Magnetic resonance imaging protocol

Magnetic resonance images (MRIs) were taken prior to orthodontic treatment and after completion of treatment (i.e. after removal of the orthodontic appliances). The mean time lapse, after surgery, for the post treatment scans was 28 months (range 10–63 months). MRI examinations were performed with a 1.0 T MR system (Siemens, Erlangen, Germany). The patients were scanned in a supine position with the Frankfurt Horizontal (FH) plane oriented perpendicular to the scan table. The patients were instructed to close the teeth but to avoid clenching. Axial images were made with a multislice T1 spin-echo sequence (TR/TE = 700 ms/15 ms) with 5 mm thickness and 1.25 mm interslice gap. Sagittal and coronal imaging was performed in the same sequence with 4 mm thickness and 1 mm interslice gap. Images parallel to the right and left ascending ramus of the mandible were made with oblique sagittal multislice T1 spin-echo sequences (TR/TE 400 ms/15 ms) with 3 mm thickness and 1 mm interslice gap.

Cephalometrics

Craniofacial morphology was assessed on preoperative lateral cephalographs digitized with Viewbox ^® software (dHal software, Kifissia, Greece). The cephalometric analysis was used to calculate the MPA (S–N to Go–Me) and assisted in the diagnosis of the skeletal deformity.

Mandibular advancement and sagittal rotation of the proximal segments

The advancement achieved at surgery and the sagittal rotation of the proximal segments were presented in a previous paper. In short, the advancement achieved at surgery was determined on preoperative (T1) and 1 day postoperative (T2) lateral radiographs in a carthesian coordinate system with S–N as the X axis and a perpendicular line through S as the Y axis. The projection of the centroid of the symphysis of the mandible on both axes was used for the calculation of the horizontal and vertical components of the advancement.

The sagittal rotation of the proximal segments was defined as the difference between the pre- and postoperative angle between the tangent to the dorsal side of the ramus and the axial scan plane ( Fig. 1 ).

Sagittal rotation of the proximal segment. The tangent to the ascending ramus is drawn in the T1 weighted oblique sagittal images through the condyle parallel to the mandibular ramus. The horizontal line at the top of the image represents the axial scan plane.

Calculation of the angle of the condyle to the sagittal plane

The angle of the long axis of the condyle and the angle of the tangent to the ramus to the sagittal plane were measured in pre- and postoperative axial images ( Fig. 2 ).

Axial view of the mandible. β is the angle between the tangent to the inferior border of the ascending ramus (proximal segment). γ is the angle between the condylar axis and the sagittal plane. ICA, intercondylar angle.

Calculation of the mechanical advantage

The moment arm of the bite force was measured in the oblique sagittal images parallel to the ramus ( Fig. 3 ). To estimate the direction (vector) of the bite force, a line perpendicular to the occlusal plane was drawn at the level of the right and left first lower molar. The moment arm of the bite force was calculated as the distance from the top of the ipsilateral condyle to this bite force line (Figs 3 and 4 ).

Moment arm of the bite force. The moment arm of the bite force was drawn in the T1 weighted oblique sagittal images through the condyle parallel to the mandibular ramus at the level of the first lower molar.

Two-dimensional static model with the vectors of the masseter (Fmas), medial pterygoid muscle (Fmpm), their resultant (Fres), bite force (Fb) and joint reaction force (Fj). α is the angle between the force vectors (direction) of masseter and medial pterygoid muscle. H, height of the parallellogram of forces.

The results for the calculations of moment arms of MAS and MPM were reported in a previous study on the same patient sample. In short, in a projection on the sagittal plane, the distance from the top of the right condyle to a line representing the main direction of the muscle was calculated ( Fig. 5 ).

Sagittal main direction (yellow) and sagittal moment arm of the right masseter. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)

The mechanical advantage was defined as the ratio between the moment arm of the muscle and the moment arm of the bite force.

Forces on condyle articulating surface during mouth opening

The pre- and postoperative coordinates determining the direction of MAS, MPM, the lateral pterygoid (LPM) and anterior digastric muscles (DIG) were imported into biomechanical models of the human masticatory system. Two models were used, one representing Group I and one representing Group II. Together with the imported data on muscle cross-sectional area and volume this allowed an assessment of the forces on the condyle during jaw opening and closing movement to be made ( Fig. 6 ). The assessment was based on pre- and postoperative models. The imported data on the main direction of MAS and MPM were derived from a previous study on the same patient sample.

Dynamic loading of the condyle. The course of the joint reaction forces during opening and closing in the pre- and postoperative models of Groups I and II. Note that the largest joint reaction force is built up during opening at the moment of initial contact between the condyle–disc complex and the articular eminence. 1, closed mouth; 2, initial contact with the articular eminence; 3, maximum mouth opening.