采用相应数学模型分析软硬组织关系的曲线拟合:Ⅱ类错自然生长和功能矫治效果比较

Curve fitting of soft and hard tissue relation using mathematics models:Functional treatment and natural growth of Class Ⅱ malocclusion

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 development of the digitization in cephalometry and model,increasing mathematical methods are applied in studies of orthodontics. OBJECTIVE：To investigate whether the relationship between soft-and hard-tissue changed before and after the functional treatment and to build up mathematical models. METHODS：A total of 67 early permanent dentition Class II Division 1 malocclusion patients were selected,including 40 with functional treatment and 27 with no functional treatment.They were examined cephalometrially before and after treatment.Mathematical methods were used to evaluate effect of treatment,including 4 items,APDI,Ls-EP,U1-NA（mm）and U1-NA.To evaluate the relationship between soft-and hard-tissue movements,a linear function was initially fitted to the data.A quadratic function was fitted to the data when the linear term was not significant. RESULTS AND CONCLUSION：Mathematical models confirmed that the association for the soft and hard tissues was quadratic,by using curve-fitting polynomial approach to the cephalometric data of 4 indicators before and after the functional treatment.The pre-treatment functional formula were：U1–NAmm =-0.012 7（APDI）^2 ＋1.705 2（APDI）-0.686 1;U1–NA =-0.025 5（APDI）^2 ＋3.234 3（APDI）-67.831 8;Ls–EP =-0.003 7（APDI）^2 ＋0.380 2（APDI）-3.267 3.The post-treatment functional formula were：U1–NAmm =-0.003 1（APDI）^2 ＋0.495 8（APDI）-14.248 4;U1–NA =0.01 32（APDI）^2-1.993 9（APDI）＋98.104 5;Ls–EP =0.007 4（APDI）^2-1.264 7（APDI）＋ 55.412 4.The results showed obvious changed in the relationship between soft-to hard-tissue pre-and post the functional treatment.The functional treatment effectively improved the profile of soft-tissues of Class II malocclusion cases.