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Outflow distribution at the distal anastomosis of infrainguinal bypass grafts
ARTICLE IN PRESS
Journal of Biomechanics 37 (2004) 417–420
Short communication
Outflow distribution at the distal anastomosis of infrainguinal bypass grafts R.K. Fisher, T.V. How*, A. Bakran, J.A. Brennan, P.L. Harris Department of Clinical Engineering, Royal Liverpool University Hospital, Duncan Building, Daulby Street, Liverpool L69 3GA, UK Accepted 23 June 2003
Abstract Outflow distribution at the distal anastomosis of infrainguinal bypass grafts remains unquantified in vivo, but is likely to influence flow patterns and haemodynamics, thereby impacting upon graft patency. This study measured the ratio of distal to proximal outflow in 30 patients undergoing infrainguinal bypass for lower limb ischaemia, using a flow probe and a transit-time ultrasonic flow meter. The mean outflow distribution was approximately 75% distal to 25% proximal, with above knee anastomoses having a greater proportion of distal flow (84%) compared to below knee grafts (73%). These in vivo flow characteristics differ significantly from those used in theoretical models studying flow phenomena (50:50 and/or 100:0), and should be incorporated into future research. r 2003 Elsevier Ltd. All rights reserved. Keywords: Flow split; Haemodynamics; Infrainguinal bypass; Myointimal hyperplasia
1. Introduction Arterial reconstruction in the form of surgical bypass remains the primary treatment of critical lower limb ischaemia. Unsatisfactory patency rates are attributed to early graft occlusion, commonly due to the development of myointimal hyperplasia (MIH) within the distal endto-side anastomosis of both autologous vein and prosthetic grafts (commonly, polytetrafluoroethylene, PTFE). This neointimal thickening has been shown to occur at specific points within the anastomosis, namely at the heel, the toe and along the floor of the recipient artery (Sottiurai, 1990). These are areas known to demonstrate regions of flow separation, reduced velocities and low wall shear stress (WSS) (How et al., 2000). The haemodynamics within the distal anastomosis are believed to play an important role in the aetiology of MIH in the light of strong evidence of an inverse relationship between MIH and WSS (Sottiurai, 1999; Zarins et al., 1987; Kraiss et al., 1991; Rittgers et al., 1978). As a consequence of this, there is much interest in *Corresponding author. Tel.: +44-151-706-5606; fax: +44-151-7065803. E-mail address: [email protected] (T.V. How). 0021-9290/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0021-9290(03)00262-8
the flow phenomena within bypass grafts. Research has focussed upon the influence of anastomotic geometry, flow conditions and impedance of the run-off vessel. Experimental techniques include flow visualisation to define the flow patterns and laser Doppler anemometry to determine the velocity profiles (How et al., 2000; Rowe et al., 1999). Numerical modelling of flow patterns and predictions of WSS have also been performed in a standard end-to-side anastomosis (Sherwin et al., 1997; Lei et al., 1997). There remains however an important inconsistency between the various studies reported in that the nature of the outflow distribution within the run-off vessel remains unquantified. The outflow of blood into the proximal and distal components of the recipient artery will be determined by the extent of the atherosclerotic disease immediately adjacent to, and distant from the end-to-side anastomosis of the graft onto the vessel. The ratio of this outflow varies between studies, from even distribution (50:50), to purely distal flow (100:0), i.e. occlusion of the proximal vessel adjacent to the anastomosis. Some authors (Hughes and How, 1996; White et al., 1993) have reported on the influence of outflow ratio upon the flow patterns within models, however there remains a need to quantify the range of outflow distributions in vivo.
