Biodynamic Characteristics and Blood Pressure Effects of Stanford Type B Aortic Dissection Based on an Accurate Constitutive Model

Abstract

Aortic dissection (AD) is a highly lethal cardiovascular emergency, and clinical studies have found that a high percentage of AD patients are hypertensive. In previous studies, the AD model was simplified, such as by treating the vessel wall as a single-layer rigid material, ignoring the complex biomechanical factors of the vascular lumen. This study elucidates key biomechanical mechanisms by which hypertension promotes primary AD progression using multiscale modeling. First, based on experimental data from longitudinal and circumferential uniaxial tensile testing of porcine aortic walls (5–7-month-old specimens), a constitutive model of the aortic wall was developed using the Holzapfel–Gasser–Ogden (HGO) framework. The material parameters were calibrated via inverse optimization in ABAQUS-ISIGHT, achieving close alignment with mechanical properties of the human aorta. Using this validated model to define the hyperelastic properties of the aortic wall, a multiphysics coupling platform was constructed in COMSOL Multiphysics 6.2, integrating computational fluid dynamics (CFD) and fluid–structure interaction (FSI) algorithms. This framework systematically quantified the effects of blood pressure (bp) fluctuations on compressive stresses, von Mises stresses, and deformation of the intimal flap within the AD lesion region. With constant blood rheology, elevated blood pressure enhances wall stresses (compressive and von Mises), and intima-media sheet deformation, this can trigger initial rupture tears, false lumen dilation, and branch arterial flow obstruction, ultimately deteriorating end-organ perfusion.

1. Introduction

AD is a deadly cardiovascular emergency. Under the Stanford classification, AD is divided into type A and type B. If not diagnosed and treated properly in time, the mortality rate of AD patients increases by 1–2% per hour, with over 35% dying within 24 h and 50% within 48 h [1]. While AD’s exact pathogenesis remains unclear, it is widely accepted to involve blood and vessel biodynamics [2]. Hypertension is found in 67.3–76.6% of AD patients and in as high as 86% of Stanford type B aortic dissection (TBAD) patients [3,4]. It is considered a significant risk factor for the occurrence and evolution of AD [5,6]. Therefore, studying the effect of hypertension on the progression of TBAD is of great practical significance.

When the aortic intima of AD patients is torn, blood flows out of the intimal tear under bp, causing the aortic wall to separate into inner and outer layers. The intimal flap divides the aorta into true lumens (TLs) and false lumens (FLs) [7], with the outer wall of the FL called the FL wall. Previous studies have simulated and analyzed the biodynamic effects of hypertension on AD, confirming the effectiveness of simulations in studying AD formation and evolution. These studies have not only clarified the determinants of bp but also offered more precise clinical data. The findings reveal that while hypertension has limited effects on AD blood flow velocity, patterns, and wall shear stress, it significantly elevates vascular wall pressure [8].

Ahuja et al. dissected healthy pig aortas to create AD and performed uniaxial tensile tests on tissue samples revealing significant regional variations in the biomechanical response of porcine aortic tissue [9]. Bhat et al. (2021) found that the aortic material is stiffer longitudinally than circumferentially [10]. Naim et al.(2014) reviewed the hemodynamic numerical simulation of AD, emphasizing that vessel wall properties, complex geometric features, and biomechanical factors are closely related to the occurrence and evolution of tears [11]. Ahmed et al. (2015) studied the hemodynamic characteristics of TBAD, showing that the distal tear significantly impacts lumen pressure, with larger distal tears reducing the pressure difference between the TL and FL [12]. Pan et al. (2025) [13] studied the FL formation in AD. They found that slow blood flow enters the FL, creating vortices that worsen thrombus formation. Wang et al. (2024) observed the gradual expansion of the FL, with its surface area increasing from 82.63 cm² to 98.84 cm² and volume from 45.12 mL to 63.40 mL [14]. Tang et al. (2012) [15] used CFD to study the stress on the FL wall in AD under different bps. Their research shows that as bp rises, the stress on the FL wall increases. Wang et al. (2012) also used CFD, revealing a close link between the hemodynamic behavior of AD and bp, though the impact of bp on wall shear stress distribution is minimal [16]. Birjiniuk et al. (2019) [17] experimentally studied AD hemodynamics under varied mean pressures in vitro. They found that mean pressure changes barely affect AD vortex and retrograde flow patterns. Keramti et al. (2020) and Chong et al. (2020) used the FSI method to study the von Mises stress and intimal flap deformation in a single-layer model of AD [18,19].

