Pulsatile hemodynamics in patient-specific thoracic aortic dissection models constructed from computed tomography angiography

Abstract

PURPOSE: Thoracic aortic dissection (TAD) is considered one of the most catastrophic and non-traumatic cardiovascular diseases associated with high morbidity and mortality rates in clinical treatment. The purpose of this paper is to investigate the pulsatile hemodynamics changes throughout a cardiac cycle in a Stanford Type B TAD model with the aid of computational fluid dynamics (CFD) method.

METHODS: A patient-specific dissected aorta geometry was reconstructed from the three-dimensional (3D) computed tomography angiography (CTA) scanning. The realistic time-dependent pulsatile boundary conditions were prescribed for our 3D patient-specific TAD model. Blood was considered to be an incompressible, Newtonian fluid. The aortic wall was assumed to be rigid, and a no-slip boundary condition was applied at the wall. CFD simulations were processed using the finite volume (FV) method to investigate the pulsatile hemodynamics in terms of blood flow velocity, aortic wall pressure, wall shear stress and flow vorticity. In the experiments, blood velocity, pressure, wall shear stress and vorticity distributions were analyzed qualitatively and quantitatively.

RESULTS: The experimental results demonstrated a high wall shear stress and strong vertical flow at dissection initiation. The results also indicated that wall shear progressed along the false lumen, which is a possible cause of blood flow between aortic wall layers.

1 Introduction

Cardiovascular diseases have become the leading causes of death in many developed countries and have been increasing steadily during recent years. Clinically, aortic dissection (AD) is one of the most catastrophic and non-traumatic cardiovascular diseases associated with high morbidity and mortality rates [1]. It has been reported in the literature that AD has a case fatality rate of up to 90% when left untreated [2, 3]. AD commonly results from an intimal tear in the aortic wall which subsequently allows blood to follow within the middle layers of the wall, and splits the original aortic lumen into a true and false lumen under aortic pressure [4, 5]. The newly-generated lumen is regarded as the false lumen (FL), while the original passageway for blood flow is called the true lumen (TL). According to the site of origin and proximal or distal involvement, AD can be classified into Stanford Type A lesions, which involve the ascending aorta, and Stanford Type B lesions, which are confined to the descending aorta distal to the left subclavian artery [6]. It is generally thought that AD essentially arises from many potential causes, such as family history, genetic factors, aortic geometry, mechanical properties and hemodynamic changes [2 , 7–9]. In this study, we emphasizes the numerical simulations of cardiovascular hemodynamics in patients with Stanford Type B TAD.

Numerical simulation methods, particularly the computational fluid dynamics (CFD) approach, are able to provide detailed blood flow patterns in AD, and have received increasing attention in the investigation of cardiovascular diseases [1 , 10–12]. The numerical simulations could enhance our understanding of the pathogenesis and progression of cardiovascular diseases, as well as predict the clinical outcomes and treatment responses. In CFD simulations, both computed tomography angiography (CTA) [1 , 14] and magnetic resonance imaging (MRI) [15 –17] are the commonly-used standard imaging tools to reconstruct the realistic aorta geometries. In these two imaging modalities, CTA can be performed at high spatial and temporal resolution. By using the CTA images acquired, the anatomical features of AD, including the sizes and shapes of TL and FL, as well as the sizes and locations of entry and re-entry tears, can be observed visually. The use of time-average magnetic resonance angiography (MRA) [17 –19] has also received a lot of attention due to its capacity to obtain in vivo measurement of blood velocities with high spatial and temporal resolution. It is able to provide complementary information for hemodynamic simulations with patient-specific AD models. Recently, both phase-contrast MRA and CFD methods have been combined to perform the patient-specific hemodynamics analysis [17]. In order to enhance the accuracy of CFD simulation, Cheng et al. [20] proposed to implement the verification and validation of CTA-based CFD simulations by comparison with in vivo blood velocity data obtained by means of phase-contrast MRI (PC-MRI). However, it is intractable to directly measure other important hemodynamic parameters (e.g., pressure and wall shear stress) using the PC-MRI technique.

