Numerical analysis of wall shear stress in ascending aorta before tearing in type A aortic dissection

Accepted Manuscript Numerical analysis of wall shear stress in ascending aorta before tearing in type A aortic dissection Qingzhuo Chi, Ying He, Yong Luan, Kairong Qin, Lizhong Mu PII:

S0010-4825(17)30253-6

DOI:

10.1016/j.compbiomed.2017.07.029

Reference:

CBM 2740

To appear in:

Computers in Biology and Medicine

Received Date: 26 November 2016 Revised Date:

13 July 2017

Accepted Date: 30 July 2017

Please cite this article as: Q. Chi, Y. He, Y. Luan, K. Qin, L. Mu, Numerical analysis of wall shear stress in ascending aorta before tearing in type A aortic dissection, Computers in Biology and Medicine (2017), doi: 10.1016/j.compbiomed.2017.07.029. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Numerical analysis of wall shear stress in ascending aorta before tearing in type A

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aortic dissection

Qingzhuo Chi1, Ying He1, Yong Luan2*, Kairong Qin3, Lizhong Mu1 1

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Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian, 116024

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Department of Anesthesiology, The First Affiliated Hospital of Dalian Medical University, Dalian, China, 116011, email: [email protected] 3

Department of Biomedical Engineering, Dalian University of Technology, Dalian, 116024 Abstract

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Although the incidence of many cardiovascular diseases has declined as medical treatments have improved, the prevalence of aortic dissection (AD) has increased. Compared to type B dissections, type A dissections are more severe, and most patients with type A dissections require surgical treatment. The objective of this study was to investigate the relationships between the wall shear stress (WSS) on the aortic endothelium and the frequent tearing positions using computational fluid dynamics. Five type A dissection cases and two normal aortas were included in the study. First, the structures of the aortas before the type A dissection were reconstructed on the basis of the original imaging data. Analyses of flow in the reconstructed premorbid structures reveals that the rupture positions in three of the five cases corresponded to the area of maximum elevated WSS. Moreover, the WSS at the junction of the aortic arch and descending aorta was found to be elevated, which is considered to be related to the locally disturbed helical flow. Meanwhile, the highest WSS in the patients with premorbid AD was found to be almost double that of the control group. Due to the noticeable morphological differences between the AD cases and the control group, the WSSs in the premorbid structures without vasodilation in the ascending part were estimated. The computational results revealed that the WSS was lower in the aorta without vasodilation, but the pressure drop in this situation was higher than that with vasodilation in the ascending aorta. Significant differences were seen between the AD cases and the control group in the angles of the side branches of the aortic arch and its bending degree. Dilation of the ascending aorta and alterations in the branching angles may be the key determinants of a high WSS that leads to type A dissection. Greater

ACCEPTED MANUSCRIPT tortuosity of the aortic arch leads to stronger helical flow through the distal aortic arch, which may be related to tears in this region. Keywords: Aortic

dissection; Wall shear stress; Patient-specific model; Structured mesh generation; Computational fluid dynamics; CT images restoration

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1 Introduction

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Aortic dissection (AD), a tear in the intima under the action of pulsating blood, is one of the most complex cardiovascular diseases. The pathogenesis of AD is still unclear, but associations with hypertension and media-layer degeneration of the aorta have been suggested [1,2]. There are two main lumens in a dissected aorta. The lumen bounded by endothelium is called the true lumen, whereas the newly developed passageway of blood between the media layer and the outer vascular wall is called the false lumen. Stanford type A dissections develop along the ascending aorta and aortic arch [3,4], whereas type B dissections are confined to the descending aorta. Patients with type A aortic dissection have worse survival prospects than those with type B, which can lead to major casualties in the treatment of acute aortic dissection [5]. The mortality rate for type A aortic dissection untreated within a day can be 21% or even higher [6,7]. Several hypotheses have been proposed to explain the causes of AD, but most of these hypotheses contradict to some degree the features of the disease. Degeneration of the media is always considered to be an important risk factor for acute AD. However, more than 80% of acute dissections occur without aortic aneurysm and may be caused directly by pre-existing medial degeneration [8]. Meanwhile, aortic intramural hematoma in the ascending aorta is also considered to be a risk factor for early progression of type A AD [9]. Intimal atherosclerosis was once thought to be the cause of AD, but an association between the locations of atherosclerotic plaque and the dissection is only seen in a small proportion of patients [10]. Several studies of type B AD have shown that computational fluid dynamics (CFD) can provide information about blood flow patterns and stress information. By investigating the flow through the false lumen and the distribution of high WSS around the tear location, Cheng et al. found that most of the flow enters the false lumen, which may result in dilatation of the aorta. High wall shear stress (WSS) has been found around tears and may be associated with the likelihood of a tear expanding [11]. Further computational research considering four medical and four surgical treatment models revealed that a pressure difference between the true and false lumens may lead to sudden deterioration such as an aortic rupture [12]. Unlike those of type B dissections, the symptoms of type A dissection develop rapidly. Most patients with type A dissection require surgery to implant an artificial aorta. If the potential risks of developing a type A dissection are predictable, precautions against type A dissection can be taken. Accurate estimation of wall stress (WS) is helpful for the prediction of specific tear positions [13-15]. Nathan et al.

