Numerical Simulation Of Blood Flow Research Articles

Unresolved RBCs: An upscaling strategy for the CFD-DEM simulation of blood flow with deformable cells

Numerical simulation of blood flow is a challenging topic due to the multiphase nature of this biological fluid. The choice of a specific method among the ones available in literature is often motivated by the physical scale of interest. Single-phase approximation allows for lower computational time, but does not consider this multiphase nature. Cell-level simulation, on the other hand, requires high computational resources and is limited to small scales. This work proposes a scale-up approach for cell-level simulation of blood flow, in the framework of unresolved CFD-DEM technique. This method offers the possibility to simulate hundreds of thousands of particles with limited computational effort, but requires specific models for fluid–particle interactions. Regarding blood flow, drag and lift force acting on the red blood cells (RBCs) are responsible for several macroscopic blood characteristics. Despite several correlations available for drag and lift force acting on rigid particles, specific force models for the simulation of deformable particles compatible with RBCs physics are missing. This study employs data obtained from cell-level simulations to derive equations then used in unresolved simulation of RBCs. The strategy followed during the modeling phase is presented, together with the model verification and validation. This approach returns satisfying results when used to simulate blood flow in large-scale channels. Up to half a million RBCs are considered, and computational effort is reported to allow a comparison with other existing methods. Future perspectives include further improvement of the model, such as a deeper understanding of particle–particle interactions.

Numerical simulation of blood flow in coronary bifurcation

A numerical simulation of blood flow in a Y-shaped coronary artery was executed by constructing ideal geometric models. The influences of bifurcation angle, the initial velocity of inlet blood flow, and the diameter ratio of bifurcated vessels on the blood flow velocity field, wall shear stress, wall pressure, etc. were analyzed. The blood velocity at the bifurcation of the blood vessel was slower, while the wall shear stress and wall pressure value were higher. The wall shear stress and wall pressure increased with the increase of blood flow velocity at the entrance. Greater bifurcation angle led to higher wall shear stress. With the increase of the diameter ratio of the two branches, the maximum value of the shear stress became smaller. The probability of thrombosis formation increases as the diameter ratio increases. The numerical results showed that the bifurcation of the blood vessel is the optimal place to form the thrombosis.

Hemodynamic Study of Cerebral Arteriovenous Malformation: Newtonian and Non-Newtonian Blood Flow

ObjectiveArteriovenous malformation is a disease of the vascular system that occurs mainly in the cerebral arteries and spine. Numerical simulation as a powerful method is used to investigate the Cerebral Arteriovenous Malformation hemodynamic after occlusion of the abnormality step by step by embolization. MethodsThe CT Angiographic imaging data of two patients are used and a geometric model is extracted by the Mimics software. Numerical simulation of blood flow is performed in both Newtonian and non-Newtonian models. The Navier–Stokes, and continuity governing equations are solved by finite element method using the COMSOL Multiphysics software (the commercial computational fluid dynamics (CFD) simulation software). To validate the numerical results, the real data on blood flow rate in the feeding artery and draining veins are used, as well as angiographic images at different times. ResultsRegarding the comparison of pressure contours for different occlusions of 0, 30, 50, and 90%, by increasing the amount of occlusion in the nidus, there is an increase in the blood pressure. Regarding the comparison of the blood flow velocity in the feeding artery, draining veins, and inside the AVM nidus for Newtonian and non-Newtonian models, there is a significant difference between these two simulations in vessels with smaller dimensions (such as vessels inside the nidus). ConclusionBy increasing the amount of nidus occlusion, the blood pressure is increased, so the blood supply process is better. According to a significant difference between the Newtonian and non-Newtonian simulations in vessels with smaller dimensions (such as vessels inside the nidus), therefore, non-Newtonian simulation should be done for different occlusions of 30, 50, and 90%.

