Viscoelastic and Nonlinear Liver Modeling for Needle Insertion Simulation

Needle insertion treatments for liver tumors require accurate placement of the needle tip into the target tissue. However, it is difficult to insert the needle into the tissue because of tissue displacement due to organ deformation. Thus, path planning using numerical simulation to analyze organ deformation is important for accurate needle insertion. The objective of our work was to develop and validate a viscoelastic and nonlinear physical liver model. First, we present a material model to represent the viscoelastic and material, nonlinear properties of liver tissue for needle insertion simulation. Material properties of liver tissue were measured using a rheometer and modeled from the measured data. The liver viscoelastic characteristics were represented by differential equations, including the fractional derivative term. Next, nonlinearity with respect to the fractional derivative was measured, and the stress–strain relationship using a cubic function was modeled. Second, the experimental method to validate the model is explained. In vitro experiments that made use of porcine liver were conducted for comparison with the simulation using the model. Results of the in vitro experiment showed that the liver model reproduced with high accuracy (1) the relationship between needle displacement and force during needle insertion, (2) the velocity dependence of needle displacement and force when a puncture occurred and (3) the nonlinear and viscoelastic responses of displacement at an internally located point.