Previous studies have simplified the model material properties, such as by treating the vascular wall as a single-layer rigid material, which may compromise the credibility of simulation results. This study, based on tests of fresh aortas of 5–7-month-old Yorkshire pigs, used ABAQUS-ISIGHT inversion to refine the hyperelastic anisotropic constitutive model parameters for AD, creating an HGO-based model closest to human AD. Using FSI and CFD, it simulated blood flow and biodynamic features of TBAD with higher physiological fidelity, analyzing the effect of hypertension on the evolution of TBAD.

Previous studies on AD often simplified the vascular wall as a single-layer rigid material, neglecting the complex biomechanical factors of the vascular lumen (e.g., hyperelasticity and displacement), which reduced the credibility of the simulation. In this study, based on experimental data from the uniaxial tensile testing of fresh aortic walls from 5–7-month-old pigs, the material parameters of the AD constitutive model were revised using inverse optimization in ABAQUS-ISIGHT. A precise constitutive model was employed to define the multilayer material properties of the vascular wall, and an FSI and CFD algorithm were utilized to simulate the hemodynamics and biomechanical characteristics of AD with higher physiological fidelity. On this basis, the effects of hypertension on the progression of TBAD were analyzed.

2. Materials and Methods

2.1. The Holzapfel–Gasser–Ogden (HGO) Constitutive Model

The aortic wall is a biological soft tissue with biodynamic properties such as anisotropy, hyperelasticity, nonlinearity, and incompressibility [20]. The HGO constitutive model, based on hyperelasticity theory, formulates anisotropic material mechanics equations, making it the most effective method for studying aortic wall biomechanics [21,22].

Let the aortic wall strain energy function be composed of isotropic ${\Psi }_{iso}$ and anisotropic ${\Psi }_{aniso}$ components, expressed as:

$$\Psi ={\Psi }_{iso}+{\Psi }_{aniso}$$

(1)

According to the HGO model theory,

$${\Psi }_{iso}=C_{10}\left({\overline{I}}_1-3\right)+{\displaystyle \frac{1}{D}}\left({\displaystyle \frac{J_{el}^2-1}{2}}-\ln J_{el}\right)$$

(2)

$$\begin{array}{cc}{\Psi }_{aniso}& ={\displaystyle \frac{k_1}{2k_2}}\left(\exp \left\{k_2{\left[\kappa {\overline{I}}_1+\left(1-3\kappa \right){\overline{I}}_4-1\right]}^2-1\right\}\right)\\ & +{\displaystyle \frac{k_3}{2k_4}}\left(\exp \left\{k_4{\left[\kappa {\overline{I}}_1+\left(1-3\kappa \right){\overline{I}}_6-1\right]}^2-1\right\}\right)\end{array}$$

(3)

${\Psi }_{iso}$ is associated with the mechanical response of elastin and smooth muscle cells in the passive state, and ${\Psi }_{aniso}$ is related to the reaction of collagen fibers to the load on the tissue specimen. The TL wall, intimal flap, and FL wall in AD are assumed to be incompressible, meaning tissue shape changes do not affect volume. The Jacobian matrix of the deformation gradient is $J_{el}=1$, indicating that the material is incompressible. A simplification of the formula yields the following:

$$\Psi =C_{10}\left({\overline{I}}_1-3\right)+{\Psi }_{aniso}$$

(4)

$C_{10}$ is the material constant, $C_{10}=\mu /2$, $\mu$ is the shear modulus. ${\overline{I}}_1$ is the first invariant of the Cauchy–Green tensor; ${\overline{I}}_1=C:I$, $C=F^{T}F$, where $F$ is the deformation gradients and $I$ is the unit tensor. ${\overline{I}}_4,{\overline{I}}_6\ge 1$ characterizes the mechanical response of the fiber in the preferred direction. $k_1,k_3>0$ are stress-type parameters, and $k_2,k_4>0$ are uncaused parameters. The orientation of the fibers is represented by the invariants ${\overline{I}}_4$ and ${\overline{I}}_6$. The anisotropic orientation in the tissue is assumed to be a helical orientation of $\pm \theta$ degrees with respect to the longitudinal direction, as shown in Figure 1a. Therefore, the ${\overline{I}}_4,{\overline{I}}_6$ invariants are equal.

$${\overline{I}}_4,{\overline{I}}_6={\lambda }_{\theta }^2{\cos }^2\theta +{\lambda }_z^2{\cos }^2\theta$$

(5)

where ${\lambda }_{\theta }$ is the circumferential tensile ratio, and ${\lambda }_Z$ is the longitudinal tensile ratio.

