Evaluation of Mandibular Arch Form in A Sudanese Adult Sample With Normal Occlusion

Background: In xed orthodontic therapy, maintenance of the original mandibular arch form is considered an essential factor for stability, moreover with the popular use of elastic archwires, and because its shape cannot be easily altered, the pre-determination of mandibular arch form becomes very important for each patient. The purpose of this study is to analyze the mandibular dental arch forms of Sudanese adults with normal occlusion and provides an easy method for orthodontists to determine different types of arch form. Methods: This Descriptive analytical, cross-sectional study determined the mandibular arch in a sample of 104 Sudanese university students. Measurements were done in the mandibular dental cast. Three arch widths and three arch lengths measurements were established and ve ratios were determined. Analysis of arch form was done according to Raberin’s polynomial method. Results: The mid arch form was the most prevalent (75%), followed by narrow arch form (11.54%), wide arch form (6.73%), and pointed arch form (6.73%). There were no cases in at arch form. Conclusions: In Sudanese subjects, four types of arch form were recognized. Norms of transverse and sagittal dimensions of the mandibular arch to determine types of the mandibular arch form in Sudanese orthodontic patients become available.


Background
The shape of the dental arches has considerable implications in orthodontic diagnosis and treatment planning, affecting the space available, dental esthetics, and stability of the dentition [1]. The Dental arch is initially shaped according to the con guration of the supporting bone and following the eruption of the teeth by the circum-oral musculature and intra-oral functional forces [2,3].
In contemporary orthodontics for the ease and perfection to the orthodontists, preformed archwires have gained acceptance. Furthermore, with the use of advanced materials, and the use of elastic archwires, it became very important to determine the shape of the mandibular arch form [4].
The stability of orthodontic treatment outcome request no changes in the mandibular arch form [5]. It is known that the mandibular arch has different shapes in different people though each one has normal occlusion. Many factors predispose to differences in mandibular arch form and it is believed that during orthodontic treatment procedures, one must not try to alter the original arch form to have stable results [6].
Orthodontists should select the appropriate shape of archwire for each case separately. some clinicians try to modify archwires for every case, either by using arch guide [7][8][9], or computer-assisted technique [10]. The arch shape consists of two different areas: the anterior curvature and intercanine width and posterior curvature and intermolar width. A preformed archwire also can be customized for each patient by adjusting the anterior and posterior curvatures [11].
The symmetrical curve of dental arches was widely studied by different means. Simple qualitative descriptions were used, as the circular form of the anterior part of the arcade [12,13], tapered, ovoid, and square arch forms [11,14]. Also, human dental arch forms have been described using mathematical methods, like Catenary curves [15,16], and trifocal ellipse [7]. More complex procedures involved different curve-tting mathematical models were reviewed by many authors. Ferrario et al, [17] evaluated maxillary and mandibular arch by a fourth-order polynomial and mixed model (ellipse and parabola).
Ferrario et al [18] Proved that Euclidean Distance Matrix Analysis (EDMA) is suitable for the analysis in human dental arches. They calculated the center of gravity or centroid of each tooth from cusp tip coordinates and used these points as landmarks later used in the EDMA calculations.
Raberin et al [4] Classify mandibular dental arch into ve types (pointed, wide, narrow, mid, at) based on the k-means clustering method and the use of polynomial functions of the sixth degree.
Dental arch variations exist among different racial groups [19]. Geometric models were anticipated by several authors to identify the mean con guration of the clinical arch shapes in different populations [20]. In a previous study, a comparison of the shape and dimension of the dental arches between African subjects and Caucasian subjects revealed signi cant differences between the two ethnic samples [21]. So, every population should be managing according to it is characteristics.
Few studies have explored the predominant mandibular arch forms among Sudanese subjects. This study aims to evaluate mandibular dental arch form in Sudanese male and female adults with normal occlusion and to establish a practical mathematical technique, to identify different types of arch form, easy to be available in every orthodontics clinic.

Methods
This descriptive-analytical, cross-sectional study was carried out in the capital city of the Republic of Sudan (Khartoum), for university students of Al-Neelain University. The students were selected using the following inclusion criteria.
The subject had to be Sudanese.
Male and Female aged 16-26 years old.
The subject had Angle's Class I molar and canine relationship bilaterally.
Dental arches with well-aligned teeth and space discrepancy of 0 ± 3 mm.
All teeth were present and fully erupted from the second right molar to the second left molar.
No history of previous orthodontic treatment.
Sample size: The following equation calculated the study sample n = (Zs/e) 2 deff The sample size was equal to 52. Therefore, the overall sample became 104 (52 males and 52 females).

