Efficacy evaluation and parametric study of the novel concave triple branched stent graft system based on hemodynamic analysis of first-in-man cases

Introduction

The management of aortic arch pathologies (AAPs) remains a challenge for cardiovascular surgeons. Thoracic endovascular aortic repair (TEVAR) incorporating supra-aortic trunks (SATs) reconstruction has become a widely adopted minimally invasive treatment method for AAPs in clinical practice (1-3). However, due to the complex anatomy of aortic arch, it is difficult to reconstruct SATs with a sufficient landing zone during TEVAR (4-7). With the development of instrument technology and the accumulation of clinical experience, branched stent graft (SG) has emerged and gradually been widely applied for AAPs treatment (8,9). However, this technique is still associated with certain complications, such as peri-operative stroke, aortic insufficiency, endoleak, and an unsuitable proximal landing zone in the ascending aorta (AA) (10-14). Due to high design complexity and surgical challenges, there is still lack of a fully developed and widely used branched SG system worldwide.

In 2021, Fuwai Hospital, the Chinese Academy of Medical Sciences, first proposed the concave supra-arch triple branched SG system (CS system), a novel and off-the-shelf endovascular device that can be applied to reconstruct the aortic arch and all SATs, as shown in Figure 1 (15). Currently, the CS system technique has completed pre-clinical animal experiments and has been examined in a first-in-man clinical trial, showing satisfactory early postoperative results (15). However, to date, clinical evaluations of the efficacy of CS systems have primarily relied on imaging assessments, which are insufficient for long-term evaluation.

Figure 1 Structure and components of the CS system. CS system, concave supra-arch triple-branched stent graft system.

The concave region of the CS system provides an expanded operative space for catheter manipulation, a critical advantage for enhancing procedural success in complex SATs reconstruction. However, due to the complex anatomical structure of the aortic arch, the concave structure applicable to each patient may be different. While the presence of this concave area facilitates surgical maneuverability, it also introduces potential risks associated with altered blood flow patterns. The current CS system is limited to a single fixed concave degree, lacking the flexibility to adapt to individual patient anatomy. Thus, developing personalized CS system configurations for patients and balancing surgical accessibility with hemodynamic safety during TEVAR remain critical challenges.

Recently, numerical and structural analyses of branched and modular stent-grafts have rapidly expanded, especially for devices reconstructing supra-aortic branches across zones 0 and 1 of the aortic arch (16-18). Existing computational fluid dynamics (CFD)- and fluid-structure interactions (FSIs)-based studies of branched endograft systems have mainly focused on the analysis of hemodynamic alternations in the aorta following the SG deployment (5,8,19-23). These studies underscore the essential role of computational hemodynamics in evaluating device-vessel interactions, anatomical determinants of flow, and the comparative performance of different endovascular strategies. CFD-based analyses also support fundamental investigations using idealized models and offer insights into long-term postoperative vascular remodeling (24-26). By reconstructing patient-specific geometries from clinical imaging, CFD enables detailed prediction of postoperative flow fields and provides mechanistic insights beyond imaging alone (27-29). These capabilities make CFD an effective tool for evaluating the performance of the novel SG technique, ultimately informing pre-treatment planning and improving safety and effectiveness.

In this study, we evaluated the hemodynamic performance of the CS system using pre- and postoperative computed tomography angiography (CTA)-based patient models and further explored its potential for personalized application. Beyond assessing clinical cases, we examined the influence of the concave configuration of the CS system through aortic models with patient-specific diameters. By integrating multiple hemodynamic indicators, our work provides innovative perspectives on evaluating the therapeutic efficacy of the CS system and guiding the SG design and appropriate selection, thereby contributing to better outcomes in the management of complex AAPs.

Methods

Patient selection and CS system design

Five patients with previous aortic arch aneurysm who were treated using the CS system at three major cardiovascular centers in China (Fuwai Hospital, the Chinese Academy of Medical Sciences; Fuwai Yunnan Cardiovascular Hospital; The Second Xiangya Hospital of Central South) were included in the present study. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the Ethics Committees of The Second Xiangya Hospital of Central South University {approval No. [2022] Ethics Review [Medical Device] No. [005]}, the Fuwai Hospital (approval Nos. 2022-K74-1; 2023-K3-1; 2023-K5-1), and Fuwai Yunnan Cardiovascular Hospital (approval No. 2023-030-01). Informed consent was taken from all the patients. All participating hospitals were informed of and agreed to the study. Detailed baseline characteristics, including age, gender, and comorbidities, are summarized in the Table S1 in Appendix 1. The CS system was an endovascular device designed specifically for aortic arch lesions, which was manufactured by Lifetech Scientific (Shenzhen, China). The CS system consisted of four separate SGs (Figure 1): a three inner branched tapered aortic arch concave designed SG (ASG); two antegrade self-expanding bridging SGs (BSGs) for reconstruction of the brachiocephalic trunk (BCT) and left common carotid artery (LCCA), and one retrograde BSG for reconstruction of the left subclavian artery (LSA). The procedure was performed under general anesthesia in a hybrid operating room using the CS system during TEVAR. Bilateral brachial arteries, the LCCA, and a common femoral artery were dissected and controlled. Detailed step-by-step technical details of CS system implantation are presented in the Appendix 2.

