Unsteady Pulsatile Blood Flow Research Articles

COMPUTATIONAL STUDY OF UNSTEADY PULSATILE BLOOD FLOW THROUGH A POROUS MULTI-IRREGULAR VERTICAL STENOSED ARTERY: IMPACTS OF HOMOGENEOUS–HETEROGENEOUS REACTIONS

Homogeneous and heterogeneous reactions are significant because many chemically reactive systems, such as biochemical systems, involve both types of reactions. This paper sheds light on the effects of homogeneous–heterogeneous reactions on magnetohydrodynamic blood flow through the catheterized multi-irregular vertically stenosed artery in non-Darcy porous media. The governing partial differential equations are simplified using mild stenosis approximations and then transformed into the computational domain to simplify the numerical calculations. It has been noticed that the fluid velocity and the flow rate go to their maximum values after a short time, and they decrease with fluctuation in the case of pulsating, but in the case of nonpulsatile, the behavior is steady. Moreover, an increase in the homogeneous heat reaction parameter decelerates the blood velocity, the flow rate and elevates the fluid temperature. Furthermore, the concentration reaches the steady state faster in the absence of a homogeneous thermal reaction.

Effects of nanoparticles (Cu, TiO[formula omitted], Al[formula omitted]O[formula omitted]) on unsteady blood flow through a curved overlapping stenosed channel

In this letter, we have explored the effects of nanoparticles on unsteady pulsatile blood flow through a curved overlapping stenosed channel. The governing differential equations are derived for the given physical problem and this contains momentum and energy equations along with suitable boundary conditions. An explicit finite difference technique has been used to calculate the numerical results of the given differential equations. The numerical results for different values of curved parameter (Rc), nanoparticles (Cu, TiO2, Al2O3) and Grashof numbers (Gr) are calculated in order to analyze the effects of these parameters on blood flow pattern. A notable deviation in the results of blood flow pattern has been observed with the comparison of pure blood with nano-fluids. It is further noted that the curved parameter (Rc) of a channel has a great influence on velocity profile, flow rate and impedance/resistance to flow. It is also extracted from the velocity profiles that the shape of the velocity curves reduces to symmetric pattern for the higher values of the curved parameters (Rc). Similarly, the magnitude of temperature profiles is constricted due to the insertion of nanoparticles within blood. Moreover, streamlines are also calculated in order to analyze the effects of nanoparticles inside the circulating regions of the flow field.

Nanoparticles (Cu, [formula omitted], [formula omitted]) analysis on unsteady blood flow through an artery with a combination of stenosis and aneurysm

A theoretical and numerical study of unsteady pulsatile blood flow through an artery with a combination of stenosis and aneurysm containing nano-particles (Cu, TiO2,Al2O3) has been discussed in this article. The transport equations comprise momentum and energy partial differential equations with physiologically realistic boundary conditions. The bi-directional, non-linear, coupled differential equations are simplified by using the assumption of mild stenotic condition. The coupled differential equations are solved numerically by using robust finite difference method. The effects of nano-particles along with aneurysm on blood flow rate, wall shear stress and impedance are discussed in detail through graphs. Similarly, the graphical results of nano-particles fluid show notable deviation when compared with pure blood profiles. At the end, it is also concluded from the calculated results that both source/sink β parameter and Grashof number (Gr) facilitates the blood to maximize its flow within the vessel and minimize the hemodynamic factors such as wall shear and impedance. The circulating regions inside the flow field are also investigated through instantaneous patterns of streamlines for different parameters of interest.

Effects of nanoparticles (Cu (Copper), Silver (Ag)) and slip on unsteady blood flow through a curved stenosed channel with aneurysm

The present article is concerned with the slip effects on unsteady pulsatile blood flow through a curved channel containing nano-particles in the presence of stenosis and aneurysm. The nano-particles momentum and thermal energy equations are developed using curvilinear co-ordinates. The suitable slip boundary conditions are imposed at the channel walls. Employing mild stenotic condition, the governing differential equations are solved numerically using a robust explicit finite difference scheme. The effects of slip on various hemo-dynamical variables such as velocity, flow rate, wall shear stress and resistance to flow are shown through plots. The effects of nano-scale particles and thermo fluid parameters on flow and heat transfer characteristics of blood have been discussed in detail in this article. The flow patterns are also shown through plotting streamlines. Calculated results reveal that velocity, flow rate and shear stress increase while resistance to flow decreases with greater volume fraction of nanoparticles. The current work has many applications in the field of nano-pharmacological transport phenomena, a new and exciting area of modern medical fluid dynamics which is used to integrate the coupled diffusion and nano-scale drug delivery mechanisms.

