# Evaluation of Deviations Produced by Soft Tissue Fitting in Virtually Planned Orthopathic Surgery
## 1 Introduction  
Dentofacial deformity (DFD) is a multifactorial condition affecting the position and/or the size of the jaw, suffered by around 15% of the general population [1]. Patients with DFD may appear to have an upper or lower jaw or chin that is too large or too small, which can manifest within the dentition as a malocclusion (e.g., Class I, II, or III) [2]. Patients with DFD often exhibit facial asymmetry, and previous studies have shown that approximately 21-67% of patients with prognathism or retrognathism exhibit facial asymmetry, with chin deviation being the most notable manifestation [3,4]. Patients with DFD exhibit a range of symptoms, including impaired chewing, swallowing, breathing, speech articulation, and facial aesthetics [1,5, 6, 7]. These symptoms can result in decreased well-being and, consequently, a lower quality of life (QOL) [8]. Furthermore, several studies have shown that this disease is closely related to obstructive sleep apnea syndrome (OSA, particularly in Class II patients) [4,9,10]. OSA is a sleep disorder characterized by repeated obstruction of the airway during sleep, resulting in a decrease in oxygen saturation and arousal from sleep, and consequently fragmented, nonrestorative sleep [11]. There are several therapies that have been proven to be effective for all these disorders, with orthognathic surgery (OS) for maxilla-mandibular advancement being the required option for patients who do not tolerate long-term non-invasive treatment [5,6,12]. Orthognathic surgery involves repositioning of the maxillary and mandibular bones to improve function and aesthetic release of the upper airway and maintain correct dental occlusion [13]. The precision required for the development of this technique places special value on the use of new technical advances in virtual surgical planning (VSP) and computer-aided design/computer-aided manufacturing (CAD/CAM) three-dimensional models of the patient [14, 15, 16]. This methodology for virtual surgical planning is based on three-dimensional reconstructions from specialized radiological tests, such as computed tomography (CT) and intraoral scanning (IS), taken as a starting point [17,18]. The necessary bone movements for normal positioning, airway release, and preservation of an optimal dental occlusion are simulated on them. Once both jaws have been virtually repositioned using CAD, occlusal splints are obtained using 3D printing (CAM). These splints provide the necessary information for correct positioning of the bones while maintaining optimal occlusion [15, 16, 17,19]. VSP has been shown to be highly accurate and reproducible for orthognathic treatment planning. Studies have demonstrated that VSP can achieve a mean difference of less than 2 mm between the planned and actual surgical outcomes, which is considered clinically acceptable [20,21]. For example, one study reported an overall mean of root mean square deviation (RMSD) of 1.37 mm, with the greatest deviation, 1.76 mm, occurring in the sagittal direction, which is still below the 2 mm threshold [22]. Another study found that the mean 3D error met the clinical success standards, at less than 2 mm [23]. Furthermore, combining cone-beam computed tomography (CBCT) and intraoral scans for imaging has been shown to enhance the accuracy of VSP even further [21]. Studies consistently demonstrate that VSP achieves high accuracy in orthognathic surgery, with deviations typically remaining within the clinically acceptable range of 2 mm. For a good outcome with VSP, one of the most important factors to consider is soft tissue predictability and simulation on CAD software v12. Accurate soft tissue simulation contributes to greater reliability in the VSP system's proposed repositioning. However, modelling soft tissue behavior is complex and VSP systems have shown varying degrees of accuracy in predicting soft tissue outcomes, with the precision of these predictions varying between different facial regions [24]. Despite advancements, challenges remain in achieving perfect soft tissue predictability.