A numerical investigation of the dependence of NMR signal from pulsatile blood flow in CINE pulse sequences

The Bloch equations have been solved using numerical techniques for a uniform fluid undergoing periodic pulsatile flow in an NMR imaging experiment. The magnetization and NMR signal have been calculated for experimental parameters appropriate for a CINE sequence (TR = 40 ms, (TE = 14 ms) applied to the study of pulsatile aortic or other arterial flows. The flow velocity profile is obtained by Fourier superposition of different harmonics and it is shown that the steady-state NMR signal has reduced high-frequency components. There is also a time delay between peak signal intensity and flow because the backflow effects that can be as much as 100 ms. The apparent pulsatility depends on the NMR sequence parameters. Some limitations of the phase contrast flow-imaging method are also discussed for nonuniform flow.     

Simple calculation of the velocity profiles for pulsatile flow in a blood vessel using Mathematica

The online version of the original article can be found at     

Simple calculation of the velocity profiles for pulsatile flow in a blood vessel using mathematica

Conclusion The numerical solution of Womersley flow can provide important physical insights to the student of Biofluid dynamics. This computer program is less than 70 lines and can be entered rapidly without extensive knowledge of Mathematica. Through manipulations, the effect of changes in the unsteadiness parameter, Reynolds number, and waveform shape on the pulsatile hemodynamics in straight tubes, can be explored. The exercise reinforces the importance of unsteady forces on the complex processes of physiologic flow and illustrates the usefulness of computers in fluid mechanics analyses.     

Large-Eddy simulation of pulsatile blood flow

Large-Eddy simulation (LES) is performed to study pulsatile blood flow through a 3D model of arterial stenosis. The model is chosen as a simple channel with a biological type stenosis formed on the top wall. A sinusoidal non-additive type pulsation is assumed at the inlet of the model to generate time dependent oscillating flow in the channel and the Reynolds number of 1200, based on the channel height and the bulk velocity, is chosen in the simulations. We investigate in detail the transition-to-turbulent phenomena of the non-additive pulsatile blood flow downstream of the stenosis. Results show that the high level of flow recirculation associated with complex patterns of transient blood flow have a significant contribution to the generation of the turbulent fluctuations found in the post-stenosis region. The importance of using LES in modelling pulsatile blood flow is also assessed in the paper through the prediction of its sub-grid scale contributions. In addition, some important results of the flow physics are achieved from the simulations, these are presented in the paper in terms of blood flow velocity, pressure distribution, vortices, shear stress, turbulent fluctuations and energy spectra, along with their importance to the relevant medical pathophysiology.     

Turbulence downstream from the Ionescu-Shiley bioprosthesis in steady and pulsatile flow

The turbulence generated downstream from an aortic Ionescu-Shiley bioprosthesis has been investigated in vitro with both steady and pulsatile flow; Instantaneous point velocities were measured using laser-Doppler anemometry (LDA) at numerous preselected locations in the flow. The mean and RMS velocities from these data at each location were then used to estimate the laminar and turbulent shear in the bulk flow as a function of radial position on a cross-section of the flow system downstream from the mounted prosthesis. Estimated total shear stresses were found in the bulk flow that were of sufficient magnitude to possibly cause haemolysis and initiate platelet chemical-release reactions. For steady flow and at peak pulsatile flow, maximum total shear stresses were estimated to be 120 N m⁻² and 100 N m⁻², respectively, over more than 5 per cent of the flow cross-section. The spatial distribution of the elevated shear stresses correlates well with the valve superstructure. It is concluded that these elevated stresses are a direct consequence of the notable flow constriction generated by the valve’s fully opened leaflets. deceased     

In vitro comparison of steady and pulsatile flow characteristics of jellyfish heart valve

In examining the hydrodynamic performance of artificial heart valves in vitro, experiments are carried out under either steady or pulsatile flow conditions. Steady flow experiments are simple to set up and analysis of the data is also simple; however, their validity and accuracy have been questioned. In this study, the flow characteristics of jellyfish valves are evaluated and analyzed for steady and pulsatile flow conditions. The analysis is given in terms of velocity and shear stress distributions for a cardiac flow rate of 4.5l/min, and the corresponding steady flow rate is measured at two locations, 0.5D and 1D downstream of the valve face (D being the diameter of the pipe). At the 0.5D location, the velocity profile results obtained for both flow conditions indicated that jetting flow occurred close to the wall, and flow reversal as well as stagnation zones occurred in the core of the valve chamber. These phenomena were also evident in the shear stress profiles for both pulsatile and steady flow conditions. At this location, the maximum difference between the steady and pulsatile values of peak velocity is about 18%. However, the maximum difference between the peak shear stresses was in the range of 5%–7%. At the 1D location, the flow characteristics observed under both the pulsatile and steady flow conditions were almost identical, with a maximum difference between the peak values of less than 4%. From the data presented here, it can be stated that, at least in the initial optimization of the valve hemodynamic performance, the steady hydrodynamic evaluation of the valve could be an effective tool for analyzing the flow characteristics.     

