In this paper, a bidirectional fluid‒solid coupling finite element analysis model of the abdominal aorta was established with the use of vascular elastic modulus as the main indicator of atherosclerosis, in consideration of blood dynamic viscosity and compressibility, and pulse-wave propagation time-course calculations were carried out by the application of full-coupling analysis of the arbitrary Lagrangian‒Eulerian algorithm in COMSOL Multiphysics. The effect of atherosclerosis degree on the propagation characteristics of pulse waves in the bifurcated abdominal aorta was quantitatively analyzed. An increase in the modulus of elasticity of the arterial wall resulted in a considerable decrease in the peak pressure pulse wave, an increase in the pressure wave velocity, and a decrease in the axial wave velocity. Arterial bifurcation caused a substantial attenuation of the peak pressure pulse wave and an increase in wave velocity during the cardiac cycle. The modulus of elasticity and bifurcation properties of the arterial wall directly affected the peak value and wave velocity in the propagation of the pressure pulse wave. In addition, the stress concentration effect was evident at the bifurcation site, which was prone to the occurrence of lesions, such as arterial lumen stenosis, and the formation of arterial plaques. In conclusion, in atherosclerotic disease, the time course of pulse-wave propagation changes due to alterations in the geometry and material properties of the vessel wall. The preliminary results of this research will be crucial in guiding the evolution of the pressure pulse wave and the initial diagnosis of atherosclerotic disease through its waveform.
Research Article
Analysis of pulse wave propagation characteristics in abdominal aortic sclerosis disease
https://doi.org/10.21203/rs.3.rs-3230865/v1
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pulse wave
arteriosclerosis
vascular bifurcation
fluid-structure coupling analysis model
numerical simulation
Pulse waves collectively refer to the pulsations of blood pressure, blood flow velocity, and blood flow during the periodic contraction and diastole of the heart and deformation of the vascular wall propagating through the vascular system (Qiao and Wu 2000). Pulse waves contain a wealth of information about human physiology and pathology (Zhang et al. 2019) and can be applied clinically to assess the cardiovascular status of patients with hypertension, coronary artery disease, and other diseases (Qi et al. 2018; Kim et al. 2014; Gajdova et al. 2017; Peng et al. 2018). Geometrically, the human arterial vasculature is complex, with fractal growth of different degrees of curvature and bifurcation; meanwhile, arteries have a fractal structure (Yan et al. 2022) that carries blood from the heart to other organs along the trunk of the fractal tree. At the arterial bifurcation, the hemodynamic circulatory system is determined by the redistribution of blood flow field and the high gradient of temporal and spatial changes in tangential stresses on the vessel wall surface. Atherosclerotic disease is prone to develop with aging. One of the pathological bases of atherosclerosis is the change in the microstructure. Clinical studies have also revealed that physiological changes in arterial elasticity precede changes in vessel wall elasticity, that is, they occur before they cause evident clinical symptoms (Gong et al. 2018). In addition, thickening of the arterial wall and narrowing of the arterial lumen occur when noninflammatory lesions develop in the arteries. This condition is due to the deposition of lipids in the arterial lining and the gradual formation of atherosclerotic plaques, which lead to a great resistance to blood flow and the lack of blood and oxygen supply to the body’s organs that results in organic dysfunction. Therefore, a study on the effect of arterial wall elasticity and wall thickness on the propagation characteristics of pulse waves is important to further understand the mechanobiological mechanisms of atherosclerotic disease. The early screening of atherosclerotic disease by monitoring of pulse-wave waveform in vitro serves as an essential clinical guide.