ARTICLE IN PRESS R.K. Fisher et al. / Journal of Biomechanics 37 (2004) 417–420
418
It was the aim of this study to analyse how blood flow was distributed between proximal and distal components of the outflow vessel at the distal anastomosis of infrainguinal end-to-side bypass grafts in patients with critical limb ischaemia.
the entire group. The results where also stratified according to the level of the anastomosis, into those to above knee, below knee and tibial vessels. Statistical comparison using a single sample t-test compared the outflow distribution data against the commonly quoted ratios of 50:50 and 100:0, with significance taken as po0:05:
3. Methods
4. Results
Regional ethical approval for the study was obtained, and informed consent granted by the patients. An unselected and consecutive group of patients undergoing infrainguinal bypass surgery for lower limb ischaemia were included, irrespective of graft material. Intraoperative flow volumes within distal and proximal outflow components of the recipient artery were measured, using a perivascular flow probe (3S, 4S and 6S Probes, Transonic Systems Inc, Ithaca, NY, USA) and a transit-time ultrasonic flowmeter (HT107, Transonic Systems Inc, Ithaca, NY, USA). After completing the end-to-side anastomosis, the correctly sized probe was secured around the recipient artery approximately 1 cm distal to the toe and proximal to the heel, and left in situ for about 1 min to allow the reading to stabilise. Adequate contact was facilitated by application of sterile ultrasound gel around the artery and probe (Fig. 1). The probe measured the blood flowing through the vessel using the transit-time ultrasound technique. Pharmacological agents were not used to counteract the effects of arterial spasm. The data were analysed using SPSS software, producing mean outflow distributions of
A total of 30 patients was incorporated into the study over a 1-year period, 19 male, median age 69 years. The indication for surgery was critical limb ischaemia as defined by the Second European consensus in all patients (Anonymous, 1992). Autologous vein was used in 23 patients (77%) and PTFE in 7 (23%). The distal anastomosis was to the above knee popliteal artery in 9 operations (30%), and to a below knee vessel in 21 reconstructions; 8 (27%) to below knee popliteal and 13 (43%) to tibial arteries (Table 1). The total cohort of patients had a mean outflow volume of 108.9 ml min1 within the distal run-off vessel (range 22–320; SD 69.7, 95% CI 25.0) and 33.3 ml min1 within the proximal vessel (range 0–145; SD 34.1, 95% CI 12.2). This represents an outflow distribution ratio of 76.8% distally to 23.2% proximally. When compared to those ratios incorporated into experimental models of 50:50 and 100:0, using the single sample t-test, there were highly significant differences, p value=0.0001 and 0.0001, respectively. Distal anastomoses to the above knee popliteal artery had a mean outflow distribution ratio of 84.2% distally
2. Aim
Fig. 1. Transit-time ultrasonic flow probe, correctly sized and positioned around the distal and proximal run-off vessels after an arterial reconstruction, using vein, to a tibial vessel.
Table 1 Patient demographics with stratification according to the level of anastomosis
Total Above knee Below knee
Total
Age (years)
Male:female
CLI:IC
Vein graft
Prosthetic graft
30 9 21
69 66 69
19:11 6:3 13:8
25:5 6:3 19:2
23 7 16
7 2 5
Critical limb ischaemia (CLI); intermittent claudication (IC).
ARTICLE IN PRESS R.K. Fisher et al. / Journal of Biomechanics 37 (2004) 417–420
419
Table 2 Mean outflow distribution ratios, with stratification according to the level of the distal anastomosis n Total AK pop BK pop Tibial
30 9 8 13
% distal 76.8 84.2 73.2 73.9
%proximal 23.2 15.8 26.8 26.1
SD
p(50:50)
p(100:0)
16.7 18.8 18.8 13.2
0.0001 0.001 0.01 0.0001
0.0001 0.05 0.006 0.0001
p values are derived from a single sample t-test comparing the results with an outflow ratio of 50:50 and 100:0. Statistical significance po0.05.
to 15.8% proximally; p ¼ 0:001 and 0.05 vs. 50:50 and 100:0, respectively. Reconstructions to the below knee vessel had a mean outflow ratio of 73.2% distally to 26.8% proximally; p ¼ 0:01 and 0.006 vs. 50:50 and 100:0, respectively. Infragenicular bypasses to tibial vessels had a mean outflow ratio of 73.9% distally to 26.1% proximally; p ¼ 0:0001 and 0.0001 vs. 50:50 and 100:0, respectively. (Table 2).
