Cardiovascular computational fluid dynamics (CFD) based on patient-specific modeling is increasingly used to predict changes in hemodynamic parameters before or after surgery/interventional treatment for aortic dissection (AD). This study investigated the effects of flow boundary conditions (BCs) on patient-specific aortic hemodynamics. We compared the changes in hemodynamic parameters in a type A dissection model and normal aortic model under different BCs: inflow from the auxiliary and truncated structures at aortic valve, pressure control and Windkessel model outflow conditions, and steady and unsteady inflow conditions. The auxiliary entrance remarkably enhanced the physiological authenticity of numerical simulations of flow in the ascending aortic cavity. Thus, the auxiliary entrance can well reproduce the injection flow from the aortic valve. In addition, simulations of the aortic model reconstructed with an auxiliary inflow structure and pressure control and the Windkessel model outflow conditions exhibited highly similar flow patterns and wall shear stress distribution in the ascending aorta under steady and unsteady inflow conditions. Therefore, the inflow structure at the valve plays a crucial role in the hemodynamics of the aorta. Under limited time and calculation cost, the steady-state study with an auxiliary inflow valve can reasonably reflect the blood flow state in the ascending aorta and aortic arch. With reasonable BC settings, cardiovascular CFD based on patient-specific AD models can aid physicians in noninvasive and rapid diagnosis.
Aortic dissection (AD), caused by intimal splitting induced by pulsating blood, is one of the most complex cardiovascular diseases. The pathogenesis of AD is still unclear, but several associated conditions include hypertension and degeneration of the aortic media [
Through computed tomography, three-dimensional reconstruction, and computational fluid dynamics (CFD) simulation, the blood flow behaviors and wall shear stress (WSS) of specific patients can be obtained. Moreover, tear locations can be predicted by the accurate estimation of WSS. High WSS or a high WSS gradient plays a role in vascular wall remodeling [
The boundary condition (BC) settings, including outflow and inflow conditions, for computational simulation are important for modeling the flow of the cardiovascular system. These settings are directly associated with the authenticity of CFD results, particularly the flow pattern and WSS distribution, and affect the reliability and comparability of the computational results. Liang et al. [
In addition, the valve, which is the only entrance for blood flow into the aorta, directly influences the flow field patterns of the ascending aorta (AAo), consistent with MRI-based inlet velocity profiles, [
In this study, two patient-specific models, namely, a type A dissection case and a normal aortic model, were used by reconstructing the computed tomography (CT) imaging data of the subjects. The effect of the flow BC on patient-specific aortic hemodynamics was investigated with or without the consideration of injection flow from the aortic valve, pressure control and 3-EWK model outlet conditions, and steady and unsteady inflow conditions.
This section presents detailed information on geometric reconstruction. The CT images used in this research had good resolution, with an in-plane resolution of 0.84 mm. The AAo and descending aorta (DAo) can be observed in
The “repairing” process of CT images of the tear features involved three steps. First, the areas of the true and false lumens and the gap between them were identified (
The main aim of this study is to investigate the hemodynamics differences caused by the auxiliary structure at the aortic valve. In the computational domain, the proximal truncation began at two regions: the middle of the AAo and the aortic valve, and an auxiliary structure was established for models with the proximal truncation at the aortic valve [
The auxiliary field was created by “blending” the shape of a patient-specific aortic valve opening during peak systole with a circular face of 30 mm at a normal distance of 200 mm (
As depicted in
The Fluent Meshing ver. 17.2 model and ICEM model were adopted for mesh generation. For AD-1 and C-1, a hexahedral O-grid was adopted because of its excellent performance and low computational cost. For AD-2 and C-2, a polyhedral mesh with 10 prismatic layers near the wall was generated to capture the geometric features around the aortic sinus (
All of the grids passed the mesh sensitivity test. Independent mesh experiments were conducted. A coarse hexahedral O-grid mesh and a corresponding fine mesh with 100% refinement, containing 251,264 and 809,417 cells, respectively, were tested. A relatively coarse polyhedral mesh with 700,000 polyhedral cells and a corresponding fine mesh with 100% refinement were tested. In the mesh sensitivity test, the relative changes in facet maximum WSS were less than 6% of the second-order truncation error. Moreover, according to the turbulence model, the Y+ values of all of the grids were less than 2. Considering the computational cost, a relatively coarse scheme was adopted.