Current studies related to bifurcation vessels and atherosclerotic disease include the following. The carotid artery were observed that geometry had an important effect on hemodynamics by performing numerical simulations (Perk et al. 1990, 1991). Three-dimensional modeling and numerical simulation of the pulsatile blood flow field were carried out under three different outlet flow distribution ratio conditions, and the effects of blood flow distribution ratio and bifurcation geometry characteristics on local hemodynamics were analyzed (Wang et al. 2019). The effect of sudden changes in hemodynamic characteristics on the development of bifurcated arterial vascular lesions were determined using numerical calculations (Peng et al. 2010), which revealed that the aggravation of bifurcated arterial main branch lesions is highly likely to lead to the appearance of atheromatous plaque lesions at the branch bifurcations. Atherosclerosis had a greater effect on the control of hypertension by linear regression statistical analysis (Liu et al. 2022). A geometric model of carotid bifurcation was constructed using Gambit software based on a solid model of human carotid bifurcation (Yu et al. 2007). The characteristics of pulse signals were studied in patients with coronary artery disease and compared them with those of healthy adults (Li et al. 2015), they concluded the potential role of pulse signals in coronary artery disease diagnosis. The pulse waveforms of six volunteers were analyzed to investigate the relationship between cardiovascular function, fatigue, and autonomic function and pulse waveforms and used it to assess the health status of the volunteers (Shi et al. 2017). The model-based analysis of arterial pulse signals were investigated in arterial wall parameters using a microfluidic-based tactile sensor. A dynamic system model of the arterial wall and a hemodynamic model of the blood flow were developed to interpret the extracted key features for estimating arterial wall parameters (Wang et al. 2019). However, studies on the propagation characteristics of pulse waveforms in abdominal aortic sclerosis have not been reported.
Therefore, a two-way fluid-structure coupled finite element analysis model of the abdominal aorta was developed in this paper, with consideration of the conditions of blood viscosity and blood compressibility and the different elastic moduli and wall thicknesses of the vessel wall as the main indications of atherosclerosis.
2.1 Biomechanical geometric model construction
The human arterial system contains numerous bifurcated vessels, but only one is approximately symmetrically bifurcated, namely, the common iliac artery at the abdominal aorta. In this area, atherosclerosis often occurs due to the specificity of the arterial structure. The symptoms of atherosclerosis can be summarized in three major aspects, such as thickening of the vessel wall, reduction of the internal diameter of the vessel, and decrease in vessel elasticity, which lead to biomechanical changes in blood flow and vascular expansion and contraction in the arterial system (Wang 2003). Therefore, the human abdominal aorta–common iliac artery, which features a high pulse wave, was the object of this study. The simulation software COMSOL Multiphysics was applied to establish a geometric model of the abdominal aorta, where the red and green parts represents the blood and arterial wall, respectively, the abdominal aorta is a straight thin-walled circular tube of equal thickness, and the common iliac artery is a curved thin-walled circular tube of variable thickness. The center of the circle at the upstream end of the abdominal aorta is the origin, and the axial direction of the vessel as the y-axis was used to establish a spatial right-angle coordinate system (Fig. 1).
According to the geometry of the human abdominal aorta– common iliac artery (Liu et al. 1990, 1991; Liu et al. 2022), the length L0 = 130 mm, internal diameter D0 = 13.8 mm, wall thickness h0 = 1.1 mm, and diameter–thickness ratio D0/h0 = 12.55; the downstream end face of the iliac artery D1 = 8.2 mm, thickness h1 = 0.9 mm, and length L1 = 65 mm upstream of the abdominal aorta. The end face and downstream end face of the common iliac artery are also called the inlet and outlet of blood flow, respectively. Three different points at the prebifurcation, bifurcation, and postbifurcation sites of the abdominal aorta were denoted as monitoring points A, B, and C, respectively.
2.2 Blood flow control equations and description of arterial material properties
In this paper, blood was considered a compressible Newtonian fluid, and subscripts b and v were used to distinguish the physical quantities in the blood and vessel wall. The density, bulk compression modulus, and dynamic viscosity coefficient of blood were denoted as ρb, Kb, and µ, respectively, and in this paper, according to the literature (Urick 1947; Wang et al. 2001), Kb = 2.5 GPa, the dynamic viscosity is µ = 0.004 Pa⋅s (Laurent et al. 1994 ), and the density of healthy human arterial walls is expressed by ρv. The bulk compression modulus of blood can be converted into the blood density ρb as a function of pressure p, as shown in Eq. (1).
