Characteristics of Transition to Turbulence in a Thoracic Aorta Using Large Eddy Simulation

Characteristics of Transition to Turbulence in a Thoracic Aorta Using Large Eddy Simulation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Characteristics of Transition to Turbulence in a Thoracic Aorta Using Large Eddy Simulation Kuiyu Cheng, Shehnaz Akhtar, Kwan Yong Lee, Sang-Wook Lee This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4967194/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 25 Jan, 2025 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract This study employed Large Eddy Simulation (LES) with the wall-adapting local eddy-viscosity (WALE) model to investigate transitional flow characteristics in an idealized thoracic aortic model. The OpenFOAM solver pimpleFoam was used to simulate blood flow as an incompressible Newtonian fluid, with the aortic walls treated as rigid boundaries. Simulations were conducted for 30 cardiac cycles and ensemble averaging was employed to ensure statistically reliable results. Main hemodynamic parameters, such as velocity fields, turbulence intensity and wall shear stress (WSS) were analyzed throughout the circulatory system. Through 3D computational fluid dynamics (CFD) visualization, we explained the transition from laminar to turbulent flow and its development throughout the cardiac cycle. Results demonstrated that turbulence originates in the aortic arch following the peak systole phase and further develops in the aortic arch and descending aorta during the mid-deceleration and end-systole phases. The WSS at the aortic arch is relatively high, which may be related to the development of various diseases, such as type A aortic dissection and atherosclerosis. Physical sciences/Engineering Physical sciences/Engineering/Biomedical engineering Aortic arch Large eddy simulation OpenFOAM Laminar-turbulent transition Turbulence intensity Wall shear stress Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1. Introduction The aorta is the largest artery in the human body, characterized by extensive curvature. The ascending aorta originates from the left ventricle of the heart and extends down to the abdomen. The aortic arch consists of three main branches: the brachiocephalic artery (BCA), the left common carotid artery (LCCA), and the left subclavian artery (LSA). The descending thoracic aorta travels downward through the thoracic vertebrae 1 , 2 . Aorta serving as the main cardiac output is continuously exposed to high pulsatile pressure and shear stress, making it susceptible to biomechanical damage 3 . The complex velocity fluctuation in the aortic arch and descending thoracic aorta with a high Reynolds number can lead to a transition to turbulent flow 4 – 6 . Numerous in vivo studies have demonstrated that turbulence can develop in the healthy normal aorta. Ha et al. 7 used four-dimensional flow magnetic resonance imaging (4D Flow MRI) to quantify turbulent kinetic energy (TKE), a metric of turbulence intensity, in the aortas of two groups: young healthy individuals and older healthy individuals. Their study revealed that turbulent flow was present in the aortas of all subjects. Stein et al. 8 employed a hot film anemometer probe to measure point velocities in the ascending aorta of seven individuals with normal aortic valves and those with aortic valvular disease, confirming turbulent flow in both groups. Sundin et al. 9 , 10 suggested that while blood flow in the normal cardiovascular system is predominantly laminar, it operates close to the turbulence threshold. They also noted that high stress and elevated cardiac output can increase turbulence intensity in the healthy thoracic aorta. Arzani et al. 11 compared numerical predictions of turbulence intensity with in vivo measurements using time-resolved three-directional phase-contrast (PC) MRI data, demonstrating good agreement between MRI measurements and CFD-predictions of turbulence intensity. With the remarkable advancement of numerical ta valuables and computing power, computational fluid dynamics (CFD) has become valuable tool to understand the detailed complex blood flow fields, which are difficult or impossible to quantify using clinical imaging modalities. Shahcheraghi et al. 12 established the idealized symmetrical aorta model and computed the detailed flow field based on laminar flow assumption. They observed that velocity profiles were skewed towards the inner wall, with the extensive secondary flow motion in the aorta influenced by the presence of branches. Benim et al. 13 assumed Newtonian fluid and rigid wall conditions to simulate the human aorta, focusing on the aortic arch and its major branches under steady-state and pulsatile flow conditions using \(\:k-\omega\:\:\) SST turbulent model. Lantz et al. 6 applied in vivo flowrate waveform measured by MRI as the inlet boundary condition to quantify the human specific aortic flow with large eddy simulation (LES) and described the effects of turbulent fluctuations on wall shear stress (WSS). Casacuberta et al. 14 performed aortic simulation by using the OpenFOAM, and compared it with Ansys Fluent, while Zakaria et al. 15 investigated blood flow in the elderly man’s aorta using OpenFOAM with the LES k -equation eddy viscosity model and provided detailed visual results. However, transitional flow and highly turbulent flow conditions in aortic models have not been directly quantified by previous studies, indicating a significant area for further investigation. The complex boundaries of aortic models impose limitations on computational resources. Building on the findings of previous studies, the LES wall-adapting local eddy-viscosity (WALE) model is employed to investigate the development and extent of turbulence in the aorta under pulsatile flow conditions. The resulting maps, based on 3D model visualization, provide multi-scale and multi-view visualization images that accurately quantify the turbulence development and its extent. By analyzing multiple cardiac cycles, we provide insights into flow dynamics, turbulent features, flow patterns, and hemodynamic wall parameter such as WSS variations across different phases of the cardiac cycle, contributing significantly to cardiovascular research. 2. Numerical method 2.1 3D geometric model and computational mesh The aorta model was constructed based on the geometry of Shahcheraghi et al. 12 and Vasava et al. 16 using SolidWorks as shown in Fig. 1 . The geometric model is characterized by the extensive curvature for the ascending aorta and small torsional curvature in the descending thoracic aorta. In addition, three major branches such as the BCA, LCCA, and LSA are included. The diameter of the ascending aorta is 25 mm. The diameters of the BCA, LCCA, and LSA are 8.8 mm, 8.5 mm, and 9.9 mm, respectively. The computational domain was discretized into a free tetrahedral mesh, using ICEM-CFD. A coarse mesh was initially employed to validate the setup and identify areas requiring refinement. The mesh was progressively refined based on initial simulation results with the regions exhibiting high-velocity gradients and turbulence intensity. Near-wall refinement included 10 prism layers to accurately capture boundary layer effects and turbulence dynamics. Solver settings were adjusted to ensure stability and accuracy, with criteria including Y + below 0.5, maximum non-orthogonality below 60° (average 8°), maximum skewness of 0.6, and maximum aspect ratio of 8. High aspect ratio cells, typically observed in fine boundary layers, may reduce convergence speed without critically compromising solver stability. 2.2 Boundary conditions In this study, blood was modeled as an incompressible Newtonian fluid in the aorta, with a constant viscosity of 0.0035 Pa·s and a density of 1050 kg/m 3 . The no-slip condition was applied to the rigid wall. The pulsatile flowrate waveform, as shown in Fig. 2 was applied at the entrance of the aorta. For the flow division to the three major branch outlets, 10% of total flow was directed to the BCA outlet, while another 10% of the total flow was equally distributed between the LCCA and LSA outlet 17 . The pressure at the outlet of the descending aorta was set to 0. The mean Reynolds number is 1,492, with the maximum Reynolds number of 5,966 during peak systole. 2.3 LES model The LES was carried out with the wall-adapting local eddy-viscosity (WALE), which is one of the major subgrid-scale (SGS) models 18 . Although the WALE model is an algebraic eddy viscosity model, it is capable of handling transition to turbulent flow. The governing equations for incompressible fluid flow in LES are derived by filtering the Navier-Stokes equations as follows: $$\:\frac{\partial\:{\stackrel{-}{\varvec{u}}}_{\varvec{i}}}{\partial\:\varvec{t}}+{\stackrel{-}{\varvec{u}}}_{\varvec{j}}\frac{\partial\:{\stackrel{-}{\varvec{u}}}_{\varvec{i}}}{\partial\:{\varvec{x}}_{\varvec{j}}}=-\frac{1}{\varvec{\rho\:}}\frac{\partial\:\stackrel{-}{\varvec{p}}}{\partial\:{\varvec{x}}_{\varvec{i}}}+\varvec{\nu\:}\frac{{\partial\:}^{2}{\stackrel{-}{\varvec{u}}}_{\varvec{i}}}{\partial\:{\varvec{x}}_{\varvec{j}}\partial\:{\varvec{x}}_{\varvec{j}}}-\frac{\partial\:{\varvec{\tau\:}}_{\varvec{i}\varvec{j}}}{\partial\:{\varvec{x}}_{\varvec{j}}}$$ 1 where, the subgrid-scale Reynolds stress tensor is \(\:{\tau\:}_{ij}=\stackrel{-}{{u}_{i}{u}_{j}}-{\stackrel{-}{u}}_{i}{\stackrel{-}{u}}_{j}\) . This subgrid-scale Reynolds stress through the eddy viscosity hypothesis is computed as: $$\:{\tau\:}_{ij}-\frac{1}{3}{\tau\:}_{kk}{\delta\:}_{ij}=-2{\nu\:}_{\text{s}\text{g}\text{s}}{\stackrel{-}{S}}_{ij},\:\:\:\:\:\:\:\:\:\:{\stackrel{-}{S}}_{ij}=\frac{1}{2}\left(\frac{\partial\:{\stackrel{-}{u}}_{i}}{\partial\:{x}_{j}}+\frac{\partial\:{\stackrel{-}{u}}_{j}}{\partial\:{x}_{i}}\right)$$ 2 Here, \(\:{\delta\:}_{ij}\) is the Kronecker delta function. In the WALE model, the subgrid-scale eddy viscosity \(\:{\nu\:}_{\text{s}\text{g}\text{s}}\) is computed as: $$\:{\nu\:}_{\text{s}\text{g}\text{s}}={C}_{k}\varDelta\:\sqrt{{k}_{\text{s}\text{g}\text{s}}}$$ 3 where \(\:{C}_{k}\) is a model constant which set to 0.094 19 , and \(\:{k}_{\text{s}\text{g}\text{s}}\) is the subgrid-scale kinetic energy, which can be computed as follows: $$\:{k}_{\text{s}\text{g}\text{s}}={\left(\frac{{C}_{w}^{2}\varDelta\:}{{C}_{k}}\right)}^{2}\frac{{\left({S}_{ij}^{d}{S}_{ij}^{d}\right)}^{3}}{{\left({\left({\stackrel{-}{S}}_{ij}{\stackrel{-}{S}}_{ij}\right)}^{5/2}+{\left({S}_{ij}^{d}{S}_{ij}^{d}\right)}^{5/4}\right)}^{2}}$$ 