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obtained the WS of 47 patients and found that the maximum stress was located near the sinotubular junction and the left subclavian artery [13]. Using the CT imaging data of the individuals with different levels of aortic valve disease, Doyle et al. found that the highest WS region was highly coincident with the splitting region of type A dissections [14]. These findings suggest that increased vascular WS is an important factor in damage to the intima. Doyle et al. further noted that the region with the highest WS was closely related to the geometric character of the aortic arch, including the aortic diameter, bifurcation angle, and degree of curvature. However, because the aortas of normal subjects are quite different from those of patients with AD, more validations from pre-dissection data are required to support these findings. WS is usually used when investigating the direct influence of blood on vascular walls, whereas WSS is more often used to investigate biological processes that are influenced by flow patterns [16]. The pathogenesis of atherosclerosis is strongly associated with WSS [17]. However, as Ross pointed out, elevated shear stress can modify endothelial behavior [18] and is a feature of many self-regulation processes that maintain the stability of the fluid transport system [19]. Furthermore, several studies have reported that a very high WSS (from 10 to 30 Pa) can trigger endothelial cells to express unique transcriptional profiles and result in expansive arterial remodeling [20]. A WSS gradient can also influence endothelial expressions [21,22]. The importance of WSS in the aorta has long been investigated using patientspecific imaging data. However, due to limitations of image handling, data on the relationship between tear location and WSS in type A AD are still insufficient [23]. It is believed that AD may be the end-point of a series of different damaging pathological processes [8]. Moreover, recent research on patients with classical and atypical AD has revealed further associations between high WSS with less severe atherosclerosis, which could prompt the occurrence of an intimal tear that develops into AD [24]. To date, the role of WSS in a pre-dissection aorta model has not been thoroughly investigated. In this study, seven patient-specific models were used, five of which were of type A dissections and two of which were of normal aortas. By reconstructing the CT imaging data using image processing techniques, geometric models of the lumens in pre-type A dissection and pre-enlargement aortas were constructed. CFD analyses of the three groups (pre-type A dissection, pre-enlargement, and normal structure) were carried out. Wall shear stresses and morphological parameters, including the diameter of the ascending aorta, the bifurcation angles of the branching vessels, and the bending degree of the aortic arch, were compared. The relationships among WSS, tear location, and morphological parameters are discussed.

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2 Methods

2.1 Image acquisition










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The original CT imaging data of five patients with type A AD and two normal subjects were used in this study. The inter-slice distance and the in-plane resolution of the sequential CT images were 0.5 and 0.84 mm, respectively. In clinical practice, it is difficult to obtain CT images of type A AD before tearing because most type A dissections occur very suddenly. Once a type A AD is diagnosed, the patient should remain still. Thus, only one set of CT images is available for most patients with type A AD. An example of a cross-sectional image from this study is shown in Fig. 1a, in which the true and false lumen can be clearly identified. The DICOM data were imported into the image processing package Simpleware to reconstruct the images. Then, for images taken after contrast medium had been injected, the aortic area of each slice was extracted according to the gray intensity in the images. The five reconstructed models of the type A dissecting aortas are shown in Fig. 1b. By comparing the splitting positions in the cross-sectional images and the corresponding 3D models, the tears can be identified exactly, as shown by the red circles in Fig. 1b. Fig. 1c shows models of the two normal structures in the control patients. It is believed that in general, alteration of aorta morphology is a long-term process [16]. Because the time from the occurrence of type A AD to CT imaging should be short, it is assumed that there were no significant changes in aorta morphology before and after tearing. Thus, we can reconstruct the aorta before the tear by “repairing” the dissection. Based on this assumption, operations to remove tear features in the images were carried out by adjusting the threshold of the gray intensity between the true and false lumens. After the repair was performed, hematoma positions and the lumen were carefully distinguished for all patients with AD. A series of operations was performed to estimate the aortic structures before the pathological changes. The image processing procedures (shown in Fig. 2) included the following steps: The areas of the true and false lumens were identified, and the Boolean sum of the two parts was calculated (Fig. 2a-b). The area of the gap between the true and false lumens was identified with the vascular threshold (Fig. 2c). The Boolean sum of the gap and the area of the blood vessel lumen were further calculated, and the lumen of the aorta before the tear was estimated (Fig. 2d). If abnormal vascular inflation, such as a triangle shape, was observed, further repairs were performed manually by comparing the shape of the lumen in neighboring slices. Finally, after a filtering operation was implemented to eliminate the noise in the

ACCEPTED MANUSCRIPT images, 3D models of the aorta before the tear were constructed (Fig. 2e).