NUMERICAL SIMULATIONS OF BLOOD FLOW THROUGH LEFT VENTRICLE USING SPH AND FVM METHODS – A COMPARATIVE STUDY

This paper presents a comparative analysis of numerical simulations of blood flow through the left ventricle using SPH (LS-DYNA) and FVM (Ansys Fluent) solvers. Numerical simulations based on SPH and FVM methods can provide a more comprehensive understanding of cardiac blood flow patterns. In Fluent, left ventricle walls were modeled as boundary conditions with zero fluid velocity, while in the LS-DYNA software the walls were modeled with fixed particles. Boundary conditions were also prescribed on the appropriate regions (inlet, outlet, symmetry). In both programmes, inlet and outlet velocities were defined using table functions corresponding to the real cardiac cycle. For generating fluid flow in SPH, injection particles at mitral valve and deactivation planes at aortic semilunar valve were used. Numerical analysis results are given comparatively in both cases at the corresponding times. By comparing the results, it can be concluded that SPH can be efficiently used for the analysis of blood flow through the left ventricle. Although the modeling procedure, as well as the calculation itself, takes much longer to execute using SPH, this method offers possibilities such as studying FSI phenomena or tracking the movement of particles through the fluid domain.

Simulation of blood flow in a stenosed and bifurcating artery using Finite Volume Methods and OpenFOAM

The article focuses on the shear-thinning and viscoelastic constitutive modelling and numerical simulation of blood flow in a stenosed and bifurcating artery. Specifically, the shear-thinning and viscoelastic behaviour of blood are modelled and implemented via the Oldroyd-B and Generalized Oldroyd-B constitutive models. A robust and efficient general purpose numerical (and computational) methodology for the simulation of blood flow in a stenosed and bifurcating artery is also developed and implemented. The numerical algorithm is developed more generally to resolve the mathematical model equations arising out of the all-encompassing Generalized Giesekus constitutive model. This model reduces to the Generalized Oldroyd-B model and subsequently also to the standard Oldroyd-B model simply by switching off certain material parameters. The inclusion of the Generalized Giesekus model must therefore be viewed in this context, to facilitate the development of an all encompassing general purpose numerical code. The blood flow modelling is otherwise done via the Oldroyd-B and Generalized Oldroyd-B constitutive models. The shear-thinning effects are implemented via the Cross model for shear-viscosity. The Generalized Oldroyd-B model results all illustrate that the velocity is directly proportional to the constriction caused by the stenosis. The higher the blockage from the constriction, the higher would the velocity spurt through the constriction. This velocity behaviour correspondingly enhances the wall shear-stresses as the constriction increases, caused by the presence of the stenosis. High wall shear-stresses greatly increase the possibility of rupture of the stenosis. This can lead to catastrophic consequences in the usual case where the stenosis is caused, say, by tumor growth. As demonstrated near the contraction of a standard 4:1 contraction flow geometry, dramatic fluid flow effects, which are attributable to the polymeric-stresses, specifically to the first normal stress difference, are observed in the vicinity of the constrictions resulting from the presence of the stenosis. Such effects, include, flow recirculation and reversal, vortex formation, and spurt phenomena.

Numerical Simulation of Blood Flow in Aortoiliac Bifurcation with Increasing Degree of Stenosis

The worldwide lethal prevalence of atherosclerotic diseases has made it a crucial topic of research, the descending aorta is a major artery with complex geometry involving curvature, branches, and bifurcation leading to common iliac arteries. This paper aims to scrutinize the intricate blood flow patterns and the flow parameters with the increasing degree of stenosis in the infrarenal aorta, which has been accomplished through computational fluid dynamics modeling. A 3D CAD model of the healthy aortoiliac bifurcation was constructed from MR images, and three diseased models with 32%, 47%, and 71% occlusion in the infrarenal aorta region were constructed. At the inlet, pulsatile velocity and at the outlet pressure boundary conditions were applied, blood was considered Newtonian and turbulence was modeled using Large Eddy Simulation (LES). The numerical simulation was carried out using finite volume method on ANSYS. The predicted hemodynamic parameters like velocity, wall shear stress (WSS), oscillating shear index (OSI), Q-Criterion and turbulence intensity were post-processed for all the models, the analysis of which provides an insight into the myriad processes involved in the inception and evolution of atherosclerosis. The transition of blood flow from laminar to turbulent with increase in the degree of stenosis is a very eminent feature of this study, turbulence is identified in cases with 47%, and 71% occlusion and is dominant in the latter.