The vessel wall is a hyperelastic material, as described by the Mooney–Rivlin intrinsic model (Gao et al. 2009; Wu et al. 2021). Table 1 shows the material parameters of the arteries.
|
Parameters |
C10 |
C01 |
C20 |
C02 |
C11 |
|---|---|---|---|---|---|
|
Values |
-8418 |
9189 |
70101 |
12834 |
-18538 |
The blood volume force vector (Fb), flow velocity vector (vb), and pressure (p) must be set. In this paper, we considered the dynamic viscosity coefficient of blood, i.e., the magnitude of the internal friction force per unit area when the blood flow velocity gradient was 1 s− 1. According to the fluid dynamics theory, the blood flow in the human abdominal artery also satisfies the law of conservation of mass, law of conservation of momentum, and law of conservation of energy. Eq. (2) shows the controlling equation of the blood flow field.
$$\left\{ \begin{gathered} \frac{{\partial {\rho _\text{b}}}}{{\partial t}}+\nabla \cdot ({\rho _\text{b}}{{\mathbf{v}}_{\mathbf{b}}})=0 \hfill \\ {\rho _\text{b}}\frac{{\partial {{\mathbf{v}}_{\mathbf{b}}}}}{{\partial t}}+{\rho _\text{b}}{{\mathbf{v}}_{\mathbf{b}}} \cdot \nabla {{\mathbf{v}}_{\mathbf{b}}}=\nabla \left( { - p{\mathbf{I}}+{{\mathbf{\tau }}_{\mathbf{b}}}} \right)+{{\mathbf{F}}_{\mathbf{b}}} \hfill \\ (\frac{{\partial E}}{{\partial t}}+{{\mathbf{v}}_{\mathbf{b}}} \cdot \nabla E)={\rho _\text{b}}Q - \nabla \cdot {\mathbf{q}}+{\rho _\text{b}}{{\mathbf{F}}_{\mathbf{b}}} \cdot {{\mathbf{v}}_{\mathbf{b}}} - \nabla \cdot (p{{\mathbf{v}}_{\mathbf{b}}})+\nabla \cdot ({{\mathbf{\tau }}_{\mathbf{b}}} \cdot {{\mathbf{v}}_{\mathbf{b}}}) \hfill \\ \end{gathered} \right.$$
2
where \({{\mathbf{\tau }}_{\mathbf{b}}}\) is the viscous stress tensor obtained using Eq. (3):
$${{\mathbf{\tau }}_{\mathbf{b}}}{\text{=}}\mu \left( {\nabla {{\mathbf{v}}_{\mathbf{b}}}+{{\left( {\nabla {{\mathbf{v}}_{\mathbf{b}}}} \right)}^T}} \right)$$
3
In Eqs. (2)–(3), is the second-order unit tensor, i.e., t is the blood flow time, E refers to the blood system energy, Q denotes the heat transferred to the blood system per unit mass from thermal radiation or endothermic sources, and q indicates the heat flux. This paper disregarded the effect of gravity, heat transfer, and heat dissipation during blood flow, i.e., Fb =0, Q = 0, and q = 0. Thus, Eq. (2) can be simplified as follows:
$${\rho _\text{b}}(\frac{{\partial E}}{{\partial t}}+{{\mathbf{v}}_{\mathbf{b}}} \cdot \nabla E)= - \nabla \cdot (p{{\mathbf{v}}_{\mathbf{b}}})+\nabla \cdot ({{\mathbf{\tau }}_{\mathbf{b}}} \cdot {{\mathbf{v}}_{\mathbf{b}}})$$
4
The circumferential stress σθ and circumferential strain εθ of the thin-walled vessel under the action of the internal pressure p in the abdominal artery were derived using Eqs. (5) and (6), respectively.
$${\sigma _\theta }{\text{=}}\frac{{p{D_0}}}{{2{h_0}}}$$
5
2.3 Continuity conditions and computational units for bidirectional blood vessel-wall flow–solid coupling
In the human physiological environment, the macroscopic biomechanical process of the abdominal aorta is mainly the interaction between blood and the vessel wall, and abdominal aortic sclerosis disease is directly related to the elasticity of the vessel wall and affects blood flow velocity and fraction. To this end, we calculated and analyzed the effect of changes in the elastic modulus of the vessel wall on pulse-wave propagation velocity by establishing a blood-vessel wall bidirectional flow–solid coupling model at a local scale.
