Application of curve fitting based on least square method in mandibular osteotomy
10.3760/cma.j.cn114453-20220517-00151
- VernacularTitle:基于最小二乘法的曲线拟合在下颌截骨术中的应用
- Author:
Antong DU
1
;
Neng DING
;
Yingnan GENG
;
Jie ZHU
;
Jian ZHANG
;
Lie ZHU
Author Information
1. 海军军医大学第二附属医院（上海长征医院）烧伤、整形外科，上海 200003
- Keywords:
Osteotomy;
Prominent mandibular angle;
Esthetics;
Curve fitting;
Facial recognition
- From:
Chinese Journal of Plastic Surgery
2023;39(9):974-983
- CountryChina
- Language:Chinese
-
Abstract:
Objective:To use the least square method to curve fit the mandibular contours of Chinese women, obtain an ideal fitting function model, and explore the effectiveness of using mathematical curves for bone cutting line design in mandibular osteotomy.Methods:(1) Female cranial CT data were selected from the Second Affiliated Hospital of Naval Medical University and Shanghai Universal Medical Imaging Diagnostic Center. The mandibular morphology of the CT reconstructed images was evaluated using the Likert scale, and samples were selected from individuals with mandibular angle hypertrophy, aesthetically pleasing mandibular morphology, and aesthetically pleasing appearance after osteotomy as references. The Python platform Spyder module was used to analyze the curve fitting of mandibular contour morphology and the goodness of fitting was measured by the coefficient of determination R2( R2 ≥ 0.800 was considered acceptable for the fitted function, while R2≥ 0.900 was deemed sufficient to meet clinical application requirements). The fitting degree of polynomial functions, logarithmic functions, and other mathematical curves in the facial contours of individuals with aesthetically pleasing mandibular morphology were analyzed to obtain an ideal mandibular contour curve fitting function model. (2) Patients with mandibular angle hypertrophy who underwent intraoral mandibular osteotomy from March 2020 to March 2021 at the Department of Plastic and Reconstructive Surgery of Second Affiliated Hospital of Naval Medical University were divided into a mathematical template group (guided by a mathematical curve-based bone cutting plan), a traditional template group (guided by traditional bone cutting templates), and a manual osteotomy group. Three-dimensional reconstruction technology was used to evaluate the efficacy postoperatively. Preoperative preparation time, bone cutting time, surgical time, and postoperative complications were compared among the three groups. Patient self-evaluation of surgical outcomes was assessed using the jawline component of the Face-Q questionnaire. Results:(1) A total of 205 female cranial CT data were selected, including 73 cases of mandibular angle hypertrophy, 32 cases of aesthetically pleasing mandibular morphology, and 5 cases of aesthetically pleasing appearance after osteotomy as reference samples for mandibular contour curve fitting. The result showed that the third-degree polynomial function ( R2=0.918±0.027) and logarithmic function ( R2=0.930±0.039) could be used to simulate the mandibular contour morphology in individuals with aesthetically pleasing mandibular morphology. (2) The mathematical template group (using logarithmic function for bone cutting design), traditional template group, and manual osteotomy group included 28, 14, and 11 patients with mandibular angle hypertrophy, respectively. All patients were satisfied with the postoperative mandibular contour morphology and no complications such as deformity or significant asymmetry were observed. The mathematical template group outperformed the manual osteotomy group in terms of the total score of the jawline questionnaire, surgical time, and bone cutting time(all P<0.01). The preoperative preparation time in the mathematical template group was shorter than that in the traditional template group [(82.39±9.77) min vs. (97.07±17.49) min, P<0.01], and the jawline questionnaire evaluation showed that the patients in the mathematical template group had higher scores in evaluating the lateral view of the mandible and the smoothness of the lower facial contour compared to the traditional template group [3.75±0.44 vs. 3.14±0.36, 3.71±0.46 vs. 3.36±0.50, both P<0.05]. Conclusion:Curve fitting based on the least square method can be used to simulate mandibular angle osteotomy. Models such as logarithmic functions can be used for preoperative design of mandibular osteotomy and have advantages in terms of contour smoothness and symmetry after surgery. Bone cutting design based on mathematical curves can meet patient demands and aesthetic standards, providing precise and individualized solutions for surgery.
