Prediction of the anastomosis angle of arteriovenous fistula in hemodialysis to standardize the surgical technique

Abstract

BACKGROUND:

Arteriovenous fistula (AVF) is the preferred route of vascular access in hemodialysis. The primary reason of fistula failure is intimal hyperplasia (IH), which leads to stenosis. Wall shear stress (WSS) and disturbed flow are the critical parameters in the formation of IH.

OBJECTIVE:

The primary goal of this study is to explore the influence of anastomosis angle on WSS and venous outflow rate, as well as to find the ideal angle of anastomosis for AVF to standardize surgical technique.

METHODS:

Three-dimensional idealized geometries of end-to-side type AVF for the five various angles of anastomosis are considered in this study. The WSS, blood flow rate at the venous outlet for non-Newtonian, pulsatile blood flow are calculated using a numerical simulation technique.

RESULTS:

The WSS is higher at 75° compared to other angles and least at 45° for pulsating arterial inflows. The WSS is moderate at 30°, 60° and 90°. On the arterial bed and outer wall of the vein, immediately after the anastomosis, the recirculation zone is observed. At an angle of 45° and 90° anastomosis, the outflow rate is greater at distal venous end.

CONCLUSIONS:

If one believes that high wall shear stress causes IH within the AVF, the results suggest that the AVF should be formed at a 45° angle to avoid IH. However, if one believes that low wall shear stress causes IH within the AVF, the results suggest that AVF should be formed at either 30° or 75° to avoid IH. The findings spotlight the importance of anastomosis angle in determining AVF hemodynamics.

Keywords

Arteriovenous fistula anastomosis angle hemodialysis vascular access wall shear stress

1. Introduction

When the kidney stops working or works less than 10%, the patients requires hemodialysis. For the hemodialysis, the blood is extracted from the human blood vessels and supplied to the dialyzer, and returned to the body after filtration. This transportation of blood requires vascular access needs to be surgically created in the patient’s body. AV fistulas are the best type of vascular access, according to the National Kidney Foundation (NKF), the Centers for Medicare and Medicaid Services (CMS), and Dialysis Patient Citizens (DPC).

Over the last two decades, there has been a lot of research done on arteriovenous fistulas and their complications. The Computational Fluid Dynamics (CFD) technique was used to investigate the effects of steady and transient (pulsatile) flow, Newtonian and non-Newtonian fluid, turbulence and secondary flows on the flow field and other parameters such as wall shear stress, pressure, and velocity of 3D idealized AVF and AV graft geometries [1–6]. Ethier et al. studied the detailed understanding of 2D end-to-side anastomosis model to identified the hemodynamic patterns that could leads to intimal hyperplasia (IH) [7]. Some researchers include patient-specific geometries in their computational research to study the hemodynamics of AVF [8,9]. Barber et al. collected 100 CFD models of patient-specific data to develop a tool which predict model for AVF failure [10]. Particle image velocimetry (PIV), noncontracted-enhanced MRI, and 3D ultrasound imaging are some of the experimental techniques used to validate computational results and study the hemodynamics of AVF [11–14]. The AV graft was subjected to a computational (CFD) study to investigate hemodynamics and the effects of anastomosis angle and size [15–17]. Sivanesan identified the stenosis as well as the locations of the end-to-side radiocephalic fistulae [18]. Roy-Chaudhury et al. conducted the first in-person experiment with the Optiflow device, an implant that produces a highly reproducible anastomosis with controlled geometry between the artery and vein [19]. Roy-Chaudhury et al. conducted another pilot study of AVF placement using the novel Optiflow device on a total of 41 subjects, concluding that the device appears to be safe and effective in the placement of AVFs, with high maturation rates [20]. To the best of the researchers’ knowledge, no work on the range of anastomosis angle of radio-cephalic, end-to-side AVF with non-Newtonian pulsatile blood flow has been not seen yet.

The novelty in the present study included the range of idealized AVF geometries of anastomotic angle ranges from 30° to 90° with the difference of 15°, incorporated with the non-Newtonian, pulsatile blood flow to observe the effect of anastomosis angle on the wall shear stress and venous outflow rate. This study only focused on radio-cephalic, end-to-side anastomosis of AVF at wrist, shown in Fig. 1.

Fig. 1.

Creation of AVF of the radial artery side and the cephalic vein end at 90° of anastomosis.

