Computational simulation of biomechanics in e-PTFE and venous Miller's cuffs: implications for intimal hyperplasia.

A computational distal end-to-side Miller's cuff anastomotic model was used to analyse the possible difference in intimal hyperplasia (IH) formed between e-PTFE and venous cuffs. A large strain FEA model was used to compute the strain after physiological loading and the deformed geometries used as wall boundaries for CFD analysis. Regression analysis was performed to investigate relationships between mechanical factors and prior IH. The results showed that the venous Miller's cuff anastomosis deformed twice as much as the e-PTFE cuff and that the expansion of both cuffs generated elevated strains in the artery floor while the fluid shear indices were qualitatively similar in each case. In the e-PTFE cuff, the strain and OSI correlated with IH in a proportional and equivalent manner; however, these regressions grossly over-estimated the predicted IH in the vein cuff. Thus, biomechanical effects may be important in synthetically cuffed anastomoses, but do not account for the reduced IH in venous cuffed anastomoses.

Intimal hyperplasia and wall shear in arterial bypass graft distal anastomoses: an in vivo model study.

The observation of intimal hyperplasia at bypass graft anastomoses has suggested a potential interaction between local hemodynamics and vascular wall response. Wall shear has been particularly implicated because of its known effects upon the endothelium of normal vessels and, thus, was examined as to its possible role in the development of intimal hyperplasia in arterial bypass graft distal anastomoses. Tapered (4-7 mm I.D.) e-PTFE synthetic grafts 6 cm long were placed as bilateral carotid artery bypasses in six adult, mongrel dogs weighing between 25 and 30 kg with distal anastomotic graft-to-artery diameter ratios (DR) of either 1.0 or 1.5. Immediately following implantation, simultaneous axial velocity measurements were made in the toe and artery floor regions in the plane of the anastomosis at radial increments of 0.35 mm, 0.70 mm, and 1.05 mm using a specially designed 20 MHz triple crystal ultrasonic wall shear rate transducer Mean, peak, and pulse amplitude wall shear rates (WSRs), their absolute values, the spatial and temporal wall shear stress gradients (WSSG), and the oscillatory shear index (OSI) were computed from these velocity measurements. All grafts were harvested after 12 weeks implantation and measurements of the degree of intimal hyperplasia (IH) were made along the toe region and the artery floor of the host artery in 1 mm increments. While some IH occurred along the toe region (8.35+/-23.1 microm) and was significantly different between DR groups (p<0.003), the greatest amount occurred along the artery floor (81.6+/-106.5 microm, mean +/- S.D.) (p < 0.001) although no significant differences were found between DR groups. Linear regressions were performed on the paired IH and mean, peak, and pulse amplitude WSR data as well as the absolute mean, peak, and pulse amplitude WSR data from all grafts. The mean and absolute mean WSRs showed a modest correlation with IH (r = -0.406 and -0.370, respectively) with further improvements seen (r = -0.482 and -0.445, respectively) when using an exponential relationship. The overall best correlation was seen against an exponential function of the OSI (r = 0.600). Although these correlation coefficients were not high, they were found to be statistically significant as evidenced by the large F-statistic obtained. Finally, it was observed that over 75 percent of the IH occurred at or below a mean WSR value of 100 s(-1) while approximately 92 percent of the IH occurred at or below a mean WSR equal to one-half that of the native artery. Therefore, while not being the only factor involved, wall shear (and in particular, oscillators wall shear) appears to provide a stimulus for the development of anastomotic intimal hyperplasia.

Hemodynamic factors at the distal end-to-side anastomosis of a bypass graft with different POS:DOS flow ratios.

A pulsatile flow in vitro model of the distal end-to-side anastomosis of an arterial bypass graft was used to examine the effects that different flow ratios between the proximal outlet segment (POS) and the distal outlet segment (DOS) have on the flow patterns and the distributions of hemodynamic factors in the anastomosis. Amberlite particles were tracked by flow visualization to determine overall flow patterns and velocity measurements were made with Laser Doppler anemometry (LDA) to obtain detailed hemodynamic factors along the artery floor and the graft hood regions. These factors included wall shear stress (WSS), spatial wall shear stress gradient (WSSG), and oscillatory index (OSI). Statistical analysis was used to compare these hemodynamic factors between cases having different POS:DOS flow ratios (Case 1-0:100, Case 2-25:75, Case 3-50:50). The results showed that changes in POS:DOS flow ratios had a great influence on the flow patterns in the anastomosis. With an increase in proximal outlet flow, the range of location of the stagnation point along the artery floor decreased, while the extent of flow separation along the graft hood increased. The statistical results showed that there were significant differences (p<0.05) for the mean WSS between cases along the graft hood, but no significant differences were detected along the artery floor. There were no significant differences for the spatial WSSG along both the artery floor and the graft hood. However, there were significant differences (p<0.05) in the mean OSI between Cases 1 and 2 and between Cases 1 and 3 both along the artery floor and along the graft hood. Comparing these mechanical factors with histological findings of intimal hyperplasia formation obtained by previous canine studies, the results of the statistical analysis suggest that regions exposed to a combination of low mean WSS and high OSI may be most prone to the formation of intimal hyperplasia.

