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Bioinspired helical graft with taper to enhance helical flow
Author’s Accepted Manuscript Bioinspired helical graft with taper to enhance helical flow Xiao Liu, Libing Wang, Zhenze Wang, Zhengxing Li, Hongyan Kang, Yubo Fan, Anqiang Sun, Xiaoyan Deng www.elsevier.com/locate/jbiomech
PII: DOI: Reference:
S0021-9290(16)31015-6 http://dx.doi.org/10.1016/j.jbiomech.2016.09.028 BM7892
To appear in: Journal of Biomechanics Received date: 9 April 2016 Revised date: 9 September 2016 Accepted date: 19 September 2016 Cite this article as: Xiao Liu, Libing Wang, Zhenze Wang, Zhengxing Li, Hongyan Kang, Yubo Fan, Anqiang Sun and Xiaoyan Deng, Bioinspired helical graft with taper to enhance helical flow, Journal of Biomechanics, http://dx.doi.org/10.1016/j.jbiomech.2016.09.028 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Bioinspired helical graft with taper to enhance helical flow Xiao Liu 1¶, Libing Wang1 ¶, Zhenze Wang2, Zhengxing Li, Hongyan Kang1, Yubo Fan1,2, Anqiang Sun1*, Xiaoyan Deng1* 1
Key Laboratory for Biomechanics and Mechanobiology of the Ministry of Education,
School of Biological Science and Medical Engineering, Beihang University, Beijing, China, 2National Research Center for Rehabilitation Technical Aids, Beijing, China.
¶These authors contributed equally to this work.
*
Address for correspondence: Dr. X.Y. Deng and Dr. Sun, School of Biological
Science & Medical Engineering, Beihang University, Beijing 100191 , China. Tel.: +86 10 8233 9724; Fax: +86 10 8233 9962; E-mail: [email protected], [email protected]
Bioinspired helical graft with taper to enhance helical flow
Abstract: Helical flow has been introduced to improve the hemodynamic performance of vascular devices such as arterial grafts, stents and arteriovenous shunts to overcome the flow induced thrombus formation and intimal hyperplasia. However, the quite low intensity of helical flow in the existing devices may limit their function. To obtain desirably high intensity, inspired by the helical flow and tapered configuration of the arterial system, we proposed a new conceptual design of the medical devices, which take the form of a tapered helical shape. We demonstrated its effectiveness in arterial grafts by numerically comparing the hemodynamic performance of helical grafts with different smooth tapers. The results show that the helicity density quantifying the helical flow enlarges sharply with the increase of the taper under both steady and pulsatile flow conditions. Moreover, the amplified helical flow induced by the taper would lead to highly elevated wall shear stress, remarkably reduced oscillating shear index and relative residence time at both the grafts and the anastomosis of the host vessel. The present findings therefore indicated that the new helical graft with taper would significantly enhance the helical flow in the grafts and host vessel, which may reduce the possibility of thrombus formation in the graft and intimal hyperplasia in the host vessel and hence improve the graft patency. In addition, the concept of helical shape with taper may also be applied to design arterial stents and arteriovenous shunts to obtain better hemodynamic performance.
Key words: Helical flow, graft, intimal hyperplasia, thrombosis, taper
2
1 Introduction Helical blood flow has been observed in several arteries and may be a normal physiological flow phenomenon of the arterial system. (Liu et al., 2015) Preliminary studies demonstrated that the widely existing helical flow may have several positive physiological roles such as stabilizing blood flow transport, reducing blood flow disturbance, enhancing mass transport and suppressing platelet and monocyte adhesion. (Chen et al., 2012; Gallo et al., 2012b; Ha et al., 2015; Ha et al., 2014; Liu et al., 2010; Liu et al., 2011; Liu et al., 2013; Liu et al., 2009; Liu et al., 2014; Morbiducci et al., 2011; Zhan et al., 2010) Due to these hemodynamic benefits, researchers probed into the possibility to apply the mechanism of helical flow to the design of vascular devices to reduce thrombus formation and intimal hyperplasia caused by abnormal flow conditions. (Caro et al., 2005; Caro et al., 2014; Fan et al., 2008; Kokkalis et al., 2016; Stonebridge et al., 2012; Sun et al., 2009; Sun et al., 2010, 2012; Van Canneyt et al., 2013; Wen et al., 2011a; Zheng et al., 2014) For instance, Caro et al. designed small amplitude helical grafts (Swirl Graft) and self-expanding helical stents to generate physiological type helical flows in the hope of reducing thrombus formation and intimal hyperplasia in artery bypass grafts and stented arteries. (Caro et al., 2005; Caro et al., 2014) In addition, Stonebridge and the colleagues proposed a type of spiral laminar flow graft with spiral folds on the endo-luminal surfaces to reduce the disturbed flow at the distal anastomosis in arterial bypass grafts and arteriovenous shunts. (Jahrome et al., 2011; Stonebridge et al., 2012) However, the beneficial effects of the vascular devices based on helical flow are still controversial. Bechara reported that when compared with normal grafts, the helical flow based grafts would not lead to better clinical benefits. (Bechara, 2014) Previous studies demonstrated that although the hemodynamic performance is truly enhanced in these vascular devices, the intensity of helical flow is usually quite low, which may be one of the reasons that limit their clinical benefits. (Sun et al., 2010) We believe properly enlarging the intensity of helical flow may improve its function. Another feature of the arterial system is that the diameter of the artery would diminish successively down to the arteriole, i.e. the artery usually has some taper. Black and 3
How experimentally showed that when compared with the cylindrical straight graft, the tapered one would significantly reduce the poststenotic disturbance intensity. (Black and How, 1989) Our previous simulations on the flow of blood and the transport of low-density lipoproteins in the human aorta found that the taper of the aorta could stabilize the flow of blood and delay the attenuation of the helical flow, which would significantly reduce the accumulation of low-density lipoproteins on the luminal surface of aorta. (Liu et al., 2009) Therefore, taper should be an important consideration in the design of vascular devices such as arterial grafts, stents and arteriovenous shunts. Inspired by the helical flow and tapered configuration of the arterial system, we proposed that vascular devices with both helical and tapered shape may achieve desirably high helical flow. In order to evaluate the new conceptual design, we took arterial grafts as an example and compared the hemodynamic performance of helical grafts with different smooth tapers by computational fluid dynamics. Hemodynamic parameters including helicity density, wall shear stress (WSS), oscillating shear index (OSI) and relative residence time (RRT) were used to evaluate the performance of the helical grafts. 2 Methods Geometrical modeling The geometrical models of conventional graft and helical grafts with different tapers were built using the computer aided design software, SolidWorks (Dassault Systemes). As shown in Figure 1a, the conventional graft with angle of 45° was created along the arc of a circle between the anastomosis and the circle arc was also used as guide cylinder axis to construct the helical grafts. All the internal diameters (D) of arteries and graft inlets were set at 6 mm, which is close to the size of nominal femoral arteries. (Ethier et al., 1998) The pitch and amplitude of all the helical grafts were choose as 10D and 0.5D, respectively. (Caro et al., 2005) The internal diameter of the tapered helical graft decreases gradually from inlet to outlet and five helical grafts with different tapers were constructed. For instance, the tapered 6-2 mm helical graft 4