A numerical investigation on the steady and pulsatile flow characteristics in axi-symmetric abdominal aortic aneurysm models with some experimental evaluation

Steady and pulsatile flow characteristics in rigid abdominal aortic aneurysm (AAA) models were investigated computationally (using Fluent v. 4.3) over a range of Reynolds number (from 200 to 1600) and Womersley number (from 17 to 22). Some comparisons with measurements obtained by particle image velocimetry under the pulsatile flow conditions are also included. A sinusoidal inlet flow waveform 1 + sin omega t with thin inlet boundary layers was used to produce the required pulsatile flow conditions. The bulk features of the mean flow as well as some detailed features, such as wall shear stress distributions, are the foci of the present investigation. Recirculating vortices appeared at different phases of a flow cycle causing significant spatial and temporal variations in wall shear stresses and static pressure distributions. A high level of shear stresses usually appeared at the upstream and downstream ends of the bulge. Effects of pressure rise caused by the increase in cross-sectional area were transmitted into the downstream tube. Further simulation studies were conducted using simulated physiological waveforms under resting and exercise conditions so as to determine the possible implication of vortex dynamics inside the AAA model.     

A numerical investigation on the steady and pulsatile flow characteristics in axi-symmetric abdominal aortic aneurysm models with some experimental evaluation

Steady and pulsatile flow characteristics in rigid abdominal aortic aneurysm (AAA)models were investigated computationally (using Fluent v.4.3) over a range of Reynolds number (from 200 to 1600)and Womersley number (from 17 to 22). Some comparisons with measurements obtained by particle image velocimetry under the pulsatile flow conditions are also included. A sinusoidal inlet flow waveform 1+sin omega t with thin inlet boundary layers was used to produce the required pulsatile flow conditions. The bulk features of the mean flow as well as some detailed features, such as wall shear stress distributions, are the foci of the present investigation. Recirculating vortices appeared at different phases of a flow cycle causing significant spatial and temporal variations in wall shear stresses and static pressure distributions. A high level of shear stresses usually appeared at the upstream and downstream ends of the bulge. Effects of pressure rise caused by the increase in crosssectional area were transmitted into the downstream tube. Further simulation studies were conducted using simulated physiological waveforms under resting and exercise conditions so as to determine the possible implication of vortex dynamics inside the AAA model.     

Effect of pulsatile swirling flow on stenosed arterial blood flow

The existence of swirling flow phenomena is frequently observed in arterial vessels, but information on the fluid-dynamic roles of swirling flow is still lacking. In this study, the effects of pulsatile swirling inlet flows with various swirling intensities on the flow field in a stenosis model are experimentally investigated using a particle image velocimetry velocity field measurement technique. A pulsatile pump provides cyclic pulsating inlet flow and spiral inserts with two different helical pitches (10D and 10/3D) induce swirling flow in the stenosed channel. Results show that the pulsatile swirling flow has various beneficial effects by reducing the negative wall shear stress, the oscillatory shear index, and the flow reverse coefficient at the post-stenosis channel. Temporal variations of vorticity fields show that the short propagation length of the jet flow and the early breakout of turbulent flow are initiated as the swirling flow disturbs the symmetric development of the shear layer. In addition, the overall energy dissipation rate of the flow is suppressed by the swirling component of the flow. The results will be helpful for elucidating the hemodynamic characteristics of atherosclerosis and discovering better diagnostic procedures and clinical treatments.     

Detection of pulsatile blood flow cycle in frog microvessels by image velocimetry

The detection of pulsatile blood flow velocity through one section of a curved branching frog mesenteric microvessel during a flow cycle, by analysis of a sequence of videomicroscopic images recorded at a frame rate 25 frames s⁻¹, is presented. From these data, 64 sequential digitised frames of 128×128 pixels and 256 grey level were selected. By processing sequential pairs of frames by image velocimetry, the corresponding displacement vector was calculated. Dividing this by the frame rate gave the vector velocity. The same procedure was repeated for all frames, and the corresponding maximum (0.36–0.38 mm s⁻¹), minimum (0.0–0.025 mm s⁻¹) and other velocity values were obtained and plotted. The preliminary data analysis showed that the separation between two velocity maxima was about 20 video frames, which corresponded to one cardiac cycle of time interval 0.8 s.     

Effect of pulsatile arterial diameter variations on blood flow estimated by Doppler ultrasound

High-resolution measurements of common carotid and femoral arterial diameters have been performed by ultrasound echo devices. When combined with pulsed Doppler measurements of cross-sectional averaged velocity in the same vessels, exact calculations of flow were made possible. The median peak-to-peak pulsatile diameter variations were 0.19 mm (2.8 per cent) in the femoral artery and 0.49mm (6.7 per cent) in the common carotid artery. Flow values were calculated either by taking the time-averaged diameter as a constant value, or by taking into account the dynamic variations in diameter. In comparing the two values, a quantification of the magnitude of error introduced by the averaging of the diameter was made possible. An error in the range 1.5–3.8 per cent was found for the femoral artery, whereas the error in the common carotid artery was in the range 0.4–3.6 per cent despite the larger amplitude of the pulsations in this vessel.     

