Corotational cut finite element method for real-time surgical simulation: Application to needle insertion simulation

We present the corotational cut Finite Element Method (FEM) for real-time surgical simulation. The only requirement of the proposed method is 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 which is applied to elements of the background mesh that are cut by the surface. Dirichlet boundary conditions can be implicitly imposed on the surface using Lagrange multipliers, whereas traction or Neumann boundary conditions, which is/are applied on parts of the surface, can be distributed to the background nodes using shape functions. The implementation is verified by convergences studies, of the geometry and of numerical solutions, which exhibit optimal rates. To verify the reliability of the method, it is applied to various needle insertion simulations (e.g. for biopsy or brachytherapy) into brain and liver models. The numerical results show that, while retaining the accuracy of the standard FEM, the proposed method can (1) make the discretisation independent from geometric description, (2) avoid the complexity of mesh generation for complex geometries, and (3) provide computational speed suitable for real-time simulations. Thereby, the proposed method is very suitable for patient-specific simulations as it improves the simulation accuracy by automatically, and properly, taking the simulated geometry into account, while keeping the low computational cost.