Hemodynamics and Oxygen Transport through Pararenal Aortic Aneurysm Treated with Multilayer Stent: A Numerical Study

Accepted Manuscript Hemodynamics and Oxygen Transport through Pararenal Aortic Aneurysm Treated with Multilayer Stent: Numerical Study Zhongyou Li, Fei Yan, Jingru Yang, Yu Chen, Zhizhi Xu, Wentao Jiang, Ding Yuan PII:

S0890-5096(18)30538-7

DOI:

10.1016/j.avsg.2018.05.040

Reference:

AVSG 3937

To appear in:

Annals of Vascular Surgery

Received Date: 27 November 2017 Revised Date:

14 May 2018

Accepted Date: 28 May 2018

Please cite this article as: Li Z, Yan F, Yang J, Chen Y, Xu Z, Jiang W, Yuan D, Hemodynamics and Oxygen Transport through Pararenal Aortic Aneurysm Treated with Multilayer Stent: Numerical Study, Annals of Vascular Surgery (2018), doi: 10.1016/j.avsg.2018.05.040. 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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Hemodynamics and Oxygen Transport through Pararenal

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Aortic Aneurysm Treated with Multilayer Stent: Numerical

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Study

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(3)Department of Vascular Surgery of West China Hospital, Sichuan University, Chengdu, 610065, China *

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Corresponding authors: Yu Chen, Senior Engineer, Department of Applied Mechanics, Sichuan University, NanYihuan Road No.24, WuHou District, Chengdu, 610065,China, Tel:86-28-85405140; Fax: 86-28-85405140; [email protected] Wentao Jiang, Professor, Department of Applied Mechanics, Sichuan University, NanYihuan Road No.24, WuHou District, Chengdu, 610065,China, Tel:86-28-85405140; Fax: 86-28-85405140; [email protected]

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(1)Department of Applied Mechanics, Sichuan University, Chengdu, 610065, China (2)School of Manufacturing Science & Engineering, Sichuan University, Chengdu, 610065, China

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Zhongyou Li1, Fei Yan1, Jingru Yang2, Yu Chen*1, Zhizhi Xu1, Wentao Jiang *1, Ding Yuan3

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Background: As opposed to an endoluminal stent-graft, a multilayer stent (MS) consists of a porous mesh, which allows for the possibility of treating pararenal aortic aneurysms (PRAAs) that involve a significant branch vessel. However, the choice of the density of the MS plays a vital role in isolating the aneurysm and allowing unobstructed blood flow in the branch vessel.

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Method

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double-layer stents) via numerical simulations to explore the feasibility of the MSs used in the treatment of such aneurysms and estimate whether there is a more appropriate or optimal stent density. Results: With stent intervention, the velocity of blood flow in the sac decreased, but the pressure on the surface of the aneurysm did not decrease though it became more uniform. In addition, the “region of double low” (with low wall shear stress and a low Sherwood number) enlarged after stent implantation. Even with the double-layer stent, however, the flux of the branch vessel was still above normal, and we could predict that the optimal stent porosity was approximately 49.9%. Conclusion: Unlike in previous studies, an MS could not be feasibly applied to high-risk PRAAs. However, an MS can induce sac thrombosis in the later stages while maintaining visceral vessel patency, and our results suggest that the optimal stent may be a four-layer stent. Key words—multilayer stent, pararenal aorta aneurysm, numerical simulation, rupture, stent density, flux of branch vessel

Abstract

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In present study, we examine three cases (without a stent and with single-layer and

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1 Introduction

An aneurysm, which is a localized, blood-filled balloon-like bulge in the wall of a

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blood vessel, is a common form of angiopathy, with nearly 150000 new aneurysm

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cases being reported and diagnosed each year globally1. Most individuals suffering

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from aneurysms are older than 65 years of age2, and recent years have seen increased

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incidences of the disease 1. Aneurysms are usually associated with the risk of rupture

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and bleeding3, and once a rupture occurs, the mortality rate can be as high as

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70-95%4,5. In this context, the use of an endoluminal stent-graft for aneurysm

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treatment has gradually become prevalent6; however, for a more intricate and complex

