Fluid Dynamics Simulation Analysis for Identifying Optimal Anastomosis Sites in Superficial Temporal Artery to Middle Cerebral Artery Bypass Surgery in Cerebrovascular Occlusive Disease

Abstract

This study investigated the hemodynamic effects of anastomosis site selection in superficial temporal artery to middle cerebral artery bypass surgery using computational fluid dynamics based on three-dimensional cerebral vascular models. By noninvasively reproducing blood flow changes that are difficult to evaluate in clinical settings, we visualized and quantified the effects of different bypass locations under both normal and stenotic conditions. To our knowledge, this is the first study to noninvasively evaluate the validity of anastomosis site selection in superficial temporal artery to middle cerebral artery bypass surgery using computational fluid dynamics simulation. The results demonstrated that factors, such as the distance from the anastomosis site to the target territory, flow direction, recipient vessel diameter, and pressure gradient, significantly influenced cerebral perfusion. In particular, bypass configurations that ensured antegrade flow, minimized the distance to the target region, and involved a larger recipient vessel diameter showed greater improvement in blood flow. These findings offer practical guidance for preoperative planning and are expected to contribute to the safer and more effective selection of bypass sites.

Introduction

Superficial temporal artery to middle cerebral artery (STA-MCA) bypass surgery is a well-established neurosurgical procedure commonly performed to improve cerebral blood flow in patients with cerebrovascular occlusive disease. In this technique, the extracranial STA is anastomosed to a distal branch of the MCA, typically at the M3-M4 segment.¹⁾ However, the optimal anastomosis site within this segment remains unclear and has not been sufficiently investigated.

Computational fluid dynamics (CFD) has recently been used to visualize and analyze hemodynamic changes following cerebral bypass surgery.²⁾ In this study, CFD simulations based on three-dimensional (3D) models of the MCA were performed to evaluate the distribution of additional blood flow from the STA. The aim was to identify the optimal anastomosis site that maximizes the effectiveness of STA-MCA bypass surgery. Detailed analysis of blood flow changes may provide valuable insights for preoperative planning and improving cerebral perfusion.

Two types of 3D cerebrovascular models―normal and stenotic―were constructed for this analysis. In addition, the clinical relevance of the acetazolamide challenge test, which is commonly used in the evaluation of chronic cerebral ischemia, was considered.³⁾ According to the Japanese Extracranial-Intracranial (EC-IC) Bypass Trial, indications for bypass surgery include cerebral blood flow below 80% on single-photon emission computed tomography (SPECT) and vascular reactivity exceeding 10% in response to acetazolamide. A postoperative improvement in cerebral blood flow of more than 80% is regarded as an indicator of successful revascularization.⁴⁾

This study also incorporated four key parameters known to influence post-bypass hemodynamics: pressure gradient,^5,6) flow reversal,^6-9) vessel diameter,⁹⁾ and the distance between the anastomosis site and the perfusion target territory. These factors were quantitatively assessed to determine their respective impacts on bypass effectiveness.

Methods

In this simulation study, the bypass point that most effectively improved cerebral blood flow was determined. Cerebral blood flow was calculated using a customized numerical simulation platform based on KIVA-4, a framework originally developed for compressible flow analysis in internal combustion engines.¹⁰⁾ In this study, the solver was adapted to model incompressible, Newtonian blood flow within cerebral arteries by implementing vessel-specific boundary conditions and solving the governing equations under both normal and stenotic conditions. Simulations were executed with approximately 1,600 to 2,200 iterations, and computation was terminated upon achieving numerical convergence. The mean values of the stabilized flow parameters were extracted and reported as final simulation results.

Cerebrovascular reserve was not modeled and therefore was not considered in the analysis. Boundary conditions were set to minimize significant velocity differences among the four outlets. In this study, pressure-pressure boundary conditions were adopted because the customized KIVA-based solver was originally designed for pressure-driven problems, and patient-specific inlet velocity data were not available.

Bypass simulation

In the stenotic model, the STA was connected to four different locations along the M3-M4 segment of the MCA (designated as Bypass Points 1-4) (Figure 1). For each scenario, blood flow distribution was evaluated at four outlet points (labeled A, B, C, and D) within the MCA.

