Shear stress in cerebral arteries supplying arteriovenous malformations

Arteries supplying cerebral arteriovenous malformations (AVMs) are known to dilate with time. These changes are reversible, and the feeders have been shown to slowly decrease in calibre after removal of the AMV. There is evidence that arteries alter their internal diameters in response to sustained changes of blood flow so that shear stress is kept constant. This implies that blood flow-induced shear stress might be the driving force for remodelling of the cerebral vascular network in the presence of an AVM, and for reversion of these changes after radical operation. The objective of this study is to examine the hypothesis that the shear stress in cerebral arteries supplying AMVs is of the same magnitude as in arteries supplying normal brain tissue in spite of larger blood flow rate. Fifteen patients with supratentorial cerebral AVMs admitted for endovascular treatment were examined with transcranial Doppler ultrasound in the distal Willisian vessels. Vessel calibres were measured in angiograms with magnification correction. Shear stress was estimated assuming a constant value for blood viscosity. Corresponding arteries in the cerebral hemisphere with AVM and in the contralateral one were compared in pairs. Thirty-four pairs of homonymous arteries were studied. The arteries on the AVM side presented larger calibres, higher axial blood flow velocities, lower pulsatility index and larger blood flow rates than the contralateral side. There was a clear positive correlation between blood flow velocities and vessel calibres. The estimates of shear stress did not differ significantly in corresponding arteries of both hemispheres (p = 0.18). The results indicate a precise adjustment of cerebral arterial calibre and blood flow-induced shear stress that presumably induces the progressive dilation of AVM feeders, and the slow regression of the vessel calibres to average dimensions after removal of the lesion. Each vessel seems to remodel itself in response to long-term changes in blood flow rate so that the vessel calibre is reshaped to maintain a constant level of wall shear stress.     

Flow patterns in dog aortic arch under a steady flow condition simulating mid-systole

To elucidate the possible connection between blood flow and localized pathogenesis and the development of atherosclerosis in humans, we studied the flow patterns and the distribution of fluid axial velocity and wall shear stress in the aortic arch in detail. This was done by means of flow visualization and high-speed cinemicrographic techniques, using transparent aortic trees prepared from the dog. Under a steady flow condition at inflow Reynolds numbers of 700-1600, which simulated physiologic conditions at early- to mid-systole, slow, spiral secondary, and recirculation flows formed along the left anterior wall of the aortic arch and at the entrance of each side branch adjacent to the vessel wall opposite the flow divider, respectively. The flow in the aortic arch consisted of three major components, namely, an undisturbed parallel flow located close to the common median plane of the arched aorta and its side branches, a clockwise rotational flow formed along the left ventral wall, and the main flow to the side branches, located along the right dorsal wall of the ascending aorta. Thus, looking down the aorta from its origin, the flow in the aortic arch appeared as a single helical flow revolving in a clockwise direction. Regions of low wall shear stress were located along the leading edge of each side branch opposite the flow divider where slow recirculation flows formed, and along the left ventral wall where slow spiral secondary flows formed. If we assume that the flow patterns in the human aortic arch well resemble those observed in the dog, then it is likely that atherosclerotic lesions develop preferentially at these sites of low wall shear stress in the same manner as in human coronary and cerebral arteries.     

Leptin indirectly affects estrous cycles by increasing metabolic fuel oxidation

The pulsatile flow field in an anatomically realistic model of the bifurcation of the left anterior descending coronary artery (LAD) and its first diagonal branch (D1) was simulated numerically and measured by laser Doppler anemometry. The inlet velocity profiles used in the computer simulation and in the physical experiments were physiologically realistic. The computational geometric model was developed on the basis of a digitized arterial cast. The curvature of the LAD over the cardiac surface leads to axial velocity profiles which are slightly skewed towards the epicardial wall. Downstream of the bifurcation, a strong skewing occurs towards the flow divider walls as a result of branching. Locally, the wall shear stress component caused by the complex secondary velocity can be as high as the axial component. The wall shear stress representation from a cell-based perspective exhibits low shear stress and large deviation from the time-averaged shear stress direction during systole. In diastole, the instantaneous wall shear stress direction nearly corresponds to the mean direction. The comparison of computed and measured axial velocity results shows generally good agreement. In contrast to computed flow patterns in simpler geometries constructed from cylindrical tubes, the flow field is found to be smoother, presumably reflecting the adaptation of the vascular contour to the contained flow.     