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pararenal aortic aneurysm (PRAA) that involves significant branch vessels, the

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stent-graft (excluding the chimney technique and fenestrated stent graft; the chimney

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technique7 is highly tailored and costly, and the clinical operation of this technique is

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very difficult, whereas an multilayer stent may play a role in a small subset of

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aneurysms where a fenestrated stent graft is not possible due to device restrictions,

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especially in the United States) is inapplicable because it also blocks the branch vessel

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organ and tissues. Meanwhile, the low cost of a multilayer stent (MS) and the porosity

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of the stent mesh allows for the isolation of the aneurysm, such that it not only

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prevents its rupture but also causes it to shrink8-11 while not completely shielding the

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branch vessel. Therefore, MSs can form a possible solution to treating such PRAAs.

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However, the excessive density of the MS will block blood flow in the branch

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vessel, and if the density of the MS is insufficient, it cannot adequately cut off blood

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flow to ensure quick pressure reduction in the sac; consequently, it is not possible to

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reduce the wall shear stress and oxygen to induce the formation of a thrombus8-10.

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This in turn can lead to a situation where the aneurysm continues to expand and even

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ruptures. Thus, the density of the MS plays an important role in isolating the

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aneurysm and ensuring unobstructed blood flow in the branch vessel; further, the stent

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density is a key factor in the success of its clinical application. In this context, we

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evaluate the velocity of blood flow, pressure, wall shear stress (WSS), and oxygen

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transport characteristics in three cases (without a stent and with single-layer and

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double-layer stents) by means of numerical simulation to estimate whether an MS can

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effectively isolate the aneurysm to achieve pressure reduction and induce thrombosis

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in the sac. We also investigate whether a stent or stents can ensure that the branch

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blood vessel remains unobstructed while preventing target organ damage, so as to

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provide a reference for clinical application.

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2. Methodology

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Geometry and grid

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Although thrombus may form in the sac even in the absence of a stent, but it is

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difficult to depict the feature because of considerable individual differences, so we

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established three simplified 3D models with the use of the SolidWorks (version 16.0)

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commercial software package to simulate. The three models studied are depicted in

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Figure 1: (Case 1) with no stent, (Case 2) with a single-layer stent (Sinus-XL stent,

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Optimed, Germany, mesh porosity = 85.2%, thickness = 0.2mm), and (Case 3) a

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double-layer stent (mesh porosity = 72.2%). For a fairer comparison, the diameter of 3

ACCEPTED MANUSCRIPT the abdominal aorta was set to 20 mm in all three cases, and the diameter of the renal

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branch was angled at 45° with respect to the abdominal aorta set to 6 mm12,13. The

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axis of the aorta and the renal artery are in the same plane, that is, 45° inferior

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angulation without anterior or posterior defection. We selected three true aneurysms

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with a diameter of 30 mm for the study 9.

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The computational grid (Figure 2) was generated by means of the ANSYS

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pre-processing software ICEM CFD (version 16.0, ANSYS, Inc.). Because the

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configuration of the stent is complicated, we selected an unstructured grid so as to

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cater to the geometric boundary. As shown in Figure 2, two different grid sizes were

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adopted at the abdominal aorta and renal artery, and the grid was refined in “sensitive”

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regions such as the areas close to the wall, stent-implantation position, and the area

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where the main vessel meets the branch. The grids for Case 1, Case 2, and Case 3

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comprised 311,464 cells, 2,949,774 cells, and 3,216,286 cells, respectively. In

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ANSYS Fluent, we utilized the grid adaption command to ensure grid independence

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of the results, and grid refining was stopped when the grid was observed to become

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independent.

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Assumptions

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The characteristics of the flow field and oxygen transport can be analyzed

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qualitatively for the cases considered14,15. Therefore, in order to simplify the

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calculations, we assumed steady blood flow in our study. In addition, blood was

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treated as a uniform and incompressible Newtonian fluid16,17, and the wall of the

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vessel was treated as a non-slip rigid wall17. Here, we remark that a previous study

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determined that ignoring the coupling effect between the vessel wall and blood flow

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does not affect the distribution of oxygen, but rather only changes the concentration of

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oxygen 18.

