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

Area of Science:

• Biomechanics
• Materials Science
• Computational Modeling

Background:

• Biological soft tissues exhibit significant inhomogeneity, leading to scattered stress-strain curves under compression.
• Existing deterministic models struggle to capture the inherent variability in tissue mechanical properties.

Purpose of the Study:

• To develop a nondeterministic approach for modeling the scattered stress-strain relationship in biological soft tissues.
• To represent material parameters of liver tissue using statistical functions, specifically normal distributions.
• To validate the proposed method against experimental data and computer simulations.

Main Methods:

• Utilized the Mooney-Rivlin hyperelastic constitutive equation to model liver tissue.
• Employed an inverse finite element method (FEM) to determine the mean of material parameters.
• Applied the inverse mean-value first-order second-moment (IMVFOSM) method to find the standard deviation of material parameters.
• Verified the model using direct Monte-Carlo (MC) simulations.

Main Results:

• The proposed nondeterministic approach successfully modeled the scattered stress-strain behavior of liver tissue.
• Simulated cumulative distribution functions (CDF) closely matched experimental stress-strain data.
• The determined nondeterministic material parameters accurately predicted stress-strain curves from independent liver tissue compression tests.

Conclusions:

• The developed nondeterministic constitutive model effectively captures the inherent variability in soft tissue mechanics.
• This probabilistic approach enhances the predictive capability of computational models for biological tissues.
• The methodology provides a robust framework for analyzing and predicting the mechanical behavior of inhomogeneous soft materials.