5. Discussion Arteriography and Duplex assessment of in vivo bypass grafts confirms the presence of bi-directional outflow in the recipient artery. This study represents the first quantification of how blood flow divides at the distal anastomosis, and demonstrates that after infrainguinal arterial reconstruction, an average of approximately 75% of the outflow is distal and 25% proximal. This result is significantly different from those outflow distributions often incorporated into models reported in the literature of 50:50 and 100:0 (Rowe et al., 1999; Sherwin et al., 1997; Lei et al., 1997). Some studies (How et al., 2000; Lei et al., 2001; Loth et al., 2002) have reported the haemodynamic flow patterns in models with similar distributions to those found here. It is hoped, however, that quantification of the outflow distribution in vivo will potentially standardise experimental techniques in future. The ratio appears to be dependant upon the level of the distal anastomosis, with outflow approaching a purely distal distribution in supragenicular reconstructions. There may be a causal link with the anatomy of the atherosclerotic disease, in that above knee grafts often anastomose to the popliteal artery immediately adjacent to the proximal superficial femoral artery occlusion, thereby precluding proximal outflow. In the case of infragenicular reconstruction, however, the proximal component is often patent, all be it diseased and ectatic, with the genicular and collateral vessels facilitating run-off. This potential variation in disease distribution above and below the knee joint may influence the proximal vessel impedance, resulting in the differing outflow ratios.
Further influences may be imparted by distal anastomotic geometry, which is variable between each individual case. As such, it is hard to standardise and its influence is likely to be small compared to that of anastomotic level and disease distribution. Studies by Hughes and How (1996) and White et al. (1993) described the effects of outflow distribution on flow patterns. One may extrapolate that flow division therefore influences the haemodynamics within the distal anastomosis, thereby impacting upon graft patency. Whilst further studies are required to define this, the confirmation that proximal outflow does exist in vivo, especially after infragenicular reconstruction, has clinical importance. Outflow through the proximal vessel may promote graft patency and limb perfusion in spite of distal vessel occlusion, therefore contraindicating the use of an end-to-end anastomosis. The transit-time ultrasonic flowmeter is a recognised technique for measuring flow volume, which we elected over Duplex assessment. This was in view of the large handling errors incurred by Duplex, which is a highly user dependant technique, especially when considering small diameter vessels (3 mm) with comparatively low flow (130 ml/min).
6. Conclusion There is an average flow ratio at the distal anastomosis of an infrainguinal bypass of 3:1, distal:proximal, with above knee anastomoses tending to have a greater proportion of distal outflow compared to below knee. Outflow distribution is an important parameter in determining flow patterns in the distal anastomosis, and in order that theoretical and laboratory models reflect the in vivo situation, they should incorporate a range of flow divisions.
References Anonymous, 1992. Second European Consensus Document on Chronic Critical Limb Ischaemia. European Journal of Vascular Surgery 6 (Suppl. A) 1–32.
ARTICLE IN PRESS 420
R.K. Fisher et al. / Journal of Biomechanics 37 (2004) 417–420
How, T.V., Row, C.S., Gilling-Smith, G.L., Harris, P.L., 2000. Interposition vein cuff anastomosis alters wall shear stress distribution in recipient artery. Journal of Vascular Surgery 31, 1008–1018. Hughes, P.E., How, T.V., 1996. Effects of geometry and flow division on flow structures in models of the distal end-to-side anastomosis. Journal of Biomechanics 29, 855–872. Kraiss, L.W., Kirkman, T.R., Kohler, T.R., Zierler, B., Clowes, A.W., 1991. Shear stress regulates smooth muscle proliferation and neointimal thickening in porous polytetrafluoroethylene grafts. Arteriosclerosis and thrombosis 11, 1844–1852. Lei, M., Archie, J.P., Kleinstreuer, C., 1997. Computational design of a bypass graft that minimizes wall shear stress gradients in the region of the distal anastomosis. Journal of Vascular Surgery 25, 646. Lei, M., Giddens, D.P., Jones, S.A., Loth, F., Bassiouny H, .S., 2001. Pulsatile flow in an end-to-side vascular graft model: comparison of computations with experimental data. Journal of Biomechanical Engineering. 123 (1), 80–87. Loth, F., Jones, S.A., Zarins, C.K., Giddens, D.P., Nassar, R.F., Glagov, S., Bassiouny, H.S., 2002. Relative contribution of wall shear stress and injury in experimental intimal thickening in PTFE end-to-side arterial anastomoses. Journal of Biomechanical Engineering 124, 44–51.
