The Effect of Arterial Curvature on Blood Flow in Arterio-Venous Fistulae: Realistic Geometries and Pulsatile Flow.

Arterio-Venous Fistulae (AVF) are regarded as the "gold standard" method of vascular access for patients with End-Stage Renal Disease (ESRD) who require haemodialysis. However, up to 60% of AVF do not mature, and hence fail, as a result of Intimal Hyperplasia (IH). Unphysiological flow and oxygen transport patterns, associated with the unnatural and often complex geometries of AVF, are believed to be implicated in the development of IH. Previous studies have investigated the effect of arterial curvature on blood flow in AVF using idealized planar AVF configurations and non-pulsatile inflow conditions. The present study takes an important step forwards by extending this work to more realistic non-planar brachiocephalic AVF configurations with pulsatile inflow conditions. Results show that forming an AVF by connecting a vein onto the outer curvature of an arterial bend does not, necessarily, suppress unsteady flow in the artery. This finding is converse to results from a previous more idealized study. However, results also show that forming an AVF by connecting a vein onto the inner curvature of an arterial bend can suppress exposure to regions of low wall shear stress and hypoxia in the artery. This finding is in agreement with results from a previous more idealized study. Finally, results show that forming an AVF by connecting a vein onto the inner curvature of an arterial bend can significantly reduce exposure to high WSS in the vein. The results are important, as they demonstrate that in realistic scenarios arterial curvature can be leveraged to reduce exposure to excessively low/high levels of WSS and regions of hypoxia in AVF. This may in turn reduce rates of IH and hence AVF failure.

The effect of in-plane arterial curvature on blood flow and oxygen transport in arterio-venous fistulae.

Arterio-Venous Fistulae (AVF) are the preferred method of vascular access for patients with end stage renal disease who need hemodialysis. In this study, simulations of blood flow and oxygen transport were undertaken in various idealized AVF configurations. The objective of the study was to understand how arterial curvature affects blood flow and oxygen transport patterns within AVF, with a focus on how curvature alters metrics known to correlate with vascular pathology such as Intimal Hyperplasia (IH). If one subscribes to the hypothesis that unsteady flow causes IH within AVF, then the results suggest that in order to avoid IH, AVF should be formed via a vein graft onto the outer-curvature of a curved artery. However, if one subscribes to the hypothesis that low wall shear stress and/or low lumen-to-wall oxygen flux (leading to wall hypoxia) cause IH within AVF, then the results suggest that in order to avoid IH, AVF should be formed via a vein graft onto a straight artery, or the inner-curvature of a curved artery. We note that the recommendations are incompatible-highlighting the importance of ascertaining the exact mechanisms underlying development of IH in AVF. Nonetheless, the results clearly illustrate the important role played by arterial curvature in determining AVF hemodynamics, which to our knowledge has been overlooked in all previous studies.

Discovery of the role of wall shear in atherosclerosis.

The suggestion was made in the 1870s that mechanical irritation of the arterial wall is a cause of atherosclerosis, because the changes were chiefly found at points "exposed to the full stress and impact of the blood." The mechanical damage theory persisted until well into the 20th century when, with interest increasing in multidisciplinary research, two fluid mechanical proposals were advanced for the patchy distribution of the lesions. One advocated high- and the other low-wall shear. Arterial wall shear stress levels appeared, however, insufficiently high to damage the endothelium. In contrast, examination of cadaver human arteries, combined with flow studies in models and casts of arteries, implied that the lesions occurred preferentially in regions expected to experience low-wall shear; a mechanism, involving arterial wall lipid metabolism and shear-dependent blood-wall mass transport, was suggested to account for that distribution. These proposals helped stimulate extensive investigation of arterial fluid mechanics/mass transport and vascular biology/pathology, revealing mechanisms that may explain the now widely confirmed preferred occurrence of atherosclerosis in low wall shear regions in adult human beings.

A helical PTFE arteriovenous access graft to swirl flow across the distal anastomosis: results of a preliminary clinical study.

