Influence of an Arterial Stenosis on the Hemodynamics Within an Arteriovenous Fistula (AVF): Comparison Before and After BalloonAngioplasty
 226 Downloads
 1 Citations
Abstract
The study focuses on arterial stenoses in arteriovenous fistulae (AVF), the occurrence of which was long underestimated. The objective is to investigate their influence on the hemodynamic conditions within the AVF. A numerical simulation of the blood flow is conducted within a patientspecific arteriovenous fistula that presents an 60% stenosis on the inflow artery. In order to find the vessel shape without stenosis and compare the flow conditions with and without stenosis, the endovascular treatment of balloonangioplasty is simulated by modeling the vessel deformation during balloon inflation implicitly. Clinically, balloonangioplasty is considered successful if the posttreatment residual degree of stenosis is below 30%. Different balloon inflation pressures have been imposed numerically to obtain residual degrees of stenosis between 30 and 0%. The comparison of the computational fluid dynamic simulations carried out in the patientspecific native geometry and in the treated ones shows that the arterial stenosis has little impact on the blood flow distribution. The venous flow rate remains unchanged as long as thrombosis does not occur: the nominal flow rate needed for hemodialysis is maintained, which is not the case for a venous stenosis. An arterial stenosis, however, causes an increase in the pressure difference across the stenosed region. A residual degree of stenosis below 20% is needed to guarantee a pressure difference lower than 5 mmHg, which is considered to be the threshold stenosis pressure difference.
Keywords
Arteriovenous fistula Stenosis Balloonangioplasty Hemodynamics Stenosis pressure dropIntroduction
An arteriovenous fistula (AVF) is a permanent vascular access created surgically in patients with endstage renal disease waiting for kidney transplantation.22 It enables circulating blood extracorporeally to a filtering machine during the sessions of hemodialysis: blood is cleaned from metabolic waste products and excess of water.19 The most common approach used to create the arteriovenous fistula is to suture a vein onto an artery in the forearm or in the arm. Autologous fistulas have a 3 to 6month maturation, during which the vein dilates and the wall collagen content increases.8,10 Over maturation, the venous flow rate increases by a factor 20–50 and reaches a value larger than 500 mL/min, which is required for hemodialysis.22,40 The fistula acts as a shortcut between the high pressure arterial vasculature and the low pressure venous tree causing a significant change of the hemodynamic conditions.
The issue is that more than half the AVF fail within 2 years.4 Loss of patency of the vascular access can result in underdialysis, leading to increased morbidity and mortality. For many years venous stenoses (also called outflow stenosis) were considered to be the main complication affecting arteriovenous fistulas.7,23 They typically form in the draining vein near the veintoartery junction (called the anastomosis) or in the central veins located downstream of the anastomosis.28,37 Coentrao and TurmelRodrigues pointed out that venous stenoses are so common that many clinicians do not diagnose their presence.7 They directly compromise the hemodialysis treatment, because they reduce the venous blood flow or even block it when they cause thrombosis.14
For a long time, the occurrence of arterial inflow stenoses was considered a rare complication in hemodialysis fistula.36 Recent studies have, however, provided a very different picture of the reality. Arterial stenoses have been shown to occur in 40% of patients when the AVF is created in the forearm.2,11 The occurrence rate is lower when the AVF is in the upper arm (presumably around 0–4%). Relatively little is known about arterial stenoses. Indeed they remain often undiagnosed because they hardly affect the parameters monitored during hemodialysis, unless they are close to the anastomosis.31,34 They could easily be detected by ultrasound scans or angiography, but neither are part of the routine exam conducted on hemodialyzed patients.
