## Introduction

Maintenance of the intercanine and intermolar distances reduces the risk of relapse and increases the chance of stability; these values represent the limits of the arch, resulting from the muscular balance of each patient. The ideal would be to reproduce the patient’s arch form individually. The Ricketts pentamorphic arch forms allow the clinician to choose among 5 shapes, the one that best fits the patient’s arch form. The objective of this study was to evaluate the effect of orthodontic treatment without extraction according to the pentamorphic arch forms on mandibular arches of different forms.

## Methods

Fifty patients were included in the study. For each patient, the pretreatment and end-of-treatment models were scanned by 3Shape Trios (3Shape, Copenhagen, Denmark) and transferred to the OrthoAnalyzer software (3Shape) version 2017-11.7.1.3 for measurements and superimpositions. The following measurements were made on the mandibular arches for both initial and final digital models: arch depth; intercanine distance, the distance between the first premolars, the distance between the second premolars, the distance between the first molars, and the distance between the second molars. Three superimpositions were made: superimposition between the initial arch and the corresponding form of the pentamorphic arch forms, superimposition between the final arch and the corresponding form of the pentamorphic arch forms, and superimposition between the initial arch and the final arch. The largest difference between the superimposed arches in each region was measured.

## Results

This study showed that intercanine distance ( *P* = 0.236), the distance between the first premolars ( *P* = 0.074), and the distance between the first molars ( *P* = 0.616) did not significantly change after orthodontic treatment. In contrast, the distance between the second molars ( *P* = 0.028) and the arch depth ( *P* <0.001) increased significantly after orthodontic treatment. The mean of the largest difference in the absolute value of all the superimpositions is significantly different from the theoretical value 0 ( *P* <0.001), but clinically, this difference is significant only in certain premolars and molars regions.

## Conclusions

This study has shown that the pentamorphic arch forms maintained the arch shape in the sagittal and transverse directions, except for an expansion of the distance between the mandibular second molars.

## Highlights

- •
Pentamorphic arch forms maintain arch shape in sagittal and transverse directions.

- •
Pentamorphic arch forms caused an expansion at the second mandibular molars level.

- •
Individualization with pentamorphic arch forms is in favor of long-term stability.

- •
Superimpositions show anterior perfect fit of initial and pentamorphic arch forms.

Stability, function, and aesthetics have always been the main goals of any orthodontic treatment. The instability of the dental arches is a major problem. Relapse is partly due to the change of the arch shape during treatment. The respect of the initial dental arch is mandatory for the stability of the orthodontic treatment. Several authors have proved that the deformation of the arch shape by expansion is rarely permanent, and eventually relapses by a contraction. Maintaining the initial intercanine and intermolar distances is a key to stability, ^{,} because these values represent the position of the teeth, resulting from the muscular balance of each patient. ^{,} Several studies have reported arch form changes at the end of orthodontic treatment, by measuring parameters either on photocopies of plaster models or on digital models. Several studies have tried to find the arch shape that could represent all the arches of a population. ^{,} All studies found great interindividual variability of arch shapes. Therefore, no arch form can represent all the arches of a population ^{,} —hence the need for individualization, including specific arch form within each facial type (Brachy, Meso, Dolicho)—during orthodontic treatment.

Dental arch diagrams allow the practitioner to choose the arch form that best fits the patient’s mandibular dental arch. Ricketts pentamorphic arch forms include 5 different shapes: normal, ovoid, narrow ovoid, tapered, and narrow tapered. To our knowledge, there have been no studies on superimpositions of mandibular arches before and after treatment, based on pentamorphic arch forms, using only the 3Shape OrthoAnalyzer software (3Shape, Copenhagen, Denmark). The objective of this study was to evaluate the effect of orthodontic treatment on mandibular arch forms, using the pentamorphic arch forms as a guide.

## Material and methods

This retrospective clinical study was approved by the ethical committee of the Saint Joseph University of Beirut on November 13, 2018 (approval no. USJ-2018-155).

Mandibular dental casts of 50 patients were assessed for changes in arch dimensions during orthodontic treatment. All patients received nonextraction treatment in the mandibular arch. Patients were included in the study if (1) they had initial and final models found in the archive, (2) they were adult patients (aged >18 years, to eliminate the growth effect), (3) they presented crowding between 1 mm and 5 mm, (4) they were in Class I or Class II malocclusion treated by maxillary molars distalization or by extraction of maxillary premolars, or Class III malocclusion treated without extraction in the mandibular arch, (6) a clinically acceptable occlusion was established after active treatment, and (7) the pentamorphic arch forms were used to choose the arch form that best fits the arch of each case.

Patients were excluded if they had (1) a previous orthodontic treatment and were seeking a new treatment after relapse, (2) an orthognathic surgery, (3) teeth with prosthetic crowns, (4) fractured teeth, (5) teeth with ectopic positions, (6) dental arches with temporary teeth, (7) agenesis, (8) extracted teeth, and (9) malformed teeth.