A parallel monolithic approach for fluid-structure interaction in a cerebral aneurysm

Abstract A parallel fully-coupled numerical algorithm has been developed for the fluid-structure interaction problem in a cerebral artery with aneurysm. For the fluid part of the problem, an Arbitrary Lagrangian-Eulerian formulation based on the side-centered unstructured finite volume method is employed for the governing incompressible Navier–Stokes equations. The deformation of the solid domain is governed by the constitutive laws for the nonlinear Saint Venant-Kirchhoff material and the classical Galerkin finite element method is used to discretise the governing equations in a Lagrangian frame. The time integration method for the structure domain is based on the Newmark type generalized − α method while the second-order backward difference (BDF2) is used in the fluid domain. A special attention is given to construct an algorithm obeying the local/global discrete geometric conservation laws (DGCL) in order to conserve fluid volume at machine precision when the fluid domain is entirely enclosed by solid domain boundary. Therefore, a compatible kinematic boundary condition is applied at the interface between the solid and fluid domains. The parallel implementation of the present fully coupled unstructured fluid-structure solver is based on the PETSc library and a one-level restricted additive Schwarz preconditioner with a block-incomplete factorization within each partitioned sub-domains is utilized for the resulting fully coupled system. The proposed algorithm is initially validated for a pressure pulse propagating in a flexible tube and the mass conservation accuracy is tested for a thin elastic sphere filled with an incompressible fluid in a circular tube. Then the numerical method is applied to a complicated problem involving unsteady pulsatile blood flow in a cerebral artery with aneurysm as a realistic fluid-structure interaction problem encountered in biomechanics. Various hemodynamic quantities of interest like fluid velocities, blood pressure and wall shear stresses (WSS) are computed as well as the time dependent artery wall deformations.

UNSTEADY MAGNETOHYDRODYNAMIC BLOOD FLOW IN A POROUS-SATURATED OVERLAPPING STENOTIC ARTERY — NUMERICAL MODELING

Unsteady pulsatile flow of blood through a porous-saturated, tapered and overlapping stenotic artery in the presence of magnetic field is examined theoretically and computationally. The power law constitutive model is employed to simulate hameo-rheological characteristics. The governing equation is derived assuming the flow to be unsteady, laminar, uni-directional and one-dimensional (1D). A robust, finite difference method is employed for the solution of the governing equation, subject to appropriate boundary conditions. Based on this solution, an extensive quantitative analysis is performed to analyze the effects of blood rheology, body acceleration, magnetohydrodynamic parameter, permeability parameter and arterial geometrical parameters of stenosis on various quantities of interest such as axial velocity, flow rate, resistance impedance and wall shear stress. The computations demonstrate that velocity, flow rate and shear stress increase while resistance to flow decreases with greater permeability parameter. Additionally, the effects of magnetic field are observed to be converse to those of permeability i.e., flow is decelerated and resistance is increased, demonstrating the powerful utility of exploiting magnetic fields in hemodynamic flow control (e.g., intra-corporeal surgical procedures). Furthermore, the size of trapped bolus of fluid is also found to be reduced for large values of the permeability parameter indicating that progressively more porous media circumvent bolus growth.

Numerical study of unsteady blood flow through a vessel using Sisko model

A mathematical study for two-phase unsteady pulsatile flow of blood through a vessel in the presence of body acceleration is presented in this paper. The blood in the core region is modeled as a non-Newtonian fluid while in the peripheral region it is described as a Newtonian fluid. The effects of body acceleration are also taken into account in this study. The continuity and momentum equations are used to model the proposed problem in terms of a nonlinear partial differential equation. This equation along with initial and boundary conditions is made dimensionless and then solved numerically using finite difference method. The behavior of various flow quantitates is analyzed through a parametric study.

Pulsatile Flow of Blood in a Vessel Using an Oldroyd-B fluid

Abstract This paper is concerned with the effects of body acceleration on an unsteady pulsatile flow of blood in a vessel. The non-Newtonian behavior of blood is modeled by the constitutive equation of an Oldroyd-B fluid. The behavior of the blood is assumed as an Oldroyd-B fluid in the core and a viscous fluid in the periphery. This new model predicts the relaxation and retardation phenomena in a pulsatile flow. Our interest lies in investigating the effects of stress relaxation and retardation in unsteady pulsatile flow of an Oldroyd-B fluid. The modeled equations are normalized and solved numerically using finite difference method. The results are graphically displayed and influence of the pertinent parameter on various physical quantities of interest is analyzed.