2. Methods

2.1. Idealized AVF geometry

Three-dimensional geometries are used for numerical modelling of end-to-side connections in AVF at various anastomotic angles. It is not possible to obtain information for each patient every time; however, performing a Doppler or MRI to search for 30°, 45°, 60°, 75°, and 90° angles of AVF is a time-consuming process. Hence, ideal geometry is used in this work. The current study investigated five geometries in all. Each of the five radial artery and cephalic vein configurations illustrated in Fig. 2 is examined with a fixed arterial diameter DA of 4 mm and an inflammatory venous diameter DV of 6 mm. This combination of diameters is fixed with each other at different anastomosis angles of 30°, 45°, 60°, 75°, and 90° to form an AVF. Mesh elements ranging from 2,40,000 to 2,70,000 are employed for ideal geometries. The grid independent study is performed to prevent the impact of the grid on the numerical results. As a result, with a time step size of 0.01 s, 2,10,000 (20% fewer elements) and 3,20,000 (20% more elements) are examined. In comparison, the maximum change in velocity at the vein outlet is less than 0.25%.

Fig. 2.

Schematic representation of the idealized geometries of AVF at angles of 30°, 45°, 60°, 75° and 90°.

2.2. Governing equations

In this work, blood is modelled as an incompressible [4,21,22]. The continuity and incompressible Navier–Stokes equations for a pulsatile blood flow are used to stimulate blood flow, which may be expressed as $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle {\nabla}\cdot u=0,\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle {\rho}\left({\displaystyle \frac{\partial u}{\partial t}}+u\cdot {\nabla}u\right)={\nabla}\cdot {\sigma}+f,\nonumber\end{eqnarray}$ where 𝜌, u, 𝜎 and f are the constant density, velocity vector, the stress tensor and external body force. In this study the body forces assumed to be zero. Hydrostatic and deviatoric stresses may be dissected from the stress tensor. $\begin{eqnarray}\displaystyle {\sigma}=-pI+{\tau}, & & \displaystyle \nonumber\end{eqnarray}$ where p denotes pressure, I is the identity tensor, and 𝜏 is the deviatoric stress tensor which is a function of the shear rate tensor. $\begin{eqnarray}\displaystyle {\tau}={\mu}(\overset{\cdot }{{\gamma}})D, & & \displaystyle \nonumber\end{eqnarray}$ where 𝜇 is the dynamic viscosity and 𝛾 is the shear rate. Defining the shear rate as follows $\begin{eqnarray}\displaystyle D={\displaystyle \frac{1}{2}}({\nabla}u+{\nabla}u^{T}). & & \displaystyle \nonumber\end{eqnarray}$

And therefore, 𝛾 is defined by a function of D $\begin{eqnarray}\displaystyle \overset{\cdot }{{\gamma}}=\sqrt{{\displaystyle \frac{1}{2}}\mathop{\sum }_{i}\mathop{\sum }_{j}D\mathit{ij}Dji}. & & \displaystyle \nonumber\end{eqnarray}$

Constitutive equations are required to compute the viscosity of the blood in order to use the system of equations. The most basic model is a Newtonian fluid, which assumes constant viscosity. The viscosity models, on the other hand, can correctly represent the shear thinning characteristic of blood flow. Also, Because of the predominance of low shear rates in the vein, the non-Newtonian blood model is required to predict the hemodynamics in the AVF. In this work, 𝜌 = 1060 $\text{kg}/\text{m}^3$ are employed [12,21,23]. The mass and momentum equations were solved using the finite volume technique (FVM) using a commercially available CFD software, ANSYS Fluent 2021 with the time step size of 0.0005 s. For the pressure velocity coupling, the SIMPLE algorithm is used. The momentum equation is discretized using the second-order upwind technique. The under relaxation factors are set as 0.3 for pressure, 1 for density, 1 for body forces, 0.7 for momentum, and 1 for viscosity.

2.3. Fluid model

Blood parameters such as density and viscosity are difficult to quantify since they are affected by human factors such as age, gender, illness, lifestyle, and food. The blood density ranges from 1030 to 1070 $\text{kg}/\text{m}^3$ . The blood density used in this investigation was 1060 $\text{kg}/\text{m}^3$ . Blood is considered a non-Newtonian fluid, and various rheological models are available in the literature to support this [24]. The Carreau model used for the simulations and the dynamic viscosity is specified as $\begin{eqnarray}\displaystyle {\eta}={\eta}\infty +({\eta}0-{\eta}\infty )[1+({\lambda}\dot{{\gamma}})^{2}]^{\frac{n-1}{2}}, & & \displaystyle \nonumber\end{eqnarray}$ where 𝜆 = 3.313 s, n = 0.3568, 𝜂₀ = 0.056 Pa s and 𝜂_∞ = 0.00345 Pa s [25]. Heat transfer and temperature are neglected in this study.

