Ethics statement

All animal procedures were approved by institutional guidelines and approved by the University of North Carolina at Chapel Hill’s Institutional Animal Care and Use Committee and performed in accordance with National Institute of Health guidelines. Proper care was taken to minimize animal suffering.

Animal model

This study used male C57BL/6J mice aged 14–16 weeks that were obtained from The Jackson laboratory. Imaging and ultrasound data were collected at days 7 and 21 post-surgery to characterize the early and late stages of AVF development.

Surgical procedure

AVF surgery was performed following established protocols [29,30]. The mouse was anesthetized using a combination of isoflurane inhalation (1–3%) with prior surgery analgesia (buprenorphine, 0.1 mg/kg).

A 1 cm longitudinal incision was made in the middle of the neck. Under a surgical microscope (12.5-25X magnification), the right external jugular vein and common carotid artery were carefully exposed through blunt dissection. The jugular vein was ligated distally and divided, while the carotid artery was temporarily clamped using micro-vascular clamps. An end-to-side anastomosis was created between the jugular vein and carotid artery: first, an arteriotomy (approximately 0.4-0.5 mm) was made in the carotid artery, then the jugular vein was anastomosed to the artery using interrupted 10–0 nylon sutures. Fig 1 illustrates the surgical creation of the AVF, showing the end-to-side anastomosis between the jugular vein and carotid artery.

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Fig 1. AVF creation using end-to-side anastomosis between jugular vein and carotid artery in the murine model.

The white arrow shows the direction of venous outflow.

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Imaging protocol

High-resolution micro-computed tomography (micro-CT) imaging was performed in vivo at days 7 and 21 post-surgery using a Quantum GX2 system (Revvity; Waltham, MA USA) with the following parameters: 90 kV of peak energy, 88 μA of current, 72 μm isotropic voxel size, and 2 min of acquisition time. For day 21 imaging, an additional scan with 14 min acquisition time was performed to achieve a high signal-to-noise ratio. Prior to imaging, either Fenestra-HDVC (day 7) or mvivoAU (day 21) (MediLumine Inc, Montreal, Quebec CA) was administered intravenously via a tail vein catheter (5 µl/g for both agents) to provide vascular contrast for vessel segmentation.

Blood flow velocity acquisition

Prior to micro-CT imaging, a high-frequency Doppler ultrasound system (Vevo F2, FUJIFILM VisualSonics) with a UHF57x linear array transducer with center frequency at 32 MHz was used to obtain blood flow velocity measurements on the same day. Mice were anesthetized using 1.5-2% isoflurane, and body temperature was maintained at 37°C during measurements.

Velocity measurements were obtained using pulsed-wave Doppler mode imaging at three locations: the proximal artery (1.5 mm upstream of anastomosis), distal artery (1.5 mm downstream of anastomosis), and venous segment of the AVF. The angle between the wave beam and flow direction was kept below 60° either by either animal positioning or by using additional 15° beam steering. At each location, pulsatile velocity waveforms were recorded over multiple cardiac cycles. Three consecutive cycles were extracted and averaged to generate representative velocity profiles for each location. Peak velocity in mm/s was determined for each location. The volumetric flow rate was calculated using , in which is the cross-sectional area obtained from the micro-CT data and is the mean velocity. The cross-sectional velocity was assumed to follow a parabolic profile. This assumption is justified by the low Womersley number (≈ 1) in this study, which indicates that viscous effects dominate over inertial effects, making the parabolic profile a reasonable approximation for pulsatile flow in small vessels [31]. Heart rate was monitored throughout the measurements and remained stable at approximately 450 beats per minute. The acquired velocity data served as boundary conditions for the subsequent CFD simulations.

Image processing and geometry reconstruction

Image processing and three-dimensional vessel reconstruction were performed using a multi-step approach. The micro-CT scans were first processed in ITK-SNAP (Version 4.2) [32,33] for initial segmentation (Fig 2A).

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Fig 2. Contrast-enhanced CT images and segmented vascular structure.

(a) CT images in three orientations, coronal, sagittal, and axial, near the AVF. A volume rendering of the CT images is shown in the upper right to visualize vasculature and bone structure. The AVF and surrounding veins and arteries are annotated in yellow. (b) and (c) Segmented vasculature near the AVF at day 7 and day 21 post-surgery, respectively. Color coding represents distinct vessel segments: red indicates the carotid artery (with the proximal segment at bottom and distal segment at top), yellow highlights the AVF region (4 mm of length), and blue shows the main venous drainage with its characteristic ballooning of the vein starting 4 mm from the anastomosis.

