The propagation of turbulence produced by a stenosis

Micro-Rheological Changes of Red Blood Cells in the Presence of an Arterio-Venous Fistula or a Loop-Shaped Venous Graft in the Rat

Introduction: In case of kidney failure, hemodialysis is the primary kidney replacement technique. Several vascular access methods used for the therapy, one of which is the arterio-venous fistula (AVF). In the AVF, the blood flow is altered, which can elevate the mechanical stress on the red blood cells (RBCs). This can affect the RBC hemorheological properties, and it can further cause systemic changes. To lower the turbulence and shear stress, we performed a loop-shaped arterio-arterial venous interposition graft (loop-shaped graft) to compare its effect to the conventional AVF.

Materials and Methods: Thirty male Wistar were used (permission registration Nr.: 25/2016/UDCAW). The animals were randomly divided into sham-operated, AVF, and loop groups (n = 10/each). The superficial inferior epigastric vein (SIEV) was used to create the AVF and the loop-shaped graft. Blood samples were taken before/after the surgery and at the 1st, 3rd, and 5th postoperative weeks. We measured hemorhelogical, hematological, and blood gas parameters. The microcirculation of the hind limbs was also monitored using Laser Doppler fluxmetry.

Results: Hematocrit, RBC count, and hemoglobin decreased by the 1st postoperative week. The erythrocyte aggregation values significantly increased in the fistula group by the 5th week (6.43 ± 2.31 vs. 13.60; p < 0.0001; vs. before operation). At the postoperative 1st week in the loop group, the values showed a significant decrease in RBC deformability. During the maturation period, dominantly at the 5th week, all values were normalized. The operated hind limb’s skin microcirculation significantly increased in the sham and loop group by the 1st week (39 ± 10.57 vs. 73.93 ± 1.97 BFU, p < 0.01). This increase wasn’t observed in the fistula group probably due to a steal-effect.

Conclusion: Unlike in the loop group, in the presence of the fistula, several rheological parameters have changed. The loop-shaped graft had only minimal impact on micro-rheological parameters.

Large eddy simulations for blood dynamics in realistic stenotic carotids

In this paper, we consider large eddy simulations (LES) for human stenotic carotids in presence of atheromasic plaque, a pathological condition where transitional effects to turbulence may occur, with relevant clinical implications such as plaque rupture. We provide a reference numerical solution obtained at high resolution without any subgrid scale model, to be used to assess the accuracy of LES simulations. In the context we are considering, ie, hemodynamics, we cannot refer to a statistically homogeneous, isotropic, and stationary turbulent regime; hence, the classical Kolmogorov theory cannot be used. For this reason, a mesh size and a time step are deemed fine enough if they allow to capture all the features of the velocity field in the shear layers developed after the bifurcation. To assess these requirements, we consider a simplified model of the evolution of a 2D shear layer, a relevant process in the formation of transitional effects in our case. Then, we compare the results of LES σ model (both static and dynamic) and mixed LES models (where also a similarity contribution is considered). In particular, we consider a realistic scenario of a human carotid, and we use the reference solution as gold standard. The results highlight the accuracy of the LES σ models, especially for the static model.

Analyzing transient turbulence in a stenosed carotid artery by proper orthogonal decomposition

High-resolution three-dimensional simulations (involving 100 million degrees of freedom) were employed to study transient turbulent flow in a carotid arterial bifurcation with a stenosed internal carotid artery (ICA). The geometrical model was reconstructed from MRI images, and in vivo velocity measurements were incorporated in the simulations to provide inlet and outlet boundary conditions. Due to the high degree of the ICA occlusion and the variable flow rate, a transitional and intermittent flow between laminar and turbulent states was established. Time- and space-window proper orthogonal decomposition (POD) was applied to quantify the different flow regimes in the occluded artery. A simplified version of the POD analysis that utilizes 2D slices only--more appropriate in the clinical setting--was also investigated.