has the inlet and outlet diameter of 6mm and 2 mm, respectively. In addition, to exclude the effects of entrance and exit flow, the host arteries were extended 10D at inlet and outlet, which were not shown in Figure 1a. All the geometrical models were meshed with hexahedral cells and refined near the wall of the host arteries and the grafts. In order to assure that the results were mesh-independent, the grid-adaptation technique was used, which refined the grid based on the geometric and numerical solution data. The final hexahedral cells for the models were approximately one million. The information about meshing is described in detail in the Supplementary data. Numerical approaches The flow simulation is based on the three-dimensional incompressible Navier-Stokes and continuity equations. The blood is assumed as homogeneous, incompressible, and Newtonian fluid, with a density of ρ=1060 kg/m 3 and a constant viscosity of 3.45 ×10−3 kg/ m﹒s. A time-dependent flat inlet flow velocity profile is used for the pulsatile flow simulation, as shown in Figure 2 based on the femoral blood flow waveform. (Steinman and Ethier, 1994) The averaged Reynolds number at the inlet is 125, resulting in the time averaged velocity as 0.0678m/s, which is applied to the steady flow simulation. The outlet boundary condition was defined as outflow. The grafts and host arteries were assumed to be rigid and non-slip wall. (Owida et al., 2012) The flow analysis were completed by the commercial CFD software Fluent (Ansys. Inc.), which was based on the finite volume method. MATLAB (MathWorks) and Tecplot (Tecplot) were used as postposing for analyzing the data and observing the results. Quantities of interest In order to characterize the helical flow, area-weighted average of helicity density H a is calculated as follows(Gallo et al., 2012a; Gallo et al., 2012b): Ha
1 H d dS S
(1) 5
where S is the cross-sectional area, H d the helicity density (the scalar product of velocity and vorticity in the flow field), defined by Eq. (2):
H d V V
(2)
Hemodynamic indicators based on wall shear stress including time averaged wall shear stress (TAWSS), oscillating shear index (OSI) and relative residence time (RRT) were calculated for unsteady simulations. TAWSS based on the following equation: 1
T
TAWSS = T ∫0 |WSS(s, t)|dt
(3)
where T is the lasting time of a pulsatile cycle, WSS is the instantaneous wall shear stress vector, and s is the position on the vessel wall. OSI is an index to denote the change frequency of the WSS, and a higher value occurs particularly in regions characterized by disturbance flow (Ku et al., 1985), described as: 1
OSI = 2 [1 − (
T
|∫0 WSS(s,t)∙dt| T
∫0 |WSS(s,t)|dt
)]
(4)
RRT can be used to evaluate the resident time of the blood flow(Himburg et al., 2004) and indicate the regions suffering both low and oscillating WSS(Lee et al., 2009), quantified as: 1
RRT = (1−2∙OSI)∙TAWSS (5)
3 Results Helicity analysis Figure 3 shows the contours of helicity density and secondary velocity vectors at five representative slices along the graft models under steady flow condition. As shown in the figure with velocity vectors, the flow patterns in the conventional-type graft model exhibit two symmetrically counter-rotating helices (Fig. 3a). However, two asymmetric helices with a predominantly left-handed single one are observed in all the helical grafts, which is also demonstrated from the contours of helicity density, 6
where the left-handed helical flow with negative helicity density is much bigger and stronger than the right-handed one with positive value. Moreover, the helicity density in all the helical grafts increases along the grafts. In addition, the contours clearly indicate that the taper would significantly enhance the helicity density in the helical grafts and the more taper it has, the stronger helical flow it obtains. To quantify the effects of tapers on the helical flow in the helical grafts, we further compared the area-weighted average of helicity density (Ha) of these slices. As evident from Figure 4, the taper would sharply enlarge Ha in the helical grafts. For instance, the Ha of slice 5 in the tapered 6-2mm helical graft is 20 times more than that in the helical graft without taper. To further investigate the influence of taper on the helical flow, simulations were carried out under pulsatile flow condition. The slice at the middle of the grafts (Slice 3) was choose to demonstrate the flow pattern at different characteristic times of a pulse cycle (more information is shown in the Supplementary data). As shown in Fig. 5, the taper would greatly affect the distribution of helicity density in the helical grafts. As the taper increases, the proportion of area with negative helicity density would increase. Fig. 6 further demonstrates that with the increase of taper the area-weighted average of helicity density (Ha) is sharply enlarged during the whole cardiac cycle, especially the systole phase, and hence the time averaged Ha is significantly elevated (Fig. 6). Moreover, the time averaged Ha under pulsatile flow condition is much higher than that under steady flow condition, which indicates that pulsation of blood flow can significantly enhance the helicity density of blood flow. WSS distribution The indicators based on wall shear stress including WSS, TAWSS, OSI, RRT for the six computational models under steady and pulsatile flow condition are illustrated in Fig. 7 and the average of these values at bypass grafts and host artery bed are further demonstrated in Fig. 8. Fig.7A shows the distribution of wall shear stress (WSS) for the six computational models under steady flow condition and Fig.8A shows the area-weighted average of WSS. When compared with the conventional graft 7
(Fig.7A-a, Fig.8A-a), helical graft without taper (Fig.7A-b, Fig.8A-b) could increase WSS at both the graft segment and the host artery bed. However, the increment of WSS induced by the helical graft without taper is quite limited. As evident from Fig.8A, the average of WSS at the host artery bed is increased from approximately 0.27 Pa for the conventional graft to approximately 0.51 Pa for the helical graft without taper. As evident from the figure (Fig.7A-b-f, Fig.8A-b-f), the taper would greatly affect the distribution of WSS in the helical graft and the host artery. WSS on the tapered helical grafts is increased gradually from the inlet of the grafts to the outlet. Moreover, the region with low wall shear stress at the host artery bed is completely eliminated in the tapered helical grafts. As expected, WSS is greatly increased with the rise in the taper of the graft. For instance, the average of WSS in the 6-2mm helical graft is more than twice of that in the helical graft without taper. TAWSS, OSI, and RRT To further investigate the influence of taper, we observe the distribution of TAWSS, OSI, RRT for the six computational models under pulsatile flow condition. As shown in Fig. 7B, TAWSS in the conventional-type graft model is relatively low at both the graft segment and the host artery bed. As evident from Fig.7B TAWSS at most region of the host artery bed is about 1 Pa. Compared with the conventional-type graft, although the helical graft without taper enhance the TAWSS, the increment is not prominent. However, as evident from Fig. 7B and Fig. 8B, the taper has an obvious influence on the TAWSS. With the increase of taper, TAWSS on the grafts and host artery bed, increases correspondingly. To reflect the directional variation of the WSS vector during a pulsatile cycle, a definition of OSI was used here. It is an index to denote the change frequency of the WSS, and a higher value occurs particularly in regions characterized by disturbed flow. As for OSI in Fig. 7C and Fig.8 C, it is quite high in the conventional graft that the value of OSI in most areas is more than 0.3. The contours clearly indicate that the helical graft would significantly reduce the value of OSI at both the grafts and the host artery bed, and the more taper it has, the lower value it obtains. As evident from 8
Fig.8C, the value of OSI at the host artery bed in the conventional graft is four times more than that in the tapered 6-2mm helical graft. Moreover, it is possible to see that the region with high OSI values is usually located in the regions where TAWSS is low. RRT, a useful parameter of the shear environment that combines TAWSS and OSI, was also measured. RRT can be used to evaluate the resident time of the blood flow and indicate the regions suffering both low WSS and high oscillating WSS. Fig. 7D clearly shows that the value of RRT in the helical graft model is significantly lower than that in the conventional graft. Especially with the increase of taper, RRT decreases correspondingly. Fig.8D further demonstrates that with the increase of taper， RRT decreases. For example, Fig. 8D, the value of RRT of graft and host artery bed in the tapered 6-2mm helical graft is less than 0.3, while it is approximately 3.5 for the conventional graft and approximately 1.1 for the helical graft without taper. Examining TAWSS and RRT in combination, it is possible to determine that the regions with high values of RRT almost correspond to those with low values of TAWSS. Pressure drop (Δp) Pressure drop can be used to evaluate the resistance of the grafts to flow. Fig.9 shows that the Δp is low in the conventional-type graft model and with the increase of taper, Δp increases. The difference in pressure drop between the two models is not significant when the taper is not high. When the taper is high, however, Δp increases correspondingly.
