基于最小二乘法的曲线拟合在下颌截骨术中的应用  

Application of curve fitting based on least square method in mandibular osteotomy

作　　者：杜安通 丁能 耿英楠 祝捷 张建 朱鴷 Du Antong;Ding Neng;Geng Yingnan;Zhu Jie;Zhang Jian;Zhu Lie(Department of Plastic and Reconstructive Surgery,Second Affiliated Hospital of Naval Medical University(Shanghai Changzheng Hospital),Shanghai 200003,China;Shanghai Universal Medical Imaging Diagnostic Center,Shanghai University,Shanghai 200237,China)

机构地区：[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 [2]上海大学上海全景医学影像诊断中心,上海200237

出　　处：《中华整形外科杂志》2023年第9期974-983,共10页Chinese Journal of Plastic Surgery

基　　金：上海长征医院创新型临床研究项目(2020YLCYJ-Y16)。

摘　　要：目的采用最小二乘法对国内女性下颌轮廓进行曲线拟合,获取理想的拟合函数模型,并探索在下颌截骨术中应用数理曲线进行截骨线设计的效果。方法(1)选择2010年1月至2020年12月海军军医大学第二附属医院和上海全景医学影像诊断中心的青年女性头颅CT资料,采用Likert量表对CT重建图像的下颌形态进行评估,筛选出下颌角肥大人群、下颌美观人群、截骨术后美观人群,作为参考样本。采用Python平台Spyder模块进行下颌轮廓形态的曲线拟合分析,以拟合度R^(2)衡量拟合效果(R^(2)均值≥0.800视为可作为拟合函数,R^(2)均值≥0.900视为可满足临床应用需求)。分析多项式函数、对数函数等数理曲线在下颌美观人群面部轮廓中的拟合程度,获取理想的下颌轮廓曲线拟合函数模型。(2)选择2020年3月至2021年3月海军军医大学第二附属医院烧伤、整形外科接受口内入路下颌截骨术的下颌角肥大患者,采用基于数理曲线设计的截骨方案指导手术(数理导板组),术后应用三维重建技术评估疗效。并同接受徒手截骨(徒手截骨组)、传统截骨导板指导截骨(传统导板组)的患者相比较。统计3组的术前准备时间、截骨时间、手术时间、术后并发症发生情况,术后6个月采用Face-Q量表的jawline分量表进行患者手术效果满意情况自评。结果(1)选取205例青年女性头颅CT资料,从中筛选出下颌角肥大人群73例,下颌美观人群32例,截骨术后美观人群5例,作为参考样本,开展下颌轮廓曲线拟合。结果显示,3次多项式函数(R^(2)=0.918±0.027)和对数函数(R^(2)=0.930±0.039)可用于模拟美观人群下颌轮廓曲线形态。(2)数理导板组(选用对数函数进行截骨设计)、传统导板组和徒手截骨组分别纳入28、14和11例下颌角肥大患者。所有患者对术后下颌轮廓形态满意,未见畸形、显著不对称等并发症。数理导板组在jawline量表总分、�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 R^(2)(R^(2)≥0.800 was considered acceptable for the fitted function,while R^(2)≥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 compo

关 键 词：截骨术 下颌角肥大 美学 曲线拟合 人脸识别 

分 类 号：R782.2[医药卫生—口腔医学]