* Corresponding author: pgmenon@andrew.cmu.edu 1 Copyright © 2014 by ASME

IN-SILICO EVALUATION OF EFFECTS OF SWIRL DIRECTION AND INTENSITY ON AORTIC FLOW PATTERNS INDUCED BY AN AORTIC PUMP USING

COMPUTATIONAL FLUID DYNAMICS

Priti G. Albal Department of Electrical & Computer Engineering,

Sun Yat-sen University - Carnegie Mellon University (SYSU-CMU) Joint Institute of

Engineering, Pittsburgh, PA (USA)

Prahlad G. Menon* Department of Electrical & Computer Engineering,

Sun Yat-sen University - Carnegie Mellon University (SYSU-CMU) Joint Institute of

Engineering, Pittsburgh, PA (USA) pgmenon@andrew.cmu.edu

ABSTRACT

Congestive heart failure has reached epidemic proportions in developed countries afflicting an estimated 23 million patients worldwide and more than 5.7 million patients suffering from it annually in USA. Left ventricular assist devices (LVADs) have gained acceptance for non-transplant NYHA Class III & IV HF patients to provide full or partial circulatory support as a bridge to transplant or destination therapy. Recently, investigators have suggested advantages of deploying a continuous flow pump within the aorta, through transcatheter deployment (eg: Abiomed Impella pump) and an anchoring device to lodge the pump across the diameter of the ascending aorta (AAo). In this study we evaluate feasibility of such a device anchored virtually at the AAo of a patient-specific aortic arch, using computational fluid dynamics (CFD). Constant inflow rate conditions of 0.7 m/s in the axial direction with varying swirl / tangential intensity at the AAo inlet (viz. pump outlet) was modeled simulative of a range of conditions affecting aortic helical grade (viz. secondary flow), using FLUENT 14.5 (ANSYS Inc.). A change of swirl intensity from +30% (right-handed, physiological) to -30% (left-handed) swirl led to increases in peak WSS (by 10.31%) and mean WSS (by 13.04%). This simulation based pilot study indicates that WSS in transverse aortic arch is a versatile indicator of non-physiological helical flow grade and may be a promising design parameter for hemodynamics-informed aortic pump design.

1. INTRODUCTION LVADs are mechanical circulatory systems adopted as

therapeutic options for end-stage heart failure patients, either as destination therapy or as a bridge to cardiac transplantation [1, 2]. LVAD pumps have evolved over the past few decades from

pulsatile to continuous flow devices, and have steadily improved patient outcomes [3-5]. These devices are usually connected to the heart through the ventricular apex, and placed in an abdominal pocket or pericardial sac [6] which requires open heart surgery. However investigators have suggested that it might be advantageous to deploy a pump directly within the aorta and using an anchoring device [7]. Such pumps can be operated using an external driving force such as a permanent magnet with many advantages such as reduced total energy introduced into body and decreased chances of wound after the pump implantation in the body [8].

In 1993, Kilner et al [9] proposed that the physiological flow path in the aortic arch takes the form of a right-handed helix, and this was also confirmed through observations from clinical imaging [10]. Such helical flows in the upper aortic arch minimize flow separation and turbulence. Helicity in the descending aorta (DAo) is regarded as a contributor to optimizing naturally occurring transport processes in the cardiovascular system, avoiding excessive energy dissipation. As per our recent studies modeling aortic hemodynamics in conjunction with a virtual continuous flow (CF) pump anchored in the ascending aorta (AAo) [11], a swirling pump outflow with varying intensity and direction (i.e. handedness) can be obtained at the ascending aorta based on the operating characteristics of the pump, each resulting in different consequences as identified in terms of biomechanical loading in the aortic arch. Further numerical simulation studies are required to explore the hemodynamic consequences specifically focusing on biomechanical signature of the wall shear stress (WSS) in the aortic arch as a result of non-physiological swirling flow in the AAo resulting from such a pump. In this study, we conduct a series of high-resolution computational fluid dynamics (CFD) simulations in order to

Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition IMECE2014

November 14-20, 2014, Montreal, Quebec, Canada

IMECE2014-39711

2 Copyright © 2014 by ASME

examine the secondary helical flow patterns in a patient-specific virtual aortic arch model under a range of possible operating conditions of a CF pump virtually positioned in the AAo.