CFD investigation of steady flow in bi-leaflet heart valve hinge

This paper focuses on local flow patterns inside the hinge socket of a bi-leaflet mechanical heart valve (MHV), where experimental measurements are difficult due to the extremely small flow region of about 40 microm. The overall objective of this study is to simulate the steady flow in this confined micro channel within the hinge region of a partially protruded ball hinge concept. A CFD simulation of flow through a bi-leaflet heart valve hinge was carried out. Steady flow with the valve leaflet in the fully open position during the valve systole phase was studied using FLUENT 4.4.7 running on Silicon Graphics. Body Fitted Coordinates (BFC) grid distribution was applied in the overall flow domain and great care was taken at the mesh distribution within the hinge local area. The flow study focused on local flow patterns inside the hinge socket of the valve where experimental measurements in the actual size valve are not practical. CFD results show evidence of flow in local area of hinge and no evidence of stagnation. Flow migrates across the clearance, and small vortices are formed after the hinge stoppers. The results indicate that flow in the hinge region is complex and critical for the valve to function effectively.     

血液流体动力学研究与生物反应器在组织工程血管构建的应用

利用生物反应器构建组织工程化血管是近年来诞生的一项新技术。本文综述了其理论基础即血液流体动力学的研究进展,生物反应器的原理、结构、应用及评估,同时提出存在的问题并展望其应用前景。     

Effects of pulsatile flow pattern and each stage of pressure increasing, constant and decreasing, respectively upon inelastic deformation of blood vessel.

The aim of this study is to elucidate the relation of the inelastic expansive deformation of natural blood vessel and the degradation of elasticity to the time pattern of circulating pulsatile pressure flow. When pulsatile pressure amplitude (delta P = Pmax - Pmin) becomes smaller due to Pmin increasing, the blood vessel is subject to creep deformation. In this sense, pulsating pressure will play a role in avoiding creep effect. Fluctuation of maximum pressure Pmax will induce the increase of inelastic deformation and the decrease of rigidity of the blood vessel. The inelastic deformation and the decrease of rigidity in blood vessel is induced at the stage of pressure amplitude rising from a lower one to a higher, but not during pressure amplitude (delta P) kept constant nor at the pressure amplitude decreasing stage. In order to reduce the degradation of mechanical properties of blood vessel, it may be effective to avoid the increase of Pmin and the variability of Pmax.     

In vitro velocity measurements down strem from the lonescu-Shiley aortic bioprosthesis in steady and pulsatile flow

Velocity measurements were made in vitro using laser Doppler anemometry (LDA) downstream from an lonescu-Shiley (IS) bioprosthetic aortic heart valve. Velocity measurements were made in both steady and pulsatile flow. A systematic, flow mapping approach to the measurement methodology showed that the IS valve generated a large jetlike flow constriction. The acceleration ratio, defined as the maximum mean velocity for the IS valve divided by that for no valve obstructing the flow, was as high as 2·4 for steady flow and 2·6 for pulsatile flow. It was concluded that the IS valve generated a flow quite unlike that observed by other in vestigators for the natural human aortic valve, after which the leaflet design of the IS valve was modelled. In addition, a comparative analysis of steady and pulsatile results was undertaken. It was found that the pulsatile flow results for the systolic ejection interval could be divided into three phases, denoted early, mid, and late systole, as defined by the flow structure at the data plane location. Only during midsystole were the pulsatile flow results approximated by the steady flow results. Also, it was found that the magnitude of the flow disturbance measured in steady flow tended to be an upper bound on that measured for pulsatile flow.     

Modelling of pulsatile blood flow in arterial trees of retinal vasculature

The paper presents a numerical investigation of the pulsatile blood flow in the detailed arterial vasculatures of a mouse retina using the mathematical model based on frequency domain incorporating an appropriate outlet boundary impedance at the end of the terminal vessels of the arterial trees. The viscosity in the vessels was evaluated considering the Fahraeus-Lindqvist effect, the plasma skimming effect and in vivo viscosity effect in the microcirculation. Comparative studies of the pulsatile circulation were carried out for cases of rigid vessels, constant viscosity, zero and non-zero outlet boundary impedances. In addition, the dependence of the oscillating input impedance at the inlet of the arterial trees on angular frequencies of the oscillation and vessel elasticises was also studied. The study shows that the pressure wave continues in the pre-capillary vessels throughout the retina. In elastic vessels, the amplitude of oscillatory velocity and wall shear stress in larger vessels and in vessels at the periphery region of the retina is amplified. The pulsatile blood flow is significantly influenced by the outlet boundary (or load) impedance which simulates the effect of the capillary and venous vasculatures. The oscillating input impedance at the inlet of the arterial trees is also found to be dependent on the angular frequency and the Young modulus of the vessel segment. Insights into the potential variations of the dynamic responses of the system under retinal pathological condition of arteriosclerosis may be inferred from the findings of the present study.