Prediction of soft tissue deformations after CMF surgery with incremental kernel ridge regression

Facial soft tissue deformation following osteotomy is associated with the corresponding biomechanical characteristics of bone and soft tissues. However, none of the methods devised to predict soft tissue deformation after osteotomy incorporates population-based statistical data. The aim of this study is to establish a statistical model to describe the relationship between biomechanical characteristics and soft tissue deformation after osteotomy. We proposed an incremental kernel ridge regression (IKRR) model to accomplish this goal. The input of the model is the biomechanical information computed by the Finite Element Method (FEM). The output is the soft tissue deformation generated from the paired pre-operative and post-operative 3D images. The model is adjusted incrementally with each new patient's biomechanical information. Therefore, the IKRR model enables us to predict potential soft tissue deformations for new patient by using both biomechanical and statistical information. The integration of these two types of data is critically important for accurate simulations of soft-tissue changes after surgery. The proposed method was evaluated by leave-one-out cross-validation using data from 11 patients. The average prediction error of our model (0.9103mm) was lower than some state-of-the-art algorithms. This model is promising as a reliable way to prevent the risk of facial distortion after craniomaxillofacial surgery.