Computational hemodynamics in arteries with the one-dimensional augmented fluid-structure interaction system: viscoelastic parameters estimation and comparison with in-vivo data

Abstract

Mathematical models are widely recognized as a valuable tool for cardiovascular diagnosis and the study of circulatory diseases, especially to obtain data that require otherwise invasive measurements. To correctly simulate body hemodynamics, the viscoelastic properties of vessels walls are a key aspect to be taken into account as they play an essential role in cardiovascular behavior. The present work aims to apply the augmented fluid-structure interaction system of blood flow to real case studies to assess the validity of the model as a valuable resource to improve cardiovascular diagnostics and the treatment of pathologies. First, the ability of the model to correctly simulate pulse waveforms in single arterial segments is verified using literature benchmark test cases. Such cases are designed taking into account a simple elastic behavior of the wall in the upper thoracic aorta and in the common carotid artery. Furthermore, in-vivo pressure waveforms, extracted from tonometric measurements performed on four human common carotid arteries and two common femoral arteries, are compared to numerical solutions. It is highlighted that the viscoelastic damping effect of arterial walls is required to avoid an overestimation of pressure peaks. An effective procedure to estimate the viscoelastic parameters of the model is herein proposed, which returns hysteresis curves of the common carotid arteries dissipating energy fractions in line with values calculated from literature hysteresis loops in the same vessel.variations are determined by the physical and mechanical properties of blood and vessels walls, which are the essence of a complex fluid-structure interaction (FSI) mechanism, as well as by the anatomy of the entire cardiac network [33,48]. Viscoelastic properties of vessels play an essential role in the cardiovascular behavior [39,33,20]. In fact, viscoelasticity is one of the features that must be realistically included in the mathematical model when accurate numerical results are sought [20,1,26]. Vessel walls manifest viscoelastic properties that are summed up in three main attributes: creep, stress relaxation and hysteresis [6,39,22]. Among the existing linear viscoelastic models, the Standard Linear Solid (SLS) model provides a better representation of the arterial wall mechanics than the generally adopted Kelvin-Voigt model [1,26,46,32,23], being the latter unable to describe an exponential decay of stress over time [49,10,45]. On the other hand, when modeling the vessel mechanics by means of an elastic behaviour, the information related to hysteresis (i.e. the energy dissipated by viscoelastic effects) vanishes and pressure peaks are overestimated [1,6,20].The augmented FSI (a-FSI) system for blood flow modeling, presented in [7,8], is herein extended to real case studies in single arteries, to assess the capability of the model to serve as a valuable tool for practical medical applications, cardiovascular diagnosis and the study of circulatory pathologies. The extension of the model underlines the importanc...

Assessment of cardiac function by pulse wave analysis. A computational study

“…The vascular network model has been thoroughly tested in previous studies 3,5,33 . Here, we focused on verifying the ability of the cardiac contractility model coupled to the vas- presenting its characteristic double-peaked morphology 19,38 .…”

“…The aim of this study is to investigate the effect of cardiac properties on pulse wave morphology using a 1-D model of the arterial vasculature 33 coupled to a 0-D model of cardiac contraction. The 1-D model considers the viscoelastic behaviour of vessel walls 3,5 .…”

Computationally efficient finite element formulation for blood flow analysis in multi‐layered aorta modeled as viscoelastic material

“…However, most of the 1D wave propagation models of the blood flow consider elastic constitutive relation 4,6,7,21,34‐40 to model the arterial wall. There are a only few literature available on the one‐dimensional blood flow study considering viscoelastic arterial model 2,23,41‐43 . Viscoelasticity is one of the important features of blood vessels regulating their physical damping and significantly affecting the clinically important information of the blood flow such as pressure variation and flow rate.…”

Identifying the parameters of viscoelastic model for a gel-type material as representative of cardiac muscle in dynamic tests

“…By contrast, the Voigt model fails in affecting the relaxation behavior and is unable to explain the exponential decay of stress over time. 15,16 On the other hand, the analytical standard linear solid model predicts both mentioned phenomena and widely proposed in modeling soft tissues which provides a better insight into the biological tissue mechanics than the other classic models. 15,[17][18][19][20] This model combines aspects of Maxwell and Kelvin-Voigt models and accurately describes the overall behavior of a viscoelastic material under a given set of loading conditions.…”

“…15,16 On the other hand, the analytical standard linear solid model predicts both mentioned phenomena and widely proposed in modeling soft tissues which provides a better insight into the biological tissue mechanics than the other classic models. 15,[17][18][19][20] This model combines aspects of Maxwell and Kelvin-Voigt models and accurately describes the overall behavior of a viscoelastic material under a given set of loading conditions. 21 Wang et al 17 used the standard linear solid model for modeling porcine liver sample, Li et al 22 proposed the standard linear solid model to model the soft tissue deformation for virtual surgical simulation and Pelkie 19 characterized the viscoelastic behaviors in bovine pulmonary arterial tissue utilizing the standard linear solid model.…”