Personalized Orthodontics: From the Sagittal Position of Lower Incisors to the Facial Profile Esthetics

Background: One of the goals of orthodontic treatment is to obtain maximum facial harmony. The sagittal position of the lower incisors plays a significant role in the planning of orthodontic treatment. The aim of the study was to evaluate the relationship between the sagittal position of lower incisors and facial profile esthetics with reference to the skeletal vertical dimension. Methods: There were 200 patients included in the study. Patients were allocated into three groups, depending on the vertical growth pattern: normal-angle, low-angle, and high-angle cases. Tweed–Merrifield cephalometric analysis was used to assess the sagittal and vertical position of the mandible, as well as to assess the sagittal position of the lower incisors. Results: Z-angle and Frankfort mandibular incisor plane angle (FMIA) decreased significantly (p < 0.001) with the increase of the skeletal vertical dimension. Incisor mandibular plane angle (IMPA) was significantly higher (p < 0.001) in low-angle patients compared to the high-angle ones. Z-angle appeared to be the most accurate parameter (area under curve, AUC = 0.957) describing patients with a convex profile. The cutoff value of Z-angle 68.0° was characterized by the sensitivity of 94.1% and the specificity of 84.3%. Conclusions: The sagittal position of the lower incisors significantly affects the facial profile convexity. The Z-angle is the parameter which most accurately describes the patients with a convex profile.


Introduction
The sagittal position of the lower incisors plays a significant role in the planning of orthodontic treatment [1,2]. Several different aspects related to the position of the lower incisors have been discussed in the literature. These are: the amount of crowding and the dentoalveolar discrepancy [3,4], the long-term stability of orthodontic treatment [5][6][7][8], the relationship between the lower incisors' position and the presence of gingival recessions [9][10][11], and finally, the facial profile esthetics [6,[12][13][14]. Obtaining maximum facial harmony is one of the most important goals of orthodontic treatment [13].
Margolis [15] was the first one who analyzed the relationship between the long axis of the mandibular incisor and the base of the mandible, known as the incisor mandibular plane angle (IMPA). However, Tweed [16][17][18] noticed that both the occlusion and facial esthetics were interdependent. He constructed the diagnostic facial triangle [19], the valuable tool used for cephalometric analysis, with the three lines: the Frankfort horizontal plane, the mandibular plane, and the long axis of the mandibular incisor. There are three angles within the facial triangle between the abovementioned lines: the Frankfort mandibular 2 of 14 plane angle (FMA), Frankfort mandibular incisor plane angle (FMIA), and the previously mentioned IMPA [19][20][21]. Tweed emphasized that in cases of class I malocclusion, class II malocclusion, and bimaxillary protrusion (all cases without severe skeletal discrepancies), to achieve the balanced facial esthetics, the recommended value of an IMPA angle was 90 • ± 5 • [16,20]. However, according to further observations by Tweed, the FMIA angle appeared to have the most important impact on facial esthetics. The rule of thumb was to achieve an FMIA of 65 • -68 • at the end of orthodontic treatment. These values were found to be associated with the best facial results [20,21].
Merrifield [13] introduced the term of the profile line, which connected the most prominent point on soft-tissue chin with the most prominent point on either the upper or lower lip, depending on which lip was more protruded. The profile line was extended to the Frankfort horizontal plane. The angle between the profile line and the Frankfort horizontal plane was named the Z-angle, and its recommended value was from 75 • to 78 • [20]. The aim of the profile line was to present the amount of lip protrusion [13]. Facial profile convexity may be easily assessed by the distance of the profile line from the tip of the nose. The more anteriorly from the tip of the nose the profile line localized is, the more convex the profile is. The well-balanced facial profile is characterized by the profile line crossing the nose [12].
The orthodontic achievements and clinical observations of Dr. Charles Tweed, as well as the results of further studies performed by the members of the Charles H. Tweed International Foundation for Orthodontic Research, including the studies by Dr. Levern Merrifield, were used to prepare the differential diagnostic analysis system [20,22]. Differential diagnosis includes skeletal, dental, and facial diagnosis. Moreover, it respects the anterior, posterior, lateral, and vertical limits of the dentition [20].
The aim of the study was to evaluate the relationship between the sagittal position of the lower incisors and facial profile esthetics with reference to the skeletal vertical dimension. The null hypothesis was that the sagittal position of the lower incisors does not affect the facial profile esthetics.