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Compared with the AD models in Fig. 1b, it can be seen that the repaired geometries retained the structures of the original models without considerable distortion. Thus, the five models were used to analyze flow behavior before the tear. In Fig. 2e, aortic widening of different levels can be observed. To investigate how aortic dilation influences WSS, a diameter-reduced AD model was artificially acquired by amending the CT images of AD subject 3 in Fig. 1b. It can be seen in the obtained images that the diameter of the ascending aorta in AD is about 58% larger than that of the normal structure. In the image processing, two times of corroding operations were first performed on the CT images, and the images of the descending aorta that were considered to be excessively corroded were manually adjusted based on the original CT imaging data. The diameter of the new model was reduced by 21% of its original size, which may reflect the state of the ascending aorta before dilation. A sectional comparison of the modified and original images is shown in Fig. 3.

2.2 Computational mesh generation

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After image processing, five ADs and two normal and one diameter-reduced AD model were obtained. The computational domain was designed to begin at the ascending aorta and end at the abdominal aorta. Three branching arteries—the brachiocephalic artery (BA), the left common carotid artery (LCCA), and the left subclavian artery (LSA)—were considered. Some of the branching vessels were extended to ensure that their flow boundary conditions did not affect the flow field acting on the aortic arch. Unstructured mesh has advantages in capturing details of complicated geometries. However, the research applied on a model with unstructured meshes needed much higher resolution than that with structured ones to reach mesh independence. Meanwhile, the wall shear stress shows less stability than that with structured mesh [25]. In this case, a structured mesh was designed because of its good performance in patient-specific analysis of computational fluid dynamics [26]. The appearance of the mesh and the block relationship are shown in Fig. 4 and Fig. 5a. The structured mesh generation method was based on that of de Santis et al. [25]. ScanIP is one of the modules of software package Simpleware. It can not only provide visualizations of different data such as DICOM, but also give a geometric model in STL format. With the help of ScanIP, the geometric surface of the aorta was described into triangular surface network in STL format (Fig 4a). The STL file was later imported into ANSYS workbench and several subdomains were obtained by mixing the surface triangular meshes into different areas (Fig. 4b). Subsequently, the information of the aorta surface structure and the subdomains were further imported into ICEM software package and the hexahedral meshes were generated in turn from the inlet block to the outlet blocks (Fig. 4c and d).

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2.3 Flow model and boundary conditions

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A mesh-independent test was carried out to improve the stability of the calculation. Further optimization of the boundary layer was carried out to reduce the total mesh scale while keeping the experiment stable. The maximum facet WSS and the average volume velocity were included in the test. Multiple meshing schemes were generated by increasing the node distribution in the aorta block edges. The coarse mesh we induced contained 251,264 cells. The fine mesh under a refinement of 100% contained 809,417 cells. With the second-order truncation error in this numerical experiment, the relative changes in facet maximum WSS and volume average velocity were about 3.6% and 0.12%, respectively. The finer mesh scheme was adopted for its stable performance.

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The commercial CFD solver Ansys FLUENT ver. 15.0 was used to approximately solve the Navier-Stokes equations. A turbulence model of shear stress transport (SST) was adopted to capture the gradually varying flow from the inner region to the interior lumen [27]. The turbulence intensity was set to 1 [11,27]. Because it is believed that regions of high WSS are not significantly altered by wall motion [28], the arterial wall was assumed to be rigid. A boundary condition (BC) strategy was designed with one inflow inlet at the ascending aorta and four pressure outflow BCs. Fig. 5a illustrates the BC strategy.

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For the steady-state simulation, the inflow information in the peak systole was used because the peak systole has the largest flow rate in the cardiac cycle and therefore the highest value of WSS [29]. At the inlet, a constant-in-space velocity was set as 0.2 m/s, which was obtained from the available literature [30]. Steady pressure BCs on branches and a zero-pressure BC at the main outlet were assigned. Due to the difficulty of obtaining type A AD patient-specific BCs in branches, we adopted the aortic flow distribution scheme used by Cheng et al. [12], in which 30% of the inflow leaves the aorta through branch vessels on the aortic arch. It has been shown that the outflow proportion obtained by MRI ranges from 24.5% to 45% [31]. The 30% proportional value we adopted was obtained from the averaged flow loss through the branches based on phase-contrast MRI data from a group of four patients with type B dissection. It has been noted that the time-averaged flow loss over the entire cycle varies significantly among patients due to the noise and uncertainties associated with MR flow mapping in the diastole period, but systolic time-averaged flow loss is generally consistent at around 30% of inflow rate [12]. Currently, it is difficult to find AD-susceptible individuals and obtain imaging data. The MRI data about the flow rate of patients with type B AD provide a reasonable boundary condition strategy for our research. In addition, because our focus is on investigating the WSS before tearing, it is assumed that no significant changes occurred in the outflow boundary conditions before tearing. Meanwhile, the specific

