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.

为了在计算机辅助外科手术训练和辅助系统中优化保真度，需要对生物材料进行逼真的建模。肝组织的建模由于其非线性粘弹性和应力-应变关系的高滞后性而仍然具有挑战性。尽管先前的研究已经描述了在加载状态（在伸长，压缩或压痕测试中）或在卸载状态（在应力松弛或蠕变测试中）期间肝组织的行为，但在加载和卸载过程中的磁滞曲线均未完全定义。我们寻求使用单一的材料模型来表征整个活体压痕周期中离体的肝组织的机械性能灌注，然后切成薄片。基于从离体灌流的猪肝中获取的测量结果，我们将力-位移曲线转换为应力-应变曲线，并建立了粘-超弹性本构模型，以表征在不同压痕率下不同位置的肝脏的机械行为（1、2， 5、10和20 mm / s）。所提出的模型是具有最多6个系数的混合粘-超弹性模型。在低（$<0.05$）和高应变（$>0.3$）条件。