Intimal hyperplasia develops preferentially in regions where the blood flow is stagnant and wall shear stress low. The small amplitude helical geometry of the SwirlGraft was designed to ensure physiological-type swirling flow, and thus suppress the triggers. We report the first conceptual testing of the SwirlGraft. Primary, assisted primary and secondary patency rates at 6 months in 20 patients were 57.9+/-11.4%, 84.4+/-8.3% and 100+/-0.0%. There was angiographic evidence of reduction of helical geometry in a proportion of the grafts. The helical graft is associated with high assisted primary and secondary patency. Elaboration of the surgical implantation techniques and an improved SwirlGraft design can be expected to exploit the advantages of the helical concept.

Local and global geometric influence on steady flow in distal anastomoses of peripheral bypass grafts.

We consider the effect of geometrical configuration on the steady flow field of representative geometries from an in vivo anatomical data set of end-to-side distal anastomoses constructed as part of a peripheral bypass graft. Using a geometrical classification technique, we select the anastomoses of three representative patients according to the angle between the graft and proximal host vessels (GPA) and the planarity of the anastomotic configuration. The geometries considered include two surgically tunneled grafts with shallow GPAs which are relatively planar but have different lumen characteristics, one case exhibiting a local restriction at the perianastomotic graft and proximal host whilst the other case has a relatively uniform cross section. The third case is nonplanar and characterized by a wide GPA resulting from the graft being constructed superficially from an in situ vein. In all three models the same peripheral resistance was imposed at the computational outflows of the distal and proximal host vessels and this condition, combined with the effect of the anastomotic geometry, has been observed to reasonably reproduce the in vivo flow split. By analyzing the flow fields we demonstrate how the local and global geometric characteristics influences the distribution of wall shear stress and the steady transport of fluid particles. Specifically, in vessels that have a global geometric characteristic we observe that the wall shear stress depends on large scale geometrical factors, e.g., the curvature and planarity of blood vessels. In contrast, the wall shear stress distribution and local mixing is significantly influenced by morphology and location of restrictions, particular when there is a shallow GPA. A combination of local and global effects are also possible as demonstrated in our third study of an anastomosis with a larger GPA. These relatively simple observations highlight the need to distinguish between local and global geometric influences for a given reconstruction. We further present the geometrical evolution of the anastomoses over a series of follow-up studies and observe how the lumen progresses towards the faster bulk flow of the velocity in the original geometry. This mechanism is consistent with the luminal changes in recirculation regions that experience low wall shear stress. In the shallow GPA anastomoses the proximal part of the native host vessel occludes or stenoses earlier than in the case with wide GPA. A potential contribution to this behavior is suggested by the stronger mixing that characterizes anastomoses with large GPA.

Automated classification of peripheral distal by-pass geometries reconstructed from medical data.

Abnormal haemodynamic conditions are implicated in the development of anastomotic myointimal hyperplasia (MIH). However, these conditions are difficult to determine in vivo, prompting research using ex vivo idealised models. To relate the understanding gained in idealised geometries to anatomically correct conditions we have investigated a reproducible approach to classify in vivo distal graft anastomoses and their inter-patient variability. In vivo distal anastomotic geometries were acquired by magnetic resonance (MR) angiography from 13 patients who had undergone infrageniculate autologous venous by-pass surgery. On average, the images were acquired 2 weeks post-operatively. Five patients also underwent repeat examinations 2 to 7 weeks later. For each geometry, the surface of the arterial lumen is represented by the zero level set of an implicit function constructed from radial basis functions that minimise curvature. The three-dimensional binary image created from the interpolated surface is processed using a skeletonisation algorithm to obtain the centreline of each branch in the geometry. This allows for the measurement of the branching angles between straight line approximations of the centrelines of each vessel, averaging them over a characteristic length of each anastomosis. The main finding in the application of the proposed classification methodology to this set of patients is that the spectrum of anastomoses can be reduced to a small subset of cases characterised by two angles: the angle between the graft and the plane of the host artery and the angle between the graft and the proximal branch of the artery.

Parallel-plate flow chamber for studies of 3D flow-endothelium interaction.

