Surface deformation and reaction force estimation of liver tissue based on a novel nonlinear mass-spring-damper viscoelastic model.

Rheological soft tissue models play an important role in designing control methods for modern teleoperation systems. In the meanwhile, these models are also essential for creating a realistic virtual environment for surgical training. The implementation of model-based control in teleoperation has been a frequently discussed topic in the past decades, offering solutions for the loss of stability caused by time delay, which is one of the major issues in long-distance force control. In this paper, mass-spring-damper soft tissue models are investigated, showing that the widely used linear models do not represent realistic behavior under surgical manipulations. A novel, nonlinear model is proposed, where mechanical parameters are estimated using curve fitting methods. Theoretical reaction force curves are estimated using the proposed model, and the results are verified using measurement results from uniaxial indentation. The model is extended with force estimation by nonuniform surface deformation, where the surface deformation function is approximated according to visual data. Results show that using the proposed nonlinear model, a good estimation of reaction force can be achieved within the range of 0-4 mm, provided that the tissue deformation shape function is appropriately approximated.