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mass flow rates of branching were scaled according to the cross-sectional area of each branch outlet. The optimum pressure conditions in the three outlets were obtained by a trial and error approach. The pressures in the branching outlets were initially given. Then they were adjusted iteratively after each run of numerical test by matching two conditions simultaneously, which are to maintain 30% of inflow rate to go through the branches and let the ratio of the outlet flow rate among these branches be 1.5:1:1.2. In the unsteady-state condition, the pulsating velocity inlet and outflow boundary conditions were included. The velocity profile of the inlet was obtained from the reference [30] and assigned as the constant-in-space velocity. Fig. 5b illustrates the extracted velocity profile [30] and the three representative points we observed. The time point t1 was selected as 0.1 s because it is representative of the pulsating feature in systole. The time point t2 was selected at the peak systole. The third time point was selected at 0.25 s as characteristic of the deceleration period. To meet the outflow scheme, a pulsatile pressure profile for branch vessels was included. An opening BC with 0 Pa relative static pressure was applied on the main outlet. Trial and error approach for the pulsatile outlet pressure profiles were employed to meet the outflow condition that 30% proportional outflow leaves the aorta through branches at every time point.

2.4 Quantification of aortic geometry

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Several geometric parameters were included to assess the morphological features of AD. First, it was noticed that aortic widening, which has been reported in previous articles relating to intimal tears [13,16], was also observed in this research. To measure the diameter of the ascending aorta, we used the image-based modeling package vmtk. Based on the locations of the beginning and ending points of the aorta, the centerline coordinates and diameter data along the centerline were extracted. The diameter at the inlet of the ascending aorta was selected as the feature mark for all subjects. Fig. 6 shows the variation in diameters along the aortic center line for the seven subjects. It is apparent from Fig. 6 that the aortas in the AD group have larger diameters than those in the control group. For further comparison of the AD and control groups, the angle of the side branching vessels was examined. Noticeable differences in geometric features were found. To measure the bifurcation angles of the three branching vessels, the skeletons of the aorta and branching vessels were extracted from the 3D models using vmtk software. Four points were manually selected on the central lines to mark the orientation of branch vessels relative to the main vessel (Fig. 7a). The bifurcation angle of the BA and the aortic arch was obtained by calculating the angle between

ACCEPTED MANUSCRIPT lines AB and CD. This same method was used to evaluate the angles of the other branching vessels.

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We then evaluated the bending degree of the aortic arch. Three characteristic positions were selected in the skeleton of the aorta to set up an “aortic arch hypothesis plane” (Fig. 7b). Kilner et al. used a similar method, which they called the “arch plane,” to observe the velocity distribution in the aorta in MR images [32]. The first position is the beginning point of the ascending aorta where the extension volume is excluded. In this study, one third of all points in the center line were included by the ascending aorta and aortic arch. Thus, the second point was selected at a distance of one third of the aorta from the starting point. To obtain the third point, we calculated the arithmetic mean values of every point for the left two thirds of the aorta (descending part) and chose a point with the mean value of the coordinates as the third point. Thus, the hypothesis plane of the aorta was obtained. Fig. 7b and 7c illustrate the three points with red, green, and blue cross markers. The auxiliary plane was based on these points and illustrated as the gray plane. The bending state of the patients with AD and normal subjects can be seen in Fig. 7b and 7c, respectively. Black arrows are used to show the largest vertical distance from the aortic arch to the hypothesis plane.

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• 3 Computational Results and Discussion

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3.1 Unsteady simulation in peak systole A simulation test of WSS in steady and unsteady flow was firstly carried out. The WSS distributions on the aortic arch at t1, t2, and t3 are shown in Fig. 8a-c. For comparison, Fig. 8d gives the WSS distribution at the steady state. The highest WSS was during peak systole, as shown in Fig. 8b. As Fig. 8 reveals, the patterns of WSS in the steady-state simulation show some similarity with the WSS during peak systole in the unsteady simulation. To obtain the maximum WSS value in the three side branches, the WSS at the node containing the maximum WSS and eight surrounding nodes were measured by probing function of FLUENT. Subsequently, the mean value of these nine nodes was adopted as the maximum WSS of that region. The maximum WSS values of the three side branches in the unsteady simulation were 12.07 Pa, 6.28 Pa, and 11.63 Pa (Fig. 8b), which were similar to those of the steady-state simulation (11.95 Pa, 8.19 Pa, and 11.95 Pa) (Fig. 8d), and there is no obvious difference for the maximum WSS value on aortic arch under the unsteady and steady flow situation. This similarity between the unsteady simulation in peak systole and the steady-state simulation may relate to the acceleration period, in which the pulsating flow is fully developed at peak systole. Based on this simulation we infer that, under the same outflow scheme, the value and distribution of WSS on the aortic arch in the steady-

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state simulation can be considered representative of the unsteady simulation at peak systole. Thus we adopted the steady-state simulation as the main research scheme. 3.2 Flow patterns Fig. 9a shows the pressure distributions of a patient with AD (AD subject 3 in Fig. 1b) and a normal subject (normal subject 2 in Fig. 1b). It can be seen that the pressure remains high in the whole area of the aortic arch. The pressure drop in the patient with AD is larger than that in the normal subject.