If detected, correction of the arterial stenosis needs to be considered before thrombosis and vascular access loss. The indications for treatment are so far the same as for venous stenoses: a lumen narrowing greater than 50% or a pressure drop higher than 5 mmHg.2,14 The lumen criterion is thought to be universally valid14 but less can be said on the critical pressure drop across an arterial stenosis. The stenosis can be treated either surgically or endovascularly, the former being more invasive and usually performed when the vascular anatomy is likely to affect the success rate of the endovascular procedure.37 Balloonangioplasty is the endovascular treatment of choice: it consists in inflating a balloon to restore the stenosed vessel patency. After treatment, the diameter at the stenosis throat is rarely restored to its physiological value, and a residual stenosis remains. Treatment is considered successful when the degree of residual stenosis is below 30%.3,6,14,37
The objective of the study is to provide a better understanding of the consequences of an arterial stenosis. We aim at investigating its influence on the hemodynamic conditions in a patientspecific AVF: the blood flow conditions are hence compared with and without the lesion. The approach used is based on computational fluiddynamic (CFD) simulations, which have been reported to be effective in the evaluation of the AVF hemodynamics.12,21,27 Previous studies have, however, not yet investigated the consequences of a stenosis in a fistula. Numerical simulations present the advantage of providing quantitative information on flow parameters such as the wall shear stress and stenosis pressure difference that cannot be measured in vivo. Such information can be useful to set the guidelines for the treatment of arterial stenoses in AVF, which so far do not exist. The treatment of balloonangioplasty is simulated numerically to get the posttreatment vascular geometry in the case of degrees of residual stenosis ranging from 30 to 0%. A technique is proposed to set patientspecific boundary conditions from the only clinical data that can be measured in vivo on the patients, i.e., the flow rates.
The manuscript is structured as follows. The techniques used to generate the patientspecific vessel geometry, simulate balloonangioplasty and conduct computational fluid dynamic studies are detailed in §2, along with the validation of the numerical simulations. In §3, we compare the geometries and flow conditions before and after balloonangioplasty. The evolution of the hemodynamic flow parameters is studied as a function of the degree of posttreatment residual stenosis. We conclude with a discussion on the possible clinical implications of the study.
Methods
PatientSpecific Geometry
Numerical Method to Simulate BalloonAngioplasty
Numerical Procedure
The treatment by balloonangioplasty was simulated numerically using ANSYSStructural (ANSYS, Inc.). Our objective was not to study the transient balloon deformation, but to obtain the equilibrium configuration of the stenosed wall. We hence used an implicit formulation of the solid problem, which is one of the original aspects of the study. A balloon was positioned across the stenosis; it was inflated (and deflated) by imposing an internal pressure in an implicit structural simulation. The simulation was conducted with the Lagrangian multiplierbased mixed deformationpressure numerical scheme (uP formulation). Neither translation nor rotation was allowed at the extremities of the balloon and vessel walls. The convergence criteria on force, momentum, displacement and rotation were set to be 10\( ^{4} \). In all the simulations (solid and fluid), the reference pressure was the atmospheric pressure, which was set to zero to obtain gauge pressure results. No wrinkle was observed on the balloon, since the inner balloon pressure always remained higher than the outer pressure.
Modeling of the Angioplasty Balloon
Modeling of the Arterial Vessel
For the simulation of balloonangioplasty, only the portion around the stenosed artery was modeled. The simulated zone had a total length of 4.2 cm and was centered onto the stenosis. No direct measurement of wall thickness was possible in vivo. Measurements in arteries of similar caliber found the thickness to be about 1/10th of the arterial diameter.18 The thickness of the nonstenosed artery was therefore set to be 0.6 mm. In the stenosed part, an average thickness value equal to 0.8 mm was imposed. The vascular wall was meshed with a monolayer of discreteKirchhoff theorybased, fournode lineartriangular shell finite elements. Prior to meshing, the AVF wall was subdivided in order to impose different mechanical properties to the healthy artery and to the stenosed arterial portion (Fig. 1).
The stenosed part of the artery was modeled with the Maxwell model, which is a viscoplastic model composed of an elastic spring in series with a viscous dashpot. The law parameters were chosen following two criteria. We imposed that the stenosed and nonstenosed parts of the artery had the same stiffness at small deformation in order to ensure mechanical continuity at the interface between them. At large deformations the parameter values were set in order to fit the data of Maher et al. 24
Description of the Various Stages of the Simulation
At each instant of time, the structural simulation consisted in finding the mechanical equilibrium between the deformable artery and the elastic balloon implicitly. The vessel residual stresses were neglected due to a lack of existing data: to estimate them, the unloaded vessel geometry would have needed to be determined, since the artery was under pressure and already stretched when the imaging data were obtained in vivo. But such a process was not feasible in the case of a stenosed vessel, as no information was known on the actual wall thickness and properties in the stenosed region. It is likely that assuming zero residual stress mainly affects the balloon inflation pressures needed to reach the targeted degree of residual stenosis. But one can hypothesize that it will have a negligible effect on the actual vessel shape that is obtained.