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The Sherwood number (Sh) is a dimensionless parameter that is used to denote the

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flux of oxygen to the arterial wall; as the Sh number decreases, the tissue

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consumption rate reduces due to the lack of oxygen supply from the blood 19. The Sh 4

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number is defined as follows 20,21:

∂PO 2 w a ∂n Sh = K L ( K L = ), D PO 2inlet - PO 2wall -D

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(1)

where K L denotes the mass transfer coefficient, a the mean diameter of the blood

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vessel, D the diffusion coefficient of oxygen, and PO2 the partial pressure of

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oxygen.

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Governing equations

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The numerical calculations were based on the 3D incompressible Navier–Stokes

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equations (Equations 2 and 3, below) and the oxygen diffusion equation (Equation

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4)22: r

r

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ρ ( u ∇ ) u + ∇p − µ∆u = 0

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r ∇ u=0

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 [ Hb ] dS 1 + α dPO 2 

r  u ∇PO 2 = ∇ 

  [ Hb ] D c dS   Db 1 +  ∇PO 2  α D b dPO 2    

(2) (3)

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r Here, u and p represent the fluid velocity and pressure, respectively. Parameters

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ρ and µ denote the density and viscosity of blood, respectively ( ρ = 1050kg / m3 ,

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µ = 3.5 × 10-3 kg / m s ) 23,24. In the diffusion equation, the oxygen-carrying capacity of

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hemoglobin in the blood is expressed as [Hb] ( [ Hb ] =0.2ml O 2 /ml blood )25, and α

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denotes the solubility of oxygen in plasma ( α = 2.5 × 10-5 ml O2 /ml blood/mmHg )26.

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Further, Dc and Db represent the diffusivities of oxyhemoglobin and free oxygen,

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respectively, in blood ( Dc = 1.5 × 10-11 m2 / s

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the saturation function that is given by the Hill equation:

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S=

Db = 1.2 × 10−9 m2 / s ) 25, and S denotes

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n = 26.6mmHg 25. where n denotes a constant (=2.7) and PO50

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(5)

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Boundary conditions For all three cases, we used a full development inlet velocity profile, and further,

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the mean velocity was 0.12 m/s

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vessel diameter, and the blood viscosity was 720. The outlets of the abdominal aorta

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and renal artery were subjected to pressure boundary conditions of 86.47 mmHg

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(11500 pa) and 82.70 mmHg (11000 pa), respectively13. In addition, at the inlet and

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vascular wall, the boundary condition of the oxygen partial pressure was specified as

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85 mmHg and 60 mmHg, respectively25, and the gradient of the oxygen partial

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pressure was zero at two outlets, whose direction was perpendicular to the outlets.

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Computation procedures

, the related Reynolds number depended on the

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The relevant equations were solved using the commercial computational fluid

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dynamics software Fluent (version 16.0, ANSYS Inc.) based on the finite volume

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method, and a user-defined function (UDF) was utilized to provide the development

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inlet velocity and solve the oxygen diffusion equation. The SIMPLEC solution for

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pressure–velocity coupling was selected; the discrete form of the gradient was

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Least-Squares Cell-Based, and standard and second-order upwind schemes were used

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for pressure and momentum, respectively.

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3. Results

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Blood flow field

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The blood flow streamlines for the three cases are shown in Figure 3. We note that

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the direction of flow at the entrance of the aneurysm is nearly parallel to the

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abdominal aorta. We can also infer that after blood flows into the aneurysm, there is

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scouring and collision at the distal part (region S) of the aneurysm, and part of the

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blood flows into the branch vessel, whereas the remaining blood forms a vortex

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(region R) in the sac. From the velocity profile (Figure 3), it can be observed that

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when compared with the posterior region (region Q) of the aneurysm, the blood flow

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in the frontal region of the aneurysm (region S) is apparently more rapid, thereby

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indicating greater scouring and collision with the wall. Moreover, due to the existence

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of the branch vessel, blood flow is deflected at the bifurcation, thus leading to the

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implanted, blood can only flow into the intracavity through the stent gaps (Figure 3),

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and the eddy intensity decreases with an increase in the stent density outside the

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abdominal aorta. Further, as shown in Figure 4, blood flow becomes chaotic near the

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stent (slice A) because of flow disturbance and blocking by the stent. The flow

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velocity in the sac gradually decreases with an increase in the stent density, and the

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flow velocity near the stent decreases by 4% for every 1% increase in stent porosity.

