Bio-Medical Materials and Engineering 24 (2014) 853–860 DOI 10.3233/BME-130877 IOS Press
853
Comparison between experimentally measured flow patterns for straigth and helical type graft Sandor I. Bernad a, Alin Bosioc a, Elena S. Bernad b, * and Marius L. Craina b a
Romanian Academy – Timisoara Branch, Centre for Fundamental and Advanced Technical Research, Bd. Mihai Viteazul 24, RO-300223, Timisoara, Romania b University of Medicine and Pharmacy “Victor Babes” Timisoara, Universitary Clinic “Bega”, P-ta Eftimie Murgu 2, RO-300041, Timisoara, Romania
Abstract. The long-term success of arterial bypass surgery is often limited by the progression of intimal hyperplasia at the anastomosis between the graft and the native artery. The experimental models were manufactured from glass tubing with constant internal diameter of 8 mm, fashioned into a straight configuration and helical configuration. The aim of this study was to determine the three-dimensional flow structures that occur at the proximal anastomosis under pulsatile flow conditions, to investigate the changes that resulted from variations in the anastomosis angle and flow division, and to establishing the major differences between the straight and helical graft. In the anastomosis domain, a strong region of recirculation is observed near the occluded end of the artery, which forces the flow to move into the perfused host coronary artery. The proximal portion of the host tube shows weak counter-rotating vortices on the symmetry plane. The exact locations and strengths of the vortices in this region are only weakly dependent on Re. A detailed comparison of experimentally measured axial velocity patterns for straight and helical grafts confirm the very strong nature of the secondary flows in the helical geometry. The helical configuration promotes the mixing effect of vortex motion such that the flow particles are mixed into the blood stream disal to the anastomotic junction. Keywords: Bypass graft, helical graft, hemodynamics, anastomosis
1. Introduction The long-term success of arterial bypass surgery is often limited by the progression of intimal hyperplasia at the anastomosis between the graft and the native artery [14]. Many factors such as compliance mismatch, effects of sutures, and the hemodynamic environment, may contribute to the initiation and progression of intimal hyperplasia [14]. As it has been widely reported that end-to-side vascular bypass grafts generally fail at the distal anastomosis [1,6,9], this study argues that junction hemodynamics are of primary concern in attempting to find a solution to the problem of low long-term patency rates for the vascular bypass graft.
*
Corresponding author. E-mail: [email protected]
0959-2989/14/$27.50 © 2014 – IOS Press and the authors. All rights reserved
854
S.I. Bernad et al. / Comparison between experimentally measured flow patterns
Studies have also shown that disturbed blood flow patterns can affect the wall shear stress magnitudes and gradients, which in turn may lead to atherosclerosis and intimal hyperplasia [11, 7, 4, 10]. Disturbed flow patterns are initiated by a change in the geometry of the vessel through which the blood flows. The region of flow stagnation in the end-to-side anastomosis with high pressure and high stress may also be a site of intimal hyperplasia and platelet deposition [12, 8]. On the other hand, regions with low flow, e.g., stagnation or recirculation, were also identified as the sites of thrombotic depositions in other systems [15]. The aim of this study was to determine the three-dimensional flow structures that occur at the proximal anastomosis under pulsatile flow conditions, to investigate the changes that resulted from variations in the anastomosis angle and flow division, and to establishing the major differences between the straight and helical graft. The objectives of the study were: − To examine the flow features in the the straight and helical graft model over a range of Reynolds numbers for pulsatile flow conditions. − To locate the flow features in the both model under pulsatile flow conditions for comparison with the known locations of intimal hyperplasia in vivo. − To estimate the likely physical effects of the flow on the walls of the both model and from them the effects of blood flow on the walls of the blood vessels. 2. Methods Flow structures were determined predominantly in the 60 deg model, in planes parallel and perpendicular to the symmetry plane of the anastomosis.
Fig. 1. Experimental bypass models manufactured from glass tubing with constant internal diameter of 8 mm. Helical and straight type model.