4 Discussion The mechanism of helical flow has been used to design vascular devices such as arterial grafts, stents and arteriovenous shunts to overcome flow induced acute thrombus and intimal hyperplasia (Kokkalis et al., 2016; Liu et al., 2015). However, the clinical results are still mixed (Bechara, 2014; Stonebridge et al., 2012). One of 9
the reasons may be attributed to the limited helical flow in the existing devices. We proposed a new conceptual design of a tapered helical graft to obtain desirably high helical flow. The simulation results demonstrated that the helicity density in the helical grafts would increase sharply with the increase of graft taper under both steady and pulsatile flow condition. Moreover, the induced helical flow would significantly enhance wall shear stress (WSS) and greatly reduce the oscillating shear index (OSI) and relative residence time (RRT) in both the grafts and the host artery. The present study used the helicity density to qualify the helical flow in the graft, which is defined as the scalar product of velocity and vorticity in the flow field. The sign of helicity density can be used to indicate the direction of rotation of helical structures (Gallo et al., 2012b; Grigioni et al., 2005). When viewed in the direction of the forward movement, positive and negative values of helicity density demonstrate right and left handed helical structures, respectively. The simulation results shows that a predominantly left-handed single one are observed in all the helical grafts (Fig. 3). Therefore, the area-weighted average of helicity density in all the grafts has a negative value (Fig. 4). The results further demonstrated that the negative helicity density sharply increases with the taper of grafts. This phenomenon is caused by the combined effects of the taper and helical properties of the grafts on the velocity and vorticity vector. According to continuity equation, the velocity vector will increase in tapered grafts with smaller cross section area. Moreover, the vorticity vector would be enhanced, as the helical grafts have a role in mixing flow transport. In addition, the time averaged Ha under pulsatile flow condition is much higher than that under steady condition. This is because not only the velocity but also the vorticity is greatly increased during the systole period and hence leads to sharp increase in Ha. Our results further showed that when compared with the conventional graft, the helical graft without taper could enhance the hemodynamics performance by increasing wall shear stress, reducing OSI and RRT in the grafts and the host arteries, but still have some low wall shear stress regions, which is consist with previous studies. (Sun et al., 2010; Wen et al., 2011b; Zheng et al., 2014) The simulation results indicated that these regions could be completely eliminated by the tapered helical 10
grafts. Moreover, the WSS is significantly enhanced and, OSI and RRT is remarkably reduced in the tapered helical grafts and the host arteries. It is well established that low WSS and high OSI play an important role in intimal hyperplasia by affecting the function of endothelial cells. (Chiu and Chien, 2011) High OSI and RRT would lead to thrombus formation by stimulating platelet aggregations, enhancing the collision of activated
platelets
and
increasing
the
residence
time
of
procoagulant
microparticles.(Jimenez and Davies, 2009) Therefore, the proposed helical grafts with taper may reduce the possibility of intimal hyperplasia and thrombus formation in the grafts and the host artery. The tapered grafts are clinically used as arteriovenous grafts for hemodialysis vascular access to increase the hemodynamic resistance and hence prevent the steal syndrome where too much blood goes through the grafts (Rosental et al., 1980). Due to the design purpose of the tapered arteriovenous grafts is not to prevent intimal hyperplasia at the venous anastomosis, the major complications in the grafts, the application of the tapered hemodialysis grafts is still controversial. Some clinical statistical studies demonstrated that when compared to conventional straight 6 mm grafts, the tapered 6-8mm grafts are associated with significantly higher patency rates and lower complications as dialysis access grafts. (Garcia-Pajares et al., 2003; Polo et al., 2004) Computational simulations further demonstrated that less disturbed flow patterns within the venous anastomosis were observed in the tapered grafts. (Sarmast et al., 2014) However, some clinical and simulation researches indicated that the taped arteriovenous grafts did not show better outcomes. (Dammers et al., 2003; Van Tricht et al., 2006) Actually, the tapered helical grafts we proposed are fundamentally different from the existing tapered arteriovenous grafts, where the blood flow direction is from the smaller caliber end to the bigger one, which may lead to unstable flow condition. On contrast, the tapered helical grafts proposed in the present study would be a good design for the arteriovenous grafts because it could not only increase the hemodynamic resistance and hence prevent the steal syndrome, but also enhance the hemodynamics performance at the anastomosis, and hence inhibit the formation of intimal hyperplasia. Besides arteriovenous grafts, the taped helical shape may be also 11
used to enhance the helical flow in the stents. (Zeller et al., 2016) It should be noted that despite the fact that the tapered helical grafts could reduce the unfavorable hemodynamics in the grafts and the host arteries, the practical use of the grafts should be carefully designed. Compared with other grafts, the advantage of the tapered helical grafts is that the helical flow and the wall shear stress based flow index could be easily controlled by adjusting the extent of taper. It does not mean the more taper the helical graft has, the better outcomes it induces. The threshold of shear rate for platelet activation ranges from 103 to 107 s-1, depending on the exposure time. (Wootton and Ku, 1999) As shown in the Fig. 7, the time averaged wall shear stress of highly tapered helical graft is quite high, which may activate platelets. Another consideration is the pressure drop over the grafts. Previous simulations showed that the pressure drop would increase with increasing helicity (Sun et al., 2010; Van Canneyt et al., 2013). Although the absolute increase is quite low (only a few mmHg), the effect should be considered in some situations sensitive to blood pressure (Sun et al., 2010; Van Canneyt et al., 2013). As the grafts are used in different locations in the artery system where the hemodynamics varies considerably, to obtain the best clinical results, the suitable taper of the helical grafts should be carefully designed based on the optimization of the hemodynamic performance in the practical situations. In the present study, the grafts and the host arteries were simplified as idealized geometric models, which were not realistic. Moreover, the non-Newtonian blood was assumed as Newtonian flow and the grafts and arteries were assumed to be rigid wall. In addition, the artery is completely stenosed without considering the effects of different degrees of stenosis. It has been demonstrated that the partial competitive flow in moderate and severe stenosis has little effects on the hemodynamics at end-to-side anastomosis. (Ding et al., 2012; Nordgaard et al., 2010) As a pilot study, the competitive flow was not included in the present study. As the main purpose of the present study is to numerically verify the conceptual design of the tapered helical grafts, although the above simplifications would affect the accuracy of the simulation results but they would not influence the main conclusions. Another limitation is that the biological response of platelets and endothelial cells to the shear stress is not 12
included in the design of grafts. Therefore, in the practical usage of the tapered helical grafts, geometry based on medical images, patient-specific flow conditions and more accurate transport parameters should be considered in optimizing the graft design to avoid the activation of platelets and the dysfunction of endothelium.