Alterations in pulmonary artery flow patterns and shear stress determined with three-dimensional phase-contrast magnetic resonance imaging in Fontan patients

OBJECTIVE: This study compares in vivo pulmonary blood flow patterns and shear stresses in patients with either the direct atrium-pulmonary artery connection or the bicaval tunnel connection of the Fontan procedure to those in normal volunteers. Comparisons were made with the use of three-dimensional phase contrast magnetic resonance imaging. METHODS: Three-dimensional velocities, flows, and pulmonary artery cross-sectional areas were measured in both pulmonary arteries of each subject. Axial, circumferential, and radial shear stresses were calculated with the use of velocities and estimates of viscosity. RESULTS: The axial velocities were not significantly different between subject groups. However, the flows and cross-sectional areas were higher in the normal group than in the two patient groups in both pulmonary arteries. The group with the bicaval connection had circular swirling in the cross section of both pulmonary arteries, causing higher shear stresses than in the controls. The disorder caused by the connection of the atrium to the pulmonary artery caused an increase in some shear stresses over the controls, but not higher than those found in the group having a bicaval tunnel. CONCLUSIONS: We found that pulmonary flow was equally reduced compared with normal flow in both patient groups. This reduction in flow can be attributed in part to the reduced size of the pulmonary arteries in both patient groups without change in axial velocity. We also found higher shear stress acting on the wall of the vessels in the patients having a bicaval tunnel, which may alter endothelial function and affect the longevity of the repair.     

Numerical study on the effect of steady axial flow development in the human aorta on local shear stresses in abdominal aortic branches

The three-dimensional flow through a rigid model of the human abdominal aorta complete with iliac and renal arteries was predicted numerically using the steady-state Navier Stokes equations for an incompressible. Newtonian fluid. The model adapted for our purposes was determined from data obtained from cine-CT images taken of a glass chamber that was constructed based on anatomical averages. The iliac arteries had a bifurcation angle of approximately 35 and a branch-to-trunk area ratio of 1.27. whereas the renal arteries had left and right branch angles of 40 and an area ratio of 0.73. The numerical tool FLOW3D (AEA Industrial Technology, Oxfordshire, UK) utilized body-fitted coordinates and a finite volume discretization procedure. Purely axial velocity profiles were introduced at the entrance of the model for a range of cardiac outputs. The four-branch numerical model developed for this investigation produced flow and shear conditions comparable to those found in other reported works. The total wall shear stress distribution in the iliac and renal arteries followed standard trends. with maximum shear stresses occurring in the apex region and lower shear stresses occurring along the lateral walls. Shear stresses and flow rate ratios in the downstream arteries were more effected by inlet Re than the upstream arteries. These results will be used to compare further simulations which take into effect the rotational component of flow which is present in the aortic arch.     

Viscous Effect on the Roll Motion of a Rectangular Structure

The viscous effect on the roll motion of a rectangular structure was investigated in a two-dimensional wave tank. The structure was used to simulate a simplified barge in the beam sea condition. The structure with a draft one-half of its height was hinged at the center of gravity and free to roll (1 degree of freedom) by waves. The dynamic characteristics of the structure were first identified, including its roll natural period. The dynamic response of the barge-like structure under wave actions was then tested with regular waves with a range of wave periods that are shorter, equal to, and longer than its roll natural period. Particle image velocimetry was used to obtain the velocity field in the vicinity of the structure. The coupled interactions between the incident waves and the structure were demonstrated by examining the vortical flow fields to elucidate the effect of viscous damping (also called the eddy making damping) to the roll motion of the structure over wave periods. For incoming waves with a wave period same as the roll natural period, the structure roll motion was, as expected, greatly reduced by the viscous-damping effect. At wave periods shorter than the roll natural period, the structure roll motion was slightly reduced by the viscous effect. However, at wave periods longer than the roll natural period, the viscous effect due to flow separation at structure corners indeed amplified the roll motion. This indicates that not only can the viscous effect damp out the roll motion, it can also amplify the roll motion.     

Experiments on Unsteady Turbulent Pipe Flow

The paper explores the time-wise evolution of selected turbulence parameters during gravity-driven flow establishment of incompressible fluids in rigid circular pipes. Two initial conditions are considered: flow starting from rest, passing through laminar-to-turbulent transition, and terminating in a turbulent steady state; and transient flow between two turbulent steady states. It is found that, in the second case, the properties considered, i.e., local temporal mean velocity and its transverse distribution, axial turbulence intensity, and wall shear stress, are monotonically increasing with time. However, for flow starting from rest, all properties are strongly affected by the development of turbulence. In particular, at the critical moment when laminar-to-turbulent transition is complete, the wall shear stress changes abruptly from one to the other, identifying wall shear stress as a very sensitive indicator of criticality.     