The fiber parameter is $\kappa \in$ [0, 1/3] in the HGO model, with values of $\kappa$ close to 0 indicating a concentration of fibers along the preferential orientation $\theta$, while values close to 1/3 indicate a dispersion of fibers. Using $\rho \left(\theta \right)$ to represent the risk density function, the distribution of the number of fibers is normalized over the range [θ, θ + dθ], and the value of $\kappa$ is denoted as:

$$\kappa ={\displaystyle \frac{1}{4}}{{\displaystyle \int }}_0^{\pi }\rho \left(\theta \right)\sin {\theta }^{3}d\theta$$

(6)

Each family of fibers is assumed to have the same mechanical response along the same $\theta$-angle direction, so that $k_1=k_3$ and $k_2=k_4$. Because ${\Psi }_{aniso}$ is only valid when the tissue is stretched, it is zero when ${\overline{I}}_4$ or ${\overline{I}}_6<1$.

In summary, the basis for constructing parametric equations for the human aortic wall model of HGO lies in obtaining the C₁₀, k₁, k₂, θ, and κ in the above equations.

2.2. Establishment of the Constitutive Model

The determination of material property parameters determines the accuracy of creating the native model. Previous studies have proved that there is no significant difference in the mechanical property constants and elastic modulus between the human aortic wall and the 4–10-month-old porcine aortic wall [23,24]; so, the porcine aorta was chosen as the test object in this study, and the circumferential and longitudinal stress–strain relationship curves were obtained through longitudinal and circumferential tensile tests; then, the parameter corrections were carried out by using inverse optimization methods to obtain the material mechanical property parameters of the porcine aortic wall, and the material mechanical property parameters of the porcine aortic wall were ultimately constructed based on the results. This parameter is used to construct the HGO model of the human aortic wall.

From 5–7-month-old pigs, select the fresh descending aorta, which has a wall thickness of about 2.96 mm. Fix it on a glass plate, cut it into segments of about 120 mm in length from the same location, and divide them into two groups. Use one group to dissect the intima, media, and adventitia; use the other group to create an AD entry at the proximal third and an exit at the distal end symmetrically, with a distance of 30 mm between the two tears. Use forceps to extend the AD and connect it to an in vitro simulation platform [25] for expansion, to ensure its biomechanical properties are closer to those of a real AD. Figure 1b,c show samples of the aorta before and after expansion, respectively. Then, dissect the intimal flap and FL wall. Cut the separated intima, media, adventitia, intimal flap, and FL wall into samples of about 90 × 10 mm along the circumferential and longitudinal directions.

The MARK-10 ESM 1500S single-column tensile teste (Mark-10 Corporation, Copiague, NY, USA) was used for the biological tissue tensile tests. The fixture was clamped 15 mm from the upper and lower edges of the sample, with an initial distance of 60 mm between fixtures. A preload of 0.5 N was applied to eliminate the viscoelastic effects of the aortic wall. The tester was started, and the sample was stretched at 1.2 mm/min until complete rupture, as shown in Figure 2.

Uniaxial tensile tests were performed on the adventitia, media, intima, FL wall, and intimal flap to obtain stress–strain curves. This study focuses on the intimal flap group. Eight valid datasets were acquired in the circumferential and longitudinal directions. The results showed the material exhibited distinct linear and nonlinear elastic phases, with directional mechanical variations (Figure 3a,b), consistent with the anisotropic hyperelasticity of the aortic wall.

A sample model was built in ABAQUS-ISIGHT with a length of 60 mm and a width of 10 mm. The HGO anisotropic hyperelastic material was selected, with a density of 1100 kg/m³. Initial parameter values were set based on Fischer [21]: C₁₀ = 0.02918 MPa, k₁ = 0.01037 MPa, k₂ = 2.03, θ = 42.4°, and κ = 0. During the tensile simulation, one end of the sample was fixed, while the other was subjected to a velocity condition of 1.2 mm/min. Experimental data on the tensile force and displacement from circumferential and longitudinal tests were used to compare the experimental and simulation results. The least squares method was applied to fit the experimental data, followed by optimization using a multi-island genetic algorithm.

The material parameter inversion and correction method identifies candidate constitutive parameters within a specified range, updating them iteratively during correction to minimize the objective function value, thereby inverting and optimizing the aortic tissue constitutive parameters. In this study, the correction objective is to minimize the error between the experimental and simulation data, quantified by the mean square error (MSE).

Table 1. Material parameters table of intimal flap samples.