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Fig. 9b presents a comparison of streamlines of the patient with AD and the normal subject. Streamlines colored by velocity indicate the blood perfusion state, which contains helical flow and high speed zones as reported in the literature [27]. It is apparent that helical flow formed in the region of the aortic arch, which agrees with a previous finding about helical and retrograde features that are influenced partly by the curvature of the aortic arch [32]. The highest axial flow was observed near the inner aortic arch. According to other research, the highest axial flow will develop outwardly [33]. Although there is also helical flow in the normal subject, it is much weaker than that in the patients with AD. This may result from the dilation of the ascending aorta leading the helical flow to become larger and last longer [34].

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3.3 Wall shear stress on AD and normal group Wall shear stress is an important hemodynamic quantity, which is difficult to measure directly in vivo. In this study, to collect information on high WSS on the aortic arch, the pattern of WSS distribution was observed in advance. To bring other regions of elevated WSS to light, the upside was rescaled lower to 5.5 Pa. It can be seen from Fig. 10 that most of the peak values of WSS are located at the bifurcating areas, which may be associated with sharp geometric change. Additional elevated WSS can also be seen in Fig. 11 with scale upside at 5.5 Pa. The observations of the five patients with AD show that not only the maximum WSS around the ostia of the aorta but also other types of elevated WSS may relate to the location of the tear. Three of the five patients with AD had tears around the branching vessels on aortic arch, who were AD subjects 1, 3, and 5, as shown in Fig. 10. Normal subjects are also illustrated in Fig. 10 for comparison. The WSS at the maximum node and eight surrounding nodes that caused sudden geometric change at bifurcations was measured by probing function of FLUENT. The arithmetic means obtained from these nine nodes are listed in Table 1. The maximum values of high WSS region for the five patients with AD were 13.44, 10.32, 11.95, 9.18, and 18.5 Pa. Considerably greater WSS was observed in the AD group, which agrees with the trend of increasing diameter of the ascending aorta. More associations between the high WSS area and tear location were also found. The tear in subject 1 (Fig. 1a) was located at the bifurcation of the LSA, which corresponds to the high-WSS region 3 in Fig. 10a. Subject 3 had three identifiable tears, two of which were at the bifurcation of the aortic arch (Fig. 1b). The third one appeared at the beginning of the ascending aorta. There is a strong overlap between the two tear locations and the WSS-concentrated regions at high-WSS regions 1 and 3. Subject 5 has two noticeable tears located distal

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to the third branch and proximal to the LSA, respectively. The WSS proximal to the LSA was the most elevated in this subject. The results reveal that tears around bifurcations may relate to a larger WSS. In order to validate the influence of bifurcation on the elevated WSS, a 2D idealized model with a bifurcation was employed, whose geometric dimensions are shown in Fig. 12a. The diameters of the inlet and outlet of the main vessel were set to be 25 and 20mm which are the same as those of normal ascending aorta. The boundary conditions imitate the patient-specific numerical research that contains one velocity inlet and two pressure outlets. Error and trial approach was also involved to seek the optimal pressure on branch vessel that maintains the outflow rate to be 10%. Flow patterns and WSS were obtained by changing the bifurcate angle from 85 to 55 degree. Fig.12b shows the WSS distributions around the root of bifurcation (indexed as line abc). It’s seen that the peak values of WSS are at the curve part of line ab. Meanwhile, with the bifurcation angle decreasing, the peak value of WSS increases gradually. It is noted that at the root of bifurcation the WSS is determined from those of the ascending aorta and branching vessel. When the branching angle is nearly vertical (for example 85 degree), the WSS component from the branch is extremely small. However, when the angle decreased, the WSS component from the branch becomes larger. Thus the total WSS at the root of bifurcation increases with the reduction of bifurcation angle. This validation helps to explain the WSS elevation at the bifurcate region. It is seen from Fig 10 that the wall shear stresses at the bifurcation root of AD subject 1 and 3 become elevated, which corresponds to the small bifurcation angles.