5 Conclusion Inspired by the helical flow and tapered configuration of the arterial system, we proposed a new tapered helical graft and numerically investigated its hemodynamic performance. The new helical graft with taper would significantly enhance the helical flow in the grafts and host vessel, which may reduce the thrombus formation and intimal hyperplasia in the grafts and host vessels.
6 Acknowledgments This work is supported by Grants-in-Aid from the National Natural Science Research Foundation of China (No. 11332003, 31570947, 11572028, 61533016, 11472031, 31500763, 11421202), Special Fund for Excellent Doctor Degree Dissertation of Beijing (20131000601) and the 111 Project (B13003).
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2004. Randomized comparison of 6-mm straight grafts versus 6- to 8-mm tapered grafts for brachial-axillary dialysis access. J Vasc Surg 40, 319-324. Rosental, J.J., Bell, D.D., Gaspar, M.R., Movius, H.J., Lemire, G.G., 1980. Prevention of high flow problems of arteriovenous grafts. Development of a new tapered graft. Am J Surg 140, 231-233. Sarmast, M., Niroomand-Oscuii, H., Ghalichi, F., Samiei, E., 2014. Evaluation of the hemodynamics in straight 6-mm and tapered 6- to 8-mm grafts as upper arm hemodialysis vascular access. Med Biol Eng Comput 52, 797-811. Steinman, D.A., Ethier, C.R., 1994. The effect of wall distensibility on flow in a two-dimensional end-to-side anastomosis. Journal of biomechanical engineering 116, 294-301. Stonebridge, P.A., Vermassen, F., Dick, J., Belch, J.J., Houston, G., 2012. Spiral laminar flow prosthetic bypass graft: medium-term results from a first-in-man structured registry study. Ann Vasc Surg 26, 1093-1099. Sun, A., Fan, Y., Deng, X., 2009. Numerical investigation of blood flow in the distal end of an axis-deviated arterial bypass model. Biorheology 46, 83-92. Sun, A.Q., Fan, Y.B., Deng, X.Y., 2010. Numerical Comparative Study on the Hemodynamic Performance of a New Helical Graft With Noncircular Cross Section and SwirlGraft. Artif Organs 34, 22-27. Sun, A.Q., Fan, Y.B., Deng, X.Y., 2012. Intentionally induced swirling flow may improve the hemodynamic performance of coronary bifurcation stenting. Catheter Cardio Inte 79, 371-377. Van Canneyt, K., Morbiducci, U., Eloot, S., De Santis, G., Segers, P., Verdonck, P., 2013. A computational exploration of helical arterio-venous graft designs. J Biomech 46, 345-353. Van Tricht, I., De Wachter, D., Tordoir, J., Verdonck, P., 2006. Comparison of the hemodynamics in 6mm and 4-7 mm hemodialysis grafts by means of CFD. J Biomech 39, 226-236. Wen, J., Zheng, T., Jiang, W., Deng, X., Fan, Y., 2011a. A comparative study of helical-type and traditional-type artery bypass grafts: numerical simulation. 17
Asaio Journal 57, 399-406. Wen, J., Zheng, T.H., Jiang, W.T., Deng, X.Y., Fan, Y.B., 2011b. A Comparative Study of Helical-Type and Traditional-Type Artery Bypass Grafts: Numerical Simulation. Asaio Journal 57, 399-406. Wootton, D.M., Ku, D.N., 1999. Fluid mechanics of vascular systems, diseases, and thrombosis. Annu Rev Biomed Eng 1, 299-329. Zeller, T., Gaines, P.A., Ansel, G.M., Caro, C.G., 2016. Helical Centerline Stent Improves Patency: Two-Year Results From the Randomized Mimics Trial. Circulation. Cardiovascular interventions 9. Zhan, F., Fan, Y.B., Deng, X.Y., Xu, Z.P., 2010. The Beneficial Effect of Swirling Flow on Platelet Adhesion to the Surface of a Sudden Tubular Expansion Tube: Its Potential Application in End-to-End Arterial Anastomosis. Asaio Journal 56, 172-179. Zheng, T., Wen, J., Jiang, W., Deng, X., Fan, Y., 2014. Numerical investigation of oxygen mass transfer in a helical-type artery bypass graft. Comput Methods Biomech Biomed Engin 17, 549-559.
Figure legends Fig. 1. The geometrical models of the grafts. (a) the conventional graft model, where D is the diameter of the host artery. (b) the helical graft without taper. The 5 representative slices (s1, s2, s3, s4, and s5) and the region in the host artery bed in b1 are chosen for analyzing the flow in the graft models. b2 and b3 show the helical-type model from side and top views. (c) tapered 6-5 mm helical graft. (d) tapered 6-4 mm helical graft. (e) tapered 6-3 mm helical graft. (f) tapered 6-2 mm helical graft.
Fig.2. the flow waveform at the inlet of the host artery.
Fig. 3 Contours of helicity density of the six graft models under steady flow condition 18
at the five representative cross sections indicated by the slice letters. The contour is colored by the magnitude of helicity density and the vector is the velocity vector. (a) the conventional graft model; (b) the helical graft without taper (c) tapered 6-5 mm helical graft. (d) tapered 6-4 mm helical graft. (e) tapered 6-3 mm helical graft. (f) tapered 6-2 mm helical graft.
Fig.4 Area-weighted average of helicity density at the five cross sections of the six models under steady flow condition.
Fig.5 Contours of helicity density of the six graft models at Slice 3 at different characteristic times of a pulse cycle.
Fig.6 The helicity density of the six models at Slice 3 chosen to show the helicity density under unsteady flow condition. (A) the area-weighted average of helicity density (Ha) in the pulse cycle. (B) the time-averaged Ha.
Fig.7 Hemodynamic indicators based on wall shear stress of the six graft models. (A) wall shear stress(WSS). (B) time averaged wall shear stress (TAWSS). (C) oscillating shear index (OSI). (D) relative residence time (RRT).
Fig.8 The area-weighted average of WSS, TAWSS, OSI, RRT at bypass grafts and host artery bed of the six models. (A) Area-weighted average of WSS; (B) Area-weighted average of TAWSS; (C) Area-weighted average of OSI.; (D) Area-weighted average of RRT.
Fig.9 Pressure drop (Δp) along the six graft models under steady flow condition.