At the beginning of the simulation the balloon was not in contact with the artery (Fig. 2a). The balloon was inflated by an increasing linear ramp in pressure. Figure 2b shows when contact occurred between the balloon and arterial wall. The contact problem was solved using the augmentedLagrange method; it was supposed to be frictionless.15 The balloon was further inflated until the maximum pressure was reached (Fig. 2c). It was then deflated following a decreasing linear pressure ramp, leaving the vessel wall in its posttreatment configuration (Fig. 2d). Different values of balloon pressure were imposed (6, 5.6, 5.1, 4.7 bar). They respectively led to a degree of residual stenosis equal to 0, 10, 20 and 30% after angioplasty (Fig. 2e).
Numerical Method to Simulate the Hemodynamics Inside the AVF
Numerical Procedure
ANSYSCFX (ANSYS, Inc.) was used to solve the continuity and momentum equations in their conservative convectiondiffusion form.1 The equations were solved implicitly with the RhieChow interpolation method.30 We used the highresolution, secondorder backward Euler scheme implemented in the ANSYSCFX fluid solver (ANSYS, Inc.). It is an implicit timestepping scheme recommended for nonturbulent flow simulations.1 The system of algebraic equations was solved iteratively using a timestep \(\Delta t\) equal to 5 ms. At each time step, the residual was calculated and reported as a measure of the overall conservation of the flow properties. The maximum residual allowed was \(10^{4}\). Convergence was verified in less than 10 subiterations at the first time step and in less than five iterations at all the following time steps.
Modeling of Blood in the Lumen
The patientspecific lumen was meshed starting from the triangulation of the lateral face of the reconstructed AVF lumen (right insert in Fig. 1). The mesh was made of an hybrid grid created in ANSYS TGrid. First the boundary layer was meshed with seven layers of prismatic elements of decreasing thickness along the radius. The core was then meshed with tetrahedrons. Both cell element types were linear.
Boundary Conditions
A timedependent velocity \(v_a^i\) was set at the arterial inlet \(S_a^i\): it was measured by echoDoppler in the proximal radial artery of the patient on the day of the CTscan (Fig. 1). The measurements corresponded to a systolic Reynolds number of 1230, a timeaveraged Reynolds number of 1020 (timeaveraged inlet flow rate \( \overline{Q}_a^i = 1.1\) L min\(^{1}\)) and a Womersley number of 4. The inlet velocity was imposed as a flat velocity profile.
At each of the two outlets \(S_a^o\) and \(S_v^o\), a Windkessel model was imposed, which consists in imposing a pressureflow relationship as boundary condition.38 The Windkessel model is based on the hypothesis that the blood flow is a function of the compliance and resistance of the network. If one models the vessel compliance as a capacitor and the hydraulic resistance as an electrical resistance, one can generate a zerodimensional model of the flow in the network through a simple electrical analog circuit.

the pulse pressure, defined as the difference between the systolic pressure \(P_s\) and the diastolic pressure \(P_d\) at the considered outlet;

the timeaveraged pressure \(\overline{P}\) at the flow outlet;

the timeaveraged blood flow rate \(\overline{Q}\) at the same flow outlet.
Values of the venous and arterial resistances (\(R_v\) and \(R_a\)) and compliances (\(C_v\) and \(C_a\)) for the different values of timeaveraged inlet pressure \(\overline{P}_a^i\)
\(\overline{P}_a^i\)  \(P_{a_s}^i\)  \(P_{a_d}^i\)  \(R_a\)  \(C_a\)  \(R_v\)  \(C_v\) 

55  63  51  11.9  4.98  4.77  11.5 
70  78  66  30  5  6.5  12 
90  98  86  41  5.04  7.4  12.1 
The same \(R\) and \(C\) values were used for all the simulations, both before and after the treatment by angioplasty. The postangioplasty simulations therefore model the situation shortly after treatment, before the occurrence of any physiological adaptation in the distal circulation.
