Supporting Document

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Supporting Document Successful Use of Retrograde Branched Extension Limb Assembling Technique in Endovascular Repair of Pararenal Abdominal Aortic Aneurysm

Jiang Xiong1 ‡ , Zhongzhou Hu1 ‡ , Hongpeng Zhang1, Huanming Xu2, Duanduan Chen2*, Wei Guo1* 1

Department of Vascular and Endovascular Surgery, Chinese PLA General Hospital, China.

2

School of Life Science, Beijing Institute of Technology, China

‡

Jiang Xiong and Zhongzhou Hu are co-first authors

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I. Image Acquisition, 3D Reconstruction and Mesh Discretization The studied patient underwent Computed Tomography Angiography (CTA) pre- and postendovascular repair via a dual-source CT scanner (SOMATOM Definition Flash, SIEMENS, Germany). CTA was carried out with injection of 70~90ml of contrast with 50ml of saline chaser, threshold 80HU; rotation speed: 500ms; collimation: 64; slice: 1.0mm; pitch: 1.0; voltage: 100kV; current: 200~350mAs. The segmentation and surface reconstruction of the aorta were accomplished by a semi-automatic segmentation tool (Mimics 17.0, Materialise, Belgium). Detailed views of the reconstructed surface of the aorta are shown in Fig.S1a-b. The reconstructed geometry was meshed in ICEM (ANSYS 12.1Inc, Canonsburg, USA) with tetrahedral elements in the core region and prismatic cells in the boundary layer near the aortic wall (10 layers of prismatic cells define the near-wall region). The pre- and post-treatment models resulted in 2,215,688 and 2,280,981 cells, respectively.

Fig.S1 3D reconstruction of the aorta pre- (a) and post- (b) treatment.

II. Boundary Conditions The vessel wall in the computational models are assumed rigid with no-slip boundary conditions. The models also contain several velocity and pressure boundaries. The inlet of the ascending aorta (AA) and the outlets of the brachiocephalic trunk (BT), left common carotid (LCCA) and left subclavian (LSA) arteries are velocity boundaries. The time-variant flow rate at these boundaries were measured by Doppler ultrasound. The velocity of AA was measured through the apical 5-chamber view and the suprasternal long axis view of aortic arch. The two results have been compared to each other to ensure the maximum velocity at AA could be captured. The velocity at other velocity boundaries was measured at the proximal and distal region of the specific vessel (detailed positions refer to Table S1). The two results of one particular vessel have been compared. If the difference is more than 5%, the measurement should be re-done, in order to ensure the accuracy of the measured velocity. At each measurement site, appropriate ultrasound probe was employed, the Doppler gate was positioned at the centre of the blood vessel, and the Doppler angle cursor was accurately

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aligned with the vessel axis. The outlets of celiac trunk (pre-treatment only), superiormesenteric artery (SMA), renal arteries and the common iliac arteries are pressure outlets, however, the actual pressures at these sites are difficult to be accurately measured. Thus, at the pressure outlets, we extended the geometry with a length of 15-times diameter of each visceral arteries and extended the common iliac arteries with a length of 25-times diameter. The outlets of visceral arteries and common iliac arteries are assigned with zero pressure in the extended models, so that the computed physical quantities like velocity and pressure could be obtained in the original models. Table S1. Parameters of Doppler ultrasound velocimetry Site AA

BT LCCA LSA

Position -

2.5cm above aortic valve

Distal

0.8cm below bifurcation

Proximal

0.9cm above aortic arch

Distal

3.0cm below bifurcation

Proximal


Distal


Proximal


View Suprasternal long axis view of aortic arch apical 5-chamber view long axis view of BT long axis view of LCCA long axis view of LSA

Doppler Angle 30 22 47 47 47 36 30 36

III. Numerical Models The blood was treated as Newtonian and incompressible with density of 1044kg/m3 and dynamic viscosity of 0.00365kg·m-1·s-1. The average Reynolds number in pre- and posttreatment models were 2003 and 2137, respectively; the blood flow is usually assumed to be laminar in large vessels due to the low mean flow velocity [1]. Our previous study also confirmed that laminar simulations with adequately fine mesh resolutions, especially refined near the walls, can capture flow patterns as turbulence model [2]. A finite volume solver, CFD-ACE+ (ESI Group, France), was employed for the numerical solution of the transport equations – the Naviér-Stokes equations. A second order accurate discretization (central differences) was used to solve the flow velocity. Algebraic MultiGrid acceleration was employed and the SIMPLEC-type pressure correction was used for pressure-velocity coupling. The averaged cardiac cycle of this patient pre- and post-treatment is 70 beat/min. Temporal discretization of numerical models was assigned as 45 step/cycle. Simulation was carried out for 5 cardiac cycles to achieve a periodic solution and results of the final cycle were presented in the paper.

IV. Grid and Time Independency Study To confirm the insensitivity of the results to the spatial resolution and time, grid independence analysis and time step sensitivity test were conducted on the pre-treated model, since the flow in the abdominal region is highly vortical. The base grid discretizations are with 2,215,688 cells and the base time steps are 0.01905s. Solutions on finer grids (5,565,622 cells) and finer temporal discretizations (0.00857s) were investigated. To compare the results, a point in the

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centre of the aneurysm has been studied, shown in the Fig.S2a (arrow indicated). The maximum discrepancies of the velocity magnitude and pressure at this point during a cardiac cycle between the two grids are 8.43% and 1.22%, respectively; and the resulted differences between the two temporal discretizations are 8.29% and 6.46% for the velocity magnitude and pressure respectively. As shown in Fig.S2b-c, exact same trends of the variation of velocity magnitude and pressure are observed between the tested models. Thus, for the purposes of our study the base resolutions with the base time step are adequate.

Fig.S2 Grid and temporal independency study. (a) displays the point selected for the independency study, which is in the centre of the aneurysm; (b) and (c) show the results of velocity magnitude and pressure respectively.

V. Hemodynamic Parameters In the current study, two hemodynamic parameters derived from wall shear stress have been discussed. The time-averaged wall shear stress (TAWSS) and relative residence time (RRT)  are defined as equ.1 and 2, respectively, where,  is the instantaneous wall shear stress and T is the pulse period.

 TAWSS 

T

0

RRT 



 dt T

equ.1

1 1  2  OSI   TAWSS

T    0  dt  1  OSI   1  T   2   dt   0 

equ.2

VI. References 1. 2.

Morris, L., et al., A mathematical model to predict the in vivo pulsatile drag forces acting on bifurcated stent grafts used in endovascular treatment of AAA. J. Biomech., 2004. 37: p. 1087-1095. Chen, D., et al., A patient-specific study of type-B aortic dissection: evaluation of true-false lumen blood exchange. Biomed Eng Online, 2013. 12: p. 65.