# Symmetry and Asymmetry of the Antegonial Notch

^{1}

^{2}

^{3}

^{4}

^{5}

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## Abstract

**:**

## 1. Introduction

- (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].

## 2. Materials and Methods

#### 2.1. Study Material

#### 2.2. Measurement of the Antegonial Notch

_{1}, y

_{1}and z

_{1}are the coordinates for the first point and x

_{2}, y

_{2}, z

_{2}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

#### 2.4. Statistical Methods

## 3. Results

#### FA1 and FA2 Indices

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**A**) Measurement landmarks for the antegonial notch. Point

**a**was designated at the most posterior edge of the notch,

**b**—foremost. Point

**c**is the highest designable point. The ABC triangle height is defined as the shortest distance between

**ab**segment and the

**c**point. (

**B**) Exemplary CT image used in current study.

**Figure 2.**Distributions of relative differences between the right- and left-hand sides (R−L) of distinct segments. All measurements are given in mm. (

**A**) Distribution for segment AB (antegonial notch maximum length), (

**B**) segment AC (posterior) and (

**C**) segment BC (anterior).

**Figure 3.**Comparison of the segments of the pre-angular notch on the right- and left-hand sides. Differences between right and left side for segment BC were statistically significant (p = 0.022).

**Figure 4.**Comparisons of (

**A**) the surface area and (

**B**) the depth of the pre-angular notch on the right- and left-hand sides.

**Figure 5.**Compared histograms of notch-segment distributions. Absolute differences ((

**A**); FA1) shows notch depth as the segment least prone to asymmetrical development, although when correction for individual variability was applied ((

**B**); FA2), it appears to be the most asymmetrical.

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

Feature | Mean [mm or mm^{2}] | Min-Max [mm or mm^{2}] | 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 |

**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 |

**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 |

Variable | N | Mean Diff. (SD) | T | Z | p |
---|---|---|---|---|---|

Area under notch [mm^{2}] | 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 |

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 |

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**MDPI and ACS Style**

Mączka, G.; Kulus, M.J.; Grzelak, J.; Dobrzyński, M.; Staniowski, T.; Skośkiewicz-Malinowska, K.; Dąbrowski, P.
Symmetry and Asymmetry of the Antegonial Notch. *Symmetry* **2022**, *14*, 1558.
https://doi.org/10.3390/sym14081558

**AMA Style**

Mączka G, Kulus MJ, Grzelak J, Dobrzyński M, Staniowski T, Skośkiewicz-Malinowska K, Dąbrowski P.
Symmetry and Asymmetry of the Antegonial Notch. *Symmetry*. 2022; 14(8):1558.
https://doi.org/10.3390/sym14081558

**Chicago/Turabian Style**

Mączka, Grzegorz, Michał Jerzy Kulus, Joanna Grzelak, Maciej Dobrzyński, Tomasz Staniowski, Katarzyna Skośkiewicz-Malinowska, and Paweł Dąbrowski.
2022. "Symmetry and Asymmetry of the Antegonial Notch" *Symmetry* 14, no. 8: 1558.
https://doi.org/10.3390/sym14081558