The blood used in the simulation was treated as a Newtonian and incompressible fluid governed by the Navier–Stokes equations, which were solved using the finite volume method and spatially discretized using a second-order upwind scheme. The working fluid had the following physical parameters: viscosity of 4.0 m Pa⋅s and density of 1,060 kg/m^{3}. The pressure velocity coupling was solved using the semi-implicit method for pressure-linked equations. The turbulence model, named shear stress transport (SST-Tran), was adopted in both steady- and unsteady-state simulations [
Inflow structure | Inflow condition | Outflow condition | |
---|---|---|---|
Case 1 | Truncated structure | Steady state | Pressure control |
Auxiliary structure | Steady state | Pressure control | |
Case 2 | Auxiliary structure | Steady state | Pressure control |
Auxiliary structure | Steady state | 3-EWK | |
Case 3 | Auxiliary structure | Steady state | 3-EWK |
Auxiliary structure | Unsteady state | 3-EWK |
For the inflow condition, steady-state simulation was performed on all the aortic models, while unsteady-state simulation was performed only on models involving the aortic sinus. For models AD-1 and C-1, the constant (in-space) velocity was set as 0.2 m/s based on the literature [
Meanwhile, the outlet conditions included pressure control and the 3-EWK parameters. The pressures assigned to the aortic branches were adjusted such that the total outflow rate of the aortic branches was 30%. The specific outflow rate of each bifurcation was related to its truncation area. A zero-pressure condition was assigned to the abdominal outlet.
The 3-EWK model provides a lumped parameter description of the vasculature located downstream of the outlet boundaries of the 3D domain. The model consists of a proximal (or characteristic) resistance (
BA | 1.04 × 10^{8} | 8.74 × 10^{−10} | 1.63 × 10^{9} |
LCCA | 1.19 × 10^{8} | 7.7 × 10^{−10} | 1.84 × 10^{9} |
LSA | 0.97 × 10^{8} | 9.34 × 10^{−10} | 1.52 × 10^{9} |
DAo | 0.188 × 10^{8} | 48.2 × 10^{−10} | 0.295 × 10^{9} |
Furthermore, in the unsteady-state simulations, seven cardiac cycles were needed to ensure the convergence of the pulsating pressure cycle. Convergence was reached when the residuals of both the mass and momentum conservation equations were less than 10^{−3}. A second-order implicit time-stepping scheme was adopted with the fixed time-discrete scheme. The fixed time step was set less than or equal to 0.005 s, it did not depend on for the time step. The eighth cardiac cycle was prepared for the data extraction. Important hemodynamic parameters include WSS distribution, streamline, time-averaged WSS (TAWSS), and OSI contours [
The TAWSS on the vascular wall is quantified in a cardiac cycle by the flowing expression:
The OSI, which measures the degree of change in
However, compared with the results provided by four-dimensional magnetic resonance imaging (4D-MRI) [
According to the results in
The TAWSS distributions in the AAo, aortic arch, and DAo under steady state were similar to those under unsteady state. As shown by the red arrows, the maximum TAWSS in the C-2 case under steady state was slightly larger than that under unsteady state, while the TAWSS in AD-2 under unsteady state was much larger. The streamline of C-2 under steady state shared many similarities with that under unsteady state in a helical flow pattern. However, the streamline of AD-2, in which the AAo could be considered dilated, exhibited a more intense vortex pattern under unsteady state than under steady state, as indicated by the red arrows in the upper panels of
Although the steady-state results display comparable streamlines and TAWSS distributions with those under unsteady state at a specific moment, unsteady-state simulation can provide additional details of hemodynamics parameters.
Cardiovascular CFD can provide patient-specific aortic models to assist physicians in noninvasive AD diagnosis and can predict the hemodynamic characteristics of the aorta after AD surgery. It has been reported that changes in the aortic hemodynamic parameters, such as the WSS gradient and OSI, are associated with tear occurrence and AD development. Chi et al. [
However, owing to the difficulty of the in vivo measurement of flow and pressure in patients, the accurate information required for CFD is often lacking. A reasonable BC setting is important to improve the calculation reality and approximate patients’ physiological state. In this study, the introduction of an auxiliary entrance structure made the numerical results closer to the physiological state and effectively improved the numerical authenticity, as the results were close to published 4D-MRI results [
Furthermore, several studies have adopted the 3-EWK parameters for the outflow conditions [
However, this study has some limitations. The values of the 3-EWK model were based on the literature [
In this study, we compared the changes in hemodynamic parameters in a type A dissection model and normal aortic model under different BCs: inflow from the aortic valve, pressure control and 3-EWK outflow conditions, and steady and unsteady inflow conditions. The auxiliary entrance structure remarkably enhanced the physiological authenticity of numerical studies of flow in the AAo. The steady-state and unsteady-state simulations of the aortic model with auxiliary entrance exhibited highly similar TAWSS distributions at the AAo wall and aortic arch branches. Moreover, the pressure and 3-EWK model outlet conditions had little effect on the numerical results, indicating that the inflow structure plays a crucial role in hemodynamic simulations. With reasonable BC settings, such as the combination of the auxiliary entrance and the 3-EWM at all of the outlets, it could enhance the calculated hemodynamic parameters prediction (WSS, OSI, etc.) of the aorta close to its physiological authenticity, which is much more important for CFD based researches on aortic hemodynamic analysis, such as, the influence of aortic morphology (elongation accompanied by dilation of the ascending aorta [