Modeling Soft-tissue Deformation Prior to Cutting for Surgical Simulation: Finite Element Analysis and Study of Cutting Parameters

This paper presents an experimental study to understand the localized soft-tissue deformation phase immediately preceding crack growth as observed during the cutting of soft tissue. Such understanding serves as a building block to enable realistic haptic display in simulation of soft tissue cutting for surgical training. Experiments were conducted for soft tissue cutting with a scalpel blade while monitoring the cutting forces and blade displacement for various cutting speeds and cutting angles. The measured force-displacement curves in all the experiments of scalpel cutting of pig liver sample having a natural bulge in thickness exhibited a characteristic pattern: repeating units formed by a segment of linear loading (deformation) followed by a segment of sudden unloading (localized crack extension in the tissue). During the deformation phase immediately preceding crack extension in the tissue, the deformation resistance of the soft tissue was characterized with the local effective modulus (LEM). By iteratively solving an inverse problem formulated with the experimental data and finite element models, this measure of effective deformation resistance was determined. Then computational experiments of model order reduction were conducted to seek the most computationally efficient model that still retained fidelity. Starting with a 3-D finite element model of the liver specimen, three levels of model order reduction were carried out with computational effort in the ratio of 1.000:0.103:0.038. We also conducted parametric studies to understand the effect of cutting speed and cutting angle on LEM. Results showed that for a given cutting speed, the deformation resistance decreased as the cutting angle was varied from 90 degrees to 45 degrees. For a given cutting angle, the deformation resistance decreased with increase in cutting speed.