4 where \(\:{C}_{w}\) is a constant that set to 0.5 6,18,19 . \(\:{S}_{ij}^{d}\) is the trace free symmetric part of the square of the velocity gradient tensor, computed as follows: $$\:{S}_{ij}^{d}=\frac{1}{2}\left(\frac{\partial\:{\stackrel{-}{u}}_{k}}{\partial\:{x}_{i}}\frac{\partial\:{\stackrel{-}{u}}_{j}}{\partial\:{x}_{k}}+\frac{\partial\:{\stackrel{-}{u}}_{k}}{\partial\:{x}_{j}}\frac{\partial\:{\stackrel{-}{u}}_{i}}{\partial\:{x}_{k}}\right)-\frac{1}{3}{\delta\:}_{ij}\frac{\partial\:{\stackrel{-}{u}}_{k}}{\partial\:{x}_{l}}\frac{\partial\:{\stackrel{-}{u}}_{l}}{\partial\:{x}_{k}}$$ 5 Finally substituting Eq. ( 4 ) into Eq. ( 3 ), that summarized as: $$\:{\nu\:}_{\text{s}\text{g}\text{s}}={\left({C}_{w}\varDelta\:\right)}^{2}\frac{{\left({S}_{ij}^{d}{S}_{ij}^{d}\right)}^{3/2}}{{\left({\stackrel{-}{S}}_{ij}{\stackrel{-}{S}}_{ij}\right)}^{5/2}+{\left({S}_{ij}^{d}{S}_{ij}^{d}\right)}^{5/4}}$$ 6 Temporal discretization was applied with a second-order backward Euler scheme, and the spatial discretization used second-order central differencing 6 . To reduce the computational time, initial conditions were set using the k-ω SST model with a lower uniform velocity corresponding to a Reynolds number of 67. Subsequently, a timestep of dt = 1.0 × 10 − 5 s was employed for LES over 30 cycles to average the data, maintaining a Courant-Friedrichs-Lewy (CFL) number below. Simulation was conducted using OpenFOAM 4.1 on the Nurion supercomputing system at Korea Institute of Science and Technology Information (KISTI) in Daejeon, Korea. The system features Intel Xeon 6148 (Skylake) processors with a computational performance of 1.536 TFLOPS and utilized 128 nodes for the simulation. 3. Results 3.1 Flow patterns Figure 3 shows the ensemble-averaged velocity distribution at four phases of the cardiac cycle: near peak systole, mid-deceleration phase, end-systole, and diastole (refer to Fig. 2 for corresponding time points). During peak systole, the flow remains predominantly laminar with minimal fluctuation, and the high-velocity zone is primarily situated near the inner wall. However, during the mid-deceleration phase, the flow becomes unstable, indicating a transition to turbulence. This is accompanied by a shift of the high-velocity zone to the outer wall, which can be attributed to Dean flow caused by the significant curvature of the aortic arch. The division of flow into three major branches induces instability, creating low-velocity zones on the proximal wall and high-velocity zones on the distal wall of the branches. This flow division is a pivotal factor in the inception of turbulent flow, with the degree of turbulence potentially contingent on the flow division ratio. In the end-systolic phase, velocity declines markedly, and flow becomes chaotic, exhibiting no dominant flow direction. This is clearer in Figs. 4 and 5 . Figures 4 and 5 illustrate the ensemble-averaged velocity contours in six distinct streamwise planes (refer to Fig. 1 for locations) and a three-dimensional representation of the velocity vectors, respectively. It is noteworthy that at the peak systolic phase, the flow is consistently oriented towards the inner wall throughout the descending aorta. This can be attributed to high Reynolds numbers in conjunction with accelerated flow. This behavior is in contrast to the typical Dean flow observed at low or medium Reynolds numbers, where the flow deviates towards the outer region of a curved pipe. Given this velocity pattern, it is anticipated that high WSS would occur on the inner wall during the peak systolic phase. During the mid-deceleration phase, flow begins to separate at the aortic arch, becoming unstable in the descending aorta. Note that the velocity vector size was magnified for better visualization due to the low velocity in end-systole (Fig. 5 (c)). During this phase, reverse flow and highly disturbed, complex flow patterns are observed. The flow patterns in the aortic arch are visualized through streamlines at four different phases of the cardiac cycle, as shown in Fig. 6 . During the acceleration phase, the helical flow begins from the ascending aorta and follows the inner wall of the aortic arch. As the flow transitions to the deceleration phase, the intensity of the helical flow decreases, and the highest velocity shifts towards the outer wall of the descending aorta. This shift leads to the formation of many small eddies along the inner wall of the aortic arch. At diastole, rotational and recirculating secondary flows are observed but are relatively small in magnitude. 3.2 Turbulence characteristics Figure 7 shows the eddy viscosity distribution at four different phases of cardiac cycle (refer to Fig. 2 for the corresponding time points), indicating the turbulence intensity. In the near peak systolic phase, the eddy viscosity is almost zero within the aorta, indicating laminar flow. However, the eddy viscosity is rather high in the major branches, particularly near the proximal wall of the branches, indicating stronger turbulence in the branches compared to the aortic arch. In the mid-deceleration phase, the eddy viscosity increases, suggesting the development of stronger turbulence in the inner wall of the aortic arch region, which remains high until the distal region of the descending aorta. By the end-systole, turbulence decreases, spreading more evenly throughout the aorta and mostly disappears by the diastolic phase. This is more evident in the transverse vorticity plot in Fig. 8 . In Fig. 8 (a), during peak systole, vorticity is predominantly observed in the three branches and the inner wall of the aortic arch, adhering closely to its curvature. In the branches, turbulence continues to propagate upwards, but due to the short length of the branches, the full effect of turbulence has not fully appeared. Initially, small-scale vortical structures exhibit well-organized laminar flow with uniform patterns. However, by the mid-deceleration phase, there is a transition from these organized and laminar patterns to larger and irregular vortical structures. The vortices at the inner wall of the aortic arch are notably large and concentrated. The branches of the arch significantly contribute to instability of flow resulting in development of small-scale vortices, facilitating their spread downward to the bottom of the descending aorta. During diastole, the strength of the vortices decreases and eventually disappears with returning to laminar flow. Time traces of velocity magnitude at six different locations (a)-(f), (Refer Fig. 1 for locations) are shown in Fig. 9 . We can roughly determine the location and intensity of the transitional flow fluctuations. Flow disturbance with random fluctuations are observed at locations (b)–(f), with the highest fluctuations at the distal point (c). Fluctuations were present only during the mid-deceleration and end-systole phases, with no significant disturbances during diastole. Note that the velocity amplitude at location (a) is greater than the velocity amplitude at locations (b)-(f), due to the dean flow which shifts the peak away from the centerline where the trace data were collected. This indicates that turbulence is likely to occur in the aortic arch during the mid-deceleration phase. 3.3 Wall shear stress Figure 10 depicts the WSS distribution at phases of the cardiac cycle: (a) near peak systole (t = 0.102 s), (b) mid-deceleration phase (t = 0.302 s), (c) end-systole (t = 0.502 s), and (d) diastole (t = 0.702 s). The peak value of WSS occurs at near peak systole followed by mid deceleration phase. During early peak systole, maximum WSS reaches up to 30 Pa, predominantly on the inner walls of the ascending aorta, gradually decreasing along its length. At the junction of the three branch outlets, WSS peaks between 7 to 11 Pa. Transitioning into the mid-deceleration phase, high WSS shifts towards the center of the aortic arch, with lower values observed along the inner walls of the aortic arch. During peak systole, the high-velocity zone is predominantly near the inner wall in laminar flow, correlating with the maximum WSS observed along the inner walls of the aorta. The transition to the mid-deceleration phase indicates unstable flow and a shift of high velocity towards the outer wall due to Dean flow induced by the large aortic arch curvature. This change in flow dynamics likely contributes to the redistribution of WSS towards the center of the wall during this phase (Fig. 3 a&b). In the diastolic phase, low and oscillating wall shear stresses are observed in the aortic arch and descending aorta. The cycle-averaged WSS distribution in Fig. 11 highlights elevated levels concentrated at the mid-anterior and inner posterior walls of the aortic arch. This distribution can be attributed to the strong helical flow pattern in the aortic arch. Furthermore, Fig. 11 reveals elevated WSS at the proximal segments of arterial branches, notably with the LSA exhibiting the highest values. 