数学函数模型在腭裂骨缺损形态分类中的应用

Application of mathematical function model in morphological description and classification of bone defect in cleft palate cases

目的对腭裂骨缺损形态进行分类并建立符合腭裂骨缺损形态的函数曲线模型,以期更精准地显示腭裂患者的骨缺损程度。方法纳入2018年1月至12月北京大学口腔医学院·口腔医院唇腭裂住院患者143例,所有患者均患腭裂(Veau分类Ⅰ类、Ⅱ类)并具有术前头部螺旋CT资料,年龄7个月~25岁,平均1.6岁,中位年龄1.0岁;男女比例为0.57∶1。根据CT三维重建后的腭部骨组织影像将腭裂骨缺损形状分为三类:"儿"字形、倒"V"形和倒"U"形,由5位评定人进行所属类型的判定,选取3人以上(含3人)评定一致的腭部图像为研究对象。分别采取与三类腭裂骨缺损形状近似的曲线函数在Excel软件中进行拟合分析,即与"儿"字形近似的上凹曲线——指数函数(y=ae^bx)、与倒"V"形近似的直线——线性函数(y=ax+b)和与倒"U"形近似的上凸曲线——对数函数(y=alnx+b)。统计分析骨缺损类型构成比,三种类型骨缺损与相应三类函数曲线的拟合度(R2),主观评定与函数曲线拟合类型之间的对应一致性。结果143例腭裂患者中,"儿"字形骨缺损占18%(26/143),倒"V"形骨缺损占31%(44/143),倒"U"形骨缺损占51%(73/143);"儿"字形骨缺损与指数函数符合率为96%,倒"V"形骨缺损与线性函数符合率为82%,倒"U"形骨缺损与对数函数之间的符合率为93%;三种骨缺损类型("儿"字形、倒"V"形和倒"U"形)分别对应的三种函数曲线拟合度R2值的总体差异有统计学意义(P<0.05)。结论本研究根据腭裂骨缺损形态不同进行分类,建立符合腭裂骨缺损形态的函数曲线模型,指数函数、线性函数及对数函数的曲线模型能够准确有效地对"儿"字形、倒"V"形和倒"U"形三种腭裂骨缺损形态进行描述与分类,并且具有各自对应的曲线基本性质及其函数特点,可以更精准地显示腭裂骨缺损的畸形程度。

Objective To establish the functional models based on various shapes of bone defects in isolated cleft palate patients and to classify the bone defects of the cleft palate cases using different functional curves.Methods Tracking back from January 2018 to December 2018,143 patients with cleft palate (Veau Ⅰ&Ⅱ) treated in Department of Oral and Maxillofacial Surgery,Peking University School and Hospital of Stomatology,were included (age of 7 months to 25 years,average age 1.6 years,median age 1.0 year,the male to female ratio was 0.57∶1).The pre-operative (CT) data sets were reconstructed into a three dimensional model to produce a direct image of the cleft palate.According to the shapes of the bone defect,cleft palate cases were divided into three types,i.e."儿" shape,inverted "V" shape and inverted "U" shape,and then the cases were assessed and reviewed by five examiners independently.Using Microsoft Excel software,the curves of the bone defect were placed in the coordinate system for mathematical modeling,including exponential function (y=ae^bx),linear function (y=ax+b) and logarithm function (y=alnx+b).The function of the maximum fit R2 value was used as the final fit curve.Statistical analysis was performed in four aspects:① The reliability and feasibility of the curve fitting of the functions;② The calculation of the composition ratio of the types of bone defect;③Analyzing the correspondence between the subjective judgment results and fitting function curves;④ The R2 values of three types of functional curves homologous to different morphological types,and the data were tested by variance analysis and P values were shown.Results Among the 143 patients with cleft palate,the "儿" shaped defect accounted for 18%(26/143),the inverted "V" shaped defect accounted for 31%(44/143),and the inverted "U" shaped defect accounted for 51%(73/143).The coincidence rate of the "儿" shaped defect with the exponential function (y=aebx) was 96%,the coincidence rate of the inverted "V" shaped defect with the linear function (y=ax+b) was 82%,and the coincidence rate of the inverted "U" shaped defect with the logarithmic function (y=alnx+b) was 93%.The differences in R2 values amongst the three groups were statistically significant (P<0.05).Conclusions The shapes of bone defects of the incomplete cleft palate can be described by functional curve models which include exponential,linear and logarithmic functions and can be used to classify and lay the foundation for digital classification of cleft lip and palate cases.