Non-Newtonian effects of blood on LDL transport inside the arterial lumen and across multi-layered arterial wall with and without stenosis

2016 ◽  
Vol 27 (01) ◽  
pp. 1650003
Author(s):  
Amin Deyranlou ◽  
Hamid Niazmand ◽  
Mahmood-Reza Sadeghi ◽  
Yaser Mesri
Keyword(s):  
Arterial Wall ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Accurate Estimation ◽  
Ldl Transport ◽  
Arterial Lumen ◽  
Newtonian Model ◽  
Stenosis Severity ◽  
Luminal Flow ◽  
Concentration Patterns

Blood non-Newtonian behavior on low-density lipoproteins (LDL) accumulation is analyzed numerically, while fluid-multilayered arteries are adopted for nonstenotic and 30%–60% symmetrical stenosed models. Present model considers non-Newtonian effects inside the lumen and within arterial layers simultaneously, which has not been examined in previous studies. Navier–Stokes equations are solved along with the mass transport convection–diffusion equations and Darcy’s model for species transport inside the luminal flow and across wall layers, respectively. Carreau model for the luminal flow and the modified Darcy equation for the power-law fluid within arterial layers are employed to model blood rheological characteristics, appropriately. Results indicate that in large arteries with relatively high Reynolds number Newtonian model estimates LDL concentration patterns well enough, however, this model seriously incompetent for regions with low WSS. Moreover, Newtonian model for plasma underestimates LDL concentration especially on luminal surface and across arterial wall. Therefore, applying non-Newtonian model seems essential for reaching to a more accurate estimation of LDL distribution in the artery. Finally, blood flow inside constricted arteries demonstrates that LDL concentration patterns along the stenoses inside the luminal flow and across arterial layers are strongly influenced as compared to the nonstenotic arteries. Additionally, among four stenosis severity grades, 40% stenosis is prone to more LDL accumulation along the post-stenotic regions.

A NONLINEAR UNSTEADY RESPONSE OF NON-NEWTONIAN BLOOD FLOW PAST AN OVERLAPPING ARTERIAL CONSTRICTION

2007 ◽  
Vol 07 (04) ◽  
pp. 463-489
Author(s):  
S. SEN ◽  
S. CHAKRAVARTY
Keyword(s):  
Blood Flow ◽  
Flow Field ◽  
Arterial Wall ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Physiological Flow ◽  
Arterial Lumen ◽  
Shear Dependent Viscosity

The present study deals with an appropriate mathematical model describing blood flow through a constricted artery that is used to analyze the physiological flow field. The time-variant geometry of the arterial segment having an overlapping type of constriction in the arterial lumen — which frequently occurs in diseased arteries, causing flow disorder and leading to malfunction of the cardiovascular system — is framed mathematically. Blood flow contained in the stenosed artery is treated as non-Newtonian (having shear-dependent viscosity) and is considered to be two-dimensional. The motion of the arterial wall and its effect on local fluid mechanics are not ruled out from the present pursuit. The flow analysis applies the time-dependent, two-dimensional incompressible nonlinear Navier–Stokes equations for non-Newtonian fluids. The flow field can be obtained by first transforming radial coordinates with the use of appropriate boundary conditions, and then adopting a suitable finite difference scheme numerically. The unsteady response of the system and the influence of the arterial wall distensibility, the non-Newtonian rheology of blood, and the presence of stenosis on the important aspects of the physiological flow phenomena are quantified in order to indicate the susceptibility to atherosclerotic lesions and thereby validate the applicability of the present theoretical model.