The persistence of electrostatically seeded endothelial cells lining a small diameter expanded polytetrafluoroethylene vascular graft.

PURPOSE: The purpose of this study was to evaluate the persistence of electrostatically seeded endothelial cells (ECs) lining an expanded polytetrafluorethylene (e-PTFE) graft after one week exposure to in vivo circulation in a canine femoral artery bypass model. This was accomplished by visualizing the PKH 26 (red fluorescent) label placed in the EC membranes prior to the seeding procedure. Furthermore, this study was performed to confirm that the source of the ECs lining the graft were those from the initial inoculum. METHODS: This evaluation consisted of harvesting autologous, canine jugular vein ECs, PKH 26 labeling of the ECs, electrostatic EC seeding the e-PTFE grafts (4mm GORE-TEX, Length=6cm), implanting the grafts (femoral artery model) for one week, and explanting the grafts for light, fluorescent and scanning electron microscopy evaluations of the luminal surface. RESULTS: The unseeded grafts (controls) had a mean fluorescence surface coverage of 6.82 +/- 7.19%, while the EC seeded grafts had a mean of 90.3 +/- 14.3% which is significantly (p <0.001) different from the controls. Overall, the seeding time including the EC harvesting and PKH 26 labeling protocol was approximately 75 min. CONCLUSIONS: The electrostatically seeded ECs persisted after implantation of the graft as demonstrated by the PKH 26 labeling data. The fluorescent data also demonstrated that the neointima formed (EC luminal surface coverage) one week after implantation was in fact derived from the ECs initially seeded as determined by the abundance of the labeled ECs.

Determination of the prime electrostatic endothelial cell transplantation procedure for e-PTFE vascular prostheses.

The purpose of this study was to evaluate the extent of cellular adhesion (density and morphological maturation), cellular membrane damage, and cellular viability after an electrostatic transplantation of human umbilical vein endothelial cells (HUVECs) onto 6-cm segments of 4-mm I.D. e-PTFE (GORE-TEX) vascular prostheses using a prototype electrostatic endothelial cell transplantation device (EECTD). The electrostatic transplantation parameters evaluated were the apparatus-applied voltage and transplantation time. By our definition, the combination of applied voltage and transplantation time that met the a priori criteria of: 1) maximum transplanted cellular viability, 2) maximum transplantation density, 3) maximum morphological maturation (degree of cellular flattening), and 4) minimal cellular membrane damage would be the prime transplantation procedure. The results of the experimentation indicated that the prime conditions for HUVEC transplantation were obtained when +1.0 V was applied for a transplantation time of 16 min. These conditions achieved an average viable graft surface coverage of 97.4+/-1.6% with an average transplantation density of 73,540+/-8.514 HUVECs/cm2. Furthermore, the transplanted HUVECs were morphologically mature (flattened) with minimal apparent cellular membrane damage (lysis or pitting). The overall clinical significance of this study is that viable endothelial cell transplantation to synthetic vascular grafts can be accomplished at high cellular densities and morphological maturation in 16 min using the EECTD. With the promising in vitro transplantation results, the next logical investigations will include additional in vitro evaluations (cellular retention upon shear stress exposure and biochemical assays) followed by in vivo evaluations to examine thromboresistance and influence on intimal/anastomotic hyperplasia.

The effect of graft caliber upon wall shear within in vivo distal vascular anastomoses.

