In order to create accurate anatomical models for medical training and research, mechanical properties of biological tissues need to be studied. However, non-linear and viscoelastic behaviour of most soft biological tissues complicates the evaluation of their mechanical properties. In the current study, a method for measuring hyperelasticity and viscoelasticity of bovine and porcine hepatic parenchyma in tension is presented.

First, non-linear stress–stretch curves resulting from ramp loading and unloading, were interpreted based on a hyperelastic framework, using a Veronda–Westmann strain energy function. Strain-specific elastic moduli, such as initial stiffness $E_{\mathrm{I}}$, were thereupon defined in certain parts of the stress–stretch curves. Furthermore, dissipated and stored energy density were calculated. Next, the viscoelastic nature of liver tissue was examined with two different methods: stress relaxation and dynamic cyclic testing. Both tests yielded dissipated and stored energy density, as well as loss tangent ($tan\delta$), storage modulus ($E^{\prime }$), and loss modulus ($E^{\prime \prime }$). In tension, stress relaxation was experimentally more convenient than dynamic cyclic testing. Thus we considered whether relaxation could be used for approximating the results of the cyclic tests.

Regarding the resulting elastic moduli, initial stiffness was similar for porcine and bovine liver ($E_{\mathrm{I}}\sim 30\mathrm{kPa}$), while porcine liver was stiffer for higher strains. Comparing stress relaxation with dynamic cyclic testing, $tan\delta$ of porcine and bovine liver was the same for both methods ($tan\delta =0.05-0.25$ at 1 Hz). Storage and loss moduli matched well for bovine, but not as well for porcine tissue.

In conclusion, the utilized Veronda–Westmann model was appropriate for representing the hyperelasticity of liver tissue seen in ramp tests. Concerning viscoelasticity, both chosen testing methods – stress relaxation and dynamic cyclic testing – yielded comparable results for $E^{\prime }$, $E^{\prime \prime }$, and $tan\delta$, as long as elasticity non-linearities were heeded.

The here presented method provides novel insight into the tensile viscoelastic properties of hepatic tissue, and provides guidelines for convenient evaluation of soft tissue mechanical properties.

为了创建用于医学训练和研究的准确的解剖模型，需要研究生物组织的机械特性。但是，大多数软生物组织的非线性和粘弹性行为使它们的机械性能评估变得复杂。在当前的研究中，提出了一种在张力下测量牛和猪肝实质的超弹性和粘弹性的方法。

首先，使用Veronda-Westmann应变能函数基于超弹性框架解释了由斜坡加载和卸载产生的非线性应力-拉伸曲线。应变特定的弹性模量，例如初始刚度${Ë}_{\mathrm{一世}}$因此，在应力-拉伸曲线的某些部分中定义了。此外，计算了耗散和存储的能量密度。接下来，用两种不同的方法检查肝脏组织的粘弹性，即应力松弛和动态循环测试。两项测试均产生了耗散和存储的能量密度，以及损耗角正切（$棕褐色\delta$），储能模量（${Ë}^{\prime }$）和损耗模量（${Ë}^{\prime \prime }$）。在张力下，应力松弛在实验上比动态循环测试更方便。因此，我们考虑了是否可以使用松弛来近似循环测试的结果。

关于产生的弹性模量，猪和牛肝的初始刚度相似（${Ë}_{\mathrm{一世}}〜30\mathrm{千帕}$），而猪肝对于较高的品系则较硬。将应力松弛与动态循环测试进行比较，$棕褐色\delta$ 两种方法的猪肝和牛肝都相同（$棕褐色\delta =0。05-0。25$在1 Hz）。牛的储存和模量匹配很好，但猪组织却不一样。

总之，使用的Veronda-Westmann模型适合于代表在斜坡测试中看到的肝组织的超弹性。关于粘弹性，两种选择的测试方法–应力松弛和动态循环测试–产生了可比的结果。${Ë}^{\prime }$， ${Ë}^{\prime \prime }$和 $棕褐色\delta$，只要注意弹性非线性即可。

本文介绍的方法为肝组织的拉伸粘弹性提供了新的见识，并为方便评估软组织的机械性能提供了指导。