4. Discussion It is well established that the blood flow within a healthy aorta exhibits laminar flow, while the presence of turbulence is well-documented in patients with obstructive diseases in major vessels. However, catheter-based measurements in both human and canine studies have demonstrated that turbulence can develop in the aorta not only in the presence of disease but also with normal aortic valves 8 , 20 , 21 . Despite these observations, comprehensive description of turbulence in a healthy aorta has been lacking. In this study, LES was employed to investigate turbulent flow characteristics in an idealized thoracic aortic model, with the focus on analyzing turbulence development and its extent in the aorta. This research enhances the broader understanding of cardiovascular health and disease progression, particularly in relation to conditions such as aortic dissection, aortic aneurysm and atherosclerotic stenosis. By examining the mechanisms and extent of hemodynamic changes during the transition from laminar to turbulent flow, this research offers critical implications for clinical management and treatment strategies. In recent years, biomechanical research has increasingly focused on aortic flow through steady-state simulations employing various CFD models and patient-specific geometries of aortas 22 – 25 . While steady-state simulations show overall wall WSS behavior, they fail to capture the dynamic changes induced by pulsatile blood velocity, especially in regions such as the aortic arch and branch junctions 26 . These areas are significantly influenced by the acceleration phase where turbulent effects are pronounced, particularly at the curved section of the aorta. Some studies have considered the k-ε and k-ω models, which provide mean values of turbulence parameters and overall flow behavior 27 – 29 . However, small eddies in transitional flow increase WSS, potentially contributing to further aneurysm dilation, as the aorta adjusts its diameter to maintain shear stress below physiological thresholds 30 . In medical contexts with relatively high Reynolds numbers, high-resolution visualization and accuracy are crucial. Reynolds-Averaged Navier-Stokes (RANS) models are based solely on mean flow equations, relying on averaged quantities to approximate turbulence effects, which are the least computationally expensive turbulence modeling methods 31 . In contrast, Direct Numerical Simulation (DNS) represents the gold standard of simulation because it accounts for the effects of every scale of eddy when solving the flow equations. This approach maintains high fidelity by using computational cells smaller than or equal to the size of the smallest eddy, but it demands substantial computational resources 32 . DNS has been applied effectively in various studies: Dimakopoulos 33 performed a DNS analysis on a 2D stent-type aortic valve, while Lee et al. 34 used the spectral element method to simulate weakly turbulent flow in a patient-specific stenosed carotid bifurcation, predicting the complex flow field, turbulence levels, and distribution of hemodynamic parameters. Tullio et al. 35 conducted a detailed DNS flow analysis on an aortic bileaflet mechanical heart valve, verifying the strong agreement between DNS and experimental results. Despite its accuracy, DNS is limited by its high computational cost. LES, which resolves larger turbulent eddies while modeling smaller ones, offers a more computationally efficient alternative to DNS. This method captures most of the flow dynamics while significantly reducing computational costs compared to DNS. The LES conducted in our study provides detailed insights into the complex flow patterns in a generic thoracic aorta. During the acceleration phase, flow in the aorta is predominantly laminar from the ascending aorta to the aortic arch. However, during the mid-deceleration phase, there was a noticeable transition from well-organized laminar flow patterns observed during peak systole to small-scale irregular vortical structures. The aortic arch appears to be the beginning of the transition from laminar to turbulent flow. This transition is crucial, as it is characterized by high turbulence intensity and elevated shear stress, which can lead to potential vascular risks. High velocity fluctuations during this transition can lead to increased shear stress and vibrations in the aortic wall, potentially damaging the vessel and may contribute to vascular occlusion 36 . Our observations of complex vortices and reverse flow in the aortic arch during this transition are consistent with the findings of Fukuda et al. 37 from PIV experiments, demonstrating a similar flow pattern. Helical flow is observed in the ascending aorta through streamlines plots in our study. A similar helical flow pattern was also observed in MRI flow filed study by Kilner et al. 38 , and CFD study by Tse et al. 39 which validates our qualitative results. In our simulation results, WSS is highest during near-peak systole and mid-deceleration phase. The aortic arch exhibits significantly elevated WSS, measuring 2–5 times higher than surrounding areas. This elevated WSS can be a contributing factor to the development of aortic dissection. For type A dissection, which involves the ascending aorta and aortic arch, we observed high WSS at the proximal ascending aorta and the aortic arch. These coincide with the predilection sites for aortic dissection reported by Chi et al. 22 . High WSS is also observed at the proximal segments of the arterial branches. Notably LSA exhibits higher WSS compared to the BCA and LCCA, indicating a potentially higher risk of tearing at the LSA. Furthermore, the elevated WSS at the proximal segments of arterial branches is associated with typical locations reported for atherosclerotic lesions in the thoracic aorta 40 . For type B dissection, which typically affects the descending aorta, we observed high WSS at the entrance and distal location of the descending aorta. This high WSS is consistent with known high-risk sites for type B dissection. However, due to the complex nature of type B aortic dissection and the variability in patient-specific anatomy, while high WSS might contribute to wall thinning or increased biological stress, accurately quantifying and predicting the risk of type B aortic dissection remains challenging in healthy aortas 41 , 42 . In addition to aortic dissection, the regions of high WSS in our study, particularly near the aortic arch and branch bifurcations, may also be one of the contributing factors in the formation of aortic aneurysms. The persistent elevated WSS in these areas can lead to localized degeneration of the aortic wall, which, over time, may result in vessel wall dilation and an increased risk of aneurysm formation. The diffusion of vorticity during mid-deceleration and end-systole result in turbulent flow with repeated reverse flow, which leads to repeated oscillations of WSS. These oscillating can contribute to the development of atherosclerosis, as studies have shown that low-level and oscillating WSS can induce endothelial changes, contributing to plaque formation 43 – 45 , which may subsequently lead to thrombus formation 46 – 48 . In our study, WSS levels decrease significantly from systole to the beginning of diastole, with higher shear stress localized near the branches and the inner curvature of the aortic arch. These findings are consistent with the LES results of Lantz et al. 6 . Despite the comprehensive insights gained from our study, several limitations should be noted. Our study does not account for individual variations in aortic anatomy. While patient-specific models offer precise representations of individual anatomy, they may not be as widely applicable. An idealized model, such as ours, offers general insights that can be relevant to a broad range of individuals. Our model assumes rigid walls and a Newtonian fluid. While the rigid wall assumption may not fully capture the dynamic interactions between the flow and the vessel wall, Alimohammadi et al. 49 noted that this assumption in CFD can slightly overestimate WSS. However, it does not significantly alter the overall WSS distribution. Although non-Newtonian and Newtonian fluids exhibit different behaviors, many studies have shown similar vortex structures and WSS distributions for both type of fluids, with the main differences primarily observed in low Reynolds number regions. Therefore, the Newtonian fluid assumption is appropriate for simulating flow in arteries with high Reynolds numbers 50 – 52 . Lastly, we used a predefined flow division (10% of the total flow was directed to the BCA, and 10% was equally divided between the LCCA and LSA). This approach may not fully reflect the natural variations in flow distribution among individuals. Anatomical differences can result in varying flow distribution, and incorporating subject-specific flow data could provide a more accurate representation of the blood flow dynamics within the aorta. 5. Conclusion In this study, we used LES to investigate the transition from laminar to turbulent flow in an idealized thoracic aortic model, with the focus on analyzing turbulence development and its extent in the aorta. It was observed that turbulence is present in a healthy aorta, particularly in the aortic arch and descending aorta. As turbulence develops, it induces oscillatory and secondary flows, which affect the intensity and distribution of WSS. This study enhance the fundamental understanding of transition to turbulent flow, highlighting its dependence on aorta geometry under pulsatile flow conditions. Future work could involve applying DNS to patient-specific models to extend these findings, including a detailed comparison of hemodynamic characteristics and further exploration of turbulence variations in patient-specific models. Declarations Author Contributions Statement Kuiyu Cheng, Kwan Yong Lee, and Sang-Wook Lee contributed to the conception and design of the study. Kuiyu Cheng performed the simulation and the statistical analysis for the study. Kuiyu Cheng, Shehnaz Akhtar, and Sang Wook Lee wrote the first draft of the manuscript. Shehnaz Akhtar, Kwan Yong Lee and Sang-Wook Lee revised it critically for important intellectual content. All authors contributed to the manuscript revision, read, and approved the submitted version. Acknowledgements This research was supported by the Basic Science Research Program, funded by the National Research Foundation of Korea (NRF). (2020R1I1A3066617) Data Availability The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. References Maton, A. et al. Human Biology Health (Prentice Hall, 1995). Drake, R. L., Vogl, W. & Adam, W. M. Mitchell & Henry Gray. Gray’s Anatomy for Students 2nd edn (Churchill Livingstone (Elsevier, 2010). Matsuzawa, T., Gao, F., Qiao, A., Ohta, O. & Ok, H. 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Evaluating uncertainties in CFD simulations of patient-specific aorta models using Grid Convergence Index method. Mech. Res. Commun. 133 , 104188 (2023). Perinajová, R. et al. Geometrically induced wall shear stress variability in CFD-MRI coupled simulations of blood flow in the thoracic aortas. Comput. Biol. Med. 133 , (2021). Vinoth, R. et al. Steady and transient flow CFD simulations in an aorta model of normal and aortic aneurysm subjects vol. 50629–43 (Springer, 2019). in Lecture Notes in Electrical Engineering. Kousera, C. A. et al. A numerical study of aortic flow stability and comparison with in vivo flow measurements. J. Biomech. Eng. 135 , (2013). Khanafer, K. M., Bull, J. L. & Berguer, R. Fluid-structure interaction of turbulent pulsatile flow within a flexible wall axisymmetric aortic aneurysm model. Eur. J. Mech. B. Fluids . 