Modeling the arterial wall mechanics using a novel high-order viscoelastic fractional element

Abstract

The fractional viscoelastic models (FVMs) have provided promising results for modeling the behavior of complex materials such as polymers and living tissues. These viscoelastic models are composed by springs, dashpots and the fractional element called spring-pot. In this paper we prove that the accuracy of these models can be improved through the use of a modified version of the spring-pot element, called high-order spring-pot (HOSP). We describe and implement a numerical method for characterization of mechanical properties of FVMs. The method consists of minimizing the misfit among experimental measures of strains or stresses and the respective values predicted by the model. The method is validated by solving four numerical examples. In the first three examples the data is artificially generated using different models such as the Double Maxwell-arm Wiechert one. The characterization is performed using FVMs models including the traditional spring-pot element and the new HOSP element proposed in this article. In these examples we assume small strains and homogeneous material properties. In a final example the method is applied to the characterization of the mechanical properties of FVMs using stress–strain data obtained from in vitro ovine arterial wall measurements reported in the literature. The results obtained show that the proposed method properly determines the mechanical parameters even in presence of noise in the data. In addition, it is evident from the results that the proposed modification of the spring-pot element increases the accuracy of the FVMs models. The results obtained allow us to conclude that the FVMs can model better the behavior of complex materials when a HOSP element is included. In particular, it was shown that these models are appropriate for modeling the arterial wall mechanics with higher accuracy, as well as other materials with complex behavior.