Materials and Methods
The Medical Board Ethical Committee (KB-18/21) approved the study. The study was conducted with the ethical principles of the World Medical Association Declaration of Helsinki. All patients received and signed informed consent.
There were 200 generally healthy patients included in the study, who had come for a specialist orthodontic consultation. The specialist orthodontic consultation was performed in the specialist orthodontic private practice in Grudziadz (Poland). None of the included patients had ever been treated orthodontically with either a removable or fixed orthodontic appliance. Table 1 presents inclusion and exclusion criteria for the examined patients. All of the patients who had been included in the study underwent orthodontic examination. Specialist orthodontic examination included: medical history, extraoral and intraoral examination, analysis of extraoral and intraoral photographs, analysis of plaster casts and analysis of radiographs, and both the lateral cephalograms (taken in the natural head position) and dental panoramic tomograms. The radiographs were taken on MyRay Hyperion X9 3D (Cefla, Imola, Italy).
Tweed-Merrifield cephalometric analysis was used to assess the sagittal and vertical position of the mandible, as well as to assess the sagittal position of the lower incisors [16][17][18][19][20][21][22]. We used Wits analysis to measure the sagittal jaw relationship. The FMA angle was used to assess the vertical position of the mandible with reference to the Frankfort horizontal plane. FMIA and IMPA angles were used to measure the sagittal position of the lower incisors. Figure 1 presents the lateral cephalogram with marked lines and angles, presented in Table 2. Facial profile convexity was assessed by the distance of the Z-line from the tip of the nose. The facial profile was classified as: convex when the Z-line was moved forward from the tip of the nose, normal when the Z-line was crossing the nose, and borderline when the Z-line was crossing the tip of the nose. The Z-angle was used to measure the convexity of the facial profile.
All patients were allocated into groups, depending on the vertical growth pattern, estimated with the FMA angle. There were three groups included in the study: normalangle cases (control group) with an FMA angle from 22° to 28° (76 patients), low-angle cases (group 1) with an FMA angle below 22° (51 patients), and high-angle cases (group 2) with an FMA angle above 28° (73 patients).
Statistical analysis was performed with Statistica 13.0 software (Dell Inc., Aliso Viejo, CA, USA). Quantitative variables were characterized with the usage of mean values, standard deviation, range, median, and upper and lower quartiles. To check if the differences between the examined groups were statistically significant, the analysis of variance (ANOVA) and chi-square test were used. The statistical significance level was set at p = 0.05.  Table 2. FMA-Frankfort mandibular plane angle, FMIA-Frankfort mandibular incisor plane angle, IMPA-incisor mandibular plane angle, ML linemandibular line, FH line-Frankfort horizontal line, L1 line-long axis of lower incisor, Z-line-the profile line. Table 2. List of points, lines, and angles used to analyze the mandibular position and morphology, as well as the position of the lower incisors on the basis of the literature [16][17][18][19][20][21][22][23].   Facial profile convexity was assessed by the distance of the Z-line from the tip of the nose. The facial profile was classified as: convex when the Z-line was moved forward from the tip of the nose, normal when the Z-line was crossing the nose, and borderline when the Z-line was crossing the tip of the nose. The Z-angle was used to measure the convexity of the facial profile.

Points/Lines/Angles Description of Points/Lines/Angles
All patients were allocated into groups, depending on the vertical growth pattern, estimated with the FMA angle. There were three groups included in the study: normalangle cases (control group) with an FMA angle from 22 • to 28 • (76 patients), low-angle cases (group 1) with an FMA angle below 22 • (51 patients), and high-angle cases (group 2) with an FMA angle above 28 • (73 patients).
Statistical analysis was performed with Statistica 13.0 software (Dell Inc., Aliso Viejo, CA, USA). Quantitative variables were characterized with the usage of mean values, standard deviation, range, median, and upper and lower quartiles. To check if the differences between the examined groups were statistically significant, the analysis of variance (ANOVA) and chi-square test were used. The statistical significance level was set at p = 0.05.

