A numerical study on the effect of hematocrit on hemodynamic characteristics in arteriovenous graft

Transcription

1 Korea-Australia Rheology Journal, Vol.26, No.3, pp (August 2014) DOI: /s x A numerical study on the effect of hematocrit on hemodynamic characteristics in arteriovenous graft Ji Tae Kim, Kun Hyuk Sung and Hong Sun Ryou* Department of Mechanical Engineering, Chung-ang University, Dongjak-gu, Seoul , Republic of Korea (Received April 9, 2014; final revision June 7, 2014; accepted June 28, 2014) Stenosis at an arteriovenous graft is related with the critical ranges of hemodynamic characteristics. Hematocrit has a significant effect on the blood viscosity. During hemodialysis, hematocrit is changed by the dialysis machine. The effect of hematocrit on hemodynamic characteristics is investigated by numerical study. A multiphase non-newtonian blood model was used to analyze the changes of hematocrit. The hematocrit of blood flows at injection needle changed 40%, 50%, and 60%. As a result, the blood viscosity increased by about 6% point. Also, the high wall shear stress region (over 3 Pa) increased about 6% point when the hematocrit at the vein anastomosis increased by about 2% point. When the hematocrit increased by 4% at the vein anastomosis, an extremely high wall shear stress region (over 7.5 Pa) increased by 3 times. Thus, the variation of hematocrit should be predicted using a multiphase blood model to avoid the critical range of wall shear stress when hematocrit changes regionally. Keywords: hematocrit, arteriovenous graft, computational fluid dynamics, hemodialysis, viscosity 1. Introduction Treatments for chronic kidney disease (CKD) patients aim to prevent the development of renal disorders and to recover kidney function (National Collaborating Centre for Chronic Conditions., 2008). CKD patients receive continuous renal replacement therapy as treatment. Hemodialysis is the most commonly used renal replacement therapy for controlling the free water and waste products in the blood. For stable hemodialysis, maintaining vascular access is important. Vascular accesses are classified into arteriovenous fistula and arteriovenous graft. An ateriovenous graft is used in patients with injured native blood vessel. However, an arteriovenous graft can induce many complications, such as stenosis, thrombosis and infection (Woods et al., 1997). Especially, stenosis and thrombosis occur frequently around a vein anastomosis. Only 22% of CKD patient use a PTFE-graft without complication. Therefore, much research has been done on the cause of stenosis in an arteriovenous graft (Malovrh, 2002). The etiology of arteriovenous graft stenosis is the injury of the vein endothelial cell by arterial circulation. A normal vein carries low pressure, non-pulsatile flow, at shear stress of about Pa. During hemodialysis, the vein endothelial cell is exposed to arterial circulation. Arterial circulation is a high pressure, pulsatile flow at shear stress of about 1-7 Pa (Malek et al., 1999). Research on the arteriovenous graft showed that stenosis occurred at the vein anastomosis and 2-5 cm downstream of a vein junction, where abdominal hemodynamic characteristics appear (Hiroaki and Teraoka, 2003). During *Corresponding author: cfdmec@cau.ac.kr dialysis, a low wall shear stress region (less than 0.5 Pa) and a high wall shear stress region (over 3 Pa) associated with the development of intimal hyperplasia occur at vein anastomosis (Van Tricht et al., 2006). Levels of shear stress up to 0.8 Pa completely block protein to prevent leukocytes adhesion. Also, an extremely high wall shear stress (over 10 Pa) activates platelets aggregation, which may lead thrombosis (Golledge, 1997). Animal experiments and numerical analysis showed that intimal hyperplasia appears at reverse flow (He et al., 2013). These researches also showed that the critical ranges of hemodynamic characteristics can cause stenosis during hemodialysis. Thus, numerical and experimental studies on arteriovenous grafts have presented advanced graft models and hemodialysis methods that can avoid the critical ranges of hemodynamic characteristics (Van Tricht et al., 2006; Ryou et al., 2013). The hematocrit has an important influence on blood viscosity at low shear-rates (Wells Jr. and Merrill, 1962). Thus, specific blood models have been used to consider the effect of hematocrit in many numerical studies. Kanaris et al performed a numerical study on a small bifurcated artery by using the Casson model (Kanaris et al., 2012). They showed that a high hematocrit is related to vascular damages and may cause thrombosis (Box et al., 2005). performed a numerical study on the hemodynamic characteristics in carotid bifurcation by using the KSCN model. They showed that the diameter of blood vessel and the blood viscosity have a large effect on the wall shear stress. These numerical studies showed the influence of hematocrit on hemodynamic characteristics. During hemodialysis, hematocrit is changed by hemodialysis machine. Therefore, the blood viscosity at the arte The Korean Society of Rheology and Springer 327

