Combined compression and elongation experiments and non-linear modelling of liver tissue for surgical simulation

Uniaxial stress-strain data were obtained from in vitro experiments on 20 porcine livers for compressions, elongations and cycles of compression and then elongation. There were about 70 cylindrical samples, with diameter 7mm and varying height (4-11 mm). The combined compression and elongation test provide a unified framework for both compression and elongation for applications such as computer-aided surgical simulation. It enable the zero stress state of the experimental liver sample to be precisely determined. A new equation that combined both logarithmic and polynomial strain energy forms was proposed in modelling these experimental data. The assumption of incompressibility was justified from a preliminary Poisson's ratio for elongation and compression at 0.43+/-0.16 and 0.47+/-0.15, respectively. This equation provided a good fit for the observed mechanical properties of liver during compression-elongation cycles and for separate compressions or elongations. The root mean square errors were 91.92+/-17.43 Pa, 57.55+/-13.23 Pa and 29.78+/-17.67 Pa, respectively. In comparison with existing strain energy functions, this combined model was the better constitutive equation. Application of this theoretical model to small liver samples and other tissues demonstrated its suitability as the material model of choice for soft tissue.