28 , 88–102 (2009). Khanafer, K. M., Bull, J. L., Upchurch, G. R. & Berguer, R. Turbulence Significantly Increases Pressure and Fluid Shear Stress in an Aortic Aneurysm Model under Resting and Exercise Flow Conditions. Ann. Vasc Surg. 21 , 67–74 (2007). Ryo et al. Investigations into the Potential of Using Open Source CFD to Analyze the Differences in Hemodynamic Parameters for Aortic Dissections (Healthy versus Stanford Type A and B). Ann. Vasc Surg. 79 , 310–323 (2022). Giddens, D. P., Zarins, C. K. & Glagov, S. Response of Arteries to Near-Wall Fluid Dynamic Behavior. Appl. Mech. Rev. 43 , S98–S102 (1990). Wolfgang, R. Turbulence Modeling and Simulation in Hydraulics: A Historical Review. J. Hydraul. Eng. 143 , 03117001 (2017). Tiselj, I., Flageul, C., Oder, J. & Flageul, C. Direct Numerical Simulation and Wall-Resolved Large Eddy Simulation in Nuclear Thermal Hydraulics. Nucl. Technol. 1–15 10.1080/00295450.2019.1614381ï (2019). Dimakopoulos, Y., Bogaerds, A. C. B., Anderson, P. D., Hulsen, M. A. & Baaijens, F. P. T. Direct numerical simulation of a 2D-stented aortic heart valve at physiological flow rates. Comput. Methods Biomech. Biomed. Engin . 15 , 1157–1179 (2012). Lee, S. E., Lee, S. W., Fischer, P. F., Bassiouny, H. S. & Loth, F. Direct numerical simulation of transitional flow in a stenosed carotid bifurcation. J. Biomech. 41 , 2551–2561 (2008). De Tullio, M. D., Cristallo, A., Balaras, E. & Verzicco, R. Direct numerical simulation of the pulsatile flow through an aortic bileaflet mechanical heart valve. J. Fluid Mech. 622 , 259–290 (2009). Asbury, C. L., Ruberti, J. W., Bluth, E. I. & Peattie, R. A. Experimental investigation of steady flow in rigid models of abdominal aortic aneurysms. Ann. Biomed. Eng. 23 , 29–39 (1995). Fukuda, I. et al. Breakdown of Atheromatous Plaque Due to Shear Force From Arterial Perfusion Cannula. Ann. Thorac. Surg. 84 , e17–e18 (2007). Kilner, P. J., Yang, G. Z., Mohiaddin, R. H., Firmin, D. N. & Longmore, D. B. Helical and retrograde secondary flow patterns in the aortic arch studied by three-directional magnetic resonance velocity mapping. Circulation . 88 , 2235–2247 (1993). Tse, K. M. et al. A computational fluid dynamics study on geometrical influence of the aorta on haemodynamics. Eur. J. Cardiothorac. Surg. 43 , 829–838 (2013). Wasilewski, J., Głowacki, J. & Poloński, L. Not at random location of atherosclerotic lesions in thoracic aorta and their prognostic significance in relation to the risk of cardiovascular events. Polish Journal of Radiology vol. 78 38–42 Preprint at (2013). https://doi.org/10.12659/PJR.883944 Marrocco-Trischitta, M. M. et al. Prevalence of type III arch configuration in patients with type B aortic dissection. Eur. J. Cardiothorac. Surg. 56 , 1075–1080 (2019). Wen, J. et al. Risk evaluation of type B aortic dissection based on WSS-based indicators distribution in different types of aortic arch. Comput. Methods Programs Biomed. 221 , (2022). Burris, N. S. & Hope, M. D. 4D Flow MRI Applications for Aortic Disease. Magn. Reson. Imaging Clin. N Am. 23 , 15–23 (2015). Cheng, C. et al. Atherosclerotic Lesion Size and Vulnerability Are Determined by Patterns of Fluid Shear Stress. Circulation . 113 , 2744–2753 (2006). Slager, C. J. et al. The role of shear stress in the generation of rupture-prone vulnerable plaques. Nat. Clin. Pract. Cardiovasc. Med. 2 , 401–407 (2005). Motomiya, M. & Karino, T. Flow patterns in the human carotid artery bifurcation. Stroke . 15 , 50–56 (1984). Giddens, D. P., Mabon, R. F. & Cassanova, R. A. Measurements of disordered flows distal to subtotal vascular stenoses in the thoracic aortas of dogs. Circ. Res. 39 , 112–119 (1976). Lee, B. K. et al. Hemodynamic Effects on Atherosclerosis-Prone Coronary Artery: Wall Shear Stress / Rate Distribution and Impedance Phase Angle in Coronary and Aortic Circulation. Yonsei Med. J. 42 , 375 (2001). Alimohammadi, M., Agu, O., Balabani, S. & Díaz-Zuccarini, V. Development of a patient-specific simulation tool to analyse aortic dissections: Assessment of mixed patient-specific flow and pressure boundary conditions. Med. Eng. Phys. 36 , 275–284 (2014). Guerciotti, B. & Vergara, C. Computational comparison between Newtonian and non-Newtonian blood rheologies in stenotic vessels vol. 84169–183 (Springer, 2018). in Lecture Notes in Applied and Computational Mechanics. Dutra, R. F., Zinani, F. S. F., Rocha, L. A. O. & Biserni, C. Effect of non-Newtonian fluid rheology on an arterial bypass graft: A numerical investigation guided by constructal design. Comput. Methods Programs Biomed. 201 , 105944 (2021). Keslerová, R. Numerical modeling of generalized Newtonian fluids flow in S-type geometry of bypass. J. Comput. Appl. Math. 429 , 115237 (2023). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 25 Jan, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 23 Sep, 2024 Reviews received at journal 19 Sep, 2024 Reviews received at journal 10 Sep, 2024 Reviewers agreed at journal 29 Aug, 2024 Reviewers agreed at journal 28 Aug, 2024 Reviewers invited by journal 28 Aug, 2024 Editor assigned by journal 28 Aug, 2024 Editor invited by journal 27 Aug, 2024 Submission checks completed at journal 26 Aug, 2024 First submitted to journal 24 Aug, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4967194","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":357729700,"identity":"5c75ea43-c503-42e9-a13d-b865140922a3","order_by":0,"name":"Kuiyu Cheng","email":"","orcid":"","institution":"University of Ulsan","correspondingAuthor":false,"prefix":"","firstName":"Kuiyu","middleName":"","lastName":"Cheng","suffix":""},{"id":357729701,"identity":"efa4d188-3d08-4d67-b0aa-6ab457865985","order_by":1,"name":"Shehnaz Akhtar","email":"","orcid":"","institution":"University of Ulsan","correspondingAuthor":false,"prefix":"","firstName":"Shehnaz","middleName":"","lastName":"Akhtar","suffix":""},{"id":357729702,"identity":"c4fd3393-a030-41aa-a670-d962b65d1bae","order_by":2,"name":"Kwan Yong Lee","email":"","orcid":"","institution":"Seoul St. Mary’s Hospital","correspondingAuthor":false,"prefix":"","firstName":"Kwan","middleName":"Yong","lastName":"Lee","suffix":""},{"id":357729703,"identity":"1f359d35-e495-4ef3-a5a4-f859e002def8","order_by":3,"name":"Sang-Wook Lee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAw0lEQVRIiWNgGAWjYBACPjBZwSADEzAgqIUNTJ5h4CFRC2MbSVrYmw9/5p13mEe+/ewBhh81DMbmDYS08BxLk+bddpjH4ExeAmPPMQYzmQOEtEjkmDHngrQw5Bgw8DYw2EgQdJj8+8+fc+cAHdb/xoDxL1FaJHgYpHMbDvMw3MgxYAbaYkZYC0+amfSfY+k8BjfeGByWOSZhTFALP/vhxx9n1FjLyffnGD58U2NjOIOQFhRwgIGBoB2jYBSMglEwCogBAENOM+01MJyaAAAAAElFTkSuQmCC","orcid":"","institution":"University of Ulsan","correspondingAuthor":true,"prefix":"","firstName":"Sang-Wook","middleName":"","lastName":"Lee","suffix":""}],"badges":[],"createdAt":"2024-08-24 04:44:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4967194/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4967194/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-86983-z","type":"published","date":"2025-01-25T15:58:01+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":65257035,"identity":"ee6e7431-2cb4-493f-95d8-0ca5ef241610","added_by":"auto","created_at":"2024-09-25 10:04:35","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":81707,"visible":true,"origin":"","legend":"\u003cp\u003eThe ideal aortic arch model. The insects denote the cross-sectional slices for velocity variation from A-A to F-F and the axial position of the velocity time traces (a)-(f).\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4967194/v1/231e8f931d6ae574f6dc3856.png"},{"id":65257989,"identity":"36732ac9-ac39-4794-8f02-c5b60805ed33","added_by":"auto","created_at":"2024-09-25 10:12:35","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":267738,"visible":true,"origin":"","legend":"\u003cp\u003eThe pulsatile flow waveform for inlet boundary condition.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4967194/v1/3f05b41c3ec73801a913b35d.jpeg"},{"id":65257039,"identity":"395dd6c8-6ad1-4ee8-8685-711557903284","added_by":"auto","created_at":"2024-09-25 10:04:35","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":101569,"visible":true,"origin":"","legend":"\u003cp\u003eEnsemble-averaged velocity profiles on the mid-planes at various flow phases: (a) near peak systole (\u003cem\u003et\u003c/em\u003e= 0.102 s), (b) mid-deceleration phase (\u003cem\u003et\u003c/em\u003e = 0.302 s), (c) end-systole (\u003cem\u003et\u003c/em\u003e= 0.502 s), and (d) diastole \u003cem\u003e(t\u003c/em\u003e = 0.702 s). Refer to Fig. 2 for the corresponding time points.\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4967194/v1/688dfd44aa43ce4208c96856.jpeg"},{"id":65257044,"identity":"7304a8d3-5808-4189-9400-233fd581ff65","added_by":"auto","created_at":"2024-09-25 10:04:36","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":597239,"visible":true,"origin":"","legend":"\u003cp\u003eEnsemble-averaged velocity distribution at six cross sections in axial direction: (a) near peak systole (\u003cem\u003et\u003c/em\u003e= 0.102 s), (b) mid-deceleration phase (\u003cem\u003et\u003c/em\u003e = 0.302 s), and (c) end-systole (\u003cem\u003et\u003c/em\u003e = 0.502 s). Refer to Fig. 2 for the corresponding time points.\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4967194/v1/12512a3c817d099f9fdf40fe.jpeg"},{"id":65257991,"identity":"dac773c7-9556-46ec-9576-de2924fef374","added_by":"auto","created_at":"2024-09-25 10:12:36","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":496737,"visible":true,"origin":"","legend":"\u003cp\u003eInstantaneous velocity vector at various flow phases: (a) near peak systole (\u003cem\u003et\u003c/em\u003e = 0.102 s), (b) mid-deceleration phase (\u003cem\u003et\u003c/em\u003e = 0.302 s), (c) end-systole (\u003cem\u003et\u003c/em\u003e= 0.502 s), and (d) diastole \u003cem\u003e(t\u003c/em\u003e = 0.702 s). Refer to Fig. 2 for the corresponding time points.\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4967194/v1/f5a224c61ca4f8384b3f3729.jpeg"},{"id":65257043,"identity":"2f979376-0db6-4a51-a0d3-c7031288ddbf","added_by":"auto","created_at":"2024-09-25 10:04:36","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":848995,"visible":true,"origin":"","legend":"\u003cp\u003eStreamlines at various flow phases: (a) near peak systole (\u003cem\u003et\u003c/em\u003e = 0.102 s), (b) mid-deceleration phase (\u003cem\u003et\u003c/em\u003e = 0.302 s), (c) end-systole (\u003cem\u003et\u003c/em\u003e = 0.502 s), and (d) diastole \u003cem\u003e(t\u003c/em\u003e= 0.702 s). Refer to Fig. 2 for the corresponding time points.