Comparative Fluid-Structure Interaction Analysis on Inuence of Banding Conditions to Ascending Aorta Aneurysm Formation in Rat

Background: Ascending aortic aneurysm in an important cause of mortality in cardiovascular diseases. Stenosis of aortic is considered to be a risk factor as the ascending aortic aneurysm grows. Animal models have been demonstrated that ascending aortic aneurysm could be induced by supra valvular banding of the ascending aortic. Our objective is to compare different banding conditions on the formation of aneurysms for more precise experiment and improving the preclinical value. Therefore, three comparison banding groups of banding altitude, banding severity and banding angle are established based on rat. Then ow pattern, wall shear stress (WSS) and vessel deformation of each model are calculated and discussed using transient two-way uid-structure interaction (FSI) analysis in order to explore the inuence of different banding methods on the generation of ascending aorta aneurysm. Results: Banding methods lead to different shapes or amplitudes of ow beam, WSS and vessel dilation. Eccentric ow beam, local high WSS accompany with vessel dilation are formed above the banding ring in all banding models because of the banding operation compared with normal model. More concentrated ow beam with bigger velocity, higher local WSS and more obvious expansion deformation above the banding ring are prone to happen in the middle segment banding with 60% banding severity and banding angle of 30 degree. Conclusion: According to the results, a higher position, relatively severe banding, and an acute banding angle are more favor to promote the generation of ascending aortic aneurysm.


Background
Aortic aneurysm is a potentially dangerous disease that often causes death by dissection or rupture [1] in general, people with aortic stenosis or bicuspid aortic valve (BAV) are considered to have an increased risk of developing an ascending aortic aneurysm [2][3][4].Many studies attribute this phenomenon to abnormal hemodynamic factors caused by stenosis in addition to genetic effects [5][6][7][8].
Animal models have been successfully made to study the pathogenesis of aneurysm caused by aortic stenosis [9][10][11][12], effectively obtaining longitudinal features of aneurysm than from individuals. Models in pig [11] and our previous experiment in rat [12] showed that ascending aortic aneurysm could be induced by banding supra valvular of the ascending aortic. These models went through a chronic process which had a similarity to a certain extent with clinical ascending aorta aneurysm formation accompanied by aortic stenosis or BAV, indicating a delightful underlying clinical value. Banding played a key role in leading to the coarctation of the aorta and banding methods determined the different states of aorta stenosis during the experiments. Patient-speci c studies demonstrated that different stenosis states could affect the formation of aneurysms. Schaefer et al found that valve opening orientation has been associated with the rate of ascending aortic dilation [13,14]. Although there were con icts in relationship between stenosis severity and ascending aorta aneurysm, Alessandro et al indicated that mid-ascending dilatation was proportional to stenosis severity [15]. Alexia et al acknowledged that the severity of aortic stenosis was correlated to the progression of aortic dilatation [16].However, banding methods that may largely affect the formation of aneurysms has not been discussed yet. A clear understanding of these events is critical for mechanistic exploitation in ascending aortic aneurysm. Therefore, different banding methods are worth comprehensive screening.
Since computational uid dynamics (CFD) represents a promising method which performed with notable advantages such as great convenience, high speed and effective acquisition of additional hemodynamic parameters. It is widely accepted in analyzing the correlation between aortic pathology and hemodynamic changes, predicting and ameliorating the understanding of disease progression [17].
Therefore, taking these issues into account, the current study discusses the impact of three banding conditions of altitude, angle and severity on the formation of ascending aortic aneurysms based on numerical simulation of two way transient uid-structure interaction by using nite element method, which can serve for precision experiment and improve the preclinical value of aortic aneurysm research.

Results
Velocity, WSS and wall displacement (with the same scale) were obtained in all models at the time of 0.23 s in the acceleration segment of systolic phase. Hemodynamic changes, especially between banding ring and brachiocephalic, where the ascending aortic aneurysm formed (we denoted this zone to be the region of interested (ROI)), were contrasted and analyzed during each group. 'A','B','C' points in Fig. 3(a), descending aorta(C). WSS and displacement data are extracted along the outer edge of ascending aorta as indicated in red line in Fig. 3 (b-1) in each group.

Comparison of models with different banding altitudes
The pro le of velocity streamline in normal model is uniform and parallel along the aortic wall ( Fig. 3(a-1)). Flow beam is generated after blood owing through the banding ring, impinging against the convex wall of ascending aorta due to the curvature in the origination of aorta arch and then de ects to the direction of the aortic arch. This ow beam is less converged in proximal segment model than that in middle segment one ( Fig. 3 (a-2), Fig. 3(a-3)). Average velocities in regions of A, B and C are showed in Higher WSS can be observed in aortic arch in normal model ( Fig. 3(b-1)) and in the area adjacent to owimpinging zone in ROI in banding models( Fig. 3(b-2) and(b-3)). Dilation is obvious in banding models both above and under banding ring (Fig. 3(c-2)(c-3)). Furthermore, in the ROI, there is more evident dilation in middle banding model than that in proximal banding model. We can see that WSS and displacement of ROI in middle segment model is larger than that in proximal segment and normal models( Fig. 4(b)and (c)).