Quantifying Vessel Material Properties Using MRI Under Pressure Condition and MRI-Based FSI Mechanical Analysis for Human Atherosclerotic Plaques

2006 ◽  
Author(s):  
Chun Yang ◽  
Xueying Huang ◽  
Jie Zheng ◽  
Pamela K. Woodard ◽  
Dalin Tang
Keyword(s):  
Material Properties ◽  
Stokes Equations ◽  
Maximum Shear Stress ◽  
Maximum Principal Stress ◽  
Mechanical Analysis ◽  
Navier Stokes ◽  
Atherosclerotic Plaques ◽  
Navier Stokes Equations ◽  
Stenosis Severity ◽  
Set Up

Atherosclerotic plaques may rupture without warning and cause acute cardiovascular syndromes such as heart attack and stroke. Mechanical image analysis using MRI-based models with fluid-structure interactions (FSI) and MRI-determined material properties may improve the accuracy of plaque vulnerability assessment and rupture predictions. A plaque-phantom was set up to acquire plaque MR images under pressurized conditions. The 3D nonlinear modified Mooney-Rivlin (M-R) model was used to describe the material properties with parameters selected to fit the MRI data. The Navier-Stokes equations were used as the governing equations for the flow model. The fully-coupled FSI models were solved by ADINA. Our results indicate that doubling parameter values in the M-R model led to 12.5% decrease in structure maximum principal stress (Stress-P1) and 48% decrease in maximum principal strain (Strain-P1). Flow maximum shear stress (MSS) was almost unchanged. Results from a modified carotid plaque with 70% stenosis severity (by diameter) showed that Stress-P1 at the plaque throat from the wall-only model is 145% higher than that from the FSI model. MSS from a flow-only model is about 40% higher than that from the FSI model. This approach has the potential to develop non-invasive patient screening and diagnosis methods in clinical applications.

Effect of Non-Newtonian Blood Flow on Coronary Artery Hemodynamics in a Cohort of Patients With Stenosed Artery

2018 ◽  
Author(s):  
Majid Abbasian ◽  
Mehrzad Shams ◽  
Ziba Valizadeh ◽  
Abouzar Moshfegh ◽  
Ashkan Javadzadegan
Keyword(s):  
Blood Flow ◽  
Coronary Artery ◽  
Stokes Equations ◽  
Full Range ◽  
Navier Stokes ◽  
Patient Specific ◽  
Navier Stokes Equations ◽  
Cross Section Area ◽  
Stenosis Severity ◽  
The Difference

Wall shear stress (WSS) distribution in stenosed arteries has been known as an important hemodynamic factor to correlate with atherosclerosis and associated disturbances in blood flow. WSS depends on various factors such as geometric complexity and tortuosity of the artery, stenosis severity and morphology as well as blood rheological properties. We conducted a numerical simulation of blood flow using Ansys CFX software in 9 patient-specific coronary artery models with 3 classes of stenosis severity: mild, moderate and severe. For this purpose, we compared some numerical results between two non-Newtonian models and Newtonian blood flow viscosity using 9 patient-specific coronary artery models including the full range of real (physiological) stenosis, reconstructed from 3DQCA (quantities coronary angiography). Incompressible and steady state form of Navier-Stokes equations were used as governing equations. Flow was considered laminar and artery walls were assumed to be rigid. Results showed that the magnitude of WSS usually increases by decreasing the cross-section area of arteries. Despite the difference in the WSS magnitude between different models in each artery, the trend of variation of WSS along the artery was the same in all three models. The local peak point of WSS along the artery occurs at the stenosis location, same for all models.

Multiphysics Simulation of Blood Flow and LDL Transport in a Porohyperelastic Arterial Wall Model

2006 ◽  
Vol 129 (3) ◽  
pp. 374-385 ◽  
Author(s):  
Nobuko Koshiba ◽  
Joji Ando ◽  
Xian Chen ◽  
Toshiaki Hisada
Keyword(s):  
Blood Flow ◽  
Flow Field ◽  
Arterial Wall ◽  
Interaction Analysis ◽  
Concentration Field ◽  
Coupled Analysis ◽  
Filtration Flow ◽  
Ldl Transport ◽  
Arterial Lumen ◽  
Rigid Model