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The vascular lumen was segmented using a combination of threshold-based and region-growing techniques. Initial thresholding (300–1000 HU) isolated contrast-enhanced vessels and bones from the neck area, followed by seed-based region-growing to further segment connected voxels to form vessel lumens. Manual editing was performed where necessary, particularly at the anastomosis region to ensure accurate geometry capture.

The segmented vasculature was exported as STL files and further processed in Autodesk Meshmixer [34] to remove artifacts and smooth surface irregularities. The inlet and outlet regions of the artery were extended by 2 mm to ensure fully developed flow, and geometric landmarks were defined for consistent analysis.

Centerline analyses were performed using the VMTK module (Vascular Modeling Toolkit [35]) in 3D Slicer [36] to extract vessel centerlines and calculate cross-sectional areas and diameters. These measurements provided geometric metrics for quantitative comparison between timepoints. The final reconstructed geometry consisted of the proximal artery (inflow), distal artery (outflow), and the arteriovenous fistula, which was defined as the 4 mm length of vessel extending from the anastomosis, as shown in Fig 2B and 2C.

Computational fluid dynamics

All simulations used OpenFOAM v2306 [37], an open-source finite volume based computational fluid dynamics software package. OpenFOAM provides numerical solvers, utilities, and tools for solving continuum mechanics problems involving fluid flow, chemical reactions, and heat transfer, among others [38]. Simulations were performed on a single node of a high-performance computing cluster with 64 cores (AMD EPYC 7313 @ 3.6 GHz) and 300 GB allocated memory. The computational cost scaled approximately linearly with the number of mesh elements and timesteps, with the medium mesh (~1.3 million elements) simulations requiring 60–72 hours of wall clock time to complete three cardiac cycles.

Governing equations

The blood flow within the arteriovenous fistula is modeled using the incompressible Navier-Stokes equations:

(Eq 1)

(Eq 2)

in which is the density of blood (1,040 kg/m³), is the dynamic viscosity of blood (), is the velocity vector of the blood flow, is pressure, and is time.

In this study, blood was modeled as a Newtonian fluid, which is an appropriate assumption because the vessel diameters (0.3-1.0 mm) exceed the threshold (0.2-0.3 mm) where non-Newtonian effects become significant [39,40]. Additionally, the wall shear rates in our regions of interest (anastomosis and stenosis) predominantly exceed 200 s ⁻ ¹, which is a shear rate at which blood is known to exhibit nearly Newtonian behavior [40]. This assumption aligns with our comparative analysis approach, focusing on relative hemodynamic patterns between timepoints rather than absolute values. The non-Newtonian behavior of blood (primarily due to red blood cell aggregation and deformation) becomes most significant in smaller vessels [41], particularly when vessel diameter approaches the scale of blood cells [42].

We employed a rigid wall assumption throughout this study, which is reasonable given that arteriovenous fistula wall displacement during the cardiac cycle is typically small compared to vessel diameter, particularly in mature fistulas with thickened walls [43].

Mesh generation and grid independence

The computational domain encompasses the proximal artery, distal artery, fistula (4 mm length from anastomosis) (Fig 3A), and vein. The domain was discretized using tetrahedral meshes with five prismatic boundary layers (first layer thickness 1–3 µm, growth ratio 1.2) near the walls to ensure accurate flow gradient calculations.

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Fig 3. Computational model setup and flow rate boundary conditions for murine AVF analysis.

(a) Computational domain, boundary conditions, and mesh configuration. The three-dimensional computational domain represents the murine carotid artery-jugular vein arteriovenous fistula model (day 7 geometry shown). Boundary conditions include: velocity-based inlet conditions at both proximal and distal carotid artery ends derived from ultrasound Doppler measurements, no-slip conditions at all vessel walls, and zero-pressure outlet conditions at the venous exit. The computational mesh consists of tetrahedral elements with five prismatic boundary layers near vessel walls (upper inset) to capture near-wall flow gradients. The lower inset shows detailed mesh refinement at the arteriovenous junction. (b) Flow rate waveforms for boundary condition implementation. Pulsatile flow rate waveforms for the proximal artery (PA) and distal artery (DA) derived from ultrasound Doppler velocity measurements at day 7 and day 21 post-fistula creation. These waveforms serve as time-varying inlet boundary conditions for the computational fluid dynamics simulations, capturing the physiological flow patterns and their temporal evolution during fistula maturation.

