Chalmers University of Technology

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2 What is an Abdominal Aortic Aneurysm(AAA)and how is it rectified? AAA's are caused due to local dilation of the abdominal aortic vessel common among males 60 years or over How do we treat it? Common surgical procedures are Open aortic repair(oar) and Endovascular aortic repair(evar) EVAR is gaining popularity due to lower morbidity Aneurysm Proximal End Stent graft Distal End Figure showing EVAR procedure

3 Aim Develop a computational model to evaluate forces in the proximal and distal end of the stent graft and compare them to the experimental results initially with water Compare these results with blood to justify the usage of water and to highlight the significance of viscosity(rather the lack of it) Evaluate different non-newtonian blood viscosity models and simulate a chosen one with the given problem and compare the displacement forces with Newtonian blood. Evaluate primary and secondary flow structures formed(for 60BPM,145/80.mmHg)

4 Assumptions and Simplifications Symmetry BC which is assumed may not be valid may not be valid. Blood is considered as modelled as a single phase whereas its truly a multiphase fluid. Only the graft material is modelled(as linear isotropic) and the stent material is not considered while modelling. Only one distal extension is considered and the bend is considered initially stress free. Gravity is neglected

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6 Consider a rigid pipe of diameter(d)and length '30d' with a Reynold's number(re)=750. As per literature, the Carreau model seems to match the experimental viscosity If we notice the relation for Carreau, it is a bounded function which means computational time if used would reduce according to Biasetti.et.al(2011). Hence, Carreau model is chosen as the non-newtonian viscosity model

7 FSI process Strong coupling Pressure and viscous force increments are transferred from fluid to solid side Increase in displacement and velocity are transferred from structure to fluid side IQN-ILS under relaxation is used to accelerate the coupling process

8 Computational and Experimental setup Rigid Rigid Flexible

9 Material Properties Fluid Properties Structural Properties Graft material is e-ptfe which is considered Linear isotropic and stent material is NiTiNol(not considered for modelling)

10 Numerical setup OF cell count: 108, 360 hexahedral elements using ANSYS ICEM CFD Inlet: Physiological Velocity input as per the experiment. Outlet: Distal pressure as measured in the experiment. (timevaryinguniformfixedval ue) Rigid Walls: No-slip Flexible Walls: Moving wall velocity

11 Solver settings Solver used: fsifoam in FOAM-extend 3.2 Time step size: sec Discretization: Linear upwind for the advective terms FlowModel: consistenticoflow for Newtonian case PISOFlow for Non-Newtonian case Fluid solver utilizes PISO algorithm and a partitioned strong coupling method is used

12 Velocity is calculated from the experimental flow rate Experimentally obtained beats Ensemble average the velocity Same procedure for pressure

13 Results Inlet velocity and Outlet pressure used in the simulations are shown below for 60BPM, 145/80.mmHg. Results can be split up as: Displacement force calculations(water), Displacement force calculations(blood) and Flow structures developed. Results produced are for the 2nd consecutive heartbeat

14 Results(Displacement Forces)

15 Results(Displacement Forces)

16 Results(Displacement Forces)

17 Results(Displacement Forces) Experimental Results for 145/80, 170/90 and 195/100 mm.hg respectively FSI Results Results for 145/80, 170/90 and 195/100 mm.hg respectively

18 Results(Displacement Forces-Blood)

19 Results(Displacement Forces-Blood)

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21 Results(Velocity Contours t=0.1 sec)

22 Results(Velocity Contours t=0.4 sec)

23 Results(Velocity Contours t=0.6 sec)

24 Results(Velocity Contours t=0.85 sec)

25 Conclusions The experimental results match the computational results only for a pressure of 195/100.mm.Hg for all cases. Displacement forces are of the same magnitude for blood and water showing that viscosity plays a minor role in calculation of displacement forces. Hence, the usage of water could be justified in the experiments by Roos.et.al(2014) Using a Newtonian or Non-Newtonian model does not affect the displacement forces, however the flow structures are different while comparing both. Vortices are transient in nature and weakened vortices are formed at low Reynolds number for non-newtonian fluids. However, further analysis in the form of Lambda2 method needs to be performed to get a better understanding of 3D vortices