Comparison of physiological and simple pulsatile flows through stenosed arteries

Numerical computation of pulsatile hemodynamics and diagnostic concern of coronary bifurcated artery flow for Newtonian and non-Newtonian fluid

Atherosclerotic with the high occurrence of plaque formation due to stenosis has attracted wide attention among researchers. The left coronary artery has been studied in two-dimensional and in three-dimensional (3D) bifurcation as the models of blood flow through Newtonian and non-Newtonian fluids to better understand the physical mechanism. The computational Fluid Dynamics (CFD) technique is incorporated in COMSOL Multiphysics and then it is justified by satisfactory validation. It is found that the Newtonian model shows larger recirculation zones than non-Newtonian does. The present study also focuses on the evaluations of the lesion of diagnostic and the coefficient of pressure drop assessments on the basis of the diagnostic parameter's critical values affected by the rheological model. Nevertheless, the leading concentration of the subsisting investigation works is confined to the change of importance factor (IFc) affected by arterial blockage. But the IFc of non-Newtonian fluid for 3D left coronary artery bifurcation model decreases with increasing bifurcation angle and the time-averaged inlet pressure is the least for smaller bifurcation angles. The current research further concentrates that the flow separation length reduces with developing bifurcation angle in bifurcated geometry. It is significant to mention that non-Newtonian blood flow model incorporating hemodynamic and diagnostic parameters has great impacts on instantaneous flow systems.

Effect of stenosis shape on the sound emitted from a constricted blood vessel

Effect of stenosis shape on the post-stenotic pressure fluctuations and the sound emitted from a constricted blood vessel is studied numerically. Large eddy simulations are performed using OpenFOAM under pulsatile flow conditions with a non-Newtonian fluid model. Findings indicate that the high slope at the stenosis entrance and overlap of more than one stenosis shorten the length of the flow jet, trigger turbulence, and increase vortical activity, turbulent kinetic energy, and magnitude of pressure fluctuations at the post-stenotic region. Also, these morphological parameters strengthen the audible signal especially in the systolic phase of the pulsatile flow. On the other hand, asymmetry of the stenosis creates an opposite effect. Based on the wall pressure data, it is shown that the stenosis shape affects the intensity and the pattern of the murmurs generated. Stenosis shape is found to be an essential factor for the acoustic-based non-invasive diagnosis of stenosis. Graphical abstract Wall pressure content of the elliptic stenosis shape.

Computation of hemodynamics in eccentric coronary stenosis: A morphological parametric study

BACKGROUND

Flow recirculation occurs in eccentric coronary stenosis, which can lead to adverse outcome. The complex local geodesic patterns of eccentric stenosis are critical factors in determining the flow characteristics in post-stenotic flow.

OBJECTIVE

The main objective of this study is to relate the relationship between the detailed morphological parameters in eccentric coronary stenosis and the post-stenotic flow characteristics.

METHODS

Several idealized eccentric coronary stenosis models with variable morphological parameters are created to conduct a series of computational fluid dynamics analysis. The impact of four specific lesion morphological parameters, eccentricity index (EI), diameter stenosis (DS), stenosis length (SL) and shape of lesion, are investigated.

RESULTS

When EI is small (< 0.33), the length of recirculation zones would increase as EI increase; while when EI is large (> 0.33), it would decreased as EI increase; Larger magnitude of retrograde flow occurs in models with smaller EIs. Both the recirculation zone length and maximum shear rate increase significantly as DS increases. Increase of SL will lead to increase of recirculation zone length. Higher maximum shear rate and larger recirculation zone are observed in models with sharper stenosis shape.

CONCLUSIONS

Except DS, the detailed geometry patterns (EI, SL and shape of the stenosis) also have great impact on post-stenotic flow behaviors in eccentric coronary stenosis.

