# Differential Relapse of Proximal and Distal Segments after Mandibular Setback Surgery
## 1 Introduction  
Mandibular prognathism is a malocclusion in which the lower jaw is abnormally large compared to the upper jaw. It occurs when the lower jaw overgrows or the upper jaw undergrows. Mandibular setback surgery is used to correct mandibular prognathism. Bilateral mandibular ramus sagittal split osteotomy (BSSRO) is one of the most commonly used orthographic procedures to improve mandibular prognathism. BSSRO allows mandibular setback or advancement by splitting the mandible through two incisions: a lateral incision extending from the second molar to the inferior border, and a medial incision running posteriorly along the ramus, avoiding the mandibular nerve canal. The anteroposterior relapse rate of mandibular setback surgery varies from 14 to 20% [1, 2, 3], while the pattern of relapse varies depending on the surgical technique [4]. After mandibular setback surgery with BSSRO, relapse occurs in the form of rotational relapse, where the mandible rotates counterclockwise [5]. Forward movement of the chin is observed in the postoperative period due to the counterclockwise rotation of the mandible [1, 4, 6, 7]. Specifically, posterior displacement of the proximal segments during surgery, which appears as clockwise rotation, induces stretching of the pterygomasetetric sling, which causes the mandible to relapse with counterclockwise rotation [8, 9, 10]. This counterclockwise rotation increases the prominence of the chin point and mandibular border. In addition, factors that contribute to stability after mandibularsetback surgery have been reported to include the amount of setback, tension of the soft tissues surrounding the mandible, and the method of bone fixation [9; 11; 12; 13]. It is known that condylar displacement during orthognathic surgery significantly impacts early postsurgical relapse and temporomandibular joint disorders [14; 15; 16]. As the distal segment setbacks along the occlusal plane, a vertical height difference between the lower borders of the proximal and distal segments of the mandible, known as the vertical bony step (VBS), occurs inevitably due to the divergence between the occlusal plane and mandibular plane. This VBS has been reported to be associated with relapse after mandibular BSSRO surgery [17; 18].  
Using a computer-based three-dimensional simulation technique, it is possible to measure and analyze the anatomical structures of the maxillofacial region in three dimensions prior to surgery and predict the position of the bone segments after osteotomy in three dimensions. At this time, it is necessary to determine the amount of simulation surgery by considering the postoperative relapse of the bone segments. To our knowledge, the relapse of the proximal and distal segments has rarely been investigated separately. Previous studies have suggested that postsurgical relapse patterns differ between them [17; 19]. Since chin point prominence is often the chief complaint of patients undergoing mandibular setback surgery, it is crucial to account for rotational relapse in advance. Therefore, incorporating proximal and distal segment relapse simulations into the three-dimensional simulation of mandibular setback surgery is desirable. However, this requires information about the center of rotation (C\({}_{\text{Rot}}\)) of proximal and distal segments and the amount of rotation during the relapse of mandibular setback surgery. This study aimed to evaluate the condylar displacement pattern and the C\({}_{\text{Rot}}\) of the rotational relapse of the proximal and distal segments of the mandible.