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Pressure

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The pressure associated with blood flow in the sac is one of the main factors

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underlying rupture and expansion of the aneurysm27; thus, reducing the blood flow

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velocity can reduce the aneurysm pressure, which reduces the risk of aneurysm

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rupture10,28. The pressure acting on the aneurysm wall is shown in Figure 5 for the

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three cases considered in the study. We note from the figure that the pressure

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distribution on the aneurysm wall is very uneven, and the pressure peaks in the frontal

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region of the sac (region S) where the blood flow velocity is larger for Case 1 (with

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no stent). With stent intervention, the pressure on the wall of the aneurysm is slightly

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lower, particularly in the case of the double-layer stent (Case 3), and the peak pressure

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in the frontal region of the aneurysm (region S) almost vanishes while the pressure on

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the aneurysm wall becomes increasingly uniform.

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Wall shear stress

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Previous studies have shown that low WSS values are one of the main causes of

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angiopathy such as thrombosis15,23,29. Figure 6 depicts the WSS for the three cases,

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and the results indicate that a low WSS (< 2 dyne/cm2)29 exists at both the abdominal

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aorta and aneurysm. Further, the WSS is low outside the abdominal aorta (region P,

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view 1) due to blood deflection at the bifurcation, and the low WSS at the surface of

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the aneurysm mainly exists in region Q (view 1), where the vortex is formed. With

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stent intervention, the high-WSS area (region S, view 2) gradually narrows, and the

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WSS across the entire aneurysm surface markedly reduces with increase in the stent

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density so the low-WSS area on the surface of aneurysm is also significantly enlarged

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(view 3) with stent implantation.

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Oxygen In general, other than low WSS values, hypoxia also forms the main adverse

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environment for thrombosis formation25,30,31,32. Previous studies have shown that the

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arterial-wall local hypoxia increases endothelial permeability to large molecules24 and

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increases the accumulation rate of plaque25, and therefore, we did not neglect the

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effect of stent implantation on oxygen distribution. Whenever the Sh number is

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smaller than the Damkholer number ( D a =

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for the surface reaction)33 within the arterial wall, hypoxia occurs22,25,33. Because the

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pararenal aorta lies close to thoracic aorta, Da is approximately 185 25. Interestingly,

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the distribution of the Sh number is similar to that of the WSS (Figure 7), and

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previous studies have reported analogous characteristics22,25,33. From the figure, we

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note that the Sh number is relatively higher at the surface of the aneurysm frontal

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region (region S) and branch vessel where the WSS is also higher, and low Sh

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numbers mainly correspond to the low-WSS region. Although the Sh number on the

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aneurysm wall decreases with the increase in stent density, hypoxia only occurs when

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the double-layer stent is implanted (Figure 7, region Q).

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4. Discussion

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Kτa , where K τ denotes the rate constant D

Our results indicate that stent implantation strongly influences the local blood flow

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field, and because of flow disturbance, the flow field near the position of implantation

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is increasingly chaotic. Moreover, the flow velocity in the sac decreases with the

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blockage of the stent, and the greater the stent density, the slower the blood flow in

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the aneurysm. In particular, most of the blood in the sac flows towards the frontal

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region of the aneurysm where the disturbance by stent intervention is most obvious,

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which is the essential cause of the drop in pressure in this region. As regards Case 3,

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the peak pressure disappears, and the pressure of the entire aneurysm becomes

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increasingly uniform after the double-layer stent is implanted, which aids in reducing

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the risk of aneurysm rupture due to stress concentration10.

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reduce the risk of rupture. With stent intervention, in addition to reducing erosion and

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pressure, the area of the “double low” (low WSS and low Sh) increases with an

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increase in the stent density, which is beneficial for the induction of thrombosis in the

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sac and to increase the wall thickness25,30-32. Under ideal conditions, the axial tensile

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stress can be approximately defined as σ = PD

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D the diameter of the aneurysm, with σ decreasing when the thickness of sac wall

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δ increases. However, hypoxia is observed to occur only in Case 3, but the low-WSS

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area is significantly greater than that of the hypoxia when the double-layer stent is

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implanted (Figure 8); therefore, low WSS plays a dominant role in the formation of a

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thrombus within an aneurysm.