2.4. Boundary conditions

Pulsatile blood flow is used as the artery inlet boundary condition as shown in Fig. 3 and mathematically represented as $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle u(t)=0.5\sin (4{\pi}(t+0.0160236))\quad \text{for }0.5n<x\leq 0.5n+0.218\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle u(t)=0.1\quad \text{for }0.5n+0.218<x\leq 0.5(n+1).\nonumber\end{eqnarray}$

Because of the changing pressures throughout systole and diastole, the computations used the average of the two. During systole and diastole, the pressure in a normal healthy person is about 120 mmHg and 80 mmHg, respectively. As a result, the average of two is 100 mmHg, and the constant static gauge pressure is employed at the artery and vein outlets. In this study, the walls of all vessels are assumed to be rigid and non-deformable [4,26,27]. The venous part becomes more rigid as it matures, and could thus be considered a rigid wall [11]. At the vessel wall, a no-slip boundary condition is applied.

Fig. 3.

The user-defined waveform used as an inlet boundary condition.

3. Validation

There is a requirement in the numerical study to calculate accurate results. A hemodynamic simulation is performed for this requirement using the model of the human carotid bifurcation from the study by Bharadvaj et al. [28]. The laser-Doppler anemometer is used to investigate the velocity profile as the flow approached the bifurcation. The same CAD model is developed and simulated in this study, with similar boundary conditions, an upstream Reynolds number of 400, and a 70:30 distribution of flow through the internal and outer carotid arteries.

The current computational study’s results are compared to those of Bharadvaj et al. [28], and the curve of axial velocity in the plane of bifurcation is depicted in Fig. 4. This shows that the results are closer to those of the laser-Doppler anemometer. Therefore, the results can be said to be validated by the computational methodology used.

Fig. 4.

Results of Bharadvaj et al. [28] and computational study for axial velocity profile in the carotid artery in the bifurcation plane.

4. Results and discussion

4.1. Velocity analysis

Figure 5 depicts velocity contours on a sagittal plane of AVF geometries at 0.05 s, 0.1 s (peak systole), and 0.2 s for various anastomosis angles, giving a good sense of the velocity parameter’s transient features. When it comes to AVF anastomosis, the flow must be fully developed inside the domain before it may approach the anastomosis. Figure 6 depicts the various parts of the AVF geometry like PA, DA, DV, and anastomosis, while Fig. 7 includes velocity distribution inside the AVF domain at several places such as the Proximal Artery (line 1), Anastomosis (line 2), Distal Artery (line 3) and Distal Vein (line 4). The flow of blood becomes fully developed at the plot of line 1 before it reaches the anastomosis. The plot of lines 2 and 4 indicates that the velocity at the arterial bed and the inner side of the vein are completely or nearly nil due to recirculation. The blood has natural tendency to flow inside the artery. However, from the anastomosis blood gets diverted into the venous part of the AVF and tightly flows by following the outer wall of the vein. This result can be noticed in the plot of line 4, where the centre of the parabolic profile is shifted slightly upward and the same result is shown in the distal artery line 3 plot.

Fig. 5.

Velocity contours of velocity for each anastomosis angle at 0.05 s, 0.1 s [peak systole], and 0.2 s of a pulse.

Fig. 6.

Various parts of the AVF geometry: proximal artery [PA], anastomosis, distal artery [DA], distal vein [DV].

Fig. 7.

For the case of 30°, velocity profile at proximal artery [line 1], anastomosis [line 2], distal artery [line 3], and distal vein [line 4] for the different time steps.

4.2. Wall shear stress on AVF geometry

Initially, three constant inflow rates of 350 ml/min, 500 ml/min, and 900 ml/min were acquired, and some simplifying assumptions were made for blood, which was deemed incompressible and Newtonian. The results reveal a WSS range of 58–79 Pa, 32–42 Pa, and 22–25 Pa at a rate of 350, 500, and 900 ml/min respectively. Finally, transient (pulsatile), non-Newtonian simulations were conducted and results were extracted for the pulse of 0.5 s. The flow was largely affected by anastomosis and the venous section of AVF.

