[Application of mathematical function model in morphological description and classification of bone defect in cleft...

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."" 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 R(2) 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 R(2) 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 "" 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 "" shaped defect with the exponential function (y=ae(bx)) 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 R(2) 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.