The influences of stenosis on the downstream flow pattern in curved arteries

The influence of stenosis on the pulsatile blood flow pattern in curved arteries with stenosis at inner wall was investigated by computer simulations. Numerical calculations were performed with various values of physiological parameters to examine the effect of a stenosis on the hemodynamic characteristics such as secondary flow, flow separation, wall shear stress (WSS) and pressure drop. The results demonstrated that when the severity of a stenosis at the inner wall of a curved artery reaches a certain level, the flow pattern in the downstream of the artery shows a dramatic change compared to that of a curved artery with no stenosis. According to previous studies, a flow separation occurs at the inner wall of the bend in a curved artery. The present work reports an analysis of such a flow separation area at the inner wall of the post stenosis region in curved arteries with a stenosis. In addition, another area of flow separation with low and oscillating WSS and blood pressure at the outer wall in a downstream tube was also found and investigated. The observed characteristic change of the flow downstream may suggest a formation of a new plaque at the outer wall downstream.

Numerical analysis of flow through a severely stenotic carotid artery bifurcation

The results of computational simulations may supplement MR and other in vivo diagnostic techniques to provide an accurate picture of the hemodynamics in particular vessels, which may help demonstrate the risks of embolism or plaque rupture posed by particular plaque deposits. In this study, a model based on an endarterectomy specimen of the plaque in a carotid bifurcation was examined. The flow conditions include steady flow at Reynolds numbers of 300, 600, and 900 as well as unsteady pulsatile flow. Both dynamic pressure and wall shear stress are very high, with shear values up to 70 N/m2, proximal to the stenosis throat in the internal carotid artery, and both vary significantly through the flow cycle. The wall shear stress gradient is also strong along the throat. Vortex shedding is observed downstream of the most severe occlusion. Two turbulence models, the Chien and Goldberg varieties of k-epsilon, are tested and evaluated for their relevance in this geometry. The Chien model better captures phenomena such as vortex shedding. The flow distal to stenosis is likely transitional, so a model that captures both laminar and turbulent behavior is needed.

Experimental and numerical study of pulsatile flows through stenosis: wall shear stress analysis

Different shapes of pulsatile flows through a model of stenosis are experimentally and numerically modeled to validate both methods and to determine the wall shear stress temporal evolution downstream from the stenosis. Two-dimensional velocity measurements are performed in a 75% severity stenosis using a pulsed Doppler ultrasonic velocimeter. Finite element package is employed for the transient numerical simulations. Polynomial method, based on the experimental velocity values, is proposed to determine the wall shear stress temporal evolution. There is a good agreement between the numerical and experimental results. The wall shear stress temporal analysis shows oscillating wall shear stress values during the cycle with high wall shear stress values at the throat of about 120 dyn/cm2, and low values downstream from the stenosis of about - 2.5 dyn/cm2. The key result of the study is that the presence of the stenosis leads the artery to work in a direction which is opposite to the direction of a healthy artery.

Experimental analysis of unsteady flows through a stenosis

In this paper we present a study of the post-stenotic velocity flow field corresponding to oscillatory, pulsatile and physiological flow waveforms. Two-dimensional velocity measurements are performed in a 75% severity stenosis using a pulsed Doppler ultrasonic velocimeter. Emphasis is placed on the analysis of the experimental velocity-profile patterns. It is recognized that, beyond the influence of the flow parameters such as the Reynolds number and the frequency parameter, velocity profiles (hence wall-shear stresses) highly depend on the flow waveform. In addition to this analysis, a model of the stenosis influence length is proposed in the case of oscillatory flow.

MR pulsatility measurements in peripheral arteries: preliminary results

Phase contrast flow velocity measurements were performed in six healthy volunteers and 30 patients with arteriosclerotic disease. The iliac arteries were investigated in 8 cases and the femoral arteries in 28 cases. In the first 24 patients, 16 evenly distributed data sets were acquired during one cardiac cycle. In the last 12 patients, a trigger pulse followed by the acquisition of 30 evenly distributed data sets was applied every second heart beat. This procedure allowed data to be acquired over a full heart cycle without any acquisition gap. The measured flow velocities were displayed as function of time. Systolic acceleration, postsystolic deceleration and pulsatility of flow velocity were calculated and compared with stenosis grades determined from DSA angiograms. Flattening of the flow velocity patterns was found to correlate with the local severity of arteriosclerotic disease.

