Soft Tissue Deformation Modeling in the Procedure of Needle Insertion: A Kriging-Based Method

The simulation and planning system (SPS) requires accurate and real-time feedback regarding the deformation of soft tissues during the needle insertion procedure. Traditional mechanical-based models such as the finite element method (FEM) are widely used to compute the deformations of soft tissue. However, it is difficult for the FEM or other methods to find a balance between an acceptable image fidelity and real-time deformation feedback due to their complex material properties, geometries and interaction mechanisms. In this paper, a Kriging-based method is applied to model the soft tissue deformation to strike a balance between the accuracy and efficiency of deformation feedback. Four combinations of regression and correlation functions are compared regarding their ability to predict the maximum deformations of ten characteristic markers at a fixed insertion depth. The results suggest that a first order regression function with Gaussian correlation functions can best fit the results of the ground truth. The functional response of the Kriging-based method is utilized to model the dynamic deformations of markers at a series of needle insertion depths. The feasibility of the method is verified by investigating the adaptation to step variations. Compared with the ground truth of the finite element (FE) results, the maximum residual is less than 0.92 mm in the Y direction and 0.31 mm in the X direction. The results suggest that the Kriging metamodel provides real-time deformation feedback for a target and an obstacle to a SPS.