Finite element modeling of three-dimensional pulsatile flow in the abdominal aorta: relevance to atherosclerosis

The infrarenal abdominal aorta is particularly prone to atherosclerotic plaque formation while the thoracic aorta is relatively resistant. Localized differences in hemodynamic conditions, including differences in velocity profiles, wall shear stress, and recirculation zones have been implicated in the differential localization of disease in the infrarenal aorta. A comprehensive computational framework was developed, utilizing a stabilized, time accurate, finite element method, to solve the equations governing blood flow in a model of a normal human abdominal aorta under simulated rest, pulsatile, flow conditions. Flow patterns and wall shear stress were computed. A recirculation zone was observed to form along the posterior wall of the infrarenal aorta. Low time-averaged wall shear stress and high shear stress temporal oscillations, as measured by an oscillatory shear index, were present in this location, along the posterior wall opposite the superior mesenteric artery and along the anterior wall between the superior and inferior mesenteric arteries. These regions were noted to coincide with a high probability-of-occurrence of sudanophilic lesions as reported by Cornhill et al. (Monogr. Atheroscler. 15:13-19, 1990). This numerical investigation provides detailed quantitative data on hemodynamic conditions in the abdominal aorta heretofore lacking in the study of the localization of atherosclerotic disease.     

Evaluation of oxygen uptake and delivery in critically ill patients: a statistical reappraisal

Computer simulation of pulsatile non-Newtonian blood flow has been carried out in different human carotid artery bifurcation models. In the first part of the investigation, two rigid walled models are analysed, differing in the bifurcation angle (wide angle and acute angle bifurcation) and in the shape of both the sinus (narrow and larger sinus width) and the bifurcation region (small and larger rounding of the flow divider), in order to contribute to the study of the geometric factor in atherosclerosis. The results show a significant difference in the wall shear stress and in the flow separation. Flow recirculation in the sinus is much more pronounced in the acute angle carotid. An important factor in flow separation is the sinus width. In the second part of the study, flow velocity and wall shear stress distribution have been analysed in a compliant carotid artery bifurcation model. In the mathematical model, the non-Newtonian flow field and the idealized elastic wall displacement are coupled and calculated iteratively at each time step. Maximum displacement of approximately 6% of the diastolic vessel diameter occurs at the side wall of the bifurcation region. The investigation demonstrates that the wall distensibility alters the flow field and the wall shear stress during the systolic phase. Comparison with corresponding rigid wall results shows that flow separation and wall shear stress are reduced in the distensible wall model.     

Review of cardiovascular effects of fluoxetine, a selective serotonin reuptake inhibitor, compared to tricyclic antidepressants

The objective of this study is to find out which mathematical model best explains the temporal fluctuations of the axial blood flow velocity waveforms in the basal arteries of the brain. Blood flow velocity time series were sampled by transcranial Doppler (TCD) examination of the middle cerebral arteries in 10 healthy volunteers. A recently developed mathematical test (surrogate data analysis) was used to examine whether the spectral Doppler maximum waveform consistent with some prespecified model (null hypothesis). We tested four different null hypothesis. 1. Uncorrelated white noise. 2. Linearly filtered noise. 3. Linearly filtered noise with a static nonlinear amplitude transformation. 4. Noisy nonlinear limit cycle. All null hypotheses except the last one could be rejected. We conclude that the TCD waveforms are best described as nonlinear limit cycle with some percentage of noise, either dynamical and/or observational, which is uncorrelated from one single oscillation to the next. These results are a strong argument to perform nonlinear analysis in future TCD studies in order to obtain a better understanding of the cerebral hemodynamics.     

Effects of radial wall motion and flow waveform on the wall shear rate distribution in the divergent vascular graft

Among the hemodynamic factors influencing intimal hyperplasia in the anastomotic region of a vascular graft, wall shear rate is believed to be one of the most important. We would like to study the effects radial wall motion on the wall shear rate distribution in the end-to-end anastomosis model of an artery and a divergent graft. Rigid and elastic models are constructed and the wall shear rate distributions are measured along the anastomosis using photochromic flow visualization method for carotid and femoral flow waveform. The mean and peak of shear rate decrease along the divergent graft, and the decreases are more significant in the elastic model. The shear rate waves are decomposed using the Fourier transform in order to separate the effects of radial wall motion and geometry. The percentage reductions of mean wall shear rates compared to steady shear rates at mean flow are calculated, and additional 8% (carotid) and 22% (femoral) reductions are observed in the elastic models near the end of the divergent graft. Also radial wall motion decreases the amplitudes of higher harmonics of wall shear rates in the elastic models. Since radial wall motion may affect the flow field differently for different geometry, wall elasticity should be considered in studying arterial hemodynamics.     

