computational fluid dynamics analysis of surgical adjustment of

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COMPUTATIONAL FLUID DYNAMICS ANALYSIS OF SURGICAL ADJUSTMENT OF LEFT VENTRICULAR ASSIST DEVICE IMPLANTATION TO MINIMIZE STROKE RISK Andres F. Osorio1 [email protected] Ruben Osorio1 [email protected] Andres Ceballos1 [email protected] Reginald Tran1

[email protected] William Clark1 [email protected] Eduardo A. Divo1,2

[email protected]; [email protected]

I. Ricardo Argueta-Morales3

[email protected] Alain J. Kassab1 [email protected] William M. DeCampli3,4 [email protected] 1 Department of Mechanical, Materials and Aerospace Engineering, College of Engineering and Computer Science, University of Central Florida, Orlando, FL, USA 2 School of Engineering Technology, Daytona State College, Daytona Beach, Florida, USA 3 Congenital Heart Institute at Arnold Palmer Hospital for Children, Orlando, FL, USA 4 Department of Surgery, College of Medicine, University of Central Florida, Orlando, Florida, USA __________________________________________________________________________________

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Abstract

Background: Currently, mechanical support is the most promising alternative to cardiac transplantation. Ventricular Assist

Devices (VADs) were originally used to provide mechanical circulatory support in patients awaiting planned heart

transplantation (“bridge-to-transplantation” therapy). The success of short-term bridge devices led to clinical trials

evaluating the clinical suitability of long-term support (“destination” therapy) with left ventricular assist devices (LVADs).

The first larger-scale, randomized trial that tested long-term support with a LVAD reported a 44% reduction in the risk of

stroke or death in patients with an LVAD. In spite of the success of LVADs as bridge-to-transplantation and long-term

support, patients managed by these devices are still at risk of several adverse events. The most devastating complication

is caused by embolization of thrombi formed within the LVAD or inside the heart into the brain. Prevention of thrombi

formation is attempted through anticoagulation management and by improving LVADs design; however there is still

significant occurrence of thromboembolic events in patients. Investigators have reported that the incidence of

thromboembolic cerebral events ranges from 14% to 47% over a period of 6-12 months.

Methods and Approach: An alternative method to reduce the incidence of cerebral embolization is proposed by the co-

authors, and the hypothesis is that it is possible to minimize the number of thrombi flowing into the carotid arteries by an

optimal placement of the LVAD outflow conduit, with or without the addition of aortic bypass connecting the ascending

aorta (AO) and the innominate artery (IA), or left carotid artery (LCA). This paper presents the computational fluid

dynamics (CFD) analysis of the aortic arch hemodynamics using a representative geometry of the human aortic arch with

or without an alternative aortic bypass.. In order to study the trajectory of the thrombi within the aortic arch bed, the CFD

code Fluent 6.3 is utilized to resolve the flow field and to solve the Lagrangian particle-tracking of thrombi released

randomly at the inlet of the LVAD cannula.

Results: Results are presented for simulations of thrombi in the range of 2mm-5mm. Percentage of individual diameter as

well as aggregate diameter thrombi flowing to the carotid arteries as a function of LVAD conduit placement and aortic

bypass implantation are reported. The influence of the LVAD conduit implantation and bypass reveal a nearly 50%

variation in predicted cerebral embolism rates.

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Conclusions: The adjustment of the location of the anastomosis of the LVAD inflow cannula as well as its angle of

incidence plays a significant role in the level of thromboembolisms. By proper adjustment in this CFD study of a synthetic

model of an aortic arch bed, we found nearly a 50% reduction of cerebral embolism could be achieved for a configuration

consisting of a shallow angle of implantation over a baseline normal incidence of the LVAD cannula. Within the limitations

of our model we have established that the LVAD implantation geometry is an important factor and should be taken into

consideration when implanting an LVAD. It is possible that other parameters such as distance of the LVAD outflow cannula

to the root of the IA, could affect the thrombi embolization probabilities. However, the results of this study suggest that the

risk of stoke may be significantly reduced by as much as 50% by tailoring the VAD implantation by a simple surgical

maneuver. The results of this line of research may ultimately lead to techniques that can be used to estimate the optimal

LVAD configuration in a patient specific manner by pre-operative imaging.

Key words: LVAD, CFD, Lagrangian tracking, thromboembolism.

