scholarly journals Effects of Stenting on Blood Flow in a Coronary Artery Network Model

2006 ◽  
Vol 3 (2) ◽  
pp. 77-86
Author(s):  
R. Raghu ◽  
A. Pullan ◽  
N. Smith
Keyword(s):  
Blood Flow ◽  
Coronary Artery ◽  
Finite Difference Method ◽  
Vessel Wall ◽  
Flow Patterns ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Computationally Efficient ◽  
Navier Stokes Equation ◽  
Local Flow

The effect of stenting on blood flow is investigated using a model of the coronary artery network. The parameters in a generic non-linear pressure–radius relationship are varied in the stented region to model the increase in stiffness of the vessel due to the presence of the stent. A computationally efficient form of the Navier–Stokes equation is solved using a Lax–Wendroff finite difference method. Pressure, vessel radius and flow velocity are computed along the vessel segments. Results show negative pressure gradients at the ends of the stent and increased velocity through the middle of the stented region. Changes in local flow patterns and vessel wall stresses due to the presence of the stent have been shown to be important in restenosis of vessels. Local and global pressure gradients affect local flow patterns and vessel wall stresses, and therefore may be an important factor associated with restenosis. The model presented in this study can be easily extended to solve flows for stented vessels in a full, anatomically realistic coronary network. The framework to allow for the effects of the deformation of the myocardium on the coronary network is also in place.

scholarly journals Computer Simulation of Platelet Adhesion around Stent Struts in the Presence and Absence of Tissue Defects around Them

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yota Kawamura ◽  
Noriko Tamura ◽  
Shinichi Goto ◽  
Shinya Goto
Keyword(s):  
Computer Simulation ◽  
Blood Flow ◽  
Membrane Protein ◽  
Vessel Wall ◽  
Platelet Adhesion ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Stent Strut ◽  
Platelet Accumulation ◽  
Tissue Defects

Aim. To predict platelet accumulation around stent struts in the presence or absence of tissue defects around them. Methods. Computer simulations were performed using virtual platelets implementing the function of the three membrane proteins: glycoprotein (GP) Ibα, GPIIb/IIIa, and GPVI. These platelets were perfused around the stent struts implanted into the vessel wall in the presence or absence of tissue defects around them using within the simulation platform. The number of platelets that adhered around stent struts was calculated by solving the blood flow using Navier–Stokes equation along with the adhesion of membrane protein modeled within the platform. Results. Platelet accumulation around stent struts occurred mostly at the downstream region of the stent strut array. The majority of platelets adhered at the downstream of the first bend regardless of the tissue defect status. Platelet adhesion around stent struts occurred more rapidly in the presence of tissue defects. Conclusion. Computer simulation using virtual platelets suggested a higher rate of platelet adhesion in the presence of tissue defects around stent struts.

Pulsatile Flow in Tapered Tubes: A Model of Blood Flow With Large Disturbances

1983 ◽  
Vol 105 (2) ◽  
pp. 112-119 ◽  
Author(s):  
E. Kimmel ◽  
U. Dinnar
Keyword(s):  
Blood Flow ◽  
Pulsatile Flow ◽  
Mean Value ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Pressure Gradients ◽  
Navier Stokes Equation ◽  
Rigid Tube ◽  
Flow Through ◽  
Uniform Tube

Blood flow-through segments of large arteries of man, between adjacent bifurcations, can be modeled as pulsatile flow in tapered converging tubes, of small angle of convergence, up to 2 deg. Assuming linearity, rigid tube and homogeneous Newtonian fluid, the physiological flow field is governed by the Navier-Stokes equation with dominant nonlinear and unsteady terms. Analytical solution of this problem is presented based on an integral method technique. The solution shows that even for small tapering the flow pattern is markedly different from the flow obtained for a uniform tube. The periodic shear stresses at the wall and pressure gradients increase both in their mean value and amplitude with increased distance downstream. These results are highly significant in the process of atherogenesis.

scholarly journals Physiologic blood flow is turbulent

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Khalid M. Saqr ◽  
Simon Tupin ◽  
Sherif Rashad ◽  
Toshiki Endo ◽  
Kuniyasu Niizuma ◽  
...  
Keyword(s):  
Blood Flow ◽  
Stokes Equation ◽  
Initial Conditions ◽  
Hydrodynamic Instability ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Frequency Spectra ◽  
Hydrodynamic Stability Theory

