东南大学学报（英文版）2022，Vol.38Issue(2)：118-125,8.DOI:10.3969/j.issn.1003-7985.2022.02.003
基于福克-普朗克方程与析取克里金模型的柔性针路径预测
Path prediction of flexible needles based on Fokker-Planck equation and disjunctive Kriging model
摘要
Abstract
Path prediction of flexible needles based on the Fokker-Planck equation and disjunctive Kriging model is proposed to improve accuracy and consider the nonlinearity and anisotropy of soft tissues.The stochastic differential equation is developed into the Fokker-Planck equation with Gaussian noise,and the position and orientation probability density function of flexible needles are then optimized by the stochastic differential equation.The probability density function obtains the mean and covariance of flexible needle movement and helps plan puncture paths by combining with the probabilistic path algorithm.The weight coefficients of the ordinary Kriging are extended to nonlinear functions to optimize the planned puncture path,and the Hermite expansion is used to calculate nonlinear parameter values of the disjunctive Kriging optimization model.Finally,simulation experiments are performed.Detailed comparison results under different path planning maps show that the kinematics model can plan optimal puncture paths under clinical requirements with an error far less than 2 mm.It can effectively optimize the path prediction model and help improve the target rate of soft tissue puncture with flexible needles through data analysis and processing of the mean value and covariance parameters derived by the probability density and disjunctive Kriging algorithms.关键词
柔性针穿刺/非线性/福克-普朗克方程/析取克里金/误差分析Key words
flexible needle puncture/nonlinear/Fokker-Planck equation/disjunctive Kriging/error analysis分类
信息技术与安全科学引用本文复制引用
熊鹏文,周学婷,黎倩,宋爱国,刘小平..基于福克-普朗克方程与析取克里金模型的柔性针路径预测[J].东南大学学报（英文版）,2022,38(2):118-125,8.基金项目
The National Natural Science Foundation of China(No.61903175,62163024,62163026),the Academic and Technical Leaders Foundation of Major Disciplines of Jiangxi Province under Grant(No.20204BCJ23006). （No.61903175,62163024,62163026）