Effects of unsteadiness and non-Newtonian rheology on blood flow through a tapered time-variant stenotic artery

A two-dimensional model is used to analyze the unsteady pulsatile flow of blood through a tapered artery with stenosis. The rheology of the flowing blood is captured by the constitutive equation of Carreau model. The geometry of the time-variant stenosis has been used to carry out the present analysis. The flow equations are set up under the assumption that the lumen radius is sufficiently smaller than the wavelength of the pulsatile pressure wave. A radial coordinate transformation is employed to immobilize the effect of the vessel wall. The resulting partial differential equations along with the boundary and initial conditions are solved using finite difference method. The dimensionless radial and axial velocity, volumetric flow rate, resistance impedance and wall shear stress are analyzed for normal and diseased artery with particular focus on variation of these quantities with non-Newtonian parameters.

Unsteady blood flow through a tapered stenotic artery using Sisko model

A mathematical study is presented for unsteady pulsatile flow of blood through a tapered stenotic artery. The constitutive equation for Sisko model is utilized to capture the rheology of blood. A realistic geometry of the time-variant stenosis is considered for the present analysis. The problem is modeled under the assumption that the lumen radius is sufficiently smaller than the wavelength of the pulsatile pressure wave. A radial coordinate transformation is used to immobilize the effect of the vessel wall. Employing the finite difference method, the governing equations are integrated along with the prescribed boundary conditions over the whole arterial segment under consideration. The radial and axial velocity, volumetric flow rate, resistance impedance and wall shear stress are analyzed for various values of the emerging parameters through graphical results.

Unsteady MHD Pulsatile Blood Flow through Porous Medium in a Stenotic Channel with Slip at the Permeable Walls Subjected to Time Dependent Velocity (Injection/Suction)

AbstractThe flow through porous boundaries is of great importance both in technological as well as biophysical flows. The present paper is concerned with the study of unsteady pulsatile flow of blood through porous medium in a time dependent constricted porous channel subjected to time dependent suction/injection at the walls of the channel. The blood flow is subjected to a constant transverse magnetic field considering blood as an incompressible electrically conducting fluid. Due to the permeability of the arterial wall the no slip condition at the wall is no longer valid and one has to consider a slip condition at the channel wall. It was obliviously better and more realistic approach to obtain the flow behaviors. Perturbation analysis is used to solve the system of equations governing the flow. With a view to illustrating the applicability of the mathematical model developed here the analytic explicit expressions of axial velocity, volumetric flow rate and wall shear stress are obtained. The computed numerical results are presented graphically for different values of the physical parameters of interest to depict the variations in axial velocity, volumetric flow rate and wall shear stress.

Numerical Study of Slip Effect of Unsteady MHD Pulsatile Flow through Porous Medium in an Artery Using Generalized Differential Quadrature Method (Comparative Study)

The unsteady pulsatile flow of blood through porous medium in an artery has been studied under the influence of periodic body acceleration and slip condition by considering blood as incompressible Newtonian electrically conducting fluid in the presence of magnetic field. In this paper, a new technique of differential quadrature method is introduced to find numerical solution of non-linear partial differential equations such as the equation of motion of this problem “Navier-Stokes equation”. The presence of the nonlinearity in the problem leads to severe difficulties in the solution approximation. In construction of the numerical scheme “a new algorithm” a generalized differential quadrature method (GDQM) is to use for derivatives with respect to space variables of differential equations and for the time derivative applying fourth order RungeKutta Method (RKM). The GDQM changed the nonlinear partial differential equations into a system of nonlinear ordinary differential equations (ODEs). The obtained system of ODEs is solved by 4th order RKM. This combination of DQM and 4th order RKM gives a very good numerical technique for solving time dependent problems. The algorithm is coded in Matlab 7.14.0.739 and the simulations are run on a Pentium 4 CPU 900 MHz with 1 GB memory capacity. The effects of slip condition, magnetic field, porous medium, and body acceleration have been discussed. The numerical results show that the proposed method is more accurate and convergent than other numerical methods in literature. The method is illustrated and compared with the exact and analytical solutions and it is found that the proposed method gives a better accuracy and is quite easy to implement.

