INTRODUCTION

The cephalic vein is superficial and the course is constant in the arm. It is often used for arteriovenous fistula creation. Variations in the cephalic vein are common in clinical cases [14]. The variant cephalic vein may affect normal surgical procedures. Hence, anatomical variation of cephalic vein is of clinical and surgical significance, and healthcare professionals must be aware of the variation of this vessel [2]. Here, we found a rare anatomic variant of a single-conduit supraclavicular cephalic arch draining into the external jugular vein. The venous blood drainage in this variant cephalic arch may not be problematic in vivo under physiological conditions [12]. However, in disease conditions, such as brachiocephalic fistula, the blood pressure and haemodynamics in this variant cephalic arch may change dramatically, which related to the adverse effects on patients [4]. There is a case report of a patient with similar cephalic vein variation who underwent brachiocephalic fistula [11]. The first stenosis of variant cephalic vein was dilated with a balloon. After that, the stenoses presented with re­current in cephalic arch. This phenomenon indicates that stenosis is more likely to occur in this variant condition. However, the mechanism of fistula stenosis in this variant cephalic vein should be further analysed in order to provide a reasonable theoretical explanation for the recurrent stenosis and provide valuable reference in clinical practice. Therefore, we try to use 3D computational haemodynamic modelling to simulate the in vivo states of the single-conduit supraclavicular cephalic arch draining into the external jugular vein variant and predict adverse effects due to abnormal haemodynamic changes after brachiocephalic fistula.

Computational fluid dynamics (CFD) uses numerical methods for calculating physical parameters to simulating the haemodynamic environment based on real-world flow field. Changes in the haemodynamic environment can alter the stress on vascular endothelial cells, which is an important mechanism for the pathogenesis of many vascular diseases [20]. CFD models can simulate haemodynamic changes in various vascular disease states. With the advancement of computational sciences and technique, CFD tools can be used to simulate haemodynamic parameters such as fluid flow velocity, pressure, and wall shear stress at any point of the model, more accurately explaining the pathological process of the disease. Currently, it is mostly used in fields such as coronary heart disease and cerebrovascular diseases [23]. CFD tools have been used to investigate the pathological basis of arteriovenous fistula maturation and stenosis [19]. In our present study, CFD was used for imitating haemodynamic alterations in anatomical variation. Although using 3D computational haemodynamic models to simulate the blood flow in normal and variant states in vivo cannot fully explain the mechanism of stenosis in this variant cephalic arch after brachiocephalic fistula, the computational simulation data of the present study will usher us for better understanding of the occurrence and development of the haemodynamic abnormalities.

We raised several concerning scientific questions based on this specific “T-junction” single-conduit supraclavicular cephalic arch draining into the external jugular vein underwent brachiocephalic fistula: (1) the features of the haemodynamic abnormalities during maturation; (2) the theoretical reasons of stenosis and maturation failure; (3) the existence of the risk after stenosis. This study will propose new theoretical explanations for the above-mentioned questions by means of 3D computational haemodynamic modelling, provide reference for clinical practice, and point out the research direction for further in-depth study on the mechanism of haemodynamic changes and the deep-seated causes of the stenosis in this specific “T-junction” single-conduit supraclavicular cephalic arch draining into the external jugular vein.

MATERIALS AND METHODS

Discovery of a jugulocephalic vein variant

A variation of a “T-junction” single-conduit supraclavicular cephalic arch draining into the external jugular vein was found in a male embalmed cadaver (body height 173 cm) during routine dissection.

The variant cephalic vein has abnormal routing and drainage. The diameter of this variant cephalic vein is quite smaller than the normal cephalic vein, and the variant vein routed lateral to deltopectoral groove. Instead of penetrating clavipectoral fascia, the variant cephalic arch went superficial to clavicle and drained into external jugular vein.

The measurement of parameters of right cephalic arch variation

Based on anatomical morphology of cephalic vein, clinical operation process of arteriovenous fistula creation, theoretical and practical purpose of computational modelling, our present computational fluid model intends to collect anatomical data of normal and variant cephalic vein, which begin from the midpoint of the arm: (1) It is conducive to defining vascular segment and measuring anatomical parameters, so that we can conduct 3D simulation of both normal and variant cephalic vein for comparative investigation. (2) We defined the inlet of computational fluid model at the midpoint of the arm for preventing the interference of the disturbed blood flow near the anastomosis, so the blood flow around the computational fluid inlet was regarded as laminar flow. (3) Since the curved segment has both theoretical and practical significance for haemodynamic modelling, our computational fluid model start from the straight segment to form a smooth transition from the straight segment to the curved segment, so that the haemodynamic characteristics of the curved segment can be conducted precisely.

