## 3 Results and Discussion  
The width of the alveolar cleft (PP') in the maxillary model is an important index to evaluate the effect of orthodontic treatment. In the normal maxillary model, point I, point C, and point T, point C', and point T', the axis of point I, (namely the median sagittal plane), showed a certain degree of symmetry in the XOY plane. In the traditional PNAM appliance design method and the design method proposed in this paper, the relative position of point C, point T, point C', and point T' are unchanged in the design process. Therefore, this paper only describes the symmetry of the maxillary model by the position relationship between point I, point C and point C'. As shown in Figure 5A, in the XOY plane, let the distance between point I and point C be IC, and the distance along the x and y axes be IC\({}_{\rm V}\) and IC\({}_{\rm H}\), respectively. Let the distance between point I and point C' be IC', and the distancesalong the x-axis and y-axis be IC\({}^{\prime}\)V and IC\({}^{\prime}\)H, respectively. Based on the above parameters, e definition are shown in Formula (13):  
\[\left\{ \begin{array}{c}t=IC/IC^{\prime}\\ s=IC_{\rm{\tau}}/IC_{H}\\ s^{\prime}=IC^{\prime}_{\rm{\tau}}/IC^{\prime}_{H}\end{array} \right. \tag{13}\]  
Among these, t describes the size relationship between IC and IC\({}^{\prime}\), and s and s' describes the shape of IC and IC\({}^{\prime}\), respectively. The symmetry of the maxillary alveolar bone model is described by the size and shape of IC and IC\({}^{\prime}\). When t approaches 1, the distance from point I to point C is equal to the distance from point C', which is called length similarity. When the values of s and s' are similar, the shape of IC and IC\({}^{\prime}\) are similar, which is called shape similarity. When the values of s and s' are close, the shapes of IC and IC\({}^{\prime}\) are similar, which is called morphological similarity. At this point, the above five feature points show good symmetry, that is, the maxillary model has good symmetry. Therefore, this paper describes the symmetry of the maxillary model by calculating \(|\)1 - t\(|\) and \(|\)1 - s/s' \(|\) of the maxillary model before and after treatment. Therefore, this paper describes the symmetry of the maxillary model by calculating \(|\)1 - t\(|\), \(|\)1 - s/s' \(|\) before, after, and after orthodontic treatment, in which \(|\)1 - s/s' \(|\) is used to describe the morphological similarity (MS) of the IC and IC\({}^{\prime}\), where the smaller the value, the more similar the morphology, \(|\)1 - t\(|\) is used to describe the length similarity (LS) of the IC and the IC\({}^{\prime}\), where the smaller the value, the more similar the length. According to the original maxillary model of unilateral complete cleft lip and palate, this paper designed the PNAM appliance model in the final stage through the proposed  
Figure 5: **(A)** Symmetry map of the alveolar bone model of the oral maxilla. Comparison of PP’ (**B**), length similarity (**C**), and morphologic similarity (**D**), of 11 samples before, after, and after orthodontic treatment. PNAM appliance design algorithm. In this section, the design results of the PNAM appliance were compared with the original maxillary model, and the design results of the PNAM appliance were compared with the model after correctional treatment in the hospital from two aspects of alveolar fissure width and symmetry to verify that the PNAM digital design algorithm proposed in this paper can improve the correction effect of unilateral complete cleft lip and palate, which has certain application value in the clinical correction of unilateral complete cleft lip and palate. The clinical correction results mainly refer to the maxillary dental model made after wearing the appliance in the 8 th stage.