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S0021-9290(16)31015-6 http://dx.doi.org/10.1016/j.jbiomech.2016.09.028 BM7892
To appear in: Journal of Biomechanics Received date: 9 April 2016 Revised date: 9 September 2016 Accepted date: 19 September 2016 Cite this article as: Xiao Liu, Libing Wang, Zhenze Wang, Zhengxing Li, Hongyan Kang, Yubo Fan, Anqiang Sun and Xiaoyan Deng, Bioinspired helical graft with taper to enhance helical flow, Journal of Biomechanics, http://dx.doi.org/10.1016/j.jbiomech.2016.09.028 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Bioinspired helical graft with taper to enhance helical flow Xiao Liu 1¶, Libing Wang1 ¶, Zhenze Wang2, Zhengxing Li, Hongyan Kang1, Yubo Fan1,2, Anqiang Sun1*, Xiaoyan Deng1* 1
Key Laboratory for Biomechanics and Mechanobiology of the Ministry of Education,
School of Biological Science and Medical Engineering, Beihang University, Beijing, China, 2National Research Center for Rehabilitation Technical Aids, Beijing, China.
¶These authors contributed equally to this work.
*
Address for correspondence: Dr. X.Y. Deng and Dr. Sun, School of Biological
Science & Medical Engineering, Beihang University, Beijing 100191 , China. Tel.: +86 10 8233 9724; Fax: +86 10 8233 9962; E-mail: [email protected], [email protected]
Bioinspired helical graft with taper to enhance helical flow
Abstract: Helical flow has been introduced to improve the hemodynamic performance of vascular devices such as arterial grafts, stents and arteriovenous shunts to overcome the flow induced thrombus formation and intimal hyperplasia. However, the quite low intensity of helical flow in the existing devices may limit their function. To obtain desirably high intensity, inspired by the helical flow and tapered configuration of the arterial system, we proposed a new conceptual design of the medical devices, which take the form of a tapered helical shape. We demonstrated its effectiveness in arterial grafts by numerically comparing the hemodynamic performance of helical grafts with different smooth tapers. The results show that the helicity density quantifying the helical flow enlarges sharply with the increase of the taper under both steady and pulsatile flow conditions. Moreover, the amplified helical flow induced by the taper would lead to highly elevated wall shear stress, remarkably reduced oscillating shear index and relative residence time at both the grafts and the anastomosis of the host vessel. The present findings therefore indicated that the new helical graft with taper would significantly enhance the helical flow in the grafts and host vessel, which may reduce the possibility of thrombus formation in the graft and intimal hyperplasia in the host vessel and hence improve the graft patency. In addition, the concept of helical shape with taper may also be applied to design arterial stents and arteriovenous shunts to obtain better hemodynamic performance.
Key words: Helical flow, graft, intimal hyperplasia, thrombosis, taper
2
1 Introduction Helical blood flow has been observed in several arteries and may be a normal physiological flow phenomenon of the arterial system. (Liu et al., 2015) Preliminary studies demonstrated that the widely existing helical flow may have several positive physiological roles such as stabilizing blood flow transport, reducing blood flow disturbance, enhancing mass transport and suppressing platelet and monocyte adhesion. (Chen et al., 2012; Gallo et al., 2012b; Ha et al., 2015; Ha et al., 2014; Liu et al., 2010; Liu et al., 2011; Liu et al., 2013; Liu et al., 2009; Liu et al., 2014; Morbiducci et al., 2011; Zhan et al., 2010) Due to these hemodynamic benefits, researchers probed into the possibility to apply the mechanism of helical flow to the design of vascular devices to reduce thrombus formation and intimal hyperplasia caused by abnormal flow conditions. (Caro et al., 2005; Caro et al., 2014; Fan et al., 2008; Kokkalis et al., 2016; Stonebridge et al., 2012; Sun et al., 2009; Sun et al., 2010, 2012; Van Canneyt et al., 2013; Wen et al., 2011a; Zheng et al., 2014) For instance, Caro et al. designed small amplitude helical grafts (Swirl Graft) and self-expanding helical stents to generate physiological type helical flows in the hope of reducing thrombus formation and intimal hyperplasia in artery bypass grafts and stented arteries. (Caro et al., 2005; Caro et al., 2014) In addition, Stonebridge and the colleagues proposed a type of spiral laminar flow graft with spiral folds on the endo-luminal surfaces to reduce the disturbed flow at the distal anastomosis in arterial bypass grafts and arteriovenous shunts. (Jahrome et al., 2011; Stonebridge et al., 2012) However, the beneficial effects of the vascular devices based on helical flow are still controversial. Bechara reported that when compared with normal grafts, the helical flow based grafts would not lead to better clinical benefits. (Bechara, 2014) Previous studies demonstrated that although the hemodynamic performance is truly enhanced in these vascular devices, the intensity of helical flow is usually quite low, which may be one of the reasons that limit their clinical benefits. (Sun et al., 2010) We believe properly enlarging the intensity of helical flow may improve its function. Another feature of the arterial system is that the diameter of the artery would diminish successively down to the arteriole, i.e. the artery usually has some taper. Black and 3
How experimentally showed that when compared with the cylindrical straight graft, the tapered one would significantly reduce the poststenotic disturbance intensity. (Black and How, 1989) Our previous simulations on the flow of blood and the transport of low-density lipoproteins in the human aorta found that the taper of the aorta could stabilize the flow of blood and delay the attenuation of the helical flow, which would significantly reduce the accumulation of low-density lipoproteins on the luminal surface of aorta. (Liu et al., 2009) Therefore, taper should be an important consideration in the design of vascular devices such as arterial grafts, stents and arteriovenous shunts. Inspired by the helical flow and tapered configuration of the arterial system, we proposed that vascular devices with both helical and tapered shape may achieve desirably high helical flow. In order to evaluate the new conceptual design, we took arterial grafts as an example and compared the hemodynamic performance of helical grafts with different smooth tapers by computational fluid dynamics. Hemodynamic parameters including helicity density, wall shear stress (WSS), oscillating shear index (OSI) and relative residence time (RRT) were used to evaluate the performance of the helical grafts. 2 Methods Geometrical modeling The geometrical models of conventional graft and helical grafts with different tapers were built using the computer aided design software, SolidWorks (Dassault Systemes). As shown in Figure 1a, the conventional graft with angle of 45° was created along the arc of a circle between the anastomosis and the circle arc was also used as guide cylinder axis to construct the helical grafts. All the internal diameters (D) of arteries and graft inlets were set at 6 mm, which is close to the size of nominal femoral arteries. (Ethier et al., 1998) The pitch and amplitude of all the helical grafts were choose as 10D and 0.5D, respectively. (Caro et al., 2005) The internal diameter of the tapered helical graft decreases gradually from inlet to outlet and five helical grafts with different tapers were constructed. For instance, the tapered 6-2 mm helical graft 4
has the inlet and outlet diameter of 6mm and 2 mm, respectively. In addition, to exclude the effects of entrance and exit flow, the host arteries were extended 10D at inlet and outlet, which were not shown in Figure 1a. All the geometrical models were meshed with hexahedral cells and refined near the wall of the host arteries and the grafts. In order to assure that the results were mesh-independent, the grid-adaptation technique was used, which refined the grid based on the geometric and numerical solution data. The final hexahedral cells for the models were approximately one million. The information about meshing is described in detail in the Supplementary data. Numerical approaches The flow simulation is based on the three-dimensional incompressible Navier-Stokes and continuity equations. The blood is assumed as homogeneous, incompressible, and Newtonian fluid, with a density of ρ=1060 kg/m 3 and a constant viscosity of 3.45 ×10−3 kg/ m﹒s. A time-dependent flat inlet flow velocity profile is used for the pulsatile flow simulation, as shown in Figure 2 based on the femoral blood flow waveform. (Steinman and Ethier, 1994) The averaged Reynolds number at the inlet is 125, resulting in the time averaged velocity as 0.0678m/s, which is applied to the steady flow simulation. The outlet boundary condition was defined as outflow. The grafts and host arteries were assumed to be rigid and non-slip wall. (Owida et al., 2012) The flow analysis were completed by the commercial CFD software Fluent (Ansys. Inc.), which was based on the finite volume method. MATLAB (MathWorks) and Tecplot (Tecplot) were used as postposing for analyzing the data and observing the results. Quantities of interest In order to characterize the helical flow, area-weighted average of helicity density H a is calculated as follows(Gallo et al., 2012a; Gallo et al., 2012b): Ha
