Predictive capabilities of various constitutive models for arterial tissue

Abstract

Introduction: Aim of this study is to validate some constitutive models by assessing their capabilities in describing and predicting uniaxial and biaxial behavior of porcine aortic tissue.

Methods: 14 samples from porcine aortas were used to perform 2 uniaxial and 5 biaxial tensile tests. Transversal strains were furthermore stored for uniaxial data. The experimental data were fitted by four constitutive models: Holzapfel-Gasser-Ogden model (HGO), model based on generalized structure tensor (GST), Four-Fiber-Family model (FFF) and Microfiber model. Fitting was performed to uniaxial and biaxial data sets separately and descriptive capabilities of the models were compared. Their predictive capabilities were assessed in two ways. Firstly each model was fitted to biaxial data and its accuracy (in term of R-2 and NRMSE) in prediction of both uniaxial responses was evaluated. Then this procedure was performed conversely: each model was fitted to both uniaxial tests and its accuracy in prediction of 5 biaxial responses was observed.

Results: Descriptive capabilities of all models were excellent. In predicting uniaxial response from biaxial data, microfiber model was the most accurate while the other models showed also reasonable accuracy. Microfiber and FFF models were capable to reasonably predict biaxial responses from uniaxial data while HGO and GST models failed completely in this task.

Conclusions: HGO and GST models are not capable to predict biaxial arterial wall behavior while FFF model is the most robust of the investigated constitutive models. Knowledge of transversal strains in uniaxial tests improves robustness of constitutive models.