Corotational Cut Finite Element Method for real-time surgical simulation: application to needle insertion simulation

TL;DR

This paper introduces a corotational cut FEM approach for real-time, patient-specific surgical simulations that simplifies mesh generation while maintaining accuracy, demonstrated through needle insertion into brain and liver models.

Contribution

The paper presents a novel corotational cut FEM method that automatically incorporates complex geometries from images into real-time surgical simulations without complex mesh generation.

Findings

Method achieves convergence with optimal rates.

Simulation accuracy is maintained despite simplified mesh.

Applicable to real-time needle insertion procedures.

Abstract

This paper describes the use of the corotational cut Finite Element Method (FEM) for real-time surgical simulation. Users only need to provide a background mesh which is not necessarily conforming to the boundaries/interfaces of the simulated object. The details of the surface, which can be directly obtained from binary images, are taken into account by a multilevel embedding algorithm applied to elements of the background mesh that cut by the surface. Boundary conditions can be implicitly imposed on the surface using Lagrange multipliers. The implementation is verified by convergence studies with optimal rates. The algorithm is applied to various needle insertion simulations (e.g. for biopsy or brachytherapy) into brain and liver to verify the reliability of method, and numerical results show that the present method can make the discretisation independent from geometric description, and can avoid the complexity of mesh generation of complex geometries while retaining the accuracy of the standard FEM. Using the proposed approach is very suitable for real-time and patient specific simulations as it improves the simulation accuracy by taking into account automatically and properly the simulated geometry.