1 H d dS S
(1) 5
where S is the cross-sectional area, H d the helicity density (the scalar product of velocity and vorticity in the flow field), defined by Eq. (2):
H d V V
(2)
Hemodynamic indicators based on wall shear stress including time averaged wall shear stress (TAWSS), oscillating shear index (OSI) and relative residence time (RRT) were calculated for unsteady simulations. TAWSS based on the following equation: 1
T
TAWSS = T ∫0 |WSS(s, t)|dt
(3)
where T is the lasting time of a pulsatile cycle, WSS is the instantaneous wall shear stress vector, and s is the position on the vessel wall. OSI is an index to denote the change frequency of the WSS, and a higher value occurs particularly in regions characterized by disturbance flow (Ku et al., 1985), described as: 1
OSI = 2 [1 − (
T
|∫0 WSS(s,t)∙dt| T
∫0 |WSS(s,t)|dt
)]
(4)
RRT can be used to evaluate the resident time of the blood flow(Himburg et al., 2004) and indicate the regions suffering both low and oscillating WSS(Lee et al., 2009), quantified as: 1
RRT = (1−2∙OSI)∙TAWSS (5)
3 Results Helicity analysis Figure 3 shows the contours of helicity density and secondary velocity vectors at five representative slices along the graft models under steady flow condition. As shown in the figure with velocity vectors, the flow patterns in the conventional-type graft model exhibit two symmetrically counter-rotating helices (Fig. 3a). However, two asymmetric helices with a predominantly left-handed single one are observed in all the helical grafts, which is also demonstrated from the contours of helicity density, 6
where the left-handed helical flow with negative helicity density is much bigger and stronger than the right-handed one with positive value. Moreover, the helicity density in all the helical grafts increases along the grafts. In addition, the contours clearly indicate that the taper would significantly enhance the helicity density in the helical grafts and the more taper it has, the stronger helical flow it obtains. To quantify the effects of tapers on the helical flow in the helical grafts, we further compared the area-weighted average of helicity density (Ha) of these slices. As evident from Figure 4, the taper would sharply enlarge Ha in the helical grafts. For instance, the Ha of slice 5 in the tapered 6-2mm helical graft is 20 times more than that in the helical graft without taper. To further investigate the influence of taper on the helical flow, simulations were carried out under pulsatile flow condition. The slice at the middle of the grafts (Slice 3) was choose to demonstrate the flow pattern at different characteristic times of a pulse cycle (more information is shown in the Supplementary data). As shown in Fig. 5, the taper would greatly affect the distribution of helicity density in the helical grafts. As the taper increases, the proportion of area with negative helicity density would increase. Fig. 6 further demonstrates that with the increase of taper the area-weighted average of helicity density (Ha) is sharply enlarged during the whole cardiac cycle, especially the systole phase, and hence the time averaged Ha is significantly elevated (Fig. 6). Moreover, the time averaged Ha under pulsatile flow condition is much higher than that under steady flow condition, which indicates that pulsation of blood flow can significantly enhance the helicity density of blood flow. WSS distribution The indicators based on wall shear stress including WSS, TAWSS, OSI, RRT for the six computational models under steady and pulsatile flow condition are illustrated in Fig. 7 and the average of these values at bypass grafts and host artery bed are further demonstrated in Fig. 8. Fig.7A shows the distribution of wall shear stress (WSS) for the six computational models under steady flow condition and Fig.8A shows the area-weighted average of WSS. When compared with the conventional graft 7
(Fig.7A-a, Fig.8A-a), helical graft without taper (Fig.7A-b, Fig.8A-b) could increase WSS at both the graft segment and the host artery bed. However, the increment of WSS induced by the helical graft without taper is quite limited. As evident from Fig.8A, the average of WSS at the host artery bed is increased from approximately 0.27 Pa for the conventional graft to approximately 0.51 Pa for the helical graft without taper. As evident from the figure (Fig.7A-b-f, Fig.8A-b-f), the taper would greatly affect the distribution of WSS in the helical graft and the host artery. WSS on the tapered helical grafts is increased gradually from the inlet of the grafts to the outlet. Moreover, the region with low wall shear stress at the host artery bed is completely eliminated in the tapered helical grafts. As expected, WSS is greatly increased with the rise in the taper of the graft. For instance, the average of WSS in the 6-2mm helical graft is more than twice of that in the helical graft without taper. TAWSS, OSI, and RRT To further investigate the influence of taper, we observe the distribution of TAWSS, OSI, RRT for the six computational models under pulsatile flow condition. As shown in Fig. 7B, TAWSS in the conventional-type graft model is relatively low at both the graft segment and the host artery bed. As evident from Fig.7B TAWSS at most region of the host artery bed is about 1 Pa. Compared with the conventional-type graft, although the helical graft without taper enhance the TAWSS, the increment is not prominent. However, as evident from Fig. 7B and Fig. 8B, the taper has an obvious influence on the TAWSS. With the increase of taper, TAWSS on the grafts and host artery bed, increases correspondingly. To reflect the directional variation of the WSS vector during a pulsatile cycle, a definition of OSI was used here. It is an index to denote the change frequency of the WSS, and a higher value occurs particularly in regions characterized by disturbed flow. As for OSI in Fig. 7C and Fig.8 C, it is quite high in the conventional graft that the value of OSI in most areas is more than 0.3. The contours clearly indicate that the helical graft would significantly reduce the value of OSI at both the grafts and the host artery bed, and the more taper it has, the lower value it obtains. As evident from 8
Fig.8C, the value of OSI at the host artery bed in the conventional graft is four times more than that in the tapered 6-2mm helical graft. Moreover, it is possible to see that the region with high OSI values is usually located in the regions where TAWSS is low. RRT, a useful parameter of the shear environment that combines TAWSS and OSI, was also measured. RRT can be used to evaluate the resident time of the blood flow and indicate the regions suffering both low WSS and high oscillating WSS. Fig. 7D clearly shows that the value of RRT in the helical graft model is significantly lower than that in the conventional graft. Especially with the increase of taper, RRT decreases correspondingly. Fig.8D further demonstrates that with the increase of taper， RRT decreases. For example, Fig. 8D, the value of RRT of graft and host artery bed in the tapered 6-2mm helical graft is less than 0.3, while it is approximately 3.5 for the conventional graft and approximately 1.1 for the helical graft without taper. Examining TAWSS and RRT in combination, it is possible to determine that the regions with high values of RRT almost correspond to those with low values of TAWSS. Pressure drop (Δp) Pressure drop can be used to evaluate the resistance of the grafts to flow. Fig.9 shows that the Δp is low in the conventional-type graft model and with the increase of taper, Δp increases. The difference in pressure drop between the two models is not significant when the taper is not high. When the taper is high, however, Δp increases correspondingly.
