Numerical Investigation of Pulse Wave Propagation in Arteries Using Fluid Structure Interaction Capabilities (original) (raw)
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Journal of Biomechanical Engineering, 2012
Pulse wave imaging (PWI) is an ultrasound-based method for noninvasive characterization of arterial stiffness based on pulse wave propagation. Reliable numerical models of pulse wave propagation in normal and pathological aortas could serve as powerful tools for local pulse wave analysis and a guideline for PWI measurements in vivo. The objectives of this paper are to (1) apply a fluidstructure interaction (FSI) simulation of a straight-geometry aorta to confirm the Moens-Korteweg relationship between the pulse wave velocity (PWV) and the wall modulus, and (2) validate the simulation findings against phantom and in vitro results. PWI depicted and tracked the pulse wave propagation along the abdominal wall of canine aorta in vitro in sequential Radio-Frequency (RF) ultrasound frames and estimates the PWV in the imaged wall. The same system was also used to image multiple polyacrylamide phantoms, mimicking the canine measurements as well as modeling softer and stiffer walls. Finally, the model parameters from the canine and phantom studies were used to perform 3D two-way coupled FSI simulations of pulse wave propagation and estimate the PWV. The simulation results were found to correlate well with the corresponding Moens-Korteweg equation. A high linear correlation was also established between PWV 2 and E measurements using the combined simulation and experimental findings (R 2 ¼ 0.98) confirming the relationship established by the aforementioned equation.
Journal of Biomechanics, 2008
Time-domain-based one-dimensional wave propagation models of the arterial system are preferable over one-dimensional wave propagation models in the frequency domain since the latter neglect the non-linear convection forces present in the physiological situation, especially when the vessel is tapered. Moreover, one-dimensional wave propagation models of the arterial system can be used to provide boundary conditions for fully three-dimensional fluid-structure interaction computations that are usually defined in the time domain. In this study, a time-domain-based one-dimensional wave propagation model in a cross-sectional area, flow and pressure ðA; q; pÞformulation is developed. Using this formulation, a constitutive law that includes viscoelasticity based on the mechanical behaviour of a Kelvin body, is introduced. The resulting pressure and flow waves travelling through a straight and tapered vessel are compared to experimental data obtained from measurements in an in vitro setup. The model presented shows to be well suited to predict wave propagation through these straight and tapered vessels with viscoelastic wall properties and hereto can serve as a time-domain-based method to model wave propagation in the human arterial system.
A physics based approach to the pulse wave velocity prediction in compliant arterial segments
Journal of biomechanics, 2016
Pulse wave velocity (PWV) quantification commonly serves as a highly robust prognostic parameter being used in a preventative cardiovascular therapy. Being dependent on arterial elastance, it can serve as a marker of cardiovascular risk. Since it is influenced by a blood pressure (BP), the pertaining theory can lay the foundation in developing a technique for noninvasive blood pressure measurement. Previous studies have reported application of PWV, measured noninvasively, for both the estimation of arterial compliance and blood pressure, based on simplified physical or statistical models. A new theoretical model for pulse wave propagation in a compliant arterial segment is presented within the framework of pseudo-elastic deformation of biological tissue undergoing finite deformation. An essential ingredient is the dependence of results on nonlinear aspects of the model: convective fluid phenomena, hyperelastic constitutive relation, large deformation and a longitudinal pre-stress lo...
Fluid-structure interaction within three-dimensional models of an idealized arterial wall
2014
The ascending branch of the aorta is one of the most stressed organ of the arterial system. We aim to design a biomechanical model for analysing the aorta dynamics under a shock. The model includes the aorta layers and the influence of the blood pressure. We undertake a three-dimensional modal analysis of the coupled aorta-blood system. We determine in the present work the coupled natural frequencies and the modes shapes of the system of the aorta and blood. Three models are presented in this study: three-layers model, twolayers model and one layer model. For the analytical solving a potential technique is used to obtain a general solution for an aorta domain. The finite element model is then validated by these original analytical solutions. The results from the proposed method are in good agreement with numerical solutions. combination of mechanisms including shear, torsion and stretching . These loadings are coupled with the blood pressure and propagation of wave within the aorta. To this end, it seems necessary to include the blood and the vessel undergoing deformation and interacting with the blood flow . In sum, there are still no definitive answers as to what the fundamental mechanisms are that cause this injury, though a great deal of speculation exists on what these might be. However, the high level of reproducibility of the site and nature of blunt traumatic rupture intuitively suggests that there is a reproducible mechanism of injury.