Phase-contrast pulsatility measurements: preliminary results in normal and arteriosclerotic iliofemoral arteries. Work in progress

Magnetic resonance (MR) flow measurements were obtained in six healthy volunteers and 30 patients with arteriosclerotic disease with a 1.5-T imager and a pulse sequence for flow quantification based on flow-induced phase shifts. The iliac arteries were investigated in eight and the femoral arteries in 28 subjects. A trigger pulse, followed by the acquisition of 30 evenly distributed data sets, was applied every second heartbeat, thus eliminating any acquisition gap in a full heart cycle. For quantitative analysis, flow velocity was plotted as a function of time. Systolic acceleration, postsystolic deceleration, and pulsatility of flow were calculated and compared with stenosis grades determined from recent intraarterial digital subtraction angiograms. The flattening of the temporal flow patterns correlated with local severity of vascular occlusive disease.

Changes in ultrasonic Doppler backscattered power downstream of concentric and eccentric stenoses under pulsatile flow

The main objective of the present work was to investigate, under pulsatile flow, the patterns of variation of the Doppler power backscattered by blood and Sephadex particles upstream and downstream of concentric and eccentric stenoses ranging from 47% to 91% area reduction. Doppler measurements were performed at 5 diameters upstream and 5, 10, 15 and 20 diameters downstream of the constriction. For the concentric 75% and 85%, and the eccentric 79% and 91% area reduction stenoses, a progressive increase of the power backscattered by red cell suspensions at 40% hematocrit was measured downstream of the narrowing. The maximal power usually occurred around 10 diameters after the stenosis and dropped further downstream. In addition to the increase in the power, a cyclic variation of the backscattered intensity was observed within the flow cycle. For the concentric 52% and eccentric 47% area reduction stenoses, no variation of the Doppler power was measured during flow acceleration and deceleration for all recording sites. A coefficient of correlation of 0.82 was measured between the percentage of area reduction and the ratio of the Doppler mean power at 10 diameters downstream to that at 5 diameters upstream of the stenoses. Using Sephadex particles at low concentration, no increase of the Doppler power was found downstream of the 85% and 91% area reduction stenoses. The possible link between the intensity of turbulence and the power backscattered by blood is discussed along with the influence of the correlation between the scattering particles, under turbulent flow.

Haemodynamic model of a unilateral iliac stenosis with an aortoiliac bypass

A hydrodynamic model for the part of the human arterial network below the renal arteries has been constructed using specially fabricated distensible tubes and a pulsatile pump to simulate an aortoiliac bypass. The experiments and the computer model indicated that no 'steal' occurred due to the insertion of the bypass graft. Also, the results showed that the length of the stenosis had a non-systematic apparent effect on the physiological significance of the obstruction and that the kinetic power represented only a small percentage of the total power. The total power efficiency of the bypass graft was unaffected by its elastic properties. The experimental investigation also indicated that the pressure drop across the stenosis was considerably larger than the drop calculated using the Poiseuille flow relationship when the stenosis was severe. Therefore, a critical arterial stenosis value cannot be defined as an obstruction of a constant percentage reduction of luminal area. It varies directly with the effective cross-sectional area and inversely with the flow rate. The value of angiography in assessing the functional significance of any arterial stenosis is therefore limited. A better method for evaluation requires quantitative measurements of local blood pressure and blood flow, not only at rest, but also under conditions creating augmented flows due to exercise.