, where P denotes the pressure and

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After stent implantation, the WSS and oxygen concentration in the branch vessel

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are still relatively high at the entrance of the branch vessel, which means that it is

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difficult for a thrombus to form in this region and prevent branch vessel blockage.

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However, since the stent density is still low, in addition to the high WSS, the WSS

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gradient remains at a high level at the entrance of the branch vessel, which we refer to

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as the “double high” (Figure 9). Therefore, since the branch entrance can continue to

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expand34, it is necessary to monitor the aneurysm periodically for signs of expansion

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in this region in the later stages of treatment.

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With increased stent density, the aneurysm is further isolated, lowering the chance

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of aneurysm rupture. Meanwhile, considering that damage to the target organ may be

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caused by a lack of blood supply, it is important to monitor the flow rate in the branch

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vessel. Obviously, the flow rate in the branch vessel is closely related to the stent

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density. As the velocity in the sac decreases, the pressure decreases, which means that

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the pressure drop of the aneurysm to the target organ will decrease, ultimately leading

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to a reduction in the branch-vessel flow rate. The flow rate in the branch vessel is

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depicted in Figure 10 in a normal case and for Cases 1–3; we note that with stent

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intervention, the flow rate in the branch vessel decreases slightly. Compared to the

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normal case, however, the flux in the three cases is higher because the resistance of

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Case 3, there is still enough blood flow to the kidneys. Thus, within the scope of the

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normal branch vessel flux, in our study, we determined that there is a more suitable

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stent density that can be refined on basis of the double-layer stent to obtain better

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isolation of the aneurysm and guarantee normal operation of the target organ. We can

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predict that the optimal stent porosity is approximately 49.9%, according to the

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relationship of stent mesh density to flux, as shown in Figure 11, and that the mesh

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porosity will be 60.5%, 52.4%, and 44.6%, for three layers, four layers and five layers,

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respectively. Therefore, the optimal number of stent layers for PRAA may be four.

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4.1 Limitations of the work

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It must be emphasized that the simulation is limited by our assumptions. Indeed, it

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is premature to conclude that an MS is feasible for PRAA. This research is based on

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simplified models. In practice, for example, the vascular diameter, aneurysm size, and

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branch angle differs among patients. All of the cases were given a steady inflow

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boundary condition, which may affect the accuracy of results, but not the main

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hemodynamics features induced by stenting8. Although pressure outlets also differ

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among patients, there is no doubt that the pressure drop from the aorta to the target

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organ is considerable13.

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Present studies have not explained how long (six months9 or two years35) it would

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take for an aneurysm to thrombose, although the aneurysm may shrink with the

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intervention of MS9,35. Indeed, it is especially difficult to quantify the detailed

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relationship between hemodynamics and thrombosis.

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5. Conclusion

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An MS could not be applied to high-risk PRAAs, because the pressure on the sac

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did not decrease, although it became more uniform. However, an MS can induce sac

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thrombosis in the later stages while maintaining visceral vessel patency, and our

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results suggest that the optimal stent may be a four-layer stent.

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Acknowledgments

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This project was supported by Grants-in-Aid from the National Natural Science

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Research Foundation of China (Nos.11772210) and Applied Basic Research Programs

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of Science & Technology Department of Sichuan Province (No.2015JY0216). References