Results
We estimated the sample size on the basis of an initial pilot study. We considered a power of 80% and a probability of the type I error 0.05. At least 50 patients in each group were necessary in order to detect a 20% difference in the Z-angle value between the groups.

Cephalometric Assessment of the Sagittal Jaw Relationship
The examined groups differed significantly regarding the sagittal jaw relationship. The majority of patients in the control group (46.1%) and in Group 2 (45.2%) were diagnosed with skeletal class I. However, the vast majority of low-angle patients (56.9%) presented with skeletal class II. The distribution of skeletal class II was significantly higher in Group 1 compared to the control group (56.9% vs. 34.2%; p = 0.013) and also compared to Group 2 (56.9% vs. 27.4%; p = 0.001). The distribution of skeletal class III was significantly higher in Group 2 compared to Group 1 (27.4% vs. 9.8%; p = 0.018).
The average values of the Wits analysis were significantly higher in Group 1 compared to the control group (p < 0.05), as well as compared to Group 2 (p < 0.01). There were no statistically significant differences regarding the average values of the Wits analysis between the control group and Group 2 (p > 0.05). Table 4 presents the Wits analysis among the examined groups. Figure 2 presents the comparison of the average Wits values among the examined groups and the results of the analysis of variance (ANOVA).

Analysis of the Facial Profile Convexity
The examined groups differed significantly regarding the facial profile convexi

Analysis of the Facial Profile Convexity
The examined groups differed significantly regarding the facial profile convexity. The distribution of the convex profile was significantly higher in Group 2 compared to the control group (28.8% vs. 11.8%; p = 0.011), as well as comparing to Group 1 (28.8% vs. 7.8%; p = 0.005). Of all convex profiles, 61.8% were diagnosed among high-angle cases.
The average value of the Z-angle was significantly higher in Group 1 compared to the control group (p < 0.01), as well as comparing to Group 2 (p < 0.001). Moreover, the average value of the Z-angle was significantly higher in the control group compared to Group 2 (p < 0.001). High-angle patients (group 2) presented the lowest values of the Z-angle. Table 5 presents the distribution of the Z-line position and the values of the Z-angle among the examined groups. Figure 3 presents the comparison of the average Z-angle values among the examined groups and the results of the analysis of variance (ANOVA).   Patients diagnosed with Z-line crossing the nose (normal profile) presented a significantly higher average value of the Z-angle compared to the patients diagnosed with a convex profile-Z-line in front of the nose (75.9 • vs. 60.5 • , p < 0.001), as well as compared to the patients diagnosed with a borderline profile-Z-line crossing the tip of the nose (75.9 • vs. 66.5 • , p < 0.01). The differences regarding the Z-angle average value between the patients with convex and borderline profiles were statistically insignificant. Table 6 presents the average values of the Z-angle with reference to the position of the Z-line.

Assessment of the Cephalometric Angles: FMIA, IMPA
There were statistically significant differences between the examined groups regarding the average values of the IMPA and FMIA angles.
The average value of the IMPA angle was significantly lower in Group 2 compared to Group 1 (p < 0.01). The differences regarding the average value of the IMPA angle between the control group and Group 1, as well as between the control group and Group 2, were statistically insignificant (p > 0.05).
Group 2 presented the lowest average values of the FMIA angle. The average value of the FMIA angle was significantly lower in Group 2 compared to the control group (p < 0.001), as well as comparing to Group 1 (p < 0.001). Moreover, the average value of the FMIA angle was significantly lower in the control group compared to Group 1 (p < 0.01). Table 7      Patients diagnosed with Z-line crossing the nose (normal profile) presented a s icantly higher average value of the FMIA angle compared to the patients diagnosed   Patients diagnosed with Z-line crossing the nose (normal profile) presented a icantly higher average value of the FMIA angle compared to the patients diagnose  There was a statistically significant positive correlation between the Z-angle and FMIA angle (r = 0.801, p < 0.001). Figure 6 presents the correlation diagram between the Z-angle and FMIA angle, correlation coefficient, and regression straight-line equation. There was a statistically significant positive correlation between the Z-an FMIA angle (r = 0.801, p < 0.001). Figure 6 presents the correlation diagram betwee angle and FMIA angle, correlation coefficient, and regression straight-line equati There was also a statistically significant negative correlation between the Z-a IMPA angle (r = −0.450, p < 0.001). Figure 7 presents the correlation diagram betw Z-angle and IMPA angle, correlation coefficient, and regression straight-line equ There was also a statistically significant negative correlation between the Z-angle and IMPA angle (r = −0.450, p < 0.001). Figure 7 presents the correlation diagram between the Z-angle and IMPA angle, correlation coefficient, and regression straight-line equation.