In order to simulate the configuration of vascular accurately, we conducted precise and detailed measurements on the anatomical data of the variant right cephalic vein together with external jugular vein, the abnormal drainage in this case. According to the configuration features, the variant cephalic vein was divided into 5 segments from the midpoint of the right arm to the end of the cephalic vein draining into the right external jugular vein: straight segment, planar curved segment, convex segment, segment anterior to clavicle, and segment superior to clavicle. The segmentation of the variant cephalic vein and measurement of anatomical parameters were started from the midpoint of the arm to provide morphological information for 3D computational modelling, as the modelling starts from the midpoint of the arm. Rather than using existing anatomical segmentation of the cephalic vein, the segmentation in our present study is customized which is completely based on the configuration of the blood vessels to adapt to 3D computational modelling.

Due to the fact that the high-velocity blood in the variant cephalic vein of arteriovenous fistula flow through the external jugular vein to drain into the subclavian vein, we also measured and calculated the anatomical data of the external jugular vein related to the variant cephalic vein, in order to provide sufficient information for 3D computational modelling. We integrated morphological data of external jugular vein and variant cephalic vein into the 3D computational modelling system, to simulate the haemodynamic characteristics of blood returning to the subclavian vein under the special variant route of the cephalic vein in this case.

The measurement of parameters of normal right cephalic vein as a control

As a comparison for the variant cephalic vein, we conducted precise measurements on the anatomical parameters of a right normal cephalic vein to provide configuration parameters for 3D computational modelling. Due to the fact that the variant cephalic arch becomes narrow than other segments, we selected a normal running cephalic vein with narrowing of the diameter of the cephalic vein arch in order to control the metrics and prove that the differences in haemodynamics are completely caused by abnormal drainage, and compared it with the haemodynamic parameters of the variant cephalic vein for analysis. The normal cephalic vein was divided from the midpoint of the right arm to the end of the cephalic vein injecting into the right subclavian vein into three segments: straight segment, oblique segment, and cephalic arch. Starting from the midpoint of the arm, the anatomical parameters of the normal cephalic vein were measured and segmented to collect precise data for computer 3D modelling, as modelling starts from the midpoint of the arm. The segmentation of the cephalic vein described here is customized according to the shape of the blood vessels to adapt to 3D modelling, instead of using the existing anatomical segmentation of the normal cephalic vein. This segmentation method is defined completely according to the shape of the blood vessels. Computational modelling with this morphological definition will conform to the actual haemodynamics parameters of the cephalic vein under physiological conditions.

In addition, we took pictures in the sagittal plane, coronal plane and cross sections of the variant and normal cephalic vein, so as to obtain the bending angle of the blood vessels on the pictures. In order to ensure that the angle of the photo coincides with the Cartesian coordinate system used in computational modelling, we used the level function when taking photos. Every photo included the vessel and a 10.00 mm vernier calliper next to the blood vessel as a scale, so that length data can be calculated proportionally on the image.

Software used in this study

Adobe Photoshop 2022 (RRID:SCR_014199) was used to process images. To acquire morphological data that cannot directly measured, the photo of vessel can be imported into Photoshop and measured on computer.

AutoCAD 2021 (Autodesk, San Francisco, CA, USA; RRID: SCR_021072) is a computer-aided design software used for three-dimensional modelling. Based on morphological data, the software can be used to build the geometry accurately to represent the segment of corresponding blood vessels.

COMSOL Multiphysics 5.6 (Stockholm, Sweden, RRID: SCR_014767) is one of the powerful CFD tool. After setting the boundary conditions and inherent physical characteristics of the fluid, the software can simulate blood flow based on real-world processes. As a software for finite element analysis, COMSOL can discretizing the geometry with meshes and solve the Navier-Stokes equation at any element of the model. By using COMSOL, we can analyse haemodynamic environment and calculate some parameters of blood flow.