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22. Yan F, Jiang W T, Dong R Q, et al. Blood Flow and Oxygen Transport in Descending Branch of Lateral Femoral Circumflex Arteries After Transfemoral Amputation: A Numerical Study[J]. Journal of Medical & Biological Engineering, 2017, 37(1):1-11. 23. Wen J, Zheng T, Jiang W, et al. A comparative study of helical-type and traditional-type artery bypass grafts: numerical simulation.[J]. Asaio Journal, 2011, 57(5):399-406. 24. Coppola G, Caro C. Oxygen mass transfer in a model three-dimensional artery[J]. Journal of the Royal Society Interface, 2008, 5(26):1067-1075. 25. Liu X, Fan Y, Deng X. Effect of spiral flow on the transport of oxygen in the aorta: a numerical study.[J]. Annals of Biomedical Engineering, 2010, 38(3):917-926. 26. Hardman D, Semple S I, Richards J M, et al. Comparison of patient-specific inlet boundary conditions in the numerical modelling of blood flow in abdominal aortic aneurysm disease[J]. Int J Numer Method Biomed Eng, 2013, 29(2):165–178. 27. Dias N V, Ivancev K, Kölbel T, et al. Intra-aneurysm sac pressure in patients with unchanged AAA diameter after EVAR[J]. European Journal of Vascular & Endovascular Surgery, 2010, 39(1):35-41. 28. Antón R, Chen C Y, Hung M Y, et al. Experimental and computational investigation of the patient-specific abdominal aortic aneurysm pressure field.[J]. Computer Methods in Biomechanics & Biomedical Engineering, 2015, 18(9):981. 29. Wen J, Yuan D, Wang Q, et al. A computational simulation of the effect of hybrid treatment for thoracoabdominal aortic aneurysm on the hemodynamics of abdominal aorta[J]. Scientific Reports, 2016, 6:23801. 30. Tarbell J M. Mass Transport in Arteries and the Localization of Atherosclerosis[J]. Annual Review of Biomedical Engineering, 2003, 5(5):79-118. 31. Lee E S, Caldwell M P, Tretinyak A S, et al. Supplemental oxygen controls cellular proliferation and anastomotic intimal hyperplasia at a vascular graft-to-artery anastomosis in the rabbit - Journal of Vascular Surgery[J]. Journal of Vascular Surgery, 2001, 33(3):608-613. 32. Lee E S, Bauer G E, Caldwell M P, et al. Association of Artery Wall Hypoxia and Cellular Proliferation at a Vascular Anastomosis[J]. Journal of Surgical Research, 2000, 91(1):32-37. 33. Zheng T, Wen J, Jiang W, et al. Numerical investigation of oxygen mass transfer in a helical-type artery bypass graft[J]. Computer Methods in Biomechanics & Biomedical Engineering, 2014, 17(5):549-559. 34. Meng H, Wang Z, Hoi Y, et al. Complex Hemodynamics at the Apex of an Arterial Bifurcation Induces Vascular Remodeling Resembling Cerebral Aneurysm Initiation[J]. Stroke, 2007, 38(6):1924-1931. 35.Balderi A, Antonietti A, Pedrazzini F, et al. Treatment of visceral aneurysm using multilayer stent: two-year follow-up results in five consecutive patients.[J]. Cardiovascular & Interventional Radiology, 2013, 36(5):1256-1261.

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Case 1 Case 2 Case 3 stent element Figure 1. Models of the three abdominal aortic aneurysm (AAA) cases considered in the study. Case 1 corresponds to AAA geometry with no stent, Case 2 corresponds to AAA geometry with a single-layer stent, and Case 3 corresponds to AAA geometry with a double-layer stent.

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Case 1 Case 2 Case 3 Figure 2. Meshes corresponding to the three cases.

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Case 1 Case 2 Case 3 Figure 3. Velocity streamlines in the three cases.

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Figure 4. Velocity contours at different slices of arterial aneurysm in the three cases. a) Case 1; b) Case 2; c) Case 3.

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Figure 5. Distribution of pressure for the three cases considered in the study.

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Case 1 Case 2 Case 3 Figure 6. Distribution of wall shear stress for the three cases.

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Figure 7. Sherwood number distribution on the wall of the aneurysm for the three cases.

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Figure 8. Ratios of low wall shear stress (WSS) and hypoxia areas on the wall of aneurysm to the entire area of the sac for Case 3.

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Figure 9. Distribution of wall shear stress along the x-axis for the three cases. The region indicated by the dotted red line denotes the “double high” region.

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Figure 10. Comparison of flow rates in renal branch in a normal case and in Cases 1– 3.

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Figure11. Relationship between stent mesh porosity and branch flux.

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