Cephalometric Parameters Describing Patients with Convex Profile
Receiver operating characteristic (ROC) curves were used to find the mos cephalometric parameters describing patients with a convex profile. Table 9 pr results of the analysis of the ROC curves. Table 9. The results of the analysis of the ROC curves.

Cephalometric Parameters Describing Patients with Convex Profile
Receiver operating characteristic (ROC) curves were used to find the most accurate cephalometric parameters describing patients with a convex profile. Table 9 presents the results of the analysis of the ROC curves. FMIA-Frankfort mandibular incisor plane angle, IMPA-incisor mandibular plane angle, CI-confidence interval.
The Z-angle appeared to be the most accurate parameter (AUC = 0.957) describing patients with a convex profile. The cutoff value Z-angle ≤ 68.

Discussion
This study evaluates the relationship between the sagittal position of the lower sors and facial profile esthetics with reference to the skeletal vertical dimension. Mo ver, according to our knowledge, this is the only study which analyzes different ceph metric parameters to find these parameters which most accurately describe patients a convex profile.
We analyzed a group of 200 patients who had been allocated into one of three groups, depending on the skeletal vertical dimension. We have found statistically sig

Discussion
This study evaluates the relationship between the sagittal position of the l sors and facial profile esthetics with reference to the skeletal vertical dimensio ver, according to our knowledge, this is the only study which analyzes differen