Flow induced shear stress influences vascular cellular biology and pathophysiology in numerous ways. Previous in vitro studies on interactions between flow and endothelial cells using parallel-plate flow chambers involve two-dimensional flows, whereas flows in larger vessels are commonly three-dimensional. We have constructed a parallel plate flow chamber with a backward facing step aligned oblique to the axis of the chamber. Flow visualisation by steady injection of ink through a hypodermic tube reveals swirling flow in the recirculation region downstream of the step. At given angles of the step, theta; (to the axis of the chamber), the pitch of the swirl and the width of the separation region, as measured in the direction perpendicular to the step, increase with the Reynolds number (Re). On the other hand, at given values of Re, reduction of theta; results in increases in the swirl pitch but decreases in the width of the separation zone. Furthermore, clearance time of ink from the separation region is shorter with an oblique step than a perpendicular one at given Re. Computer simulation confirms the 3D swirling flow created by the oblique step and provides detailed distribution of wall shear stresses in the flow chamber.

Combined MR imaging and numerical simulation of flow in realistic arterial bypass graft models.

We report methods for (a) transforming a three-dimensional geometry acquired by magnetic resonance angiography (MRA) in vivo, or by imaging a model cast, into a computational surface representation, (b) use of this to construct a three dimensional numerical grid for computational fluid dynamic (CFD) studies, and (c) use of the surface representation to produce a stereo-lithographic replica of the real detailed geometry, at a scale convenient for detailed magnetic resonance imaging (MRI) flow studies. This is applied to assess the local flow field in realistic geometry arterial bypass grafts. Results from a parallel numerical simulation and MRI measurement of flow in an aorto-coronary bypass graft with various inlet flow conditions demonstrate the strong influence of the graft inlet waveform on the perianastomotic flow field. A sinusoidal and a multi harmonic coronary flow waveform both with a mean Reynolds number (Re) of 100 and a Womersley parameter of 2.7 were applied at the graft inlet. A weak axial flow separation region just distal to the toe was found in sinusoidal flow near end deceleration (Re = 25). At the same location and approximately the same point in the cycle (Re = 30) but in coronary flow, the axial flow separation was stronger and more spatially pronounced. No axial flow separation occurred in steady flow for Re = 100. Numerical predictions indicate a region in the vicinity of the suture line (where there is a local narrowing of the graft) with a wall shear magnitude in excess of five times that associated with fully developed flow at the graft inlet.

The influence of out-of-plane geometry on the flow within a distal end-to-side anastomosis.

This paper describes a computational and experimental investigation of flow in a proto-type model geometry of a fully occluded 45 deg distal end-to-side anastomosis. Previous investigations have considered a similar configuration where the centerlines of the bypass and host vessels lie within a plane, thereby producing a plane of symmetry within the flow. We have extended these investigations by deforming the bypass vessel out of the plane of symmetry, thereby breaking the symmetry of the flow and producing a nonplanar geometry. Experimental data were obtained using magnetic resonance imaging of flow within perspex models and computational data were obtained from simulations using a high-order spectral/hp element method. We found that the nonplanar three-dimensional flow notably alters the distribution of wall shear stress at the bed of the anastomosis, reducing the peak wall shear stress peak by approximately 10 percent when compared with the planar model. Furthermore, an increase in the absolute flux of velocity into the occluded region, proximal to the anastomosis, of 80 percent was observed in the nonplanar geometry when compared with the planar geometry.

Blood velocity profiles in the human renal artery by Doppler ultrasound and their relationship to atherosclerosis.

Blood velocity profiles were measured in the renal branch (diameter 5.9 +/- 1.3 mm) of the aortorenal bifurcation using a 20-MHz 80-channel pulsed Doppler velocimeter during retroperitoneal surgery in 10 patients. The peak Reynolds number was 1145 +/- 140 and the frequency parameter (Wormersley parameter) was 3.0 +/- 0.8. Immediately distal to the ostium of the renal artery, reverse flow, indicating flow separation, was observed near the cranial wall mainly during the first part of the cardiac cycle. There were flows from the cranial to the caudal side of the artery at this location, indicating the presence of strong secondary flows. Two diameters downstream of the ostium, the velocity profiles were skewed to the caudal side in all patients. Four diameters downstream, the flow profile was symmetrical (3 patients) or only slightly skewed (7 patients) and virtually parabolic throughout the cardiac cycle. These observations mean that the flow on the cranial side of the renal branch of the human aortorenal bifurcation is characterized by (1) a bidirectional oscillation of the flow, (2) separation of the flow during systole, and (3) low time-averaged shear rate. These blood velocity patterns may be related to the localization and development of atheromatous plaque that occurs preferentially in this region of the renal artery. Conversely, the unidirectional, axisymmetrical flow found in more distal parts of the renal artery are associated with a very low incidence of lesions.

