Identification and Determination of Material Properties for Porohyperelastic Analysis of Large Arteries

Abstract

A “porohyperelastic” (PHE) material model is described and the theoretical frame-work presented that allows identification of the necessary material properties functions for soft arterial tissues. A generalized Fung form is proposed for the PHE constitutive law in which the two fundamental Lagrangian material properties are the effective strain energy density function, We , and the hydraulic permeability, k̃ij . The PHE model is based on isotropic forms using We = Ue(φ) = 1/2C0(eφ − 1) and the radial component of permeability, k̃RR = k̃RR(φ), with φ = C′1(Ī1 − 3) + C′2(Ī2 − 3) + K′(J − 1)2. The methods for determination of these material properties are illustrated using experimental data from in situ rabbit aortas. Three experiments are described to determine parameters in Ue and k̃RR for the intima and media of the aortas, i.e., (1) undrained tests to determine C0 , C′1 , and C′2 (2) drained tests to determine K′; and (3) steady-state pressurization tests of intact and de-endothelialized vessels to determine intimal and medial permeability (adventitia removed in these models). Data-reduction procedures are presented that allow determination of k̃RR for the intima and media and Ue for the media using experimental data. The effectiveness and accuracy of these procedures are studied using input “data” from finite element models generated with the ABAQUS program. The isotropic theory and data-reduction methods give good approximations for the PHE properties of in situ aortas. These methods can be extended to include arterial tissue remodeling and anisotropic behavior when appropriate experimental data are available.