Discussion
This study evaluates the relationship between the sagittal position of the lower incisors and facial profile esthetics with reference to the skeletal vertical dimension. Moreover, according to our knowledge, this is the only study which analyzes different cephalometric parameters to find these parameters which most accurately describe patients with a convex profile.
We analyzed a group of 200 patients who had been allocated into one of three subgroups, depending on the skeletal vertical dimension. We have found statistically significant differences between the groups with reference to the sagittal jaw relationship (based on Wits analysis). Patients diagnosed with FMA < 22 • most often presented a skeletal class II relationship. There were no statistically significant differences between normal-angle and high-angle patients regarding the sagittal jaw relationship. Interestingly, Linjawi [24] noticed that only patients with a decreased skeletal vertical dimension presented changes in the inclination and position of the lower incisors related to age and gender.
The majority of patients included in our study, who were diagnosed with a convex profile, presented an increased vertical dimension. We have observed that Z and FMIA angles' values decreased significantly with the increase of the skeletal vertical dimension. Both the Z and FMIA angles were measured with reference to the Frankfort horizontal line (FH line). Thus, with the increase of the skeletal vertical dimension and posterior rotation of the mandible, we observed the decrease in the values of the Z and FMIA angles. This was also related with the increased facial profile convexity.
Conversely, the IMPA angle was significantly higher in low-angle patients compared to the high-angle ones. There were no other significant differences between the examined groups. The IMPA angle describes the sagittal position of the lower incisor with reference to the mandibular line. The above-described difference of the IMPA values can be explained with the process of the dentoalveolar compensation of the skeletal types of malocclusions. Alhammadi [25] described that there is an association between the sagittal jaw discrepancy and the sagittal position of the incisors; namely, he observed a proclination of the lower incisors with an increased sagittal jaw relationship (or increased overjet). He also described the significant negative correlation between the skeletal vertical dimension and inclinations of the maxillary and mandibular incisors. This means that with increased vertical dimension, both the upper and lower incisors become more retroclined.
Furthermore, we have found that the facial convexity was most accurately described with the Z-angle measurement. The value of the Z-angle ≤ 68.0 • characterizes the patients with a convex profile with a sensitivity of 94.1% and specificity of 84.3%. The second parameter most accurately describing patients with a convex profile was the FMIA angle ≤ 55.3 • with a sensitivity of 82.4% and specificity of 81.3%.
Facial analysis is the onset of orthodontic diagnosis [26]. Facial profile esthetics depend on several different factors, including, among others: facial anatomy, the skeletal vertical and horizontal position of the maxilla and mandible, dentoalveolar sagittal position, thickness of lips, activity of facial muscles, and ethnicity [27]. The vast majority of the available manuscripts discuss the relationship between the facial profile convexity and the proclination of incisors in terms of bimaxillary protrusion treatment. It is generally known that the extraction of four premolars, especially the first ones, creates spaces to straighten and retract the anterior teeth. This approach allows correction of dentoalveolar protrusion, and therefore leads to improvement of facial balance [27][28][29]. Contini et al. [30] indicated that the facial balance is not only affected by orthodontic treatment, but also by facial growth. Krooks et al. [31] performed esthetic evaluation of facial attractiveness. They found that facial sagittal dimensions affected more facial esthetics than the vertical dimensions.
The sagittal position of the lower incisors should always be assessed with reference to the skeletal vertical dimension. To obtain the harmony of the facial profile, hyperdivergent patients require a more upright position of the lower incisors than the hypodivergent patients do. Dr. Tweed's formula recommends, for patients with FMA from 21 • to 29 • , to obtain the FMIA angle of 68 • ; for patients with FMA 30 • , the FMIA should be 65 • ; and finally, for patients with FMA 20 • or less, the IMPA angle should not exceed 92 • [2].
A few factors affecting the position of the mandibular incisors have been listed, namely: natural oral function, facial harmony, and support by the periodontal tissues [32]. The final position of the lower incisors is the result of the abovementioned factors [32]. However, not only do the periodontal tissues affect the position of the lower incisors, but the position of the lower incisors also affects the condition of the periodontal tissues. Proclination of the lower incisors may lead to reduction of gingival thickness, shortening of the free gingival margin, and may also lead to increased clinical crown height [33]. Hasegawa et al. [32] found that there was no relationship between the morphology of the upper incisors (labiolingual crown thickness of maxillary incisors) and the position of the mandibular incisors. Gütermann et al. [34] noticed that inclination of lower incisors is associated with sex, age, and the skeletal vertical pattern. Furthermore, according to their studies, there is only one symphysial distance-symphysial depth-which is related to inclination of the lower incisors. Finally, the position of the tongue and length of the lingual frenum may affect the shape of the dental arch, and consequently change the position of the incisors [35,36]. It has also been proven that the orofacial balance may affect the posture of the entire body [37].
We have found only one clinical study which assessed the relationship between repositioning of the lower incisors during orthodontic treatment and enhancement of the profile in patients with different vertical growth patterns. The study was performed by Contini et al. [30]. The authors compared the clinical outcomes of the orthodontic treatment in two groups of patients with different vertical growth patterns. Contini et al. found that patients with unfavorable growth patterns presented bigger changes in FMIA angles than patients with favorable growth patterns. Changes in the values of the Z-angle were similar in both groups. Contini et al. observed improvements in facial profile esthetics in both groups of patients. The authors indicated that the increase of the anterior facial height is related to the increase in facial profile convexity, and that the retraction of lower incisors (increase of FMIA angle) leads to lip retraction (increase of Z-angle), and therefore improves facial balance. Contini et al. confirmed that the position of the lower incisors affects the facial profile esthetics, and therefore, the facial profile esthetics may be improved with orthodontic treatment. Our observations stay in accordance with the research by Contini et al. [30].
There are a few limitations to our study. Firstly, this study was based only on people aged 15-25 years old. Therefore, the results from this study should not be generalized to the population of elderly patients. Facial profile esthetics in elderly patients is strongly affected by the process of aging. That is why further studies ought to be performed to assess the relationship between the sagittal position of the lower incisors and facial profile esthetics in different age groups. Secondly, we did not analyze patients' body mass index (BMI). It may be speculated that obesity may affect the value of the Z-angle. Finally, we did not evaluate patients' satisfaction related to their facial profile. It should be remembered that there may exist differences in the perception of facial esthetics between patients and orthodontic specialists.

Conclusions
The sagittal position of the lower incisors significantly affects facial profile convexity. The Z-angle and FMIA angle are the parameters which most accurately describe the patients with convex profiles. We found a strong positive correlation between the Z-angle and the FMIA angle. The soft tissue facial profile indicates the sagittal position of the anterior limit of the dentition.