the normality of the distribution was found (measurements of the sides of the pre-angular notch), the Student’s t-test for dependent variables was used. The symmetry of the surface area and the symmetry of the indentation depth were tested using a non-parametric test for two dependent variables (Wilcoxon’s of pairwise order).

The analysis was performed using the Statistica 13 program (TIBCO Software Inc., Palo Alto, CA, USA).

3. Results

For each of the examined features, descriptive statistics for the right-hand and left-hand sides were calculated and the normality of the distribution was examined (

Table 1. Results of descriptive statistics and the test of distribution normality for all examined features.

Feature	Mean [mm or mm2]	Min-Max [mm or mm2]	SD	Normality of Distribution
AB right	37.75	17.56–56.00	6.81	Yes
AC right	24.26	9.38–47.21	6.10	Yes
BC right	13.88	6.73–23.25	3.21	Yes
surface area right	47.13	2.90–142.54	29.66	No
indentation depth right	2.37	0.16–5.73	1.21	Yes
AB left	36.52	16.81–61.06	6.99	Yes
AC left	23.72	10.69–53.25	6.40	Yes
BC left	13.15	5.76–45.16	3.78	Yes
surface area left	42.66	1.56–137.52	26.92	Yes
indentation depth left	2.20	0.12–40.69	3.09	No

).

Based on the distribution of differences between the measurements on the right- and left-hand sides, the nature of the asymmetry was estimated.

The distributions of the differences in the lengths of the sides of the angle notch on the right- and left-hand sides are close to the normal distribution (the Kolmogorov–Smirnov test showed no statistically significant differences between the normal distribution and the distribution of differences in the measurements on the right- and left-hand sides, Figure 2,

Table 2. Differences in measurements on the right- and left-hand sides (right-hand side minus left-hand side).

Variable	Mean	Min-Max [mm]	SD [mm]
AB	1.22	−12.18–27.40	5.29
AC	0.54	−15.97–11.81	4.94
BC	0.73	−34.99–11.16	4.14

). Such a distribution of features is characteristic of fluctuating or directional asymmetry.

Segment BC is significantly longer on the right side (

Table 3. Results of the Student’s t-test for dependent variables. Statistically significant p-value is bolded.

	Variable	Mean [mm]	SD [mm]	Mean Difference [mm]	t-Value	p
Segment AB	Right side	37.75	6.81
	Left side	36.52	6.99	1.22	1.72	0.086
Segment AC	Right side	24.26	6.10
	Left side	23.72	6.40	0.54	0.84	0.399
Segment BC	Right side	13.88	3.21
	Left side	13.15	3.78	0.73	2.28	0.022

).

A statistically significant difference occurred only in the case of the anterior segment (the length of segment BC). In the case of the remaining measurements describing the posterior notch segment (segment AC) or antegonial notch length (segment AB) there were no statistically significant differences on the right- and left-hand sides (Table 3, Figure 3). Therefore, segment BC shows directional asymmetry, whereas other segments—fluctuating one.

The area under the pre-angular notch is also larger on the right-hand side. The depth of the pre-angular indentation, unlike in the case of the other examined features, does not differ significantly between sides (

Table 4. Wilcoxon’s pairwise-order test results.

Variable	N	Mean Diff. (SD)	T	Z	p
Area under notch [mm2]	187	4.48 (24.53)	7030.0	2.265	0.030
Notch depth [mm]	187	0.09 (1.03)	7247.0	1.970	0.071

).

A statistically significant difference was found only in the case of the area of the pre-angular notch: it is larger on the right-hand side (Table 1 and Table 4, Figure 4). However, no such difference was found in the case of the depth of the pre-angular notch.

FA1 and FA2 Indices

FA1 and FA2 indices (according to the Palmer classification [32]) show absolute rather than relative aspects of fluctuating asymmetry.

Table 5. Descriptive data for FA1 and FA2 indices for distinct segments of antegonial notch.