Wall shear has been widely implicated as a contributing factor in the development of intimal hyperplasia in the anastomoses of chronic arterial bypass grafts. Earlier studies have been restricted to either: (1) in vitro or computer simulation models detailing the complex hemodynamics within an anastomosis without corresponding biological responses, or (2) in vivo models that document biological effects with only approximate wall shear information. Recently, a specially designed pulse ultrasonic Doppler wall shear rate (PUDWSR) measuring device has made it possible to obtain three near-wall velocity measurements nonintrusively within 1.05 mm of the vessel luminal surface from which wall shear rates (WSRs) were derived. It was the purpose of this study to evaluate the effect of graft caliber, a surgically controllable variable, upon local hemodynamics, which, in turn, play an important role in the eventual development of anastomotic hyperplasia. Tapered (4-7 mm I.D.) 6-cm-long grafts were implanted bilaterally in an end-to-side fashion with 30 deg proximal and distal anastomoses to bypass occluded common carotid arteries of 16 canines. The bypass grafts were randomly paired in contralateral vessels and placed such that the graft-to-artery diameter ratio, DR, at the distal anastomosis was either 1.0 or 1.5. For all grafts, the average Re was 432 +/- 112 and the average Womersley parameter, alpha, was 3.59 +/- 0.39 based on artery diameter. There was a sharp skewing of flow toward the artery floor with the development of a stagnation point whose position varied with time (up to two artery diameters) and DR (generally more downstream for DR = 1.0). Mean WSRs along the artery floor for DR = 1.0 and 1.5 were found to range sharply from moderate to high retrograde values (589 s-1 and 1558 s-1, respectively) upstream to high antegrade values (2704 s-1 and 2302 s-1, respectively) immediately downstream of the stagnation point. Although there were no overall differences in mean and peak WSRs between groups, there were significant differences (p < 0.05) in oscillatory WSRs as well as in the absolute normalized mean and peak WSRs between groups. There were also significant differences (p < 0.05) in mean and peak WSRs with respect to axial position along the artery floor for both DR cases. In conclusion, WSR varies widely (1558 s-1 retrograde to 2704 s-1 antegrade) within end-to-side distal graft anastomoses, particularly along the artery floor, and may play a role in the development of intimal hyperplasia through local alteration of mass transport and mechano-signal transduction within the endothelium.

Particle motion within in vitro models of stenosed internal carotid and left anterior descending coronary arteries.

Asymmetric 75% and 95% area reduction, transparent Sylgard stenotic models were operated under internal carotid artery (ICA) [Womersley parameter, alpha=5.36, Re(mean) =213 and 180, respectively, and Re(peak)=734 and 410, respectively] and left anterior descending coronary artery (LAD) flow wave forms (alpha=2.65, Re(mean)=59 and 57, respectively, and Re(peak)= 137 and 94, respectively) to evaluate the effect of these conditions on particle residence times downstream of the stenoses. Amberlite particles (1.05 g/cm3, 400 microm) were added to the fluid to simulate platelets and their motion through the stenotic region and were traced using a laser light sheet flow visualization method with pseudo-color display. Two-dimensional (2D) particle motions were recorded and particle washout in the stenotic throat and downstream section were computed for all cases. All four model cases demonstrated jetting through the stenosis which followed an arching pattern around a large separation zone downstream. Considerable mixing was observed within these vortex regions during high flow phases. Particle washout profiles showed no clear trend between the degrees of stenosis although particles downstream of the stenoses tended to remain longer for LAD conditions. The critical washout cycle (1% of particles remaining downstream of the stenosis), however, was longer for the 95% stenoses cases under each flow condition due to the larger protected region immediately downstream and maximal for the LAD 95% case. Results of this study suggest that particle residence times downstream of 75% and 95% stenoses (approximately 3-6 s for ICA and approximately 8-10 s for LAD) exceed the minimum time for platelet adhesion (approximately 1 s) for at least 1% of cells and, thus, may be sufficient to initiate thrombus formation under resting conditions.

In vitro evaluation of electrostatic endothelial cell transplantation onto 4 mm interior diameter expanded polytetrafluoroethylene grafts.