S.I. Bernad et al. / Comparison between experimentally measured flow patterns
855
Subsequent experiments and numerical simulation for the straight and helical graft were performed in the 30 and 45 deg models to assess the effects of the angle of anastomosis. The experimental model of the graft-to-artery anastomosis is illustrated in Figure 1. We assumed that the proximal portion of the parent vessel is completely occluded, so that all flow entered the anastomosis through the graft. In the first phase of the study, unsteady flow in the model was obtained using a computer-controlled pump at a variety of flow rates, leading to Reynolds numbers (based on mean inlet velocity and tube diameter) of 280 to 950 (Figure 2). Both in experimental setup and in numerical simulations the unsteady flow model was used.
Fig. 2. Pulsatile inlet flow condition. A) Pulsatile wave used in experimental investigation. B) Pulsatile wave used for numerical simulations.
2.1. Experimental setup The experimental models were manufactured from glass tubing with constant internal diameter of 8 mm, fashioned into an straight configuration and helical configuration with an approximately 8 cm straight segment proximally and 11 cm distally (Figure 1). The flow system consisted of: a constant storage head tank; test section; floating ball flowmeter; collecting tank; and variable speed centrifugal pump. The mean flow rate was measured by a metric size 10 rotameter with a stainless steel float. The rotameter leg served the extra purpose of preventing air from travelling upstream from the flow outlet. A blood analog fluid was prepared having dynamic viscosity () of 0.00408 Pa.s and a density () of 1050 kg/m3. The flow visualization study involved the injection of a bolus of ink into water flowing at a different Reynolds numbers. Both numerical simulations and experimental investigations have been carried out over a range of Reynolds numbers (based on the centreline temporally averaged streamwise velocity and the bypass radius) from 250 to 1200. The maximum Reynolds number during the cycle was about 1118.
856
S.I. Bernad et al. / Comparison between experimentally measured flow patterns
2.2. Numerical techniques The authors have used simplified geometry (Figure 3) for the by-pass graft model with graft angles of 30°, 45°, and 60° for the analysis of the flow around the graft junction, and across the bed of the host tube. The internal diameter for the graft was taken to be D=8 mm with a graft–tube diameter ratio of 1:1 (Figures 3 and 4).
Fig. 3. By-pass graft geometry along the longitudinal plane for three graft angles (30°, 45° and 60°).
Fig. 4. Different section used for hydrodynamic parameters investigation.
Due to the elliptical nature of the flow conditions, boundary conditions must be specified at all the domain boundaries. Inlet: a uniform inflow velocity profile for the axial velocity component and a zero transverse velocity component are used. Outlet: the outlet pressure was defined to be 0 Pa. Wall: the vessel wall was assumed to be rigid and nonslip, considering that blood vessel prostheses usually deform very little under pressure. The fluid is incompressible having dynamic viscosity () of 0.00408 Pa.s and a density () of 1050 kg/m3. The bypass walls are considered rigid and impermeable. The numerical simulation is performed using the commercial CFD software FLUENT 6.3 [5]. 3. Results Two models studies were undertaken to increase understanding of the flow in a straight, one involving computational fluid dynamics (CFD) and the other, flow visualization. In both studies, the geometry and time-average flow were similar. Boundary layer separation is a well known phenomenon associated with sudden changes in surface geometry. The free shear layer resulting from a flow separation is likely to contain pressure, velocity and consequently local shear fluctuations which could be felt at the wall at the points of separation and of reattachment. Figures 5 and 6 shows the flow structure in the 60 degree proximal anastomosis under pulsatile flow conditions corresponding to the first peak of the velocity waveform (Figure 2) for the experimental setup and the numerical simulations. Note the presence of two vortices in the occluded part of the bypass graft, and strong helical flow in the distal artery is observed in both models. The secondary vortex (V1), that is the larger vortex closest to the anastomosis, rotated clockwise (as viewed in the Figures 5
S.I. Bernad et al. / Comparison between experimentally measured flow patterns
857
and 6), whereas the distal primary vortex (V2) rotated anti-clockwise. In the anastomosis domain, a strong region of recirculation is observed near the occluded end of the artery, which forces the flow to move into the perfused host coronary (distal) artery as indicated in Figures 5 and 6.