In current literature, rigid wall CFD and elastic wall fluid-structure interaction (FSI) have been widely used to numerically simulate the hemodynamics to assist clinical researchers. Rigid wall CFD simulations of blood flow in patient-specific AD models have been reported [1 , 21]. For instance, Alimohammadi et al. [1] implemented the dynamic boundary conditions by coupling a three element Windkessel (RCR) model to the outlets. Chen et al. [18] conducted a longitudinal CFD-based study of a patient with Stanford Type B AD at initial presentation and after 4-year of best medical treatment (BMT). A CFD study with pulsatile boundary conditions was also implemented to investigate six different biomechanical factors involved in Stanford Type B AD [21]. To further improve the accuracy of numerical results, FSI has proven to be an effective simulation tool [22 –24]. The FSI has also been implemented to simulate the patient-specific hemodynamics in patients with thoracic aortic aneurysm [25] and intracranial aneurysm [26].

In this study, we focused our main attention on the numerical simulation of blood flow in a patient with thoracic aortic dissection (TAD). It has been scientifically proven that FSI was not applicable when the intimal flap in the dissection site was too thin [2]. Moreover, previous studies also proved that the region of high wall shear stress were not significantly different between rigid vessel wall and elastic one [27]. For a practical clinical application study, regions with low wall shear stress is in less concern. Thus we will adopt rigid wall CFD instead of FSI to investigate the aortic hemodynamics in our patient-specific TAD model with a thin intimal flap. To the best of our knowledge, there are a very limited number of publications concerning the pulsatile hemodynamics in patient-specific TAD models during the cardiac cycle [1, 2]. To achieve better understanding of the pathogenesis of TAD, the pulsatile hemodynamics including blood flow velocity, aortic wall pressure, wall shear stress and flow vorticity, which are intractable to achieve in vivo, are investigated using CFD technique throughout the cardiac cycle. From the clinical point of view, the simulation results could provide complementary information of pulsatile hemodynamics to clinicians for better treatment planning and monitoring in the future.

The remainder of this paper is organized into several sections. Material and methods section briefly introduces the patient-specific dissected aorta geometry modeling, CFD modeling as well as boundary and flow conditions. Experimental results on pulsatile hemodynamics in a 3D patient-specific TAD model during the cardiac cycle are performed in results and discussions section. Limitations section presents the limitations of our current work on CFD simulations. Finally we conclude this paper by summarizing our contributions in conclusions section.

2 Material and methods

2.1 Patient-specific geometry modeling

Three representative cases of dissected aorta were obtained from the medical dataset – patients who have been diagnosed as suffering from TAD. The patients underwent the 3D CTA using a commercially available 16-slice CT system (Somatom Sensation 16, Siemens, Forchheim, Germany) during aspiratory breath-hold with the following parameters: acquisition matrix 512×512, tube voltage 120 kV, tube current 600 mA, field of view 340 mm and slice thickness 0.6 mm. The total number of scanning slices is 1567 and the range of scanning is from neck to buttocks. From the initial CTA images, the segmentation and surface reconstruction of the patient-specific dissected aorta model were performed by using an image processing package MIMICS (Materialise HQ, Louvain, Belgium). Detailed anatomical structures of the reconstructed TAD surface and exported in STL formation as shown in Fig. 1. The final reconstructed geometries were volume meshed by ICEM (ANSYS 12.1 Inc. Canonsburg, USA) with tetrahedral elements in 1 mm unit size. 36431, 29823 and 24933 tetrahedral elements were generated for patient 1–3 respectively in the volume meshing procedure. The study protocol was approved by the ethics committee of the university and hospital, and written informed consent were obtained from the subjects.

2.2 Computational fluid dynamics modeling

It has been proven that non-Newtonian behavior on blood flow is only non-negligible in small vessels (less than 0.1 mm in diameter) where the shear rates are small. Meanwhile the blood flow is usually considered as a laminar flow in large arteries. In this study, the blood flowing through both the FL and TL was assumed to be a homogeneous, laminar, incompressible Newtonian fluid with a dynamic viscosity of 0.0035 Pa⋯ and a constant density of 1050 kg/m³. The aortic wall was assumed to be rigid, and a no-slip boundary condition was applied at the wall during CFD simulations. The 3D incompressible continuity and Navier-Stokes equations that govern the blood flow in TAD can be expressed as follows

1) Mass conservation equation: $\nabla \cdot u = 0$ (1)

2) Momentum conservation equation: $\frac{\partial u}{\partial t} + u \cdot \nabla u = \frac{1}{ρ} \nabla \cdot [- pI + η (\nabla u + (\nabla u)^{T})]$ (2) where u is the velocity field, ρ is the blood density, p is the static pressure and η denotes the dynamic viscosity. The general-purpose CFD solver ANYSYS CFX-14.0 with finite volume (FV) method was implemented to solve the Navier-Stokes equations (1) and (2), then to simulate the patient-specific blood flow in both FL and TL. K-Epsilon turbulence control was adopted with continuity equation class. Iteration would terminate when the root mean square (RMS) residual reached 10^∧-4. The final simulation results in terms of blood velocity, pressure distribution, wall shear stress and flow vorticity were visualized using the Paraview 4.4.

