Abstract: Objective: To establish the quantitative relationshipequationof the crantiofacial vertical points in the skeletal classⅡ malocclusion patients with various vertical types by using genetic algorithms method,and to express the measured values in the patients with different gender with the same formula.Methods: A total of 155 skeletal class Ⅱ malocclusion patients without treatment,aged from 10 to 18 years old,were selected and divided into high-angle group(n=50),average-angle group(n=58),low-angle group(n=47);5 samples were randomly selected in each group as the test samples,the rest as the experimental sample.The cephalometic radiographs were performed and measured.The relevant influencing factors of craniofacial structure were ensured.The genetic algorithm was used to optimize the equation parameters to obtain the correlation equation.The error between the predicted value and the measured value was compared.Results: The various parameters had no significant differences between different gender in high-angle,average-angle and low-angle groups(P>0.05);then the men and the women with same type were combined,most of the indicators had statistically significant differences between three groups (P<0.05).The correlation analysis results showed that there was a positive correlation between age and Ans-U1(r=0.470),there was a positive correlation between N-Me and Ans-Me(r=0.964);for Ans-U1,there was a positive correlation with Ans-Me(r=0.805)and negative correlation with facial angle;there was a positive correlation between N-Go and N-Me (r=0.926);for L1-Me,there was a positive correlation with Ans-Me(r=0.898)and negative correlation with the angle of Go(r=-0.468)in high-angle group. In average-angle group,there was a positive correlation between age and N-Me (r=0.531);for Ans-U1,there was a positive correlation with Ans-Me(r=0.878)and negative correlation with the facial angle(r=-0.262);for Ans-Me,there was a positive correlation with N-Me(r=0.920), negative correlation with N-Ans(r=-0.560)and negative correlation with Ar-Go(r=-0.652);for N-Go,there was a positive correlation with S-Go(r=0.867), positive correlation with N-Ans(r=0.252)and positive correlation with L1-Me(r=0.754).For S-Ar,there was a positive correlation with S-Go(r=0.671), negative correlation with Ar-Go(r=-0.250),and positive correlation with L1-Me(r=0.552).In low-angle group,for age,there was a positive correlation with S-Go(r=0.602), negative correlation with the angle of Go(r=-0.346),and positive correlation with L1-Me(r=0.576);for N-Me,there was a positive correlation with Ans-Me(r=0.869),and positive correlation with N-Go(r=0.859),and negative correlation with the facial angle(r=-0.177);for N-Ans,there was a positive correlation with N-Me(r=0.605) and negative correlation with Ans-U1(r=-0.113);for Ans-Me,there was a positive correlation with N-Me(r=0.869),positive correlation with the facial angle(r=0.070),and positive correlation with Ans-U1(r=0.785);for N-Go,there was a positive correlation with N-Me(r=0.859)and positive correlation with S-Go(r=0.829).The quantitative relationship equations of the crantiofacial vertical points in skeletal class Ⅱmalocclusion patients with various vertical types in each group were established by using genetic algorithms.In high-angle group:Age=5.883 6+0.269×Ans-U1,N-M=22.026 6+1.494 5×Ans-Me,Ans-U1=34.959 4+0.454 5×Ans-Me-0.409 7×Facial angle,N-Go=-4.588 2+0.472 4×N-Me,L1-Me=-12.590 5+0.5322×Ans-Me+0.124 3×∠Go.In average-angle group:Age=-2.944 1+0.146 8×N-Me,Ans-U1=18.917+0.476 4×Ans-Me-0.230 2×Facial angle,Ans-Me=-0.620 5+1.014 5×N-Me-0.974 1×N-Ans-0.057 6×Ar-Go,N-Go=1.631 1+0.897 8×S-Go+ 0.919 7×N-S+0.168 8×L1-Me,S-Ar=-1.823 1+ 0.845 3×S-Go-0.867 0×Ar-Go+0.202 4×L1-Me.In low-angle group:Age=11.740 6+0.152 7×S-Go-0.169 9×∠Go+0.252 5×L1-Me,N-Me=61.153 0+0.964 3×Ans-Me+0.628 6×N-Go-0.689 2×Facialangle,N-Ans=-4.949 2+1.065 8×N-Me-2.316 5×Ans-U1,Ans-Me=-25.180 0+0.418 4×N-Me+0.280 3×Facial angle+0.477 6×Ans-U1,N-Go=8.684 2+0.409 9×N-Me+0.403 3×S-Go.There was no significant difference between the predicted values of equation established with genetic algorithms and the measured data (P>0.05).Conclusion: The quantitative relationship equation of the crantiofacial vertical points in the skeletal class Ⅱmalocclusion patients with various vertical types established with genetic algorithms may show the vertical quantitative relationship and predict the growth to a certain degree.

Key words: vertical crantiofacial types, skeletal class Ⅱ malocclusion, growth prediction, genetic algorithms