\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4967194/v1/f1c2c12c8bf1212ae7f24089.jpeg"},{"id":65258221,"identity":"ef57cc10-ae0a-4e0a-80cd-0eb297cfecce","added_by":"auto","created_at":"2024-09-25 10:20:35","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":103652,"visible":true,"origin":"","legend":"\u003cp\u003eSubgrid-scale eddy viscosity \u0026nbsp;vsgs on the mid-planes at various flow phases: (a) near peak systole (\u003cem\u003et\u003c/em\u003e = 0.102 s), (b) mid-deceleration phase (\u003cem\u003et\u003c/em\u003e = 0.302 s), (c) end-systole (\u003cem\u003et\u003c/em\u003e = 0.502 s), and (d) diastole \u003cem\u003e(t\u003c/em\u003e= 0.702 s). Refer to Fig. 2 for the corresponding time points.\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4967194/v1/f99cea35ad81e1bb50bf3322.jpeg"},{"id":65257036,"identity":"7c46f0f9-6d0a-4681-8126-8cca708a8441","added_by":"auto","created_at":"2024-09-25 10:04:35","extension":"jpeg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":93705,"visible":true,"origin":"","legend":"\u003cp\u003eTransverse vorticity distribution on the mid-planes at various flow phases: (a) near peak systole (\u003cem\u003et\u003c/em\u003e = 0.102 s), (b) mid-deceleration phase (\u003cem\u003et\u003c/em\u003e = 0.302 s), (c) end-systole (\u003cem\u003et\u003c/em\u003e= 0.502 s), and (d) diastole \u003cem\u003e(t\u003c/em\u003e = 0.702 s). Refer to Fig. 2 for the corresponding time points.\u003c/p\u003e","description":"","filename":"floatimage8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4967194/v1/7771becc59e7c98f232fa3cc.jpeg"},{"id":65257045,"identity":"19159e63-9972-4962-83c0-ea3b9e12beba","added_by":"auto","created_at":"2024-09-25 10:04:36","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":96386,"visible":true,"origin":"","legend":"\u003cp\u003eTime traces of velocity magnitude at six streamwise locations (see Fig. 1) for four cardiac cycles.\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-4967194/v1/2583ef5ab44f64986adfc8c1.png"},{"id":65257042,"identity":"68a32c55-2670-447b-a0c9-c7bcc118c0b8","added_by":"auto","created_at":"2024-09-25 10:04:36","extension":"jpeg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":117025,"visible":true,"origin":"","legend":"\u003cp\u003eEnsemble-averaged WSS distribution at various flow phases: (a) near peak systole (\u003cem\u003et\u003c/em\u003e = 0.102 s), (b) mid-deceleration phase (\u003cem\u003et\u003c/em\u003e = 0.302 s), (c) end-systole (\u003cem\u003et\u003c/em\u003e= 0.502 s), and (d) diastole \u003cem\u003e(t\u003c/em\u003e = 0.702 s). Refer to Fig. 2 for the corresponding time points.\u003c/p\u003e","description":"","filename":"floatimage10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4967194/v1/b3301bb56f615435d6ac5f21.jpeg"},{"id":65257040,"identity":"037c771b-e3ff-4661-ae3e-eaf502cd87c2","added_by":"auto","created_at":"2024-09-25 10:04:35","extension":"jpeg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":56841,"visible":true,"origin":"","legend":"\u003cp\u003eCycle-averaged WSS distribution.\u003c/p\u003e","description":"","filename":"floatimage11.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4967194/v1/96a3115167036aee0fee4948.jpeg"},{"id":74858493,"identity":"de208cff-f193-4d3a-9550-a74fc064d884","added_by":"auto","created_at":"2025-01-27 16:10:20","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3554475,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4967194/v1/dcac6ad0-0505-4626-b49c-a0f6eaabb392.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Characteristics of Transition to Turbulence in a Thoracic Aorta Using Large Eddy Simulation","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe aorta is the largest artery in the human body, characterized by extensive curvature. The ascending aorta originates from the left ventricle of the heart and extends down to the abdomen. The aortic arch consists of three main branches: the brachiocephalic artery (BCA), the left common carotid artery (LCCA), and the left subclavian artery (LSA). The descending thoracic aorta travels downward through the thoracic vertebrae \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Aorta serving as the main cardiac output is continuously exposed to high pulsatile pressure and shear stress, making it susceptible to biomechanical damage \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. The complex velocity fluctuation in the aortic arch and descending thoracic aorta with a high Reynolds number can lead to a transition to turbulent flow \u003csup\u003e\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eNumerous in vivo studies have demonstrated that turbulence can develop in the healthy normal aorta. Ha et al. \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e used four-dimensional flow magnetic resonance imaging (4D Flow MRI) to quantify turbulent kinetic energy (TKE), a metric of turbulence intensity, in the aortas of two groups: young healthy individuals and older healthy individuals. Their study revealed that turbulent flow was present in the aortas of all subjects. Stein et al. \u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e employed a hot film anemometer probe to measure point velocities in the ascending aorta of seven individuals with normal aortic valves and those with aortic valvular disease, confirming turbulent flow in both groups. Sundin et al. \u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e suggested that while blood flow in the normal cardiovascular system is predominantly laminar, it operates close to the turbulence threshold. They also noted that high stress and elevated cardiac output can increase turbulence intensity in the healthy thoracic aorta. Arzani et al. \u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e compared numerical predictions of turbulence intensity with in vivo measurements using time-resolved three-directional phase-contrast (PC) MRI data, demonstrating good agreement between MRI measurements and CFD-predictions of turbulence intensity.\u003c/p\u003e \u003cp\u003eWith the remarkable advancement of numerical ta valuables and computing power, computational fluid dynamics (CFD) has become valuable tool to understand the detailed complex blood flow fields, which are difficult or impossible to quantify using clinical imaging modalities. Shahcheraghi et al. \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e established the idealized symmetrical aorta model and computed the detailed flow field based on laminar flow assumption. They observed that velocity profiles were skewed towards the inner wall, with the extensive secondary flow motion in the aorta influenced by the presence of branches. Benim et al. \u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e assumed Newtonian fluid and rigid wall conditions to simulate the human aorta, focusing on the aortic arch and its major branches under steady-state and pulsatile flow conditions using \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:k-\\omega\\:\\:\\)\u003c/span\u003e\u003c/span\u003eSST turbulent model. Lantz et al. \u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e applied in vivo flowrate waveform measured by MRI as the inlet boundary condition to quantify the human specific aortic flow with large eddy simulation (LES) and described the effects of turbulent fluctuations on wall shear stress (WSS). Casacuberta et al. \u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e performed aortic simulation by using the OpenFOAM, and compared it with Ansys Fluent, while Zakaria et al. \u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e investigated blood flow in the elderly man\u0026rsquo;s aorta using OpenFOAM with the LES \u003cem\u003ek\u003c/em\u003e-equation eddy viscosity model and provided detailed visual results. However, transitional flow and highly turbulent flow conditions in aortic models have not been directly quantified by previous studies, indicating a significant area for further investigation. The complex boundaries of aortic models impose limitations on computational resources. Building on the findings of previous studies, the LES wall-adapting local eddy-viscosity (WALE) model is employed to investigate the development and extent of turbulence in the aorta under pulsatile flow conditions. The resulting maps, based on 3D model visualization, provide multi-scale and multi-view visualization images that accurately quantify the turbulence development and its extent. By analyzing multiple cardiac cycles, we provide insights into flow dynamics, turbulent features, flow patterns, and hemodynamic wall parameter such as WSS variations across different phases of the cardiac cycle, contributing significantly to cardiovascular research.\u003c/p\u003e"},{"header":"2. Numerical method","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 3D geometric model and computational mesh\u003c/h2\u003e \u003cp\u003eThe aorta model was constructed based on the geometry of Shahcheraghi et al. \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e and Vasava et al. \u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e using SolidWorks as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The geometric model is characterized by the extensive curvature for the ascending aorta and small torsional curvature in the descending thoracic aorta. In addition, three major branches such as the BCA, LCCA, and LSA are included. The diameter of the ascending aorta is 25 mm. The diameters of the BCA, LCCA, and LSA are 8.8 mm, 8.5 mm, and 9.9 mm, respectively.\u003c/p\u003e \u003cp\u003eThe computational domain was discretized into a free tetrahedral mesh, using ICEM-CFD. A coarse mesh was initially employed to validate the setup and identify areas requiring refinement. The mesh was progressively refined based on initial simulation results with the regions exhibiting high-velocity gradients and turbulence intensity. Near-wall refinement included 10 prism layers to accurately capture boundary layer effects and turbulence dynamics. Solver settings were adjusted to ensure stability and accuracy, with criteria including Y\u0026thinsp;+\u0026thinsp;below 0.5, maximum non-orthogonality below 60\u0026deg; (average 8\u0026deg;), maximum skewness of 0.6, and maximum aspect ratio of 8. High aspect ratio cells, typically observed in fine boundary layers, may reduce convergence speed without critically compromising solver stability.