Exponential Elastic Model and Its Application in Real-Time Simulation

The development of accurate material models and computational methods are two fundamental components in building a real-time realistic surgery simulator. In this paper, we use a least-squares method to calibrate an exponential model of pig liver based on the assumption of incompressible material under a uniaxial testing mode. With the obtained parameters, the stress-strain curves generated from the least-squares approach are compared to those from the corresponding model built in ABAQUS and to experimental data, resulting in mean deviations of 1.9% and 4.8%, respectively. Furthermore we demonstrate equivalence between the parameters of the exponential material model and those of linear or other nonlinear models under small strains. Finally, we incorporate this calibrated exponential model into a nonlinear finite element framework to simulate the behavior of liver during an interventional procedure, and achieve real-time performance through use of an interpolation approach.