Fig. 5. Flow pattern in straight bypass graft demosntrating secondary flow. Spontaneous periodic disturbances in the distal part of the host artery. This kind of disturbances fade distally.
Fig. 6. Flowfields are shown for the 60° graft angle. Three-dimensional view of the pathline of the high inertia fluid showing development of the double helix. Dean vortices development in distal part of the host artery. Results prezented are obtained from numerical simulation.
858
S.I. Bernad et al. / Comparison between experimentally measured flow patterns
Just downstream of the toe, at axial position of X = 0.15 m, the axial velocity profile was skewed toward the far wall, and flow separation was observed along the near wall (Figure 6). The trace at X = 0.15 m, clearly displayed the presence of secondary flow, which consisted of low inertia fluid swirling circumferentially around the vessel towards the near wall and the high inertia fluid from the core region being forced toward the far wall. Once the high inertia fluid approaches the far wall, it too travels circumferentially in a spiraling manner because of the centrifugal force generated by the change in flow direction (Figure 6). Figure 6 shows the path line for the longitudinal section through the bypass junction for anastomotic angles of 60°. The highly transient character of the disturbed pulsatile flowfields became most apparent at the beginning of each cycle. It is clear that reversed flow at the wall decreases near the heel and increases near the toe with an increase in anastomotic angle. A detailed comparison of numerically computed and experimentally measured flow patterns shows generally good agreement (Figures 5 and 6). The agreement on the symmetry plane is particularly good, with the minor exception that the numerical results predict a slightly larger second retrograde flow zone than was measured experimentally (Figure 6). 4. Discussion Arterial geometry is commonly three-dimensional [2], and the properties of inertial dominated flows in such geometries include swirling, in-plane mixing, a relatively uniform distribution of wall shear, and inhibition of flow stagnation, separation and instability [3, 13].
Fig. 7. Comparison between flow pattern corresponding to the straight bypass graft and helical type bypass graft.
S.I. Bernad et al. / Comparison between experimentally measured flow patterns
859
Based on experimental data and numerical results, the following general features of the velocity field can be identified: − A core of high-momentum fluid enters the junction from the graft tube and travels towards a stagnation point on the bed of the host tube. In the neighborhood of this stagnation point, the flow splits into forward and retrograde components having large near-wall velocities (Figure 5 and Figure 7). − The proximal portion of the host tube shows weak counter-rotating vortices on the symmetry plane. The exact locations and strengths of the vortices in this region are only weakly dependent on Re. − Extremely strong secondary flows are present in the downstream section of the host tube, qualitatively similar to Dean-type vortices (Figure 6). The magnitude of the secondary flows increases with increasing Re, leading to a tighter pitch of the helical fluid paths within the host tube. − During the accelerating part of the second velocity peak (Figure 2), two distinct zones of retrograde flow exist: a first zone immediately distal to the toe, and a second zone further downstream (Figure 7). Although the length of the first retrograde flow zone is only very weakly dependent on Re, the length of the second zone increases with Re. A detailed comparison of experimentally measured axial velocity patterns for straight and helical grafts is presented in Figure 7. The axial velocity patterns on the symmetry plane show a doublepeaked profile that is reminiscent of entry flow in a curved tube (Figure 7), confirming the very strong nature of the secondary flows in the helical geometry. On the symmetry plane of the straight graft model, the experimental data show evidence of flow asymmetry (Figure 7). The velocity near the vessel wall and the wall shear rate are enhanced in the helical graft model. We believe that the enhanced blood velocity near the vessel wall and the wall shear rate can impede the staying and adherence of platelets and leucocytes to the surface of the graft, reducing the possibility of thrombosis formation. 5. Conclusions For a 60 degree anastomotic junction we have clearly demonstrated the complex nature of the flow pattern. To determine the relationship between hemodynamic factors and intimal hyperplasia, we feel that additional studies should be conducted to assess the influence of the angle of the anastomosis, elasticity, impedance mismatch, and other factors. Two model studies were undertaken to increase understanding of the flow in straight tubes, one involving computational fluid dynamics (CFD) and the other, flow visualization. In both studies, the geometry and time-average flow were similar. In helical model a mixing zone with vortex motion provides an environment for coagulant factors to be in transit without being stagnant near the surface such that activation of the intrinsic coagulation process can be suppressed. Furthermore, the helical configuration promotes the mixing effect of vortex motion such that the anti-coagulant mixed vigorously into the blood stream. The present results can provide a better understanding of the effect of geometrical configurations of helical vascular prostheses on the hemodynamic flow. We believe that the swirling flow created in this kind of helical graft may also have an advantage of suppressing flow disturbance at the distal anastomsis.