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On the other hand, two subjects in had tears unrelated to bifurcations. The tear in subject 2 was located on the inner curve distal to the upper arch (Fig. 1b), where locally high WSS can be observed around the tear location. Further comparison of all subjects at this location shows that elevated WSS was found in this region. Comparing Fig. 10b of AD subject 3 with the streamlines in Fig. 9b, it can be seen that helical flow acting directly on the intima may be the reason for this elevated WSS. Normal morphology may protect the intima from intensive helical flow, whereas the larger bending degree of the AD subject may lead to the direct acting of intensive helical flow on the intima. Subject 4 has two noticeable tear, one of which is located at the beginning of the BA (Fig. 1b). The WSS on the tear locations shown in Fig. 11b and 11c do not relate to the branch vessel’s ostia on the aortic arch. These two areas were also found to contain locally elevated WSS. Interpreted cautiously, the elevated WSS in Fig. 11c may result from helical flow at the beginning of the BA. The WSS elevation in Fig. 11b may relate to locally sudden changes in aortic diameter. The equivalent diameter before the tear circled in Fig. 11b is about 35.16 mm. It has been reduced by about 6.73% at the circle position to 32.79 mm. A further investigation about WSS influenced by a widened ascending aorta was carried out. Fig. 13 shows the WSS distributions in an AD and the diameter-reduced

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3.4 Quantification analysis of aortic morphology

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model. Table 2 lists the highest WSS values and pressure drop for AD subject 3, diameter-reduced AD subject 3, and normal subject 2. It can be seen that the highest WSS in the modified model decreased remarkably. The WSS distal to the bifurcation of the BA and LSA has been reduced by about 2 Pa. Meanwhile, the WSS distal to the bifurcation of the LCCA was elevated by about 2.2 Pa. The overall WSS in the areas unrelated to bifurcation was found to be lower. On the other hand, the pressure drop between the ascending and abdominal aorta in the model with the reduced diameter was found to be greater than that in the model of AD subject 3.

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The above CFD results suggest that the excessive increase in WSS is closely related to the location of the tear in the aorta. Previous researches about AD mainly concerns about the changes of flow dynamics after tear, especially for the flow pattern differences in true and false lumen in type B AD [11,12]. It is interesting to note that Dillon-Murphy compared the hemodynamics in type B AD to those in an equivalent ‘healthy aorta’ created by virtually removing the intimal flap, whose method is exactly the same as what we are now employing [35]. However, only one AD subject was modeled in their work. Recently, the hemodynamics of type A AD has been paid more attention [36]. Shi et al. constructed a geometric model basing on the CTA data of a normal aorta and inserted a thin layer along the aorta axis as the dissection flap. By changing the tear size and location at the entry, they compared the difference of flow pattern and false lumen intimal wall pressure. In the work based on patient-specific modeling for aorta with different levels of valve diseases [14], Doyle et al. pointed out the ascending aortic diameter, arch radius, and tortuosity were all significantly related to elevated wall stresses and coincides with the splitting region of type A dissection. It is suggested that three dimensional geometric analyses potentially improve the diagnosis of aortic dissection. On the other hand, a very high WSS can lead to endothelial damages and the subsequent pathological responses [20,37]. In the work of Liu et al [38] about the influence of basketball exercise on WSS and arterial stiffness, it is presented that the higher maximum WSS corresponds to the higher pressure-strain elastic modulus and stiffness of carotid artery. Thus, higher maximum WSS may be an initiative factor for arterial vascular expansive remodeling. In our research, the main concern is abnormal elevated maximum WSS in the predissection state of type A AD and geometric factors causing WSS elevated. To investigate the geometric factors that cause the increase in WSS, the diameters of the ascending aorta, the branching vessel angle with the aorta, and the bending degree of the aortic arch were compared in detail. Table 1 lists the wall shear stress and diameter of ascending aorta at the high WSS region for all subjects. It is seen that the diameters for the AD group were significantly larger than those for the normal group. By further comparing the