2. METHODS 2.1 Image Acquisition & Patient-specific Model Creation

The patient specific aorta model was constructed using magnetic resonance images (MRI). The anatomy was prepared by segmenting the aorta from the acquired volumetric image data, with expert guidance using ITK-SNAP [12]. The solid geometric models of the anatomy was re-constructed in three main steps by: a) exporting an extracted set of points (i.e. 3D contours) approximating the outer boundary of the aorta; b) Interpolating the 2D contour and developing a smooth 3D polygonal surface after applying surface-correction operations, using Geomagic Studio 10 (Durham, NC); and finally c) Lofting a parametric surface patches (NURBS) through the polygonal surface from step (b). The final surface (or collection of multiple surface patches) was exported as an IGS file into SolidWorks (Dassault Systems, Waltham, Massachusetts, USA) for joining of surface patches together to form a final bounded volume. For virtual insertion of a cylindrical pump above the aortic root, anchored in the AAo [11]., the effective diameter of the fluid-region of the model at the AAo was reduced to 2/3rd of its original size.

2.2 CFD analysis in patient-specific models Blood flow was accurately represented as an

isothermal, incompressible fluid flow, Newtonian model with a density of 1060 kg/m3 and viscosity 0.00371 Pa-s. Steady inflow simulations were conducted in FLUENT 14.5 (ANSYS Inc., Canonsburg, PA, USA) employing second-order spatial discretization scheme with rigid, impermeable walls.

2.3 Solver Details The aorta model was meshed in ANSYS Workbench

14.5 with a curvature-based advanced mesh function tool. A mesh containing ~500,000 tetrahedral elements was considered for the FLUENT simulations after conducting appropriate mesh independence studies. The pressure-velocity coupling algorithm was set as SIMPLE in FLUENT, which implements a pressure based segregated algorithm. The SIMPLE algorithm uses a relationship between velocity and pressure corrections to enforce mass conservation and to obtain the pressure field. A second-order discretization of pressure and momentum terms was employed. The pressure discretization method was set as PRESTO!, recommended for complex geometries which induce swirl flow such as this case study. 2.4 Boundary conditions

A constant effective velocity of 0.7 m/s was prescribed at the inlet of the aorta model simulative of the peak velocity at the aortic root in a cardiac cycle [13]. Varying swirl angles were created by applying varied axial and tangential velocities at the

inlet. Tangential velocities were considered to be varying percentages (10%, 20%, and 30%) of this effective velocity and the axial velocities were subsequently calculated by vector addition (see Figure 1).

Figure 1. Calculation of the effective velocity to obtain constant mass flow rate.

Right handed (i.e. physiological) flows were represented as positive tangential components whereas left handed (i.e. non-physiological) flows were represented as negative tangential components. Aortic outlets were numerically modeled based on defined constant resistance boundary conditions at all outlets (Table 1). Head–neck outlets were modeled using a constant outflow resistance equation which regulated blood flow and pressure at the outlets of the aorta arch, while preserving flow continuity (converged to within O (10-4)) [11]. The constant outflow resistances, Ri, applied at an outlet, i, was used to iteratively update normal pressure, Pn, at an outlet based upon the net outflow rate, Qi, after each iteration, for steady inflow conditions. A relaxation parameter, α, was employed during outlet pressure correction to ensure stability of the solution (α <1.0). This was achieved in the following simple two-step procedure:

𝑷𝒊 = 𝑸𝒊𝑹𝒊 + 𝑷𝟎 (1)

𝑷𝒊 = 𝜶(𝑷𝒊 − 𝑷𝒏) (2)

Here, P0 is the operating pressure which was set at 5 mmHg. Equation (2) defines a relaxation approach to help with simulation convergence while iteratively adjusting the pressure measured at planes normal to the aortic outlets, Pn , to match the computed target pressure Pt , in order to achieve the eventual outflow distributions characteristic of the modeled aortic configuration.

Table 1: Modeled aortic outflow resistances.

Aortic Outlet Resistance (Pa-s/kg)

Brachiocephalic artery (BCA) 7.00 x 109

Left common carotid artery (LCCA) 2.90 x 105

Left subclavian artery (LSA) 1.00 x 1010

Descending Aorta (DAo) 9.28 x 10

3

The flow-independent vascular resistances (see Table 1) applied at the outlet boundaries were tuned such that they ensured 41.55% flow through the head-neck vessels and 58.45% flow through the descending aorta for normal (no swirl/tangential component) inflow conditions. Initial guess for the resistances

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of the individual vessels were set relative to each other as per Poiseuille equation i.e., vascular resistance is inversely related to the fourth power of outlet diameter.

3. Results and Discussions With reference to the zero-swirl (no tangential

component for inflow profile) inlet case, a decline in perfusion at each of the head-neck vessels and increased DAo flow was observed when right-handed inlet swirl intensity was modeled (3.18% increase in DAo perfusion at +30%). In contrast, with non-physiological left-handed inlet swirl although a general downstream shift (towards DAo) of the flow streamlines was observed, this was associated with increased flow in the left subclavian artery (LSA) and the DAo (2.42% and 1.47% increase, respectively) (see Table 2).