Rittgers, S.E., Karayannacos, P.E., Guy, J.F., Nerem, R.M., Shaw, G.M., Hostetler, J.R., Vasko, J.S., 1978. Velocity distribution and intimal proliferation in autologous vein grafts in dogs. Circulation Research 42, 792–801. Rowe, C.S., Carpenter, T.K., How, T.V., Harris, P.L., 1999. Local haemodynamics of arterial bypass graft anastomosis. Proceedings of the Institution of Mechanical Engineers 213, 401–409. Sherwin, S.J., Shah, O., Doorly, D.J., 1997. Visualization and computational study of flow at model planar and non-planar end-to-side arterial bypass grafts. Marine Biological Association, Plymouth Meeting, 52pp. Sottiurai, V.S., 1990. Biogenesis and aetiology of distal anastomotic intimal hyperplasia. International Journal of Angiology 9, 59–69. Sottiurai, V.S., 1999. Distal anastomotic intimal hyperplasia: histocytomorphology, pathophysiology, etiology, and prevention. International Journal of Angiology 8, 1–10. White, S.S., Zarins, C.K., Giddens, D.P., Bassiouny, H., Loth, F., Jones, S.A., Glagov, S., 1993. Haemodynamic patterns in two models of end-to-side vascular graft anastomosis: effects of pulsatility, flow division, Reynolds number, and hood length. Journal of Biomechanical Engineering 115, 104–111. Zarins, C.K., Zatina, M.A., Giddens, D.P., Ku, D.K., Glagov, S., 1987. Shear stress regulation of artery lumen diameter in experimental atherogenesis. Journal of Vascular Surgery 5, 413–420.
Journal of Biomechanics 37 (2004) 417–420
Short communication
Outflow distribution at the distal anastomosis of infrainguinal bypass grafts R.K. Fisher, T.V. How*, A. Bakran, J.A. Brennan, P.L. Harris Department of Clinical Engineering, Royal Liverpool University Hospital, Duncan Building, Daulby Street, Liverpool L69 3GA, UK Accepted 23 June 2003
Abstract Outflow distribution at the distal anastomosis of infrainguinal bypass grafts remains unquantified in vivo, but is likely to influence flow patterns and haemodynamics, thereby impacting upon graft patency. This study measured the ratio of distal to proximal outflow in 30 patients undergoing infrainguinal bypass for lower limb ischaemia, using a flow probe and a transit-time ultrasonic flow meter. The mean outflow distribution was approximately 75% distal to 25% proximal, with above knee anastomoses having a greater proportion of distal flow (84%) compared to below knee grafts (73%). These in vivo flow characteristics differ significantly from those used in theoretical models studying flow phenomena (50:50 and/or 100:0), and should be incorporated into future research. r 2003 Elsevier Ltd. All rights reserved. Keywords: Flow split; Haemodynamics; Infrainguinal bypass; Myointimal hyperplasia
1. Introduction Arterial reconstruction in the form of surgical bypass remains the primary treatment of critical lower limb ischaemia. Unsatisfactory patency rates are attributed to early graft occlusion, commonly due to the development of myointimal hyperplasia (MIH) within the distal endto-side anastomosis of both autologous vein and prosthetic grafts (commonly, polytetrafluoroethylene, PTFE). This neointimal thickening has been shown to occur at specific points within the anastomosis, namely at the heel, the toe and along the floor of the recipient artery (Sottiurai, 1990). These are areas known to demonstrate regions of flow separation, reduced velocities and low wall shear stress (WSS) (How et al., 2000). The haemodynamics within the distal anastomosis are believed to play an important role in the aetiology of MIH in the light of strong evidence of an inverse relationship between MIH and WSS (Sottiurai, 1999; Zarins et al., 1987; Kraiss et al., 1991; Rittgers et al., 1978). As a consequence of this, there is much interest in *Corresponding author. Tel.: +44-151-706-5606; fax: +44-151-7065803. E-mail address: [email protected] (T.V. How). 0021-9290/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0021-9290(03)00262-8
