Liver tissue characterization from uniaxial stress–strain data using probabilistic and inverse finite element methods

Biological soft tissue is highly inhomogeneous with scattered stress–strain curves. Assuming that the instantaneous strain at a specific stress varies according to a normal distribution, a nondeterministic approach is proposed to model the scattered stress–strain relationship of the tissue samples under compression. Material parameters of the liver tissue modeled using Mooney–Rivlin hyperelastic constitutive equation were represented by a statistical function with normal distribution. Mean and standard deviation of the material parameters were determined using inverse finite element method and inverse mean-value first-order second-moment (IMVFOSM) method respectively. This method was verified using computer simulation based on direct Monte-Carlo (MC) method. The simulated cumulative distribution function (CDF) corresponded well with that of the experimental stress–strain data. The resultant nondeterministic material parameters were able to model the stress–strain curves from other separately conducted liver tissue compression tests. Stress–strain data from these new tests could be predicted using the nondeterministic material parameters.