Anatomical data processing and 3D reconstruction of the cephalic arch

In addition to the data measured directly on the cadaver specimen, we also need data for 3D reconstruction, such as the direction and angle of blood vessel bending, which needs to be further processed on the photos. Anatomical data were processed by Photoshop. According to segment of cephalic vein setting previously, we plotted segmented straight lines on the photos along the blood vessels. Then the length on photos and angle data of the variant vein can be obtained in the shape property. In photos with 10.00 mm vernier calliper, we drew a straight line between the two feet of the vernier calliper and obtained the length measured in the photo. Then we can know how long the actual 10 mm in picture for reference. According to the scale plate, we can calculate the actual length of each segment in reality by the same scale. For each segment, we took at least two pictures in mutually perpendicular planes for the data measurement and processing, and take the average value of the length of the same segment.

After processing the anatomical parameter exactly, we used AutoCAD to perform the 1:1 scale 3D computational model of the variant jugulocephalic vein together with the draining external jugular vein to represent geometrical characters of the variant cephalic arch precisely [10]. According to the shape parameters of each segment, we constructed a spline as the backbone of variant vein on the top view, and each anchor points on the spline were based on the junction points of adjacent vessel segments and extreme point of blood vessel. After establishing the plane model of the backbone, we shift to the left view to adjust the longitudinal bending and curve of the spline. According to the data extracted from photos on the left side and top view, we constructed the geometric solid structure of the spline to obtain the three-dimensional model of the backbone of the variant vein.

In order to study the blood flow direction and reflux situation of the abnormal drainage system, in addition to the variant cephalic vein, we established a 3D computational model of the external jugular vein together with its tributaries. In order to control the boundary conditions at the end of the blood vessels, the transverse jugular vein, supraclavicular vein, and anterior jugular vein were extended in a straight line of 1 cm according to the relative position and direction between the real blood vessels.

Boundary and initial conditions

Blood flow parameters in the arteriovenous fistula was used as the boundary condition to simulate the haemodynamic environment in the computational fluid model of the variant vein. Thus the blood flow environment and various haemodynamic parameters can be simulated in the venous outflow tract during the initial construction of the arteriovenous fistula. Based on these results, our present study further investigated the possible consequences of the maturation process of the arteriovenous fistula with the variant vein as the outlet. In order to establish a comparison with the haemodynamics of the variant cephalic vein, the initial conditions used for modelling the normal cephalic vein were the same as those of the variant cephalic vein.

As boundary conditions, blood was assumed as non-Newtonian fluid with Carreau rheological model based on actual blood analysis data [8] and blood density was considered as 1.045 g/cm3. With no-slip boundary condition, blood vessel walls were considered to be rigid. The direction of gravity was set to be positive along the y-axis to simulate the haemodynamic characteristics of the variant cephalic arch in upright position. The inlet of our model is located at midpoint of arm on cephalic vein, with velocity of 0.9045 m/s. The main outlet of our model is the end of external jugular vein, and the total pressure was set as 2666 Pa. In the model of variant cephalic vein draining into the external jugular vein, the external jugular vein had 4 tributaries, so the entrances of these tributaries were set as additional outlets, with total pressure of 1599 Pa.

Computational fluid dynamics model

Based on the 3D geometrical model, we simulated blood flow field with CFD package inside COMSOL, the software for multiphysics simulation. After importing the 3D geometrical model into the system, our present study was defined as steady-state study of the laminar flow model. The idealized vascular model was processed with fillets and feature repair to make the geometric modelling closer to the true vascular shape, ensure that the blood flow model remains smooth, and reduce the non-convergent site. After forming a union of all geometric elements, define the boundary conditions of the fluid.

Then we built the grid onto the simulating fluent model using computational method to discretize the model into infinitesimal elements. The resulting grids of variant vessel model contained approximately 3.29 million tetrahedral elements.

After all of the simulating fluent model having been defined, we used CFD tool to solve the continuity Navier–Stokes equations numerically for single-phase blood flow. The influent field inside the variant jugulocephalic vein can be mathematically modelled to get a detailed description of haemodynamic environment. The free degree of our present computational model is 3296712. After calculation, the flow rate, shear rate, and other haemodynamic data at each position on the computational model can be accurately read by adjusting the data range of the plot.

