Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review.

Modelling the mechanical behaviour of biological tissues is of vital importance for clinical applications. It is necessary for surgery simulation, tissue engineering, finite element modelling of soft tissues, etc. The theory of linear elasticity is frequently used to characterise biological tissues; however, the theory of nonlinear elasticity using hyperelastic models, describes accurately the nonlinear tissue response under large strains. The aim of this study is to provide a review of constitutive equations based on the continuum mechanics approach for modelling the rate-independent mechanical behaviour of homogeneous, isotropic and incompressible biological materials. The hyperelastic approach postulates an existence of the strain energy function--a scalar function per unit reference volume, which relates the displacement of the tissue to their corresponding stress values. The most popular form of the strain energy functions as Neo-Hookean, Mooney-Rivlin, Ogden, Yeoh, Fung-Demiray, Veronda-Westmann, Arruda-Boyce, Gent and their modifications are described and discussed considering their ability to analytically characterise the mechanical behaviour of biological tissues. The review provides a complete and detailed analysis of the strain energy functions used for modelling the rate-independent mechanical behaviour of soft biological tissues such as liver, kidney, spleen, brain, breast, etc.

Mechanics of fresh, frozen-thawed and heated porcine liver tissue.

PURPOSE: For a better understanding of the effects of thermally altered soft tissue, the biothermomechanics of these tissues need to be studied. Without the knowledge of the underlying physical processes and the parameters that can be controlled clinically, thermal treatment of cancerous hepatic tissue or the preservation of liver grafts are based primarily on trial and error. MATERIALS AND METHODS: Thus, this study is concerned with the investigation of the influence of temperature on the rheological properties and the histological properties of porcine liver. RESULTS: Heating previously cooled porcine liver tissue above 40 °C leads to significant, irreversible stiffness changes observed in the amplitude sweep. The increase of the complex shear module of healthy porcine liver from room temperature to 70 °C is approximately 9-fold. Comparing the temperatures -20 °C and 20 °C, no significant difference of the mechanical properties was observed. Furthermore, there is a strong relation between the mechanical and histological properties of the porcine liver. Temperatures above 40 °C destroy the collagen matrix within the liver tissue. This results in the alteration of the biomechanical properties. The time-temperature superposition principle is applied to generate temperature-dependent shift factors that can be described by a two-part exponential function model with an inflection temperature of 45 °C. CONCLUSIONS: Tumor ablation techniques such as heating or freezing have a significant influence on the histology of liver tissue. However, only for temperatures above body temperature an influence on the mechanical properties of hepatic tissues was noticeable. Freezing up to -20 °C did not affect the liver mechanics.