Hyperelastic and viscoelastic characterization of hepatic tissue under uniaxial tension in time and frequency domain

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 EI, 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 6), storage modulus (E '), and loss modulus (E ''). 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 (EI similar to 30 kPa), while porcine liver was stiffer for higher strains. Comparing stress relaxation with dynamic cyclic testing, tan 6 of porcine and bovine liver was the same for both methods (tan6 = 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 ', E '', and tan 6, 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.