Numerical Simulation Of Blood Flow Research Articles

Numerical Simulation of Red Blood Cell-Induced Platelet Transport in Saccular Aneurysms

We present a numerical simulation of blood flow in two aneurysmal vessels. Using a multicomponent continuum approach, called mixture theory, the velocity fields and spatial distribution of the red blood cells (RBCs) and the plasma are predicted. Platelet migration is described by a convection-diffusion equation, coupled to the RBC concentration field. The model is applied to study a two-dimensional straight vessel and multiple two-dimensional aneurysm vessels with different neck sizes. The model accurately predicts the enrichment of the platelets near the wall in the straight vessel, agreeing with the experimental measurement quantitatively. The numerical results also show that the near-wall enrichment of the platelets in the parent vessel highly influences the platelet concentration within the aneurysm. The results also indicate that the platelet concentration within the aneurysm increases with Reynolds number and decreases with a smaller neck size. This might have significance on the formation of thrombus (blood clot) within the aneurysm, which in turn may have a protective effect on preventing ruptures. Based on the success with the problems studied, we believe the current model can be a useful tool for analyzing the blood flow and platelets transport within patient specific aneurysms in the future.

Blood Flow Simulation in Patient-Specific Segmented Hepatic Arterial Tree

PurposeSelective Internal Radiation Therapy is an emerging, minimally invasive therapy of liver cancer. Millions of microspheres are injected through a catheter into tumor vascular supply. Microspheres distribution in liver is strongly dependent on patient's arteries geometry and catheter tip positioning, which is currently chosen by the physician based on qualitative image interpretation. A patient-specific numerical simulation of blood flow would have a crucial importance in therapy optimization, allowing in-silico research of microspheres trajectories. Material and methodsWe developed a procedure to segment patient's hepatic arterial vasculature with a Hessian based approach on 3D angiography, and to perform blood flow numerical simulation in the extracted geometry with ANSYS Fluent. In vivo blood velocity measurements were performed using phase contrast MRI to constrain these simulations. ResultsFlow results in the larger vessels are coherent with literature, but very little is known for smaller arteries: simulation results are compared to velocity measures on hepatic arteries down to 2.2 mm of diameter on phase contrast MRI, which gave encouraging results for validation. ConclusionA viable procedure for arteries segmentation and patient-specific blood flow simulation is proposed, phase contrast MRI allowing for tuning and validation of velocity values. The proposed personalized blood flow simulation is compulsory for the simulation of microspheres trajectories in the aim of tumor targeting.

Rôle of contrast media viscosity in altering vessel wall shear stress and relation to the risk of contrast extravasations

Iodinated contrast media (CM) are the most commonly used injectables in radiology today. A range of different media are commercially available, combining various physical and chemical characteristics (ionic state, osmolality, viscosity) and thus exhibiting distinct in vivo behaviour and safety profiles. In this paper, numerical simulations of blood flow with contrast media were conducted to investigate the effects of contrast viscosity on generated vessel wall shear stress and vessel wall pressure to elucidate any possible relation to extravasations. Five different types of contrast for Iodine fluxes ranging at 1.5–2.2gI/s were modelled through 18G and 20G cannulae placed in an ideal vein at two different orientation angles. Results demonstrate that the least viscous contrast media generate the least maximum wall shear stress as well as the lowest total pressure for the same flow rate. This supports the empirical clinical observations and hypothesis that more viscous contrast media are responsible for a higher percentage of contrast extravasations. In addition, results support the clinical hypothesis that a catheter tip directed obliquely to the vein wall always produces the highest maximum wall shear stress and total pressure due to impingement of the contrast jet on the vessel wall.

Modified Navier–Stokes equations for the outflow boundary conditions in hemodynamics

We present a new approach for the outflow boundary conditions of Navier–Stokes equations in hemodynamics. We first describe some existing 3D–0D coupling methods and highlight benefits and disadvantages of each of them. We then introduce a new method that consists in adding a 3D artificial part where the Navier–Stokes equations are modified to obtain an equivalent energy balance to a standard coupling with a 3-element Windkessel model. We investigate theoretically the stability of the system and compare it to previously introduced methods. Finally we compare these coupling methods for numerical simulations of blood flow in three patient-specific models, which represent different flow regimes in the pulmonary and systemic circulations. The new method, especially in its hybrid form, is a possible alternative to existing methods. It can be in particular convenient in codes that do not allow users to implement non-standard boundary conditions.

Alterations of Blood Flow Through Arteries Following Atherectomy and the Impact on Pressure Variation and Velocity.