Image acquisition and geometry reconstruction

Pre- and postoperative CTA images of all patients were acquired (Figure 2A). Image segmentation and three-dimensional (3D) reconstruction of the pre- and post-TEVAR CTA datasets were performed via Mimics Research 19.0 (Materialise, Leuven, Belgium) (Figure 2B). For each patient, segmentations were performed from AA to descending aorta (DA), as shown in Figure 2B. The implanted CS system was modeled as a thin wall with a uniform thickness of 0.5 mm (determined based on manufacturer-provided device specifications), and was extracted from the aortic arch via Boolean operations (Figure 2C). Reconstructed models were finally exported as a triangle mesh and were smoothed via Geomagic Wrap 2017.0.0 (3D Systems, Inc., Rock Hill, SC, USA) to facilitate computational analysis (Figure 2D). Morphological parameters were measured based on 3D vascular models, and details are provided in Table 1.

Figure 2 Procedure of 3D reconstruction and processing of aortic model. (A) CTA images. (B) Preoperative and postoperative reconstruction of 3D models. (C) Geometry segmentation and CS extraction. (D) Smoothed postoperative models extracted CS system. 3D, three-dimensional; BCT, brachiocephalic trunk; CS system, concave supra-arch triple-branched stent graft system; CTA, computed tomography angiography; LCCA, left common carotid artery; SG, stent graft.

Configuration of parametric analysis for the CS system

To identify the concave angle that yields a more favorable hemodynamic outcome for different anatomies, we created and compared models with three representative angles (α =120°, 150°, and 180°). This comparative parametric study serves to guide the selection of a more suitable CS system configuration for personalized treatment. Detailed schematic diagrams of the CS system are depicted in Figure 3A,3B. Concave degree was quantified via the central angle α of the cross-section, with the concave region simplified as an arch. Idealized 3D preoperative and postoperative models were constructed using Spaceclaim (ANSYS, Inc., Canonsburg, PA, USA) based on the anatomical structure of Patient #3 (Figure 3C). Three different angles were designed with the fixed position and diameter (d1, d2 and d3) of the inner branches, including 120° (baseline of the actual CS system specification), 150° and 180° (Figure 3D). To assist clinicians in formulating personalized treatment plans, idealized 3D preoperative aortic geometries with varying diameters (D1, D2, and D3) were constructed and set as the control group (CG) (Figure 3E). Based on the idealized preoperative models, 36 postoperative aortic models implanted with CS system with different angles α were virtually modified and obtained under the assumption that the stent size was aligned with the anatomical size of the patient. Table 2 shows the schematic of the aortic models and CS system structure with the geometric measurement details. All the designations of the diameter and length were based on the manufactured size of the CS system.

Figure 3 Schematic design of the CS system and configuration of idealized aortic models for parametric study. (A) Composition of the CS system. (B) Schematic design of the CS system in the plan view. (C) Idealized preoperative and postoperative models. (D) Aortic models implanted with CS system with different angles. (E) Postoperative models with different aortic diameters. The model shown in (C) and (D) is taken as an example with D1 = D2 = D3 =48 mm, and the model shown in (E) is taken as an example with α of 120°. D1, proximal ASG main body diameter; D2, ASG main body diameter at the distal end of the concave; D3, distal ASG main body diameter; d1, d2, proximal BSG diameter; d3, distal BSG diameter; L1, proximal segment length of antegrade inner branched section; L2, concave length; L3, distal segment length of ASG. ASG, aortic arch concave designed stent graft; BSG, bridging stent graft; CS system, concave supra-arch triple-branched stent graft system.

Mesh generation

Computational domains were discretized into unstructured tetrahedral meshes in the core region with ten prism layers near the walls using Fluent Meshing (ANSYS Inc., Canonsburg, USA). Mesh sensitivity tests were conducted to ensure grid independence (see Appendix 3 for details). Based on the results, a grid number ranging from 1.2 million to 1.3 million was selected to balance computational accuracy and cost.

Computational model and numerical simulation

Blood was considered as an incompressible and non-Newtonian fluid with a uniform density ρ of 1,060 kg/m³. The continuity equation and Navier-Stokes equation were applied as governing equations for the fluid dynamic simulation, which were expressed as follows (30):

∇⋅u→=0[1]

ρ[∂u→∂t+(u→⋅∇)u→]=−∇P+μ∇2u→+ρg[2]

where u→ is the velocity vector of fluid, P represents the pressure, g is the gravity acceleration (−9.81 m/s²), and μ is the blood viscosity, defined using the Carreau-Yasuda model as follows:

μ=(μ0−μ∞)[1+(λγ˙)a](n−1a)+μ∞[3]

where µ₀ is the zero shear rate viscosity (0.16 Pa·s), µ_∞ is the infinite shear rate viscosity (0.0035 Pa·s), λ is the relaxation time (8.2 s), γ˙ is the shear rate (s⁻¹), a is the Yasuda exponent (0.64) and n is the power law index (0.2128) (31,32).

Based on the finite volume method, commercial software Fluent 2021 R1 (ANSYS, Inc., Canonsburg, PA, USA) was employed to simulate the blood flow. The flow pattern was assessed based on calculations of the peak Reynolds number (Re_p), Womersley number (α), and the critical Reynolds number (Re_c) for transition to turbulence reported by Kousera et al. (33). Given that Re_p was less than Re_c in all the simulations, the flow could be modeled as laminar flow. The incompressible flow was discretized in time using the second-order implicit Euler scheme. For spatial discretization: the convective terms were solved using a second-order upwind scheme; the diffusive terms were discretized using a second-order central differencing scheme. The velocity-pressure coupling was resolved using the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm. The pressure at cell faces was approximated using the standard pressure interpolation scheme, and gradients were computed using the cell-based least squares method. The maximum residual for convergence of all equations was set to 10⁻⁵.