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Boundary conditions\u003c/h2\u003e \u003cp\u003eIn this study, blood was modeled as an incompressible Newtonian fluid in the aorta, with a constant viscosity of 0.0035 Pa\u0026middot;s and a density of 1050 kg/m\u003csup\u003e3\u003c/sup\u003e. The no-slip condition was applied to the rigid wall. The pulsatile flowrate waveform, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e2\u003c/span\u003e was applied at the entrance of the aorta. For the flow division to the three major branch outlets, 10% of total flow was directed to the BCA outlet, while another 10% of the total flow was equally distributed between the LCCA and LSA outlet \u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. The pressure at the outlet of the descending aorta was set to 0. The mean Reynolds number is 1,492, with the maximum Reynolds number of 5,966 during peak systole.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 LES model\u003c/h2\u003e \u003cp\u003eThe LES was carried out with the wall-adapting local eddy-viscosity (WALE), which is one of the major subgrid-scale (SGS) models \u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Although the WALE model is an algebraic eddy viscosity model, it is capable of handling transition to turbulent flow. The governing equations for incompressible fluid flow in LES are derived by filtering the Navier-Stokes equations as follows:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\frac{\\partial\\:{\\stackrel{-}{\\varvec{u}}}_{\\varvec{i}}}{\\partial\\:\\varvec{t}}+{\\stackrel{-}{\\varvec{u}}}_{\\varvec{j}}\\frac{\\partial\\:{\\stackrel{-}{\\varvec{u}}}_{\\varvec{i}}}{\\partial\\:{\\varvec{x}}_{\\varvec{j}}}=-\\frac{1}{\\varvec{\\rho\\:}}\\frac{\\partial\\:\\stackrel{-}{\\varvec{p}}}{\\partial\\:{\\varvec{x}}_{\\varvec{i}}}+\\varvec{\\nu\\:}\\frac{{\\partial\\:}^{2}{\\stackrel{-}{\\varvec{u}}}_{\\varvec{i}}}{\\partial\\:{\\varvec{x}}_{\\varvec{j}}\\partial\\:{\\varvec{x}}_{\\varvec{j}}}-\\frac{\\partial\\:{\\varvec{\\tau\\:}}_{\\varvec{i}\\varvec{j}}}{\\partial\\:{\\varvec{x}}_{\\varvec{j}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere, the subgrid-scale Reynolds stress tensor is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\tau\\:}_{ij}=\\stackrel{-}{{u}_{i}{u}_{j}}-{\\stackrel{-}{u}}_{i}{\\stackrel{-}{u}}_{j}\\)\u003c/span\u003e\u003c/span\u003e. This subgrid-scale Reynolds stress through the eddy viscosity hypothesis is computed as:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{\\tau\\:}_{ij}-\\frac{1}{3}{\\tau\\:}_{kk}{\\delta\\:}_{ij}=-2{\\nu\\:}_{\\text{s}\\text{g}\\text{s}}{\\stackrel{-}{S}}_{ij},\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:{\\stackrel{-}{S}}_{ij}=\\frac{1}{2}\\left(\\frac{\\partial\\:{\\stackrel{-}{u}}_{i}}{\\partial\\:{x}_{j}}+\\frac{\\partial\\:{\\stackrel{-}{u}}_{j}}{\\partial\\:{x}_{i}}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eHere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\delta\\:}_{ij}\\)\u003c/span\u003e\u003c/span\u003e is the Kronecker delta function. In the WALE model, the subgrid-scale eddy viscosity \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\nu\\:}_{\\text{s}\\text{g}\\text{s}}\\)\u003c/span\u003e\u003c/span\u003e is computed as:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{\\nu\\:}_{\\text{s}\\text{g}\\text{s}}={C}_{k}\\varDelta\\:\\sqrt{{k}_{\\text{s}\\text{g}\\text{s}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{k}\\)\u003c/span\u003e\u003c/span\u003e is a model constant which set to 0.094 \u003csup\u003e19\u003c/sup\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{k}_{\\text{s}\\text{g}\\text{s}}\\)\u003c/span\u003e\u003c/span\u003e is the subgrid-scale kinetic energy, which can be computed as follows:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{k}_{\\text{s}\\text{g}\\text{s}}={\\left(\\frac{{C}_{w}^{2}\\varDelta\\:}{{C}_{k}}\\right)}^{2}\\frac{{\\left({S}_{ij}^{d}{S}_{ij}^{d}\\right)}^{3}}{{\\left({\\left({\\stackrel{-}{S}}_{ij}{\\stackrel{-}{S}}_{ij}\\right)}^{5/2}+{\\left({S}_{ij}^{d}{S}_{ij}^{d}\\right)}^{5/4}\\right)}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{w}\\)\u003c/span\u003e\u003c/span\u003e is a constant that set to 0.5 \u003csup\u003e6,18,19\u003c/sup\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{S}_{ij}^{d}\\)\u003c/span\u003e\u003c/span\u003e is the trace free symmetric part of the square of the velocity gradient tensor, computed as follows:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{S}_{ij}^{d}=\\frac{1}{2}\\left(\\frac{\\partial\\:{\\stackrel{-}{u}}_{k}}{\\partial\\:{x}_{i}}\\frac{\\partial\\:{\\stackrel{-}{u}}_{j}}{\\partial\\:{x}_{k}}+\\frac{\\partial\\:{\\stackrel{-}{u}}_{k}}{\\partial\\:{x}_{j}}\\frac{\\partial\\:{\\stackrel{-}{u}}_{i}}{\\partial\\:{x}_{k}}\\right)-\\frac{1}{3}{\\delta\\:}_{ij}\\frac{\\partial\\:{\\stackrel{-}{u}}_{k}}{\\partial\\:{x}_{l}}\\frac{\\partial\\:{\\stackrel{-}{u}}_{l}}{\\partial\\:{x}_{k}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFinally substituting Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) into Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), that summarized as:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{\\nu\\:}_{\\text{s}\\text{g}\\text{s}}={\\left({C}_{w}\\varDelta\\:\\right)}^{2}\\frac{{\\left({S}_{ij}^{d}{S}_{ij}^{d}\\right)}^{3/2}}{{\\left({\\stackrel{-}{S}}_{ij}{\\stackrel{-}{S}}_{ij}\\right)}^{5/2}+{\\left({S}_{ij}^{d}{S}_{ij}^{d}\\right)}^{5/4}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eTemporal discretization was applied with a second-order backward Euler scheme, and the spatial discretization used second-order central differencing \u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. To reduce the computational time, initial conditions were set using the \u003cem\u003ek-ω\u003c/em\u003e SST model with a lower uniform velocity corresponding to a Reynolds number of 67. Subsequently, a timestep of dt\u0026thinsp;=\u0026thinsp;1.0 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e s was employed for LES over 30 cycles to average the data, maintaining a Courant-Friedrichs-Lewy (CFL) number below. Simulation was conducted using OpenFOAM 4.1 on the Nurion supercomputing system at Korea Institute of Science and Technology Information (KISTI) in Daejeon, Korea. The system features Intel Xeon 6148 (Skylake) processors with a computational performance of 1.536 TFLOPS and utilized 128 nodes for the simulation.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Flow patterns\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the ensemble-averaged velocity distribution at four phases of the cardiac cycle: near peak systole, mid-deceleration phase, end-systole, and diastole (refer to Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e2\u003c/span\u003e for corresponding time points). During peak systole, the flow remains predominantly laminar with minimal fluctuation, and the high-velocity zone is primarily situated near the inner wall. However, during the mid-deceleration phase, the flow becomes unstable, indicating a transition to turbulence. This is accompanied by a shift of the high-velocity zone to the outer wall, which can be attributed to Dean flow caused by the significant curvature of the aortic arch. The division of flow into three major branches induces instability, creating low-velocity zones on the proximal wall and high-velocity zones on the distal wall of the branches. This flow division is a pivotal factor in the inception of turbulent flow, with the degree of turbulence potentially contingent on the flow division ratio. In the end-systolic phase, velocity declines markedly, and flow becomes chaotic, exhibiting no dominant flow direction. This is clearer in Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Figures\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrate the ensemble-averaged velocity contours in six distinct streamwise planes (refer to Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e1\u003c/span\u003e for locations) and a three-dimensional representation of the velocity vectors, respectively. It is noteworthy that at the peak systolic phase, the flow is consistently oriented towards the inner wall throughout the descending aorta. This can be attributed to high Reynolds numbers in conjunction with accelerated flow. This behavior is in contrast to the typical Dean flow observed at low or medium Reynolds numbers, where the flow deviates towards the outer region of a curved pipe. Given this velocity pattern, it is anticipated that high WSS would occur on the inner wall during the peak systolic phase.\u003c/p\u003e \u003cp\u003eDuring the mid-deceleration phase, flow begins to separate at the aortic arch, becoming unstable in the descending aorta. Note that the velocity vector size was magnified for better visualization due to the low velocity in end-systole (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e5\u003c/span\u003e(c)). During this phase, reverse flow and highly disturbed, complex flow patterns are observed.\u003c/p\u003e \u003cp\u003eThe flow patterns in the aortic arch are visualized through streamlines at four different phases of the cardiac cycle, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e6\u003c/span\u003e. During the acceleration phase, the helical flow begins from the ascending aorta and follows the inner wall of the aortic arch. As the flow transitions to the deceleration phase, the intensity of the helical flow decreases, and the highest velocity shifts towards the outer wall of the descending aorta. This shift leads to the formation of many small eddies along the inner wall of the aortic arch. At diastole, rotational and recirculating secondary flows are observed but are relatively small in magnitude.