Neurosurgery Simulation Using Non-linear Finite Element Modeling and Haptic Interaction

Abstract

Real-time surgical simulation is becoming an important component of surgical training. To meet the real-time requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary element method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.

Keywords: finite element method; haptic rendering; non-linear biomechanics; surgical simulation.

Figure 1

Screenshots of the interactive simulation of a cube and a brain; left: rest state; right: after interaction with a rigid ball. The orange ball represents the haptic input.

Figure 2

Plots of critical time step (sec) versus Young’s modulus (kPa) in a simulation where a rigid sphere collides with a deformable cube (see first row of Fig. 1); each curve shows the results when the sphere moves in a different speed (m/s). The stability depends on both the stiffness and the speed of colliding object.