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Grid independence was established using three mesh resolutions for the day-7 model: coarse (0.62M elements, average spacing ~4 μm near walls, ~ 50 μm in bulk); medium (1.34M elements, average spacing ~2 μm near walls, ~ 30 μm in bulk); and fine (2.52M elements, average spacing ~1.5 μm near walls, ~ 20 μm in bulk). Convergence was assessed by comparing velocity magnitude and pressure distributions at multiple cross-sectional planes throughout the domain, including the inlet sections, the anastomosis, stenotic region, and downstream sections. Point-wise differences were calculated using the maximum norm between consecutive mesh refinements [44] at identical spatial locations during peak systole. The maximum point-wise differences between medium and fine meshes were below 1% for both velocity and pressure fields across all evaluation planes and timepoints, confirming grid convergence. Fig 4 illustrates the pressure comparison at the proximal inlet across three sets of mesh; other flow quantities demonstrated similar convergence behavior. Following this analysis, the medium mesh resolution was adopted for all analyses, corresponding to 1.34M and 1.97M elements for day-7 and day-21 models, respectively, with average grid spacing of approximately 2 μm near the wall and 30 μm away from the wall.

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Fig 4. Grid convergence and temporal convergence analysis.

Pressure time history at the proximal inlet demonstrates: (i) grid independence between medium and fine meshes, with differences less than 1% throughout the cardiac cycle and (ii) periodic steady-state was achieved after two cycles, with the first cycle influenced by initial conditions. Data from the third cycle, computed with medium mesh resolution, was used for all subsequent analyses.

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Boundary conditions and numerical methods

Velocity boundary conditions derived from ultrasound Doppler measurements were applied at artery inlets (Fig 3B), and zero-pressure conditions imposed at the venous outlet. No-slip conditions were enforced at vessel walls. Parabolic profiles were used in the numerical model, consistent with the experimental data analysis described in Blood flow velocity acquisition. Additionally, our model implemented extended inlet sections exceeding 4 diameters in length, allowing the flow to fully develop before reaching the region of interest. Previous work [45] has shown that different inlet velocity profiles (including plus flow, parabolic flow, and Womersley profiles) converge within 1–2 diameters downstream in CFD models, and our analysis primarily focuses on the AVF region and anastomosis, which are positioned at least 10–15 diameters downstream from the prescribed inflow and outflow velocity profiles. This approach balances computational efficiency with accuracy in the regions of interest, which is particularly important for our comparative temporal analysis.

Although impedance-based outflow conditions such as the Windkessel model can provide more physiologically realistic representations of downstream vascular networks, we applied a zero-pressure (free outflow) condition at the venous outlet. This choice is consistent with the rigid wall assumption employed throughout this study. Under the rigid wall modeling framework with prescribed inflow velocities, whether a simple boundary condition (zero pressure) or a complex one (Windkessel model) was implemented, the choice only affected the absolute pressure values within the domain. All pressures reported herein are relative to the outlet pressure. The zero-pressure boundary condition is therefore preferable as it introduces no additional fittable parameters to the modeling pipeline while maintaining consistency with our rigid wall assumptions and comparative analysis approach focusing on relative hemodynamic patterns between timepoints.

The time discretization employed the backward Euler scheme for temporal derivatives, and the nonlinear convective terms were handled through iterative coupling within each time step. The time step size was adjustable during the simulations to ensure the advective CFL number was not greater than 0.1. The spatial discretization used second-order upwind schemes for the convective terms and Gauss linear gradient calculations for the diffusive terms. The iterative PIMPLE algorithm (a combination of PISO and SIMPLE) handles pressure-velocity coupling, with convergence achieved once the absolute residual for all governing equations (continuity and momentum) drops below 10^-6. Simulations ran for three cardiac cycles, and periodic steady-state was achieved after two cycles, with the first cycle influenced by initial conditions; therefore, only the final cycle was used for analysis.

