The widespread adoption of cone-beam computed tomography (CBCT) and intraoral scanning has revolutionized virtual surgical planning into the standard of care in modern orthognathic surgery (Reyneke and Sullivan; Kwon, 2024). Despite these technological advances, the fundamental principles of surgical planning remain consistent. In two-jaw surgery, whether through traditional model or contemporary virtual techniques, the process begins with maxillary alignment, followed by mandibular positioning based on occlusion (Xia et al., 2015; Chin et al., 2017; Reyneke and Sullivan; Melhem-Elias et al., 2023; Kwon, 2024). Therefore, optimal maxillary alignment is crucial for achieving favorable surgical outcomes (Reyneke and Sullivan).

The facial midsagittal plane, which bisects a stable reference region unaffected by orthognathic procedures, serves as the standard for determining the transverse position of the maxilla. This position is achieved by aligning midline landmarks with the midsagittal plane and symmetrically positioning bilateral landmarks (Gateno et al., 2011; Huang and Chen, 2015). However, the approach to defining the facial midsagittal plane differs between conventional and virtual planning. Traditionally, clinicians determined the soft-tissue midsagittal plane through visual assessment, then replicated it on an articulator using a facebow (D'Albis et al., 2021; Ryser et al., 2024). Conversely, virtual planning employs mathematical and geometric techniques to construct a skeletal midsagittal plane that digitally represents craniofacial morphology (Xia et al., 2015; Gateno et al., 2016).

Numerous studies have explored skeletal midsagittal plane construction. Optimized midsagittal planes, generated through techniques such as Procrustes analysis, least-squares approximation, or iterative closest point algorithms, offer high accuracy (Hajeer et al., 2004; Wong et al., 2014; Green et al., 2017; Han et al., 2020; Zhu et al., 2020; Feng et al., 2021; Grissom et al., 2022; Ajmera et al., 2023, 2024). However, their clinical application is limited by the need for customized programs and training (Damstra et al., 2012; Shin et al., 2016; Ajmera et al., 2024). Conventional geometric midsagittal planes may provide a practical alternative (AlHadidi et al., 2011; Damstra et al., 2012; Shin et al., 2016; Green et al., 2017). Prior research has proposed landmark-based geometric guidelines for defining skeletal midsagittal planes that approximate optimized ones (Damstra et al., 2012; Shin et al., 2016; Green et al., 2017). The influence of facial asymmetry on skeletal midsagittal plane construction has also been documented (Noh et al., 2023).

However, an evident knowledge gap exists regarding facial soft-tissue midsagittal planes. To the best of our knowledge, no study has defined a geometric soft-tissue midsagittal plane that closely approximates an optimized version. Moreover, the effect of facial asymmetry on soft-tissue midsagittal plane accuracy remains poorly understood. Furthermore, the relationship between soft-tissue and skeletal midsagittal planes remains unexplored. Notably, the transverse position of the maxillary central incisors serves not only as a marker of skeletal alignment but also as an essential determinant of facial aesthetics (Cardash et al., 2003; Huang and Chen, 2015; Xia et al., 2015; Gillot et al., 2022; Melhem-Elias et al., 2023). Studies recommend positioning the interproximal point of the maxillary central incisors within 2 mm of the facial soft-tissue midline (Beyer and Lindauer, 1998; Johnston et al., 1999; Cardash et al., 2003; Jayalakshmi et al., 2013). While this is readily achievable with conventional model surgery, its feasibility in current virtual protocols remains uncertain, as the soft-tissue and skeletal midsagittal planes may not coincide (Huang and Chen, 2015). Despite its clinical relevance, no standardized guideline exists for integrating these two reference planes.

This study aimed to identify the optimal geometric facial soft-tissue midsagittal plane and to establish a clinical guideline for reconciling soft-tissue and skeletal midsagittal planes when positioning the upper incisors in virtual surgery. The investigators hypothesized that the accuracy of geometric soft-tissue midsagittal planes and the resulting incisor deviation would significantly vary depending on facial asymmetry and the midsagittal plane construction method. Specifically, the specific objectives were to: 1) compare the accuracy of various geometric soft-tissue midsagittal planes with an optimized midsagittal plane derived from ordinary Procrustes analysis in symmetric and asymmetric groups, and 2) assess upper incisor deviations when measured using selected geometric soft-tissue and skeletal midsagittal planes across these cohorts.