For the blood vessel-wall bidirectional flow–solid coupling model, according to the continuous medium mechanics theory, at the blood vessel-wall flow–solid coupling interface, the blood and vessel wall should satisfy the displacement continuity and stress continuity boundary conditions (Eq. (7)):
$$\left\{ \begin{gathered} {{\mathbf{u}}_{\mathbf{b}}}={{\mathbf{u}}_{\mathbf{v}}} \hfill \\ {{\mathbf{\sigma }}_{\mathbf{b}}}={{\mathbf{\sigma }}_{\mathbf{v}}} \hfill \\ \end{gathered} \right.$$
7
where ub and uv denote the displacement vectors on the blood and vessel walls, respectively. Meanwhile, σb and σv are the stress vectors on the blood and vessel walls, respectively. The inlet and outlet end surfaces of the local artery calculation model are fixed constraints, and the vessel wall does not produce axial motion but only radial up-and-down deformation. The blood and vessel wall were divided into calculation cells separately, and both tetrahedral cells were used. The relative error of the calculation result was 0.005%, and the mesh irrelevance was verified. A total of 289,594 tetrahedral cells and 51,753 mesh vertices were selected for the calculation model in this paper, which can meet the accuracy of 0.005%. Second, the blood flow and pulse-wave propagation cause the vascular wall to undergo a periodic rise and contraction consistent with the cardiac cycle. The periodic rise and contraction deformation field of the vascular wall has an effect on the blood flow and pulse-wave propagation. Therefore, in this model, the interactions between blood and vessel wall deformation were combined, and the control equations at each node of the blood and vessel wall were assembled to form the stiffness and displacement matrices of the local arterial system. Third, the pulse waveform of a 23-year-old healthy male volunteer was collected from the human biomechanics laboratory of Ningbo University, with the application of the Dawson DS01-C pulse diagnostic instrument (Fig. 2). An informed consent was obtained from the subject, ethical review was passed, and authorization for use of the collected data was obtained. As a loading condition, the relative pressure at the exit boundary was controlled at 0 Pa. The computational period was 0.1 s, the time step was 10− 4 s, and the maximum number of iterations in each time step was 50. The fully coupled analysis algorithm, the arbitrary Lagrangian‒Eulerian method in COMSOL Multiphysics, was applied to obtain the local decoupling solution of the displacement matrix of the arterial system to achieve the solution of the control equations of the abdominal arterial system. The waveform period was shortened by a factor of 10 for calculation based on dimensionless data analysis to improve the computational efficiency.
3.1 Pressure pulse-wave peak decay analysis before and after bifurcation
Three different locations, namely, A, B, and C, on the central axis of the abdominal aorta were selected as monitoring points to analyze the propagation of the pressure pulse wave and axial velocity pulse wave in the abdominal aorta (Fig. 3).
Figure 3 shows the characteristics of pressure pulse-wave propagation at three different monitoring points on the abdominal aorta. The pressure pulse wave at the three monitoring points underwent multiple reflections, and the wave amplitude magnitude was unaffected by the reflected wave during the first ascending phase of the cardiac cycle in any of the three monitoring points. At monitoring point A, which was close to the entrance end, the pulse wave propagating through the entrance was superimposed on the reflected wave generated at the border of the exit end, which resulted in a pronounced change in the pulse waveform during the first descending branch phase, which manifested as a heavy beat wave. Comparison of the three different monitoring points revealed the considerable decay in the pressure pulse-wave amplitude before and after the bifurcation of the abdominal aorta. The highest pressure pulse-wave peak was observed at monitoring point A in the main vessel before the bifurcation and the lowest at monitoring point C in the branch vessel after the bifurcation. When monitoring point A was used as the base point, the peak pressure pulse wave at monitoring point B near the bifurcation and at monitoring point C after the bifurcation decreased by 22.06% and 41.25%, respectively. Thus, the bifurcation geometry feature can reduce effectively the wave amplitude in pulse-wave propagation and equalize the distribution of bioenergy carried by the pulse wave.
3.2 Analysis of the peak attenuation of the velocity pulse wave before and after bifurcation
Three different locations, namely, A, B, and C, on the central axis of the abdominal aorta were selected as monitoring points to analyze the propagation of the pulse-wave velocity in the abdominal aorta (Fig. 4).