4 Discussion The mechanism of helical flow has been used to design vascular devices such as arterial grafts, stents and arteriovenous shunts to overcome flow induced acute thrombus and intimal hyperplasia (Kokkalis et al., 2016; Liu et al., 2015). However, the clinical results are still mixed (Bechara, 2014; Stonebridge et al., 2012). One of 9
the reasons may be attributed to the limited helical flow in the existing devices. We proposed a new conceptual design of a tapered helical graft to obtain desirably high helical flow. The simulation results demonstrated that the helicity density in the helical grafts would increase sharply with the increase of graft taper under both steady and pulsatile flow condition. Moreover, the induced helical flow would significantly enhance wall shear stress (WSS) and greatly reduce the oscillating shear index (OSI) and relative residence time (RRT) in both the grafts and the host artery. The present study used the helicity density to qualify the helical flow in the graft, which is defined as the scalar product of velocity and vorticity in the flow field. The sign of helicity density can be used to indicate the direction of rotation of helical structures (Gallo et al., 2012b; Grigioni et al., 2005). When viewed in the direction of the forward movement, positive and negative values of helicity density demonstrate right and left handed helical structures, respectively. The simulation results shows that a predominantly left-handed single one are observed in all the helical grafts (Fig. 3). Therefore, the area-weighted average of helicity density in all the grafts has a negative value (Fig. 4). The results further demonstrated that the negative helicity density sharply increases with the taper of grafts. This phenomenon is caused by the combined effects of the taper and helical properties of the grafts on the velocity and vorticity vector. According to continuity equation, the velocity vector will increase in tapered grafts with smaller cross section area. Moreover, the vorticity vector would be enhanced, as the helical grafts have a role in mixing flow transport. In addition, the time averaged Ha under pulsatile flow condition is much higher than that under steady condition. This is because not only the velocity but also the vorticity is greatly increased during the systole period and hence leads to sharp increase in Ha. Our results further showed that when compared with the conventional graft, the helical graft without taper could enhance the hemodynamics performance by increasing wall shear stress, reducing OSI and RRT in the grafts and the host arteries, but still have some low wall shear stress regions, which is consist with previous studies. (Sun et al., 2010; Wen et al., 2011b; Zheng et al., 2014) The simulation results indicated that these regions could be completely eliminated by the tapered helical 10
grafts. Moreover, the WSS is significantly enhanced and, OSI and RRT is remarkably reduced in the tapered helical grafts and the host arteries. It is well established that low WSS and high OSI play an important role in intimal hyperplasia by affecting the function of endothelial cells. (Chiu and Chien, 2011) High OSI and RRT would lead to thrombus formation by stimulating platelet aggregations, enhancing the collision of activated
platelets
and
increasing
the
residence
time
of
procoagulant
microparticles.(Jimenez and Davies, 2009) Therefore, the proposed helical grafts with taper may reduce the possibility of intimal hyperplasia and thrombus formation in the grafts and the host artery. The tapered grafts are clinically used as arteriovenous grafts for hemodialysis vascular access to increase the hemodynamic resistance and hence prevent the steal syndrome where too much blood goes through the grafts (Rosental et al., 1980). Due to the design purpose of the tapered arteriovenous grafts is not to prevent intimal hyperplasia at the venous anastomosis, the major complications in the grafts, the application of the tapered hemodialysis grafts is still controversial. Some clinical statistical studies demonstrated that when compared to conventional straight 6 mm grafts, the tapered 6-8mm grafts are associated with significantly higher patency rates and lower complications as dialysis access grafts. (Garcia-Pajares et al., 2003; Polo et al., 2004) Computational simulations further demonstrated that less disturbed flow patterns within the venous anastomosis were observed in the tapered grafts. (Sarmast et al., 2014) However, some clinical and simulation researches indicated that the taped arteriovenous grafts did not show better outcomes. (Dammers et al., 2003; Van Tricht et al., 2006) Actually, the tapered helical grafts we proposed are fundamentally different from the existing tapered arteriovenous grafts, where the blood flow direction is from the smaller caliber end to the bigger one, which may lead to unstable flow condition. On contrast, the tapered helical grafts proposed in the present study would be a good design for the arteriovenous grafts because it could not only increase the hemodynamic resistance and hence prevent the steal syndrome, but also enhance the hemodynamics performance at the anastomosis, and hence inhibit the formation of intimal hyperplasia. Besides arteriovenous grafts, the taped helical shape may be also 11
used to enhance the helical flow in the stents. (Zeller et al., 2016) It should be noted that despite the fact that the tapered helical grafts could reduce the unfavorable hemodynamics in the grafts and the host arteries, the practical use of the grafts should be carefully designed. Compared with other grafts, the advantage of the tapered helical grafts is that the helical flow and the wall shear stress based flow index could be easily controlled by adjusting the extent of taper. It does not mean the more taper the helical graft has, the better outcomes it induces. The threshold of shear rate for platelet activation ranges from 103 to 107 s-1, depending on the exposure time. (Wootton and Ku, 1999) As shown in the Fig. 7, the time averaged wall shear stress of highly tapered helical graft is quite high, which may activate platelets. Another consideration is the pressure drop over the grafts. Previous simulations showed that the pressure drop would increase with increasing helicity (Sun et al., 2010; Van Canneyt et al., 2013). Although the absolute increase is quite low (only a few mmHg), the effect should be considered in some situations sensitive to blood pressure (Sun et al., 2010; Van Canneyt et al., 2013). As the grafts are used in different locations in the artery system where the hemodynamics varies considerably, to obtain the best clinical results, the suitable taper of the helical grafts should be carefully designed based on the optimization of the hemodynamic performance in the practical situations. In the present study, the grafts and the host arteries were simplified as idealized geometric models, which were not realistic. Moreover, the non-Newtonian blood was assumed as Newtonian flow and the grafts and arteries were assumed to be rigid wall. In addition, the artery is completely stenosed without considering the effects of different degrees of stenosis. It has been demonstrated that the partial competitive flow in moderate and severe stenosis has little effects on the hemodynamics at end-to-side anastomosis. (Ding et al., 2012; Nordgaard et al., 2010) As a pilot study, the competitive flow was not included in the present study. As the main purpose of the present study is to numerically verify the conceptual design of the tapered helical grafts, although the above simplifications would affect the accuracy of the simulation results but they would not influence the main conclusions. Another limitation is that the biological response of platelets and endothelial cells to the shear stress is not 12
included in the design of grafts. Therefore, in the practical usage of the tapered helical grafts, geometry based on medical images, patient-specific flow conditions and more accurate transport parameters should be considered in optimizing the graft design to avoid the activation of platelets and the dysfunction of endothelium.