2 Ji Tae Kim, Kun Hyuk Sung and Hong Sun Ryou riovenous graft changes locally according to the local hematocrit. However, previously researches on arteriovenous grafts had difficulty considering the variation of local hematocrit because they assumed blood as a bulk fluid. Thus, we use the multiphase non-newtonian blood model suggested by Jung et al. to consider the local effect of hematocrit distribution (Jung and Hassanein, 2008). The multiphase blood model can consider the behavior of blood cells in plasma. Thus, this model can analyze the wall shear stress more accurately with variation of hematocrit. We performed a numerical study on the hemodynamic characteristics at the arteriovenous graft. The hematocrit at the artery inlet was fixed to 40% and then the blood from the hemodialysis machine was injected through a injection needle with the hematocrit changing from 40% to 60%. 2. Numerical Detail 2.1. Governing Equations A multiphase non-newtonian blood model was used to analyze the variation of blood viscosity according to hematocrit distribution. We adopted the multiphase blood model proposed by Jung et al. (Jung and Hassanein, 2008). Compared to the single phase models, the multiphase model accounted for volume fraction, mass exchange, momentum exchange, and energy exchange between the hematocrit and plasma. The equations of the multiphase blood model are as follows: Continuity equation: The continuity equation of the multiphase model is represented as equation (1). Subscript k denotes the plasma phase or the RBC phase, and ρ is the density, t is the time, v is the velocity and ε is the volume fraction. In equation (2), np is the number of phase. The volume fraction of each phase cannot be occupied by other phases. The sum of the volume fractions must be one. ( ρ k ε k ) ( ρ k ε k v k ) = 0 t np ε k k = 1 = 1.0 Blood mixture density (3) ρ mix = ε plasma ρ plasma + ε RBC ρ RBC. Momentum equations (4): exchange coefficient ( ρ k ε k ) ( ρ k ε k v k v k ) = t β kl (1) (2) (3) is interphase momentum ε k p + τ k + ε k ρ k g + β kl ( v l v k ) + F k. (4) l= l, m, n l k Plasma stress tensor (5): τ plasma = εµ plasma ( v + ( v) T ) + εκ 2. (5) 3 -- vi RBC stress tensor (6): τ RBC = pδ + εµ RBC ( v + ( v) T ) + εκ 2. (6) 3 -- vi Blood mixture viscosity (7): RBC shear viscosity µ RBC was calculated from the equation for dimensionless relative blood viscosity η. η ε RBCµ RBC + ε plasma µ = plasma = m[ 1 + ( λγ ) 2 ] n 1 µ plasma. (7) In this model, the percentage of red blood cells is assumed as the hematocrit. For γ greater than 6: 3 2 n = ε RBC ε RBC ε RBC + 1 m = ε RBC For γ less than 6: where k 0 = ln( lnγ ) lnγ. ( ) ε RBC ε RBC n = ε RBC ε RBC ε RBC k 0 m = ε RBC ε RBC ε RBC Geometry Fig. 1 shows the complete geometry of an arteriovenous graft. The 3D geometry of an arteriovenous graft is obtained from a patient s computed tomography. Computed tomography data are converted to point cloud data by the 3D-Doctor(Able Software Corp, USA). Point cloud data are reconstructed into geometry by Catia V5. The final geometry is calibrated with ultrasound sonography data. In Fig. 1, the artery inlet (1) and vein outlet (6) lengths are extended to 120 mm for a fully - developed flow. The artery outlet (2) length is increased to 40 mm, and the artery inlet and outlet diameters are 5.7 mm. NIPRO-HC-30W is used as the suction and injection needles at (3), (4) respectively. The diameters of the suction (3) and injection (4) needles are 1.5 mm. In order to exclude the influence of the needle angle, the needle is arranged parallel along the arteriovenous graft at the center of graft. The diameters of the vein outlet and vein distal are 9.3 mm. The vein distal (5) is assumed closed, because generally, a vein valve is closed by high pressure. Graft diameter is 6 mm Validation To validate the multiphase non-newtonian blood model, the velocity profile is compared with experimental results. 328 Korea-Australia Rheology J., Vol. 26, No. 3 (2014)