RESULTS

Characteristics of jugulocephalic vein variation

The variant jugulocephalic vein lies in the lateral bicipital groove. Then it ascends anterior to deltoid muscle, rather than enters the interval between deltoid and pectoralis major. 13.74 mm from the beginning of the deltoid muscle pectoralis major groove, 26.80 mm from the deltoid muscle pectoralis major groove, and 12.68 mm from the end of the deltoid muscle pectoralis major groove. The variant cephalic vein runs anterior to the clavicle and then runs superomedially to enter the descending external jugular vein in a “T” shape (Fig. 1). After receiving the variant cephalic vein, the external jugular vein also receives the superficial jugular vein and two transverse jugular veins. Afterwards, the external jugular vein suddenly becomes larger. The external jugular vein also receives the anterior jugular vein just before draining into the subclavian vein, further increasing the diameter of the external jugular vein.

Figure 1. Comparison of cephalic vein draining into external jugular vein with “T-junction” shape variation and normal cephalic vein. A. Cephalic vein draining into external jugular vein with “T-junction” shape variation in a cadaver. B. Normal cephalic vein in a cadaver. C. Illustration for cephalic vein draining into external jugular vein with “T-junction” shape variation. D. Illustration for normal cephalic vein.

Parameters of right cephalic arch variation for 3D reconstruction

The length of the five segments of the variant cephalic vein from the midpoint of the right arm to the end of the cephalic vein where it drains into the right external jugular vein is 54.52 mm in a straight segment, 41.00 mm in a planar curved segment, 77.00 mm in a convex segment, 16.98 mm in the segment anterior to clavicle, and 11.34 mm in the segment superior to clavicle. The parameters used for 3D modelling of each segment of the vein are shown in Table 1. The parameters used for 3D modelling related to external jugular vein are shown in Table 2.

Parameters of normal right cephalic vein for 3D reconstruction

The normal cephalic vein from the midpoint of the right arm until the end of the cephalic vein injects into the right subclavian vein, the length of each segment is 92.56 mm in straight segment, 79.90 mm in oblique segment, and 52.66 mm in curved segment of the cephalic vein arch. The parameters used for 3D modelling of each segment of the normal cephalic vein are shown in Table 3.

Simulating flow in 3D computational model of variant cephalic arch

The special variant we found in cadaver can be encountered when creating arteriovenous fistula during haemodialysis in clinical practice. Therefore, we simulated the possible haemodynamic changes that may occur in vivo through modelling.

Alteration and distribution of wall shear stress

In the variant cephalic arch model, the wall shear rates of the straight segment (1.602 × 103/s–1.810 × 103/s) and planar curved segment (1.792 × 103/s–2.477 × 103/s) were lower than other segments, and the distribution of wall shear rates in these vascular segments appeared more even and steady (Fig. 2A). At the inner wall of the bend vessel, the shear rate was slightly higher, while the shear rate in straight vessel segment was lower. The contour line of shear rate roughly arranged as parallel circular form, indicating stable haemodynamic environment in these segments. From convex segment, the wall shear stress (1.775 × 103/s–4.686×103/s) began to rise gradually. To shows the distribution and alterations of wall shear rate in variant cephalic vein in multiple direction of view, an animation was provided as Supplement data 1.

Figure 2. The isopleth of wall shear rate in variant cephalic vein and normal cephalic vein. A. The distribution and alterations of isopleth of wall shear rate in the model of variant cephalic vein and external jugular vein. This model was showed in XY plane with contour lines defined at 100 lines. B. The distribution and alterations of isopleth of wall shear rate in the model of normal cephalic vein. This model was showed in XY plane with contour lines defined at 100 lines. C. Enlargement of the box in A, which shows the isopleth of “T-junction”. The contour lines range from 100 to 26000 with intervals as 200. D. The same parameters of C at lateral side. E. Median side of C with parameters of contour lines range from 0 to 450 with intervals as 10.