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Turbulence characteristics\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the eddy viscosity distribution at four different phases of cardiac cycle (refer to Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e2\u003c/span\u003e for the corresponding time points), indicating the turbulence intensity. In the near peak systolic phase, the eddy viscosity is almost zero within the aorta, indicating laminar flow. However, the eddy viscosity is rather high in the major branches, particularly near the proximal wall of the branches, indicating stronger turbulence in the branches compared to the aortic arch. In the mid-deceleration phase, the eddy viscosity increases, suggesting the development of stronger turbulence in the inner wall of the aortic arch region, which remains high until the distal region of the descending aorta. By the end-systole, turbulence decreases, spreading more evenly throughout the aorta and mostly disappears by the diastolic phase. This is more evident in the transverse vorticity plot in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e8\u003c/span\u003e. In Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e8\u003c/span\u003e(a), during peak systole, vorticity is predominantly observed in the three branches and the inner wall of the aortic arch, adhering closely to its curvature. In the branches, turbulence continues to propagate upwards, but due to the short length of the branches, the full effect of turbulence has not fully appeared. Initially, small-scale vortical structures exhibit well-organized laminar flow with uniform patterns. However, by the mid-deceleration phase, there is a transition from these organized and laminar patterns to larger and irregular vortical structures. The vortices at the inner wall of the aortic arch are notably large and concentrated. The branches of the arch significantly contribute to instability of flow resulting in development of small-scale vortices, facilitating their spread downward to the bottom of the descending aorta. During diastole, the strength of the vortices decreases and eventually disappears with returning to laminar flow.\u003c/p\u003e \u003cp\u003eTime traces of velocity magnitude at six different locations (a)-(f), (Refer Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e1\u003c/span\u003e for locations) are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e9\u003c/span\u003e. We can roughly determine the location and intensity of the transitional flow fluctuations. Flow disturbance with random fluctuations are observed at locations (b)\u0026ndash;(f), with the highest fluctuations at the distal point (c). Fluctuations were present only during the mid-deceleration and end-systole phases, with no significant disturbances during diastole. Note that the velocity amplitude at location (a) is greater than the velocity amplitude at locations (b)-(f), due to the dean flow which shifts the peak away from the centerline where the trace data were collected. This indicates that turbulence is likely to occur in the aortic arch during the mid-deceleration phase.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Wall shear stress\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e10\u003c/span\u003e depicts the WSS distribution at phases of the cardiac cycle: (a) near peak systole (t\u0026thinsp;=\u0026thinsp;0.102 s), (b) mid-deceleration phase (t\u0026thinsp;=\u0026thinsp;0.302 s), (c) end-systole (t\u0026thinsp;=\u0026thinsp;0.502 s), and (d) diastole (t\u0026thinsp;=\u0026thinsp;0.702 s). The peak value of WSS occurs at near peak systole followed by mid deceleration phase. During early peak systole, maximum WSS reaches up to 30 Pa, predominantly on the inner walls of the ascending aorta, gradually decreasing along its length. At the junction of the three branch outlets, WSS peaks between 7 to 11 Pa. Transitioning into the mid-deceleration phase, high WSS shifts towards the center of the aortic arch, with lower values observed along the inner walls of the aortic arch. During peak systole, the high-velocity zone is predominantly near the inner wall in laminar flow, correlating with the maximum WSS observed along the inner walls of the aorta. The transition to the mid-deceleration phase indicates unstable flow and a shift of high velocity towards the outer wall due to Dean flow induced by the large aortic arch curvature. This change in flow dynamics likely contributes to the redistribution of WSS towards the center of the wall during this phase (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e3\u003c/span\u003ea\u0026amp;b). In the diastolic phase, low and oscillating wall shear stresses are observed in the aortic arch and descending aorta.\u003c/p\u003e \u003cp\u003eThe cycle-averaged WSS distribution in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e11\u003c/span\u003e highlights elevated levels concentrated at the mid-anterior and inner posterior walls of the aortic arch. This distribution can be attributed to the strong helical flow pattern in the aortic arch. Furthermore, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e11\u003c/span\u003e reveals elevated WSS at the proximal segments of arterial branches, notably with the LSA exhibiting the highest values.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eIt is well established that the blood flow within a healthy aorta exhibits laminar flow, while the presence of turbulence is well-documented in patients with obstructive diseases in major vessels. However, catheter-based measurements in both human and canine studies have demonstrated that turbulence can develop in the aorta not only in the presence of disease but also with normal aortic valves \u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. Despite these observations, comprehensive description of turbulence in a healthy aorta has been lacking.\u003c/p\u003e \u003cp\u003eIn this study, LES was employed to investigate turbulent flow characteristics in an idealized thoracic aortic model, with the focus on analyzing turbulence development and its extent in the aorta. This research enhances the broader understanding of cardiovascular health and disease progression, particularly in relation to conditions such as aortic dissection, aortic aneurysm and atherosclerotic stenosis. By examining the mechanisms and extent of hemodynamic changes during the transition from laminar to turbulent flow, this research offers critical implications for clinical management and treatment strategies.\u003c/p\u003e \u003cp\u003eIn recent years, biomechanical research has increasingly focused on aortic flow through steady-state simulations employing various CFD models and patient-specific geometries of aortas \u003csup\u003e\u003cspan additionalcitationids=\"CR23 CR24\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. While steady-state simulations show overall wall WSS behavior, they fail to capture the dynamic changes induced by pulsatile blood velocity, especially in regions such as the aortic arch and branch junctions \u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. These areas are significantly influenced by the acceleration phase where turbulent effects are pronounced, particularly at the curved section of the aorta. Some studies have considered the k-ε and k-ω models, which provide mean values of turbulence parameters and overall flow behavior \u003csup\u003e\u003cspan additionalcitationids=\"CR28\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. However, small eddies in transitional flow increase WSS, potentially contributing to further aneurysm dilation, as the aorta adjusts its diameter to maintain shear stress below physiological thresholds \u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. In medical contexts with relatively high Reynolds numbers, high-resolution visualization and accuracy are crucial. Reynolds-Averaged Navier-Stokes (RANS) models are based solely on mean flow equations, relying on averaged quantities to approximate turbulence effects, which are the least computationally expensive turbulence modeling methods \u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. In contrast, Direct Numerical Simulation (DNS) represents the gold standard of simulation because it accounts for the effects of every scale of eddy when solving the flow equations. This approach maintains high fidelity by using computational cells smaller than or equal to the size of the smallest eddy, but it demands substantial computational resources \u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. DNS has been applied effectively in various studies: Dimakopoulos \u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e performed a DNS analysis on a 2D stent-type aortic valve, while Lee et al. \u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e used the spectral element method to simulate weakly turbulent flow in a patient-specific stenosed carotid bifurcation, predicting the complex flow field, turbulence levels, and distribution of hemodynamic parameters. Tullio et al. \u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e conducted a detailed DNS flow analysis on an aortic bileaflet mechanical heart valve, verifying the strong agreement between DNS and experimental results. Despite its accuracy, DNS is limited by its high computational cost. LES, which resolves larger turbulent eddies while modeling smaller ones, offers a more computationally efficient alternative to DNS. This method captures most of the flow dynamics while significantly reducing computational costs compared to DNS.\u003c/p\u003e \u003cp\u003eThe LES conducted in our study provides detailed insights into the complex flow patterns in a generic thoracic aorta. During the acceleration phase, flow in the aorta is predominantly laminar from the ascending aorta to the aortic arch. However, during the mid-deceleration phase, there was a noticeable transition from well-organized laminar flow patterns observed during peak systole to small-scale irregular vortical structures. The aortic arch appears to be the beginning of the transition from laminar to turbulent flow. This transition is crucial, as it is characterized by high turbulence intensity and elevated shear stress, which can lead to potential vascular risks. High velocity fluctuations during this transition can lead to increased shear stress and vibrations in the aortic wall, potentially damaging the vessel and may contribute to vascular occlusion \u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. Our observations of complex vortices and reverse flow in the aortic arch during this transition are consistent with the findings of Fukuda et al. \u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e from PIV experiments, demonstrating a similar flow pattern. Helical flow is observed in the ascending aorta through streamlines plots in our study. A similar helical flow pattern was also observed in MRI flow filed study by Kilner et al. \u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e, and CFD study by Tse et al. \u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e which validates our qualitative results.