Nonlinear visco-hyperelastic constitutive relation for brain tissue with parametric sensitivity study

Biological tissues are known to be hyperelastic with strong viscous properties. Constitutive equations employing Mooney and Hart-Smith strain energy functions have been developed approximating brain as a thick hollow spherical shell. The model incorporates the visco-elastic characteristics of the tissues by modifying the energy functions to include the rate dependent material response. Thus the strain energy function has been modified into power function for both Mooney and Hart-Smith models. The two constitutive equations have been analysed in detail and the paper highlights the salient features of the two models. A parametric variation study has also been done to analyse the sensitivity of the various material constants in the constitutive equations. This study is of importance in visco-hyperelastic characterization of the brain tissues and provides a theoretical construct for the same. This also identifies and highlights the parameters that are significantly sensitive in influencing the response of the models