5 Conclusion Inspired by the helical flow and tapered configuration of the arterial system, we proposed a new tapered helical graft and numerically investigated its hemodynamic performance. The new helical graft with taper would significantly enhance the helical flow in the grafts and host vessel, which may reduce the thrombus formation and intimal hyperplasia in the grafts and host vessels.
6 Acknowledgments This work is supported by Grants-in-Aid from the National Natural Science Research Foundation of China (No. 11332003, 31570947, 11572028, 61533016, 11472031, 31500763, 11421202), Special Fund for Excellent Doctor Degree Dissertation of Beijing (20131000601) and the 111 Project (B13003).
7 Conflict of interest statement There is no conflict of interest involved in the manuscript. 8 References Bechara, C.F., 2014. Comparing short and midterm Infrainguinal bypass patency rates between two ePTFE prosthetic grafts: spiral laminar flow and propaten. Vascular Disease Management 11, E54-58. Black, R.A., How, T.V., 1989. Attenuation of flow disturbances in tapered arterial grafts. J Biomech Eng 111, 303-310. Caro, C.G., Cheshire, N.J., Watkins, N., 2005. Preliminary comparative study of small amplitude helical and conventional ePTFE arteriovenous shunts in pigs. J R Soc Interface 2, 261-266. 13
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2004. Randomized comparison of 6-mm straight grafts versus 6- to 8-mm tapered grafts for brachial-axillary dialysis access. J Vasc Surg 40, 319-324. Rosental, J.J., Bell, D.D., Gaspar, M.R., Movius, H.J., Lemire, G.G., 1980. Prevention of high flow problems of arteriovenous grafts. Development of a new tapered graft. Am J Surg 140, 231-233. Sarmast, M., Niroomand-Oscuii, H., Ghalichi, F., Samiei, E., 2014. Evaluation of the hemodynamics in straight 6-mm and tapered 6- to 8-mm grafts as upper arm hemodialysis vascular access. Med Biol Eng Comput 52, 797-811. Steinman, D.A., Ethier, C.R., 1994. The effect of wall distensibility on flow in a two-dimensional end-to-side anastomosis. Journal of biomechanical engineering 116, 294-301. Stonebridge, P.A., Vermassen, F., Dick, J., Belch, J.J., Houston, G., 2012. Spiral laminar flow prosthetic bypass graft: medium-term results from a first-in-man structured registry study. Ann Vasc Surg 26, 1093-1099. Sun, A., Fan, Y., Deng, X., 2009. Numerical investigation of blood flow in the distal end of an axis-deviated arterial bypass model. Biorheology 46, 83-92. Sun, A.Q., Fan, Y.B., Deng, X.Y., 2010. Numerical Comparative Study on the Hemodynamic Performance of a New Helical Graft With Noncircular Cross Section and SwirlGraft. Artif Organs 34, 22-27. Sun, A.Q., Fan, Y.B., Deng, X.Y., 2012. Intentionally induced swirling flow may improve the hemodynamic performance of coronary bifurcation stenting. Catheter Cardio Inte 79, 371-377. Van Canneyt, K., Morbiducci, U., Eloot, S., De Santis, G., Segers, P., Verdonck, P., 2013. A computational exploration of helical arterio-venous graft designs. J Biomech 46, 345-353. Van Tricht, I., De Wachter, D., Tordoir, J., Verdonck, P., 2006. Comparison of the hemodynamics in 6mm and 4-7 mm hemodialysis grafts by means of CFD. J Biomech 39, 226-236. Wen, J., Zheng, T., Jiang, W., Deng, X., Fan, Y., 2011a. A comparative study of helical-type and traditional-type artery bypass grafts: numerical simulation. 17
Asaio Journal 57, 399-406. Wen, J., Zheng, T.H., Jiang, W.T., Deng, X.Y., Fan, Y.B., 2011b. A Comparative Study of Helical-Type and Traditional-Type Artery Bypass Grafts: Numerical Simulation. Asaio Journal 57, 399-406. Wootton, D.M., Ku, D.N., 1999. Fluid mechanics of vascular systems, diseases, and thrombosis. Annu Rev Biomed Eng 1, 299-329. Zeller, T., Gaines, P.A., Ansel, G.M., Caro, C.G., 2016. Helical Centerline Stent Improves Patency: Two-Year Results From the Randomized Mimics Trial. Circulation. Cardiovascular interventions 9. Zhan, F., Fan, Y.B., Deng, X.Y., Xu, Z.P., 2010. The Beneficial Effect of Swirling Flow on Platelet Adhesion to the Surface of a Sudden Tubular Expansion Tube: Its Potential Application in End-to-End Arterial Anastomosis. Asaio Journal 56, 172-179. Zheng, T., Wen, J., Jiang, W., Deng, X., Fan, Y., 2014. Numerical investigation of oxygen mass transfer in a helical-type artery bypass graft. Comput Methods Biomech Biomed Engin 17, 549-559.
Figure legends Fig. 1. The geometrical models of the grafts. (a) the conventional graft model, where D is the diameter of the host artery. (b) the helical graft without taper. The 5 representative slices (s1, s2, s3, s4, and s5) and the region in the host artery bed in b1 are chosen for analyzing the flow in the graft models. b2 and b3 show the helical-type model from side and top views. (c) tapered 6-5 mm helical graft. (d) tapered 6-4 mm helical graft. (e) tapered 6-3 mm helical graft. (f) tapered 6-2 mm helical graft.
Fig.2. the flow waveform at the inlet of the host artery.
Fig. 3 Contours of helicity density of the six graft models under steady flow condition 18
at the five representative cross sections indicated by the slice letters. The contour is colored by the magnitude of helicity density and the vector is the velocity vector. (a) the conventional graft model; (b) the helical graft without taper (c) tapered 6-5 mm helical graft. (d) tapered 6-4 mm helical graft. (e) tapered 6-3 mm helical graft. (f) tapered 6-2 mm helical graft.
Fig.4 Area-weighted average of helicity density at the five cross sections of the six models under steady flow condition.
Fig.5 Contours of helicity density of the six graft models at Slice 3 at different characteristic times of a pulse cycle.
Fig.6 The helicity density of the six models at Slice 3 chosen to show the helicity density under unsteady flow condition. (A) the area-weighted average of helicity density (Ha) in the pulse cycle. (B) the time-averaged Ha.
Fig.7 Hemodynamic indicators based on wall shear stress of the six graft models. (A) wall shear stress(WSS). (B) time averaged wall shear stress (TAWSS). (C) oscillating shear index (OSI). (D) relative residence time (RRT).
Fig.8 The area-weighted average of WSS, TAWSS, OSI, RRT at bypass grafts and host artery bed of the six models. (A) Area-weighted average of WSS; (B) Area-weighted average of TAWSS; (C) Area-weighted average of OSI.; (D) Area-weighted average of RRT.
Fig.9 Pressure drop (Δp) along the six graft models under steady flow condition.
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