Assessment Of The Soft And Hard Tissue Changes Of Class Ⅱ Malocclusion Cases After Functional Treatment By Using Applied Mathematics Models

Objectives: To use mathematics models to step-by-step identify key indicators towards functional treatment; to build up mathematics models before and after the functional treatment of the key indicators; to objectively evaluate the result of functional treatmentMethods: Sixty-seven Class II Division 1 malocclusion subjects with hand-wrist radiographs in FG-G stage were selected. Among the sixty-seven samples, twenty-seven abandoned treatment were put into the Control Group (Group C) and observed for fourteen and a half months without any treatment. The remaining forty subjects, put into Treatment Group (Group T), received functional treatment and retention for 14.2 months. Thirty-three common hard tissue variables and twenty-five soft tissue variables were selected for careful measurement. All the subjects were taken cephalometric radiographs before treatment (observation). After scanning into computer and identifying cephalometric landmarks, the data was processed by using Matlab 7.0, an applied mathematics software, and SPSS13.0, a statistical software.Results: 1. Four key indicators for the success of Class II malocclusion treatment were identified by using mathematics methods in five steps to screen off the cephalometric values of all the fifty-eight variables (thirty-three hard tissue variables and twenty-five soft tissue variables), which are U1-NA(mm), U1-NA, APDI and Ls-EP. a) In the 1st step, data from Group C (without treatment) and Group T (before treatment) were concluded to be comparable as the data didn't show any bias towards gender or age in the statistical analysis (by Group, by gender, by age). b) In the 2nd step, the cephalometric values of both Group T and Group C were compared with normal data and there were statistically significant differences of fourty-two variables among the total of fifty-eight. It showed that these forty-two variables are representative characteristics of Class II malocclusion soft and hard tissues. C) In the 3rd step, data before and after treatment of Group T was compared and there were statistically significant differences of twenty-two variables among the total of fourty-two. It showed that these twenty-two variables changed significantly after functional treatment. d) In the 4th step, the twenty-two variables were compared with normal data and there were no statistically significant differences of seven variables. It showed that these seven variables have improved to normal levels after functional treatment. e) In the 5th step, data from Group C was compared with normal data on the seven variables and there were no statistically significant differences of three variables which are U1-SN, U1-A, and LiSi–Pg′but for four variables, there existed statistically significant differences. It showed that among the seven variables, three can improve to normal levels through natural development, but four variables, U1-NA(mm), U1-NA, APDI and Ls-EP, cannot. These four variables were therefore concluded as key ones towards functional treatment.2. The cephalometric values of Group C were compared with normal data and there were two variables (U1-SN, U1-A) with no significant differences for both men and women and there was one variable (LiSi–Pg′) with no significant differences for men only.3. Correlation analysis of the four key indicators which completely reached normal levels after functional treatment was conducted using SPSS 13.0 and there was a linear relationship U1-NAmm and U1-NA. The linear correlation read: U1-NAmm=-2.861+0.361 (U1-NA).4 Pre- and post the functional treatment mathematics models were built up using curve-fitting polynomial approach to process the four key indicators and results before the functional treatment were: U1–NAmm =-0.0127 (APDI)2 +1.7052 (APDI) -48.6861;U1–NA =-0.0255(APDI)2+3.2343(APDI)-67.8318; Ls–EP=-0.0037(APDI)2+0.3802(APDI)-3.2673. The post-treat ment functional formula were: U1–NAmm =-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 differences of functional formulas pre- and post the treatment of the four key indicators showed how to evaluate the functional treatment results in a measurable and accurate manner.Conclusion: 1 Five variables sensitive to Class II malocclusion functional treatment were identified using applied mathematics, which are U1-NA(mm), U1-NA, APDI, and Ls-EP.2 Natural growth cannot change skeletal style for Class II malocclusion, according to the mathematical analysis results.3 Using curve-fitting method, mathematic models of correlation and functional relations between skeletal, dental soft-tissue under Class II malocclusion treatment were built up.4 Mathematic models were used to prove that functional treatment could effectively adjust the protruding upper lips and improve the profile of soft-tissues of Class II malocclusion cases.