Mathematical modeling of micropolar fluid flow through an overlapping arterial stenosis

In this study a mathematical model for two-dimensional pulsatile blood flow through overlapping constricted tapered vessels is presented. In order to establish resemblance to the in vivo conditions, an improved shape of the time-variant overlapping stenosis in the elastic tapered artery subject to pulsatile pressure gradient is considered. Because it contains a suspension of all erythrocytes, the flowing blood is represented by micropolar fluid. By applying a suitable coordinate transformation, tapered cosine-shaped artery turned into non-tapered rectangular and a rigid artery. The governing nonlinear partial differential equations under the imposed realistic boundary conditions are solved using the finite difference method. The effects of vessel tapering on flow characteristics considering their dependencies with time are investigated. The results show that by increasing the taper angle the axial velocity and volumetric flow rate increase and the microrotational velocity and resistive impedance reduce. It has been shown that the results are in agreement with similar data from the literature.

Effect of Pulsatile Flow Waveform and Womersley Number on the Flow in Stenosed Arterial Geometry

The salient hemodynamic flow features in a stenosed artery depend not only on the degree of stenosis, but also on its location in the circulatory system and the physiological condition of the body. The nature of pulsatile flow waveform and local Womersley number vary in different regions of the arterial system and at different physiological state, which affects the local hemodynamic wall parameters, for example, the wall shear stress (WSS) and oscillatory shear index (OSI). Herein, we have numerically investigated the effects of different waveforms and Womersley numbers on the flow pattern and hemodynamic parameters in an axisymmetric stenosed arterial geometry with 50% diametral occlusion. Temporal evolution of the streamlines and hemodynamic parameters are investigated, and the time-averaged hemodynamic wall parameters are compared. Presence of the stenosis is found to increase the OSI of the flow even at the far-downstream side of the artery. At larger Womersley numbers, the instantaneous flow field in the stenosed region is found to have a stronger influence on the flow profiles of the previous time levels. The study delineates how an approximation in the assumption of inlet pulsatility profile may lead to significantly different prediction of hemodynamic wall parameters.

Acoustic source separation for the detection of coronary artery sounds

Coronary artery disease (CAD) is the leading cause of death in the United States, being responsible for more than 20% of all deaths in the country. This is in large part due to the difficulty of diagnostic screening for CAD. Phonoangiography seeks to detect CAD via the acoustic signature associated with turbulent flow near an abnormally constricted, or stenosed, region. However, the usefulness of the technique is severely hindered by the low strength of the CAD signal compared to the background noise within the chest. In this work, acoustic finite element analysis (FEA) was performed on physiologically accurate chest geometries to demonstrate the feasibility of an original acoustic source separation methodology for isolating coronary sounds. This approach is based upon pseudoinversion of mixing matrices determined through a combination of experiment and computation. This allows calculation of the sound emitted by the coronary arteries based upon measurements of the acoustic velocity on the chest surface. This work demonstrates the feasibility of such a technique computationally and examines the vulnerability of the proposed approach to measurement errors.

Numerical simulation of unsteady generalized Newtonian blood flow through differently shaped distensible arterial stenoses

An updated numerical simulation of unsteady generalized Newtonian blood flow through differently shaped distensible arterial stenoses is developed. A shear-thinning fluid modelling the deformation dependent viscosity of blood is considered for the characterization of generalized Newtonian behaviour of blood. The arterial model is treated as two-dimensional and axisymmetric with an outline of the stenosis obtained from a three-dimensional casting of a mildly stenosed artery. The full Navier-Stokes equations governing blood flow are written in the dimensionless form and the solution is accomplished by finite time-step advancement through their finite difference staggered grid representations. The marker and cell (MAC) method comprising the use of a set of marker particles moving with the fluid is used for the purpose. Results are obtained for three differently shaped stenoses - irregular, smooth and cosine curve representations. The present results do agree well with those of existing investigations in the steady state, but contrary to their conclusions the present findings demonstrate that the excess pressure drop across the cosine and the smooth stenoses is caused by neither their smoothness nor their higher degree of symmetry relative to the irregular stenosis, but is rather an effect of area cover with respect to the irregular stenosis. This effect clearly prevails throughout the entire physiological range of Reynolds numbers. Further the in-depth study in flow patterns reveals the development of flow separation zones in the diverging part of the stenosis towards the arterial wall, and they are influenced by non-Newtonian blood rheology, distensibility of the wall and flow unsteadiness in order to validate the applicability of the present model.