PURPOSE: To perform an in vitro evaluation of electrostatic endothelial cell transplantation of human umbilical vein endothelial cells (HUVEC) onto segments of 4 mm internal diameter expanded polytetrafluoroethylene (ePTFE) vascular prostheses. METHODS: This evaluation consisted of exposing vascular graft segments that had been subjected to either electrostatic or gravitation transplantation with HUVEC to a physiologic shear stress (15 dynes/cm2) under steady flow conditions within a flow loop system. Biochemical assays were performed on freshly transplanted grafts by means of radioimmunoassay for prostacyclin and thromboxane A2. RESULTS: There was a 30% loss of HUVEC after 30 minutes of shear stress exposure from the grafts subjected to gravitational transplantation with no additional significant (alpha = 0.05) loss after 120 minutes. Grafts subjected to electrostatic transplantation had no significant (alpha = 0.05) loss of HUVEC during exposure to physiologic shear stress. Furthermore, after 120 minutes of shear-stress exposure, the grafts subjected to electrostatic transplantation (78,420 +/- 6274 HUVEC/cm2) retained 2.3 times more HUVEC than the counterparts subjected to gravitational transplantation (34,427 +/- 4637 HUVEC/cm2). The biochemical assay results indicated no significant (alpha = 0.05) production of prostacyclin or thromboxane A2 regardless of the method of cell transplantation. CONCLUSIONS: (1) The electrostatic transplantation technique was superior to the gravitational transplantation technique in terms of cellular retention when the ePTFE grafts were exposed to physiologic shear stress. (2) Production of prostacyclin and thromboxane A2 did not differ between transplanted HUVEC subjected to gravitational or electrostatic procedures.

Electrostatic endothelial cell seeding technique for small-diameter (<6 mm) vascular prostheses: feasibility testing.

Multiple studies have indicated the importance of surface charge in the adhesion of multiple cardiovascular cell lines including platelets and endothelial cells on the substrate materials (1,4,7-10,12-15). It is the purpose of this article to report a feasibility study conducted using an electrostatic endothelial cell seeding technique. The feasibility study was conducted using human umbilical vein endothelial cells (HUVEC), a static pool apparatus, a voltage source, and a parallel plate capacitor. The HUVEC concentration and seeding times were constant at 560,000 HUVEC/ml and 30 min, respectively. Scanning electron microscopy examination of the endothelial cell adhesion indicated that an induced temporary positive surface charge on e-PTFE graft material enhances the number and the maturation (flattening) of HUVECs adhered. The results indicated that the total number of endothelial cells adhered (70.9 mm2) was increased from 9198 +/- 1194 HUVECs on the control (no induced surface charge) e-PTFE to 22,482 +/- 4814 HUVECs (2.4 x control) on the maximum induced positive surface charge. The total number of cells in the flattened phase of adhesion increased from 837 +/- 275 to 6785 +/- 1012 HUVECs (8.1x) under identical conditions. Thus, the results of the feasibility study support the premise that electrostatic interaction is an important factor in both the endothelial cell adhesion and spreading processes and suggest that the electrostatic seeding technique may lead to an increased patency of small diameter (<6 mm) vascular prostheses.

Electrostatic endothelial cell transplantation within small-diameter (<6 mm) vascular prostheses: a prototype apparatus and procedure.

This article presents a novel, clinically relevant electrostatic endothelial cell transplantation (seeding/sodding) device (U.S. & Foreign Patent Protections Pending) for small-diameter (<6 mm) vascular prostheses. The prototype apparatus was designed and built to tissue engineer 4.0 mm, I.D. GORE-TEX (W.L. Gore & Associates, Inc.) standard wall graft segments varying in length from 4 to 12 cm. The prototype electrostatic endothelial cell transplantation apparatus is composed of an external and internal conductor, aluminum base, end supports, pillow blocks, filling apparatus, electric motor drive system, and a voltage source. The cylindrical capacitor arrangement of the device along with an electrical potential applied across the internal and external conductors creates the unique feature of this endothelial cell transplantation technique, an electric field within the cylindrical capacitor (within the graft lumen) which in turn induces a temporary positive surface charge on the graft (dielectric material) luminal surface. Multiple studies have shown that a positively charged substrate is more conducive to endothelial cell adhesion and morphological maturation (flattening) (1,2, 7,8,10,13-15). This induced positive surface charge dissipates immediately upon removal from the electrostatic endothelial cell transplantation device. Thus, after endothelial cell adhesion the graft luminal surface reverts back to its natural (nonthrombogenic) negative surface charge.

The effect of angle and flow rate upon hemodynamics in distal vascular graft anastomoses: a numerical model study.

Flow in distal end-to-side anastomoses of iliofemoral artery bypass grafts was simulated using a steady flow, three-dimensional numerical model. With the proximal artery occluded, anastomotic angles were varied over 20, 30, 40, 45, 50, 60 and 70 deg while the inlet Reynolds numbers were 100 and 205. Fully developed flow in the graft became somewhat skewed toward the inner wall with increasing angle for both Reynolds numbers. Separated flow regions were seen along the inner arterial wall (toe region) for angles > or = 60 deg at Re = 100 and for angles > or = 45 deg at Re = 205 while a stagnation point existed along the outer arterial wall (floor region) for all cases which moved downstream relative to the toe of the anastomosis with decreasing angles. Normalized shear rates (NSR) along the arterial wall varied widely throughout the anastomotic region with negative values seen in the separation zones and upstream of the stagnation points which increased in magnitude with angle. The NSR increased with distance downstream of the stagnation point and with magnitudes which increased with the angle. Compared with observations from chronic in vivo studies, these results appear to support the hypothesis of greater intimal hyperplasia occurring in regions of low fluid shear.