3 A numerical study on the effect of hematocrit on hemodynamic characteristics in arteriovenous graft Karino et al. performed experiments to investigate the behaviors of human and frog red cells on the annular vortex formed in steady flow and pulsatile flow in a sudden expansion glass tube (Karino and Goldsmith, 1977). As shown in Fig. 2 the geometry and conditions are obtained from experimental data. The inlet diameter is 151 µm, outlet diameter is 504 µm and the total length in the z-axis direction is 20 mm. The inlet velocity is m/s. The material properties of human red blood cells and water are d p = 7.5 µm, ρ = 1.13 kg m 3 and ρ = 1.0 kg m 3, µ = kg m s. Fig. 2 shows the comparison of the velocity profile at the PQ line between numerical and experimental data. The PQ line is the cross line through the vortex center located 250 µm from the zero point. Difference in the reattachment point between the numerical result and experimental result is within 2%. The maximum difference in velocity is 5.2%. The velocity distribution and reattachment point given by the numerical study almost similar with the experimental result. Fig. 1. Arteriovenous graft model Boundary conditions Boundary conditions are shows Table 1 To investigate of the effect of hematocrit on blood flow at an arteriovenous graft, we performed a numerical study for three cases of 40%, 50% and 60% hematocrit. Hematocrit is the assumed as the volume fraction of human red blood cells. The boundary conditions of the artery inlet and outlet were obtained from ultrasonic sonography. The mean velocities of the artery inlet and outlet were m/s and m/s, respectively. The blood flow rate from the suction needle to the dialysis machine was 400 ml/min, which was obtained from clinical data. The blood flow rate from the dialysis machine to the injection needle was 400 ml/min equal to the blood flow rate of the suction needle. Outlet boundary conditions are outflow applied at the vein outlet. Blood is assumed as plasma liquid with suspended solid particles. The Material properties of human red blood cells and plasma are = 8.2 µm, ρ = 1.10 kg m 3 d p Fig. 2. Comparison of computation velocity distribution at PQ line with experiment, PQ line is the cross line through the vortex center. Korea-Australia Rheology J., Vol. 26, No. 3 (2014) 329

4 Ji Tae Kim, Kun Hyuk Sung and Hong Sun Ryou Table 1. Boundary conditions of each case. Case 1 Case 2 Case 3 Velocity m/s m/s m/s Artery inlet Hematocrit 40% 40% 40% Artery outlet Velocity m/s m/s m/s Suction Velocity -3.7 m/s -3.7 m/s -3.7 m/s Velocity 3.7 m/s 3.7 m/s 3.7 m/s Injection Hematocrit 40% 50% 60% Fig. 4. High wall shear stress distribution at bottom of vein vessel. Cross line (B) is located at highest wall shear stress (HWSS). Hematocrit of Artery inlet is 40% in every cases. Hematocrit of blood flows at injection needle changed 40%, 50%, and 60%. Fig. 3. Grid independence test at cross line at downstream at vein anastomosis cells was selected within 1% error compared with cells. and ρ = 1.02 kg m 3, µ = kg m s, respectively. In this study, we assumed the vein vessel as a rigid body because based on literature reviews, the difference in the wall shear stress between a rigid body and FSI is less than 10% at vein anastomosis (Decorato et al., 2011). The no-slip condition was applied to the vessel wall. Initial velocity was set zero. And the initial hematocrit was set to 40% in all cases. The numerical studies on hemodynamics were performed with the commercial CFD software, Fluent v The computational grid consisting of hexa-hedral cells were generated by ANSYS ICEM The total number of grid 410,683 cells was selected through a grid independence test, as shown in Fig. 3. A denser grid was generated at vein and artery anastomoses, where a large curvature existed. The minimum grid size was 0.8 m. The phase - coupled SIMPLE algorithm with first order discretization was used for multiphase flows. The maximum residual was 10 6 for each case. The solution time for each case was about 1 hour on a 4-node, parallel, 3.4 GHz processor. Fig. 5. Velocity distribution at vein anastmosis. 3. Result and Discussion In this study, the critical range of wall shear stress occurs at the bottom of a vein anastomosis. Fig. 4 shows that the high wall shear stress distribution at the bottom of 330 Korea-Australia Rheology J., Vol. 26, No. 3 (2014)