Figure 1.

Hemodynamic simulation of four bypass configurations (Bypass 1-4). Red streamlines indicate the direction and velocity of blood flow from the superficial temporal artery (STA). Bypass 1 connects to the most distal cortical branch (M4), whereas Bypass 4 corresponds to a proximal M3 branch exposed by sylvian fissure dissection. Bypasses 1-2 represent typical M4 cortical branches frequently used in STA-MCA bypass, and Bypass 3 corresponds to a branch arising immediately distal to the M3 segment.

MCA: middle cerebral artery

Flow measurement and analysis

Using CFD, blood flow dynamics in each scenario were simulated, and the flow rates (g/sec) at each outlet were measured.

3D cerebrovascular model construction

The simulation results calculated using the custom KIVA-based solver were subsequently imported into ANSYS Ensight (ANSYS Inc, Canonsburg, PA, USA)¹¹⁾ to generate 3D cerebral blood flow visualization models, including both static images and dynamic videos. This integration enabled high-resolution representation of flow fields under normal and stenotic conditions, facilitating qualitative interpretation of hemodynamic patterns (Figure 2C and D).

Figure 2.

Three-dimensional CFD models of cerebral arteries with and without stenosis. A, B: Geometries of the normal and stenotic models. The stenotic model includes a 1-mm concentric narrowing at the M2 segment. Segment diameters and lengths are labeled.

C, D: Simulated blood flow streamlines and corresponding outlet pressures. Flow directions are color-coded: orange (A), green (B), light blue (C), and blue (D). In the normal model, pressures at outlets C and D are 91.5 mmHg; in the stenotic model, pressure at outlet C decreases to 86.3 mmHg.

E: Inlet pressure waveform representing the STA. A triangular waveform ranging from 80 to 120 mmHg is used, with a mean pressure of 95 mmHg.

CFD: computational fluid dynamics; STA: superficial temporal artery

3D model types (Figure 2A and B)

Normal Cerebrovascular Model: Designed to simulate normal blood flow conditions and serve as a baseline for hemodynamic analysis.

Stenotic Cerebrovascular Model: Created by introducing a concentric stenosis in the M2 segment of the normal model to replicate hemodynamic disturbances caused by cerebrovascular stenosis.

Mesh characteristics

The computational mesh was generated externally using a hexahedral grid. The total cell number ranged from approximately 0.5 to 1.0 million, depending on model geometry and local refinements. A formal mesh-independence test was not performed; however, mesh resolution was determined according to the wall-law requirement of the Reynolds-averaged Navier-Stokes (RANS) turbulence model, keeping the non-dimensional wall distance (y⁺) within the range of 30-100 to minimize mesh dependency.¹²⁾ In regions with steep velocity gradients, such as the stenotic segment, the mesh was locally refined to an element size of approximately 1/10-1/20 of the vessel diameter.

Structure of the MCA

• M1 segment: 4 mm diameter, 2 cm length

• M2 segment: 3 mm diameter, 3 cm length (a concentric stenosis with a diameter of 1 mm was introduced in the stenotic model)

• M3 segment: 2 mm diameter, 1 cm length

• M4 segment: 1 mm diameter, 2 cm length

Inlet and outlet configuration

• Inlet: Blood flow was introduced through the M1 segment.

• Outlets: Four outlets were established: two at the M4 segment (designated as A and B), one at the M3 segment (C), and one at the M2 segment (D).

Basis and methodology of parameter settings

Regarding the outlet settings, multiple trial calculations were performed to explore conditions under which convergence was achieved, and no flow reversal was observed. In the normal model, when the M1 inlet pressure was set to 95 mmHg, the outlet pressures were set to 85 mmHg for points A and B, and 91.5 mmHg for points C and D. In the stenotic model, applying the same settings caused flow disruption; therefore, the outlet pressures were gradually adjusted, and the final values were set to 85 mmHg for points A and B, 86.3 mmHg for point C, and 90 mmHg for point D. These values were adopted as the final conditions, as trial calculations confirmed that flow velocities at each outlet remained stable and balanced.