New ways of performing in vivo flow velocity measurements in the basilar artery.

The basilar artery is the only large artery in which two flows merge, and this is reflected in the flow downstream. We report quantitative flow-velocity measurements with a phase-based MR technique, i.e. the Fourier velocity encoding method, in the basilar artery of a volunteer. To our knowledge, this has not previously been performed successfully. A comparison is made with the results of flow velocity measurements in the basilar artery with transcranial Doppler ultrasonography; the techniques agreed very well. Although Doppler ultrasonography is still most widely used, no information on the flow rate and the flow velocity distribution in the basilar artery can be provided. MR flow measurement techniques appear promising when detailed information on the flow velocity distribution and flow rate is needed.

Essentials of blood flow.

We have reviewed briefly some features of the mechanics of blood flow, focusing particularly on the arterial system. Among the topics we consider are: steady and nonsteady flow in straight rigid tubes; the curvature and branching of arteries, noting that it may commonly be nonplanar; and the effects of both planar and nonplanar curvature and branching on flow. Steady flow in planar bends and branches (and to a small extent in nonplanar bends and branches) has attracted study. However, there has been little study of nonsteady flow in either planar or nonplanar bends and branches.

Influence of heart rate and vasoactive drugs on blood flow patterns at the canine ilio-femoral bifurcation.

OBJECTIVE: The aim was to study the effects of altered heart rate and vasoactive drugs on the blood velocity patterns in the region of an arterial bifurcation. METHODS: Blood velocity profiles were measured in an exposed iliofemoral bifurcation of paced dogs using a pulsed Doppler ultrasound velocimeter with high temporal and spatial resolution. RESULTS: Decrease of the heart rate from 120 beats.min-1 (2 Hz) to 60 beats.min-1 (1 Hz) increased the peak forward velocity (30%), the peak reverse velocity (20%), and the duration of reverse flow (25%). Each drug caused qualitatively similar changes in velocity patterns at both heart rates. The systemic administration of angiotensin II reduced peak forward velocity (-26% at 2 Hz and -33% at 1 Hz) and forward flow duration (-15% at 1 Hz), the peak reverse velocity (-30% at 1 Hz), and reverse flow duration (-20% at 2 Hz and -28% at 1 Hz). Glyceryl trinitrate also reduced the peak forward velocity (-19% at both 2 and 1 Hz) but prolonged forward flow duration (28% at 2 Hz and 17% at 1 Hz) and that of reverse flow (45% at 2 Hz and 24% at 1 Hz), and also decreased the degree of oscillation (-16% at 2 Hz). Barnidipine hydrochloride (a calcium channel antagonist) also increased the duration of forward flow (48% at 1 Hz) and of reverse flow (31% at 2 Hz) but reduced the peak reverse velocity (-29% at 1 Hz) and flow oscillation (-22% at 2 Hz and 20% at 1 Hz). CONCLUSIONS: These dramatic changes in the pattern of blood flow, including alterations in the amplitudes and durations of the different phases of the flow cycle, are expected to have important consequences on the shear dependent responses of endothelial cells in the region of the bifurcation.

Simultaneous detection of multiple components of motion with MRI.

OBJECTIVE: Simultaneous detection of two or more components of motion using new magnetic resonance pulse sequences was investigated. MATERIALS AND METHODS: The technique employs Fourier phase encoding to encode the first component, and phase contrast detection to encode the second. Although the technique can be generalized to any number of spatial dimensions and motional orders, applications in which one or two spatial dimensions are obtained with a single Fourier velocity or acceleration dimension are most likely to be useful. For example, Fourier-encoded velocity and phase-contrasted acceleration information can be combined into the same image. RESULTS: Several variations of the pulse sequence were investigated in phantoms and human volunteers. The first variation acquired images having an appearance similar to that of Fourier velocity-encoded images in which signal displacement is proportional to velocity, but with pixel intensity determined by acceleration. In another variation two spatial dimensions were acquired with a third dimension that uses Fourier velocity encoding to measure axial velocity within a curved tube. Radial velocity components were determined simultaneously with a second velocity-encoding gradient pulse. CONCLUSION: The phantom and in vivo results presented here suggest that simultaneous detection of two or more components of motion is feasible.