5 A numerical study on the effect of hematocrit on hemodynamic characteristics in arteriovenous graft Fig. 6. Hematocrit, viscosity,velocity and shear rate distribution at section (A),(B),(C). Dimensionless Radious 1 is top side and 0 is bottom side. Location of section (A),(B),(C) are represent at Fig. 4. a vein anastomosis ranges from 3 Pa to 10 Pa, a range correlated with stenosis (Van Tricht et al., 2006). In vivo studies showed that leukocyte adhesion is significantly associated with stenosis. Even though an increase in wall shear stress mechanically opposes leukocyte adhesion, leukocyte adhesion is increased at wall shear stress levels over 3 Pa and is activated at levels over 7.5 Pa. High wall shear stress region increases according to increasing hematocrit. Fig. 5 shows the side view of the velocity distribution Korea-Australia Rheology J., Vol. 26, No. 3 (2014) 331

6 Ji Tae Kim, Kun Hyuk Sung and Hong Sun Ryou Fig. 7. Pressure distribution at vein anastmosis. Table 2. Highest wall shear stress, hematocrit and area of wall shear stress. Case 1 (Hct 40%) Case 2 (Hct 50%) Case 3 (Hct 60%) Highest WSS (H) 9.07 Pa 9.60 Pa Pa Local hematocrit (H) 40.08% 41.90% 43.83% WSS region (over 7.5 Pa) mm² mm² mm² WSS region (over 3 Pa) mm² mm² mm² WSS region (over 0.8 Pa) mm² mm² mm² WSS region (less than 0.5 Pa) mm² mm² mm² and vector at an anastomosis. Blood flow comes from the graft to the vein anastomosis, with no flow from the vein distal into the vein anastomosis. Blood flow from the graft is bumped at the top of the vein anastomosis and its direction changes to the bottom of the vein anastomosis at an anastomosis angle of about 39 o. Therefore, the blood velocity at the bottom of the vein anastomosis increases as shown in Fig. 5. This increase in velocity means a high wall shear stress at the bottom of the vein anastomosis due to a high shear rate. The shear rates of vein anastomosis at sections (A), (B), (C) are shown in Fig. 6. Section (A) is the XY-plane cross section located at the center of the vein anastomosis, 48 mm downstream of Section (C). Section (B) is located at the point of highest wall shear stress (HWSS). All the cases had similar shear rates, because Fig. 8. Velocity and vector distribution at section (A), (B), (C). their blood velocities were similar, as shown in Fig. 6. In addition, HWSS was located the point of highest pressure at the bottom of the vein vessel, as shown in Fig. 7. The location of the highest wall shear stress was almost the same in all cases, because the velocity at the vein anastomosis was almost the same, as shown in Fig. 6B. However, the highest wall shear stress increased by about 6% point, as shown in Table 2. Especially, the highest wall shear stress in case 3 was over 10 Pa, which can induce the risk of platelets aggregation. In addition, the area of the high wall shear stress region of over 3 Pa increased by about 6% point when the hematocrit increased 10% at the injection needle. Moreover, the high wall shear stress region of over 7.5 Pa in case 2 increased by 37% from that in case 1. Also, the high wall shear stress region of over 7.5 Pa in case 3 increased by 90% from that in case 2. Wall shear stress is determined by viscosity and shear rate. As a mentioned earlier, the shear rate at the high wall shear stress region is almost the same in all cases. Therefore, high blood viscosity leads to high wall shear stress. The distributions of hematocrit, viscosity and shear rate at cross sections (A), (B), (C) are shown in Fig. 6. The trend of blood viscosity is almost the same in all cases, without the graft region, as shown in Fig. 6. The trend of blood viscosity is affected by the shear rate in sections (A), (B), (C). Especially, the blood viscosity at the bottom side of section (C) increased suddenly because of the extremely low shear rate in this region. In addition, the 332 Korea-Australia Rheology J., Vol. 26, No. 3 (2014)