The isopleth of shear rate in vessel segments anterior and superior to clavicle significantly became denser and crowded, indicating the shear rate changed rapidly. The wall shear rate in segments anterior and superior to clavicle continued to increase, without any areas where the shear rate decreased. The contour lines of wall shear rate in segment anterior to clavicle were arranged in a circular shape, indicating that the haemodynamic characteristics were still relatively stable in this segment. As the position became closer to the confluence, the isopleth of shear rate became denser, which means the change of wall shear stress became faster. The wall shear rate at the end of the segment anterior to clavicle reached to 1.651 × 104/s. The shear rate in segment superior to clavicle increased sharply, and the contour spacing narrows. The maximum wall shear rate was 2.599 × 104/s, which appeared at the confluence in the inferior wall of the cephalic vein. It is worth noting that the contour around the confluence at the end of the segment superior to clavicle became disordered, and the shear rate ranged from 2.460 × 104/s to 2.599 × 104/s. In a distance of 11.34 mm, the wall shear rate of segment superior to clavicle increased for 9.48 × 103/s, indicating a rapid increase in this segment (Fig. 2C, D).

After the blood flow in variant cephalic vein drained into the external jugular vein, the local wall shear stress was disorder. The isopleth in the wall of external jugular vein at the level of the cephalic vein confluence formed a band-shaped area with low shear rate. The shear rate in this area changed rapidly, which appeared that the isoplethes were extremely dense, and the shear rate ranged from 45/s to 329.9/s. There were elliptical high shear rate regions above and below this low shear rate band. The shear rate at the periphery of the high shear rate zone above was 329.9/s, and the closer it was to the centre, the higher the shear stress, with a maximum of 445.8/s at the centre. The shear rate in the high shear rate zone inferior to the low shear rate band was lower than that in the upper zone, with a peripheral shear rate of 236.3/s and a maximum of 397.1/s at the centre. A circular high shear rate zone was formed around the entrance of the cephalic vein, with a circular low shear rate zone above and below each, with a minimum shear rate of 15.40/s. The shear rate contour lines in the vicinity arranged in a circular pattern around these areas (Fig. 2E). Generally, the wall shear rate environment of the external jugular vein near the entrance of the cephalic vein was complex, and the haemodynamics was unstable. After crossing this area, the wall shear rate of the external jugular vein gradually decrease and tend to stable.

On the contour map of shear rate, we marked the abnormal wall shear stress areas (below 0.076 Pa and above 40 Pa) [5]. The higher wall shear stress appeared at the end of the segment anterior to clavicle and segment superior to clavicle (Fig. 3A, C, D). The wall shear stress of the small tributaries of external jugular vein was not included in this study. There was no area with low wall shear stress on the cephalic vein to external jugular vein reflux pathway. The shear stress on the wall of the external jugular vein at the injection site of the cephalic vein changed rapidly, and the haemodynamic environment was complex, but it was still within the normal range of wall shear stress.

Figure 3. The comparison of abnormal wall shear stress region between variant cephalic vein and normal cephalic vein. A. The abnormal wall shear stress region in variant cephalic vein. In XY plane of this model, abnormally higher wall shear stress region range from 13333 to 26700 with intervals as 200. Abnormally lower wall shear stress region range from 0 to 25.33 with intervals as 1. B. The abnormal wall shear stress region in normal cephalic vein. Only abnormally higher wall shear stress region exists at the turn of the cephalic arch, which ranges from 13333 to 15700 with intervals as 200. C. Enlargement of the box in A, which shows the abnormally higher wall shear stress region in the terminal segment of the variant cephalic vein. The contour lines range from 13333 to 26700 with intervals as 200. D. The same parameters of C at lateral side. E. Enlargement of the box in B, which shows the abnormally higher wall shear stress region in the cephalic arch.

Velocity profile and streamline image

After the blood flow in variant cephalic vein drained into the external jugular vein, the diameter of the blood vessel suddenly becomes larger, and the high-speed blood flow in the outlet vein of arteriovenous fistula shunted upward and downward,

On the velocity profile and streamline image, it can be observed that the full length streamline of the cephalic vein was basically parallel to the tube wall, and flowed against the lower side of the tube wall under the action of gravity. The flow velocity in the straight, planar curved, and convex segments was lower, and gradually increased in the segment anterior to clavicle. The flow velocity reached to the highest in the segment superior to clavicle (Fig. 4A). From the serial sections along the yz plane of this segment, the highest velocity existed in the central part of the flow (Fig. 4E). The blood flow in the straight and curved segments was stable, and the flow velocity did not exceed 1.5 m/s. The flow velocity in the convex segment slightly increased, with a maximum flow velocity of 2.31 m/s at the end of this segment. The flow velocity in the segment anterior to clavicle sharply increased (increase of 2.16 m/s at a distance of 16.98 mm), with a maximum flow velocity of 4.47 m/s at the end of this segment. The flow velocity in the segment superior to clavicle continued to increase rapidly, reaching the highest velocity of 6.34 m/s at the centre of the injection site (Fig. 4D, E).