A time step of 0.001 s was chosen after performing time-step independence analysis. All simulations were run for eight cardiac cycles to ensure periodic convergence. Detailed procedures and results of these independence tests are provided in Appendix 3. Results from the final cycle were extracted for hemodynamic analysis, as is standard practice in CFD studies of pulsatile flow.

Boundary conditions

The vessel wall was modeled as rigid with no-slip boundary conditions. Auxiliary computational domains were established at all the boundaries to ensure the fully developed blood flow (34). The physiological flow waveform shown in Figure 4 from the literature was used as inlet boundary condition to consider the systole and diastole (with the cardiac cycle of 0.8 s) (35-37). A three-element Windkessel model was set as the outlet boundaries to account for the flow-pressure relationship. Windkessel model parameters were obtained and tuned based on the methodology described in the previous study using MATLAB R2022b (The Mathworks Inc., Natick, USA) (38). Based on the electrical formula and the backward difference method, the iterative formula for outlet pressure was expressed as follows (39):

Pn=(R1+R2+R1β)Qn+βPn−1−R1βQn−11+β[4]

Figure 4 Detailed boundary conditions.

where β = R₂C/Δt. P and Q are pressure and volume flow rate, respectively, while the subscript n denotes the variable at the nth step. R₁, R₂, and C represents the proximal resistance, distal resistance and compliance, respectively. Rwk31,i, Rwk32,i and Cwk3,i for each outlet were summarized in the Table S2 in Appendix 4.

Hemodynamic indices

Although the first-in-man CS system had been applied in the clinic, the long-term prognosis was unknown. Hemodynamic pattern was able to describe the mechanical properties and the interactions between blood flow and the vascular wall. Therefore, hemodynamic indices were quantitatively and qualitatively analyzed to evaluate the therapeutic effect of the CS system technique.

Arterial walls could respond to hemodynamic stimuli, such as the stretch and shear stress resulting from flow and circulatory pressure. The ability was mainly mediated by vascular endothelial cells, which could sense WSS levels and regulate arterial remodeling according to the WSS level, thus abnormalities of WSS levels might cause long-term deterioration of arterial structure (40). For the important physiological meanings of WSS in blood flow simulations, parameters based on WSS including TAWSS, oscillatory shear index (OSI), and relative residence time (RRT) were selected for hemodynamic analyses. Correlated expressions were as follows:

TAWSS=1T∫0T|WSS|dt[5]

OSI=0.5[1−|∫0TWSSdt|∫0T|WSS|dt][6]

RRT=1(1−2⋅OSI)⋅TAWSS[7]

where T is the cardiac cycle.

Energy loss was commonly utilized to evaluate the blood flow resistance across the vessels (41), and was selected to investigate the CS system efficacy. Total pressure (TP) was extracted from the calculation results, expressed as the sum of dynamic pressure and static pressure. Energy loss was defined as a function of TP, specifically the difference in energy between the aortic inlet and the four outlets during a cardiac cycle, including outlets of BCT, LCCA, LSA and DA, which could be written as (42):

∫0TELdt=∫0T(ELin−ELout)dt=∫0T(Qin⋅Pin−Qout⋅Pout)dt[8]

where Q demonstrates the blood flow of the vessels, EL represents the energy loss. Subscripts in and out refer to the inlet and outlets, respectively.

Results

Evaluation of CS system efficacy

Blood perfusion

The ability of the CS system to preserve blood flow to reconstructed SATs is examined via the flow distribution ratio. Figure 5 presents the systolic flow distribution across outlets in pre- and post-TEVAR cases. Following CS system implantation, the systolic flow distribution across all SATs is preserved. Flow to the BCT and LCCA increases by 6.03%±5.00% and 4.76%±5.68%, respectively, while LSA and DA flow decrease by 2.18%±1.46% and 1.56%±1.28%. These findings demonstrate that SAT perfusion remains stable despite geometric changes induced by the concave branched structure, with a 1.13%±0.81% increase compared to the preoperative state. Additionally, as shown in Table 1, the flow of BCT and LCCA increases when the vessel diameter decreases postoperatively (with the inner branch diameter of 12 mm for BCT and LCCA and 10 mm for LSA), and similarly, the flow of LSA decreases even if the diameter increases postoperatively. Apart from diameter, the distance between the aortic sinus and proximal inner branches may also be a factor affecting the flow distribution. As we can see, perfusion to BCT and LCCA in Patient #2 after implantation of the CS system is larger than that in other patients, which is likely due to the less energy loss induced by a shorter distance between the aortic sinus and inner branches. Preoperative anatomical assessment (e.g., aortic arch type and sinus-to-branch distance) may be critical for predicting postoperative hemodynamic outcomes, which can be further utilized for assisting in developing patient-specific treatment strategies.

Figure 5 Blood flow ratio to each outlet in clinical patients at systolic peak. BCT, brachiocephalic trunk; DA, descending aorta; LCCA, left common carotid artery; LSA, left subclavian artery.

Pressure distribution

The concave region of the CS system may cause a certain degree of stenosis in the aortic arch, potentially inducing blood flow obstruction and subsequent fluctuations in aortic pressure level, which is an important factor for evaluating CS system safety. Figure 6 shows that systolic AA pressure exhibits a mild rise of 0.46%±0.42% following CS system implantation. Across all cases, pressure elevation remains below 1.2%, and the resulting absolute pressure values remained within the physiological range reported in previous clinical studies (43-45).