Initial Conditions
The velocity field was initialized with the solution of the steadystate simulation. In this simulation the fluid properties were identical to the ones described above. As boundary conditions, we imposed the timeaveraged values of the inlet velocity at \(S_a^i\) and the timeaveraged values of the venous and arterial pressures at \(S_v^o\) and \(S_a^o\), respectively.
Hemodynamic Parameters
In a healthy radial artery, \(\overline{WSS}\) is in the range 1–2 Pa,37 which we will refer to as the healthy physiological \(WSS\) range. In a vein, it was reported that neointimal hyperplasia rapidly develops when \(WSS\) values are below 0.5 Pa.20
Validation
The solid and fluid solvers were validated independently. For the fluid solver, different mesh sizes were tested in order to guarantee a maximum error of 1% on the velocity magnitude and wall shear stresses and acceptable computational time \(t_{\rm comp}\). We investigated meshes of maximum element length \(\Delta l_{\rm max}\) equal to 1, 2, 4, 5, 7 and \(10 \times 10^{3}\) mm. The results obtained with the smallest mesh size (\(10^{3}\) mm) were used as reference. In general, the relative error \(\varepsilon _u\) on the quantity \(u\) was defined as \( uu^{ref}/u^{ref}\). The relative error was calculated for \(u = v_{\rm max}\), the maximum amplitude of the velocity vector \( \mathbf v \) at the stenosis, and for \(u = \overline{WSS}\), the timeaveraged wall shear stress.
The fluid solver was further validated through comparison with measurements obtained in vitro in a rigid mold of the patientspecific AVF geometry. More details on the comparison can be found in Decorato et al. 9
The solid solver was validated by modeling the inflation of a cylinder from radius \(R\) to radius \(R(1+\alpha )\) by an internal pressure \(P\). A displacement was imposed to the shell, which induced a stretch ratio \(\lambda =1+\alpha \). For a thin shell, an analytical solution can be derived relating the radial and tangential stresses to \(\lambda \) through the strain energy function.17,35 Comparing the numerical results to the theoretical predictions, a precision of 1% was obtained when the arterial wall was discretized with 20 760 shell elements. A much smaller number of elements was needed to discretize the balloon (2100 shell elements), owing to its simple cylindrical geometry and smaller length.
Results
Comparison of Pre and Postangioplasty Geometries
Comparison of Pre and Postangioplasty Hemodynamic Conditions
Results are first shown for an inlet mean pressure of \(\overline{P}_a^i = 70\) mmHg. The influence of the boundary conditions will be examined in the next section.
Blood Flow
Wall Shear Stresses

The proximal and distal parts of the artery experience physiological values of \(\overline{WSS}\) in the range 12 Pa.37

The anastomosis experiences \(WSS\) one order of magnitude higher: the maximum instantaneous value is about 20 Pa.

On the contrary, the vein experiences \(\overline{WSS}\) values below 1 Pa or even 0.5 Pa in the dilated venous region.
Pressure Drop Across the Stenosis
Effect of the Peripheral Vascular Boundary Conditions on the Hemodynamics Inside the AVF
The effect of varying the mean arterial pressure is investigated by changing the values of the resistance and compliance at the arterial and venous boundary conditions (Table 1). The values of resistance and compliance have been obtained maintaining the pulse pressure constant.