Simulations were made of the pressure and velocity fields throughout an artery before and after removal of plaque using orbital atherectomy plus adjunctive balloon angioplasty or stenting. The calculations were carried out with an unsteady computational fluid dynamic solver that allows the fluid to naturally transition to turbulence. The results of the atherectomy procedure leads to an increased flow through the stenotic zone with a coincident decrease in pressure drop across the stenosis. The measured effect of atherectomy and adjunctive treatment showed decrease the systolic pressure drop by a factor of 2.3. Waveforms obtained from a measurements were input into a numerical simulation of blood flow through geometry obtained from medical imaging. From the numerical simulations, a detailed investigation of the sources of pressure loss was obtained. It is found that the major sources of pressure drop are related to the acceleration of blood through heavily occluded cross sections and the imperfect flow recovery downstream. This finding suggests that targeting only the most occluded parts of a stenosis would benefit the hemodynamics. The calculated change in systolic pressure drop through the lesion was a factor of 2.4, in excellent agreement with the measured improvement. The systolic and cardiac-cycle-average pressure results were compared with measurements made in a multi-patient study treated with orbital atherectomy and adjunctive treatment. The agreements between the measured and calculated systolic pressure drop before and after the treatment were within 3%. This excellent agreement adds further confidence to the results. This research demonstrates the use of orbital atherectomy to facilitate balloon expansion to restore blood flow and how pressure measurements can be utilized to optimize revascularization of occluded peripheral vessels.

Numerical simulation of blood flow through a capillary using a non-linear viscoelastic model.

In this article, a periodic developing blood flow in a capillary is simulated using a non-linear viscoelastic model for the first time. Here, the Giesekus model is used as the constitutive equation, and based on the experimental data, the best value for the mobility factor and zero shear rate viscosity are derived. The numerical solution of the problem is obtained using the finite volume method. The algorithm of the solution is pressure implicit with splitting of operators (PISO). The simulation carried out using the Giesekus, Oldroyd-B and Newtonian models and the results indicate that the Giesekus model presents a more accurate solution for the stress and velocity fields than the Newtonian and Oldroyd-B models. The previous studies on this problem were restricted to the linear and quasi-linear viscoelastic models. It is shown that only non-linear viscoelastic models can accurately describe the experimental data of unsteady blood flow in capillaries.

A shallow water with variable pressure model for blood flow simulation

We performed numerical simulations of blood flow in arteries with a variable stiffness and cross-section at rest using a finite volume method coupled with a hydrostatic reconstruction of the variables at the interface of each mesh cell. The method was then validated on examples taken from the literature. Asymptotic solutions were computed to highlight the effect of the viscous and viscoelastic source terms. Finally, the blood flow was computed in an artery where the cross-section at rest and the stiffness were varying. In each test case, the hydrostatic reconstruction showed good results where other simpler schemes did not, generating spurious oscillations andnonphysical velocities.

Numerical study of the non-Newtonian blood flow in a stenosed artery using two rheological models

The numerical simulation of blood flow in arteries using non-Newtonian viscosity model, presents two major difficulties; the first one is the choice of an appropriate constitutive equation, because no one model is universally accepted as a reflection of the true behavior of blood viscosity until now. Another difficulty lies in the numerical convergence of the complex scheme solving the highly non-linear set of equations governing the blood motion. In this paper, the pulsatile blood flow through an arterial stenosis has been numerically modeled to evaluate the flow characteristics and the wall shear stress under physiological conditions. The Navier-Stokes equations governing the fluid motion are solved using the finite element method in unsteady two-dimensional case. The behavior of blood is considered as the Generalized Power-law (Gpl) and Cross models, where the shear-thinning characteristics of the streaming blood are taken into account. Constants in the constitutive equations of previous models have been obtained by fitting experimental viscosity data. The numerical simulations are performed for a wide range of apparent shear rates (10 s-1-750 s-1) with good convergence of the iterative scheme. Results from the blood flow simulations indicate that non-Newtonian behavior has considerable effects on instantaneous flow patterns. However, it seems that the Gpl model will be slightly better for describing the non-Newtonian characteristics of blood than the Cross model.

APPLICATION OF FLUID-STRUCTURE INTERACTION TO NUMERICAL SIMULATIONS IN THE LEFT VENTRICLE

Numerical simulations of blood flow and myocardium motion for an average canine left ventricle (LV) with fluid-structure interaction were performed. The temporal variations of the LV cavity pressure and wall stress during the cardiac cycle were consistent with previous literature. LV cavity volume was conserved from one period to the next, despite sub-physiological ejection volumes and brief periods of backflow during early filling. This study improves on previous ones by presenting details of the models and results for both the fluid and solid components of the LV.

