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

Abstract

a b s t r a c tThe 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.

Quantitative Vascular Evaluation: From Laboratory Experiments to Point-of-Care Patient (Experimental Approach)

“…Only the model with two spring-pots correctly followed the activation state with the best performance. Stress relaxation of human arteries was then described with this methodology in [ 39 ] and its numerical approach was introduced in [ 40 ].…”

Fractional-Order Modeling of Arterial Compliance in Vascular Aging: A Computational Biomechanical Approach for Investigating Cardiovascular Dynamics

“…Regarding cardiovascular mod-eling, the power-law behavior has been demonstrated in describing human soft tissues' visco-elasticity and characterizing the elastic vascular arteries. The in-vivo and in-vitro experimental studies have pointed out that fractional-order calculus-based approaches are more decent to represent the hemodynamic precisely; the viscoelasticity properties of soft collagenous tissues in the vascular bed; the aortic blood rate [22]- [24]; red blood cell (RBC) membrane mechanical properties [25] and the heart valve cusp [23], [26]- [28]. In addition, recently, we developed novel fractional-order arterial Windkessel representations, [29]- [31].…”

Fractional-order model representations of apparent vascular compliance as an alternative in the analysis of arterial stiffness: an in-silico study

“…In recent research, the power-law behavior has been proved in the viscoelastic characterization of an elastic aorta. The in-vivo and in-vitro data analysis showed that the FD tools make it more convenient to accurately model and describe the arterial wall viscoelastic dynamic response (Craiem and Armentano 2007, Craiem and Magin 2010, Perdikaris and Karniadakis 2014, Zerpa et al 2015. Besides, a recent study by the authors , 2018, used fractional-order derivative tools with the wellknown arterial Windkessel paradigm, by replacing the ideal capacitor (which accounts for the total arterial compliance) with a fractional-order capacitor.…”