A Simple Deformation and Reaction Force Numerical Calculation Method for Nonlinear Brain Tissues

Presenting correct reaction force is an important functional element of a haptic surgical simulator which is used to practice surgical techniques by novice surgeons. Particularly, in neurosurgeries, novice surgeons rely on the force felt at their hands in many situations. However, it is difficult to accurately calculate the deformation and reaction force of brain tissues in real-time because of the nonlinearity of the brain tissues. In this study, a simple numerical calculation method for nonlinear brain tissues is proposed. The simulation is constructed based on the finite element method, and the nonlinear characteristics of brain tissues are reproduced. When a force is applied to the brain parenchyma, the reaction force nonlinearly increases as the deformation proceeds. The phenomenon is reproduced by increasing a scale factor of the stiffness matrix as the von Mises stress of the element increases. To validate the proposed calculation method, experiments were performed using porcine brains. In experiments, the longitudinal cerebral fissure of the brain was retracted at 1 mm/s and 10 mm/s. Necessary parameters for the proposed calculation method were identified by using experimental data of 1 mm/s. By comparing the simulation results and experimental data of 10 mm/s with the same parameters, the validity and accuracy of the proposed nonlinear calculation method of brain tissue were proved.