Numerical Simulation of Blood Flow in Centrifugal Heart Pump by Utilizing Meshless Smoothed Particles Hydrodynamic Method

Numerical Simulation of Blood Flow in Centrifugal Heart Pump by Utilizing Meshless Smoothed Particles Hydrodynamic Method

Outflow boundary conditions for blood flow in arterial trees.

In the modeling of the pulse wave in the systemic arterial tree, it is necessary to truncate small arterial crowns representing the networks of small arteries and arterioles. Appropriate boundary conditions at the truncation points are required to represent wave reflection effects of the truncated arterial crowns. In this work, we provide a systematic method to extract parameters of the three-element Windkessel model from the impedance of a truncated arterial tree or from experimental measurements of the blood pressure and flow rate at the inlet of the truncated arterial crown. In addition, we propose an improved three-element Windkessel model with a complex capacitance to accurately capture the fundamental-frequency time lag of the reflection wave with respect to the incident wave. Through our numerical simulations of blood flow in a single artery and in a large arterial tree, together with the analysis of the modeling error of the pulse wave in large arteries, we show that both a small truncation radius and the complex capacitance in the improved Windkessel model play an important role in reducing the modeling error, defined as the difference in dynamics induced by the structured tree model and the Windkessel models.

Numerical Simulation of Blood Flow through Different Stents in Stenosed and Non-Stenosed Vessels

Fluid dynamics in two different stent configurations, peak-to-valley (S1) and peak-to-peak (S2), within a fully expanded situation and a 30% restenosis is investigated. Numerical simulations are carried out in order to evaluate the conditions promoting atherosclerotic events when a self-expanding bare metal stent is applied. The conclusions are that the two configurations, S1 and S2, have a similar fluid dynamics behavior as far as wall shear stress is concerned, but oscillatory shear and relative residence time maps suggest that the peak-to-peak configuration, S2, has a better behavior than the peak-to-valley, S1.

Numerical simulation of blood flow and plaque progression in carotid–carotid bypass patient specific case

This study describes computer simulation of blood flow and plaque progression pattern in a patient who underwent surgical treatment for infected carotid prosthetic tube graft using carotid–carotid cross-over bypass. The 3D blood flow is governed by the Navier–Stokes equations, together with the continuity equation. Mass transfer within the blood lumen and through the arterial wall is coupled with the blood flow and is modelled by the convection–diffusion equation. Low-density lipoprotein (LDL) transport in lumen of the vessel is described by Kedem–Katchalsky equations. The inflammatory process is solved using three additional reaction–diffusion partial differential equations. Calculation based on a computer simulation showed that flow distribution in the left carotid artery (CA) was around 40–50% of the total flow in the right common CA. Also, the left CA had higher pressure gradient after surgical intervention. Plaque progression simulation predicted development of the atherosclerotic plaque in the position of the right common CA and the left internal CA. A novel way of atherosclerotic plaque progression modelling using computer simulation shows a potential clinical benefit with significant impact on the treatment strategy optimization.

P23 UNIQUE JUNCTIONAL MOLECULAR EXPRESSION IN HEPATIC SINUSOIDAL ENDOTHELIAL CELLS COMPARED TO CONVENTIONAL VASCULAR ENDOTHELIUM: IMPLICATIONS FOR LYMPHOCYTE RECRUITMENT

To this end, we performed numerical simulations to assess the perfusion characteristics of the dysregulated microcirculation. Methods: Vascular corrosion casting, scanning electron microscopic examination (SEM; Fig. 1a) and high-resolution micro-CT imaging of a human cirrhotic liver generated detailed datasets of two dissected microsamples. Image processing resulted in 3D reconstructions of the microcirculation, and two cubic samples (150×150×150mm3) were virtually dissected (Fig. 1b,c). Subsequently, numerical simulations of blood flow through these samples were performed to characterize their permeability behavior. Results: Permeabilities of the cirrhotic liver samples are substantially higher (at least fivefold) compared to normal liver tissue. We hypothesize that compensation mechanisms (dilated sinusoids and shunt vessels, Fig. 1a) are present in order to counteract the increased vascular resistance of the liver as a whole due to regenerative nodules and dynamic contraction mechanisms. Conclusions: Numerical modeling allows quantifying the perfusion characteristics of the cirrhotic microcirculation. Future research will focus on the development of multiscale models to couple the macroand microcirculation, enabling the integration of other cirrhotic aspects (e.g. regenerative nodules) in numerical models. Furthermore, a well-established cirrhotic rat model will be studied to model the degenerative adaptation of the cirrhotic (micro)circulation.

