Knowledge-dependent mathematical model that predicts optimal tooth extraction site

Objectives:

To develop a mathematical model that predicts the optimum tooth extraction site in orthodontic treatment.

Methods:

A total of 133 female patients who had completed orthodontic treatment with extraction were employed. Three orthodontists decided the extraction sites SJ separately and the fiducial extraction sites was defined by applying majority voting to SJ and the actual extraction site SR for each case. A total of 34 feature variables vRaw were obtained from pre-treatment cephalometric and panoramic radiographs, oral photos and dental casts for each subject. A non-linear transformation function for each variable vRaw was developed on the basis of expertise knowledge and applied to the variables vRaw to obtain the non-linear transformed variables vNL. Two thousands combinations of variables (vRaw, vNL), i.e. vector representations, were generated. The dimensions of the vector representations ranged from 2 to 34. In a vector representation space, template matching operations with 10,000 weight patterns in the distance calculation were carried out and the optimum extraction site was predicted by a majority voting function with the fiducial extraction sites corresponding to the nearest Nm (Nm =1,3,5,7,9,11,13) template vectors.

The prediction performance of the model was assessed by leave-one-out cross-validation method. When the model output coincided with the extraction sites of an input, it was assigned to be Coincided. The ratio of the number of coincidence to that of the inputs (ROC) was calculated and the model was optimized with respect to combination of variables, non-linear transformation, weigh patterns in the template matching and nm.

Results:

The ROC of the optimized model was 83.5% in the case that non-linear transformation was employed where Nm = 5.

Conclusions:

The mathematical model for predicting the optimum extraction site was developed and the performance was found to be effective for clinical use.