Figure 4. The comparison of streamline image between variant cephalic vein and normal cephalic vein. A. The streamline image in variant cephalic vein. In XY plane of this model, the colour shows the range of velocity from lower to higher. B. The streamline image in normal cephalic vein. C. Enlargement of the box in A, showing the transverse flow in the external jugular vein at “T-junction”. The velocity alterations in the external jugular vein at “T-junction” with serial sections at XY plane. D. The vortex in the external jugular vein at “T-junction” at lateral side. E. The velocity alterations in the segment superior to clavicle with serial sections at YZ plane.

After injection into the external jugular vein, the high-speed flow of arteriovenous fistula blood did not immediately flow axially along the wall of the external jugular vein. Instead, it still flowed in the same direction of the end of the cephalic vein with a speed of 4.81 m/s to the lumen centre of the external jugular vein sharply decreased to 0.64 m/s (Fig. 4C–E). Then, the flow began to upwards (0.25 m/s) and downwards (0.20 m/s) along with the external jugular vein axis. The upstream of this abnormal flow in this variant may cause obstruction of the external jugular vein reflux, which may cause congestion and oedema in the head and neck. Furthermore, local turbulence or even vortex was formed downward, which disturbed local venous blood flow and may cause local thrombosis and endothelial damage (Fig. 4D). Other abnormal flow may exist at the junction between superficial jugular vein and external jugular vein (Fig. 4C), which may cause congestion, oedema, and pain in the drainage area of the superficial jugular vein. The other tributaries of the external jugular vein, including the superior and inferior branches of the transverse jugular vein and the anterior jugular vein, did not have abnormal blood flow. It is suggested that the abnormal haemodynamic characteristics of arteriovenous fistulas caused by variant cephalic veins may cause local venous reflux disorders, but did not affect the veins in the entire blood reflux pathway. After receiving blood from the inferior branch of the transverse jugular vein, the blood flow velocity of the external jugular vein did not exceed 0.1 m/s, and the blood flow velocity returned to normal. The velocity alterations of variant cephalic vein in multiple direction of view were shown as an animation in Supplement data 2.

Range and distribution of vortex intensity

The vector reflecting eddy current intensity was represented by solid arrows which arranged with right-hand spiral direction around the wall of the blood vessel. The eddy current vector was perpendicular and right-hand spiral direction to the blood flow (Fig. 5D). The vortex intensity in the centre of the blood vessel was relatively small, while the vortex intensity near the wall of the blood vessel was relatively large. The eddy current intensity gradually increased from the straight segment and reached to the highest point at the end of the segment superior to clavicle (Fig. 5A). The eddy current value of the straight segment, planar curved segment, and convex segment did not exceed 5 × 103/s, indicating that the blood flow in these segments was stable and less eddy current formation. The eddy current intensity in the segment anterior to clavicle begins to rise, and the eddy current value did not exceed 1.5 × 104/s at the end of this segment. The eddy current intensity reached to the highest point as 1.59 × 105/s at the end of segment superior to clavicle (Fig. 5C, D). In the external jugular vein, the eddy current intensity sharply decreased near to the “T-junction” and tended to zero peripherally. The vortex intensity in variant cephalic vein in multiple direction of view was shown as an animation in Supplement Data 3.

Figure 5. The comparison of vortex intensity between variant cephalic vein and normal cephalic vein. A. The vortex intensity in variant cephalic vein. In XY plane of this model, the colour shows the range of intensity from lower to higher. The colour arrows show the vortex intensity and direction. B. The vortex intensity in normal cephalic vein. C. Enlargement of the box in A. D. The same parameters of C at lateral side. E. Enlargement of the box in B.