Specimen	C10/MPa	k1/MPa	k2	θ/°	κ
Z1	0.0935	0.3356	0.3964	31	0.1106
Z2	0.0311	0.5641	1.4087	40	0.0166
Z3	0.0858	0.5972	1.8936	23	0.2316
Z4	0.0750	0.5225	3.5600	46	0.3015
Z5	0.0847	0.5415	1.2654	13	0.2622
Z6	0.1477	0.7109	0.1236	25	0.2219
Z7	0.1495	0.1925	0.7318	60	0.3277
Z8	0.1182	0.5442	2.0111	25	0.1196
Mean value	0.0982	0.5011	1.4238	32.9	0.1990
Standard deviation	0.0369	0.1516	1.0234	14.1	0.1000

shows the fitting results of the experimental and simulation data for eight pairs of intimal flap samples tested under longitudinal and circumferential tensile tests. The fitting results of one of the intimal flap samples are shown in Figure 4. The average coefficient of determination for the aortic wall samples is 0.98. Similarly, the material parameters for the other groups of samples are inverted and optimized. The final porcine aortic wall constitutive parameters are shown in

Table 2. HGO model material parameters of AD.

Area	C10/MPa	k1/MPa	k2	θ/°	κ
Adventitia	0.0130	0.1741	0.4847	36.6	0.2740
Media	0.1710	0.5856	3.5447	22.6	0.2170
Intima	0.1828	0.8984	2.5716	34.8	0.2239
FL wall	0.1269	1.0934	5.6109	25.1	0.2354
Intimal flap	0.0982	0.5011	1.4238	32.9	0.1990

. These data will be used for the subsequent human aortic tissue model creation.

2.3. Establishment of the Geometric Model

In this study, the geometric dimensions of AD were obtained from the research of Keramati et al. [18]. The aortic segment is 150 mm long with a diameter of 25 mm. The thicknesses of the adventitia, media, and intima are 0.6 mm, 1.2 mm, and 0.2 mm, respectively. This aortic segment is enclosed in muscle tissue measuring 150 mm in length, 50 mm in width, and 80 mm in height. The TL and FL are created at the center, with 5 mm diameter tears at both ends of the intimal flap. To ensure the dissection occurs within the media, the intimal flap thickness is set to 1.2 mm and the FL wall to 0.8 mm. As shown in Figure 5, the model is divided into seven parts: adventitia, media, intima, intimal flap, FL wall, muscle tissue, and fluid domain, based on their material properties.

2.4. Mesh Generation and Mesh Independence Test

According to the material properties, the model was divided into seven parts: adventitia, media, intima, intimal flap, FL wall, muscular tissue, and fluid domain. Meshing of each part was performed using COMSOL Multiphysics 6.2.

As meshing strategy affects simulation accuracy and computational cost, a mesh sensitivity analysis was conducted. As can be seen from Figure 6, using the maximum displacement of the mid-point on the intimal flap under normal blood pressure as a reference, models with different mesh counts (471,255, 8,826,732, 1,295,123, 1,645,653, and 2,412,296) were analyzed to determine the relationship between mesh count and the simulation results. When the mesh count reached 1,295,123, the displacement was 10.292 mm, with less than 3% error compared to other meshing schemes. Considering computational time and accuracy, a mesh count of 1,295,123 was chosen. The average element quality was 0.6760, meeting the simulation requirements. The meshing pattern is shown in Figure 7.

2.5. Blood Property and Simulation Condition Settings

This study employs COMSOL Multiphysics 6.2 to conduct coupled simulations of the fluid and solid domains, thereby achieving fluid–structure interaction analysis. The time step is set to 0.001 s, and the maximum residual for convergence is set to 10⁻⁵. The numerical simulations are performed for three cardiac cycles, and all the results are obtained from the third cycle.

Blood is regarded as an isotropic, homogeneous, incompressible, inviscid non-Newtonian fluid, with its density and viscosity coefficient set at 1060 kg/m³ and 0.0035 kg/m·s, respectively. The specific viscosity of blood is characterized by shear stress and shear rate. The relationship between the viscous shear stress $\tau$ in any flow direction, viscosity $\mu$, and shear rate $\partial u/\partial y$ is as follows:

$$\tau =\mu {\displaystyle \frac{\partial u}{\partial y}}$$

(7)

A non-Newtonian fluid is defined as a fluid in which the relationship between shear stress and shear rate is not linear. When $\partial u/\partial y>100 {\mathrm{s}}^{-1}$, it behaves as a Newtonian fluid. The flow behavior and shear rate of blood in rheology differ from those of a Newtonian fluid, which has a significant impact on the biomechanical analysis of AD and aneurysms. Therefore, it is not appropriate to simply regard blood as a Newtonian fluid. The non-Newtonian fluid Carreau–Yasuda equation is as follows:

$$\mu ={\mu }_{\infty }+\left({\mu }_0-{\mu }_{\infty }\right){\left[1+{(\dot{\gamma }\lambda )}^a\right]}^{(n-1)/a}$$

(8)

In the Carreau–Yasuda equation:

${\mu }_0$ is the zero-shear viscosity in mPas, ${\mu }_{\infty }$ is the infinite-shear viscosity in mPas, $\lambda$ is the relaxation time in seconds, n is the power-law index where n < 1, and a is the Yasuda index with a ≤ 2.