Figure 6 Preoperative and postoperative systolic pressure distribution in the AA. (A) Pressure distribution at peak systole for all five patients. (B) Comparison of the averaged systolic pressure in the AA before and after TEVAR. AA, ascending aorta; TEVAR, thoracic endovascular aortic repair.

TAWSS, OSI and RRT

Figure 7 shows the results of WSS-related parameters before and after the TEVAR procedure. Quantitative analyses reveal that TAWSS in the AA decreases by 16.28%±13.32%, while OSI and RRT increase by 9.91%±7.57% and 6.22%±2.14%, respectively. Additionally, high TAWSS regions appear near the distal concave and inner branch entrances, whereas increased OSI and RRT primarily occur within the AA.

Figure 7 Preoperative and postoperative WSS-related parameters. (A) TAWSS distribution and (B) averaged TAWSS in AA. (C) OSI distribution and (D) averaged OSI in AA. (E) RRT distribution and (F) averaged RRT in AA. AA, ascending aorta; OSI, oscillatory shear index; RRT, relative residence time; TAWSS, time-averaged wall shear stress; WSS, wall shear stress.

Energy loss

Monitoring total energy loss after CS system implantation provides insights into flow resistance, serving as an effective indicator for evaluating the long-term efficacy of the device. It can be observed in Figure 8 that the total energy loss increases by 20.74%±12.92% after CS system implantation, suggesting elevated flow resistance within the aortic arch postoperatively.

Figure 8 Comparison of preoperative and postoperative total energy loss.

Flow distribution and hemodynamic parameters under different postoperative blood pressures

The assessment of CS system stability can also be approached from the perspective of hemodynamic stability under varying postoperative blood pressure levels in patients. Three postoperative target levels for diastolic and systolic pressures were selected in this study: diastolic pressures of 80, 110 and 140 mmHg, and systolic pressures of 120, 150 and 180 mmHg, with the normal pulse pressure of 40 mmHg (46).

To evaluate the stability of the CS system, flow distribution and hemodynamic parameters after intervention under varying postoperative blood pressure levels, ranging from 120/80 to 180/140 mmHg, are compared with those before intervention (Table 3). As the blood pressure gradually rises, blood flow to SATs increases and LSA perfusion may even shift from a downward to an upward trend compared to the preoperative level. The increase in SATs blood supply may become significant under higher blood pressure in some patients, such as Patient #4, which may be induced by the small diameter of DA shown in Table 1. Furthermore, as the postoperative blood pressure increases, the pressure in the AA obviously shows an elevated trend after TEVAR treatment. Patients #3, #4, and #5 show increased TAWSS with elevated pressure levels, while OSI and RRT follow an opposite trend. However, the pattern of change in hemodynamic parameters in Patients #1 and #2 is opposite to that in Patients #3, #4, and #5, which may be attributed to the differences in AA diameter. Specifically, AA diameters in Patients #1 and #2 are relatively larger, which may lead to lower TAWSS and higher OSI and RRT under higher pressure levels. Additionally, the rate of increase in energy loss relative to preoperative levels decreases as postoperative pressure levels increase, and for Patient #3, the trend may shift from increased to decreased.

Notably, all the changes in the hemodynamic environments under variant blood pressure levels are less than 50% compared to the preoperative levels, suggesting a favorable prognosis and stability of the CS system. However, although the flow distribution remains relatively stable when the postoperative blood pressure increases, such an elevation in SATs perfusion might induce cerebral hyperperfusion or other complications. Nonetheless, the issue is not unique to CS system implantation but is commonly encountered in all TEVAR procedures, even when only a descending aortic stent is deployed. Thus, continuous pressure monitoring during follow-up is essential for all TEVAR techniques, but the requirement for pressure management might be more stringent in the case of CS system implantation, just given that the stent needs to be placed in the AA.

Evaluation of the patient-specific selection scenarios on concave angles

Blood perfusion

To investigate the effects of the concave angle of CS system on the perfusion of patients with different aortic diameter, blood flow ratios after implanted with CS system with different angles are depicted in Figure 9. We can observe that blood flow variations in idealized models are similar to clinical findings. Compared to the CGs, the CS system (α =120°) reduces LSA flow by 5.27%±2.95% while increasing total SATs flow by 0.76%±0.66%. Notably, LSA perfusion shows the most significant variation among all branches, with change ratios of 2.72%±0.97% (BCT), 2.32%±1.29% (LCCA), 5.27%±2.82% (LSA), and 0.40%±0.13% (DA), respectively.

Figure 9 Comparison of the blood flow ratio crossing each outlet in models implanted with CS systems with varying α. D1, proximal ASG main body diameter; D2, ASG main body diameter at the distal end of the concave; D3, distal ASG main body diameter. ASG, aortic arch concave designed stent graft; BCT, brachiocephalic trunk; CG, control group; CS system, concave supra-arch triple-branched stent graft system; DA, descending aorta; LCCA, left common carotid artery; LSA, left subclavian artery.