WSS physiological values in healthy arteries are typically 1–2 Pa and in healthy veins, the physiological range is 0.8–3 Pa [29]. Figure 8 depicts the substantial variations in the WSS at peak systole that occur when the angle of anastomosis varies. The most noticeable shape alterations occur at several locations along with the anastomosis. Maximum WSS values were recorded along the vein’s outer wall, including anastomosis, where the flow is subjected to greater levels of WSS exposure shown in Fig. 9. These fluctuating WSS patterns may result in IH at varied AVF geometry regions. It has been discovered that the area where flow separation or recirculation occurs (artery bed and inner wall of vein) has the lowest WSS value. 45° and 90° of anastomosis have limited exposure to fluctuating WSS during systole and diastole, and hence are not prone to IH at these angles. However, the precise values at which the vessels are damaged are unknown, and they would vary from patient to patient. At an angle of 75°, the WSS is quite high, thus the predicted damage would occur within the vessels. Angles 30° and 60° have modest WSS values over the pulse.

Fig. 8.

Maximum value of wall shear stress during one pulse of 0.5 s.

Fig. 9.

WSS contours for 30°, 45°, 60°, 75°, and 90° measured along the vein’s outer wall, including anastomosis indicated by the circle.

On the proximal artery range up to the anastomosis and distal artery, the WSS values are fall within the normal physiological range. At the anastomosis area the distribution of WSS observed is abnormal and hence become the cause of interest. The higher WSS (23.5 to 30 Pa) observed during systole on the outer venous side, near the anastomosis joint. While the low WSS (1.25 to 5 Pa) is observed on the inner venous side, near the anastomosis, some portion of the artery bed where the recirculation zone is seen and on the distal vein.

WSS is seems to be one of the main factors in vascular remodeling. Local fluid patterns and wall shear stress are strictly related to the development of vascular diseases. IH has been correlated with WSS. Area of high WSS cause positive vessel remodeling and are desirable. Heterogeneous WSS causes IH to develop in area of relative low WSS. Uniform and high WSS should give the least IH [3]. In the previous studies, it is seen that there are two types of hypothesis about the WSS: (a) high WSS is the cause of development of IH and (b) low WSS will leads to IH. WSS greater than 3 Pa adds to vessel remodeling and reshaping, which increases saccular aneurysms and plaque instability [30], leading to IH and stenosis. In the present study, WSS caused by an inappropriate angle of anastomosis is considered as one of the factor which is important in causation of stenosis. However, there are other factors which contributes to the stenosis like repeated puncturing of fistula (vessels) by the needle used in hemodialysis. In 1991, Yokobori Jr. and Yokobori [31] demonstrated the importance of the puncturing testing method in estimating the quality of the vascular substitute to be punctured and developed the puncturing technique. Ensuing high WSS is designed to cause biological changes in the fibrous cap and plaque, making them more prone to cracking or breaking [32]. As a result, an angle with a low WSS is recommended for anastomosis of AVF surgery. High wall shear stress leads to affect sensitive endothelial cells on the inner vessel walls [8,33,34]. From the results it can be suggest that, the high WSS over the complete pulse cycle is seen at an angle of 75° and 30° and it can be the cause of vascular damage. However, Patrick [13] provides evidence against the high wall shear stress and suggest the further investigation for low wall shear stress. Also, some studies concluded that and support the hypothesis that the low wall shear stress is prone to develop IH [6,14]. However, Ethier et al. [7] suggest that low wall shear stress may not be the only hemodynamic initiating factor leading to the development of IH.