860
S.I. Bernad et al. / Comparison between experimentally measured flow patterns
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12] [13]
[14] [15]
P.D. Ballyk, C. Walsh, J. Butany and M. Ojha, Compliance Mismatch May Promote Graft-Artery Intimal Hyperplasia by Altering Suture-line Stresses, J. Biomech., 31 (1998), 229–237. C.G. Caro, D.J. Doorly, M. Tarnawski, K.T. Scott, Q. Long and C.L. Dumoulin, Non-planar curvature and branching of arteries and non-planar-type flow. Proc. R. Soc., A 452 (1996), 185–197. C.G. Caro, N. Watkins, D.J. Doorly, S.J. Sherwin and J. Peiro´, Influence of non-planar geometry on flow separation. J. Physiol., 513 (1998), 2. R.S. Fatemi and S.E. Rittgers, Derivation of Shear Rates from Near-wall LDA Measurements under Steady and Pulsatile Flow Conditions, J. Biomech. Eng., 116 (1994), 361–367. FLUENT 6.3 User’s Guide. Ansys Fluent Incorporated (2006). F.S. Henry, M.W. Collins, P.E. Hughes and T.V. How, Numerical Investigation of Steady Flow in Proximal and Distal End-to-side Anastomoses, J. Biomech. Eng., 118 (1996), 302–310. M. Hofer, G. Rappitsch, K. Perktold, W. Trubel and H. Schima, Numerical Study of Wall Mechanics and Fluid Dynamics in End-to-side Anastomoses and Correlation to Intimal Hyperplasia, J. Biomech., 29(10) (1996), 1297–1308. U. Krueger, J. Zanow and H Scholz, Computational fluid dynamics and vascular access. Artif Organs, 26 (2002), 571–5. S.M. Kute and D.A. Vorp, The Effect of Proximal Artery Flow on the Hemodynamics at the Distal Anastomosis of a Vascular Bypass Graft: Computational Study, J. Biomech. Eng., 123 (2001), 277–283. A. Leuprecht, K. Perktold, M. Prosi, T. Berk, W. Trubel and H. Schima, Numerical Study of Hemodynamics and Wall Mechanics in Distal Endto- side Anastomoses of Bypass Grafts, J. Biomech., 35 (2002), 225–236. F. Loth, S.A. Jones, C.K. Zarins, D.P. Giddens, R.F. Nassar, S. Glagov and H.S. Bassiouny, Relative Contribution of Wall Shear Stress and Injury in Experimental Intimal Thickening at eP.T.FE End-to-Side Arterial Anastomoses, J. Biomech. Eng., 124 (2002), 44–51. A. Quarteroni, M. Tuveri and A. Veneziani, Computational vascular dynamics: problems, models and methods. Comput Visual Sci., 2(2002), 163–97. S.J. Sherwin, O. Shah, D.J. Doorly, M. McLean, N. Watkins, C.G. Caro, J. Peiro, M. Tarnawski and C.L. Dumoulin, Visualisation and computational study of flow at model planar and non-planar end-to-side arterial bypass grafts. J. Physiol., 504 (1997), 44. V.S. Sottiurai, J.S.T. Yao, W.R. Flinn, R.C. Baston, Intimal hyperplasia and neointima: an ultrastructural analysis ofthrombosed grafts in humans. Surgery, 93 (1983), 809-17. P. Verdonck, The role of computational fluid dynamics for artificial organ design. Artif Organs, 26 (2002), 569–70.