Comparison of this variation with normal cephalic arch

The shear rate of variant cephalic vein was higher than that in normal cephalic vein at corresponding part. The highest shear rate in the variant cephalic vein (2.599 × 104/s) was much higher than that in the normal cephalic vein (1.67 × 104/s), which existed at the narrowest part of the veins (Fig. 2A, B). In addition, the dense circular contour lines around variant cephalic vein showed that the wall shear rate in the variant cephalic vein changes much more rapidly than that in the normal cephalic vein. Only variant cephalic vein exhibited abnormal reflux, multi-direction blood flow, and vortex as shown in the streamline image (Fig. 4A, B) The shear rate in external jugular vein in this variant case was much more complex for its abnormal drainage.

Overall, from the 3D computational model of variant cephalic arch, we found that compared with the normal cephalic arch, the unsteady turbulent flow and multi-directional flow appeared in the variant cephalic arch, forming several large regions with pathological flow patterns and higher gradients of wall shear stress on the variant vein (Fig. 5A, B). Disturbed flow may induce pathological wall shear stress environment, which stimulated venous endothelial cells in variant cephalic arch and prone to induce intimal hyperplasia and vascular stenosis. Therefore, the variant cephalic vein arch is prone to stenosis during remodelling and maturation after brachiocephalic fistula.

DISCUSSION

Simulating the haemodynamic changes of variant cephalic vein is not only of great theoretical significance, but also of great clinical significance correlation with the management of brachiocephalic fistula. Here, we simulated the flow in 3D computational model of “T-junction” single-conduit supraclavicular cephalic arch draining into the external jugular vein variant after brachiocephalic fistula. The results of our present study showed that: (1) the variation of cephalic arch in the “T-junction” with external jugular vein largely altered the fluid dynamics, especially in patients with brachiocephalic fistula; (2) this single-conduit supraclavicular cephalic arch draining into the external jugular vein is prone to form stenosis after brachiocephalic fistula; (3) the mechanism of stenosis of the single-conduit supraclavicular cephalic arch variant after brachiocephalic fistula might be that more flow disturbances in variant vein have pro-inflammatory effect from the simulating flow in 3D computational model. This simulating flow in 3D computational model explained the mechanism of stenosis of the single-conduit supraclavicular cephalic arch variant after brachiocephalic fistula and paved the way for further investigating the different variants of cephalic arch and developing anatomical based therapeutic interventions after brachiocephalic fistula.

The factors causing damage to the variant cephalic vein and the potentially problematic areas in the vein were found through our analysis of the 3D computational model based on this “T-junction” single-conduit supraclavicular cephalic arch draining into the external jugular vein. Vortex formation is one of the harmful factors to the vein used for anastomosis. The cause of vortex formation is the local adverse pressure gradient of blood flow [3]. On the inner side of the tight bend of blood vessel, the sharp turn of the direction is prone to form local adverse pressure gradient of blood flow, which lead to local reverse flow [17]. Thus, vortices appeared in many separate areas in the bend of the vessel. In this variant case, the “T-junction” end of the cephalic vein draining into the external jugular vein is prone to form obvious vortices comparison with the normal cephalic vein draining into the axillary or subclavian vein. The course of the cephalic arch changed obviously in this variant, which passes anterior to the clavicle. The extrinsic compression by the underlying clavicle bone may contribute to the formation of vortex. The external jugular vein received several tributaries adjacent to the end of the cephalic vein. Hence, there is a possibility that the blood of the cephalic vein can flow into these tributaries upon the increased pressure after brachiocephalic fistula. All the above harmful factors complicated the haemodynamics in this specific variant cephalic arch after brachiocephalic fistula.

Upon the establishment of brachiocephalic fistula, the blood pressure in the vein suddenly increases, leading to an increased Reynolds number with its flow pattern converting from laminar to a disturbed one. The artificially established fistula alters the haemodynamics of the variant cephalic arch, exposing venous endothelial cells to a supra-physiological shear force [21], where the wall shear stress was below 0.076 Pa or above 40 Pa. To normalize wall shear stress and maintain vasculature homeostasis, the brachiocephalic fistula should undergo extensive vascular remodelling [6]. In this situation, the shear stress below normal level (< 0.076 Pa) laterally impacts the vascular wall, which activates endothelial cells and potentially trigger inflammatory response. These pathological responses of the variant vein can leads to reactive proliferation of vascular muscle and neointimal hyperplasia [7]. The shear stress exceeding normal range (> 40 Pa) causes endothelial denudation which result in the haemodynamic insult on the vascular wall. These two factors (abnormal lower or higher wall shear stress) are the main reason of non-uniform remodelling and non-maturation of arteriovenous fistula [18]. On the other hand, the low vortex area is easily to the deposition of lipids and blood cells, resulting in the formation of early thrombosis, which further aggravates the degree of haemodynamic abnormalities. Above factors may provide possible nidus that lead to stenosis and thrombosis. Analysing the key factors affecting stenosis, solving the complex pathogenesis, and searching the effective measures to eliminate the harmful factors on stenosis might be attractive research directions.

