Real-time simulation of the nonlinear visco-elastic deformations of soft tissues

Purpose Mass-spring-damper (MSD) models are often used for real-time surgery simulation due to their fast response and fairly realistic deformation replication. An improved real time simulation model of soft tissue deformation due to a laparoscopic surgical indenter was developed and tested. Method The mechanical realization of conventional MSD models was improved using nonlinear springs and nodal dampers, while their high computational efficiency was maintained using an adapted implicit integration algorithm. New practical algorithms for model parameter tuning, collision detection, and simulation were incorporated. Results The model was able to replicate complex biological soft tissue mechanical properties under large deformations, i.e., the nonlinear and viscoelastic behaviors. The simulated response of the model after tuning of its parameters to the experimental data of a deer liver sample, closely tracked the reference data with high correlation and maximum relative differences of less than 5 and 10%, for the tuning and testing data sets respectively. Finally, implementation of the proposed model and algorithms in a graphical environment resulted in a real-time simulation with update rates of 150 Hz for interactive deformation and haptic manipulation, and 30 Hz for visual rendering. Conclusion The proposed real time simulation model of soft tissue deformation due to a laparoscopic surgical indenter was efficient, realistic, and accurate in ex vivo testing. This model is a suitable candidate for testing in vivo during laparoscopic surgery.