Quantitative measurement of velocity at multiple positions using comb excitation and Fourier velocity encoding.

An MR imaging technique that simultaneously acquires Fourier velocity encoded data from multiple stations is described. The technique employs a comb excitation rf pulse that excites an arbitrary number of slices. As the Fourier velocity phase encoding gradient pulse is advanced, the phase of each slice is the comb is advanced by a unique amount. This causes the signals from the spins in a particular slice to appear at a position in the phase encoding direction, which is the sum of the spin velocity and an offset arising from the phase increment given to that excitation slice. Acquisition of spin velocity information occurs simultaneously for all slices, permitting the calculation of wave velocities arising from pulsatile flow. These wave velocities can then be used to determine vessel distensibility.

The effect of luminal flow in rabbit carotid artery on transmural fluid transport.

The steady-state flow of fluid across the wall of the isolated rabbit common carotid artery has been measured in the presence and absence of flow within the lumen of the vessel. The perfusate solution contained either 10 or 40 mg ml-1 albumin and transmural flux was measured by monitoring the rate of movement of fluid into a chamber enclosing the artery. Vasomotion was minimized by the inclusion of the vasodilator sodium nitrite in both the perfusate and the outer bathing solution. A relatively slow luminal flow caused a reversible increase in the transmural flux by 20-30% relative to the value in the absence of flow. The mechanism responsible for the increase is not clear, but since it was not affected by the H1 antagonist, mepyramine, it would not appear to have been mediated by histamine release.

Blood velocity distributions within intact canine arterial bifurcations.

As local variations in blood flow are implicated in atherogenesis at bifurcations, we measured in vivo blood velocities in different planes within exposed iliofemoral arterial bifurcations in 8 dogs using 20-MHz, 80-channel Doppler ultrasound velocimetry. Cardiac frequency was fixed at 2 Hz by pacing. Local geometry was characterized using 25-MHz, B-mode ultrasound images, photographs, and methacrylate casts. The bifurcations were asymmetrical and planar to within 5 degrees, the diameter ratios of the daughter vessels ranged from 1.47 to 2.00, and the angles between them ranged from 40 to 76 degrees. Measured velocities indicated that just upstream of the bifurcation mean peak Reynolds numbers ranged from 196 to 564 and Womersley (frequency) parameters ranged from 2.00 to 4.1. At the level of the bifurcation, secondary flows were insignificant in the normal plane but strong in the plane of the bifurcation. As a result, two-dimensional velocity fields, reconstructed by vector addition of velocities measured in the plane of the bifurcation, differed markedly from the one-dimensional profiles calculated assuming flow parallel to the vessel axis. In the two-dimensional velocity fields, forward flow was directed toward the flow divider and reversal occurred earliest near the outer wall. Wide spatial and temporal variations in the shear stress at the endothelium are implied by these detailed, in vivo measurements of the bifurcation velocity fields.

Secondary flow in the human common carotid artery imaged by MR angiography.

The blood flow in arteries affects both the biology of the vessels and the development of atherosclerosis. The flow is three-dimensional, unsteady, and difficult to measure or to model computationally. We have used phase-shift-based magnetic resonance angiography to image and measure the flow in the common carotid arteries of a healthy human subject. There was curvature of the vessels and thin-slice dynamic flow imaging showed evidence of the presence of secondary motions. Flexing the cervical spine straightened the vessels and reduced the asymmetry of the flow.

Effects of isosorbide dinitrate on the pattern of arterial blood flow in healthy human subjects.

1. Blood velocity measurements have been made in the superficial femoral artery, 10 cm downstream of the common femoral artery bifurcation, in healthy human subjects, using a multi-channel Doppler ultrasound device. 2. In a randomized double-blind protocol, the effects of isosorbide dinitrate were examined during a 2 h period. 3. The changes induced by isosorbide dinitrate include: (i) an increase in the width of the artery and a reduction in brachial arterial blood pressure, implying relaxation of arterial smooth muscle; (ii) an increase in reverse flow and a decrease in time-averaged mean velocity associated with a relatively small decrease of the velocity excursion during the cardiac cycle, implying an increase in flow pulsatility; and (iii) an alteration of the flow pattern both in the core and near the vessel walls.