2.3 Boundary and flow conditions

In this study, the time-dependent physiologically representative pulsatile velocity and pressure waveforms were considered as the inlet and outlet boundary conditions, which were derived according to the previous studies in [25, 28]. In order to investigate the pulsatile hemodynamics in the 3D patient-specific TAD model during the cardiac cycle, the simulation adopted a steady state flow analysis over 1 s in 0.01 s time steps. Four different pulse time instants (T1 = 0.15 s, T2 = 0.20 s, T3 = 0.28 s and T4 = 0.40 s) were assigned, shown in Fig. 2. In CFD simulations, the pulsatile laminar blood flow is perpendicular to the inlet plane. Detailed analysis will be discussed in the following subsequent paragraphs, based on the steady-state cardiac cycle.

3 Results and discussions

The hemodynamic pattern for the patient-specific TAD model was investigated in terms of velocity visualization, pressure distribution and wall shear stress (WSS) at four time instants (T1 = 0.15 s, T2 = 0.20 s, T3 = 0.28 s and T4 = 0.40 s) during the cardiac cycle. These time instants were considered due to their medical importance in clinic.

3.1 Velocity

To investigate the aortic blood flow patterns, 3D visualization of the blood flow streamlines and velocity fields, shown in Fig. 3, were obtained at four consecutive critical times. The blood flow was also visually illustrated in the ascending and descending thoracic aorta. The flow patterns are obtained from 4 different cardiac stages, namely early systole (T1 = 0.15 s), mid systole (T2 = 0.20 s), late systole (T3 = 0.28 s), and early diastole (T4 = 0.40 s) respectively. At early and late systoles (T1, T3), the velocity fields have the similar velocity magnitude distribution. At mid systole (T2), the velocity magnitudes appear high in the left subclavian artery (LSA), left common carotid artery (LCCA) and brachiocephalic artery (BA). The velocity increases in the coarctation of aorta and in the regions near entry tear. The increased velocity magnitude may be associated with the initiation and progression of intimal tear. In contrast, the velocity magnitude is decreased significantly at early diastole (T4).

To further illustrate the simulation results, axial cross-sectional velocity profiles at eight different locations (P1-P8) are generated and shown in Fig. 4. The velocity profiles at the proximal ascending aorta (P1) seem to be axisymmetric and even at early systoles, late systoles and early diastole (T1, T2 and T4). During mid-systoles, a small asymmetric flow was initiated at the entrance of ascending aorta (T2, P1). When blood is further propagated to the tear entry (P2), the flow profile becomes anomalous and strongly asymmetric. The tear entry commonly starts from superior arc of aortic arch. At the descending aorta (P3-P8), the degree of non-axisymmetry seems to be dependent on the local geometric features (e.g., curvature of the descending aorta [29]). More quantitative details on velocity changes are summarized in Fig. 5, which depicts the comparison of velocity magnitude at different time instants for various axial cross-sections (P1-P8) during the cardiac cycle.

3.2 Pressure

It is generally thought that pressure is a key factor of further progression of the FL. Fig. 6 displays the pressure distribution at four consecutive critical times during the cardiac cycle. At early, mid and late systoles, the highest pressures are found in the aortic root and ascending aorta while the regions of low pressure locate in the outlet arteries. The vessel pressure in FL and TL are generally in same scale throughout the cardiac cycle. It indicates that the blood pressure in FL and TL may not be associated with the generation of descending aortic dissection along the aorta. Moreover, the pressure increases rapidly at the inlet and outlet regions; whereas the low pressure mainly distributes in the descending aorta.

It can be observed that, if the pressure magnitude is ignored, the different inlet and outlet boundary conditions have a similar effect on the blood flow patterns during whole cardiac cycle. In our opinion, the small variation in blood pressure along dissected aorta may not be a key hemodynamic feature in the mechanism of initiation and progression of dissected aorta.