Endoscopic balloon dilation of a stenosed artery stenting via cfd tool open-foam: Physiology of angioplasty and stent placement

The blood flow analysis inside an arterial segment of the left main coronary artery having stenosis is mathematically modeled. Numerical simulations are provided for the very first time for two considered cases that cover the thorough process of angioplasty and stent placement inside a coronary artery having symmetric stenosis. Firstly, the numerical simulations are disclosed for the section of a stenosed artery having a catheter placed inside it with a balloon plus stent over it. The second case covers the numerical simulations of blood flow inside the artery after a stent is placed that keeps the artery wide open and minimizes the effect of stenosis. Thus, the prime novelty of this work entertains the thorough mathematical modeling and FVM based numerical simulations for angioplasty of a coronary artery having a symmetric shape of stenosis. The current research work is modeled for the non-Newtonian Casson fluid to consider a more realistic approach of blood flow. This computational fluid dynamics (CFD) analysis is interpreted through the free source CFD C++ toolbox Open-FOAM. Numerical solutions are provided by using Open-FOAM that works on the principle of finite volume method. The detailed graphical results are disclosed for the process of angioplasty in addition to the simulation work obtained after completion of angioplasty and stent placement. The work provided is beneficial for surgical interpretations, detecting location of stenosis, place the balloon and stent at exact location via catheter, minimizing the effect of stenosis by placing a stent inside the artery, reducing the experimental cost by using simulations data. The catheter and balloon is removed after angioplasty, and the stent keeps the artery wide open to normalize the blood flow. Eventually, the coronary artery disease (CAD) is cured through this angioplasty and the risk of a heart attack is eliminated. A more developed and easily passing blood flow is revealed after the placement of stent.

Comparative analysis of numerical simulations of blood flow through the segment of an artery in the presence of stenosis

Comparative analysis of numerical simulations of blood flow through the segment of an artery in the presence of stenosis

Data-driven generation of 4D velocity profiles in the aneurysmal ascending aorta

Background and Objective: Numerical simulations of blood flow are a valuable tool to investigate the pathophysiology of ascending thoratic aortic aneurysms (ATAA). To accurately reproduce in vivo hemodynamics, computational fluid dynamics (CFD) models must employ realistic inflow boundary conditions (BCs). However, the limited availability of in vivo velocity measurements, still makes researchers resort to idealized BCs. The aim of this study was to generate and thoroughly characterize a large dataset of synthetic 4D aortic velocity profiles sampled on a 2D cross-section along the ascending aorta with features similar to clinical cohorts of patients with ATAA.Methods: Time-resolved 3D phase contrast magnetic resonance (4D flow MRI) scans of 30 subjects with ATAA were processed through in-house code to extract anatomically consistent cross-sectional planes along the ascending aorta, ensuring spatial alignment among all planes and interpolating all velocity fields to a reference configuration. Velocity profiles of the clinical cohort were extensively characterized by computing flow morphology descriptors of both spatial and temporal features. By exploiting principal component analysis (PCA), a statistical shape model (SSM) of 4D aortic velocity profiles was built and a dataset of 437 synthetic cases with realistic properties was generated.Results: Comparison between clinical and synthetic datasets showed that the synthetic data presented similar characteristics as the clinical population in terms of key morphological parameters. The average velocity profile qualitatively resembled a parabolic-shaped profile, but was quantitatively characterized by more complex flow patterns which an idealized profile would not replicate. Statistically significant correlations were found between PCA principal modes of variation and flow descriptors.Conclusions: We built a data-driven generative model of 4D aortic inlet velocity profiles, suitable to be used in computational studies of blood flow. The proposed software system also allows to map any of the generated velocity profiles to the inlet plane of any virtual subject given its coordinate set.

Classification of Blood Rheological Models through an Idealized Symmetrical Bifurcation

The assumed rheological behavior of blood influences the hemodynamic characteristics of numerical blood flow simulations. Until now, alternative rheological specifications have been utilized, with uncertain implications for the results obtained. This work aims to group sixteen blood rheological models in homogeneous clusters, by exploiting data generated from numerical simulations on an idealized symmetrical arterial bifurcation. Blood flow is assumed to be pulsatile and is simulated using a commercial finite volume solver. An appropriate mesh convergence study is performed, and all results are collected at three different time instants throughout the cardiac cycle: at peak systole, early diastole, and late diastole. Six hemodynamic variables are computed: the time average wall shear stress, oscillatory shear index, relative residence time, global and local non-Newtonian importance factor, and non-Newtonian effect factor. The resulting data are analyzed using hierarchical agglomerative clustering algorithms, which constitute typical unsupervised classification methods. Interestingly, the rheological models can be partitioned into three homogeneous groups, whereas three specifications appear as outliers which do not belong in any partition. Our findings suggest that models which are defined in a similar manner from a mathematical perspective may behave substantially differently in terms of the data they produce. On the other hand, models characterized by different mathematical formulations may belong to the same statistical group (cluster) and can thus be considered interchangeably.