Table 2: Percent outflow splits at the model outlets for a range of tested swirling inflow conditions, from -30% to +30%.

BCA LCCA LSCA DAo

-30% 27.95 4.63 8.11 59.31 -20% 28.01 4.61 8.11 59.27 -10% 28.52 4.68 8.15 58.66 0% 28.86 4.77 7.91 58.45

10% 28.66 4.88 7.80 58.65 20% 28.16 4.81 7.61 59.42 30% 27.42 4.70 7.57 60.31

It was observed that the peak WSS was consistently in the regions between the head-neck branching vessels (see Figure 2). In case of the right-handed swirling inflows, the region of peak WSS was between the BCA and LCCA branches whereas for left-handed flows the region of peak WSS was between the LCCA and LSA branches. Increasing left-handed inlet swirl intensity correlated with increased peak WSS (R2 = 0.2273, p = 0.2794) and increased mean WSS was observed in the transverse aortic arch (R2 = 0.4124, p = 0.1199, see Figure 3). Statistical significance of the decreasing relationship between mean WSS and right-handed inflow swirl improved to p = 0.012 when considering only range of -10% to +30% inflow swirl. It was noted that in case of left-handed swirling inflow, higher mean WSS were obtained at low swirl intensities (-10% to 0%) and mean WSS decreased in excess of -10% swirl flow (i.e. at -20% and -30%). A maxima in the mean WSS trend was observed between -10% to 0% swirl flow which corresponded with a minima in the peak-WSS trend, indicating a hemodynamic state associated with minimum likelihood of direct inflow impingement on the walls of the transverse aortic arch close to conditions of zero-swirl inflow.. Higher peak WSS was observed at -20% swirl flow (corresponding with a lower mean-WSS) implying the event of a greater likelihood of direct inflow impingement on the transverse arch walls. To better understand and confirm the variation in observed trends near 0% swirl flow, the curve needs to be resolved with results

from CFD studies for a greater number of lower swirl intensity cases (i.e. between -10% and 10%) in future studies.

Figure 2: WSS as observed in the aorta with annotations at the regions of peak WSS, for varying intensities of swirl flow.

Figure 3: Effect of percentage tangential flow or swirl intensity inlet on: A) Peak WSS and B) Mean WSS.

Under pump mode operation of 0.7 m/s inflow rate, a change of swirl intensity from +30% (right-handed) to -30%

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(left-handed) swirl led to increases in peak WSS by 10.31% and mean WSS by 13.04% (see Table 3). The peak and mean WSS decreased consistently with increase in right-handed (i.e. positive) swirling inflow (p = 0.2067 and p = 0.0744 for peak and mean WSS, respectively) proving that increase in tangetential component in the direction of physiological (i.e. right-handed) flows leads to lower WSS values. Table 3: Peak & mean WSS for varying inflow swirl intensity.

Percentage of tangential flow

Peak WSS (Pa)

Mean WSS (Pa)

-30% 20.91 5.64 -20% 21.34 5.82 -10% 18.31 6.27 0% 17.69 6.08

10% 19.67 5.55 20% 19.52 5.33 30% 18.96 4.98

4. Conclusion and Future Work This simulation based pilot study indicates that peak WSS and mean WSS in transverse aortic arch is a versatile indicator of non-physiological helical flow. Benchmarking these biomechanical indices against the expected normal pre-implantation hemodynamic state will be crucial to establishing target parameters for optimal pump operation and positioning in the aortic arch [14]. This study on correlating the nature of swirling pump outflow profiles to helical grade in the aorta will culminate with bench-top validation experiments attempting in-vitro deployment of a novel cylindrical CF pump anchored in the AAo of an in-vitro model of the patient-specific aorta arch, oriented and operated optimally for minimal WSS in the transverse arch, (as per results of our simulation models) in the interest of validating simulated aortic helical grade, using dye flow visualization or particle image velocimetry (PIV) studies.

NOMENCLATURE LVAD - Left Ventricular Assist Devices CFD – Computational Fluid Dynamics CF pump – Continuous Flow pump WSS – Wall Shear Stress Ri – Constant outflow resistance applied at outlet, i Pn – Normal Pressure at a given aortic outlet Qi = Outflow rate at outlet, i α – Presure relaxation parameter P0 – Initialized operating pressure in the aorta AAo – Ascending Aorta DAo – Descending Aorta BCA - Brachiocephalic Artery LCCA - Left Common Carotid Artery LSA - Left Subclavian Artery

ACKNOWLEDGMENTS This study was conducted with the support of Pittsburgh

Supercomputing Center research award: BCS120006.

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