Numerical modelling of simulated blood flow in idealized composite arterial coronary grafts: Transient flow

In composite arterial coronary grafts (CACGs), transport phenomena and geometry may considerably alter blood flow dynamics. CACGs aim at revascularizing pathological arteries according to the human anatomy. However, the exact mechanisms causing the failure of coronary bypass grafting are not yet well elucidated. In the present study, computational fluid dynamics (CFD) techniques are applied for the simulation of multi-branched CACGs under physiologically realistic inflow waveforms. The numerical solution is obtained by a finite-volume method formulated in non-orthogonal, curvilinear coordinates and a multi-grid approach. The geometrical models, consisting of idealized and rigid vessels, include the typical T- and a rather new pi-graft configuration. The stenotic effect is also investigated by comparing computational results for three different degrees of area constriction, namely 25%, 50% and 75%, as well as the case without stenosis. Different grafting distances and various inflow rate ratios are imposed, to give an insight into haemodynamical alterations of CACGs and to study the process of restenosis. The results focus on the interaction between the grafts and coronary flows in terms of spatial and temporal variations of velocity and wall shear stress (WSS) distribution. Prominent variations among the different geometries, concerning the velocity profiles and secondary flow motion, are shown. Moreover, the residual flow emerging from different degrees of area constriction shows that low and oscillating shear stresses may arise for even moderate stenotic fields.

Spatial and phasic oscillation of non-Newtonian wall shear stress in human left coronary artery bifurcation: an insight to atherogenesis

OBJECTIVE

To investigate the wall shear stress oscillation in a normal human left coronary artery bifurcation computational model by applying non-Newtonian blood properties and phasic flow.

METHODS

The three-dimensional geometry of the investigated model included the left main coronary artery along with its two main branches, namely the left anterior descending and the left circumflex artery. For the computational analyses a pulsatile non-Newtonian flow was applied. To evaluate the cyclic variations in wall shear stress, six characteristic time-points of the cardiac cycle were selected. The non-Newtonian wall shear stress variation was compared with the Newtonian one.

RESULTS

The wall shear stress varied remarkably in time and space. The flow divider region encountered higher wall shear stress values than the lateral walls throughout the entire cardiac cycle. The wall shear stress exhibited remarkably lower and oscillatory values in systole as compared with that in diastole in the entire bifurcation region, especially in the lateral walls. Although the Newtonian wall shear stress experienced consistently lower values throughout the entire cardiac cycle than the non-Newtonian wall shear stress, the general pattern of lower wall shear stress values at the lateral walls, particularly during systole, was evident regardless of the blood properties.

CONCLUSIONS

The lateral walls of the bifurcation, where low and oscillating wall shear stress is observed, are more susceptible to atherosclerosis. The systolic period, rather than the diastolic one, favors the development and progression of atherosclerosis. The blood viscosity properties do not seem to qualitatively affect the spatial and temporal distribution of the wall shear stress.

Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch

The pulsatile flow of non-Newtonian fluid in a bifurcation model with a non-planar daughter branch is investigated numerically by using the Carreau-Yasuda model to take into account the shear thinning behavior of the analog blood fluid. The objective of this study is to deal with the influence of the non-Newtonian property of fluid and of out-of-plane curvature in the non-planar daughter vessel on wall shear stress (WSS), oscillatory shear index (OSI), and flow phenomena during the pulse cycle. The non-Newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior. The non-planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of WSS along the vessel, in particular in systole phase. Downstream of the bifurcation, the velocity profiles are shifted toward the flow divider, and low WSS and high shear stress temporal oscillations characterized by OSI occur on the outer wall region of the daughter vessels close to the bifurcation. Secondary motions become stronger with the addition of the out-of-plane curvature induced by the bending of the vessel, and the secondary flow patterns swirl along the non-planar daughter vessel. A significant difference between the non-Newtonian and the Newtonian pulsatile flow is revealed during the pulse cycle; however, reasonable agreement between the non-Newtonian and the rescaled Newtonian flow is found. Calculated results for the pulsatile flow support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.