To determine whether a flow is laminar or turbulent, the Reynolds number Re is introduced, defined as follows:

$$Re={\displaystyle \frac{{\rho }_{f}Vd}{\mu }}={\displaystyle \frac{{\rho }_f{V}^2}{\mu V/d}}$$

(9)

In this formula:

${\rho }_f$ denotes fluid density, kg/m³; $V$ represents the mean velocity across the cross-section, m/s; d is the aortic diameter, m; and $\mu$ stands for dynamic viscosity of the fluid, kg/m·s.

In this study, the Womersley number of the fluid domain model is 19.18, corresponding to a Reynolds number range of 4795–19,180. Given the maximum Reynolds number of 5100, which is within the turbulent threshold, the blood flow is modeled as turbulent. The shear stress transport k-ε model is used, with a turbulence intensity of 1.5% at the vessel inlet [26].

Momentum and mass conservation equations are applied across the fluid domain. The corresponding equations are as follows:

$${\rho }_f{\displaystyle \frac{\partial v_f}{\partial t}}+{\rho }_f(v_f\cdot \nabla )v_f-\nabla \cdot \left[-p{\rm I}+K\right]-F=0$$

(10)

$$\rho \nabla \cdot v_f=0$$

(11)

$$K=\left(\mu +{\mu }_T\right)\left(\nabla u+{\left(\nabla u\right)}^T\right)$$

(12)

The equation for turbulent kinetic energy (k) is given by:

$${\rho }_f{\displaystyle \frac{\partial k}{\partial t}}+{\rho }_f(v_f\cdot \nabla )k-\nabla \left[\left(\mu +{\displaystyle \frac{{\mu }_T}{{\sigma }_t}}\right)\nabla \epsilon \right]-p_k+\rho \epsilon =0$$

(13)

The equation for the turbulent dissipation rate (ϵ) is given by:

$${\rho }_f{\displaystyle \frac{\partial k}{\partial t}}+{\rho }_f(v_f\cdot \nabla )k-\nabla \left[\left(\mu +{\displaystyle \frac{{\mu }_T}{{\sigma }_t}}\right)\nabla \epsilon \right]-C_{\epsilon 1}{\displaystyle \frac{\epsilon }{k}}{p}_k+C_{\epsilon 2}\rho {\displaystyle \frac{{\epsilon }^2}{k}}=0$$

(14)

In this formula:

$v_f$ is the velocity vector of the blood, in m/s; ${\rho }_f$ is the density of the blood, in kg/m³; p is the absolute pressure, in MPa; and $C_{\epsilon 1}$ and $C_{\epsilon 2}$ are empirical parameters, with values of 1.44 and 1.92, respectively [27].The non-Newtonian fluid properties of blood are shown in

Table 3. Non-Newtonian blood parameters.

Relaxation Time (s)	Power-Law Index	Yasuda Index	Zero-Shear Viscosity (mPas)	Infinite-Shear Viscosity (mPas)
0.1	0.392	0.664	22	2.2

.

Based on clinical data [19], boundary conditions for the vessel inlet, outlet, and surrounding tissues were set. A flow rate boundary condition was applied at the inlet, with the flow waveform shown in Figure 8a. A pressure boundary condition was applied at the outlet, with the aortic outlet pressure pulsation waveforms set to three different conditions: hypertension (160/90 mmHg), normal pressure (120/70 mmHg), and heart failure pressure (100/50 mmHg), as shown in Figure 8b. The inlet and outlet settings at both ends of the vessel were fixed, while the vessel walls were allowed to move within the physiological range to simulate the elastic deformation of the vessel.

For the AD model, the entire AD vessel wall is modeled as a hyperelastic, anisotropic HGO (Holzapfel–Gasser–Ogden), hyperelastic material. The momentum conservation equation for the solid domain in the Lagrangian coordinate system is given by:

$${\rho }_s{\displaystyle \frac{{\partial }^2{u}_s}{\partial t^2}}-\nabla \cdot {\sigma }_s=0$$

(15)

${\rho }_s$ is the density of the vessel wall, 1100 kg/m³, $u_s$ is the displacement of the vessel wall, and ${\sigma }_s$ is the Cauchy stress tensor. The strain energy function of the AD is given in Equation (1).