Comparison of models with different banding severities
Similar with banding altitude group, Fig. 5((a)(b)(c))show the velocity streamline, WSS contours and displacement contours of deformation, respectively, and we can see banding severity of 40%,50% ,60% models in the columns.
In the ROI, it is legible that more concentrated velocity streamline exists in the model of banding severity of 60% with a larger velocity value of about 0.7 m/s at position B in the impinging zone. Blood ow velocities in three models at position A and C are nearly the same ( Fig. 6(a)). Meanwhile, high WSS and dilation can be seen adjacent to the ow-impinging zone ( Fig. 5(b)(c)), and the magnitudes of WSS and this dilation are becoming more obviously from 40-60% severity model. Based on the WSS and displacement curves in Fig. 6((b)(c)), we can also see that WSS and displacement above the banding ring elevate with the increasing of banding severity.

Comparison of models with different banding angles
Velocity streamline, WSS contours and displacement with deformation are showed in Fig. 7, among whose columns represent models of banding angle of 0 degree, 30 degree and 150 degree, respectively.
Different ow jet trajectories can be seen in Fig. 7(a) because of banding angles: there is no obvious impinging zone in model of 150 degree compared with other two models in ROI. The impinging zone in 0 degree model locates at the aorta arch, while the corresponding zone in 30 degree model is slightly higher than the banding ring with a shorter distance. The 30 degree model has the biggest value of velocity in B position. The velocities in A and C positions are in the likelihood in all three models ( Fig. 8(a)).
High WSS, in the ROI, in models of 0 degree and 30 degree situates on the convex wall of ascending aorta while high WSS locates along the inner wall in 150 degree models. The deformation in Fig. 7(c) shows that expansion is more prone to happen in 30 degree model than in 0 degree model whereas retraction of the aorta can be seen in model of 150 degree. In Fig. 8(b) and (c), we can also nd that model of 30 degree have signi cant larger value in WSS and displacement above the banding ring than other two models.

Discussion
Banding the ascending aorta is a practical method in simulating aortic stenosis in experiment animals, contributing to reveal the relationship between hemodynamic characteristics and pathological features, helping us enhance our exible understanding of aneurysm [18]. In current study, three different banding factors of altitude, severity and degree are discussed for predicting the impact on the formation of ascending aortic aneurysms based on a rat. It is valuable, for one hand, since the cardiovascular system of the rat has a lot of similarity to that of human; for another hand, it's very di cult to collected invasive clinical disease data from humans in most cases, thus, animal model becomes a preferable way for producing predictable and controllable symptoms [9,19].
In this study, two basic but critical hemodynamic risk factors that of ow pattern together with WSS, which can signi cantly promote the initiation of ascending aorta aneurysm are calculated. Eccentric systolic ow, displaced from the centerline toward the vessel wall, is one of a topic of clinical interest in exploring the role of rheology in the formation of ascending aortic aneurysm. Researchers have reported that stronger eccentric blood ow jet toward the aortic wall, which may include higher velocity, signi cant ow displacement and jet-to-wall impingement, lead to vascular remodeling and aneurysm formation [11,20,21]. Ayaon-Albarran et al [11] found aortic wall that was directly hit by eccentric ow jet were thinner, given that decreased thickness in vessel wall could result in aortic dissection. Cebral et al [22,23] considered that a concentrated ow beam may cause an intracranial aneurysm to progress, and the decrease of the ow impingement size is more likely to cause aneurysm to experience growth or rupture than large impingement one. Moreover, in the context of ow jet, WSS levels are considered abnormally high adjacent to the ow impingement zone. This high WSS has long been accepted as a dangerous motivational factor predisposing a vessel wall to aneurysm initiation and development, which behave in early smooth muscle cell apoptosis or changes to extracellular matrix protein expression [24][25][26].Evidence from Guzzardi's study showed that elastin bers in regions of elevated WSS were signi cantly thinner compared with normal ones [27].Clinical data also supported ascending aorta dilatation occur in regions of elevated WSS values [28]. Displacement simulation provides us intuitive view of expansion of the vessel, indicating the suspicious location of the potential lesion. In most studies of vascular deformation, they pay more attention to the existed condition of aneurysm or its annual growth rate for the purpose of predicting rupture [29], lacking of comparison deformation information in a cardiac cycle under the background of non-aneurysm status. Rat experiment in intracranial aneurysm of Koseki et al [30] indicated that high WSS together with local vessel transient outward bulging determined the prospective site of aneurysm formation. We can see clearly that the relative angle and distance between the stenosis plane and the aortic curvature result in different ow jet forms, WSS distributions and vessel deformation above the banding ring. Therefore, combining these three calculation results, we have reasons to speculate that a higher position, relatively severe banding, and an acute banding angle are more inclined to promote the formation of ascending aortic aneurysm.
We also nd an obvious large deformation under the banding ring. This unique apace was created due to supra valvular banding of the aortic. Different with the dilation above the banding ring, velocity and WSS are changeless in this region. It is thought to be associated with increased pressure load caused by the out ow tract obstruction [31]. This type of force may play a key role in remodeling of aortic wall thickness rather than adjusting diameter of the aorta in early stage [32].
There are limitations in this study. Like some methodology of simulation, a few ideal hypotheses are adopted here, especially the morphological structure of rat's aorta. However, we believe that this kind of ideal structure is universal and commonly used for simulation calculations. As examples, Pierre et al [32] modeled mouse carotid artery as a cylinder, Gelide et al [34]simulated physiological geometry of the descending aorta with a funnel-like structure. Therefore, we think our simulation is acceptable under the background of comparison.
In summary, this study showed for the rst time, how the ascending aortic aneurysm can be induced with different banding conditions, which will do favor to promote the generation of ascending aortic aneurysm. This promising nding warrant further mechanistic investigation into the formation of aortic aneurysm.