In view of the complexity of haemodynamics after this variant brachiocephalic fistula for this “T-junction” single-conduit supraclavicular cephalic arch draining into the external jugular vein, the surgeons should pay attention to the following important issues during the clinical practice: The harmful factors of this cephalic vein variant during and after brachiocephalic fistula should be preliminary evaluated. The relevant clinical parameters should be monitored whenever necessary after brachiocephalic fistula [16]. Once the pulsatile flow disappeared at the site of brachiocephalic fistula, the effective measures should be taken to avoid severe adverse effects [13]. Nowadays, colour Doppler is the main method for evaluation of brachiocephalic fistula maturation [22]. By using the computational modelling technique, we can predict the high-risk region after creation of brachiocephalic fistula and take measure to prevent maturation-failure in time [9, 15].

Because of complexity of haemodynamic environment in brachiocephalic fistula, computational modelling is widely used for haemodynamic study of brachiocephalic fistula [1]. In intravital cases, these haemodynamic studies often use ultrasound or CT for haemodynamic simulating. Compared with the two-dimensional modelling, the 3D model can comprehensively simulate the haemodynamic changes in the blood vessels with complex courses, complicated configuration, and irregular connections with other vessels. A larger amount of haemodynamic parameters can be investigated theoretically. These advantages will contribute to access the realistic situation before and after brachiocephalic fistula. Although the model established in this study cannot precisely simulate the complicated blood flow in this variant cephalic arch after brachiocephalic fistula, the new viewpoints raised in our present study paves the way for further detailed investigation in this specific field.

Limitations of the study

Instead of reconstruction of imaging data, the geometrical model in our present study is built by computer-aid design software which was based on data from specimens. So it may have some bias compared to the reconstruction of real imaging data. However for cadaver, it is difficult to obtain imaging data. Computational simulations of haemodynamic changes can be used as an explanation for this specific state of variation.

The selection of boundary conditions is based on a reasonable range of normal values. The real data of velocity, viscosity and pressure can be measured in vivo, which cannot be obtained on cadaver specimens.

CONCLUSIONS

The results from the simulating flow in 3D computational model support the view that the variation of cephalic arch in a “T-junction” with external jugular vein largely altered the fluid dynamics, especially in haemodialysis patients with brachiocephalic fistula. This computational model underpins the concept that a regular management of haemodynamic profiles in patients with jugulocephalic vein variant after brachiocephalic fistula may help stabilize or modulate fluid dynamics in this specific situation.

ARTICLE INFORMATION AND DECLARATIONS

Acknowledgments

The authors thank Dr. Shuang Han from the International Peace Maternity & Child Health Hospital of China Welfare Institute (IPMCH) for her illustrations.

Body donors used in this study are willed to the Body Donation Acceptance Centre at Shandong University. All donations to the Body Donation Acceptance Centre are registered under the statutes and guidelines of the Shandong Red Cross Society. All body donors are used for human anatomy teaching and research program.

Funding

This work was supported by the Science and Technology Innovation Foundation of Shandong University (No. 2023-328).

Conflict of interest

None declared.

Supplementary material

Supplementary material is available on Journal’s website.

Supplementary Video 1. The isopleth of wall shear rate in variant cephalic vein. This video shows the distribution and alterations of isopleth of wall shear rate in the model of variant cephalic vein and external jugular vein. The contour lines defined at 100 lines.

Supplementary Video 2. The streamline of variant cephalic vein. This video shows the velocity alterations in the model of variant cephalic vein and external jugular vein with serial sections at YZ plane.

Supplementary Video 3. The vortex intensity in variant cephalic vein. This video shows the range of intensity from lower to higher with colour. The colour arrows show the vortex intensity and direction.