Modeling and analysis of fractional neutral disturbance waves in arterial vessels

2019 ◽  
Vol 14 (3) ◽  
pp. 301 ◽  
Author(s):  
Feixue Song ◽  
Zheyuan Yu ◽  
Hongwei Yang

The behavior of neutral disturbance in arterial vessels has attracted more and more attention in recent decades because it carries some important information which can be applied to predict and diagnose related heart disease, such as arteriosclerosis and hypertension, etc. Because of the complexity of blood flow in arteries, it is very necessary to construct accurate mathematical model and analyze the mechanical behavior of neutral disturbance in arterial vessels. In this paper, start from the basic equations of blood flow and the two-dimensional Navier–Stokes equation, the vorticity equation describing the disturbance flow is presented. Then, by use of multi-scale analysis and perturbation expansion method, the ZK equation is put forward which can reflect the behavior of the neutral perturbation flow in arterial vessels. Compared with the traditional KdV model, the model established in the paper can show the propagation of the disturbance flow in the radius direction. Furthermore, the time-fractional ZK equation is derived by semi-inverse method and Agrawal’s method, which is more convenient and accurate for discussing the feature of neutral disturbance in arterial vessels and can provide more information for analyzing some related heart disease. Meanwhile, with the help of the modified extended tanh method, the above mentioned equation is solved. The results show that neutral disturbance exists in arterial vessels and propagates in the form of solitary waves. By calculating, we find the relation of the stroke volume with vascular radius, blood flow velocity as well as the fractional order parameter α, which is very meaningful for preventing and treating related heart disease because the stroke volume is closely linked with heart disease.

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Khalid M. Saqr ◽  
Simon Tupin ◽  
Sherif Rashad ◽  
Toshiki Endo ◽  
Kuniyasu Niizuma ◽  
...  

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.


Author(s):  
Kostas Karagiozis ◽  
Marco Amabili ◽  
Rosaire Mongrain ◽  
Raymond Cartier ◽  
Michael P. Pai¨doussis

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.


2006 ◽  
Vol 3 (2) ◽  
pp. 77-86
Author(s):  
R. Raghu ◽  
A. Pullan ◽  
N. Smith

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.


1962 ◽  
Vol 17 (3) ◽  
pp. 482-486 ◽  
Author(s):  
W. B. Jones ◽  
J. B. Griffin

The probe of an electromagnetic flowmeter was placed on the ascending aorta of five dogs. Aortic blood pressure was obtained from the same area. This pressure signal was fed into a simple computer circuit designed to solve a modification of the Navier-Stokes equation. The output of this circuit was assumed to be proportional to blood velocity and was compared directly with the velocity obtained with the electromagnetic flowmeter. The peak amplitudes and the stroke volumes (represented by the area under the velocity tracings), obtained simultaneously by the two different methods, were compared. Each dog was bled, transfused, and given methoxamine and nitroglycerin to produce a wide variation in stroke volume and blood pressure. A correlation coefficient of .93 was obtained from 350 paired stroke-volume values. Thus, it appears that in a wide variety of conditions, stroke volume may be derived from the aortic pressure pulse by the computer technique. Submitted on October 27, 1961


1995 ◽  
Vol 1 (3) ◽  
pp. 245-254 ◽  
Author(s):  
N. U. Ahmed

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.


Author(s):  
Xin Chen ◽  
Jianping Tan

By analyzing fluid dynamics of blood in an artificial blood pump and simulating the flow field structure and the flow performance of blood, the blood flow and the damages in the designed blood pump would be better understood. This paper describes computational fluid dynamic (CFD) used in predicting numerically the hemolysis of blade in micro-axial blood pumps. A numerical hydrodynamical model, based on the Navier-Stokes equation, was used to obtain the flow in a micro-axial blood pump. A time-dependent stress acting on blood particle is solved in this paper to explore the blood flow and damages in the micro-axial blood pump. An initial attempt is also made to predict the blood damage from these simulations.


2021 ◽  
Vol 413 ◽  
pp. 19-28
Author(s):  
Yaroslav R. Nartsissov

A convectional diffusion of nutrients around the blood vessels in brain occurs in well-structured neurovascular units (NVU) including neurons, glia and micro vessels. A common feature of the process is a combination of a relatively high-speed delivery solution stream inside the blood vessel and a low-speed convectional flow in parenchyma. The specific trait of NVU is the existence of a tight cover layer around the vessels which is formed by shoots (end-feet) of astrocytes. This layer forms so called blood-brain barrier (BBB). Under different pathological states the permeability of BBB is changed. The concentration gradient of a chemical compound in NVU has been modelled using a combination of mathematical description of a cerebral blood flow (CBF) and further 3D diffusion away from the blood vessels borders. The governing equation for the blood flow is the non-steady-state Navier–Stokes equation for an incompressible non-Newtonian fluid flow without buoyancy effects. BBB is modeled by the flux dysconnectivity functions. The velocity of fluid flow in the paravascular space was estimated using Darcy's law. Finally, the diffusion of the nutrient is considered as a convectional reaction-diffusion in a porous media. By the example of glucose, it was shown that increased permeability of BBB yields an increased level of the nutrient even under essential (on 70%) decrease of CBF. Contrarily, a low BBB permeability breeds a decreased concentration level under increased (on 50%) CBF. Such a phenomenon is explained by a smooth enlarge of the direct diffusion area for a blood-to-brain border glucose transport having three-level organization.


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