Boundary conditions were set at the vessel inlet and outlet as well as on the vessel wall. The ends of the vessel at the inlet and outlet were fixed, allowing only radial movement of the vessel wall. The surrounding tissue has a damping effect on the deformation of the aortic wall, and Rayleigh damping was incorporated into the numerical simulation, since the damping matrix is a combination of the mass matrix and the stiffness matrix. It can be expressed as:

$$[C] = \alpha [M] + \beta [K]$$

(16)

In the equation, $[M]$ and $[K]$ represent the mass matrix and the stiffness matrix, respectively. The values of parameters $\alpha$ and $\beta$ are 5650 and 0.1 respectively.

The contact surface between the blood and the vessel wall is the inner surface of the aorta. All data exchanges between the two-way FSI are completed through this interface. The interface satisfies the coupling boundary conditions, such as displacement compatibility and traction balance. It can be expressed as:

$$u_f=u_s$$

(17)

$${\tau }_f\cdot n={\tau }_s\cdot n$$

(18)

In the equation, $u_f$ and $u_s$ represent the displacements of the blood and the arterial wall, respectively, and $n$ is the normal direction of the coupling interface.

3. Results

Using the established model, this study simulated AD with single and double intimal flap tears. Focusing on bp changes, both scenarios yielded similar conclusions. Therefore, only the double-tear case is analyzed here to present and analyze the impact of bp changes on the biodynamic characteristics of AD.

3.1. Velocity Field

Figure 9a,b show the velocity cloud diagram of the longitudinal and transverse middle cross-sections at the peak of systole and mid-diastole. At the systolic peak, a jet is observed at the proximal tear (on the left side of the figure) of the FL. Under normal blood pressure, the maximum velocity at the proximal tear is about 1.05 m/s, which is very close to the maximum velocity of 1.1 m/s observed by Pirola et al. (2019) [28] at the same location from 4D MRI. At mid-diastole, retrograde blood flow is observed in the lumen of the model, with vortex-like blood flow in the FL and basically consistent distribution areas.

Figure 9c,d show the changes in blood flow through the proximal and distal tears and the true and FL middle cross-sections within a cardiac cycle. Under the three different blood pressures, the maximum blood flow through the proximal/distal tears is 25.6963/20.2142, 20.6344/16.8429, and 16.9391/14.1941, respectively. The maximum blood flow through the TL/FL transverse middle cross-sections is 183.0072/97.8707, 140.6227/80.7917, and 107.6888/65.2094, respectively. The unit of blood flow is cm³/s.

In summary, the velocity variation trends under different blood pressures are basically consistent, and increased blood pressure generally leads to a larger distribution of blood flow velocity.

3.2. Compressive Stress

The data of three nodes of the intimal flap—the proximal node, the distal node, and the symmetric center of the inner membrane sheet on the transverse middle cross-section (intermediate node)—were analyzed, as shown in Figure 10.

Figure 11a shows the AD compressive stress distribution maps at systolic peak (left) and mid-diastole (right). Under all three bp conditions, the compressive stress contour surfaces show similar trends. At systolic peak, the TL near the proximal tear has higher compressive stress than the FL, while the opposite is true at the distal tear. The maximum compressive stress differences in the model region are 3250 Pa, 2160 Pa, and 1460 Pa for the three bp levels. During mid-diastole, the compressive stress in the TL gradually increases, with maximum differences of 49 Pa, 37 Pa, and 29.1 Pa. These results indicate that higher bp leads to increased compressive stress in the dissection.

Figure 11b shows the average compressive stress waveform of the intimal flap on the transverse mid-section between the TL and FL during a cardiac cycle. Figure 11c reflects the changes in the mean compressive stress difference between the TL and FL. Under different bp conditions, the maximum compressive stress difference (TL value minus FL value) occurred at approximately 0.113 s, with values of −1608 Pa, −978 Pa, and −593 Pa, respectively. This indicates that bp changes significantly affect the compressive stress difference between the TL and FL. Higher bp increases this difference, with the FL experiencing greater compressive stress, leading to dissection extension and enlargement.

3.3. Von Mises Stress

Von Mises stress, calculated from principal stresses, is a scalar indicator used in material failure analysis to determine whether a material is at the critical point of yielding or failure [29]. When the stress on the vascular wall exceeds its mechanical failure strength, the aortic intima may tear [30]. Research shows that evaluating vascular wall failure using von Mises stress is crucial for assessing AD [31,32].