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INTRODUCTION

Heart failure is a major public health problem affecting over 5 million people in the United States [1]. Orthotopic heart

transplantation is the best treatment option for patients with end-stage heart failure; however, the number of patients

awaiting heart transplantation far exceeds the number of donor hearts available [2]. At the present time, mechanical

circulatory support is the most promising alternative to cardiac transplantation [3]. Ventricular Assist Devices (VADs) were

originally used to provide mechanical circulatory support in patients awaiting planned heart transplantation (“bridge-to-

transplantation” therapy). The success of short-term bridge devices led to clinical trials evaluating the clinical suitability of

long-term support with left ventricular assist devices (LVADs). The first large-scale, randomized trial that tested long-term

support with an LVAD reported a 44% reduction in the risk of stroke or death in patients treated with an LVAD [4]. The

results of this study provided evidence for the Food and Drug Administration (FDA) approval of an LVAD for so-called

“destination” therapy in 2002 [5]. The well-documented imbalance between the number of potential transplant recipients

and available donor organs, and the technological advances in device design and miniaturization have allowed LVADs to

become a well-established therapy for adults and children [6], [7].

There are two types of LVADs: the 1st generation pulsatile-type that were designed to capture the cardiac output and

the 2nd generation of continuous axial-flow type LVADs such as the Heart Assist 5 (MicroMed, Houston, Texas), Jarvik

2000 (Jarvik Heart, Inc., Manhattan, New York) and Heartmate II (Thoratec Corporation, Inc., Pleasanton, California) that

are designed to augment cardiac output and provide continuous flow [8], [9]. The latter type of LVADs significantly reduce

but do not eliminate pulsatility [10], [11] associated with the native circulation. Moreover, the waveforms generated by

LVADs are closer to periodic than the natural waveform of the cardiac cycle and for a sick heart exhibit a low pulsatility

index. Continuous flow LVADs have shown much promise in terms of durability and superior clinical outcome [12], [13].

Figure 1: DeBakey LVAD and associated nomenclature.

Standard LVAD Configuration

(1) Inflow conduit(2) LVAD(3) Outflow Cannula(4) Ascending Aorta

12

1 1

13

1 4

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Preservation of organ function using continuous flow LVADs has been demonstrated in a long term study [14]. It is this

second and newest generation of continuous flow LVADs that is the subject of the proposed investigation.

Survival with LVADs is currently in the range of 50% at 1 year. Furthermore, follow up studies have reported that

patients, children or adults, requiring pre-transplantation VAD support have long-term survival similar to that of patients

not requiring mechanical circulatory support [15], [16]. However, there are numerous adverse events that may occur

following initiation of circulatory support that can substantially diminish the benefit of this life-saving technology [5].

Bleeding, right-sided heart failure, air embolism, and progressive multisystem organ failure are the most common causes

of early morbidity and mortality after placement of an LVAD. The most common complications in the late postoperative

period are infection, thromboembolism, and failure of the device [3]. The most devastating complications are neurologic,

and are caused by embolization of particulate matter or air into the brain. Particulate matter can come from a thrombus

that enters the LVAD from the atrium or ventricle, or a thrombus that forms within the LVAD [5], [17]. Systemic thrombo-

embolization has been reported to occur considerably less often than cerebral [18].

All LVADs carry a risk for thromboembolism. This risk factor has been addressed, mainly, by improving the device

design and attempting adequate anticoagulation. State of the art technology is used to generate engineering designs of

LVADs that avoid step changes in lumen size, improperly sized conduits, surface imperfections of 10µm or larger, sharp

transitions of flow, small radius, right angle bends, multiple cross-sectional flow areas, multiple joints, and surface

protrusions; with the ultimate goal of minimizing thrombus formation. Adequate anticoagulation remains a key issue with

the use of LVADs; the need to balance the risk of bleeding with that of thrombosis complicates treatment in patients with

LVADs, and the ideal regimen for device-related thrombosis prophylaxis has not been determined. Conventional

anticoagulation management includes unfractionated heparin (UFH) in the post-operative period, oral anticoagulants in

the outpatient setting, and adjunctive anti-platelet therapy (clopidogrel) [19]-[21]. Despite all of these efforts, investigators

have reported that the incidence of thromboembolic cerebral events ranges from 14% to 47% over a period of 6 to 12

months [18], [22].