For the physical properties of blood, a density of 1.05 × 10³ kg/m³ and a viscosity of 4 × 10^-3 Pa·s were adopted, based on reference values from a commercially available hemodynamic simulation software (Hemoscope™, Ziosoft Inc., Tokyo, Japan). Pulsatile flow from the STA was modeled as a triangular waveform, simulating an adult with a heart rate of 75 bpm and a blood pressure of 120/80 mmHg. The waveform was constructed based on actual arterial pressure profiles. In contrast, M1 inflow was modeled as steady because applying a pulsatile-pulsatile configuration would have required simultaneous specification of time-dependent velocity and pressure conditions at multiple boundaries, which was impractical in the absence of patient-specific data and would have introduced unnecessary assumptions for all outlets (A-D). A steady inflow at M1 was, therefore, considered more appropriate to maintain physiological consistency and numerical stability. To highlight the hemodynamic characteristics of the bypass, pulsatile inflow was applied only to the STA.

Ethical considerations

This study did not involve human participants or patient data, and therefore, institutional review board approval and informed consent was not required.

Results

In the stenotic model, reductions in blood flow compared to the normal model were observed at each outlet: 63% at outlet A, 71% at outlet B, 73% at outlet C, and 12% at outlet D.

The percentage improvements in flow following each bypass configuration are summarized in Table 1 and Figure 3A. Outlet A showed the greatest improvement with Bypass 1 (164%) and Bypass 2 (124%). In contrast, outlet D showed no improvement in any configuration.

Table 1.

Bypass Efficiency Comparison in STA-MCA Bypass Models

Outlet	Normal Model (g/sec)	Stenosis Model	Bypass 1	Bypass 2	Bypass 3	Bypass 4
A	0.20	0.076 (37%)	0.201 (99%)	0.171 (84%)	0.151 (74%)	0.104 (51%)
B	0.18	0.051 (29%)	0.057 (32%)	0.057 (32%)	0.057 (32%)	0.078 (44%)
C	0.87	0.238 (27%)	0.315 (36%)	0.333 (38%)	0.360 (41%)	0.395 (45%)
D	1.82	1.602 (88%)	1.603 (88%)	1.603 (88%)	1.604 (88%)	1.604 (88%)

Values represent blood flow rates (g/sec). Percentages in parentheses indicate values relative to the normal model.

MCA: middle cerebral artery; STA: superficial temporal artery

Figure 3.

A: Percentage increase in flow rate at each outlet (A-D) following STA-MCA bypass. Bars indicate relative improvement compared to the stenotic model without bypass (averaged over two cardiac cycles).

B: Comparison of distances from bypass points to outlet A between cases that achieved ≥80% flow improvement and those that did not. Shorter distances were associated with higher improvement.

MCA: middle cerebral artery; STA: superficial temporal artery

To investigate factors influencing flow improvement, four hemodynamic parameters were evaluated:

Flow direction (Figure 1A-1D)

Bypasses 1 to 3 demonstrated antegrade flow at outlet A, while retrograde flow was observed at outlets B and C. In Bypass 4, antegrade flow was preserved at outlets A and B, while retrograde flow was seen at outlet C. No improvement was observed at outlet D in any configuration.

Bypass distance to the target outlet (Figure 1)

Flow improvement at outlet A decreased with increasing distance from the bypass site: 164% with Bypass 1 (most proximal) and 37% with Bypass 4 (most distal).

This relationship is also illustrated in the boxplot shown in Figure 3B, which compares the distance (cm) between each bypass point and outlet A in association with whether the targeted blood flow improvement (>80%) was achieved.

Vessel diameter (Figure 2B)

Outlet C, which had a larger diameter (2 mm) than outlets A and B (1 mm), showed greater flow improvement across all configurations. Bypass 4 achieved the highest improvement at outlet C (66%) despite a smaller pressure gradient.