The axial-velocity pulse waves at all monitoring points underwent multiple reflections, and in the first ascending phase of the cardiac cycle, the wave amplitude magnitude was unaffected by the reflected waves. In the comparative analysis of the three monitoring points, the bifurcation of the abdominal aorta elevated the peak of the axial velocity pulse wave, and the first-wave peaks at the three monitoring points were analyzed. The peaks at monitoring points B and C were higher than that at monitoring point A by approximately 22.30% and 116.06%, respectively.
3.3 Pulse-wave velocity assessment of the abdominal aorta
The research on pulse wave velocity dates back to the early part of the last century. The pulse-wave velocity in arteries reflects vascular stiffness and vascular health indicators, and it is expected to gradually become an important and relatively independent predictor for cardiovascular disease assessment (Nichola et al. 2019). A noninvasive diagnostic tool for determining the degree of atherosclerosis using pulse-wave velocity can be used to aid the early screening of related diseases.
This section focuses on the conduction velocity of pressure pulse waves in the abdominal aorta, which may be noted. In general, the pulse transit time (PTT) can be obtained by measuring the PTT, as shown in Eq. (8):
$${v_{PWV}}=\frac{{{S_{PW}}}}{{{t_{PTT}}}}$$
8
where \({S_{PW}}\)denotes the pulse-wave conduction distance, and \({t_{PTT}}\) is the pulse-wave conduction time measured chronologically at the corresponding conduction distance. For the calculation of propagation velocity of the pressure pulse wave in the bifurcated vessels of the abdominal aorta, combined with the description in Section 3.1, the first wave peak at monitoring points A, B, and C was used as the timing point for calculation, and given the distance between different monitoring points and the time difference between wave peak points, the calculated average wave velocities of the pressure pulse wave were 12.50 and 19.13 m/s on the AB and BC segments in the artery, respectively. The pulse-wave velocity in the BC segment after bifurcation was approximately 53.04% higher than the average wave velocity in the AB segment before bifurcation. By contrast, the axial velocity pulse-wave speed differed in that at all three monitoring points before and after the vascular bifurcation, the axial velocity pulse wave underwent multiple reflections and was unaffected by its reflected wave during the first ascending phase of the cardiac cycle. The analysis of the first wave at the three monitoring points may be useful as an example. The peak velocity waves at position points B and C were approximately 22.30% and 116.06% higher than those at position point A, respectively. The average velocities of velocity pulse wave in the AB and BC segments of the vessel were 13.00 and 4.07 m/s, respectively, with the latter being 68.70% lower than the average velocity of the former, a trend that is the opposite of the pressure pulse-wave situation.
The bifurcated geometry of the artery reduces the propagation speed of the axial velocity pulse wave. In addition, the results of this calculation and analysis, when combined with the tradional Chinese Medicine (TCM) pulse theory, confirm that the TCM pulse theory distinguishes between “floating,” “medium,” and “sunken” pulses. The results of this calculation also confirm the Chinese medicine theory that the pulse has “floating,” “middle,” and “sinking” characteristics and “number,” “shape,” and “potential.” The large or small amplitude of the pressure pulse wave corresponds to the floating or sinking characteristics of the pulse, respectively, and the size of the velocity pulse-wave amplitude reflects the “potential” characteristics of the pulse.
3.4 Stress field distribution in the abdominal aorta
Diseases, such as abdominal aortic atherosclerosis, abdominal aortic thrombosis, and aneurysms, are clinically common and a serious health and quality of life problem for patients. These clinical conditions share disrupted balanced distribution of the healthy body stress field in the abdominal aorta, with histologically significant lesions, such as atherosclerosis, thrombosis, and aneurysm, which result in a redistribution of the stress field across the abdominal aorta.