A PARAMETRIC NUMERICAL INVESTIGATION OF LOCAL HAEMODYNAMICS IN THE END-TO-SIDE ANASTOMOSIS OF CERVICAL-TO-PETROUS BYPASS BASED ON REAL GEOMETRY OF INTERNAL CAROTID ARTERY

Bypass reconstructed from the cervical segment of internal carotid artery (ICA) to its petrous segment allows high-volume bypass flow without any risk of intracranial dissection. The purpose of this study was to investigate the geometric effect on the end-to-side anastomosis of cervical-to-petrous bypass, for its close relationship to local haemodynamic and the long-term performance of bypass. We focused on two controllable geometric parameters: diameter ratio (Φ) and angle (α) between the graft and host arteries. Different models covering a range of Φ (0.75, 1 and 1.25) and α (30°, 45°, 60° and 90°) were constructed based on real geometry of human ICA. Numerical simulations of blood flow were performed in physiological flow condition. The flow patterns, flow distributions, time-average wall shear stress (TAWSS) and oscillatory shear index (OSI) in different models were compared. Our results showed geometric factors have influence on both the local haemodynamic parameters and the flow velocity through downstream branches. Of models with different geometric parameters, the model with Φ ≥ 1 or α = 45° were the most optimized considering haemodynamic performance.

Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation.

A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies by Olufsen et al. (Ann Biomed Eng 28:1281-1299, 2012) which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of 'large' arteries is connected to its corresponding terminal vein via a network of vessels representing the vascular bed of smaller arteries and veins. We develop and implement an algorithm to calculate the admittance of each vascular bed, using bifurcating structured trees and recursion. The structured-tree models take into account the geometry and material properties of the 'smaller' arteries and veins of radii ≥ 50 μm. We study the effects on flow and pressure associated with three classes of pulmonary hypertension expressed via stiffening of larger and smaller vessels, and vascular rarefaction. The results of simulating these pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment for circulatory diseases within the lung.

Three-dimensional numerical simulation of blood flow in mouse aortic arch around atherosclerotic plaques

Atherosclerosis is a progressive disease, involving the build-up of lipid streaks in artery walls, leading to plaques. Understanding the development of atherosclerosis and plaque vulnerability is critically important since plaque rupture can result in heart attack or stroke. Plaques can be divided into two distinct types: those likely to rupture (vulnerable) or less likely to rupture (stable). In the last decade, researchers have been interested in studying the influence of the mechanical effects (blood shear stress, pressure forces and structural stress) on the plaque formation, progression and rupture processes but no general agreement has been found. The purpose of the present work is to include more realistic conditions for the numerical calculations of the blood flow by implementing real geometries with plaques in the numerical model. Hemodynamical parameters are studied in both diseased and healthy configurations. The healthy configuration is obtained by removing numerically the plaques from three dimensional geometries obtained by micro-computed tomography. A new hemodynamical parameter is also introduced to relate the location of plaques to the characteristics of the flow in the healthy configuration.

Numerical Simulation of the blood flow behavior in the circle of Willis.

Introduction: This paper represents the numerical simulation of blood flow in the circle of Willis (CoW). Circle of Willis is responsible for the oxygenated blood distribution into the cerebral mass. To investigate the blood behavior, two Newtonian and non-Newtonian viscosity models were considered and the results were compared under steady state conditions. Methods: Methodologically, the arterial geometry was obtained using 3D magnetic resonance angiography (MRA) data. The blood flow through the cerebral vasculature was considered to be steady and laminar, and the Galerkin’s finite element method was applied to solve the systems of non-linear Navier-Stokes equations. Results: Flow patterns including flow rates and shear rates were obtained through the simulation. The minimal magnitude of shear rates was much greater than 100 s-1 through the larger arteries; thus, the non-Newtonian blood viscosity tended to approach the constant limit of infinite shear viscosity through the CoW. So, in larger arteries the non-Newtonian nature of blood was less dominant and it would be treated as a Newtonian fluid. The only exception was the anterior communicating artery (ACoA) in which the blood flow showed different behavior for the Newtonian and non-Newtonian cases. Conclusion By comparing the results it was concluded that the Newtonian viscosity assumption of blood flow through the healthy, complete circle of Willis under the normal and steady conditions would be acceptably accurate.

大血管転換術後の胸部大動脈における血液流れの数値解析

大血管転換術後の胸部大動脈における血液流れの数値解析

Numerical simulation of blood flow and wall shear stress distribution in the thoracic aorta after arterial switch operation

Numerical simulation of blood flow and wall shear stress distribution in the thoracic aorta after arterial switch operation