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variation tendency with the mean values of WSS in Table 1, it can be seen that the increase in WSS tends to follow the variation in diameter. The angles of side branch vessels for subjects are presented in Fig. 14. It is shown that the deflection angles of branches on the aortic arch in the control group are more likely to be 75 degrees. As seen in Fig. 1, in the normal subjects the branches leaving the aortic arch orient to a similar vertical direction. In contrast, the angles of the branches in patients with AD are more likely to form a 45- to 60-degree deflection. A lower tension state was observed in the branches of the patients in the AD group which may relate to the sudden geometry change at bifurcations and the decrease of branch angle. Meanwhile, as the validation in section 3.3 emphasized (Fig. 12b), the decline of bifurcation angle will lead the WSS at bifurcation become concerted and elevated. To investigate the bending degree of the aortic arch, ten equally spaced points on the aortic arch were used to measure the distance between the aortic arch and the arch plane. Average distances were calculated for every subject to quantify the aortic bending degree (Fig. 15). It can be seen that the distances for the AD group are considerably larger than those of the normal group, which implies that the tortuosity of the aortic arch is greater for AD group. Clinicians have observed that aortic tortuosity can always appear in elderly individuals. A previous study indicates that moderate bending can avoid intensive helical flow [32]. This may imply a further correlation between morphology of the aortic arch and the influence of helical flow on the aorta. These results indicate remarkable differences in morphology between the patients with type A AD and those in the control group. Of the three morphological differences evaluated here, diameter enlargement is the most relevant. As illustrated in Fig. 13, the increase in WSS in the aorta is related to aortic dilatation. In addition, the larger pressure drop in the diameter-reduced model (Table 2) reveals that the enlarged diameter of the ascending aorta can reduce the overall impedance of the blood vessels, which is in agreement with the finding of Redaelli et al [39]. This also implies that ascending aorta widening may be the result of a self-adaptation when the impedance of the descending aorta increases. This process would not lead to an adverse reaction when the contractile function of smooth muscle cells is normal. However, when the contractile response of the aorta is weak, this kind of enlargement may be dangerous and lead to a tear. It is of great importance that any factors that cause an increase in aortic vascular impedance should be treated and/or avoided. 3.5 Research limitations Although some primary results have been obtained by using CFD analysis in patient-specific AD models, this study has some limitations due to some simplifications and assumptions. The first is related to the simplified computational model of AD without consideration of valve leaflets. Valve feature helps to improve the flow field patterns comparing to MRI-based inlet velocity profile [31,40]. Bonomi et al. [41] and Pasta et al. [42] reported that aortic valve features increase fluid-

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dynamics abnormalities and therefore affect WS and WSS distributions in the ascending aorta. Further research about the bicuspid aortic valve also revealed an increased and asymmetric WSS that may be related to changes in aortic morphology [43,44]. In this case, numerical research containing aortic valve should be lunch in further approach. Other limitations concern the physical and computational models used in this study. First, we considered the blood vessel as a rigid wall, thus neglecting the interaction between the flow and the wall structure. Alimohammadi et al. [28] noted that regions of high WSS were not significantly altered by wall motion. However, certain collocated regions of low and oscillatory shear stress that may be critical for disease progression were only identified in the fluid structure interaction simulation. The disease progression of atherosclerosis and high shear stress is closely related to the occurrence of an intimal tear [24]. In this case, FSI simulation should be adopted when we searching AD susceptible subject in atherosclerosis individuals. Further, although the steady-state simulation can reveal the behaviors of high WSS in the models, unsteady-state simulations are preferred if computational cost is not considered. Furthermore, the test in the models with reduced aortic diameters showed that the WSS value in a concentrated area decreased by about 50%, and other geometric factors such as aortic tortuosity and the angle of branching vessels may also have affected the WSS of our AD samples and led to the increase in WSS. In addition, the models of type A AD before tearing used for this study were developed from a tearing sample of AD, and some errors in image processing may have been included. In this case, an idealized model may be used in further research. We may employ the geometry of normal structures by changing the diameter, bifurcation angle, and tortuosity to investigate the variation of WSS. Thus, the simulation may give more information related to the occurrence of aortic dissection.

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4 Conclusions

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In this study, blood flow dynamics of five patients with type A AD under the predissection situation and two normal subjects were analyzed. Although we used the image data after the formation of the dissection, we repaired the dissection by image processing and employed the new model for analyzing the flow behaviors at the predissection state. Since type A AD occurs within a very short period, it is reasonable to assume that there are no significant changes in morphology of the aorta except the dissection. Two types of association between the region of elevated WSS and the tear location were found. The first association is between the maximum WSS around the bifurcate ostia on the aortic arch and several tear locations, which was seen in three of the five patients with AD. The second association is elevated WSS on the down side and distal to upper arch. This elevated WSS may relate to intensive helical flow. In addition, the WSS of the AD group was significantly larger than that of the control group, owing to the considerable differences in morphology revealed by comparing the diameter of the ascending aorta, the bifurcation angles of the branching vessels,

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and the bending degree of the aortic arch between the AD group and the control group. The diameters of the ascending aorta in type A AD patients were larger than those in the control group. A smaller diameter of the ascending aorta may result in lower WSS but a larger pressure drop. Increasing impedance of the aorta may occur prior to the enlargement of the aorta diameter resulting in the increase in WSS. In addition, in the normal subjects, the branching vessels leaving the aortic arch orient in a similar vertical direction, but no similar tendency was observed among the patients with AD. The smaller branch vessels angle may lead to a worse geometric regularity of bifurcation on the aorta and affect WSS, which was reported in other study [21].

