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背景:随着口腔正畸学成像、模型观测等检查手段数字化程度的提高,越来越多的学者将数学方法应用于正畸学的研究中。目的:分析功能矫治前后,软硬组织间的关系是否发生改变,并建立相应的数学模型。方法:选用恒牙早期安氏Ⅱ类1分类患者67例,其中接受功能矫治的患者40例,放弃功能矫治的患者27例。分别在治疗和观察前、后拍摄头颅侧位片。头影测量分析功能矫治前后侧位片软硬组织的变化,数学方法分析评价Ⅱ类错功能矫治疗效的4项主要指标[硬组织上下颌骨前后向不调指数(APDI)、软组织上唇突点距审美平面的距离(Ls-EP)、上切牙相对于上颌骨的线距U1-NA(mm)和角度(U1-NA)]。最初使用线性方程分析软硬组织在功能矫治前后的数据。当线性方程无意义时,使用曲线拟合。结果与结论:结果发现4项主要指标代表的软硬组织间确实存在曲线关系。治疗前曲线拟合的二次方程为:U1-NA(mm)=-0.0127(APDI)2+1.7052(APDI)-0.6861,U1-NA=-0.0255(APDI)2+3.2343(APDI)-67.8318,Ls-EP=-0.0037(APDI)2+0.3802(APDI)-3.2673。治疗后的曲线拟合方程:U1-NA(mm)=-0.0031(APDI)2+0.4958(APDI)-14.2484,U1-NA=0.0132(APDI)2-1.9939(APDI)+98.1045,Ls-EP=0.0074(APDI)2-1.2647(APDI)+55.4124。结果提示功能矫治使颅面部软硬组织关系发生明显改变,并使软组织侧貌发生明显改善。
Background: With the increasing digitization of orthodontic imaging and model observation, more and more scholars apply mathematical methods to the study of orthodontics. Objective: To analyze whether the relationship between soft and hard tissue changes before and after functional correction, and to establish the corresponding mathematical model. Methods: A total of 67 patients with early Class Ⅱ division 1 malocclusion were enrolled in this study. Of them, 40 received functional correction and 27 gave up functional correction. In the treatment and observation before and after shooting the cranial flaps. Cephalometric analysis of functional changes before and after the lateral position of the soft and hard tissue changes, mathematical methods to evaluate the efficacy of Class Ⅱ correction of functional disorder efficacy of the four main indicators [hard tissue on the mandible anteriorindoor index (APDI), soft tissue upper lip process (Ls-EP) from the aesthetic plane, U1-NA (mm) and angle (U1-NA) of the upper incisor relative to the maxilla). Linear equations were first used to analyze the data of soft and hard tissues before and after functional correction. When the linear equation is meaningless, curve fit is used. RESULTS AND CONCLUSION: The results showed that there was a curvilinear relationship between soft and hard tissue represented by 4 major indexes. The quadratic equation of curve fitting before treatment was: U1-NA (mm) = -0.0127 (APDI) 2 + 1.7052 (APDI) -0.6861, U1- NA = -0.0255 (APDI) 2 + 3.2343 (APDI) -67.8318, Ls-EP = -0.0037 (APDI) 2 + 0.3802 (APDI) -3.2673. Curve-fitting equation after treatment: U1 -NA (mm) = -0.0031 (APDI) 2 +0.4958 (APDI) -14.2484, U1- NA = 0.0132 (APDI) 2-1.9939 (APDI) +98.1045, Ls-EP = 0.0074 (APDI) 2-1.2647 (APDI) +55.4124. The results suggest that functional correction of the craniofacial soft and hard tissue significantly changed the relationship between the soft tissue profile and significantly improved.