Regarding the concave angle, BCT and LCCA perfusion increase with larger α, whereas LSA and DA flow decrease, suggesting potential LSA flow obstruction at higher angles. The variation in flow ratios is notably less pronounced between 120°–150° compared to 150°–180°. Specifically, averaged change rates are as follows: BCT, 0.72%±0.64% (120°−150°) vs. 1.85%±0.72% (150°−180°); LCCA, 0.56%±0.53% (120°−150°) vs. 2.00%±1.05% (150°−180°); LSA, 0.45%±0.39% (120°−150°) vs. 0.75%±0.38% (150°−180°); DA, 0.23%±0.16% (120°−150°) vs. 0.74%±0.35% (150°−180°). Overall, SATs perfusion increases by approximately 1–2% as α increases, with changes more pronounced when α exceeded 150°, which may be attributed to the area variation in the CS system cross-section between 120°−150° and 150°−180°.

Regarding aortic anatomy, patients with larger aortic diameters are more likely to experience a reduction in SATs flow ratios. For instance, when D2 = D3 =30 mm, increasing D1 from 30 to 42 mm results in a decrease in flow ratios of 3.80% to BCT, 3.94% to LCCA, and 0.95% to LSA, while simultaneously increasing the flow ratio to DA by 1.92%. When D1 equals 30 mm, increasing both D2 and D3 from 22 to 26 mm results in a more pronounced effect: flow ratios to BCT, LCCA, and LSA decrease by 8.17%, 8.11%, and 3.35%, respectively, while the flow ratio to DA increases by 5.87%.

Pressure distribution

As shown in Figure 10, CS system implantation slightly elevates systolic pressure in the thoracic aorta (TA), particularly in the AA. The average AA pressure rise is minimal (0.79%±0.30%), with a maximum increase of 1.09% observed in small-diameter models (D1 =30 mm).

Figure 10 Variations in systolic pressure distribution across different concave angles and aortic diameters. (A) Pressure distribution at peak systole and (B) systolic pressure of the AA in models implanted with CS systems with varying α compared to the CG. D1, proximal ASG main body diameter; D2, ASG main body diameter at the distal end of the concave; D3, distal ASG main body diameter. AA, ascending aorta; ASG, aortic arch concave designed stent graft; CG, control group; CS system, concave supra-arch triple branched stent-graft system.

Regarding the concave angle, AA pressure rises positively with α. Consistent with flow trends shown in Figure 9, the pressure increase is notably steeper from 150° to 180° (0.55%±0.52%) compared to the 120°–150° range (0.12%±0.07%). Although the pressure elevation is minor, the nonlinear increase beyond 150° implies that angle selection requires balancing surgical convenience with potential hemodynamic risks.

Conversely, larger aortic diameters are associated with lower postoperative AA pressures. When D1 increases from 30 to 48 mm, average pressures of AA are respectively 121.20 mmHg (D1 =30 mm), 120.14 mmHg (D1 =36 mm), 119.62 mmHg (D1 =42 mm), and 118.64 mmHg (D1 =48 mm). Moreover, models with CS system insertion show a reduction in AA pressure as D2 and D3 increase. When α =120°, AA pressure equals to 121.13 mmHg with D1 =30 mm, D2 = D3 =22 mm, while the pressure is 121.03 mmHg with D2 = D3 =26 mm, resulting in a 0.09% decrease. These results indicate that larger aortic diameters or reduced AA-DA diameter gradients are associated with 0.1–2% lower postoperative AA pressure.

TAWSS, OSI and RRT

Figures 11-13 compare WSS-related parameters in models before and after being implanted with CS systems with varying α, including TAWSS, OSI and RRT. As shown in Figure 11A, CS system implantation significantly increases TAWSS in TA, particularly around the high-curvature concave region. In contrast, the AA region exhibits a decrease in TAWSS alongside increased OSI and RRT (Figures 12A,13A), indicating a more disturbed flow environment upstream of the device. Quantitatively, TAWSS alterations are more profound in the TA (increases by 19.94%±9.53%) than in the AA (decreases by 1.94%±0.52%). Additionally, effects of CS system implantation on the hemodynamics appear to be more pronounced in patients with smaller aortic diameters, e.g., when D1 =30 mm, D2 = D3 =22 mm, implantation of the CS system with α =120° leads to a substantial increase in TAWSS in TA by 40.44%, with a corresponding decrease in AA TAWSS by 2.71%. In contrast, when D1 = D2 = D3 =48 mm, TAWSS in TA and AA increases by only 9.89% and 1.22%, respectively. TAWSS changes are strongly diameter-dependent, rising by ~40% in small-diameter anatomies (D1 =30 mm) but only ~10% in large-diameter models (D1 =48 mm).

Figure 11 Effect of CS system configuration on TAWSS patterns. (A) Comparison of TAWSS distribution and (B) averaged TAWSS values in the TA and AA for models with varying concave angles and aortic diameters. D1, proximal ASG main body diameter; D2, ASG main body diameter at the distal end of the concave; D3, distal ASG main body diameter. AA, ascending aorta; ASG, aortic arch concave designed stent graft; CG, control group; CS system, concave supra-arch triple-branched stent graft system; TA, thoracic aorta; TAWSS, time-averaged wall shear stress.

Figure 12 Effect of CS system configuration on OSI patterns. (A) Comparison of OSI distribution and (B) averaged OSI values in the TA and AA for models with varying concave angles and aortic diameters. D1, proximal ASG main body diameter; D2, ASG main body diameter at the distal end of the concave; D3, distal ASG main body diameter. AA, ascending aorta; ASG, aortic arch concave designed stent graft; CG, control group; CS system, concave supra-arch triple-branched stent graft system; OSI, oscillatory shear index; TA, thoracic aorta.