Data analysis methods

Hemodynamic parameters.

Several hemodynamic parameters were calculated to characterize the flow field and its potential influence on vascular remodeling. The wall shear stress (WSS), representing the tangential force exerted by blood flow on the vessel wall, was computed as

(Eq 3)

in which is the velocity component parallel to the vessel wall and is the unit vector normal to the wall.

The time-averaged wall shear stress (TAWSS) is calculated over one cardiac cycle (T) as

(Eq 4)

TAWSS provides a measure of the chronic mechanical load experienced by endothelial cells [7]. In AVF development, regions of consistently high TAWSS often trigger outward vascular remodeling as an adaptive response, whereas regions of low TAWSS may be prone to intimal hyperplasia development [21].

The oscillatory shear index (OSI) quantifies the directional changes in wall shear stress over the cardiac cycle and is computed as

(Eq 5)

OSI ranges from 0 to 0.5, in which 0 indicates unidirectional flow and 0.5 represents complete flow reversal. In AVF, high OSI regions often correlate with disturbed flow patterns and are frequently associated with stenosis development [46]. This is particularly significant at the anastomosis and in post-stenotic regions where complex flow patterns emerge [23].

The vortex structure is commonly discerned using the Q-criterion, computed as the second invariant of the velocity gradient tensor:

(Eq 6)

in which Ω and S are the antisymmetric and symmetric components of the velocity gradient tensor, respectively. Positive values of the Q-criterion indicate regions where rotation dominates strain, identifying coherent vortical structures [22].

Data analysis

Cross-sectional averages and maxima of hemodynamic parameters were computed at key locations along the vessel centerline. Temporal comparisons between day 7 and day 21 were performed for both geometric and hemodynamic parameters. Correlations between early hemodynamic conditions and subsequent geometric changes were analyzed to identify potential predictive relationships.

Clinical analysis

Temporal changes in vessel geometry.

Table 1 summarizes the lumen diameters of the carotid artery, fistula, and vein. For each segment, the values in parentheses indicate the minimum and maximum diameters. Additionally, detailed statistical analyses of the AVF region are provided for two specific segments: the initial 2 mm segment adjacent to the anastomosis and the extended 4 mm segment, to characterize the spatial variation in remodeling patterns.

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Table 1. Diameters of the AVF models for day 7 and day 21 (unit: mm).

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Temporal analysis revealed distinct changes in vessel geometry between day 7 and day 21. The proximal carotid artery showed a uniform expansion, with the average diameter increasing from 0.29 mm to 0.38 mm. In contrast, the fistula demonstrated more complex remodeling patterns that varied by region. Analysis of different fistula segments revealed varying degrees of remodeling: although the average diameter over the initial 4 mm segment remained relatively stable (slight decrease from 0.88 mm to 0.86 mm), a more focused analysis of the initial 2 mm segment showed notable narrowing, with the average diameter decreasing by 21.6% from 0.74 mm to 0.58 mm. The most severe narrowing was observed at the point of minimum diameter, which decreased substantially from 0.46 mm to 0.31 mm (32.6%). The vein exhibited the most dramatic change in the opposite direction, with its maximum diameter expanding from 1.07 mm to 1.71 mm (59.8%).

Fig 5 compares the longitudinal profiles of lumen diameter on day 7 and day 21. Both timepoints show a characteristic narrowing downstream of the anastomosis, but with distinct patterns. On day 7, the narrow region was localized and positioned close to the anastomosis. By day 21, the vessel geometry had remodeled such that the immediate anastomosis region showed expansion, while the stenotic segment had both elongated and shifted further downstream. This temporal evolution of the stenosis pattern suggests dynamic vascular remodeling during the maturation process, which has been also observed in human AVFs [47].

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Fig 5. Lumen diameter profiles along the vascular segments at day 7 (D7) and day 21 (D21).

The x-axis represents the distance from the anastomosis, with negative values indicating upstream segments (proximal artery [PA] and distal artery [DA]) and positive values indicating downstream segments (arteriovenous fistula [AVF]). The average AVF diameter is measured within the first 2 mm of the fistula. Cross-sections F1-F4, spaced 0.5 mm apart, indicate locations analyzed for hemodynamics in results.