According to the current results and observations, there is a need for something that can keep the AVF anastomosis angle at 45° or 30° until the AVF matures and beyond but it is difficult to control this angle in the actual operation. Hence, the anastomosis device is proposed to maintain the connection of artery and vein at recommended angle, as shown in Fig. 10. This technique of using anastomosis device is realistic, as in 2015 Roy-Chaudhury et al. [20] conducted a pilot study with the Optiflow device and concluded that it is safe and efficient, as well as demonstrating that high maturation rates can be achieved using Optiflow. The design proposed in this study differs from the Optiflow device but it follows the same principal. The vein will supposed to pass through the conduit in the current design, anastomosis will be performed, and the base portion will be mounted on the artery by stretching the slotted portion. The anastomosis device will hold the AVF from outer side of anastomosis at the required angle, as shown in the Fig. 10. Maintaining a certain angle of anastomosis is a constructive part of the surgery in which the position of the vein with respect to the artery should be maintained at the recommended angle with the help of an anastomosis device (biocompatible). However, the dimensions of the device might vary as per the diameter of the artery and vein of the patient. Clinically it is not verified that the recommended angle is superior to that of another angle because such experiments have not yet been done. Currently we are looking forward for the exact biocompatible material. It will then make the device using biocompatible material. Then the device should be gone through various type of testing’s like static tensile test, dynamic pulsatile pressure flow test, durability test, fatigue test as mentioned by Yokobori Jr. and Yokobori [31] and once the device is available for clinical trials, it will be possible to observe the effect of the angle on the actual clinical problem and the recommended angle needs to be clinically validated later on. After the successful clinical trials it will be feasible to control the angle of 30°, 45° and 75° with the help of the anastomosis device. In the present study the angles are recommended on the basis of the computational study of hemodynamics of AVF.

Fig. 10.

(a) CAD design of the anastomosis device. (b) The anastomosis device holds the artery [red] and vein [blue] at the required angle.

As a result, the primary action is directed toward the creation of the device. The mold for the device is created using a 3D printer, and the trial of device making done by using Liquid Silicone Rubber (LSR) to determine whether the mold is suitable for device production. The mold and device are depicted in Fig. 11.

Fig. 11.

(a) 3D printed mold. (b) The anastomosis device made by LSR with help of the mold.

Fig. 12.

Outflow rate [ml/min] at the outlet of the vein for one pulse of 0.5 s.

4.3. Venous outflow rate of blood for the hemodialysis

The creation and use of a computational model capable of assessing the hemodynamic influence of anastomosis angle on the degree flow of an AVF. The outflow rate in ml/min is determined at the distal vein’s face and is intended to create a reference plot that offers outflow rate values for a single pulse of 0.5 s of blood flow, as shown in Fig. 12. Negative outflow rate readings imply that fluid is leaving the domain. The graph clearly shows that the highest outflow rate is attained at a 45° angle. For angles 45° and 90°, the outflow rate is about the same in systole and diastole. When compared to other anastomosis angles, an outflow rate of 75° is attained. In terms of outflow rate, 30° and 60° have a moderate influence.

The flow inside the domain is rather constant throughout the geometry in the current end-to-side AVFs, with a recirculation zone in the dilated distal vein. There are some recirculation zones present in both the artery and the vein immediately after the anastomosis. The separating zone was also found in the venous portion that after the anastomosis in this study. The flow of blood in the vein reversed, with blood returning to the fistula, although this occurs only at the end of the systole. While draining the vein, there are no disruptions in systole; nevertheless, recirculation develops towards the end of systole and a short portion of the beginning of diastole. This consistent change in the phenomenon of near-wall occurs in an area of thrombosis and stenosis found in clinical studies [35].

The purpose of this study is to evaluate the effects of pulsatile flow and anastomosis angle on wall shear stress patterns, with a focus on discovering hemodynamic characteristics that might affect distal anastomotic IH development and distribution. The numerical simulation on the idealized AVF geometries has been carried out.

5. Conclusion

Simulations of blood flow undertaken in various anastomoses angled idealized AVF geometries using the CFD. The objective of this study is to suggest the optimal angle of anastomosis for AVF, with the focus on how the wall shear stresses correlate with vascular pathology such as IH. If one believes that high wall shear stress causes IH within the AVF, the results suggest that the AVF should be formed at a 45° angle to avoid IH. However, if one believes that low wall shear stress causes IH within the AVF, the results suggest that AVF should be formed at either 30° or 75° to avoid IH. One can be observe that the suggestions are incompatible, recognizing the importance of determining the precise mechanisms underlying the development of IH in AVF. However, the findings spotlight the importance of anastomosis angle in determining AVF hemodynamics.

Footnotes

Acknowledgements

The authors are thankful to the Ashwini Kidney & Dialysis Center in Nagpur, Maharashtra for the understanding of the medical terminology. The authors also thank the Mayflower Clinic in Nagpur, Maharashtra for demonstrating the surgical method employed.

Conflict of interest

None to report.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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