Thrombogenesis in LVADs is attributed to various mechanisms including platelet activation associated with non-

physiological flow patterns such as stagnation and re-circulating flows [23]-[25]. Consequently, several research groups

[23]-[30] have sought to characterize the hemodynamics of flows induced by LVADs utilizing powerful simulation

capabilities afforded by computational fluid dynamics (CFD). Most studies consider 3D models and steady flow while

some undertook transient modeling through the cardiac cycle [26], [30]. In all cases blood was modeled as a Newtonian

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fluid and while various approaches were taken utilizing either synthetic representative geometries or by retrieving

geometric data of the aortic arch from CT scans of patients [30], these studies generally focused on abnormal

hemodynamics and shear stress distributions as thrombogenic. None of these studies considered predicting the paths

taken by the thrombi as they are carried by the flow in the aortic arch and if there was a possibility to preferentially guide

the thrombi, should they occur, away from the left and right carotid arteries and vertebral arteries by controlling the LVAD

conduit outflow insertion angle and location, or by some other means such as utilizing an aortic-to-innominate or aortic-to-

left-carotid bypass graft. This is the approach investigated in this paper. Thus, we depart from the premise that, despite all

attempts for mitigation, thrombus formation is an event that is currently afflicting a significant population of VAD patients,

and we offer a possible engineering-inspired surgical solution to what is a fluid mechanics problem, that is tailoring of the

VAD implantation to preferentially direct thrombi away from vertebral and carotid arteries to the descending aorta where

their impact on the patient is lessened compared to the devastating effect of the neurological ravages of stroke or the

ultimate death of the patient. That is, in this paper we seek to test the hypothesis that there is an optimal LVAD

implantation geometry that reduces the incidence of thromboembolism to the vertebral and carotid arteries in LVAD

patients, and we employ well-established computational fluid dynamics tools to examine this hypothesis. We first present

the geometry of the aortic vasculature under consideration, we then describe the computational model we utilized to

determine the flow fields and thrombus paths along with flow rate and boundary conditions we imposed, and we present

results and conclusions.

AORTIC ARCH MODEL

The aortic arch connects the ascending aorta (AO) with the descending aorta (DA). The most common aortic arch

branching pattern in humans consists of three great vessels originating from the arch of the aorta as shown in Figure 2.

Progressing along the dorsal portion of ascending aorta, the first branch is the innominate artery (IA), which branches into

the right subclavian artery (RSA) and the right common carotid artery (RCA). The second branch in the most common

pattern [31] is the left common carotid artery (LCA), followed by the left subclavian artery (LSA).

Figure 2: Most common form of aortic arch in humans

Measurements of the diameter of the aortic arch at select locations

model of an adult human aortic arch vasculature

available, and Table 1 lists the artery diameters.

(Dassault Systèmes S.A., Vélizy, France) and the model includes the vertebral arteries as well as the coronary arteries.

Figure 3: Locations where aretery diameters measurements were

Most common form of aortic arch in humans [31].

Measurements of the diameter of the aortic arch at select locations were used to reconstruct a

vasculature [29]. Figure 3 shows the locations where diameter measurement

artery diameters. A three-dimensional solid model was generated utilizing Solid

and the model includes the vertebral arteries as well as the coronary arteries.

Locations where aretery diameters measurements were taken to build synthetic model

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construct a 3D representative solid

shows the locations where diameter measurements were

dimensional solid model was generated utilizing SolidWorks®

and the model includes the vertebral arteries as well as the coronary arteries.

taken to build synthetic model [29].

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Table 1: Artery diameters at locations identified in Figure 3.

Location Diameter [mm]

1 24.80

2 29.00

3 25.00

4 12.40

5 8.00

6 7.40

7 21.80

8 7.40

9 21.80

10 7.40

11 21.40

12 20.00

Figure 4: The complete aortic bed solid model including vertebral and coronary arteries generated for the CFD model.

Standard LVAD Configuration

LVADs are implanted by means of surgical procedure. The procedure consists of connecting an inflow cannula from

the apex of the left ventricle to the LVAD, and

adults, the LVAD outflow cannula is typically

wall of the ascending aorta.

The representative model of the adult human aortic arch was modified to add the LVAD outflow conduit. The LVAD

outflow conduit was modeled in analogy to the usual surgical approach, i.e.,

of the ascending aorta. . This model is hereon referred to as the standard configuration, and it is illustrated in

this study we refer to several parameters that are varied and these are: the LVAD implantation angle (

to the normal to the right lateral ascending aortic wall

measured from the location of the LVAD conduit implantation under the standard configuration

LVAD conduit implantation from the IA (δ). These are

the LVAD cannula from the IA to be fixed at

conduit, β=0o, 30o and 60o, and consider varying the location along the coronal plane from an angle

(a) standard configuration: β =0o. (b) intermediate configuration

Figure 5: LVAD cannula anastomosed to the ascending aorta in (a) standard configuration and (b) in an intermediate configuration with illustration of the geometric parameters angle at θ=0o.