Boundary Shear Stress in Spatially Varied Flow with Increasing Discharge

The distribution of the wall shear stress on the bed and sidewalls of an open channel receiving lateral inflow was obtained from experimental measurements of the distribution of the velocity in the viscous sublayer using a laser doppler velocimeter. The experiments were conducted in a 0.4 m wide by 7.5 m long flume. Lateral inflow was provided into the channel from above via sets of nozzles positioned toward the downstream end of the flume. Lateral inflow was provided over a length of 1.9 m. The results indicate that the local boundary shear stresses are significantly influenced by lateral inflow. The significant variation occurs near and around the region where the lateral inflow enters the channel. At various measurement positions along the lateral inflow zone, mean boundary, mean wall, and mean bed shear stresses were obtained and compared. The results indicate that the mean boundary shear stresses increase from the upstream to the downstream ends of the lateral inflow zone. The results also indicate that the mean bed shear stress is always greater than the mean wall shear stress, which are approximately 30–60% of the mean bed shear stress. The friction factor in the Darcy–Weisbach equation was obtained from both the mean boundary shear stress and from the equation describing the water surface elevation in an open channel receiving lateral inflow (equation for spatially varied flow with increasing discharge). The results indicate that the estimated friction factors from the latter approach are significantly larger. Also, the estimated friction factors from both approaches are higher than the values predicted from the Blasius equation which describes the friction factor for wide uniform open channel flows. They were also higher than values predicted from the Keulegan equation, which is an empirically derived equation for flow in roof drainage gutters. The study highlights the deficiencies in the existing equations used to predict friction factors for spatially varied flow and that further research is required to explore the distribution of boundary shear stress in an open channel receiving lateral inflow.     

Relationship between haemodynamics and morphology in pulmonary hypertension. A quantitative intravascular ultrasound study

BACKGROUND: Intravascular ultrasound imaging of the pulmonary arteries has been demonstrated to be a reliable method of quantifying vessel diameter, luminal area and pulsatility. Simultaneous measurement of flow velocity and its response to vasodilators allows the relationship between morphology and functional compromise to be studied, especially endothelial dysfunction. METHODS: In 51 patients (mean age = 49.8 +/- 12.6 years, 17 female) we performed right heart catheterization and simultaneous intravascular ultrasound of pulmonary artery branches. The patients were divided in two groups: group 1 with normal pulmonary artery pressure and pulmonary vascular resistance, and group 2 with pulmonary hypertension (peak pulmonary artery pressure > 30 mmHg and/or mean pulmonary artery pressure > 20 mmHg). Vessel wall and lumen were studied using a 2.9 F intravascular ultrasound catheter with a 30 MHz phased array transducer. Measurement of blood flow velocity was accomplished by a Doppler flow wire (0.018 inch). The maximal flow change during acetylcholine infusion (adjusted to 10(-6); 10(-5), and 10(-4) M concentration in the blood vessel) was measured. RESULTS: There were no significant differences between groups 1 and 2 with respect to age (48.5 +/- 14.3 years vs 50.3 +/- 12.3 years; P = ns), gender (4 female/8 male vs 13 female/26 male; P = ns), luminal area of the vessel segment in which the intravascular ultrasound measurements were obtained (11.8 +/- 6.1 mm2 vs 16.7 +/- 14.3 mm2; P = ns), internal diameter (3.9 +/- 1.2 mm vs 4.2 +/- 1.7 mm; P = ns), and external diameter (6.1 +/- 1.3 mm vs 6.9 +/- 2.1 mm; P = ns). Cross-sectional images of the pulmonary artery wall demonstrated a single ring with high echodensity with a thin inner layer regarded as intima in group 1. In contrast, the majority of patients (n = 35/39) in group 2 demonstrated a thickening of the intimal layer and/or a disturbance of layering of the echogenic arterial wall. The relative wall thickness was higher in group 2 than in group 1 (22.5 +/- 10.4% vs 15.3 +/- 6.5%; P < 0.05). There were no significant correlations between pulmonary artery pressure and wall thickness pulmonary artery pressure and area change in the cardiac cycle, acetylcholine-dependent increase in pulmonary flow and morphological changes in the vessel wall. CONCLUSION: We conclude that intravascular ultrasound is capable of detecting morphological changes in the pulmonary vessel wall in pulmonary hypertension and that vessel wall hypertrophy of small pulmonary segment arteries, as detected by intravascular ultrasound, is not predictive of functional vasodilatory response of resistance vessels of the same vessel area.     