Comparison of the timeaveraged venous blood flow \(\overline{Q}_v\) at \(S_v^o\), peak systolic velocity \(v_s\) and stenosis pressure drop in the patientspecific geometry, when the peripheral \(R\) and \(C\) values are modified
\(\overline{P}_a^i\) (mmHg)  55  70  90 
\(\overline{Q}_v\) (\({\rm mL}\,{\rm min}^{1}\))  750  752  754 
\(v_s\) (\( {\rm m}\,{\rm s}^{1} \))  2.20  2.20  2.20 
\(\overline{P}_{B_1}\) − \(\overline{P}_{B_2}\) (mmHg)  12.1  12  12 
Discussion and Conclusion
For the first time, the effects on the blood flow have been studied for a stenosis affecting the feeding artery of an arteriovenous fistula. The hemodynamics has been simulated numerically in a patientspecific AVF with an 60% arterial stenosis. The originality of the study comes from the fact that the removal of the stenosis by balloonangioplasty is modeled through an implicit numerical simulation. The balloon is considered to be cylindrical when unloaded. The posttreatment geometry of the vessel is efficiently computed by mimicking the viscoplastic behavior of the arterial wall in the simulation. Since the stenosis removal is rarely complete in clinical practice, we have investigated different degrees of residual stenosis ranging from 30 to 0%. It is the range of stenosis correction that is considered as successful clinically.
To recreate physiologically realistic flow conditions, we have set patientspecific boundary conditions at the two outlets of the AVF using Windkessel models. The challenge was to design a technique to estimate the Windkessel model parameters from the flow rates, which were the only clinical data that could be measured noninvasively on the patient. Indeed no data existed in the literature on the global resistance and compliance of the arterial and the venous systems downstream of the AVF. If one compares the AVF values to the healthy case,38 one finds that the venous compliance \(C_v\) is larger than in the healthy case by one order of magnitude at maximum, and that the venous resistance \(R_v\) is slightly smaller. Conversely, at the arterial side the compliance \(C_a\) is about 5 times smaller than in the healthy case and the resistance \(R_a\) is 8 times higher than the healthy case value. The \(R\) and \(C\) values calculated for the AVF translate the fact that the AVF redirects the flow preferentially into the vein.
To evaluate the influence of the arterial stenosis on the hemodynamics, we have compared the flow field within the patientspecific and treated geometries. We have shown that the arterial stenosis has no significant effect on the general hemodynamics within the AVF, leaving unchanged the blood flow split between the distal artery and the vein. This is coherent with a recent study that showed that arterial stenoses only affect the arterial outflow when they are located within 5 mm from the anastomosis.34 Our result explains why the fistula of the patient under study was still functioning despite the presence of an 60% stenosis: having no effect on the venous flow rate, the stenosis did not impact the efficiency of the hemodialysis treatment.
Various hemodynamic parameters have been computed to see whether they were influenced by the arterial stenosis:
Wall Shear Stresses
The presence of the stenosis leads to a local increase of the wall shear stresses at the stenosis neck. At this location, the timeaveraged stress \(\overline{WSS}\) is 5 times larger than in the fully corrected case (0%stenosis)—see Fig. 5c. Singh et al.33 have shown that a timeaveraged stress of 15 Pa is the threshold, above which the endothelial cells are irremediably damaged and atherosclerotic plaques might form. From a \(WSS\) criterion, the present study indicates that the stenosis needs to be corrected with a degree of residual stenosis below 30% for the \(WSS\) to be below the threshold value of 15 Pa at the neck.
Pressure Drop Across the Stenosis
The pressure drop is the other hemodynamic parameter that was significantly influenced by the presence of the arterial stenosis. This idea was already put forward by Young41 for arterial stenoses in general. It is difficult to hypothesize what the clinical consequence of the increase in pressure drop will be. Will it lead to an increase in the upstream pressure and hence in the afterload cardiac pressure? If so, the necessity to remove the arterial stenosis is particularly high in AVF patients, who are already prone to heart failure and sudden cardiac death.13,32 Does the increase in pressure drop instead lead to a decrease in the downstream pressure? It would then have a protecting heart effect. The urge to treat the arterial stenosis would be dictated by the fear of thrombosis and the necessity to preserve the AVF patency in the longterm.
All these results would need to be confirmed by other clinical studies. It would similarly be interesting to compare the predicted postangioplasty geometry with the actual in vivo one. Although conducted on a single patient geometry, the present results can provide the basis for a reflection on the clinical criteria in the case of arterial stenosis. In clinics, a stenosis is currently treated when the pressure drop across the lesion is above 5 mmHg.14 This criterion, originally set for venous stenoses, is used by default for arterial stenoses. We have found that a pressure drop of 5 mmHg corresponds to a 20% residual stenosis (Fig. 6b). The present study would therefore suggest that a 30% residual stenosis degree is too high for arterial stenoses and that the criterion for treatment needs to be reconsidered and adapted to the case of arterial stenosis. It could also be worth including the peak \(\overline{WSS}\) in the reflection. But more cases would need to be studied to check whether the present results hold on.