the flow phenomena within bypass grafts. Research has focussed upon the influence of anastomotic geometry, flow conditions and impedance of the run-off vessel. Experimental techniques include flow visualisation to define the flow patterns and laser Doppler anemometry to determine the velocity profiles (How et al., 2000; Rowe et al., 1999). Numerical modelling of flow patterns and predictions of WSS have also been performed in a standard end-to-side anastomosis (Sherwin et al., 1997; Lei et al., 1997). There remains however an important inconsistency between the various studies reported in that the nature of the outflow distribution within the run-off vessel remains unquantified. The outflow of blood into the proximal and distal components of the recipient artery will be determined by the extent of the atherosclerotic disease immediately adjacent to, and distant from the end-to-side anastomosis of the graft onto the vessel. The ratio of this outflow varies between studies, from even distribution (50:50), to purely distal flow (100:0), i.e. occlusion of the proximal vessel adjacent to the anastomosis. Some authors (Hughes and How, 1996; White et al., 1993) have reported on the influence of outflow ratio upon the flow patterns within models, however there remains a need to quantify the range of outflow distributions in vivo.
ARTICLE IN PRESS R.K. Fisher et al. / Journal of Biomechanics 37 (2004) 417–420
418
It was the aim of this study to analyse how blood flow was distributed between proximal and distal components of the outflow vessel at the distal anastomosis of infrainguinal end-to-side bypass grafts in patients with critical limb ischaemia.
the entire group. The results where also stratified according to the level of the anastomosis, into those to above knee, below knee and tibial vessels. Statistical comparison using a single sample t-test compared the outflow distribution data against the commonly quoted ratios of 50:50 and 100:0, with significance taken as po0:05:
3. Methods
4. Results
Regional ethical approval for the study was obtained, and informed consent granted by the patients. An unselected and consecutive group of patients undergoing infrainguinal bypass surgery for lower limb ischaemia were included, irrespective of graft material. Intraoperative flow volumes within distal and proximal outflow components of the recipient artery were measured, using a perivascular flow probe (3S, 4S and 6S Probes, Transonic Systems Inc, Ithaca, NY, USA) and a transit-time ultrasonic flowmeter (HT107, Transonic Systems Inc, Ithaca, NY, USA). After completing the end-to-side anastomosis, the correctly sized probe was secured around the recipient artery approximately 1 cm distal to the toe and proximal to the heel, and left in situ for about 1 min to allow the reading to stabilise. Adequate contact was facilitated by application of sterile ultrasound gel around the artery and probe (Fig. 1). The probe measured the blood flowing through the vessel using the transit-time ultrasound technique. Pharmacological agents were not used to counteract the effects of arterial spasm. The data were analysed using SPSS software, producing mean outflow distributions of
A total of 30 patients was incorporated into the study over a 1-year period, 19 male, median age 69 years. The indication for surgery was critical limb ischaemia as defined by the Second European consensus in all patients (Anonymous, 1992). Autologous vein was used in 23 patients (77%) and PTFE in 7 (23%). The distal anastomosis was to the above knee popliteal artery in 9 operations (30%), and to a below knee vessel in 21 reconstructions; 8 (27%) to below knee popliteal and 13 (43%) to tibial arteries (Table 1). The total cohort of patients had a mean outflow volume of 108.9 ml min1 within the distal run-off vessel (range 22–320; SD 69.7, 95% CI 25.0) and 33.3 ml min1 within the proximal vessel (range 0–145; SD 34.1, 95% CI 12.2). This represents an outflow distribution ratio of 76.8% distally to 23.2% proximally. When compared to those ratios incorporated into experimental models of 50:50 and 100:0, using the single sample t-test, there were highly significant differences, p value=0.0001 and 0.0001, respectively. Distal anastomoses to the above knee popliteal artery had a mean outflow distribution ratio of 84.2% distally
2. Aim
Fig. 1. Transit-time ultrasonic flow probe, correctly sized and positioned around the distal and proximal run-off vessels after an arterial reconstruction, using vein, to a tibial vessel.