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Flow rates

Flow analysis revealed a substantial temporal increase in total flow, with the AVF flow rate nearly doubling from 1.33 mL/min at day 7 to 2.57 mL/min at day 21, indicating fistula maturation. The flow distribution pattern demonstrated that the AVF served as the primary conduit at both timepoints, with 80% of proximal artery flow directed through the AVF at day 7, decreasing slightly to 70% by day 21, suggesting stenosis development within the AVF. Consequently, the proportion of blood flow through the distal artery increased from 20% to 30% between day 7 and day 21. Note that the blood in the distal artery flowed away from, rather than toward, the AVF junction. The proximal artery flow rate doubled over this period, while the heart rate remained at approximately 450 beats per minute throughout the study period.

The typical carotid artery flow rate in normal mice ranges from 0.3 to 2.1 mL/min [48]. A 10–20-fold increase in blood flow rate is considered necessary for sufficient AVF maturation in humans [49]. Therefore, the flow rate increase observed in this study suggests that the AVF may not have achieved full maturation, possibly due to the development of stenosis.

Hemodynamics analysis

Flow field characteristics.

Flow field analysis revealed distinctive patterns at both timepoints that are characterized by complex three-dimensional structures. Fig 6 uses streamlines to illustrate flow patterns and velocity distributions at peak systole. Flow separation occurred at regions of high curvature and abrupt lumen changes, resulting in asymmetric velocity profiles at these locations.

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Fig 6. Flow patterns within the AVF at peak systole for day 7 (a) and day 21 (b) models.

Streamlines colored by velocity magnitude show the three-dimensional flow trajectories. Cross-sectional velocity distributions at representative locations demonstrate the spatial evolution of the flow field. The color scale represents velocity magnitude in mm/s. Cross-sectional dimensions are not to scale.

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Comparing velocity fields between the two timepoints and across different anatomical locations revealed distinct velocity patterns. At the anastomosis, the flow velocity was higher on day 7 (maximum velocity 408 mm/s) compared to day 21 (maximum velocity 243 mm/s), with pronounced asymmetry between the upper and lower regions. In contrast, at the stenotic region, day 21 exhibited substantially higher velocities (maximum 603 mm/s) compared to day 7 (maximum 228 mm/s), consistent with the increased flow constriction.

The flow symmetry showed different recovery patterns between the two timepoints. On day 7, the flow velocity profile became symmetric beyond the 2 mm fistula region. However, on day 21, flow asymmetry persisted beyond this region, as evidenced by both streamline patterns and cross-sectional velocity distributions. Further downstream, in the main vein, the flow exhibited axisymmetric patterns in cross-sectional views, with peak velocities concentrated along the vessel centerline, consistent with developed flow characteristics in straight vessel segments.

Fig 7 presents the centerline analysis of velocity and pressure, demonstrating characteristic flow features: velocity sharply increased before the stenosis, followed by deceleration, with peak velocities occurring within 1 mm downstream of the anastomosis. Consistent with the Bernoulli principle, an abrupt pressure drop was observed immediately preceding the stenotic region. Notably, pressure drop characteristics differed between timepoints: at day 21, 99% of the total pressure drop occurred within 1.5 mm downstream of the anastomosis, compared to only 50% at day 7 over the same distance.

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Fig 7. Cross-sectional average velocity and pressure along the vessel centerline at peak systole for day 7 and day 21 models.

The plots show velocity (red) and pressure (blue) distributions relative to distance from the anastomosis. Both models exhibit characteristic features: a sharp velocity increase preceding the stenosis followed by deceleration, with large velocities occurring 1 mm downstream of the anastomosis. A corresponding abrupt pressure drop is observed immediately before the stenotic region. The pressure drop completes (99%) within 1.5 mm downstream of the anastomosis on day 21, whereas it only occurs 50% over the same distance on day 7.

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According to Poiseuille’s Law, the calculated flow resistance in the AVF segment (4mm length) on day 21 was approximately 9 times greater than that on day 7. This substantial increase in flow resistance indicates substantially higher friction forces, indicative of the more severe stenosis developed by day 21.

Wall shear stress analysis

Fig 8 illustrates the temporal and spatial evolution of TAWSS along the AVF centerline. On day 7, TAWSS distribution shows distinct spatial patterns, reaching its peak within 0.5 mm downstream from the anastomosis, with the 4 mm fistula region showing an average value of 3 Pa. This localized peak suggests early flow adaptation near the surgical connection.