Effects of curvature and stenosis-like narrowing on wall shear stress in a coronary artery model with phasic flow

To gain insight into the details of intracoronary flow we have used computational fluid dynamic techniques to determine the velocity and wall shear stress distributions in both steady- and phasic-flow models of a curved coronary artery with several degrees of stenosis. The steady-flow Reynolds number was 500 and the peak phasic flow Reynolds number was 700. Without stenosis and at 25% (area) stenosis wall shear stress and velocities are higher at the outer wall than the inner wall but retain the same direction as the superimposed flow. At higher stenoses laminar flow separation occurs and the inner wall is exposed to shear stresses that vary widely, both temporally and spatially.     

Hydrodynamic Behavior of Asymmetric Oscillatory Boundary Layers at Low Reynolds Numbers

An experimental and numerical study has been carried out to study the wave boundary layers under asymmetric waves. The experiments were conducted in an oscillating tunnel using a simple mechanical system to generate an asymmetric oscillatory motion similar to cnoidal waves. The velocities were measured by laser Doppler velocimetry and the bottom shear stress was calculated from the cross-stream velocity profile. A low Reynolds number k–ε model was used to predict the hydrodynamic properties of the cnoidal wave boundary layers. After validating the model with the experimental data, a series of numerical experiments were carried out to study the transitional behavior of these boundary layers by virtue of friction factor and phase difference between mean free-stream velocity and bottom shear stress. Finally a stability diagram was drawn to demarcate the laminar, transition, and fully turbulent regimes using the numerical results. The present study would be useful for the hydraulic and coastal engineers interested in calculating bottom shear stress in order to compute the sediment transport in coastal environments.     

Camp and Stein’s Velocity Gradient Formalization

Camp and Stein’s velocity gradient definition and its application to the study of fine sediment flocculation under flow shear are revised in the light of basic fluid mechanics concepts. Local motion and energy dissipation of a viscous fluid under laminar flow are used to prove that the Camp and Stein analysis was inaccurate for a general laminar movement. A generalization of Smoluchowski local aggregation equation and an alternative deduction for the parameter that Camp and Stein called velocity gradient are presented for a general laminar flow.     

A biomathematical model of intracranial arteriovenous malformations based on electrical network analysis: theory and hemodynamics

Hemodynamics play a significant role in the propensity of intracranial arteriovenous malformations (AVMs) to hemorrhage and in influencing both therapeutic strategies and their complications. AVM hemodynamics are difficult to quantitate, particularly within or in close proximity to the nidus. Biomathematical models represent a theoretical method of investigating AVM hemodynamics but currently provide limited information because of the simplicity of simulated anatomic and physiological characteristics in available models. Our purpose was to develop a new detailed biomathematical model in which the morphological, biophysical, and hemodynamic characteristics of an intracranial AVM are replicated more faithfully. The technique of electrical network analysis was used to construct the biomathematical AVM model to provide an accurate rendering of transnidal and intranidal hemodynamics. The model represented a complex, noncompartmentalized AVM with 4 arterial feeders (with simulated pial and transdural supply), 2 draining veins, and a nidus consisting of 28 interconnecting plexiform and fistulous components. Simulated vessel radii were defined as observed in human AVMs. Common values were assigned for normal systemic arterial pressure, arterial feeder pressures, draining vein pressures, and central venous pressure. Using an electrical analogy of Ohm's law, flow was determined based on Poiseuille's law given the aforementioned pressures and resistances of each nidus vessel. Circuit analysis of the AVM vasculature based on the conservation of flow and voltage revealed the flow rate through each vessel in the AVM network. Once the flow rate was established, the velocity, the intravascular pressure gradient, and the wall shear stress were determined. Total volumetric flow through the AVM was 814 ml/min. Hemodynamic analysis of the AVM showed increased flow rate, flow velocity, and wall shear stress through the fistulous component. The intranidal flow rate varied from 5.5 to 57.0 ml/min with and average of 31.3 ml/min for the plexiform vessels and from 595.1 to 640.1 ml/min with an average of 617.6 ml/min for the fistulous component. The blood flow velocity through the AVM nidus ranged from 11.7 to 121.1 cm/s with an average of 66.4 cm/s for the plexiform vessels and from 446.9 to 480 dyne/cm2 with an average of 463.5 dyne/cm2 for the fistulous component. The wall shear stress ranged in magnitude from 33.2 to 342.1 dyne/cm2 with an average of 187.7 dyne/cm2 for the plexiform vessels and from 315.9 to 339.7 cm/s with an average of 327.8 cm/s for the fistulous component. The described novel biomathematical model characterizes the transnidal and intranidal hemodynamics of an intracranial AVM more accurately than was possible previously. This model should serve as a useful research tool for further theoretical investigations of intracranial AVMs and their hemodynamic sequelae.     

