3D and 2D finite element analysis in soft tissue cutting for haptic display

Real-time medical simulation for robotic surgery planning and surgery training requires realistic yet computationally fast models of the mechanical behavior of soft tissue. This paper presents a study to develop such a model to enable fast haptics display in simulation of soft-tissue cutting. An apparatus was developed and experiments were conducted to generate force-displacement data for cutting of soft tissue such as pig liver. The force-displacement curve of cutting pig liver revealed a characteristic pattern: the overall curve is formed by repeating units consisting of a local deformation segment followed by a local crack-growth segment. The modeling effort reported here focused on characterizing the tissue in the local deformation segment in a way suitable for fast haptic display. The deformation resistance of the tissue was quantified in terms of the local effective modulus (LEM) consistent with experimental force-displacement data. An algorithm was developed to determine LEM by solving an inverse problem with iterative finite element models. To enable faster simulation of cutting of a three-dimensional (3D) liver specimen of naturally varying thickness, three levels of model order reduction were studied. Firstly, a 3D quadratic-element model reduced to uniform thickness but otherwise haptics-equivalent (have identical force-displacement feedback) to a 3D model with varying thickness matching that of the liver was used. Next, haptics-equivalent 2D quadratic-element models were used. Finally, haptics-equivalent 2D linear-element models were used. These three models had a model reduction in the ratio of 1.0:0.3:0.04 but all preserved the same input-output (displacement, force) behavior measured in the experiments. The values of the LEM determined using the three levels of model reduction were close to one another. Additionally, the variation of the LEM with cutting speed was determined. The values of LEM decreased as the cutting speed increased