A highly parallel fully implicit domain decomposition method for the simulation of the hemodynamics of a patient-specific artery at the full-body scale

The numerical simulation of blood flows in the human body with a certain level of clinical accuracy is important for the understanding of the human physiology. The success of the modeling relies on a robust numerical method with the corresponding software that can handle the complex geometry, the complex fluid flows and run efficiently on a supercomputer. In this work, we introduce a highly parallel domain decomposition method to solve the three-dimensional incompressible Navier-Stokes equations on a patient-specific artery at the full-body scale from neck to feet with 222 outlets and a minimum diameter around 1.0 mm. A locally refined, unstructured mesh is used to resolve the complex fluid flow. Moreover, a two-level method is introduced to determine the model parameters in the Windkessel outlet boundary condition to guarantee clinically correct flow distributions to 14 major regions. A fully implicit Newton-Krylov-Schwarz method is used to solve the nonlinear algebraic system at each time step and numerical experiments show that the proposed method is robust with respect to the complex geometry, the graph-based partition of the complex mesh, the ill-conditioned sparse systems with locally dense blocks, and different model parameters and is scalable with up to 15,360 processor cores. With the proposed method, one simulation of the blood flow in a full-body arterial network can be obtained in about 8 hours per cardiac cycle, which enables its potential use in a wide range of clinical scenarios.

Influence of right coronary artery motion, flow pulsatility and non-Newtonian rheology on wall shear stress metrics.

The patchy distribution of atherosclerosis within the arterial system is consistent with a controlling influence of hemodynamic wall shear stress (WSS). Patterns of low, oscillatory and transverse WSS have been invoked to explain the distribution of disease in the aorta. Disease of coronary arteries has greater clinical importance but blood flow in these vessels may be complicated by their movement during the cardiac cycle. Previous studies have shown that time average WSS is little affected by the dynamic geometry, and that oscillatory shear is influenced more. Here we additionally investigate effects on transverse WSS. We also investigate the influence of non-Newtonian blood rheology as it can influence vortical structure, on which transverse WSS depends; Carreau-Yasuda models were used. WSS metrics were derived from numerical simulations of blood flow in a model of a moving right coronary artery which, together with a subject-specific inflow waveform, was obtained by MR imaging of a healthy human subject in a previous study. The results confirmed that time average WSS was little affected by dynamic motion and that oscillatory WSS was more affected. They additionally showed that transverse WSS and its non-dimensional analogue, the Cross Flow Index, were affected still further. This appeared to reflect time-varying vortical structures caused by the changes in curvature. The influence of non-Newtonian rheology was significant with some physiologically realistic parameter values, and hence may be important in certain subjects. Dynamic geometry and non-Newtonian rheology should be incorporated into models designed to produce maps of transverse WSS in coronary arteries.

A geometric multiscale model for the numerical simulation of blood flow in the human left heart

<p style='text-indent:20px;'>We present a new computational model for the numerical simulation of blood flow in the human left heart. To this aim, we use the Navier-Stokes equations in an Arbitrary Lagrangian Eulerian formulation to account for the endocardium motion and we model the cardiac valves by means of the Resistive Immersed Implicit Surface method. To impose a physiological displacement of the domain boundary, we use a 3D cardiac electromechanical model of the left ventricle coupled to a lumped-parameter (0D) closed-loop model of the remaining circulation. We thus obtain a one-way coupled electromechanics-fluid dynamics model in the left ventricle. To extend the left ventricle motion to the endocardium of the left atrium and to that of the ascending aorta, we introduce a preprocessing procedure according to which an harmonic extension of the left ventricle displacement is combined with the motion of the left atrium based on the 0D model. To better match the 3D cardiac fluid flow with the external blood circulation, we couple the 3D Navier-Stokes equations to the 0D circulation model, obtaining a multiscale coupled 3D-0D fluid dynamics model that we solve via a segregated numerical scheme. We carry out numerical simulations for a healthy left heart and we validate our model by showing that meaningful hemodynamic indicators are correctly reproduced.</p>