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Fig 8. Cross-sectional maximum and average distributions of TAWSS along the centerline for day 7 and day 21.

The two horizontal lines represent the average values across the first 4 mm AVF. For day 7, peak TAWSS is localized within 0.5 mm downstream from the anastomosis, with an average value of 3 Pa across the 4 mm fistula region. By day 21, peak TAWSS shifts to 1.2 mm downstream from the anastomosis, with the average value increasing sixfold to 18 Pa across the 4 mm fistula region.

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By day 21, TAWSS showed significant changes in both magnitude and distribution. The peak TAWSS location shifted further downstream to 1.2 mm from the anastomosis, and its average value increased substantially to 18 Pa—a sixfold increase from day 7. This shift in peak location and magnitude suggests progressive vascular remodeling and potential stenosis development.

The three-dimensional TAWSS distribution (Fig 9) revealed further spatial variations. On day 7, peak TAWSS values were observed on the artery wall, with the maximum occurring at the inner side of the anastomosis on the proximal artery wall (Point A, 142 Pa) and a secondary peak at the stenosis (panel (a) Point B, 37 Pa). The proximal and distal arteries showed average TAWSS values of approximately 50 Pa and 4 Pa, respectively. By day 21, the TAWSS distribution pattern shifted substantially due to severe stenosis development in the fistula. The maximum TAWSS relocated to the AVF wall (panel (b) Point B, 200 Pa), with a secondary peak at the first stenosis (Point A, 134 Pa). The proximal and distal artery TAWSS values increased moderately to 60 Pa and 5 Pa, respectively.

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Fig 9. Time-averaged wall shear stress (TAWSS) distributions of (a) day 7 and (b) day 21 models.

Each panel shows three-dimensional TAWSS colormaps along the vessel surfaces and representative cross-sectional (F1 to F4) distributions showing circumferential variation of TAWSS at key locations (anastomosis, stenosis, and AVF). TAWSS exhibits pronounced spatial heterogeneity, with peak values localized at the stenotic region. A significant temporal increase in TAWSS magnitude is observed from day 7 to day 21, particularly in regions of geometric constriction. The color scale represents TAWSS in Pa. Points A and B (indicated by arrows) show locations of maximum TAWSS values: 142 Pa and 37 Pa on day 7, and 134 Pa and 200 Pa on day 21, respectively. Cross-sectional dimensions are not to scale.

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Oscillatory shear index analysis

The centerline analysis of OSI (Fig 10) reveals distinct temporal evolution patterns. On day 7, the maximum OSI occurred within 1.0 mm downstream from the anastomosis, with a relatively low average value of 0.0025 across the 4 mm fistula region, indicating minimal flow oscillation at the early stage.

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Fig 10. Cross-sectional maximum and average distributions of OSI along the centerline for (a) day 7 and (b) day 21.

The two horizontal lines represent the average values across the first 4mm AVF. For day 7, peak OSI occurs within 1.0 mm downstream from the anastomosis, with an average value of 0.0025 across the 4 mm fistula region. By day 21, peak OSI extends from 1.0 to 2.5 mm downstream from the anastomosis, with the average value increasing substantially to 0.016 across the 4 mm fistula region.

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By day 21, the OSI distribution showed extensive changes, with elevated values spanning a broader region from 1.0 to 2.5 mm downstream from the anastomosis. The average OSI increases more than six-fold to 0.018 across the 4 mm fistula region, indicating the development of more complex, disturbed flow patterns.

The three-dimensional OSI distribution (Fig 11) showed that OSI remained consistently low along the artery wall except near the anastomosis region. High OSI regions were primarily concentrated in two areas: at the anastomosis and downstream of stenotic segments, showing an inverse spatial relationship with TAWSS. The circumferential OSI distribution showed marked heterogeneity, particularly in regions of flow separation, indicating asymmetric flow behavior. Temporal analysis revealed a substantial increase in OSI magnitude from day 7 to day 21, most notably at the outside of the anastomosis (Point A, increasing from 0.22 to 0.48) and at Point B (increasing from 0.17 to 0.26).

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Fig 11. Oscillatory Shear Index (OSI) distributions of (a) day 7 and (b) day 21 models.