Another point that needs to be improved is the detection of arterial stenoses. We have seen that arterial stenoses cause an increase in pressure drop in the concerned artery, but such a quantity is difficult to measure clinically. It could be of interest to investigate whether the formation of an arterial stenosis is associated with an increase in systemic pressure. If so the monitoring of the blood pressure evolution could become indicative of the presence of a stenosis, if changes are looked for over long time periods.
Notes
Acknowledgments
This research is funded by the European Commission, through the MeDDiCA ITN (www.meddica.eu, Marie Curie Actions, grant agreement PITNGA2009238113) and by the French Ministère de la Recherche (Pilcam2 grant). The authors gratefully acknowledge Polyclinique St Côme (Compiègne, FRANCE) for the medical images.
Conflict of Interest
None.
Statement of Human Studies
The clinical images were acquired in 2004 in conformity to the standards of use of medical images (patient consent, secured transfer of anonymized data).
Statement of Animal Studies
N/A.
References
 1.ANSYS Academic Research, Release 13.0, Help System. ANSYS Inc, 2010.Google Scholar
 2.Asif, A., F. N. Gadalean, D. Merrill, G. Cherla, C. D. Cipleu, D. L. Epstein, and D. Roth. Inflow stenosis in arteriovenous fistulas and grafts: a multicenter, prospective study. Kidney Int. 67:1986–1992, 2005.CrossRefGoogle Scholar
 3.Asif, A. Endovascular procedures. Contrib. Nephrol. 161:30–38, 2008.CrossRefGoogle Scholar
 4.Biuckians, A., B. C. Scott, G. H. Meier, J. M. Panneton, and M. H. Glickman. The natural history of autologous fistulas as firsttime dialysis access in the KDOQI era. J. Vasc. Surg. 47:415–421, 2008.CrossRefGoogle Scholar
 5.Bogert, L. W. J., and J. J. van Lieshout. Noninvasive pulsatile arterial pressure and stroke volume changes from the human finger. Exp. Physiol. 90:437–448, 2005.CrossRefGoogle Scholar
 6.Chan, M. R., S. Bedi, R. J. Sanchez, H. N. Young, Y. T. Becker, P. S. Kellerman, and A. S. Yevzlin. Stent placement versus angioplasty improves patency of arteriovenous grafts and blood flow of arteriovenous fistulae. Clin. J. Am. Soc. Nephrol. 3:699–705, 2008.CrossRefGoogle Scholar
 7.Coentrpo, L., and L. TurmelRodrigues. Monitoring dialysis arteriovenous fistulae: its in our hands. J. Vasc. Access 14(3):209–215, 2013.CrossRefGoogle Scholar
 8.Corpataux, J. M., E. Haesler, P. Silacci, H. B. Ris, and D. Hayoz. Lowpressure environment and remodelling of the forearm vein in bresciacimino haemodialysis access. Nephrol. Dial. Transpl. 17:1057–1062, 2002.CrossRefGoogle Scholar
 9.Decorato, I., Z. Kharboutly, T. Vassallo, J. Penrose, C. Legallais, and A.V. Salsac. Numerical simulation of the fluid–structure interactions in a compliant patientspecific arteriovenous fistula. Int. J. Numer. Methods Biomed. Eng. 30:143–159, 2014.CrossRefGoogle Scholar
 10.Dixon, B. S. Why don’t fistulas mature? Kidney Int. 70:1413–1422, 2006.CrossRefGoogle Scholar
 11.Duijm, L. E. M., Y. S. Liem, R. van der Rijt, F. J. Nobrega, H. C. M. van der Bosch, P. DouwesDraaijer, P. W. M. Cuypers, and A. V. Tielbeek. Inflow stenoses in dysfunctional hemodialysis access fistulas and grafts. Am. J. Kidney Dis. 48:98–105, 2006.Google Scholar
