Efficient dynamic modeling of soft tissue deformation using a WSC-integrated order reduction method

Abstract

Background and Objectives:Computational modeling of soft tissue deformation is a fundamental issue for engineering assistive medical procedures. However, existing methods are not suitable for online clinical scenes as these methods are not efficient due to high computational cost and complexity. Methods:A new Weighted Skinning and Cubature Integrated (WSC-integrated) order reduction method is proposed for dynamic modeling of soft tissue deformation. The presented method includes two integrated-based schemes for construction of sub-space and estimation of internal elastic forces: a weighted skinning integrated scheme and a cubature integrated scheme. The weighted skinning integrated scheme derived from handle-based reduced order method is adopted to construct a reduced-order sub-space, in which dynamics of soft tissue are governed by low-order system equations. The cubature integrated scheme is adopted to estimate internal elastic forces of soft tissue. The proposed method relies on integration schemes both in sub-space construction and internal forces estimation instead of precomputation of soft tissue deformation snapshots, making it possible to achieve efficient computation of soft tissue deformation. Results:Compared to a finite element method in full-space for computing soft tissue deformation, the proposed method has a relative root mean square error for strain–stress and volumetric responses is 4.27 % and 3.11 %, respectively, and for rotation-moment and volumetric responses is 2.15 % and 2.63 %, respectively. The computation time of the proposed method achieve significant improvement (ranges from 37× to 54× ) with proper choice of sample handles and elements. Simulation of left ventricle dynamics based on the proposed method takes (21.81 ms) approximately 1/43 amount of computation time of the finite element method during online stage, and difference between their results is negligible (with relative root mean square error of 2.4 %). Conclusions:The simulation results and comparison validated that the proposed method presents higher computational efficiency and comparable accuracy to the finite element method in full-space. The high degree of computational efficiency and accuracy of the proposed method makes it suitable for online clinical scenes.