Effect of aneurysmatic artery on blood flow having permeability in human organ

Blood flow in a double aneurysmatic artery of the normal tissue is studied. A Finite Element method is used to analyze numerical simulation of blood flow through aneurysmatic arteries. The Newtonian, generalized Newtonian, Oldroyd-B and generalized Oldroyd-B models are considered due to the behavior of blood viscosity. In this paper, the effect of aneurysmatic artery on blood flow with permeability in human organ has been investigated. The non-Newtonian models have been applied to study the blood velocity, pressure, and wall shear stress in an aneurysmatic artery. A set of partial differential equations are transformed into dimensionless equations using non-dimensional variables and solved numerically. We have focused our consideration on the simulation of blood velocity and pressure in terms of blood flow rate for various Weissenberg numbers (Wi) and Peclet numbers (Pe). The important effects on blood flow of aneursymatic artery for blood velocity, pressure and wall stress profiles are presented graphically for Newtonian and non-Newtonian models.

Numerical simulation of blood flow in Cerebral aneurysms using two-phase model

ABSTRACT: Computational fluid dynamic (CFD) simulation techniques have played an essential role in simulating and understanding the initiation, growth, and rupture of cerebral aneurysms. Hemodynamic parameters are mainly used to examine the rupture risk status of cerebral aneurysms using blood flow CFD simulation. Blood was considered as single-phase flow model with both Newtonian and non-Newtonian to predict the rupture risk analysis. However, to better understand predicting the risk of cerebral aneurysm rupture, blood requires two-phase, such as plasma and red blood cells (RBCs), also known as erythrocytes. In this study, the two-phase blood flow model was solved by the discrete phase model (DPM) with Lagrangian approach, in which blood was modeled two-phase fluid as a continuous phase plasma and particulate phase RBCs. Three patient-specific aneurysm geometries have been selected to determine wall shear stress (WSS), oscillatory shear index (OSI), and relative residence time (RRT) with two-phase blood flow simulation. To analyze the velocity distribution inside the aneurysms, velocity streamlines and surface velocities were reported. The pulsatile blood flow simulation was performed for aneurysm geometries, where the mean inlet Reynolds number was calculated between 490 and 1370. The value of WSS, OSI, and RRT was quantified based on the Reynolds number. Reynolds number's minimum value indicates the low WSS, low OSI, and short RRT, and the maximum value of Reynolds number shows the high WSS, high OSI, and long RRT. The high WSS, high OSI, and long RRT, velocity streamlines distribution, surface velocity changes were determined with two-phase blood in aneurysm geometries, aneurysm geometry one and three are the medium and giant size saccular aneurysm may have a higher risk of rupture while aneurysm geometry two is medium size fusiform aneurysm has a lower risk of rupture. The two-phase blood flow model presents reasonable hemodynamic parameters that correlate with aneurysms rupture risk prediction.

Numerical Simulation of Blood Flows in Patient-specific Abdominal Aorta with Primary Organs.

The abdominal aorta is the largest artery in the abdominal cavity that supplies blood flows to vital organs through the complex visceral arterial branches, including the celiac trunk (the liver, stomach, spleen, etc.), the renal arteries (the kidneys) and the superior and inferior mesenteric arteries (the small and large intestine, pancreas, etc.). An accurate simulation of blood flows in this network of arteries is important for the understanding of the hemodynamics in various organs of healthy and diseased patients, but the computational cost is very high. As a result, most researchers choose to focus on a portion of the artery or use a low-dimensional approximation of the artery. In the present work, we introduce a parallel algorithm for the modeling of pulsatile flows in the abdominal aorta with branches to the primary organs, and an organ-based two-level method for calculating the resistances for the outflow boundary conditions. With this highly parallel approach, the simulation of the blood flow for a cardiac cycle of the anatomically detailed aorta can be obtained within a few hours, and the blood distribution to organs including liver, spleen and kidneys are also computed with certain accuracy. Moreover, we discuss the significant hemodynamic differences resulted from the influence of the peripheral branches. In addition, we examine the accuracy of the results with respect to the mesh size and time-step size and show the high parallel scalability of the proposed algorithm with up to 3000 processor cores.