Figure 13 Effect of CS system configuration on RRT patterns. (A) Comparison of RRT distribution and (B) averaged RRT values in the TA and AA for models with varying concave angles and aortic diameters. D1, proximal ASG main body diameter; D2, ASG main body diameter at the distal end of the concave; D3, distal ASG main body diameter. AA, ascending aorta; ASG, aortic arch concave designed stent graft; CG, control group; CS system, concave supra-arch triple-branched stent graft system; RRT, relative residence time; TA, thoracic aorta.

The effect of the concave angle (α) on hemodynamics was also analyzed. It can be observed that TAWSS decreases in the AA (from 1.381±0.502 Pa at CG to 1.300±0.475 Pa at α=180°) but increases in the TA (from 1.429±0.472 Pa to 2.057±0.737 Pa) with larger α, while OSI and RRT follow an opposite trend, showing an increase in the AA (OSI: 0.306±0.036 to 0.335±0.029; RRT: 3.52±1.81 to 4.77±2.22 Pa⁻¹) but a decrease in the TA (OSI: 0.275±0.031 to 0.248±0.023; RRT: 3.37±1.58 to 2.41±1.07 Pa⁻¹). Additionally, the change in TAWSS with varying α is more pronounced in TA compared to AA, with maximum change rate of 4.93% in AA and 18.53% in TA when D1 = D2 = D3 =48 mm with α varying from 150° to 180°, which is similar to the variation of OSI and RRT. Notably, the change rate of RRT with α in TA and AA show a relatively small difference, with the maximum change rate of 17.53% and 18.01%, respectively (D1 = D2 = D3 =48 mm with α varying from 150° to 180°). Similar to pressure trends, the rate of hemodynamic change is substantially steeper when α exceeded 150°. Additionally, as discussed above, for patients with smaller aortic diameters, who are typically implanted with a smaller-sized CS system, reducing the concave degree may contribute to optimizing the blood flow environment.

Along with the effects of the concave angle of the CS system, the impacts of aortic diameters on hemodynamics are investigated. As we can see, areas of high TAWSS are primarily located in the distal region of the concave section. As D2 and D3 increase, high TAWSS regions shift from the distal end of the concave toward the mid-section. The phenomenon highlights that in patients with a more homogeneous distribution of aortic diameters, the implanted stent is more uniformly stressed. As D1 increases from 30 to 48 mm, both TAWSS in TA and AA demonstrate a declined trend. Specifically, TAWSS declines from 2.75±0.58 to 1.18±0.30 Pa in TA and from 2.03±0.07 to 0.82±0.05 Pa in AA. Meanwhile, OSI in both TA and AA increase with larger D1. Specifically, OSI in TA increases from 0.23±0.01 to 0.28±0.02, while it rises from 0.29±0.02 to 0.36±0.01 in AA. Similarly, RRT increases as D1 expands, from 1.40±0.36 to 4.29±1.15 Pa⁻¹ in TA and 1.97±0.36 to 7.00±1.08 Pa⁻¹ in AA. Additionally, increasing D2 and D3 are associated with a decrease in TAWSS and increases in both OSI and RRT, following a consistent relationship with the variation of D1 across all three hemodynamic parameters. For instance, at D1 =30 mm, when D2 and D3 increase from 22 to 26 mm, TAWSS in TA declines from 3.38 to 2.61 Pa as α changes from 120° to 150°, while OSI increases from 0.22 to 0.23, marking a 5.00% rise. RRT in TA also follows an increase from 1.12 to 1.29 Pa⁻¹, reflecting a 15.28% change.

Energy loss

Figure 14 illustrates the comparison of energy loss in models implanted with a CS system with varying α. The implantation of CS system is associated with an increase in energy loss, highlighting there is a rise in flow resistance within the vascular system postoperatively, which is consistent with the findings in clinical patients in Figure 8. As discussed in Section 3.1.4, although there is an increase in energy loss, this increase remains within manageable limits.

Figure 14 Comparison of energy loss in idealized models implanted with CS systems with varying α. D1, proximal ASG main body diameter; D2, ASG main body diameter at the distal end of the concave; D3, distal ASG main body diameter. CG, control group; CS system, concave supra-arch triple-branched stent graft system.

Furthermore, an increase in α results in a gradual rise in energy loss, e.g., when D1 =30 mm and D2 = D3 =22 mm, increasing α from 120° to 150° raises the energy loss from 42.03 to 42.86 mJ, with an increase of 1.97%. Additionally, the energy loss change rate in the α range of 120° to 150° is less pronounced compared to that of 150° to 180°, with respective rates of 2.79%±1.23% (120° to 150°) and 66.34%±1.26% (150° to 180°).

Considering the patient-specific effects of the CS system, we can observe that as the D1 increases, energy loss tends to decrease. For instance, when D1 increases from 30 to 36, 42, and 48 mm, the average energy loss values are 40.38±3.31, 34.13±5.03, 28.67±4.20, and 21.81±4.56 mJ, respectively, suggesting that blood flows lower in the aorta with larger diameters, thereby reducing overall energy dissipation. Moreover, as D2 and D3 increase, patients also exhibit a reduction in energy loss, e.g., when a CS system with α =120° is implanted, total energy loss in patients with D1 =30 mm, D2 = D3 =22 mm is 42.03 mJ, compared to 40.80 mJ in those with D2 = D3 =26 mm, reflecting a decrease of 2.93%.