Derivation of shear rates from near-wall LDA measurements under steady and pulsatile flow conditions.

Atherosclerosis, thrombosis, and intimal hyperplasia are major forms of cardiovascular diseases in the United States. Previous studies indicate a significant correlation between hemodynamics, in particular, wall shear rate, and pathology of the arterial walls. While results of these studies implicate morphologic and functional changes related to wall shear rate magnitude, a standard technique for wall shear rate measurement has not been established. In this study, theoretical and in-vitro experimental fully developed steady and physiologic pulsatile flow waveforms have been used to obtain velocity profiles in the near-wall region. The estimated wall shear rates from these results are compared to the theoretical value to assess the accuracy of the approximating technique. Experimentally obtained results from LDA suggest that in order to minimize the error in velocity data, and subsequently, the wall shear rate, the first measured velocity has to be 500 microns away from the wall. While a linear approximation did not produce errors larger than 16.4 percent at peak systole, these errors substantially increased as the velocity magnitudes decreased during late systole and diastole. Overall, a third degree polynomial curve fit using four points produced the most accurate estimation of wall shear rate through out the cardiac cycle. Results of higher degree curve-fitting functions can be unpredictable due to potential oscillations of the function near the wall. Hence, based on the results of this study, use of a linear approximation is not recommended; a third degree curve-fitting polynomial, using four points provided the most accurate approximation for these flow waveforms.

Effect of controlled local acetylsalicylic acid release on in vitro platelet adhesion to vascular grafts.

Thrombosis is the most serious acute problem for small diameter arterial bypass grafts. In this research, small diameter expanded polytetrafluoroethylene (e-PTFE) vascular grafts were coated with acetylsalicylic acid (ASA) loaded poly (d,l-lactide) (PLA) by a solvent casting method. The feasibility and efficacy of this approach were evaluated by ASA release studies and platelet adhesion tests. First, the ASA release kinetics were evaluated from the ASA/PLA coated vascular grafts in an in vitro steady flow loop model. ASA release was measured by a spectrophotometric technique. Finally, the efficacy of local ASA release to reduce in vitro canine platelet adhesion to grafts was determined with epifluorescent video microscopy and quantitative image analysis. The steady state release rates from the 5%, 10%, and 15% ASA/PLA coated grafts were 13.2 x 10(-5), 32.0 x 10(-5), and 41.5 x 10(-5) micrograms/cm2.sec, respectively. Platelet adhesion to 10% and 15% ASA/PLA coated grafts was reduced with respect to the control and 5% grafts for 10 days. Platelet adhesion to 5% ASA/PLA coated grafts was reduced with respect to controls at 2 and 10 days, but not initially.

Doppler color flow images of iliofemoral graft end-to-side distal anastomotic models.

Hemodynamics within the distal anastomoses of iliofemoral bypass grafts were simulated using Plexiglas models (2.5 cm ID) within a pulsatile flow loop system (Re(mean) = 92, Re(peak) = 459 and alpha = 3.56). End-to-side distal anastomoses were constructed with angles of 30 degrees, 45 degrees and 60 degrees to bypass proximal artery segments with stenoses of 60% and 100% diameter reduction. Velocities were obtained over a two-dimensional field within the artery using an ultrasonic Doppler color flow imager operating at 5 MHz at positions from 1.5 diameters upstream to 3 diameters downstream of the anastomosis. Flow patterns downstream of an occlusion demonstrated definite skewing effects toward the outer wall with resultant flow separation along the inner wall. Presence of a partial (60% diameter reduction) arterial stenosis upstream of the anastomosis produced flow separation along both artery walls and a more symmetric profile downstream. Measurement of a separation area index (SAI) along each arterial wall demonstrated a minimum area exposed to low velocities for the 30 degrees anastomotic angle compared to the 45 degrees and 60 degrees anastomotic angles and for the occluded proximal artery cases compared to corresponding stenotic artery cases. The SAI values were minimal at peak systole compared to successive quarter cycle intervals. The findings of this study provide further information regarding the relationship between local fluid mechanics and predominant sites for intimal hyperplasia formation.