A novel method for efficient drug delivery

Local delivery of anti-thrombotic and anti-restenotic drugs is desired to achieve high concentrations of agents which may be rapidly degraded systemically or which exhibit very short half-lives in vivo. In this article, the operating characteristics of a novel local drug delivery method are described and its effectiveness demonstrated computationally and experimentally. Computational models used a finite volume method to determine the concentration field. Optical dye density measurements of Evans blue in saline were performed in an in vitro steady flow system. Modeling parameters were kept in the physiologic range. Experimental flow visualization studies demonstrated high concentrations of infusate near the vessel wall. Computational studies predicted high, clinically significant drug concentrations along the wall downstream of the infusion device. When the radial infusion velocity is large (infusion flow rate, Qinf>0.5% of the main flow rate, Q), the wall concentration of the infused drug remains high, e.g., levels are greater than 80% of the infusate concentration 5 cm downstream of the infusion device. At lower infusion rates (Qinf<0.001Q), the drug concentration at the wall decreases exponentially with axial distance to less than 25% of the infusate concentration 5 cm downstream of the infusion device, although therapeutic drug levels are still readily maintained. The near wall drug concentration is a function of flow conditions, infusion rate, and the drug diffusivity. Good agreement was obtained between computational and experimental concentration measurements. Flow simulation and experimental results indicate that the technique can effectively sustain high local drug concentrations for inhibition of thrombosis and vascular lesion formation.     

Inverse effect of chronically elevated blood flow on atherogenesis in miniature swine

The effect of chronically elevated blood flow on the development of atherosclerosis in miniature swine was studied. Fistulas connecting the right external iliac artery and vein were surgically created in four swine, while three were not fistulated. Pulsed Doppler velocity detection cuffs placed around the abdominal aorta and both iliac arteries of all pigs permitted chronic measurements of blood velocity, blood velocity distributions, and blood flow. All swine were fed an atherogenic diet consisting of 20% beef tallow, 3% cholesterol, and 5% cholic acid for 6 months. This diet elevated the serum cholesterol to values exceeding 500 mg/100 ml. Creation of the arteriovenous fistula (AVF) markedly elevated blood velocity and flow in the abdominal aorta and in the shunted iliac artery. In the shunted animals the aortic blood flow was 42.1 +/- 2.0 ml/sec compared with 17.3 +/- 1.4 ml/sec in the unshunted swine. The velocity distribution pattern across the vessel was also indicative of an elevated wall shear stress. After 6 months, the animals were killed and the arterial vessels examined macroscopically and microscopically for the presence of atherosclerotic lesions. In the shunted pigs, 17 +/- 15% of the lumenal surface was occupied by sudanophilic lesions, whereas 80 +/- 8% of the surface was covered by lesions in the unshunted (control) pigs. From these studies, it is apparent that mechanical factors related to blood flow rates can influence the development of atherosclerotic lesions in swine.     

Wall Shear Stress in Transient Turbulent Pipe Flow by Local Velocity Measurement

The modeling of unsteady wall shear stress plays a crucial role in the analysis of fast transients in pressurized pipe systems, since it allows to evaluate transient energy dissipation properly. The main aim of this paper is to give a contribution to the understanding of transient pressurized flow dynamics in turbulent regime by measuring not only pressure but also the instantaneous axial velocity profile at two sections of the laboratory pipe. Specifically, by means of ultrasonic Doppler velocimetry—a completely nonintrusive technique—instantaneous velocity gradients at pipe wall are measured allowing to evaluate the time history of the actual wall shear stress by coupling velocity measurements to a two-zone stress model. As a result, the behavior of accelerating and decelerating flows with respect to the corresponding steady ones, i.e., with the same value of the discharge, is pointed out. Due to the characteristics of the laboratory pipe—a 352-m long high density polyethylene pipe—transients phenomena are investigated both at short and long time scales.