 12.EneIordache, B., L. Mosconi, G. Remuzzi, and A. Remuzzi. Computational fluid dynamics of a vascular access case for hemodialysis. J. Biomech. Eng. 123:284–292, 2001.CrossRefGoogle Scholar
 13.Fellström, B. C., A. G. Jardine, R. E. Schmieder, H. Holdaas, K. Bannister, J. Beutler, D.W. Chae, A. Chevaile, S. M. Cobbe, C. GrönhagenRiska, J. J. De Lima, R. Lins, G. Mayer, A. W. McMahon, H.H. Parving, G. Remuzzi, O. Samuelsson, S. Sonkodi, G. Süleymanlar, D. Tsakiris, V. Tesar, V. Todorov, A. Wiecek, R. P. Wüthrich, M. Gottlow, E. Johnsson, and F. Zannad. Rosuvastatin and cardiovascular events in patients undergoing hemodialysis. N. Engl. J. Med., 360:1395–1407, 2009.Google Scholar
 14.Forauer, A. R., E. K. Hoffer, and K. Homa. Dialysis access venous stenoses: treatment with balloon angioplasty1versus 3minute inflation times. Radiology, 249(1):375–381, 2008.CrossRefGoogle Scholar
 15.Gasser, T. C., and G. A. Holzapfel. Finite element modeling of balloon angioplasty by considering overstretch of remnant nondiseased tissues in lesions. Comput. Mech. 40:47–60, 2007.CrossRefzbMATHGoogle Scholar
 16.Gervaso, F., C. Capelli, L. Petrini, S. Lattanzio, L. DiVirgilio, and F. Migliavacca. On the effects of different strategies in modelling balloonexpandable stenting by means of finite element method. J. Biomech. 41(6):1206–1212, 2008.CrossRefGoogle Scholar
 17.Green, A. E., and J. E. Adkins. Large Elastic Deformations. Oxford University Press, 1970.Google Scholar
 18.Gutierrez, M. A., P. E. Pilon, S. G. Lage, L. Kopel, R. T. Carvalho, and S. S. Furuie. Automatic measurement of carotid diameter and wall thickness in ultrasound images. Comput. Cardiol. 29:359–362, 2002.Google Scholar
 19.Horl, W. H., K. M. Koch, C. Ronco, and J. F. Winchester. Replacement of renal function by dialysis. Kluwer Academic Publishers, 2004.Google Scholar
 20.Jackson, M., N. B. Wood, S. Zhao, A. Augst, J. H. Wolfe, W. M. W. Gedroyc, A. D. Hughes, S. A. M. c. G. Thom, and X. Y. Xu. Low wall shear stress predicts subsequent development of wall hypertrophy in lower limb bypass grafts. Arter. Res. 3:32–38, 2009.CrossRefGoogle Scholar
 21.Kharboutly, Z. M. Fenech, J. M. Treutenaere, I. Claude, and C. Legallais. Investigations into the relationship between hemodynamics and vascular alterations in an established arteriovenous fistula. Med. Eng. Phys. 29(9):999–1007, 2007.CrossRefGoogle Scholar
 22.Konner, K. History of vascular access for haemodialysis. Nephrol. Dial. Transpl. 20:2629–2635, 2005.CrossRefGoogle Scholar
 23.Lee, T., and P. RoyChaudhury. Advances and new frontiers in the pathophysiology of venous neointimal hyperplasia and dialysis access stenosis. Adv. Chronic Kidney Dis. 16(5):329–338, 2009.CrossRefGoogle Scholar
 24.Maher, E., A. Creane, S. Sultan, N. Hynes, C. Lally, and D. J. Kelly. Inelasticity of human carotid atherosclerotic plaque. Ann. Biomed. Eng. 39:2445–2455, 2011.CrossRefGoogle Scholar
 25.Merril, E. W., and G. A. Pelletier. Viscosity of human blood: transition from Newtonian to nonNewtonian. J. Appl. Physiol. 23:178–182, 1967.Google Scholar
 26.Molino, P., C. Cerutti, C. Julien, G. Cusinaud, M. P. Gustin, and C. Paultre. Beattobeat estimation of windkessel model parameters in conscious rats. Am. J. Physiol. Heart Circ. Phisiol. 274:H171–H177, 1998.Google Scholar