Abstract Contemporary paradigm of peripheral and intracranial vascular hemodynamics considers physiologic blood flow to be laminar. Transition to turbulence is considered as a driving factor for numerous diseases such as atherosclerosis, stenosis and aneurysm. Recently, turbulent flow patterns were detected in intracranial aneurysm at Reynolds number below 400 both in vitro and in silico. Blood flow is multiharmonic with considerable frequency spectra and its transition to turbulence cannot be characterized by the current transition theory of monoharmonic pulsatile flow. Thus, we decided to explore the origins of such long-standing assumption of physiologic blood flow laminarity. Here, we hypothesize that the inherited dynamics of blood flow in main arteries dictate the existence of turbulence in physiologic conditions. To illustrate our hypothesis, we have used methods and tools from chaos theory, hydrodynamic stability theory and fluid dynamics to explore the existence of turbulence in physiologic blood flow. Our investigation shows that blood flow, both as described by the Navier–Stokes equation and in vivo, exhibits three major characteristics of turbulence. Womersley’s exact solution of the Navier–Stokes equation has been used with the flow waveforms from HaeMod database, to offer reproducible evidence for our findings, as well as evidence from Doppler ultrasound measurements from healthy volunteers who are some of the authors. We evidently show that physiologic blood flow is: (1) sensitive to initial conditions, (2) in global hydrodynamic instability and (3) undergoes kinetic energy cascade of non-Kolmogorov type. We propose a novel modification of the theory of vascular hemodynamics that calls for rethinking the hemodynamic–biologic links that govern physiologic and pathologic processes.

Human Aorta Buckling Related to Dissection

2010 ◽  
Author(s):  
Kostas Karagiozis ◽  
Marco Amabili ◽  
Rosaire Mongrain ◽  
Raymond Cartier ◽  
Michael P. Pai¨doussis
Keyword(s):  
Blood Flow ◽  
Nonlinear Stability ◽  
Shell Theory ◽  
Inviscid Flow ◽  
Mechanical Stresses ◽  
Surrounding Tissue ◽  
Navier Stokes ◽  
Human Aorta ◽  
Navier Stokes Equation ◽  
Viscous Stresses

Human aortas are subjected to large mechanical stresses and loads due to blood flow pressurization and through contact with the surrounding tissue and muscle. It is essential that the aorta does not lose stability for proper functioning. The present work investigates the buckling of human aorta relating it to dissection by means of an analytical model. A full bifurcation analysis is used employing a nonlinear model to investigate the nonlinear stability of the aorta conveying blood flow. The artery is modeled as a shell by means of Donnell’s nonlinear shell theory retaining in-plane inertia, while the fluid is modelled by a Newtonian inviscid flow theory but taking into account viscous stresses via the time-averaged Navier-Stokes equation. The three shell displacements are expanded using trigonometric series that satisfy the boundary conditions exactly. A parametric study is undertaken to determine the effect of aorta length, thickness, Young’s modulus, and transmural pressure on the nonlinear stability of the aorta. As a first attempt to study dissection, a quasi-steady approach is taken, in which the flow is not pulsatile but steady. The effect of increasing flow velocity is studied, particularly where the system loses stability, exhibiting static collapse. Regions of large mechanical stresses on the artery surface are identified for collapsed arteries indicating possible ways for dissection to be initiated.

scholarly journals IVUS Detection of Vasa Vasorum Blood Flow Distribution in Coronary Artery Vessel Wall

2012 ◽  
Vol 5 (9) ◽  
pp. 935-940 ◽  
Author(s):  
Regina Moritz ◽  
Diane R. Eaker ◽  
Jill L. Anderson ◽  
Timothy L. Kline ◽  
Steven M. Jorgensen ◽  
...  
Keyword(s):  
Blood Flow ◽  
Coronary Artery ◽  
Vessel Wall ◽  
Flow Distribution ◽  
Vasa Vasorum ◽  
Blood Flow Distribution

scholarly journals Mathematical problems in modeling artificial heart

1995 ◽  
Vol 1 (3) ◽  
pp. 245-254 ◽  
Author(s):  
N. U. Ahmed
Keyword(s):  
Blood Flow ◽  
Boundary Conditions ◽  
Stokes Equation ◽  
Artificial Heart ◽  
Moving Boundary ◽  
Hyperbolic Type ◽  
The Other ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Heart Chamber

In this paper we discuss some problems arising in mathematical modeling of artificial hearts. The hydrodynamics of blood flow in an artificial heart chamber is governed by the Navier-Stokes equation, coupled with an equation of hyperbolic type subject to moving boundary conditions. The flow is induced by the motion of a diaphragm (membrane) inside the heart chamber attached to a part of the boundary and driven by a compressor (pusher plate). On one side of the diaphragm is the blood and on the other side is the compressor fluid. For a complete mathematical model it is necessary to write the equation of motion of the diaphragm and all the dynamic couplings that exist between its position, velocity and the blood flow in the heart chamber. This gives rise to a system of coupled nonlinear partial differential equations; the Navier-Stokes equation being of parabolic type and the equation for the membrane being of hyperbolic type. The system is completed by introducing all the necessary static and dynamic boundary conditions. The ultimate objective is to control the flow pattern so as to minimize hemolysis (damage to red blood cells) by optimal choice of geometry, and by optimal control of the membrane for a given geometry. The other clinical problems, such as compatibility of the material used in the construction of the heart chamber, and the membrane, are not considered in this paper. Also the dynamics of the valve is not considered here, though it is also an important element in the overall design of an artificial heart. We hope to model the valve dynamics in later paper.

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