Coronary flow reserve

The ability of the coronary circulation to autoregulate is essential for the heart to respond to metabolic demands. Several alterations in function may limit maximal coronary perfusion including atherosclerosis, structural abnormalities of small coronary vessels, extravascular compressive forces, thrombosis, abnormal endothelial regulatory function, and the effect of abnormal myocardium on the coronary circulation. Coronary flow reserve is a unifying concept that examines the limitation in myocardial perfusion that certain disease states impose. At present, even with state-of-the-art technology, the measurement of coronary flow reserve is difficult in routine clinical situations. As the ability to measure regional myocardial perfusion improves, coronary flow reserve may gain more widespread clinical use with perhaps as yet undiscovered therapeutic implications.

Detailed visualization of pulsatile flow fields produced by modelled arterial stenoses

A multiple trace photochromic method was used to visualize the pulsatile flow field created by modelled arterial stenoses of 38% and 65% area reductions. Using flow parameters similar to those of a medium sized artery in man, the flow patterns at seven axial locations in relation to the stenosis were simultaneously photographed at various times throughout the flow cycle. With the 65% stenosis, the wall shear stress in the vicinity of the reattachment point was found to fluctuate quite strongly during the turbulent phase of the flow cycle, giving rise to instantaneous shear stresses that were at least eight times larger than those measured upstream. For the 38% stenosis, much smaller shear stresses were observed. These and other results are described in detail.

Asymmetry of Doppler spectrum in stenosis differentiation

The asymmetry of the spectral distribution of ultrasonic Doppler flow velocity signals, assessed using the coefficient of skewness, is discussed as a criterion of stenosis differentiation. Its performance is compared with that of the index of turbulence intensity for both in vitro and in vivo flow Doppler signals, recorded distal to a stenosis. The power spectral distributions are computed using the direct Fourier transform and maximum likelihood method. The asymmetry of spectral distribution has proved to be a more efficient criterion than the turbulence intensity. The maximum likelihood method ensures better stenosis differentiation than the direct FFT method.

Experimental validation of Doppler echocardiographic measurement of volume flow through the stenotic aortic valve

In aortic stenosis, evaluation of aortic valve area by the continuity equation assumes that the volume of flow through the stenotic valve can be measured accurately in the left ventricular outflow tract. To test the accuracy of Doppler volume-flow measurement proximal to a stenotic valve, we developed an open-chest canine model in which the native leaflets were sutured together to create variable degrees of acute aortic stenosis. Left ventricular and aortic pressures were measured with micromanometer-tipped catheters. Volume flow was controlled and varied by directing systemic venous return through a calibrated roller pump and back to the right atrium. Because transaortic volume flow will not equal roller pump output when there is coexisting aortic insufficiency (present in 67% of studies), transaortic flow was measured by electromagnetic flowmeter with the flow probe placed around the proximal descending thoracic aorta, just beyond the ligated arch vessels. In 12 adult, mongrel dogs (mean weight, 25 kg), the mean transaortic pressure gradient ranged from 2 to 74 mm Hg, and transaortic volume flow ranged from 0.9 to 3.2 l/min. In four dogs, electromagnetic flow that was measured distal to the valve was accurate compared with volume flow determined by timed collection of total aortic flow into a graduated cylinder (n = 24, r = 0.97, electromagnetic flow = 0.87 Direct +0.13 l/min). In eight subsequent dogs, electromagnetic flow was compared with transaortic cardiac output measured by Doppler echocardiography in the left ventricular outflow tract as circular cross-sectional area [pi(D/2)2] x left ventricular outflow tract velocity-time integral x heart rate.(ABSTRACT TRUNCATED AT 250 WORDS)

Prospective assessment of the aorto-iliac segment by visual interpretation of frequency analysed Doppler waveforms--a comparison with arteriography

In a group of 83 patients the prospective Doppler assessment of disease in the aorto-iliac segment, obtained from visual interpretation of the frequency analysed Doppler waveforms, is compared with subsequent arteriographic findings. The Doppler technique proved to be particularly accurate in the severely diseased vessels (sensitivity 87%, specificity 88%) but tended to underestimate the extent of the minimal/moderate disease.