Quantification of Doppler color flow images from a stenosed carotid artery model.

Velocity fields at and downstream of graded, axisymmetric stenoses of 0%, 20%, 40%, 60% and 80% diameter reduction were obtained under pulsatile flow conditions simulating that in a carotid artery (Re(mean) = 379, Re(peak) = 1137 and alpha = 5.36) using an ultrasonic Doppler Color Flow Imager. Characteristic features of flow disturbances associated with degree of stenosis, such as jetting, flow separation and reversal and turbulence were quantified using nondimensional indices at peak systole, t0, and early diastole, t1. It was found that the Reverse Area Index (RAI), the Field Profile Index (FPI) and the Velocity Gradient Indices (VGIz and VGIr) were sensitive to these changes, especially at time t1. In particular, the mean values of RAI and VGIr were significantly different for all stenotic cases. These findings may provide a more quantitative and reproducible method of interpreting flow patterns in the region of stenosed carotid arteries.

The effect of angle and flow rate upon hemodynamics in distal vascular graft anastomoses: an in vitro model study.

A steady flow, in vitro model of distal arterial bypass graft junctions was used to examine the effects of junction angle and flow rate on the local velocity field. Three test sections were fabricated from Plexiglas tubing having anastomotic junction angles of either 30, 45, or 60 deg. Flow visualization revealed velocity profiles skewed toward the outer wall with a flow split around a clear stagnation point along the outer wall. Laser Doppler anemometry [LDA] measurements confirmed a distinct stagnation point at the outer wall and both reverse and forward shear were detected immediately upstream and downstream, respectively, of this site. Axial velocities and shear rates along the outer wall were higher than along the inner wall and occurred in the junction angle order: 45, 60, and 30 deg. This study clearly identified changes in wall shear which varied with the anastomotic angle and flow rate.

Doppler color-flow images from a stenosed arterial model: interpretation of flow patterns.

The capability of the recently introduced Doppler color-flow mapping devices to accurately detect flow patterns in the region of an arterial stenosis was evaluated by use of an in vitro flow model. Pulsatile flow simulating that in a low-resistance vessel was induced through a straight acrylic tube, which alternatively contained axisymmetric stenoses of 0%, 20%, 40%, 60%, and 80% diameter reduction. Doppler color-flow mapper images were taken in realtime along the tube midplane from 0 to 8 diameters downstream of each stenosis. Comparison of the Doppler color-flow mapping results with similarly recorded flow visualization (hydrogen bubble) images showed a close correspondence of key features of the flow, including detection of a high-velocity, centerline jet and near-wall separated flow zones. Distinctive flow patterns exist with each stenotic case, and these should be of considerable value in diagnosing clinical disease conditions.

Velocity profiles in stenosed models using magnetic resonance imaging.

A time-of-flight MRI velocity measurement technique is evaluated against corresponding LDV measurements in a constriction tube model over a range of physiologic flow conditions. Results from this study show that MR displacement images can: (1) be obtained within both laminar and turbulent jets (maximum stenotic Re approximately equal to 4,200); (2) measure mean jet velocities up to 172 cm/s, and (3) detect low forward and reverse velocity regions near the tube wall just downstream of the stenosis (0 less than or equal to L/D less than or equal to 2). Regions between the jet termination point and reestablishment of laminar flow (Re greater than 1,500, greater than 1,000 and greater than 110 downstream of 40, 60 and 80% stenosis, respectively) cannot presently be detected by this technique.

MR imaging of model fluid velocity profiles.

A projection MR technique for imaging the velocity profiles of moving fluids has been applied to various steady flow models designed to simulate a variety of flow conditions. From such profiles can be readily deduced peak velocities, volume flow rates, information concerning the degree of flow development, features such as flow separation, and estimates shear stresses at the vessel wall.

Velocity profiles in stenosed tube models using magnetic resonance imaging.

A time-of-flight MRI velocity measurement technique is evaluated against corresponding LDV measurements in a constriction tube model over a range of physiologic flow conditions. Results from this study show that MR displacement images can: 1) be obtained within both laminar and turbulent jets (maximum stenotic Re approximately equal to 4,200), 2) measure mean jet velocities up to 172 cm/s, and, 3) detect low forward and reverse stenosis (0 less than or equal to L/D less than or equal to 2). Regions between the jet termination point and re-establishment of laminar flow (Re greater than or equal to 1500, greater than or equal to 1000, and greater than or equal to 110 downstream of 40, 60, and 80 percent stenosis, respectively) cannot presently be detected by this technique.