Pressure gradient (Figure 2D)

Although outlet B had a pressure gradient of 10 mmHg―greater than outlet C (8 mmHg)―outlet C demonstrated superior flow improvement. This indicates that pressure gradient alone was not a decisive factor in determining bypass effectiveness (Table 2).

Table 2.

Effect of Bypass Distance and Pressure Gradient on Blood Flow Improvement

Model	Outlet A	Outlet B	Outlet C	Outlet D
Stenotic	85	85	86.3	90
Pressure differences in comparison with the mean STA pressure (95 mmHg)	10	10	8.7	5
Changes in blood flow improvement (bypass 1)	0.125	0.006	0.077	0.001
Changes in blood flow improvement (bypass 2)	0.095	0.006	0.095	0.002
Changes in blood flow improvement (bypass 3)	0.075	0.006	0.122	0.002
Changes in blood flow improvement (bypass 4)	0.028	0.027	0.157	0.002

Values represent changes in blood flow rates (g/sec) at each outlet. Pressure differences are relative to the mean STA pressure (95 mmHg).

STA: superficial temporal artery

Discussion

In this study, we visualized and quantified the effects of different anastomosis sites on cerebral blood flow in STA-MCA bypass surgery using CFD simulations based on both normal and stenotic vascular models. Our analysis revealed that the location of the bypass significantly influenced the extent of blood flow improvement at each outlet, underscoring the importance of anastomosis site selection in postoperative cerebral revascularization. In the stenotic model, Bypasses 1 and 2 achieved the target flow improvement (>80%) at outlet A, whereas no configuration produced sufficient improvement at outlets B, C, or D. In particular, outlet D showed minimal responsiveness to any bypass, suggesting that the choice of anastomosis site plays a decisive role in determining bypass efficacy.

Bypass 1-4 correspond to clinically relevant recipient sites. Bypasses 1 and 2 represent typical M4 cortical branches commonly used in STA-MCA bypass surgery, Bypass 3 corresponds to a branch immediately after the M3 division, and Bypass 4 corresponds to a proximal M3 branch that is usually identified after opening the sylvian fissure. Thus, the present simulation reflects realistic intraoperative options for anastomosis, providing educational value in complementing surgical decision-making.

Four key hemodynamic factors were identified as contributing to improved blood flow: (1) the direction of blood flow (antegrade/retrograde), (2) the distance from the anastomosis site to the target perfusion territory, (3) the diameter of the recipient artery, and (4) the pressure gradient. Among these, ensuring antegrade perfusion and minimizing the distance were most critical.

The importance of recipient artery diameter, anastomosis distance, and flow direction in bypass selection has been repeatedly highlighted in both clinical studies and intraoperative observations. Studies using indocyanine green videoangiography (ICG-VA) have shown that branches with lower initial flow, delayed appearance, or retrograde filling tend to exhibit greater flow increase after anastomosis, indicating that flow pattern, rather than diameter alone, is a key determinant.¹³⁾ The qualitative trends observed in our CFD analysis regarding vessel diameter and flow direction are consistent with these findings. Furthermore, the concept of targeted bypass, in which the branch closest to the target territory is selected, provides a theoretical framework supporting our result that shorter anastomosis distances yield more efficient flow delivery.¹⁴⁾ Reports suggesting that the extent of retrograde flow from the STA correlates with improved revascularization outcomes further reinforce the clinical significance of evaluating antegrade versus retrograde flow.¹⁵⁾ Intraoperative assessment tools such as ICG-VA and FLOW 800 cannot substitute for quantitative perfusion studies, but they remain useful for understanding relative hemodynamic changes and are complementary to the qualitative findings of CFD.^6,16)

The purpose of this study was not to propose specific numerical thresholds, but to provide a framework of interpretation highlighting key factors to be considered when selecting an anastomosis site in clinical decision-making.

The JET study demonstrated the prophylactic effect of bypass in patients with resting cerebral blood flow(CBF) <80% and reduced cerebrovascular reactivity. However, our CFD study did not directly calculate CBF percentages, and therefore, cannot be directly mapped to these thresholds. The stenotic model used in this study should be regarded as a conceptual reproduction of low-perfusion conditions rather than an attempt to replicate quantitative thresholds. Future work should incorporate patient-specific geometries and be externally validated by comparison with clinical perfusion studies such as single-photon emission computed tomography(SPECT), arterial spin labeling magnetic resonance imaging(ASL-MRI), and computed tomography perfusion(CTP).