Numerical Study of Unsteady MHD Pulsatile Flow through Porous Medium in an Artery Using Generalized Differential Quadrature Method (GDQM)

The unsteady pulsatile flow of blood through porous medium has been studied under the influence of periodic body acceleration by considering blood as incompressible Newtonian electrically conducting fluid in the presence of magnetic field. A numerical solution of the equation of motion is obtained by applying a generalized differential quadrature method (GDQM), to derivatives with respect to space variables of differential equations and for the time derivative applying 4 th order Runge Kutta Method. This combination of DQM and 4 th order RK method gives very good numerical technique for solving time dependent problems. The algorithm is coded in Matlab 7.14.0.739 and the simulations are run on a Pentium 4 CPU 900 MHz with 1 GB memory capacity. The numerical results show and discussed with the help graphs. The study show that the axial velocity of the blood increases with increasing the permeability parameter of porous medium and the Womersley parameter, and decreases with increasing the Hartmann number. The study is useful for evaluating the role of porosity when the body is subjected to magnetic resonance imaging (MRI).

Slip Effects on the Unsteady MHD Pulsatile Blood Flow through Porous Medium in an Artery under the Effect of Body Acceleration

Unsteady pulsatile flow of blood through porous medium in an artery has been studied under the influence of periodic body acceleration and slip condition in the presence of magnetic field considering blood as an incompressible electrically conducting fluid. An analytical solution of the equation of motion is obtained by applying the Laplace transform. With a view to illustrating the applicability of the mathematical model developed here, the analytic explicit expressions of axial velocity, wall shear stress, and fluid acceleration are given. The slip condition plays an important role in shear skin, spurt, and hysteresis effects. The fluids that exhibit boundary slip have important technological applications such as in polishing valves of artificial heart and internal cavities. The effects of slip condition, magnetic field, porous medium, and body acceleration have been discussed. The obtained results, for different values of parameters into the problem under consideration, show that the flow is appreciably influenced by the presence of Knudsen number of slip condition, permeability parameter of porous medium, Hartmann number of magnetic field, and frequency of periodic body acceleration. The study is useful for evaluating the role of porosity and slip condition when the body is subjected to magnetic resonance imaging (MRI).

Haemodynamic analysis of coronary artery bypass grafting in a non-linear deformable artery and Newtonian pulsatile blood flow

A three-dimensional (3D) computational model of stenotic coronary artery bypass grafting (CABG) system with fluid-structure interaction (FSI) using realistic physiological conditions is introduced. Unsteady pulsatile blood flow is applied to the wall of non-linear deformable arteries over the systolic period. In the analysis, the arbitrarily Lagrangian-Eulerian (ALE) formulation is used to couple the fluid region and solid domain. The method couples the equations of the deformation of the artery wall and applies them as the fluid domain boundary condition. The flow distribution and haemodynamic forces are presented in terms of velocity profiles and temporal and spatial wall shear stresses (WSSs) at the distal area. Rapid changes in the flow fields are observed in the early stages of the cardiac cycle, which alters the location of the recirculation zone from the toe to the host bed and then to the heel. The migration of the recirculation zone, considering the effect of deformability of the artery wall, indicates the same trend as the rigid wall model according to the location of low and high WSSs. However, the WSSs in the critical areas such as toe, heel, and suture lines are found to have dramatic drops in magnitudes in comparison with those of the rigid wall model. This could initiate the promotion of intimal hyperplasia (IH) and may cause an early graft failure in CABG.

Pulsatile flow of blood using a modified second-grade fluid model

We study the unsteady pulsatile flow of blood in an artery, where the effects of body acceleration are included. The blood is modeled as a modified second-grade fluid where the viscosity and the normal stress coefficients depend on the shear rate. It is assumed that the blood near the wall behaves as a Newtonian fluid, and in the core as a non-Newtonian fluid. This phenomenon is also known as the Fahraeus–Lindqvist effect. The equations are made dimensionless and solved numerically.

Shape optimization in unsteady blood flow: A numerical study of non-Newtonian effects

This paper presents a numerical study of non-Newtonian effects on the solution of shape optimization problems involving unsteady pulsatile blood flow. We consider an idealized two dimensional arterial graft geometry. Our computations are based on the Navier–Stokes equations generalized to non-Newtonian fluid, with the modified Cross model employed to account for the shear-thinning behavior of blood. Using a gradient-based optimization algorithm, we compare the optimal shapes obtained using both the Newtonian and generalized Newtonian constitutive equations. Depending on the shear rate prevalent in the domain, substantial differences in the flow as well as in the computed optimal shape are observed when the Newtonian constitutive equation is replaced by the modified Cross model. By varying a geometric parameter in our test case, we investigate the influence of the shear rate on the solution.