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In conclusion, this study provides new knowledge about the hemodynamic characteristics of type A AD. The tear-removed model of type A AD revealed that the increase in WSS is related to alterations of aortic morphology. The dilation of the ascending aorta and the alterations of branching angles may be the key determinants of the higher WSS around the ostia of the aortic arch. Increased tortuosity in the aortic arch leads to stronger helical flow through the distal aortic arch, which may be the reason of tear in this region. Further CFD and statistical analyses will be conducted to predict the biomechanical behavior in possible variations of aortic structures under long-term high blood pressure. Thus, the risk of aortic dissection will be evaluated for patients and it will be possible to suggest timely therapy for prevention of the potential dissection.

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Acknowledgments This work was partially supported by the State National Science Foundation of Liaoning (2015020303), Science and Technology Foundation of Dalian (2015E12SF167) and National Science Foundation of China (No. 11602053).

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Table 1. Wall shear stress and diameter of ascending aorta at the high WSS region for all subjects. AD Group Control Group Subject Subject Subject Subject Subject Subject Subject 1 2 3 4 5 1 2 12.46 9.26 11.95 9.18 8.87 5.58 5.77 High WSS region one (Pa) 13.35 10.00 8.19 4.43 3.89 2.48 6.51 High WSS region two (Pa) 13.44 10.32 11.95 5.37 18.50 3.06 High WSS region three (Pa) 49.36 45.64 46.20 28.23 31.72 25.00 25.67 Diameter at ascending aorta(mm)

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Table 2. Wall shear stress and pressure drop of an AD subject, diameter-reduced subject, and normal subject 2. Original AD Diameter-Reduced AD Normal Subject Subject 2 Subject 11.95 9.5 5.77 High WSS region one (Pa) 8.19 10.47 6.51 High WSS region two (Pa) 11.95 10.02 3.06 High WSS region three (Pa) 827.70 990.76 307.30 Pressure drop (Pa)

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(c) Fig. 1 (a) Cross-sectional CT image showing the true lumen, false lumen, ascending aorta, and descending aorta; (b) Reconstructed geometries of the five patients with type A AD indexed as AD subject 1 to 5 from the left to the right; (c) Reconstructed models of the normal aortic structures indexed as normal subject 1 and 2.

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e) Fig. 2 Image processing steps to estimate the geometries before aortic dissection. (a) The identified area of the aortic vessel. (b) The areas of the true and false lumens. (c) The gap area of the blood vessel between the true and false lumens. (d) The lumen of the vessel after the repairs. (e) 3D geometries of the five AD subjects after the repairs.

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Fig. 3 Two slices of cross-sectional CT image with AD mask and diameter-reduced mask. The purple mask represents the aorta angiography area after the corroding operation, and the green mask represents the corroded areas by the corroding operator.

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Fig. 4 Mesh generation procedure. (a) 3D geometry of aorta with triangle faces. (b) Re-segmentation of 3D model surface. (c) Structured mesh of the aorta. (d) Structured mesh in cross section.

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Fig. 5 (a) Boundary conditions in the numerical experiments with one velocity inlet at the ascending aorta (black arrow) and four pressure outlet conditions (blue arrows). (b) Pulsatile inlet velocity profile and three selected critical time points [30].

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Fig. 6 Variations of aorta diameter along the center line of the aorta.

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(c) Fig. 7(a) Skeleton of the aorta and the four characteristic points for determining the bifurcation angles. The hypothesis plane and three characteristic positions of the aorta for (b) AD subject 1 and (c) normal subject 2.

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(c) (d) Fig. 8 WSS distribution in the aortic arch at (a) the time instant of 0.1 s at acceleration systole; (b) peak systole; (c) 0.25 s at deceleration systole. (d) WSS distribution on aortic arch in a steady state using peak systole set-up.

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(b) Fig. 9 Comparison of flow patterns between AD subject 3 and normal subject 2. (a) Pressure distribution on aorta; (b) Streamline during aortic arch.

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Fig. 10 WSS distribution on the aortic arch of (a) AD subject 1; (b) AD subject 3; (c) AD subject 5; (d) normal subject 1; (e) normal subject 2. The arrows show the positions of the top three WSS values. AD subject 1, 3, and 5 have the tears near the branching vessels.

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Fig. 11 WSS distribution on the aortic arch of (a) AD subject 2; (b, c) AD subject 4. AD subject 2 and 4 have the tear at the distal of aortic arch.

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Fig. 12 (a) Geometric dimensions of the idealized model and subgraph showing details of the curve abc at bifurcate region that participated in WSS extraction. (b)WSS distribution alone curves of model with 55, 65, 75, and 85 degree branch angles.

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Fig. 13 WSS distribution on the aortic arch of primary AD subject 3 and diameterreduced model of AD subject 3.

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Fig. 14 Comparison of the bifurcation angles between AD subjects (1–5) and normal subjects (normal subject 1 and 2)

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Fig. 15 Aortic bending quantified by an average distance of ten points from the aortic arch to the hypothesis plane.