Figure 10 labels the two surfaces of the intimal flap in the TL and FL. Figure 12c shows the average von Mises stress changes on the inner surfaces of the TL and FL over a cardiac cycle. Under the same bp, the average von Mises stress fluctuates with bp changes, and the stress trends on both surfaces are the same, with the FL’s stress being significantly higher. Under different bps, the average von Mises stress changes significantly, with both surfaces reaching maximum values near 0.113 s, indicating that the intimal flap experiences the greatest concentrated stress at this point. As bp rises, the average von Mises stress at corresponding times increases.

Table 4. The mean and maximum values of von Mises stress of the intimal flap.

Blood Pressure	Lumen	Mean ± Standard Deviation/Pa	Min/Pa	Max/Pa
High	True	5747.6 ± 1020.5	4329.2	9207.0
	False	8138.4 ± 1545.8	5983.3	12,662.0
Normal	True	4343.5 ± 521.9	3366.9	5862.5
	False	6181.8 ± 909.9	4653.3	8451.4
Heart failure	True	3067.5 ± 307.5	2404.2	3709.6
	False	4368.7 ± 566.9	3322.9	5551.9

shows the maximum von Mises stress under three bps, all occurring on the FL’s surface, with values of 12,662.0 Pa, 8451.4 Pa, and 5551.9 Pa. Compared to normal bp, the average von Mises stress on the intimal flap increases by 49.82% under hypertension.

Based on the overall average von Mises stress of the intimal flap, local simulations were conducted on both the proximal and distal, yielding consistent results. Here, the proximal end is used as an example for analysis.

Figure 12a,b illustrate the von Mises stress distribution at the proximal end during systolic peak (left) and mid-diastole (right) for the proximal node and distal node. Figure 12d presents the von Mises stress variation curve over a cardiac cycle on the proximal tear. Since the model’s inlet is at the proximal end, the stress variation is influenced by blood flow direction and sudden changes. However, the overall trend aligns with the global curve in Figure 12c, with only slight differences in the distribution of maximum values, which does not affect the analytical conclusions. Under the three bp conditions, the maximum von Mises stress in the FL was measured at 25,445 Pa, 19,466 Pa, and 13,747 Pa, while in the TL, it was 18,097 Pa, 14,057 Pa, and 9983 Pa. Compared to normal bp, hypertension results in a 30.72% increase in the maximum von Mises stress on the intimal flap.

Figure 12b,e display the data and special moment maps for the distal observation point. The von Mises stress at the FL–intimal flap junction is generally higher than that at the TL–intimal flap junction. This stress concentration exacerbates the tendency for AD to expand at the FL inlet, thereby increasing the risk of complications.

3.4. Intimal Flap Deformation

Figure 13a presents the deformation cloud maps of the intimal flap at these three observation points during systolic peak (left) and mid-diastole (right), respectively.

Table 5. The maximum, minimum, and mean displacement of different nodes of the intimal flap.

Blood Pressure	Observation Node	Mean ± Standard Deviation/mm	Max/mm	Min/mm
High	proximal node	8.2033 ± 1.0136	6.2564	10.6450
	distal node	7.7732 ± 1.1528	5.9016	10.3850
	intermediate node	7.4394 ± 2.1500	0.8004	10.2920
Normal	proximal node	6.3538 ± 0.7567	4.8648	8.2431
	distal node	6.0881 ± 0.8894	4.7038	8.1334
	intermediate node	5.8543 ± 1.3679	1.6623	7.8678
Heart failure	proximal node	4.5327 ± 0.5581	3.4733	6.0340
	distal node	4.3692 ± 0.6529	3.3475	5.8987
	intermediate node	4.3681 ± 0.7836	2.0199	5.5504

lists the numerical values of the intimal flap deformation under the three bp conditions.

The analysis of three observation points reveals significantly greater deformation near the intimal flap tear than at the central node. As shown in Figure 13b,c, they correspond to the deformation cloud maps of the proximal node and the distal node, respectively. Under identical bps, the deformation differences among the points are relatively small. However, under varying bps, though the deformation trends are consistent, noticeable differences in magnitude emerge, as depicted in Figure 13d–f. Specifically, focusing on the central point of the intimal flap (referencing Table 5 and Figure 13e), the maximum deformation occurs at 0.283 s, with values of 10.2920 mm, 7.8678 mm, and 5.5504 mm under the three bp conditions. This indicates a 30.81% increase in deformation under high bp compared to normal bp. These findings robustly demonstrate a positive correlation between intimal flap deformation and bp fluctuations.

The displacement of the vascular lumen wall significantly impacts hemodynamic characteristics [33]. In AD, the movement of the intimal flap can affect blood perfusion in branch arteries connected to the TL, such as the renal artery. Analyzing the deformation or movement of the intimal flap in AD is crucial for assessing complication risks.

