Constitutive modeling of liver tissue: experiment and theory

Realistic surgical simulation requires incorporation of the mechanical properties of soft tissue in mathematical models. In actual deformation of soft-tissue during surgical intervention, the tissue is subject to tension, compression, and shear. Therefore, characterization and modeling of soft-tissue in all these three deformation modes are necessary. In this paper we applied two types of pure shear test, un-confined compression and uniaxial tension test to characterize porcine liver tissue. Digital image correlation technique was used to accurately measure the tissue deformation field. Due to gravity and its effect on the soft tissue, a maximum stretching band was observed from the relative strain field on sample undergoing tension and pure shear test. The zero strain state was identified according to the position of this maximum stretching band. Two new constitutive models based on combined exponential/logarithmic and Ogden strain energy were proposed. The models are capable to represent the observed non-linear stress-strain relation of liver tissue for full range of tension and compression and also the general response of pure shear.