Each panel shows three-dimensional OSI colormaps along the vessel surfaces and representative cross-sectional distributions showing circumferential variation of OSI at key locations (anastomosis, stenosis, and AVF). High OSI regions are predominantly localized at the anastomosis and downstream of the stenosis. OSI demonstrates circumferential heterogeneity, with elevated values corresponding to regions of flow separation. An obvious temporal increase in OSI magnitude is observed from day 7 to day 21. The color scale represents dimensionless OSI values from 0 to 0.1. Points A and B (indicated by arrows) show locations of maximum OSI values: 0.22 and 0.17 on day 7, increasing to 0.48 and 0.26 on day 21, respectively. Cross-sectional dimensions are not to scale.

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Vortical structure

The development and evolution of vortical structures were analyzed using the Q-criterion (Fig 12). At both timepoints, vortical structures concentrated predominantly near vessel walls, especially in regions of geometric transition, such as the anastomosis and stenotic segments. These wall-adjacent vortices developed primarily because of flow separation and adverse pressure gradients associated with the complex geometry. Notably, a distinct vortex core formed within the AVF vein lumen, indicating substantial secondary flow patterns.

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Fig 12. Vortical structures visualized using the Q-criterion for (a) day 7 and (b) day 21 models.

Whereas vortical structures predominantly develop near vessel walls, a distinct vortex core (marked by circle) forms within the AVF vein lumen. Temporal comparison reveals increased vortical intensity on day 21 compared to day 7, particularly pronounced in stenotic regions. Although relatively small in magnitude, vortical structures are also observed to develop within the main vein. The color scale represents Q-criterion magnitude (), with positive values indicating regions where rotation dominates strain.

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The intensity and spatial distribution of vortical structures showed marked changes by day 21. The most noteworthy intensification occurred in stenotic regions, where the combination of flow acceleration and deceleration generated stronger rotational flow patterns. This enhanced vortical activity suggests increased flow complexity and higher energy dissipation in these regions. Although vortical structures were also present in the main vein, their magnitude remained modest compared to those in stenotic regions and near-wall areas.

Correlation analysis

The relationship between vessel geometry and hemodynamic parameters was analyzed through same-day correlations. Same-day correlations (Fig 13) showed a strong inverse relationship between TAWSS and vessel diameter, following fluid dynamic principles whereby smaller diameters exhibited higher wall shear stress under constant flow.

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Fig 13. Same-day correlations between TAWSS and AVF lumen diameter.

A strong nonlinear inverse relationship with diameter on both days was observed.

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An inverse relationship between TAWSS and OSI was observed (not shown), consistent with previous findings in various vascular studies [46,50], supporting the validity of our model.

Although the limited sample size prevented comprehensive statistical analysis of correlations between hemodynamic parameters and geometric changes, this study demonstrates the technical feasibility of identifying early hemodynamic conditions that predict subsequent remodeling and stenosis development.

The methodology established here can be applied to larger cohorts to identify associations between early hemodynamic parameters (TAWSS and OSI) and subsequent diameter changes in specific regions. This approach enables analysis of maximum and minimum stenosis at later stages (day 21) in relation to the TAWSS and OSI values at the same locations on day 7, potentially providing predictive markers for AVF maturation outcomes.

Limitations and future directions

Several limitations of the present study should be acknowledged. First, our CFD model employed a simplified approach that assumed rigid vessel walls. Although this assumption enables efficient computational analyses, it does not fully capture vessel wall dynamics, including pulsatile deformations and wall vibrations that occur in vivo. Second, although our study demonstrates the feasibility of using CFD models to analyze hemodynamic correlations in AVF development, the small sample size limits the statistical power of our findings.

Future studies should address these limitations through two key improvements. Fluid-structure interaction (FSI) simulations will better capture the dynamic interaction between blood flow and vessel wall mechanics. Future studies incorporating FSI would necessitate determining wall material properties, parameterizing more realistic outflow boundary conditions, and significantly increasing computational resources for the simulations. While such FSI modeling would provide enhanced physiological realism, the additional complexity requires careful parameter determination for both wall mechanics and outflow impedance models. Additionally, an increased sample size will enable statistical validation of the observed correlations and potentially reveal new relationships between hemodynamic parameters and vascular remodeling, particularly in using early AVF CFD parameters to predict the progression of stenosis development and AVF maturation.