3.3 Wall shear stress

It is well known that WSS plays an important role in hemodynamic studies associated with cardiovascular diseases. It is involved in the generation of TAD, since elevated values can lead to cleavage formation, and subsequently contributes to an enlargement of FL [5, 30]. In practice, WSS cannot be measured directly using current in vivo methods, but can be determined by calculating the gradient of velocity flow flied obtained by CFD technique [2]. Figure 7 shows the surface plots of WSS at four consecutive critical times. During the cardiac cycle, the high WSS can be found in the LSA, LCCA and BA, as expected. From early systole (T1) to early diastole (T4), the highest WSS values are listed are generally appears in the tear initiations and tear endings. The WSS value in the FL are significantly larger than that in the TL during mid systole (T2), which infers the possible initiation and progression of intimal tear. It has been reported in [1, 31] that high WSS could lead to increased risk of intimal tear or aortic aneurysm formation; whereas low WSS values are connected with the increased risk of aortic aneurysm expansion.

3.4 Vorticity

The pseudovector field vorticity, defined as the curl of velocity field, is a measurement of localized rotation pattern in continuum mechanics. In some fluid phenomenon, such as the blowing out of candle and convection flow, are explained in terms of vorticity instead of basic velocity and pressure. In formation and propagation of vortex rings, the fluid dynamic parameter is particularly in monitor. The surface vortex in the four featured time points is illustrated in Fig. 8. Peak vortical flow appears at aortic tear initiation points. The pattern of vortex is closely related with aortic shape. But the blood rotation strength pattern is in good agreement with WSS. The result give a hint that blood vorticity may be a feature factor that cause tear in aortic arch.

Similar to the slice strategy in velocity analysis, vorticity in early, mid, late systole and early diastole (T1-T4) are probed with 8 difference slices (P1-P4) as shown in Fig. 9. A more detailed flow distribution may refer to the box plot in Fig. 10. Strongest vortex rings are observed in P2 and P3, where the initiation of vessel tear is located. The vorticity magnitude decreases along the descending aorta. Thus it can be regarded that the high rotational magnitude plays an important role in the initiation and progression of dissected aorta.

4 Limitations

Similar to the previous numerical simulations [2 , 28], our CFD study was also implemented based on some simplifications and assumptions. They have the potential to result in some errors of computational simulations in clinical practice. The non-subject specific velocity and pressure boundary conditions of this study were derived from the published works [25, 27]. The actual boundaries of dissected aorta for the specific patient might be different. It has previously been reported in the literature that patient-specific boundary conditions were beneficial to improve the simulation accuracy [8]. The measurement of case sensitive boundary condition is challenging for the deep vessel location with dynamic movement. A direct flow velocity measurement using phase contrast magnetic resonance imaging (PC-MRI) would be an innovative tool to justify the computational result. But due to several technical reasons, such as long scanning during, expensive scanning cost, multi-modality space alignment and low scanning resolution, the application of PC-MRI in obtaining boundary profiles is still unavailable.

Moreover, the aortic walls in our study were assumed to be rigid to simplify the numerical simulation with a limiting computation resource. Actually non-linear elasticity is one of the most important mechanical properties of arterial wall, which is an important determinant in patient-specific hemodynamic simulations [25 , 32].

Since only few TAD cases were conduct rigid wall CFD simulation in this study, the result appeared to be not well justified. But the numerical simulations of the patient-specific TAD model could still enhance our knowledge of pulsatile hemodynamics during the cardiac cycle, especially the relation between wall shear stress and flow vortex. In future research, longitudinal cases will be implemented with non-rigid wall CFD simulation using in vivo aortic inlet and outlet profiles.

5 Conclusions

In this paper, we have investigated the hemodynamic changes in a patient-specific TAD model by means of CFD technique throughout a cardiac cycle. Experimental results showed that high wall shear stress difference between true and false lumens infers the possible generation of descending aortic dissection along the aorta. It is also thought that high vorticity may be associated with the initiation and progression of intimal tear. Our CFD simulation study could potentially contribute to assist clinical treatment planning by providing complementary information on the hemodynamic factors including blood flow velocity, aortic wall pressure, wall shear stress and flow vorticity, which are intractable to measure in vivo. It also serves to provide physicians with a better understanding of the pathogenesis and progression of dissected aorta. With the rapidly enhancing performances of computer technology and the clinical research achievements on cardiovascular diseases, we believe that the clinical treatment of TAD can be vastly improved in the near future.

Conflict of interest

We declare that we have no conflict of interest.

Footnotes

Acknowledgments

The work described in this paper was partially supported by grants from the Innovation and Technology Commission (Project No: ITS/149/14FP, GHP/028/14SZ), a grant from Technology and Business Development Fund (TBF) (Project No: TBF15MED004), and a grant from The Science, Technology and Innovation Commission of Shenzhen Municipality (Project No.: CXZZ20140606164105361).

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