Table 1 Patient demographics with stratification according to the level of anastomosis
Total Above knee Below knee
Total
Age (years)
Male:female
CLI:IC
Vein graft
Prosthetic graft
30 9 21
69 66 69
19:11 6:3 13:8
25:5 6:3 19:2
23 7 16
7 2 5
Critical limb ischaemia (CLI); intermittent claudication (IC).
ARTICLE IN PRESS R.K. Fisher et al. / Journal of Biomechanics 37 (2004) 417–420
419
Table 2 Mean outflow distribution ratios, with stratification according to the level of the distal anastomosis n Total AK pop BK pop Tibial
30 9 8 13
% distal 76.8 84.2 73.2 73.9
%proximal 23.2 15.8 26.8 26.1
SD
p(50:50)
p(100:0)
16.7 18.8 18.8 13.2
0.0001 0.001 0.01 0.0001
0.0001 0.05 0.006 0.0001
p values are derived from a single sample t-test comparing the results with an outflow ratio of 50:50 and 100:0. Statistical significance po0.05.
to 15.8% proximally; p ¼ 0:001 and 0.05 vs. 50:50 and 100:0, respectively. Reconstructions to the below knee vessel had a mean outflow ratio of 73.2% distally to 26.8% proximally; p ¼ 0:01 and 0.006 vs. 50:50 and 100:0, respectively. Infragenicular bypasses to tibial vessels had a mean outflow ratio of 73.9% distally to 26.1% proximally; p ¼ 0:0001 and 0.0001 vs. 50:50 and 100:0, respectively. (Table 2).
5. Discussion Arteriography and Duplex assessment of in vivo bypass grafts confirms the presence of bi-directional outflow in the recipient artery. This study represents the first quantification of how blood flow divides at the distal anastomosis, and demonstrates that after infrainguinal arterial reconstruction, an average of approximately 75% of the outflow is distal and 25% proximal. This result is significantly different from those outflow distributions often incorporated into models reported in the literature of 50:50 and 100:0 (Rowe et al., 1999; Sherwin et al., 1997; Lei et al., 1997). Some studies (How et al., 2000; Lei et al., 2001; Loth et al., 2002) have reported the haemodynamic flow patterns in models with similar distributions to those found here. It is hoped, however, that quantification of the outflow distribution in vivo will potentially standardise experimental techniques in future. The ratio appears to be dependant upon the level of the distal anastomosis, with outflow approaching a purely distal distribution in supragenicular reconstructions. There may be a causal link with the anatomy of the atherosclerotic disease, in that above knee grafts often anastomose to the popliteal artery immediately adjacent to the proximal superficial femoral artery occlusion, thereby precluding proximal outflow. In the case of infragenicular reconstruction, however, the proximal component is often patent, all be it diseased and ectatic, with the genicular and collateral vessels facilitating run-off. This potential variation in disease distribution above and below the knee joint may influence the proximal vessel impedance, resulting in the differing outflow ratios.
Further influences may be imparted by distal anastomotic geometry, which is variable between each individual case. As such, it is hard to standardise and its influence is likely to be small compared to that of anastomotic level and disease distribution. Studies by Hughes and How (1996) and White et al. (1993) described the effects of outflow distribution on flow patterns. One may extrapolate that flow division therefore influences the haemodynamics within the distal anastomosis, thereby impacting upon graft patency. Whilst further studies are required to define this, the confirmation that proximal outflow does exist in vivo, especially after infragenicular reconstruction, has clinical importance. Outflow through the proximal vessel may promote graft patency and limb perfusion in spite of distal vessel occlusion, therefore contraindicating the use of an end-to-end anastomosis. The transit-time ultrasonic flowmeter is a recognised technique for measuring flow volume, which we elected over Duplex assessment. This was in view of the large handling errors incurred by Duplex, which is a highly user dependant technique, especially when considering small diameter vessels (3 mm) with comparatively low flow (130 ml/min).