 27.Niemann, A. K., S. Thrysoe, J. V. Nygaard, J. M. Hasenkam, and S. E. Petersen. Computational fluid dynamics simulation of av fistulas: From MRI and ultrasound scans to numeric evaluation of hemodynamics. J. Vasc. Access 13(1):36–44, 2012.Google Scholar
 28.Ozyer, U., A. Harman, E. Yildirim, C. Aytekin, F. Karakayali, and F. Boyvat. Longterm results of angioplasty and stent placement for treatment of central venous obstruction in 126 hemodialysis patients: a 10year singlecenter experience. Am. J. Roentgenol. 193:1672–1679, 2009.CrossRefGoogle Scholar
 29.Prendergast, P. J., C. Lally, S. Daly, A. J. Reid, T. C. Lee, D. Quinn, and F. Dolan. Analysis of prolapse in cardiovascular stents: a constitutive equation for vascular tissue and finiteelement modelling. J. Biomech. Eng. 125:692–699, 2003.CrossRefGoogle Scholar
 30.Rhie, C. M., and W. L. Chow. Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 21:1525–1532, 1983.CrossRefzbMATHGoogle Scholar
 31.Salman, L., M. Ladino, M. Alex, R. Dhamija, D. Merrill, O. Lenz, G. Contreras, and A. Asif. Accuracy of ultrasound in the detection of inflow stenosis of arteriovenous fistulae: results of a prospective study. Semin. Dial. 23:117–121, 2010.CrossRefGoogle Scholar
 32.Sarnak, M. J. Cardiovascular complications in chronic kidney disease. Am. J. Kidney Dis. 41:11–17, 2003.CrossRefGoogle Scholar
 33.Singh, P. K., A. Marzo, C. Staicu, M. G. William, I. Wilkinson, P. V. Lawford, D. A. Rufenacht, P. Bijlenga, A. F. Frangi, R. Hose, U. J. Patel, and S. C. Coley. The effects of aortic coarctation on cerebral hemodynamics and its importance in the etiopathogenesis of intracranial aneurysms. J. Vasc. Int. Neurol. 3:17–30, 2010.Google Scholar
 34.Swinnen, J. Duplex ultrasound scanning of the autogenous arterio venous hemodialysis fistula: a vascular surgeon’s perspective. AJUM 14:17–23, 2011.Google Scholar
 35.Timoshenko, S. P., and J. N. Goodier. Timoshenko and Gore: Theory of Elastic Stability: Theory of Elasticity. McGrawHill, 1970.Google Scholar
 36.Tordoir, J. H. M., H. G. Debruin, H. Hoeneveld, B. C. Eikelboom, and P. Kitslaar. Duplex ultrasound scanning in the assessment of arteriovenous fistulas created for hemodiafysis access—comparison with digital subtraction angiography. J. Vasc. Surg. 10:122–128, 1989.CrossRefGoogle Scholar
 37.van Tricht, I., D. DeWachter, J. Tordoir, and P. Verdonk. Hemodynamics and complications encountered with arteriovenous fistulas and grafts as vascular access for hemodialysis: a review. Ann. Biomed. Eng. 33:1142–1157, 2005.Google Scholar
 38.Westerhof, N., F. Bosman, C. J. De Vries, and A. Noordergraaf. Analog studies of the human systemic arterial tree. J. Biomech. 2:121–143, 1969.CrossRefGoogle Scholar
 39.Yeoh, O. H. Some forms of the strain energy function for rubber. Rubber Chem. Technol. 66:754–771, 1993.CrossRefGoogle Scholar
 40.Yerdel, M. A., M. Kesence, K. M. Yazicuoglu ans, Z. Doseyen, A. G. Turkcapar, and E. Anadol. Effect of hemodynamic variables on surgically created arteriovenous fistula flow. Nephrol. Dial. Transpl. 12:1684–1688, 1997.Google Scholar
 41.Young, D. F. Fluid mechanics of arterial stenoses. J. Biomech. Eng. 101:157175, 1979.CrossRefGoogle Scholar