Study design:
A cluster sample technique was used for the selection of faculties. As a result, ten of nineteen faculties of Al Neelain University were selected. Then a simple random method was followed for the selection of students within each chosen faculty.
The study protocol was approved by the Central Institutional Review Board at Al-Neelain University and followed the Declaration of Helsinki Ethical principles for Medical Research Involving Human Subjects. Informed consent was obtained from students who participated in this study. Initial screening for the students was carried out under natural light illumination. The examination was conducted for each student to determine if the participant meets all the inclusion criteria. The examination comprised an intraoral inspection of the teeth and occlusion. For impression taken, Alginate hydrocolloid impression material (ALGINMAX) was mixed according to manufacture. Dental models were poured and prepared with dental stone (OrthoStone).
Reference points [4] were determined as; mid-incisal edge on the labial side, canine cusp tips, mesiobuccal cusps of rst molars, and distobuccal cusp tips of second molars.
The analysis of dental arches was divided into sex dimensions [4]. 1. Error of method: All measurements were performed by the same researcher. Furthermore, all the variables were measured twice, with a 2-week interval between the two recordings on 25 casts selected at random: intra-observer variability was calculated by using Dahlberg's formula and the measurements obtained ranged between 0.90 and 1.42.
2. Descriptive analysis including the transverse dimensions, sagittal dimensions, and calculated ratios among the sample.
3. T-test and Fisher's Exact Test were used to evaluate the presence of statistically signi cant differences between males and females.

Result
Normal distribution of the data was tested by quantile plots graphical method Fig. 2, as a result, all data were normally distributed.
The mean age of students who participated in this study was 19.5 ± 2.2 yrs. Table 1 shows descriptive statistics for mandibular arch widths and lengths measurements of the total sample.  The calculated ve ratios of arch form dimensions of the total sample. were shown in Table 3. The results of the present study showed that 75% of the Sudanese adults possess mid dental arch form, 11.54% narrow, 6.73% wide arch form and, 6.73% pointe arch form. The at arch form was not presented. Table 4. The difference in gender distribution was not signi cant Fisher's Exact Test, p = 0.607 Table 4.

Discussion
This study included young adult subjects, According to growth studies in arch width changes, intercanine and inter-molar widths did not change after 13 years in females and 16 years in males [22,23], so it was expected that this sample has reached the adult level in arch dimensions.
The present work studied the dimensions of the normal mandibular dental arcade since the mandibular dental arch is considered very important for stability after orthodontics treatment [24].
Measurements in this study were taken from the anatomical points, incisal edges, molars, and canines cusp tips as evaluated by Raberin's et al. [4] According to Raberin's (these points constitute the landmarks that de ne breaking points of the mandibular arch that limit sectors on which different muscle groups act). Previous literature and studies on dental arch shape used conventional anatomical points on the incisal edges and molar cusp tips, etc. to classify dental arch forms using various mathematical forms [5], such as spline curves [25], and the beta function [5]. Despite their clinical impact, conventional anatomic points do not provide clinical evidence of appropriate arch-wire absolute forms. On the contrary, points taken on the vestibular surface of the teeth facial axis give the exact shape of clinical arch-wire [26], as these relate directly to the position of the brackets in orthodontic xed appliances.
Arch width and Length measurements we observed in our sample, gave higher values in males. In most studies [4,6,27,28], the arch dimensions were smaller in females. Our results are in line with these studies.
Our ndings con rm that Sudanese adult with normal occlusion has no single arch form. This agrees with many studies conducted in different populations [4,6,27,28]. A comparison was done between Sudanese and other populations in Table 5. This study provides norms for mandibular transverse and sagittal dimensions, that could be applied by an easy method to classify different forms of mandibular arch in Sudanese orthodontics patients Fig. 3.

Conclusion
Based on the results of the present study, the following conclusions can be drawn: In Sudanese adults, the mid arch form is the most predominant arch form.
Arch form types were not associated with gender.
A Guide for classi cation of mandibular arch form in Sudanese orthodontics patients become available. Participation in the study was voluntary. Informed consent was obtained from students who participated in this study and from Deans of the faculties for those participants under the age of 18 years.

Consent for publication
Not applicable.

Availability of data and materials
The data that support the ndings of this study are available on reasonable request from the corresponding author. The data are not publicly available due to privacy.

Competing interests
We declare no con icts of interest.

Nil
Authors contributions: Raja AG. Mustafa was responsible for the study concept and design; data acquisition and preparation of the manuscript.