Characterization of perfused and sectioned liver tissue in a full indentation cycle using a visco-hyperelastic model

Realistic modeling of biologic material is required for optimizing fidelity in computer-aided surgical training and assistance systems. The modeling of liver tissue has remained challenging due to its nonlinear viscoelastic properties and high hysteresis of the stress-strain relation. While prior studies have described the behavior of liver tissue during the loading status (in elongation, compression, or indentation tests) or unloading status (in stress relaxation or creep tests), a hysteresis curve with both loading and unloading processes was incompletely defined. We seek to use a single material model to characterize the mechanical properties of liver tissue in a full indentation cycle ex vivo perfused and then sectioned. Based on measurements taken from ex-vivo perfused porcine livers, we converted force-displacement curves to stress-strain curves and developed a visco-hyperelastic constitutive model to characterize the liver's mechanical behavior at different locations under various rates of indentation (1, 2, 5, 10, and 20 mm/s). The proposed model is a mixed visco-hyperelastic model with up to 6 coefficients. The normalized root mean square standard deviations of fitted curves are less than 5% and 10% in low (<0.05) and high strain (>0.3) conditions respectively.