6. Conclusion There is an average flow ratio at the distal anastomosis of an infrainguinal bypass of 3:1, distal:proximal, with above knee anastomoses tending to have a greater proportion of distal outflow compared to below knee. Outflow distribution is an important parameter in determining flow patterns in the distal anastomosis, and in order that theoretical and laboratory models reflect the in vivo situation, they should incorporate a range of flow divisions.
References Anonymous, 1992. Second European Consensus Document on Chronic Critical Limb Ischaemia. European Journal of Vascular Surgery 6 (Suppl. A) 1–32.
ARTICLE IN PRESS 420
R.K. Fisher et al. / Journal of Biomechanics 37 (2004) 417–420
How, T.V., Row, C.S., Gilling-Smith, G.L., Harris, P.L., 2000. Interposition vein cuff anastomosis alters wall shear stress distribution in recipient artery. Journal of Vascular Surgery 31, 1008–1018. Hughes, P.E., How, T.V., 1996. Effects of geometry and flow division on flow structures in models of the distal end-to-side anastomosis. Journal of Biomechanics 29, 855–872. Kraiss, L.W., Kirkman, T.R., Kohler, T.R., Zierler, B., Clowes, A.W., 1991. Shear stress regulates smooth muscle proliferation and neointimal thickening in porous polytetrafluoroethylene grafts. Arteriosclerosis and thrombosis 11, 1844–1852. Lei, M., Archie, J.P., Kleinstreuer, C., 1997. Computational design of a bypass graft that minimizes wall shear stress gradients in the region of the distal anastomosis. Journal of Vascular Surgery 25, 646. Lei, M., Giddens, D.P., Jones, S.A., Loth, F., Bassiouny H, .S., 2001. Pulsatile flow in an end-to-side vascular graft model: comparison of computations with experimental data. Journal of Biomechanical Engineering. 123 (1), 80–87. Loth, F., Jones, S.A., Zarins, C.K., Giddens, D.P., Nassar, R.F., Glagov, S., Bassiouny, H.S., 2002. Relative contribution of wall shear stress and injury in experimental intimal thickening in PTFE end-to-side arterial anastomoses. Journal of Biomechanical Engineering 124, 44–51.
Rittgers, S.E., Karayannacos, P.E., Guy, J.F., Nerem, R.M., Shaw, G.M., Hostetler, J.R., Vasko, J.S., 1978. Velocity distribution and intimal proliferation in autologous vein grafts in dogs. Circulation Research 42, 792–801. Rowe, C.S., Carpenter, T.K., How, T.V., Harris, P.L., 1999. Local haemodynamics of arterial bypass graft anastomosis. Proceedings of the Institution of Mechanical Engineers 213, 401–409. Sherwin, S.J., Shah, O., Doorly, D.J., 1997. Visualization and computational study of flow at model planar and non-planar end-to-side arterial bypass grafts. Marine Biological Association, Plymouth Meeting, 52pp. Sottiurai, V.S., 1990. Biogenesis and aetiology of distal anastomotic intimal hyperplasia. International Journal of Angiology 9, 59–69. Sottiurai, V.S., 1999. Distal anastomotic intimal hyperplasia: histocytomorphology, pathophysiology, etiology, and prevention. International Journal of Angiology 8, 1–10. White, S.S., Zarins, C.K., Giddens, D.P., Bassiouny, H., Loth, F., Jones, S.A., Glagov, S., 1993. Haemodynamic patterns in two models of end-to-side vascular graft anastomosis: effects of pulsatility, flow division, Reynolds number, and hood length. Journal of Biomechanical Engineering 115, 104–111. Zarins, C.K., Zatina, M.A., Giddens, D.P., Ku, D.K., Glagov, S., 1987. Shear stress regulation of artery lumen diameter in experimental atherogenesis. Journal of Vascular Surgery 5, 413–420.