Variable	Mean [mm or mm²]	Min-Max	Std.Dev.
FA1 for segment AB	4.16	0.06–15.31	2.93
FA1 for segment AC	3.83	0.00–13.73	2.87
FA1 for segment BC	2.54	0.00–11.16	2.08
FA1 for notch area	18.50	0.30–91.87	16.68
FA1 for notch depth	0.80	0.00–3.66	0.68
FA2 for segment AB	0.11	0.00–0.36	0.08
FA2 for segment AC	0.16	0.00–0.51	0.11
FA2 for segment BC	0.19	0.00–0.72	0.14
FA2 for notch area	0.47	0.01–1.66	0.37
FA2 for notch depth	0.41	0.00–1.62	1.62

and Figure 5 show distribution of both indices calculated for each segment and area under the notch.

FA1 shows absolute differences between the distinct measurement on the right and left side, while the FA2 indicator shows those differences taking into account the variability of notch measurement between individuals. FA1 indices show segment AB as the most prone to fluctuating asymmetry, while FA2 indicates the notch depth.

4. Discussion

The measurements taken in the course of this research show characteristics of fluctuating asymmetry (besides area under notch and segment BC, which show directional asymmetry). This is a natural and common phenomenon, sometimes even noticeable by patients. In our study, the mean difference between the measurements on the right- and left-hand sides is: 1.221 mm (AB), 0.540 mm (AC) and 0.73 mm (BC), respectively. The Student’s t-test for dependent variables showed that asymmetry only significantly concerns the length of the anterior segment of notch (BC). Similarly, Wilcoxon’s test revealed asymmetry of area under notch as directional and asymmetry of notch depth as fluctuating.

Our results are slightly different from those obtained before; Ghosh et al., and Chole et al., found statistically significant differences between the indentation depth on the right- and left-hand sides in some groups [29,33], as well as Kaczkowski et al. [34]. However, measurement methods in those studies included panoramic radiographs [29,33] or callipers [34], which could be more prone to measurement error than measurements on CT scans.

Taking absolute differences into consideration (indicator FA1), the element most prone to asymmetrical development appears to be the length of the whole indentation (segment AB), then the distance between the bottom edges of the notch and its top (AC and BC; Table 5 and Figure 5A). However, after applying the correction for inter-individual variation (FA2), the notch depth and segment BC (followed AC) appear to be most asymmetrical (Figure 5B).

Defining asymmetry tends to be used for determination of “developmental stability” [35]. The results obtained in the current study allow us to select the most asymmetrical segment measurable in the antegonial notch. Theoretically, FA2 were the most variable for notch depth. However, its small dimensions must be taken into consideration; a small size (up to about 3 mm) increases the significance of the measurement error. As a result, AC and AB seem to be the best choices for determining the asymmetry of the antegonial notch, as these are bigger and still show asymmetry in FA1 as well as in FA2 indices.

Measuring the asymmetry may be used for estimation of developmental instability, but it is worthwhile to dwell on which period of ontogenesis will affect the notch dimensions. The main role in development of facial structures in utero is played by Meckel’s cartilage, which is the basic centre of mandible growth [36]. During further stages of prenatal development and after birth, mandible development includes growth of the mandibular body’s trabecular bone and angle of mandible, coronoid process), mandibular symphysis, alveolar process and articular condyle [37]. Postnatal development of the mandible is associated with the functioning of three different muscle groups, i.e., the masseter muscles from the area of the first branchial arch, the temporal muscles originating from the second branchial arch, (and also the lingual muscles originating from the occipital myotome) and the lingual muscles from the area of the occipital myotome.

However, later stages of development are unaffected; notch depth is established early and does not change throughout the growth period, besides some pathological conditions such as idiopathic condylar resorption [38]. Therefore, the measurements obtained may be used as estimators of early development (in)stability.

5. Conclusions

Differentiation of the measurements on the right- and left-hand side points to the existence of fluctuating asymmetry. Segments AC and AB seem to be the best choices for determining the asymmetry of the antegonial notch and can be used as estimators of early development stability.