A 3D Non-Newtonian Fluid-Structure Interaction Model for Blood Flow In Arteries
Journal of Computational and Applied …, 2010
The mathematical modelling and numerical simulation of the human cardiovascular system is playing nowadays an important role in the comprehension of the genesis and development of cardiovascular diseases. In this paper we deal with two problems of 3D modelling and simulation in this field, which are very often neglected in the literature. On the one hand blood flow in arteries is characterized by travelling pressure waves due to the interaction of blood with the vessel wall. On the other hand, blood exhibits non-Newtonian properties, like shear-thinning, viscoelasticity and thixotropy. The present work is concerned with the coupling of a generalized Newtonian fluid, accounting for the shearthinning behaviour of blood, with an elastic structure describing the vessel wall, to capture the pulse wave due to the interaction between blood and the vessel wall. We provide an energy estimate for the coupling and compare the numerical results with those obtained with an equivalent fluid-structure interaction model using a Newtonian fluid.
Pulse Wave Velocity Prediction in Multi-Layer Thick Wall Arterial Segments
2015
Pulse wave velocity (PWV) is an important index of arterial hemodynamics, which lays the foundation for continuous, noninvasive blood pressure automated monitoring. The goal of this paper is to re-examine the accuracy of PWV prediction based on a traditional homogeneous structural model for thin-walled arterial segments. In reality arteries are described as composite heterogeneous hyperelastic structures, where the thickness dimension cannot be considered small compared to the cross section size. In this paper we present a hemodynamic fluid structure interaction model accounting for the 3D material description of multilayer arterial segments based on its histological information. The model is suitable to account for the highly nonlinear orthotropic material undergoing finite deformation for each layer. An essential ingredient is the notable dependence of results on nonlinear aspects of the model: convective fluid phenomena, hyperelastic constitutive relation for each layer, and fini...
Numerical simulation of arterial pulse propagation using one-dimensional models
2003
The human arterial system is formed by a network of vessels that can be regarded as hollow tubes of variable diameter. To permit the flow of blood, an incompressible fluid, through the body they deform under the pressure fluctuations generated by the heart. The transmission of pressure waves at finite velocity through the blood is the result of the energy exchange between the blood and the vessel walls, therefore the modelling of the time evolution of the arterial deformation, or pulse propagation, is a fluid-structure interaction problem. This chapter presents one-dimensional nonlinear systems to model the blood pulse propagation in compliant arteries. They are obtained through the use of a suitable sectional averaging of the Navier-Stokes equations and simplified structural models of vessel compliance. We consider both an algebraic quasi-static model that relates intramural pressure to vessel section area and time-dependent models that account for wall inertia and viscoelasticity. Initially we adopt a simple algebraic pressure-area relation that results in a hyperbolic system of non-linear equations. The numerical discretization of this system is performed using both a discontinuous Galerkin method and a Taylor-Galerkin formulation. We study the effect of the implantation of a vascular prosthesis (e.g. a stent), which leads to an abrupt variation of the mechanical properties of an artery. We use this example to compare the results obtained with both methods. We then discuss the simulation of the propagation of pressure and velocity waveforms in the human arterial tree using a simplified model consisting of the 55 main arteries. The extension of the single vessel model to a network of vessels is achieved using a characteristic decomposition combined with conservation of mass and total pressure. Finally, we adopt more complex time-dependent structural models that account for wall inertia and viscoelastic behaviour and perform numerical simulations using the Taylor-Galerkin approach.
Journal of Fluid Flow, Heat and Mass Transfer, 2016
Pulse wave velocity (PWV) is an important index of arterial hemodynamics, which lays the foundation for continuous, noninvasive blood pressure automated monitoring. The goal of this paper is to examine the accuracy of PWV prediction based on a traditional homogeneous structural model for thin-walled arterial segments. In reality arteries are described as composite heterogeneous hyperelastic structures, where the thickness dimension cannot be considered small compared to the cross section size. In this paper we present a hemodynamic fluid -structure interaction model accounting for the variation of geometry and material properties in a radial direction. The model is suitable to account for the highly nonlinear orthotropic material undergoing finite deformation for each layer. Numerical analysis of single and two layer arterial segments shows that a single thick layer model provides sufficient accuracy to predict PWV. The dependence of PWV on pressure for three vessels of different thicknesses is compared against a traditional thin wall model of a membrane shell interacting with an incompressible fluid. The presented thick wall model provides greater accuracy in the prediction of PWV, and will be important for blood pressure estimation based on PWV measurements.
Journal of Biomechanics
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.
Fluid–structure interaction simulation of aortic blood flow
Computers & Fluids, 2011
The numerical tools to simulate blood flow in the cardiovascular system are constantly developing due to the great clinical interest and to scientific advances in mathematical models and computational power. The present work aims to address and validate new algorithms to efficiently predict the hemodynamics in large arteries. These algorithms rely on finite elements simulation of the fluid-structure interaction between blood flow and arterial wall deformation of a healthy aorta. Different sets of boundary conditions are devised and tested. The mean velocity and pressure time evolution is plotted on different sections of the aorta and the wall shear stress distribution is computed. The results are compared with those obtained with a rigid wall simulation. Pulse wave velocity is computed and compared with the values available from the literature. The flow boundary conditions used for the outlets are obtained using the solution of a one-dimensional model. The results of the simulations are in agreement with the physiological data in terms of wall shear stress, wall displacement, pressure waveforms and velocities.