In this study, pressure-pressure boundary conditions were adopted to allow consistent and efficient comparison of multiple bypass scenarios using the same solver framework. While inflow velocity (or flow) and resistance-type outlet conditions (e.g., Windkessel models) are more physiologically realistic, the customized KIVA-based solver was originally designed for pressure-driven problems, and patient-specific velocity data were not available. It is well-recognized that differences in boundary conditions can influence flow distribution and wall shear stress; therefore, the present results should be interpreted as relative tendencies rather than absolute values. Therefore, the present results should be interpreted as qualitative tendencies suited for relative comparisons. A potential improvement for future studies would be the introduction of velocity-inlet plus resistance-outlet conditions to enhance physiological validity. However, M1 inflow was modeled as steady because a pulsatile-pulsatile configuration would require simultaneous specification of time-dependent velocity waveforms and pressure conditions at multiple boundaries, which was impractical due to the unavailability of patient-specific velocity data. Consequently, pulsatile inflow was applied only to the STA, although ideally both inflows should be modeled as pulsatile.

Limitations

Furthermore, the computational mesh was generated externally using a hexahedral grid, with a total cell number of approximately 0.5-1.0 million depending on geometry and local refinements. The stenotic region was refined to an element size of about 1/10-1/20 of the vessel diameter, and near-wall resolution was determined according to the wall-law requirement of the RANS turbulence model, keeping y⁺ within 30-100. These specifications are reported here; however, a formal multi-level mesh-independence test was not performed, which remains a limitation for numerical accuracy.

In addition, patient-specific boundary condition data, such as time-resolved inflow waveforms and peripheral resistance values, were not available in this study. Therefore, pressure-pressure boundary conditions were applied and empirically adjusted to avoid flow reversal. In the stenotic model, outlet pressures were determined by adopting stable solutions defined by the absence of flow reversal and stable, balanced outlet velocities, without specifying explicit numerical thresholds, which may limit reproducibility. This limitation implies that the numerical values should be interpreted as relative tendencies rather than absolute quantities.

Direct validation with clinical perfusion data (e.g., SPECT, ASL-MRI, CTP, or intraoperative flow/pressure measurements) was also not performed, and such comparisons remain essential in future studies.

Clinical perspective and future directions

The next steps should include (1) rapid reconstruction of patient-specific geometries, (2) implementation of velocity-inlet plus resistance-outlet (e.g. Windkessel model) boundary conditions with optimized parameters, (3) modeling of pulsatile inflows for both M1 and STA, and (4) prospective validation against clinical perfusion studies and intraoperative hemodynamic indices. These advances are expected to improve the clinical applicability and external validity of CFD-based planning tools for STA-MCA bypass.⁸⁾

Conclusion

This study, using CFD analysis based on both normal and stenotic models, demonstrated that the selection of the anastomosis site in STA-MCA bypass has a decisive impact on postoperative cerebral blood flow improvement. Four key hemodynamic factors were identified as determinants of bypass efficacy: the distance from the anastomosis site to the target territory, the direction of blood flow, the diameter of the recipient artery, and the pressure gradient. Among these, shorter distance and maintenance of antegrade flow contributed most strongly to flow improvement.

These findings are consistent with intraoperative ICG-VA observations and the concept of “targeted bypass,” providing a conceptual framework to support clinical decision-making in recipient selection.

The optimal anastomosis site can be defined as one that is close to the target territory, maintains antegrade flow, has sufficient vessel diameter and pressure gradient, and is free of competing large-caliber branches. The insights from this study are expected to aid preoperative planning and the development of individualized bypass strategies.

Ethical Statement

This study did not involve human participants or animals. Therefore, ethics committee approval was not required.

Conflicts of Interest Disclosure

The authors declare no conflicts of interest.