\u003c/p\u003e \u003cp\u003eIn our simulation results, WSS is highest during near-peak systole and mid-deceleration phase. The aortic arch exhibits significantly elevated WSS, measuring 2\u0026ndash;5 times higher than surrounding areas. This elevated WSS can be a contributing factor to the development of aortic dissection. For type A dissection, which involves the ascending aorta and aortic arch, we observed high WSS at the proximal ascending aorta and the aortic arch. These coincide with the predilection sites for aortic dissection reported by Chi et al. \u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e. High WSS is also observed at the proximal segments of the arterial branches. Notably LSA exhibits higher WSS compared to the BCA and LCCA, indicating a potentially higher risk of tearing at the LSA. Furthermore, the elevated WSS at the proximal segments of arterial branches is associated with typical locations reported for atherosclerotic lesions in the thoracic aorta \u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFor type B dissection, which typically affects the descending aorta, we observed high WSS at the entrance and distal location of the descending aorta. This high WSS is consistent with known high-risk sites for type B dissection. However, due to the complex nature of type B aortic dissection and the variability in patient-specific anatomy, while high WSS might contribute to wall thinning or increased biological stress, accurately quantifying and predicting the risk of type B aortic dissection remains challenging in healthy aortas \u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e,\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. In addition to aortic dissection, the regions of high WSS in our study, particularly near the aortic arch and branch bifurcations, may also be one of the contributing factors in the formation of aortic aneurysms. The persistent elevated WSS in these areas can lead to localized degeneration of the aortic wall, which, over time, may result in vessel wall dilation and an increased risk of aneurysm formation.\u003c/p\u003e \u003cp\u003eThe diffusion of vorticity during mid-deceleration and end-systole result in turbulent flow with repeated reverse flow, which leads to repeated oscillations of WSS. These oscillating can contribute to the development of atherosclerosis, as studies have shown that low-level and oscillating WSS can induce endothelial changes, contributing to plaque formation \u003csup\u003e\u003cspan additionalcitationids=\"CR44\" citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e, which may subsequently lead to thrombus formation \u003csup\u003e\u003cspan additionalcitationids=\"CR47\" citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e. In our study, WSS levels decrease significantly from systole to the beginning of diastole, with higher shear stress localized near the branches and the inner curvature of the aortic arch. These findings are consistent with the LES results of Lantz et al. \u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eDespite the comprehensive insights gained from our study, several limitations should be noted. Our study does not account for individual variations in aortic anatomy. While patient-specific models offer precise representations of individual anatomy, they may not be as widely applicable. An idealized model, such as ours, offers general insights that can be relevant to a broad range of individuals. Our model assumes rigid walls and a Newtonian fluid. While the rigid wall assumption may not fully capture the dynamic interactions between the flow and the vessel wall, Alimohammadi et al. \u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e noted that this assumption in CFD can slightly overestimate WSS. However, it does not significantly alter the overall WSS distribution. Although non-Newtonian and Newtonian fluids exhibit different behaviors, many studies have shown similar vortex structures and WSS distributions for both type of fluids, with the main differences primarily observed in low Reynolds number regions. Therefore, the Newtonian fluid assumption is appropriate for simulating flow in arteries with high Reynolds numbers \u003csup\u003e\u003cspan additionalcitationids=\"CR51\" citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e. Lastly, we used a predefined flow division (10% of the total flow was directed to the BCA, and 10% was equally divided between the LCCA and LSA). This approach may not fully reflect the natural variations in flow distribution among individuals. Anatomical differences can result in varying flow distribution, and incorporating subject-specific flow data could provide a more accurate representation of the blood flow dynamics within the aorta.\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eIn this study, we used LES to investigate the transition from laminar to turbulent flow in an idealized thoracic aortic model, with the focus on analyzing turbulence development and its extent in the aorta. It was observed that turbulence is present in a healthy aorta, particularly in the aortic arch and descending aorta. As turbulence develops, it induces oscillatory and secondary flows, which affect the intensity and distribution of WSS. This study enhance the fundamental understanding of transition to turbulent flow, highlighting its dependence on aorta geometry under pulsatile flow conditions. Future work could involve applying DNS to patient-specific models to extend these findings, including a detailed comparison of hemodynamic characteristics and further exploration of turbulence variations in patient-specific models.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contributions Statement\u003c/h2\u003e\n\u003cp\u003eKuiyu Cheng, Kwan Yong Lee, and Sang-Wook Lee contributed to the conception and design of the study. Kuiyu Cheng performed the simulation and the statistical analysis for the study. Kuiyu Cheng, Shehnaz Akhtar, and Sang Wook Lee wrote the first draft of the manuscript. Shehnaz Akhtar, Kwan Yong Lee and Sang-Wook Lee revised it critically for important intellectual content. All authors contributed to the manuscript revision, read, and approved the submitted version.\u003c/p\u003e\n\u003ch2\u003eAcknowledgements\u003c/h2\u003e\n\u003cp\u003eThis research was supported by the Basic Science Research Program, funded by the National Research Foundation of Korea (NRF). (2020R1I1A3066617)\u003c/p\u003e\n\u003ch2\u003eData Availability\u003c/h2\u003e\n\u003cp\u003eThe datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eMaton, A. et al. \u003cem\u003eHuman Biology Health\u003c/em\u003e (Prentice Hall, 1995).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDrake, R. L., Vogl, W. \u0026amp; Adam, W. M. \u003cem\u003eMitchell \u0026amp; Henry Gray. 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Methods Programs Biomed.\u003c/em\u003e \u003cb\u003e201\u003c/b\u003e, 105944 (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKeslerov\u0026aacute;, R. Numerical modeling of generalized Newtonian fluids flow in S-type geometry of bypass. \u003cem\u003eJ. Comput. Appl. Math.\u003c/em\u003e \u003cb\u003e429\u003c/b\u003e, 115237 (2023).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Aortic arch, Large eddy simulation, OpenFOAM, Laminar-turbulent transition, Turbulence intensity, Wall shear stress","lastPublishedDoi":"10.21203/rs.3.rs-4967194/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4967194/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study employed Large Eddy Simulation (LES) with the wall-adapting local eddy-viscosity (WALE) model to investigate transitional flow characteristics in an idealized thoracic aortic model. The OpenFOAM solver pimpleFoam was used to simulate blood flow as an incompressible Newtonian fluid, with the aortic walls treated as rigid boundaries. Simulations were conducted for 30 cardiac cycles and ensemble averaging was employed to ensure statistically reliable results. Main hemodynamic parameters, such as velocity fields, turbulence intensity and wall shear stress (WSS) were analyzed throughout the circulatory system. Through 3D computational fluid dynamics (CFD) visualization, we explained the transition from laminar to turbulent flow and its development throughout the cardiac cycle. Results demonstrated that turbulence originates in the aortic arch following the peak systole phase and further develops in the aortic arch and descending aorta during the mid-deceleration and end-systole phases. The WSS at the aortic arch is relatively high, which may be related to the development of various diseases, such as type A aortic dissection and atherosclerosis.\u003c/p\u003e","manuscriptTitle":"Characteristics of Transition to Turbulence in a Thoracic Aorta Using Large Eddy Simulation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-09-25 10:04:31","doi":"10.21203/rs.3.rs-4967194/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-09-23T07:17:43+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-09-19T13:08:44+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-09-10T08:02:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"165918840287791607533955228588401424121","date":"2024-08-29T09:29:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"261187895769425272640112151522674831450","date":"2024-08-29T02:14:55+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-08-28T16:11:13+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-08-28T15:54:55+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-08-27T13:50:07+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-08-26T04:53:59+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-08-24T04:41:35+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c60e973f-6d20-4164-9b41-bb49ff799771","owner":[],"postedDate":"September 25th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":38052669,"name":"Physical sciences/Engineering"},{"id":38052670,"name":"Physical sciences/Engineering/Biomedical engineering"}],"tags":[],"updatedAt":"2025-01-27T16:03:52+00:00","versionOfRecord":{"articleIdentity":"rs-4967194","link":"https://doi.org/10.1038/s41598-025-86983-z","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-01-25 15:58:01","publishedOnDateReadable":"January 25th, 2025"},"versionCreatedAt":"2024-09-25 10:04:31","video":"","vorDoi":"10.1038/s41598-025-86983-z","vorDoiUrl":"https://doi.org/10.1038/s41598-025-86983-z","workflowStages":[]},"version":"v1","identity":"rs-4967194","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4967194","identity":"rs-4967194","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}