This section calculates the distributions of the stress, strain, and blood flow fields over the abdominal aorta. The stress, strain, and blood flow field distributions on the abdominal aortic wall were examined at 0.13, 0.20, 0.27, 0.41, and 0.66 s, starting with the diastolic timing of the heart during one cardiac cycle. Figure 5 shows the von Mises stress cloud over the abdominal aortic wall, without considering the various lesion scenarios, based on the bidirectional fluid‒solid coupling model described in Section 2. As shown in Fig.s 5(a) and 5(b), the stress and strain distributions on the abdominal aortic wall were relatively uniform at approximately 0.13 s. At approximately 0.20 s, stress concentrations appeared at the bifurcation, stress concentrations at the bifurcation were evident, and the strain was the greatest at 0.27 s. At approximately 0.041 s, one cycle of the pulse wave propagated to the proximal part, at which time the stress and strain in the abdominal aortic inner wall approached zero, and at 0.066 s, given the reflection of the pulse wave, the stress and strain fields were redistributed based on the superposition of multiple waves in the bifurcated vessel.
Blood flow field was also redistributed at the bifurcation, which predisposed the arterial bifurcation to a load imbalance due to its inability to resist the pressure of blood flow in the lumen; as a result, lesions of varying degrees of severity, which depends on individual patients, were observed (Mei 2007; Liu et al. 2013). This finding confirms the high clinical probability of atherosclerosis and lesions at the location of the abdominal aortic bifurcation. Analysis of the effect of elastic modulus of the abdominal aorta on the propagation characteristics of pulse waves.
In terms of the mechanical properties of the material, changes in the elastic modulus of the vessel wall are one of the causes of atherosclerosis, plaque, thrombosis, and other lesions in the inner wall of the abdominal aorta. The general trend is that as lesions occur, the elastic properties of the vessel decrease, which must also affect the propagation of pressure and velocity pulse waves in the artery. Therefore, in this section, the elastic moduli of the abdominal aorta were considered to be 2.5, 3.0, 3.5, 4.0, and 4.5 MPa for the numerical calculation of pulse-wave propagation characteristics based on the bidirectional fluid‒solid coupled finite element analysis model in Section 2 and with reference to changes in elastic modulus parameters of the arterial vessel wall of patients with atherosclerosis in the literature (Jiang et al. 2016).
4.1 Effect of the elastic modulus of the abdominal aorta on pressure pulse-wave propagation
First, the propagation of the pressure pulse wave over the abdominal artery was analyzed for arteries with different elastic moduli and various location points before and after the bifurcation, with the three typical location points in Fig. 1 used as an example. Figure 6 shows the calculation results.
Figures 6(a)–(c) show that the lower the elastic modulus of the vessel wall, the higher the peak pressure pulse wave in the artery at monitoring points in A, B, and C before and after the bifurcation of the abdominal aorta. As the modulus of elasticity of the vessel wall increased, the peak pressure pulse wave at each monitoring point decreased, and the effect of arterial elasticity on the peak pressure pulse wave became more pronounced after the bifurcation of the vessel. The peak pressure pulse wave at 3.0, 3.5, 4.0, and 4.5 MPa decreased by approximately 0.37%, 1.15%, 1.83%, and 2.57% at monitoring point A, respectively. The decreases at monitoring point B reached 0.31%, 1.00%, 1.61%, and 2.57% at 2.5 MPa. In the 2.5 MPa scenario, the pressure at monitoring point B was reduced by approximately 0.31%, 1.00%, 1.61%, and 2.40%, and by approximately 3.92%, 7.44%, 10.37% and 13.20% at monitoring point C, respectively. The peak size of pressure pulse wave highlights the elasticity of the artery, that is, the larger the peak, the less sclerosis and lesions on the vessel wall.
Second, the speed of pressure pulse-wave propagation in arteries with different moduli of elasticity was analyzed. From the distance between the monitoring points and the time difference between wave crests, the velocity of pressure pulse-wave propagation was calculated. The pressure pulse-wave propagation velocities at pressures of 3.0, 3.5, 4.0, and 4.5 MPa were approximately 8.32%, 15.52%, 20.96%, and 30.00% higher in the AB section, respectively, and 15.00%, 35.28%, 64.30% and 76.95% higher in the BC section compared with than those under 2.5 MPa. This shows that as the elastic modulus of artery increases, the pressure pulse wave propagates faster, and this phenomenon is more pronounced after artery bifurcation.
4.2 Influence of the elastic modulus of the abdominal aorta on the propagation characteristics of axial-velocity pulse waves
First, the propagation characteristics of axial-velocity pulse waves on the abdominal aorta were analyzed for different moduli of elasticity and location points before and after the bifurcation, with the three typical location points in Fig. 1 as examples. The calculation results are shown in Fig. 7.