7 A numerical study on the effect of hematocrit on hemodynamic characteristics in arteriovenous graft top side of section (C) shows the same trend, according to trend of hematocrit, as shown in Fig. 6C. Moreover, the blood flow is mixed by swirl flow downstream of section (C). Therefore, the values of the hematocrit downstream of the vein vessel are almost 40%, 42%, and 44% as shown in Fig. 6. In this section, the blood viscosity of case 2 increases by about 6% from that of case 1, and the blood velocity of case 3 increases by about 6% from that of case 2. Thus, the area of high wall shear stress is affected by the variation of viscosity due to hematocrit. On the other hand, the blood flow at the bottom of the vein vessel separates into the vein outlet and the vein distal as shown in Fig. 5. The recirculation region occurs at the separated blood flow into the vein distal. Thus, the low shear stress region appears at the recirculation region because the low shear rate is dominant in this region. The low wall shear stress region decreases by about 1% when the hematocrit of the injection needle increases 10% as shown in Table 2. Hence, effect of the hematocrit at the low wall shear stress region is much smaller than that at the high wall shear stress region. Fig. 9. Hematocrit distribution at section (A), (B), (C). 4. Conclusion This numerical study investigated the effect of hematocrit on hemodynamic characteristics by using a multiphase blood model. During hemodialysis, the hematocrit at the vein vessel increased slightly by about 2% and that at the region of high wall shear stress (over 3 Pa) increased by 6%. Moreover, extremely high wall shear stress region (over 7.5 Pa) increased 3 times when the hematocrit at the vein anastomosis increased by about 4%. Consequently, the variation of hematocrit should be considered in the calculation of hemodynamic characteristics of an arteriovenous graft. References Fig. 10. Low wall shear stress distribution at vein anastomosis. difference in hematocrit at the bottom side of section (C) was about 1%, because blood was mixed by swirl flow along the complex curvature. Fig. 8 shows the velocity and vector distributions at sections (A), (B), (C). The high-velocity blood from the graft flows into the vein vessel as shown in (C). Therefore, swirl flow continuously occurs along the downstream of the vein vessel. The hematocrit distributions at sections (A), (B), (C) are shown in Fig. 9, respectively. The hematocrit at low velocity region of section (C) appears high because hematocrit should be high at the low velocity region to satisfy the momentum equation. Thus, the blood viscosity at the Box, F.M., J. van der Geest, C. Rutten, and H. Reiber, 2005, The influence of flow, vessel diameter, and non-newtonian blood viscosity on the wall shear stress in a carotid bifurcation model for unsteady flow, Invest. Radiol. 40, Decorato, I., Z. Kharboutly, C. Legallais, and A.V. Salsac, 2011,Numerical study of the influence of wall compliance on the hemodynamics in a patient-specific arteriovenous fistula, Comput. Methods Biome. 14, Golledge, J., 1997, Vein grafts, Haemodynamic forces on the endothelium a review, Eur. J. Vasc. Endovasc. 14, Haruguchi, H., and S. Teraoka, 2003, Intimal hyperplasia and hemodynamic factors in arterial bypass and arteriovenous grafts: a review, J. Artif. Organs 6, He, Y., M. Fernandez, Z. Jiang, M. Tao, A. O'Malley, and A. Berceli, 2014, Flow reversal promotes intimal thickening in vein Korea-Australia Rheology J., Vol. 26, No. 3 (2014) 333

8 Ji Tae Kim, Kun Hyuk Sung and Hong Sun Ryou grafts, J. Vasc. Surg. 60, Jung, J., and A. Hassanein, 2008, Three-phase CFD analytical modeling of blood flow, Med. Eng. Phys. 30, Kanaris, A.G., D. Anastasiou, and V. Paras, 2012, Modeling the effect of blood viscosity on hemodynamic factors in a small bifurcated artery, Chem. Eng. Sci. 71, Karino, T., and L. Goldsmith, 1977, Flow behaviour of blood cells and rigid spheres in an annular vortex, Philos. T. Roy. Soc. B 279, National Collaborating Centre for Chronic Conditions (Great Britain) and Royal College of Physicians, 2008, Chronic kidney disease: national clinical guideline for early identification and management in adults in primary and secondary care, Royal College of Physicians. Malek, A.M., L. Alper, and S. Izumo, 1999, Hemodynamic shear stress and its role in atherosclerosis, J. Amer. Med. Assoc. 282, Malovrh, M., 2002, 5th European Basic Multidisciplinary Hemodialysis Access Course, Blood Purificat. 20, Ryou, H.S., S.Y. Kim, and K.C. Ro, 2013, A numerical study of the effect of catheter angle on the blood flow characteristics in a graft during hemodialysis, Korea-Aust. Rheol. J. 25, Wells Jr., R.E., W. Merrill, 1962, Influence of flow properties of blood upon viscosity-hematocrit relationships, J. Clin. Invest. 41, Woods, J.D., N. Turenne, L. Strawderman, W. Young, A. Hirth, K. Port, J. Held, 1997, Vascular access survival among incident hemodialysis patients in the United States, Am. J. Kidney Dis. 30, Van Tricht, I., D. De Wachter, J. Tordoir, and P. Verdonck, 2006, Comparison of the hemodynamics in 6 mm and 4 7 mm hemodialysis grafts by means of CFD, J. Biomech. 39, Korea-Australia Rheology J., Vol. 26, No. 3 (2014)