Numerical Studies of Blood Flow in Left Coronary Model

Introduction: Artery blockage is the most prevailing cause of Coronary Artery Disease (CAD). The presence of blockage inside the artery breaks the continuity of blood supply to the other part of the body and therefore causes for heart attack. Objective: Two different three-dimensional models namely; normal and 50% plaque are used for the numerical studies. Five inlet velocities 0.10, 0.20, 0.50, 0.70 and 0.80 m/s are considered corresponding to different blood flow conditions to study the effect of velocity on the human heart. Methods: Finite Volume Method (FVM) based Computational Fluid Dynamics (CFD) technique is executed for the numerical simulation of blood flow. Hemodynamic factors are computed and compared for the two geometrical models (Normal Vs. Blockage model). Results: Blood hemodynamic factor i.e. Area Average Wall Shear Stress (AAWSS) ranges from 4.1-33.6 Pa at the façade of the Left Anterior Descending (LAD) part of the Left Coronary Artery (LCA) for the constricted artery. Conclusion: The predominantly low WSS index is analogous to the normal artery affirms the existence of plaque. From the medical point of view, this can prove as an excellent factor for early diagnosis of CAD. Therefore, a hindrance can be created in the increasing frequency of Myocardial Infarction (MI). In future research we will adopt the unsteady flow with both rigid and elastic arterial wall.

Y型分叉狭窄动脉血管中血液流动的数值模拟

Y型分叉狭窄动脉血管中血液流动的数值模拟

Abstract 15940: Wall Shear Stress and Vorticity in Atrial Fibrillation, Pulmonary Hypertension, and Normal Atrial Anatomy Models

Introduction: Atrial fibrillation (AF) is a common cardiac rhythm disorder that is often comorbid with pulmonary hypertension (PH) and other conditions associated with abnormal atrial pressure and/or volume overload. In the setting of atrial dilation, mechanoelectric feedback has been linked to the development of ectopic beats that trigger paroxysmal AF mainly originating from pulmonary veins (PVs). However, the precise mechanisms remain poorly understood. Here, we aimed to characterize atrial wall shear stress (WSS) and vorticity in the left atrium of AF, healthy, and at-risk for AF (PH) patient models to develop predictors of AF risk. Methods: Magnetic resonance imaging and computed tomography data (10 AF, 10 PH, and 10 healthy volunteers) were obtained retrospectively. The left atria were manually segmented from each data set. Four-dimensional flow MRI was performed on one patient to derive PV flow data. The 30 atrial geometries and PV flow conditions were used to run numerical blood flow simulations, and atrial WSS and blood flow vorticity were analyzed. Results: As seen in Figure 1, wall shear stress was highest near the PV roots and on the posterior atrial wall, the most common sources of AF triggers. Average WSS and vorticity were significantly lower in PH patients than in both the healthy (p=0.003(WSS), p=0.011(vorticity)) and AF (p=0.046(WSS), p=0.069(vorticity)) groups. Both WSS (r=-0.66) and vorticity (r=-0.68) were moderately correlated to atrial volume in the PH group. Atrial volume was significantly larger in PH (p<0.001) and AF (p<0.001) groups than in the healthy group. Conclusions: The larger atrial volumes of PH and AF patients lead to altered flow profiles and less frequently flow jet impingement on the atrial wall models, leading to abnormal vorticity and WSS profiles. These long term flow abnormalities may influence the development and/or localization of electrical abnormalities and AF; although further study is needed to confirm this hypothesis.

Numerical Simulation of Blood Flow in a Vessel by Using COMSOL Multiphysics® Software

Dynamics of the blood flow play an important role in the development and treatment of cardiovascular diseases. In recent decades, blood flow simulation has been widely used to better understand the symptomatic spectrum of different diseases, in order to improve existing or develop new therapeutic techniques. Numerical simulation for biomagnetic fluid (such as blood) flow through a tube with rectangular cross section under the influence of magnetic field is studied in this work. Blood considered as a magnetic and incompressible fluid. The magnetic field effects on the blood stream in a tube are created by a permanent magnet outside the tube. The equations of motion which describe the flow is governed by the combination of magnetic equations for permanent magnet and Navier-Stokes equation for fluid (blood) were solved numerically by using COMSOL Multiphysics® Modeling Software.