Development of In Vivo Constitutive Models for Liver: Application to Surgical Simulation

Advancements in real-time surgical simulation techniques have provided the ability to utilize more complex nonlinear constitutive models for biological tissues which result in increased haptic and graphic accuracy. When developing such a model, verification is necessary to determine the accuracy of the force response as well as the magnitude of tissue deformation for tool–tissue interactions. In this study, we present an experimental device which provides the ability to obtain force–displacement information as well as surface deformation of porcine liver for in vivo probing tasks. In addition, the system is capable of accurately determining the geometry of the liver specimen. These combined attributes provide the context required to simulate the experiment with accurate boundary conditions, whereby the only variable in the analysis is the material properties of the liver specimen. During the simulation, effects of settling due to gravity have been taken into account by a technique which incorporates the proper internal stress conditions in the model without altering the geometry. Initially, an Ogden model developed from ex vivo tension and compression experimentation is run through the simulation to determine the efficacy of utilizing an ex vivo model for simulation of in vivo probing tasks on porcine liver. Subsequently, a method for improving upon the ex vivo model was developed using different hyperelastic models such that increased accuracy could be achieved for the force characteristics compared to the displacement characteristics, since changes in the force variation would be more perceptible to a user in the simulation environment, while maintaining a high correlation with the surface displacement data. Furthermore, this study also presents the probing simulation which includes the capsule surrounding the liver.