Prediction of outcomes of various orthodontic procedures is important for treatment planning. The use of skeletal anchorage for molar intrusion in skeletal open bite patients allowed the orthodontists to yield orthopedic changes in adults using mandibular autorotation. In the current study, data from before and after intrusion were used to provide the clinician with tools to predict changes following intrusion of maxillary posterior teeth.
The authors chose the landmarks most likely to affect the clinician treatment decision following maxillary molar intrusion, namely the horizontal position of the chin, the face height, the overbite and the overjet, and the lower lip position.
In the present study, the hard tissue pogonion was found to move forward at a ratio of 1:0.79 to the maxillary molar intrusion. This is close to the findings of Lee and Park  who reported a ratio of 1:0.9. Xun et al.  reported a ratio of 1:1.3 for the forward movement of the point B. This modest difference between the two points can be explained that they do not necessarily lie on the same arc of rotation. Bell et al.  described a 1:1 ratio of vertical and sagittal hard tissue chin movement relative to maxillary impaction. On the other hand, Fish et al.  described reported 70% advancement of the mandible relative to the amount of maxillary impaction, which approximates the ratio obtained in the present study. Wang et al.  reported a strong correlation between the amount of maxillary superior positioning and the displacement of the chin following maxillary impaction and mandibular autorotation (r = 0.79) at a ratio of 1:0.88, which are similar to the findings of the present study. Moreover, Steinhäuser et al.  found that pogonion moved forward 78.6% of the distance of maxillary impaction measured at the posterior nasal spine. When measuring the change at pogonion in exclusive posterior impaction subjects, which resembles the effects of maxillary posterior segment intrusion, the forward advancement at pogonion was found to be 80% of the amount of maxillary impaction, which is in accordance with the current results.
The reduction of the facial height reported in the study (1:1) was found to agree with several authors [18, 26,27,28, 30]. Some studies reported lower [23, 25, 33, 34] and higher ratios [19, 24, 31]. The differences did not deviate largely from the present report; however, it can be explained by the different methods of measuring the facial height used in the different studies. In addition, some studies reported measurements post-treatment that may have involved extractions that may have altered the facial height [18, 19, 24, 26, 28, 30]. In samples of orthognathic surgery subjects treated with maxillary impaction, Bell et al.  and Fish et al.  reported 1:1 ratio of vertical displacement of the hard tissue chin relative to the amount of maxillary impaction following mandibular autorotation. Steinhäuser et al.  found the vertical displacement at Me was 60.9% of the amount of maxillary impaction measured at PNS. This may be attributed to the different methods used for maxillary impaction, where they reported different displacements at Pogonion depending on whether the impaction was parallel, posterior, or posterior with anterior lowering.
The soft tissue pogonion was found to move at the same ratio as the hard tissue pogonion. Similarly, soft tissue menton showed the same ratio of change as hard tissue menton. Schendel et al.  reported that the soft tissue chin point rotated at a 1:1 ratio with the hard tissue chin point on the same arc following mandibular autorotation due to maxillary impaction surgery. In addition, Lee et al.  reported a 1:1 ratio between the mandibular soft tissue and hard tissue landmarks secondary to autorotation of the mandible following maxillary impaction. On the other hand, Mansour et al.  reported that the soft tissue chin point moved horizontally at a ratio of 0.86 relative to the corresponding hard tissue chin, whereas the soft tissue menton displaced superiorly at a ratio of 1.2 relative to hard tissue menton. The explanation stated by the authors was the stretching of the soft tissue following the upward and forward displacement of the mandible after maxillary impaction surgery. Steinhäuser et al.  found an equal ratio for the vertical displacement of Me and Me′ (60.9 and 60.4%, respectively); the ratios, however, are smaller compared to the present study which may be attributed to the cumulative effect of the different methods of maxillary impaction used in their sample.
Comparing ratios of change of dental measurement will be limited to the few studies reporting values following intrusion [23, 25, 27, 31,32,33,34]. In the present study, the ratio of overbite correction to the amount of molar intrusion was approximately 1:2. This agrees with one of the prosthodontic tenets that each millimeter of molar intrusion yields a 2 to 3 mm closure of the anterior bite . Similar ratios were reported by Xun et al.  and Hart et al. . Smaller ratios were found by several authors [23, 27, 31,32,33]. This may be attributed to the compensatory eruption of mandibular molars during maxillary molar intrusion which was reported in other studies . In the present study, a strict protocol was followed to avoid this effect .
The overjet was found to reduce by 60% of the amount of molar intrusion. Few studies reported the change in overjet immediately following intrusion. The ratios varied from as low as 1:0.03  to as high as 1:1.1 . Since the overjet is measured at the incisal edge of the lower incisor, different arcs of rotation will be displayed by the incisal edge depending on their pre-treatment position. Moreover, the axial inclination of the lower incisor may change during the autorotation of the mandible as the lower incisors are moved closer to the muscles of the lower lip out of their equilibrium zone. Predicting the change of the overjet in Class II situations, the clinician can decide whether the overjet will be entirely corrected by mandibular autorotation or other treatment procedures such as premolar extractions will be needed.
In this study, the lower lip moved forward at ratio of 1:0.8 to the amount of maxillary molar intrusion. Akan et al.  reported negligible effect on the position of the lower lip immediately following intrusion; the measurement, however, was relative to the E-line whose position will change with the autorotation of the mandible. Steinhäuser et al.  found that the lower lip moved forward 23.4% of the mean distance of maxillary impaction. Differences in the response of the soft tissue have been attributed to many factors including initial lip length, thickness, and pre-treatment labial tension [41, 42].
Approaches to predict changes using pre-treatment and post-treatment results varied from using mean ratios, linear regressions, and step-wise regressions. Ratios of means are commonly reported in the literature for the prediction of soft tissue to hard tissue changes following treatment. However, regression analyses were shown to offer more accurate predictions [6, 43]. Ratios of means were reported in this study to facilitate comparison with the published literature. In the present study, the strongest correlation coefficients were reported for the hard tissue points: pogonion (r = − 0.88, P ≤ 0.001) and menton (r = 0.91, P ≤ 0.001), whereas prediction equations for the change in soft tissue landmarks were weaker particularly for soft tissue pogonion (r = − 0.40, P ≤ 0.01) and the lower lip (r = − 0.51, P ≤ 0.01) compared to soft tissue menton (r = 0.77, P ≤ 0.001). The soft tissue pogonion and the lower lip can be considered highly susceptible to strain and least reproducible in serial radiographs . Generally, prediction equations for 3-mm molar intrusion yielded results similar to those obtained from the ratios of means obtained in this study.
The primary objective of this paper is to help the clinician predict changes that will happen in key treatment planning parameters when using molar intrusion. The prediction parameters may be used for manual cephalometric predication and to adjust computer software algorithms for visualized treatment outcome prediction. These predictions enable the patient to make informed treatment decisions based on patient satisfaction with the predicted treatment outcome. It is noteworthy that despite the use of cephalometric predictors, patient-centered outcome such as patient satisfaction and patient comfort during treatment are of prime importance and need to be addressed in future studies.