Discussion

As an innovative device, the CS system effectively addresses the challenges of reconstructing SATs due to complex aortic arch anatomies. Despite favorable clinical imaging results after CS system implantation, detailed analysis of local hemodynamics remains insufficient to demonstrate the efficacy of CS system. To fill this gap, we employed image-based CFD to investigate the postoperative blood flow field. The blood flow characteristics pre- and post-TEVAR have been previously analyzed to evaluate the pathological development and postoperative efficacy (21,23-26). Here, we employed computational hemodynamics to conduct a detailed analysis of follow-up effects in the first-in-man cases following CS system implantation. Additionally, through parametric analysis, this study provides recommendations for developing patient-specific treatment plans.

Comprehensive evaluation of CS system performance in clinical cases

In this first-in-man hemodynamic evaluation, the CS system preserved global SATs perfusion while altering branch-specific flow distribution. This agrees with prior observations that aortic flow patterns are strongly influenced by vascular morphology and branch orientation, beyond diameter alone, as described in classical relations such as the cubic or square laws (47). The increase in BCT and LCCA perfusion and reduction in LSA perfusion also align with the geometric features of the device of antegrade orientation of the proximal branches and retrograde configuration of the LSA. This interpretation is supported by prior TEVAR studies showing that branch take-off angle, flow entry orientation, and local aortic curvature play decisive roles in modulating branch perfusion (48), and is further reflected by the redistributed flow patterns observed in our simulations.

Although reduced LSA perfusion may raise concerns due to its critical role in posterior cerebral and spinal cord circulation, none of the patients developed spinal cord ischemia or posterior-circulation stroke at 12-month follow-up (15). This aligns with prior observations that neurologic complications primarily occur with more substantial LSA flow compromise or intentional branch coverage (49,50). The favorable clinical outcome may be explained by the preserved overall perfusion to the SATs, which showed an average increase of 1.13%±0.81% in total flow distribution. Furthermore, the improved total SAT inflow corresponds with the absence of anterior circulation ischemic events (15) and correlates with complete exclusion of the aortic pathology and durable postoperative branch patency on CTA images, supporting the consistency between computations and clinical outcomes.

Postoperative AA systolic pressure increased only minimally (0.46%±0.42%), indicating that hemodynamic burden introduced by the concave portion of the CS system is limited. Although elevated AA pressure can theoretically increase the risk of stent-induced sinus dilation or retrograde type A dissection (51-54), the resulting postoperative pressure values remained within the physiological range reported in previous clinical studies (43-45). This mild elevation is likely counterbalanced by the enhanced inflow to the SATs, helping maintain overall aortic impedance.

The altered flow geometry also resulted in reorganized shear environments. The AA exhibited decreased TAWSS (–16.28%±13.32%) and increased OSI (9.91%±7.57%) and RRT (6.22%±2.14%), a pattern often associated with vortical or oscillatory flow (55-59). Clinical and experimental studies have shown that low TAWSS, particularly values below 0.4–1.0 Pa, combined with high OSI (OSI ≳0.1–0.2) and RRT, has been linked to endothelial dysfunction, wall thickening and atherosclerotic progression in arterial studies (60-62). Yet, due to the inherently unidirectional nature of AA flow and its low predisposition to atherosclerosis (63), the clinical relevance of these changes appears low. Meanwhile, regions near the distal concave surface and inner-branch entrances in our models exhibited relatively high TAWSS (on the order of 2–6 Pa, i.e., above local mean values) with low OSI and RRT, which are conditions generally interpreted as stable, unidirectional shear that is less prone to thrombogenic remodeling (60,64). The hemodynamic parameters indicate stable flow dynamics that align with the absence of in-stent thrombosis during follow-up (15). Although higher local TAWSS may increase drag forces on the graft (65), the oversizing and anchoring strategy used in the CS system ensures mechanical stability.

Elevated hemodynamic energy loss has been proposed as a marker of inefficient flow and increased mechanical dissipation, and recent computational studies suggest associations between higher energy loss and the occurrence of aortic diseases (20,42,66,67). Energy loss increased by 20.74%±12.92% postoperatively, reflecting additional dissipation due to concave-induced vortices and branch reconstructions. Part of this increase is attributable to the non-physiologically large preoperative arch dilation, which yields unusually low baseline energy loss. Nevertheless, the protective function of the SG, coupled with adequate sealing to prevent endoleak, could reduce the risks of local complications. Nonetheless, continuous monitoring of energy loss after CS system deployment remains essential for assessing the current physiological status and guiding future interventions.

Across varying postoperative blood pressures (120/80–180/140 mmHg), the CS system maintained stable hemodynamic behavior: SAT perfusion generally increased with pressure, AA pressure rose moderately, and WSS-related parameters changed in a patient-specific manner largely governed by AA size. Importantly, all parameter changes remained <50% relative to preoperative levels, underscoring robust functional stability. Although elevated systemic pressures may raise concerns regarding hyperperfusion, this issue is common to all TEVAR interventions, and blood pressure control remains standard postoperative management, which is particularly important when stents extend into the AA, as in CS system implantation.

Postoperative blood pressure management in patients receiving the CS system should be individualized according to the patient’s clinical profile. For instance, in those with concomitant cerebral hypoperfusion or coronary artery disease, blood pressure should not be lowered excessively to maintain adequate end-organ perfusion. In addition to clinical assessment, hemodynamic parameters derived from this study, such as preoperative ascending aortic diameter, the diameter difference between AA and DA, and postoperative energy loss, may serve as quantitative references to guide personalized blood pressure targets. Integrating these objective metrics into postoperative management could help balance hemodynamic stability with organ perfusion, potentially improving clinical outcomes.