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853
Comparison between experimentally measured flow patterns for straigth and helical type graft Sandor I. Bernad a, Alin Bosioc a, Elena S. Bernad b, * and Marius L. Craina b a
Romanian Academy – Timisoara Branch, Centre for Fundamental and Advanced Technical Research, Bd. Mihai Viteazul 24, RO-300223, Timisoara, Romania b University of Medicine and Pharmacy “Victor Babes” Timisoara, Universitary Clinic “Bega”, P-ta Eftimie Murgu 2, RO-300041, Timisoara, Romania
Abstract. The long-term success of arterial bypass surgery is often limited by the progression of intimal hyperplasia at the anastomosis between the graft and the native artery. The experimental models were manufactured from glass tubing with constant internal diameter of 8 mm, fashioned into a straight configuration and helical configuration. The aim of this study was to determine the three-dimensional flow structures that occur at the proximal anastomosis under pulsatile flow conditions, to investigate the changes that resulted from variations in the anastomosis angle and flow division, and to establishing the major differences between the straight and helical graft. In the anastomosis domain, a strong region of recirculation is observed near the occluded end of the artery, which forces the flow to move into the perfused host coronary artery. The proximal portion of the host tube shows weak counter-rotating vortices on the symmetry plane. The exact locations and strengths of the vortices in this region are only weakly dependent on Re. A detailed comparison of experimentally measured axial velocity patterns for straight and helical grafts confirm the very strong nature of the secondary flows in the helical geometry. The helical configuration promotes the mixing effect of vortex motion such that the flow particles are mixed into the blood stream disal to the anastomotic junction. Keywords: Bypass graft, helical graft, hemodynamics, anastomosis
1. Introduction The long-term success of arterial bypass surgery is often limited by the progression of intimal hyperplasia at the anastomosis between the graft and the native artery [14]. Many factors such as compliance mismatch, effects of sutures, and the hemodynamic environment, may contribute to the initiation and progression of intimal hyperplasia [14]. As it has been widely reported that end-to-side vascular bypass grafts generally fail at the distal anastomosis [1,6,9], this study argues that junction hemodynamics are of primary concern in attempting to find a solution to the problem of low long-term patency rates for the vascular bypass graft.
*
Corresponding author. E-mail: [email protected]
0959-2989/14/$27.50 © 2014 – IOS Press and the authors. All rights reserved
854
S.I. Bernad et al. / Comparison between experimentally measured flow patterns
Studies have also shown that disturbed blood flow patterns can affect the wall shear stress magnitudes and gradients, which in turn may lead to atherosclerosis and intimal hyperplasia [11, 7, 4, 10]. Disturbed flow patterns are initiated by a change in the geometry of the vessel through which the blood flows. The region of flow stagnation in the end-to-side anastomosis with high pressure and high stress may also be a site of intimal hyperplasia and platelet deposition [12, 8]. On the other hand, regions with low flow, e.g., stagnation or recirculation, were also identified as the sites of thrombotic depositions in other systems [15]. The aim of this study was to determine the three-dimensional flow structures that occur at the proximal anastomosis under pulsatile flow conditions, to investigate the changes that resulted from variations in the anastomosis angle and flow division, and to establishing the major differences between the straight and helical graft. The objectives of the study were: − To examine the flow features in the the straight and helical graft model over a range of Reynolds numbers for pulsatile flow conditions. − To locate the flow features in the both model under pulsatile flow conditions for comparison with the known locations of intimal hyperplasia in vivo. − To estimate the likely physical effects of the flow on the walls of the both model and from them the effects of blood flow on the walls of the blood vessels. 2. Methods Flow structures were determined predominantly in the 60 deg model, in planes parallel and perpendicular to the symmetry plane of the anastomosis.
Fig. 1. Experimental bypass models manufactured from glass tubing with constant internal diameter of 8 mm. Helical and straight type model.