Conclusions
Related animal models are indispensable tools in obtaining longitude features of aneurysm than from individuals; therefore, it is necessary to make the experiment more e cient. Under the background of these banding-reduced aneurysm animal models, the banding method is a problem that cannot be ignored in affecting the growth of aneurysms.
In this paper, we modeled the ascending aorta banding operation in rat and three banding pro les of banding altitude, banding severity, banding angle were established, separately. For each banding group, blood ow patterns, WSS distributions and vessel deformation are calculated and compared. Our study suggests that banding methods could obviously produce differences in ow velocity, concentration and eccentricity of ow beam and local high WSS which are considered to have a signi cant in uence on aneurysm formation. A higher position, relatively severe banding, and an acute banding angle are more favor to promote the generation of ascending aortic aneurysm.

Methods
Three-dimensional aorta geometries with different banding patterns were created based on morphology feature of ascending aorta in rat using Ansys Designmodeler (Fig. 1). The fundamental aortas starting from aortic root were the same in shape and size for all models, including ascending aorta(AA), aortic arch with three primary branches (brachiocephalic (BCA),left common carotid (LCCA) and left subclavian artery (LSCA)) and descending aorta. The value of D A was 2.3mm [12]. D B ,D LC ,D LS ,R A and L A were set to be 1.2 mm,1.1 mm,1.1 mm, 4.5 mm and 6 mm respectively ( Fig. 1(a)). The aortic wall was assumed uniform with the thickness of 0.15 mm.
Constriction was used to represent the banding position. Banding severity was calculated by (D A -D C )/ D A (Fig. 1f).Banding angle (θ) was de ned by included angle between aorta inlet plane and banding ring plane (Fig. 1d and e). All of models were divided into three groups for comparison purpose as illustrated in Table1.  [9]and viscosity of 0.004pa s [9]. A longitudinal velocity was applied at the aorta root as given by Fig. 2, in which the heart rate of the rat was estimated at approximately 300 beats per second [9] and the peak ow velocity of was about 0.6 m/s [35]. At the outlet of BCA, LCCA, LSCA and DA, a constant reference pressure was given to be zero. Although it is not a real-data boundary condition, this is a reasonable simpli cation on account of comparison purpose in this study without ignoring main blood characters of pulsatile ow.
Vessel wall was assumed to be isotropic elasticity. Young's modulus of aorta was set to be 7.5 × 10 5 Pa according to the research of Guo and Band [36,37]. Possion's ratio and density were 0.45 [9]and 1.06 × 10 3 kg/m 3 [38] respectively. The uid-solid interface was set at the interface of blood and vessel wall, and xed constraint was given at inlet or outlet of aorta.
Blood and vessel wall were meshed separately. In the geometry of blood, 'in ation' was set to have maximum layers of 5, growth rate of 1.2 and the division in edge of ascending inlet was 15. Then, in the vessel wall, to match a good numeric resolution ,the division in the edge of ascending wall was also set to be 15, at the same time, re nement and explicit in physics preference was used to help to obtain grids of good quality. In total, there were about 50 thousand elements in blood geometry and about 35 thousand elements in vessel wall geometry in all models due to similarity in their shapes and dimensions. This kind of mesh was small enough to satisfy iteration convergence in blood-wall interface.

Availability of data and materials
All data generated or analyzed during this study are included in this published article.

Competing interests
The authors declare that they have no competing interests.