Modeling of viscoelastic and nonlinear material properties of liver tissue using fractional calculations

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. The material properties of liver tissue were represented by a simple equation with only a few parameters. We evaluated the variety of each stiffness parameter from measurements of 50 samples. The results showed a high degree of variation in each stiffness parameter, especially with respect to nonlinearity. Moreover, each parameter had a low correlation coefficient. We also modeled the probability of variation in material properties from these results to provide a basis for deformation simulations considering individual patient differences.