S.I. Bernad et al. / Comparison between experimentally measured flow patterns
855
Subsequent experiments and numerical simulation for the straight and helical graft were performed in the 30 and 45 deg models to assess the effects of the angle of anastomosis. The experimental model of the graft-to-artery anastomosis is illustrated in Figure 1. We assumed that the proximal portion of the parent vessel is completely occluded, so that all flow entered the anastomosis through the graft. In the first phase of the study, unsteady flow in the model was obtained using a computer-controlled pump at a variety of flow rates, leading to Reynolds numbers (based on mean inlet velocity and tube diameter) of 280 to 950 (Figure 2). Both in experimental setup and in numerical simulations the unsteady flow model was used.
Fig. 2. Pulsatile inlet flow condition. A) Pulsatile wave used in experimental investigation. B) Pulsatile wave used for numerical simulations.
2.1. Experimental setup The experimental models were manufactured from glass tubing with constant internal diameter of 8 mm, fashioned into an straight configuration and helical configuration with an approximately 8 cm straight segment proximally and 11 cm distally (Figure 1). The flow system consisted of: a constant storage head tank; test section; floating ball flowmeter; collecting tank; and variable speed centrifugal pump. The mean flow rate was measured by a metric size 10 rotameter with a stainless steel float. The rotameter leg served the extra purpose of preventing air from travelling upstream from the flow outlet. A blood analog fluid was prepared having dynamic viscosity () of 0.00408 Pa.s and a density () of 1050 kg/m3. The flow visualization study involved the injection of a bolus of ink into water flowing at a different Reynolds numbers. Both numerical simulations and experimental investigations have been carried out over a range of Reynolds numbers (based on the centreline temporally averaged streamwise velocity and the bypass radius) from 250 to 1200. The maximum Reynolds number during the cycle was about 1118.
856
S.I. Bernad et al. / Comparison between experimentally measured flow patterns
2.2. Numerical techniques The authors have used simplified geometry (Figure 3) for the by-pass graft model with graft angles of 30°, 45°, and 60° for the analysis of the flow around the graft junction, and across the bed of the host tube. The internal diameter for the graft was taken to be D=8 mm with a graft–tube diameter ratio of 1:1 (Figures 3 and 4).
Fig. 3. By-pass graft geometry along the longitudinal plane for three graft angles (30°, 45° and 60°).
Fig. 4. Different section used for hydrodynamic parameters investigation.
Due to the elliptical nature of the flow conditions, boundary conditions must be specified at all the domain boundaries. Inlet: a uniform inflow velocity profile for the axial velocity component and a zero transverse velocity component are used. Outlet: the outlet pressure was defined to be 0 Pa. Wall: the vessel wall was assumed to be rigid and nonslip, considering that blood vessel prostheses usually deform very little under pressure. The fluid is incompressible having dynamic viscosity () of 0.00408 Pa.s and a density () of 1050 kg/m3. The bypass walls are considered rigid and impermeable. The numerical simulation is performed using the commercial CFD software FLUENT 6.3 [5]. 3. Results Two models studies were undertaken to increase understanding of the flow in a straight, one involving computational fluid dynamics (CFD) and the other, flow visualization. In both studies, the geometry and time-average flow were similar. Boundary layer separation is a well known phenomenon associated with sudden changes in surface geometry. The free shear layer resulting from a flow separation is likely to contain pressure, velocity and consequently local shear fluctuations which could be felt at the wall at the points of separation and of reattachment. Figures 5 and 6 shows the flow structure in the 60 degree proximal anastomosis under pulsatile flow conditions corresponding to the first peak of the velocity waveform (Figure 2) for the experimental setup and the numerical simulations. Note the presence of two vortices in the occluded part of the bypass graft, and strong helical flow in the distal artery is observed in both models. The secondary vortex (V1), that is the larger vortex closest to the anastomosis, rotated clockwise (as viewed in the Figures 5
S.I. Bernad et al. / Comparison between experimentally measured flow patterns
857
and 6), whereas the distal primary vortex (V2) rotated anti-clockwise. In the anastomosis domain, a strong region of recirculation is observed near the occluded end of the artery, which forces the flow to move into the perfused host coronary (distal) artery as indicated in Figures 5 and 6.
