Abstract: Objective: To optimize the parameters of the equation of sagittal craniofacial structures with different classes of malocclusion using genetic algorithms(GAS), and to explore the rules.Methods: Atotal of 240 patients with average angle malocclusion aged 8-18 years old were divided into three groups:Angle Class Ⅰ(n=79), Angle Class Ⅱ(n=76)and Angle Class Ⅲ(n=85) groups.In each group 10 cases were randomly selected as the test samples, the rest as the experimental samples.The cephalometric analysis was performed on all the patients' cephalograms, and the results of Ba-N,Ba-A,Ba-S,S-Ptm,Ptm-A,Ba-Ar,Ar-Go,Go-PoG,Ba-PoG and N-S-Ar were analyzed by two independent samples t-test and One-Way ANOVA. The relevant influencing factors of craniofacial structures were found.The parameters of the equation was optimized to obtain the relevant equations using GAS.The predicted values of the optimized equation were compared with the measured values.Results: There were no significant differences in sex between Angle Class Ⅰ, Class Ⅱ and Class Ⅲ groups(P> 0.05);when the men and women with the same type were combined,the Ba-A,Ptm-A,Ar-Go,and Ba-PoG had statistically significant differences between Angle Class Ⅰ, Class Ⅱ, and Class Ⅲ groups (P<0.05).The correlation analysis results showed that in Angle Class Ⅰgroup:Ba-A was positively correlated with Ba-N (r=0.683),Ptm-A was positively correlated with Go-PoG (r=0.738), Ar-Go was positively correlated with Ba-PoG (r=0.833), and negatively correlated with Go-PoG (r=-0.560) and Ba-PoG was positively correlated with Go-PoG (r=0.669); in Angle class Ⅱ group,Ba-A was positively correlated with Ba-PoG and Ba-N(r=0.884,r=0.883), Ptm-A was positively correlated with Ba-A (r=0.742),Ar-Go was positively correlated with Ba-PoG (r=0.401)and negatively correlated with Go-PoG (r=-0.317) and Ba-PoG was positively correlated with Ba-A and Go-PoG(r=0.883,r=0.488);in Angle Class Ⅲ group,Ba-A was positively correlated with Ba-N and Ba-PoG(r=0.891,r=0.829),Ptm-A was positively correlated with Ba-A (r=0.807)and negatively correlated with Ba-S (r=-0.404),Ar-Go was positively correlated with S-Ptm (r=0.548) and Ba-PoG was positively correlated with Ba-A (r=0.829).The equation of sagittal craniofacial structure with different occlusal classes was established by GAS.In Angle Class Ⅰgroup:Ba-A(mm)=10.963 9+0.859 8×Ba-N,Ptm-A(mm)=6.897 6+0.557 0×Go-PoG,Ar-Go(mm)=-2.548 2+ 0.511 8×Ba-PoG-0.5272×Go-PoG,Ba-PoG(mm)=17.515 6+1.021 3×GO-POG;in Angle Class Ⅱ group:Ba-A(mm)=-2.121 3+0.567 6×Ba-PoG+0.513 2×Ba-N,Ptm-A(mm)=13.788 7+0.349 4×Ba-A,Ar-Go(mm)=2.447 7+0.368 8×Ba-PoG-0.427 9×Go-PoG,Ba-PoG(mm)=-7.140 2+0.751 3×Ba-A+0.295 4×Go-PoG;in Angle Class Ⅲgroup:Ba-A(mm)=3.281 0+0.545 3×Ba-N+0.394 4×Ba-PoG,Ptm-A(mm)=3.535 8+0.63 1×Ba-A-0.614 2×Ba-S,Ar-Go(mm)=-9.002 1+1.004 3×S-Ptm,Ba-PoG(mm)=-2.091 2+1.057 5×Ba-A.There were no significant differences between the predicted values of GAS and the measured data (P> 0.05), and the error was small.Conclusion: The optimal relation equation of craniofacial structure of sagittal malocclusion is established by GAS with the quantitative regularity.

Key words: genetic algorithms, classes of malocclusion, sagittal craniofacial structure, correlation analysis