Figure 7 shows that as the elastic modulus of the abdominal aortic vessel wall increased, a substantial and longer delay in propagation of the axial velocity pulse wave was observed after bifurcation for the same cardiac cycle timing. At 4.5 MPa, the delays were approximately 0.0019, 0.0025, and 0.024 s at monitoring points A, B, and C, respectively, compared with those at 2.5 MPa. This indicates that the artery was sclerotic, and the overall elasticity was weak, which can be verified by the axial velocity pulse wave. In addition, the axial velocity wave showed an evident superposition effect with the reflected wave, and the wave propagation velocity exhibited a fluctuating upward trend and stabilized during one cardiac cycle. As the modulus of elasticity increased, the rise of the axial velocity wave decreased, and after bifurcation, it became increasingly evident. The velocity of axial-velocity wave propagation at monitoring points A and B was approximately 0.45 m/s, and that at monitoring point C was approximately 0.55 m/s.
The abdominal aorta, as one of the most important arteries in the human body, transfuses blood to several organs. Atherosclerotic disease is highly prevalent and seriously affects human life and health. The complexity of physiological environment and blood flow in the human body and how to understand the physiological and mechanical behavior of arteries in depth and from multiple perspectives are important aspects of cognitive pathology. In this paper, in consideration of hemodynamic viscosity and compressibility, we analyzed the elastic modulus of the arterial wall as one of the main indications of the atherosclerotic phenomenon and the bifurcation geometric properties to analyze the propagation characteristics of pulse waves in the abdominal aorta using the bidirectional fluid‒solid coupled finite element analysis model of the abdominal aorta and determine atherosclerosis of the abdominal aorta in a quantitative manner on the basis of the main parameters of the characteristics of pulse waveforms. In general, if the arterial wall hardens due to various physiological reasons, and atherosclerosis occurs, the elasticity modulus of the arterial wall increases, the peak of the pressure pulse wave reduces considerably, the propagation speed of the pressure wave accelerates substantially, and the speed of the axial pulse wave is reduced. Specifically, if the elastic modulus of the arterial wall increases by an average of 20%, the average decreases in the peak value of the main wave of the pressure pulse wave at the prebifurcation section of the artery, at the point of bifurcation, and at the postbifurcation branch were approximately 0.64%, 0.6%, and 3.3%, respectively, the average speed of the pressure pulse-wave propagation were 12.50 and 19.13 m/s. The average wave speed of the pulse wave of the postbifurcation branch of the vein was approximately 53.04%. The bifurcation of the abdominal aorta creates a high concentration of stress and a high rate of lesions, such as atherosclerosis, stenosis, and other diseases, in the arterial lumen. This is consistent with the results of clinical studies. The preliminary findings of this paper may provide a new idea for the in vitro pulse-wave prediction for the prevention and noninvasive diagnosis of atherosclerotic diseases.
Acknowledgments and Fundings
This work is supported by National Natural Science Foundation of China (11872218), Zhejiang Provincial Natural Science Foundation Key Projects (Z23A020001), National Natural Science Foundation of China Regional Innovation Key Project (U21A20502), Zhejiang Province Traditional Chinese Medicine Science and Technology Foundation (2022ZB317), the first batch of Medical and Health Brand Discipline Foundation in Ningbo (PPXK2018-07).
Conflict of interest statement There are no conflicts of interest between the authors of this paper and other external researchers or organizations that could have inappropriately influenced this work.
Author contributions Fuxing Miao: Supervision, Resources, Funding acquisition, Methodology, Writing – original draft, Writing - review & editing. Xuehang Sun, Bensen Li: Conceptualization, Investigation, Formal analysis, measurement, Data curation, Validation. Yicheng Lu: Software, interpreted the analysis results. Xiabo Chen: theory of TCM. All authors read and approved the final manuscript.
Ethical Approval This work has been reviewed and approved by Ethical Committee of Ningbo Traditional Chinese Medicine Hospital, the document No. AF/SQ-01/03.1. This study do not involve animal subjects.
Human and animal rights This study does not contain studies with animals by any of the authors.
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No competing interests reported.