Fig. 5. Flow pattern in straight bypass graft demosntrating secondary flow. Spontaneous periodic disturbances in the distal part of the host artery. This kind of disturbances fade distally.
Fig. 6. Flowfields are shown for the 60° graft angle. Three-dimensional view of the pathline of the high inertia fluid showing development of the double helix. Dean vortices development in distal part of the host artery. Results prezented are obtained from numerical simulation.
858
S.I. Bernad et al. / Comparison between experimentally measured flow patterns
Just downstream of the toe, at axial position of X = 0.15 m, the axial velocity profile was skewed toward the far wall, and flow separation was observed along the near wall (Figure 6). The trace at X = 0.15 m, clearly displayed the presence of secondary flow, which consisted of low inertia fluid swirling circumferentially around the vessel towards the near wall and the high inertia fluid from the core region being forced toward the far wall. Once the high inertia fluid approaches the far wall, it too travels circumferentially in a spiraling manner because of the centrifugal force generated by the change in flow direction (Figure 6). Figure 6 shows the path line for the longitudinal section through the bypass junction for anastomotic angles of 60°. The highly transient character of the disturbed pulsatile flowfields became most apparent at the beginning of each cycle. It is clear that reversed flow at the wall decreases near the heel and increases near the toe with an increase in anastomotic angle. A detailed comparison of numerically computed and experimentally measured flow patterns shows generally good agreement (Figures 5 and 6). The agreement on the symmetry plane is particularly good, with the minor exception that the numerical results predict a slightly larger second retrograde flow zone than was measured experimentally (Figure 6). 4. Discussion Arterial geometry is commonly three-dimensional [2], and the properties of inertial dominated flows in such geometries include swirling, in-plane mixing, a relatively uniform distribution of wall shear, and inhibition of flow stagnation, separation and instability [3, 13].
Fig. 7. Comparison between flow pattern corresponding to the straight bypass graft and helical type bypass graft.
S.I. Bernad et al. / Comparison between experimentally measured flow patterns
859
Based on experimental data and numerical results, the following general features of the velocity field can be identified: − A core of high-momentum fluid enters the junction from the graft tube and travels towards a stagnation point on the bed of the host tube. In the neighborhood of this stagnation point, the flow splits into forward and retrograde components having large near-wall velocities (Figure 5 and Figure 7). − The proximal portion of the host tube shows weak counter-rotating vortices on the symmetry plane. The exact locations and strengths of the vortices in this region are only weakly dependent on Re. − Extremely strong secondary flows are present in the downstream section of the host tube, qualitatively similar to Dean-type vortices (Figure 6). The magnitude of the secondary flows increases with increasing Re, leading to a tighter pitch of the helical fluid paths within the host tube. − During the accelerating part of the second velocity peak (Figure 2), two distinct zones of retrograde flow exist: a first zone immediately distal to the toe, and a second zone further downstream (Figure 7). Although the length of the first retrograde flow zone is only very weakly dependent on Re, the length of the second zone increases with Re. A detailed comparison of experimentally measured axial velocity patterns for straight and helical grafts is presented in Figure 7. The axial velocity patterns on the symmetry plane show a doublepeaked profile that is reminiscent of entry flow in a curved tube (Figure 7), confirming the very strong nature of the secondary flows in the helical geometry. On the symmetry plane of the straight graft model, the experimental data show evidence of flow asymmetry (Figure 7). The velocity near the vessel wall and the wall shear rate are enhanced in the helical graft model. We believe that the enhanced blood velocity near the vessel wall and the wall shear rate can impede the staying and adherence of platelets and leucocytes to the surface of the graft, reducing the possibility of thrombosis formation. 5. Conclusions For a 60 degree anastomotic junction we have clearly demonstrated the complex nature of the flow pattern. To determine the relationship between hemodynamic factors and intimal hyperplasia, we feel that additional studies should be conducted to assess the influence of the angle of the anastomosis, elasticity, impedance mismatch, and other factors. Two model studies were undertaken to increase understanding of the flow in straight tubes, one involving computational fluid dynamics (CFD) and the other, flow visualization. In both studies, the geometry and time-average flow were similar. In helical model a mixing zone with vortex motion provides an environment for coagulant factors to be in transit without being stagnant near the surface such that activation of the intrinsic coagulation process can be suppressed. Furthermore, the helical configuration promotes the mixing effect of vortex motion such that the anti-coagulant mixed vigorously into the blood stream. The present results can provide a better understanding of the effect of geometrical configurations of helical vascular prostheses on the hemodynamic flow. We believe that the swirling flow created in this kind of helical graft may also have an advantage of suppressing flow disturbance at the distal anastomsis.