Atherosclerosis localizes at a bend and∕or bifurcation of an artery, and low density lipoproteins (LDL) accumulate in the intima. Hemodynamic factors are known to affect this localization and LDL accumulation, but the details of the process remain unknown. It is thought that the LDL concentration will be affected by the filtration flow, and that the velocity of this flow will be affected by deformation of the arterial wall. Thus, a coupled model of a blood flow and a deformable arterial wall with filtration flow would be invaluable for simulation of the flow field and concentration field in sequence. However, this type of highly coupled interaction analysis has not yet been attempted. Therefore, we performed a coupled analysis of an artery with multiple bends in sequence. First, based on the theory of porous media, we modeled a deformable arterial wall using a porohyperelastic model (PHEM) that was able to express both the filtration flow and the viscoelastic behavior of the living tissue, and simulated a blood flow field in the arterial lumen, a filtration flow field and a displacement field in the arterial wall using a fluid-structure interaction (FSI) program code by the finite element method (FEM). Next, based on the obtained results, we further simulated LDL transport using a mass transfer analysis code by the FEM. We analyzed the PHEM in comparison with a rigid model. For the blood flow, stagnation was observed downward of the bends. The direction of the filtration flow was only from the lumen to the wall for the rigid model, while filtration flows from both the wall to the lumen and the lumen to the wall were observed for the PHEM. The LDL concentration was high at the lumen∕wall interface for both the PHEM and rigid model, and reached its maximum value at the stagnation area. For the PHEM, the maximum LDL concentration in the wall in the radial direction was observed at the position of 3% wall thickness from the lumen∕wall interface, while for the rigid model, it was observed just at the lumen∕wall interface. In addition, the peak LDL accumulation area of the PHEM moved about according to the pulsatile flow. These results demonstrate that the blood flow, arterial wall deformation, and filtration flow all affect the LDL concentration, and that LDL accumulation is due to stagnation and the presence of filtration flow. Thus, FSI analysis is indispensable.

scholarly journals Pulsatile Non-Newtonian Laminar Blood Flows through Arterial Double Stenoses

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Mir Golam Rabby ◽  
Sumaia Parveen Shupti ◽  
Md. Mamun Molla
Keyword(s):  
Stokes Equations ◽  
Streamwise Velocity ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Newtonian Viscosity ◽  
Navier Stokes Equations ◽  
Periodic Flows ◽  
Blood Flows ◽  
Viscosity Models ◽  
Newtonian Model

The paper presents a numerical investigation of non-Newtonian modeling effects on unsteady periodic flows in a two-dimensional (2D) pipe with two idealized stenoses of 75% and 50% degrees, respectively. The governing Navier-Stokes equations have been modified using the Cartesian curvilinear coordinates to handle complex geometries. The investigation has been carried out to characterize four different non-Newtonian constitutive equations of blood, namely, the (i) Carreau, (ii) Cross, (iii) Modified Casson, and (iv) Quemada models. The Newtonian model has also been analyzed to study the physics of fluid and the results are compared with the non-Newtonian viscosity models. The numerical results are represented in terms of streamwise velocity, pressure distribution, and wall shear stress (WSS) as well as the vorticity, streamlines, and vector plots indicating recirculation zones at the poststenotic region. The results of this study demonstrate a lower risk of thrombogenesis at the downstream of stenoses and inadequate blood supply to different organs of human body in the Newtonian model compared to the non-Newtonian ones.

Numerical Simulation for the Propagation of Nonlinear Pulsatile Waves in Arteries

1992 ◽  
Vol 114 (4) ◽  
pp. 490-496 ◽  
Author(s):  
X. Ma ◽  
G. C. Lee ◽  
S. G. Wu
Keyword(s):  
Numerical Simulation ◽  
Arterial Wall ◽  
Stokes Equations ◽  
Elastic Tube ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Navier Stokes Equations ◽  
Fixed Area ◽  
Profile Flow ◽  
Numerical Discretization

The behavior of nonlinear pulsatile flow of incompressible blood contained in an elastic tube is examined. The theory takes into account the nonlinear convective terms of the Navier-Stokes equations. The motion of the arterial wall is characterized by a set of linearized differential equations. The region bounded by the flexible arterial wall is mapped into a fixed area in which numerical discretization takes place. The finite element method (Galerkin weighted residual approach) is used for the solution of this nonlinear system. The results obtained are pressure distribution, velocity profile, flow rate and wall displacements along the elastic tube (20 cm long).

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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