All the patients were treated and had initial and final models. The amount of crowding was measured for each case on the initial mandibular model, using the OrthoAnalyzer software. The initial and the final mandibular plaster models were prepared: 28 points (14 occlusal and 14 labial) were marked on each model using a fine black marker (Faber-Castell, Stein, Germany) ( Fig 1 ). The 14 occlusal points were: the mesiobuccal cusp tips of the first and second mandibular molars, the buccal cusp tips of the first and second premolars, the tips of the canines, the middle of the lateral incisor’s borders, and the mesial point of the central incisor’s borders. The 14 labial points correspond to the position of the bracket slots or tubes on the labial surface of the mandibular incisors, canines, premolars, and molars. In addition, each initial and final mandibular plaster model is superimposed with the pentamorphic arch forms printed on a transparent acetate paper, and the corresponding arch form was chosen ( Fig 2 ). For each case, the maxillary and mandibular plaster models were scanned using the 3Shape Trios (3Shape) scanner and transferred to the OrthoAnalyzer software as digital imaging and communications in medicine files.

Measurements of transversal widths and arch depth of each initial and final digital mandibular models were made using OrthoAnalyzer measurement tools ( Fig 3 ), (1) intercanine distance: the distance between the mandibular canines’ tips, (2) interfirst premolar distance: the distance between the mandibular first premolars buccal cusps tips, (3) intersecond premolar distance: the distance between the mandibular second premolars buccal cusps tips, (4) interfirst molar distance: the distance between the mandibular first molars mesiobuccal cusps tips, (5) intersecond molar distance: the distance between the mandibular second molars mesiobuccal cusps tips, and (6) arch depth at the first molars’ level: the distance between the mandibular incisal midpoint and the line that joins the mesial contact points of the mandibular first molars.

For each patient, the occlusal plane was defined on the maxillary digital model using the “Setup occlusal plane” option in OrthoAnalyzer, and the midsagittal plane was defined using “Standard Planes” option ( Fig 4 ).

An individualized arch form was drawn for the initial and final mandibular digital models using the “Dental Arch Analysis: Arch form customization tool” in OrthoAnalyzer. The individualized arch form was created by selecting the labial points of the second and first mandibular molars, the mandibular canines, and the mandibular incisors ( Fig 5 ).

The digital pentamorphic diagram was inserted in the OrthoAnalyzer software using the option “insert 2D overlay.” Each individualized arch form of every initial and final mandibular model was superimposed to the corresponding Ricketts arch form that was selected by the clinician among the pentamorphic arch forms and used to treat the case. The superimpositions were made using the best-fit method, selecting the central region as a reference.

To resume, we made 3 superimpositions for each case: (1) SIP: superimposition between the initial individualized arch form, drawn by the operator using the 3Shape OrthoAnalyzer software, and the corresponding pentamorphic form (pentamorphic shape selected for the case used as a reference) ( Fig 6 ), (2) SFP: superimposition between the final individualized arch form drawn by the operator using the 3Shape OrthoAnalyzer software and the corresponding pentamorphic form (pentamorphic shape selected for the case used as a reference) ( Fig 7 ), and (3) SIF: superimposition between the screenshot (scale 1:1) of the initial arch form inserted as a 2-dimensional overlay and the final arch form (the initial arch form used as a reference) ( Fig 8 ).

Differences between the superimposed arch forms were evaluated by splitting the digital arches into 8 segments (second molar, first molar, premolar, anterior regions on the left and right sides; Fig 9 ). The largest difference between the superimposed arches in each region was measured using the OrthoAnalyzer measurement tools. At each superimposition, the scale was fixed to a 1:1 ratio using the digital ruler of the OrthoAnalyzer and the ruler printed on the 2-dimensional image of the pentamorphic diagram or the screenshot of the initial arch form. The measurements and superimpositions were repeated for 15 patients by the same evaluator and by a second evaluator 2 weeks later.

## Statistical analysis

SPSS statistical software (version 24.0; Chicago, Ill) was used for statistical analysis of data. The significance level used corresponds to a *P* value of ≤0.05. The intraclass correlation coefficients (ICC) were calculated with their 95% confidence interval to evaluate the interexaminer and intraexaminer agreements. Kolmogorov-Smirnov tests were conducted to verify the normality of the distribution of quantitative variables. Parametric tests were used for variables that follow the normal distribution, and nonparametric tests were used for variables that do not follow the normal distribution. Student *t* tests were used for paired series, and Wilcoxon tests were used to compare the mandibular intercanine distance, the distance between the mandibular first premolars, the distance between the mandibular second premolars, the distance between the mandibular first molars, the distance between the mandibular second molars, and the arch depth before and after orthodontic treatment. Concerning the superimpositions analysis, One-sample *t* tests were conducted in order to compare the average deviations in absolute value with the theoretical value 0, which assumes a maximum precision.

## Results

The measurements were made by the same operator at 2 different times under the same conditions. The ICC was very high (>0.951), indicating an excellent measurement reproducibility. In addition, the measurements were performed by a second operator calibrated under the same conditions. The ICC was very high (>0.894), indicating an excellent interexaminer agreement.

The average amount of crowding measured on initial mandibular models is 3.01 mm, with a standard deviation of 1.33 mm. The mean and standard deviation of the transverse widths and the depth of the mandibular arch before and after orthodontic treatment are illustrated in Table I and Figure 10 . This study showed that the mandibular intercanine distance ( *P* = 0.236), the distance between the mandibular first premolars ( *P* = 0.074), and the distance between the mandibular first molars ( *P* = 0.616) did not significantly change after treatment. In contrast, the distance between the mandibular second molars ( *P* = 0.028) and the arch depth ( *P* <0.001) increased significantly after orthodontic treatment. The distance between the mandibular second premolars increased after orthodontic treatment, but the difference was not significant ( *P* = 0.059).