860
S.I. Bernad et al. / Comparison between experimentally measured flow patterns
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12] [13]
[14] [15]
P.D. Ballyk, C. Walsh, J. Butany and M. Ojha, Compliance Mismatch May Promote Graft-Artery Intimal Hyperplasia by Altering Suture-line Stresses, J. Biomech., 31 (1998), 229–237. C.G. Caro, D.J. Doorly, M. Tarnawski, K.T. Scott, Q. Long and C.L. Dumoulin, Non-planar curvature and branching of arteries and non-planar-type flow. Proc. R. Soc., A 452 (1996), 185–197. C.G. Caro, N. Watkins, D.J. Doorly, S.J. Sherwin and J. Peiro´, Influence of non-planar geometry on flow separation. J. Physiol., 513 (1998), 2. R.S. Fatemi and S.E. Rittgers, Derivation of Shear Rates from Near-wall LDA Measurements under Steady and Pulsatile Flow Conditions, J. Biomech. Eng., 116 (1994), 361–367. FLUENT 6.3 User’s Guide. Ansys Fluent Incorporated (2006). F.S. Henry, M.W. Collins, P.E. Hughes and T.V. How, Numerical Investigation of Steady Flow in Proximal and Distal End-to-side Anastomoses, J. Biomech. Eng., 118 (1996), 302–310. M. Hofer, G. Rappitsch, K. Perktold, W. Trubel and H. Schima, Numerical Study of Wall Mechanics and Fluid Dynamics in End-to-side Anastomoses and Correlation to Intimal Hyperplasia, J. Biomech., 29(10) (1996), 1297–1308. U. Krueger, J. Zanow and H Scholz, Computational fluid dynamics and vascular access. Artif Organs, 26 (2002), 571–5. S.M. Kute and D.A. Vorp, The Effect of Proximal Artery Flow on the Hemodynamics at the Distal Anastomosis of a Vascular Bypass Graft: Computational Study, J. Biomech. Eng., 123 (2001), 277–283. A. Leuprecht, K. Perktold, M. Prosi, T. Berk, W. Trubel and H. Schima, Numerical Study of Hemodynamics and Wall Mechanics in Distal Endto- side Anastomoses of Bypass Grafts, J. Biomech., 35 (2002), 225–236. F. Loth, S.A. Jones, C.K. Zarins, D.P. Giddens, R.F. Nassar, S. Glagov and H.S. Bassiouny, Relative Contribution of Wall Shear Stress and Injury in Experimental Intimal Thickening at eP.T.FE End-to-Side Arterial Anastomoses, J. Biomech. Eng., 124 (2002), 44–51. A. Quarteroni, M. Tuveri and A. Veneziani, Computational vascular dynamics: problems, models and methods. Comput Visual Sci., 2(2002), 163–97. S.J. Sherwin, O. Shah, D.J. Doorly, M. McLean, N. Watkins, C.G. Caro, J. Peiro, M. Tarnawski and C.L. Dumoulin, Visualisation and computational study of flow at model planar and non-planar end-to-side arterial bypass grafts. J. Physiol., 504 (1997), 44. V.S. Sottiurai, J.S.T. Yao, W.R. Flinn, R.C. Baston, Intimal hyperplasia and neointima: an ultrastructural analysis ofthrombosed grafts in humans. Surgery, 93 (1983), 809-17. P. Verdonck, The role of computational fluid dynamics for artificial organ design. Artif Organs, 26 (2002), 569–70.
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