4. Discussion

4.1. Constitutive Model

To address the limitations of traditional rigid wall and linear elastic models, this study innovatively developed a constitutive model for AD based on the HGO model from tests of the aortic wall in Yorkshire pigs. Bidirectional control conditions were set under different bps, and a fluid–structure interaction (FSI) method was used. The data from three aspects demonstrated the impact of hypertension on the progression of AD. This approach enhanced the physiological realism of the simulation and the scientific rigor of the data analysis, yielding favorable research outcomes.

4.2. Stress Field Analysis

Building on prior research regarding compressive stress, this study advances understanding using a novel model. Section 3.2 shows that rising bp increases dissection compressive stress; this is consistent with previous findings [15,16,17]. Notably, hypertension significantly impacts the stress difference between the TL and FL, which varies with the position on the dissection and the cardiac cycle stage. This stress difference, influenced by maximum systolic pressure and mean aortic bp, drives FL expansion and aortic rupture, key factors in AD progression. This aligns with clinical observations in AD patients and Rajagopal’s research [34].

When the von Mises stress on the vascular wall exceeds its mechanical failure strength, the inner membrane tears, with the maximum von Mises stress location being critical [35,36]. Section 3.3 reveals that under hypertension, the intimal flap experiences high stress (over 1 × 10⁴ Pa) during systole, a 30% increase compared to normal bp. Stress concentration occurs at the intimal flap–vascular wall junction. These findings confirm that hypertension exacerbates intimal flap damage near the tear, separates the distal intimal flap from the media, and enlarges the FL, all accelerating AD progression. Beyond stress considerations, the resultant deformation of the intimal flap is another critical factor influenced by hypertension.

4.3. Intimal Flap Deformation Analysis

In AD research, this study innovatively introduced von Mises stress and intimal flap deformation, inspired by methods from other vascular disease studies. Direct measurement of these parameters is unfeasible; MRI is the clinical standard for AD diagnosis, while FSI is effective for scientific research. Previous studies by Keramati and Chong used simplified single-layer, rigid vascular wall models, leading to significant deviations from clinical values [18,19].

Clinically, MRI shows AD intimal flap deformation ranges from 0 to 10.2 mm [37], while this study’s model yields 0–10.6 mm, indicating good consistency and reliability of the model and methods. Section 3.4 reveals that under three bps, the maximum intimal flap deformation occurs at the proximal and distal tears (slightly larger at the proximal end). Elevated bp causes the intimal flap at these tears to bulge into the TL, reducing blood flow and leading to perfusion issues and organ ischemia [38]. Clinically, hypertension extends the intimal flap in AD patients, dynamically obstructing branch or terminal vessel blood flow and causing complications like renal failure [6].

4.4. Mutual Promotion Between Research, AD Pathology, and Clinical Practice

This study reveals how hypertension affects TBAD from a biodynamic perspective. Robicsek et al. clinically proved that increased bp raises aortic wall pressure, leading to gradual dilation and dissection [39]. Pathologically, long-term hypertension boosts elastic breakdown and vascular smooth muscle cell dedifferentiation, causing AD [40]. Clinically, doctors use MRI and other equipment to demonstrate the impact of hypertension on AD progression based on patients’ signs and statistical data. This proves that scientific research needs mutual learning and promotion from multiple angles and methods. Clinical practice and cell biology offer research demands and directions for biodynamics, which in turn provides a theoretical basis for pathological patterns and cell differentiation, ultimately improving AD patient care.

4.5. Limitations and Suggestions for Improvement

The limitations of this study include the omission of the aortic arch and its branches in the AD geometric model, resulting in an incomplete study of arterial vessels and geometric structures. Additionally, the analysis of the intimal flap focused only on representative points of interest, underutilizing the simulation data.

In future research, the vascular wall biomechanical properties of the model need optimization. Patient-specific 3D AD models should be used, and PIV should be introduced to obtain more precise AD flow field states and intimal flap deformation, improving research accuracy.

5. Conclusions

In summary, this study established a human aortic and AD constitutive model based on uniaxial tensile tests of aortic walls from 5–7-month-old Large White pigs. Using FSI and CFD algorithms on the COMSOL platform, we investigated the impact of hypertension on AD’s biological characteristics. The simulation results were realistic and provided useful findings for future research.

Our results confirmed that increased blood pressure raises blood flow velocity, volume, compressive stress, von Mises stress, and intimal flap deformation in AD. This leads to intimal tear formation, enlargement, FL expansion, and possible dynamic blood flow obstruction in branch arteries connected to the TL, causing complications like terminal organ perfusion deficiency. These findings offer a robust biomechanical basis for AD prevention, diagnosis, treatment, and complication risk reduction.