Journal ArticleDOI
One-dimensional models for blood flow in arteries
TLDR
In this article, a family of one-dimensional nonlinear systems which model the blood pulse propagation in compliant arteries is presented and investigated by averaging the Navier-Stokes equation on each section of an arterial vessel and using simplified models for the vessel compliance.Abstract:
In this paper a family of one-dimensional nonlinear systems which model the blood pulse propagation in compliant arteries is presented and investigated. They are obtained by averaging the Navier-Stokes equation on each section of an arterial vessel and using simplified models for the vessel compliance. Different differential operators arise depending on the simplifications made on the structural model. Starting from the most basic assumption of pure elastic instantaneous equilibrium, which provides a well-known algebraic relation between intramural pressure and vessel section area, we analyse in turn the effects of terms accounting for inertia, longitudinal pre-stress and viscoelasticity. The problem of how to account for branching and possible discontinuous wall properties is addressed, the latter aspect being relevant in the presence of prosthesis and stents. To this purpose a domain decomposition approach is adopted and the conditions which ensure the stability of the coupling are provided. The numerical method here used in order to carry out several test cases for the assessment of the proposed models is based on a finite element Taylor-Galerkin scheme combined with operator splitting techniques.read more
Citations
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Journal ArticleDOI
Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements
Jordi Alastruey,Ashraf W. Khir,Koen Matthys,Patrick Segers,Spencer J. Sherwin,Pascal Verdonck,Kim H. Parker,Joaquim Peiró +7 more
TL;DR: The inclusion of wall visco-elasticity in the numerical model reduced the underdamped high-frequency oscillations obtained using a purely elastic tube law, especially in peripheral vessels, which was reported in this paper.
Journal ArticleDOI
Pulse Wave Propagation in the Arterial Tree
TL;DR: The beating heart creates blood pressure and flow pulsations that propagate as waves through the arterial tree that are reflected at transitions in arterial geometry and elasticity, and these waves carry information about the matter in which they propagate.
Book ChapterDOI
Mathematical Modelling and Numerical Simulation of the Cardiovascular System
TL;DR: This chapter addresses the problem of developing models for the numerical simulation of the human circulatory system, and particularly focuses on the issue of hemodynamics in large human arteries.
Journal ArticleDOI
A systematic comparison between 1-D and 3-D hemodynamics in compliant arterial models.
TL;DR: An iterative algorithm can be used to efficiently determine material and boundary condition parameters for 3‐D subject‐specific arterial models with deformable vessel walls by using the 1‐D theory to achieve a desired systolic and diastolic pressure at a particular vessel.
Journal ArticleDOI
A 1D arterial blood flow model incorporating ventricular pressure, aortic valve and regional coronary flow using the locally conservative Galerkin (LCG) method
TL;DR: In this article, the authors present a non-linear 1D model of coronary and systemic arterial circulations, as well as ventricular pressure and an aortic valve that opens and closes independently based on local haemodynamics.
References
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Book
Biomechanics: Mechanical Properties of Living Tissues
Yuan-Cheng Fung,Richard Skalak +1 more
TL;DR: This chapter discusses the mechanics of Erythrocytes, Leukocytes, and Other Cells, and their role in Bone and Cartilage, and the properties of Bioviscoelastic Fluids, which are a by-product of these cells.
Journal ArticleDOI
Biomechanics: Mechanical Properties of Living Tissues
Yuan-Cheng Fung,Richard Skalak +1 more
TL;DR: In this article, the authors present a sketch of the history and scope of the field of bio-physiology and discuss the meaning of the Constitutive Equation and the flow properties of blood.
Journal ArticleDOI
A new constitutive framework for arterial wall mechanics and a comparative study of material models
TL;DR: In this paper, the authors developed a constitutive law for the description of the (passive) mechanical response of arterial tissue, where the artery is modeled as a thick-walled nonlinearly elastic circular cylindrical tube consisting of two layers corresponding to the media and adventitia.
Book
Numerical Approximation of Partial Differential Equations
Alfio Quarteroni,Alberto Valli +1 more
TL;DR: In this article, the authors provide a thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation.
Journal ArticleDOI
Time-dependent boundary conditions for hyperbolic systems, II
TL;DR: In this article, nonreflecting boundary conditions are defined for multidimensional fluid dynamics problems where waves enter and leave the interior of a domain modeled by hyperbolic equations, and separate equations for each type of incoming and outgoing wave.