A mathematical description of blood spiral flow in vessels: application to a numerical study of flow in arterial bending

Local arterial haemodynamics has been associated with the pathophysiology of several cardiovascular diseases. The stable spiral blood-flows that were observed in vivo in several vessels, may play a dual role in vascular haemodynamics, beneficial since it induces stability, reducing turbulence in the arterial tree, and accounts for normal organ perfusion, but detrimental in view of the imparted tangential velocities that are involved in plaque formation and development. Being a spiral flow considered representative of the local blood dynamics in certain vessels, a method is proposed to quantify the spiral structure of blood flow. The proposed function, computed along a cluster of particle trajectories, has been tested for the quantitative determination of the spiral blood flow in a three-dimensional, s-shaped femoral artery numerical model in which three degrees of stenosis were simulated in a site prone to atherosclerotic development. Our results confirm the efficacy of the Lagrangian analysis as a tool for vascular blood dynamics investigation. The proposed method quantified spiral motion, and revealed the progression in the degree of stenosis, in the presented case study. In the future, it could be used as a synthetic tool to approach specific clinical complications.

Effects of elastic property of the wall on flow characteristics through arterial stenoses

Hemodynamic characteristics of blood flow through arterial stenoses are numerically investigated in this work. The blood is assumed as a Newtonian fluid and the pulsatile nature of flow is modeled by using measured values of the flowrate and pressure for the canine femoral artery. An isotropic elastic and incompressible material is assumed for the wall at each axial section, but a non-uniform distribution of the shear modulus in axial direction is used to model the high stiffness of the wall at the stenosis location. Full Navier equations for a thick wall are used as the governing equations for the wall displacements. A continuous grid extending over the flow field and the wall is considered and governing equations are transformed for use in the computational domain. Discretized forms of the transformed wall and flow equations, which are coupled through the boundary conditions at their interface, are obtained by control volume method and simultaneously solved using the well-known SIMPLER algorithm. To study the effects of wall deformability, solutions are obtained for both rigid and elastic walls. The results indicate that deformability of the wall causes an increase in the time average of pressure drop, but a decrease in the maximum wall shear stress. Displacement and stress distributions in the wall are presented.

Blood flow modeling in carotid arteries with computational fluid dynamics and MR imaging

RATIONALE AND OBJECTIVES

The authors' goal was to develop a noninvasive method for detailed assessment of blood flow patterns from direct in vivo measurements of vessel anatomy and flow rates.

MATERIALS AND METHODS

The authors developed a method to construct realistic patient-specific finite element models of blood flow in carotid arteries. Anatomic models are reconstructed from contrast material-enhanced magnetic resonance (MR) angiographic images with a tubular deformable model along each arterial branch. A surface-merging algorithm is used to create a watertight model of the carotid bifurcation for subsequent finite element grid generation, and a fully implicit scheme is used to solve the incompressible Navier-Stokes equations on unstructured grids. Physiologic boundary conditions are derived from cine phase-contrast MR flow velocity measurements at two locations below and above the bifurcation. Vessel wall compliance is incorporated by means of fluid-solid interaction algorithms.

RESULTS

The method was tested on imaging data from a healthy subject and a patient with mild stenosis. Finite element grids were successfully generated, and pulsatile blood flow calculations were performed. Computed and measured velocity profiles show good agreement. Flow patterns and wall shear stress distributions were visualized.

CONCLUSIONS

Patient-specific computational fluid dynamics modeling based on MR images can be performed robustly and efficiently. Preliminary validation studies in a physical flow-through model suggest that the model is accurate. This method can be used to characterize blood flow patterns in healthy and diseased arteries and may eventually help physicians to supplement imaging-based diagnosis and predict and evaluate the outcome of interventional procedures.