Hemodynamic implications of patient-specific concave angle selection

Idealized model analyses further elucidate how the concave angle (α) modulates multi-parametric hemodynamics and inform patient-specific device selection. Consistent with clinical observations, SAT perfusion declined most notably in the LSA following CS system implantation due to its downstream location and retrograde branch orientation. Larger angles intensified this effect: increasing α from 120° to 180° led to progressively greater reductions in LSA and DA flow, with substantially steeper changes beyond 150°. This suggests that excessively large angles impose greater flow obstruction. Nonetheless, previous TEVAR studies have shown that mild reductions in LSA perfusion are generally well tolerated in most patients, except in cases with a dominant left vertebral artery or incomplete circle of Willis (68-71).

Pressure distribution trends reflect changes in perfusion. CS implantation increased AA pressure slightly (~0.79%), and larger α produced more pronounced elevation. Notably, the change was more pronounced from 150° to 180°, emphasizing that extreme concavity should be avoided when possible. In contrast, larger aortic diameters or smaller diameter differences between AA and DA may mitigate these effects, indicating that patients with small luminal dimensions are more susceptible to pressure-related loading.

WSS-related parameters reflect the combined influence of α and vascular geometry. The TA experienced increased TAWSS and reduced OSI/RRT due to intensified flow acceleration around the concave region, while the AA exhibited lower TAWSS and higher OSI/RRT, consistent with the clinical patient data and prior hemodynamic studies on curvature-induced flow separation (55-59,63). Sensitivity to α was amplified in smaller aortic diameters, with large-diameter models showing more gradual responses. Notably, as α increased beyond 150°, TAWSS, OSI, and RRT exhibited sharply higher rates of change in both TA and AA, marking this range as a reference point where hemodynamic disruptions become more pronounced.

Energy loss follows a similar pattern that energy loss increased monotonically with α, with steeper rises beyond 150°. Patients with smaller aortic diameters or larger diameter differences between AA and DA experienced larger energy loss increases due to higher flow resistance and enhanced vortex formation. Although energy loss increased with larger angles, these changes were consistent with the accompanying alterations in pressure and flow rather than indicative of abnormal hemodynamic loading. This further underscores that angle selection must balance surgical feasibility with long-term hemodynamic performance.

When surgically feasible, α should be selected based on preoperative computed tomography measurements to ensure that all three supra-aortic branch ostia are fully encompassed by the concave opening, while avoiding excessively large α angles that could lead to significant alterations in branch flow rates and other hemodynamic parameters. This consideration is particularly critical in patients with smaller aortic diameters (e.g., D1 ≤30 mm) or larger diameter differences between AA and DA.

Limitations

This study provides valuable insights into CS system-associated hemodynamics and patient-specific selection guidance. However, several limitations remain: inlet conditions were based on literature rather than individualized data; the assumption of rigid vessel walls disregarded compliance; laminar flow was assumed despite potential local disturbances; and the mechanical response of the CS device was not considered. Future studies integrating patient-specific blood flow, FSI, turbulence sensing models, and device mechanical properties would significantly enhance the physiological realism and clinical relevance of research outcomes.

Conclusions

In this study, hemodynamic analyses were first conducted to numerically evaluate the therapeutic efficacy of the concave triple branched stent graft system (CS system) technique and to explore patient-specific scenarios of the CS system in clinical practice, thereby further improving the long-term therapeutic efficacy of the CS system in complex vascular disease management. Our findings show that the CS system effectively preserves SATs perfusion (improving flow by approximately 4%) while maintaining stable ascending aortic pressure and overall hemodynamic conditions under both normotensive and hypertensive states.

Device geometry and patient anatomy exert important modulating effects. Larger concave angles can enhance SAT perfusion but may also elevate pressure and alter wall-shear-related indices in the ascending aorta, with changes more pronounced when the concave angle increases beyond 150°. Hemodynamic impacts are greater in patients with smaller aortic diameters, suggesting that reducing the concave degree may be beneficial in such cases. Patients with larger AA/DA diameters or smaller diameter differences between AA and DA exhibit lower postoperative pressure, SAT perfusion, and energy loss. These observations underscore the value of geometry-guided and anatomy-informed customization to optimize CS system performance in complex aortic arch interventions.

Acknowledgments

None.

Footnote

Data Sharing Statement: Available at https://qims.amegroups.com/article/view/10.21037/qims-2025-2003/dss

Funding: This work was supported by the National Natural Science Foundation of China (grant Nos. 12202041, 82370493), National High Level Hospital Clinical Research Funding (No. 2024-GSP-TJ-3 & No.2022-GSP-QZ-2), and the Key Research and Development Plan of Yunnan Province Science and Technology Department (grant No. 202403AC100004).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-2003/coif). X.Z. reports funding from National Natural Science Foundation of China (grant No. 12202041). M.L. reports funding from National Natural Science Foundation of China (grant No. 82370493), National High Level Hospital Clinical Research Funding (Nos. 2024-GSP-TJ-3 and 2022-GSP-QZ-2), and Key Research and Development Plan of Yunnan Province Science and Technology Department (grant No. 202403AC100004). The other authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the Ethics Committees of The Second Xiangya Hospital of Central South University {approval No. [2022] Ethics Review [Medical Device] No. [005]}, Fuwai Hospital (approval Nos. 2022-K74-1; 2023-K3-1; 2023-K5-1), and Fuwai Yunnan Cardiovascular Hospital (approval No. 2023-030-01). Informed consent was taken from all the patients. All participating hospitals were informed of and agreed to the study.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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