LVAD

cannula


the apex of the left ventricle to the LVAD, and connecting an outflow cannula from the pump

typically 12mm diameter polytetrafluoroethylene graft that is sutured to the


d in analogy to the usual surgical approach, i.e., anastomosed perpendicular to the

is hereon referred to as the standard configuration, and it is illustrated in

several parameters that are varied and these are: the LVAD implantation angle (

aortic wall at the location of implantation, the angle along the coronal plane (

measured from the location of the LVAD conduit implantation under the standard configuration

). These are illustrated in Figure 5. We keep the distance of the anastomosis of

the LVAD cannula from the IA to be fixed at δ=15mm, however, we consider three angles of

, and consider varying the location along the coronal plane from an angle

(b) intermediate configuration: β =30o. (c) shallow configuration:

: LVAD cannula anastomosed to the ascending aorta in (a) standard configuration and (b) in an intermediate configuration with illustration of the geometric parameters β, θ, and δ (vertebrals and coronaries not shown)

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the pump to the ascending aorta. In

graft that is sutured to the right lateral


perpendicular to the lateral wall

is hereon referred to as the standard configuration, and it is illustrated in Figure 5. In

several parameters that are varied and these are: the LVAD implantation angle (β) measured relative

the angle along the coronal plane (θ)

measured from the location of the LVAD conduit implantation under the standard configuration, and the distance of the

. We keep the distance of the anastomosis of

three angles of incidence of the LVAD

, and consider varying the location along the coronal plane from an angle θ=0 to 45o.

(c) shallow configuration: β =60o.

: LVAD cannula anastomosed to the ascending aorta in (a) standard configuration and (b) in an intermediate (vertebrals and coronaries not shown) with coronal

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(a) β= 0o (b) β= 30o (c) β= 60o

Figure 6: Beveled conduit to tailor angle of anastomosis: (a) β= 0o, (b) β= 30o, and (c) β= 60o.

Bypass LVAD Configurations

Two variations of the Standard LVAD configuration have been proposed as an alternate method to help reduce the

incidence of thrombi flow into the left and right carotid arteries. The two variations consist of adding an alternative aortic

bypass between the AO and the IA (AO-IA bypass), or between the AO and the LCA (AO-LCA bypass).

In the IA bypass LVAD configuration, an 8mm bypass graft connects the AO to the IA. In this variation, the aortic-to-

innominate artery bypass graft proximal anastomosis is located 10mm below the LVAD conduit anastomosis with proximal

ligation of the IA. The rationale of this option is that such a procedure would be surgically feasible [32], [33] and would

allow nearly complete prevention of thrombi to the RCA. The AO-IA bypass configuration is shown in Figure 7(a). In the

AO-LCA bypass LVAD configuration, an 8mm bypass graft connects the AO to the LCA. The bypass is proximally

anastomosed to the ascending aorta below the LVAD outflow conduit anastomosis, and the distal section of the bypass is

anastomosed to the proximal LCA which is ligated at its origin. The LCA bypass configuration is shown in Figure 7(b).

(a) AO-IA bypass. (b) AO-LCA bypass

Figure 7: AO-IA and AO-LCAD Bypass LVAD Configuration models.

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CFD MODEL

The CFD analyses reported in this paper were conducted with the commercially available CFD software Fluent 6.3

(ANSYS Corp., Canonsburg, PA, USA) [34]. The flow field is resolved by numerically solving the mass and momentum

conservation equations, which neglecting gravitational and other body forces, are:

0 ( )V

V and V V pt

∂ρ ρ τ∂

∇ ⋅ = + ⋅∇ = −∇ + ∇ ⋅�

� � �

(1)

Where, ρ is the mass density, V is the velocity, and � is the viscous stress tensor. Blood is effectively an incompressible

fluid. We utilized a density of 31060 /kg mρ = and a dynamic viscosity of 20.04 /Ns mµ = . The models were meshed

in Fluent meshing software package Gambit utilizing typically approximately 2 million tetrahedral cells. This level of

discretization was determined to be adequate to ensure grid independence. This was established in a mesh convergence

study targeting the outlet mean velocity and pressures as measures of grid independence for models discretized with an

increasingly finer mesh as will be discussed in the results section where results from grid convergence studies are

provided. For our studies, a representative sick adult heart was modeled. The flow field was modeled as steady with a

cardiac ejection of 1 liter/min and a VAD flow rate of 3 liters/min resulting in a total flow of 4 liters/min. Continuous flow

LVADs significantly reduce pulsatility and, in contrast to the cardiac pulse, produce a steady flow baseline flow with a

small periodicity. A safe pulse pressure greater than 15mmHg has been suggested to open the aortic valve. With a

baseline pressure of 100mmHg, a 20mmHg pulse provides a 20% contribution to the flow. It is also noted that VAD

manufacturers recommend that VADs should be operated with a pulsatility index of 30%, with the pulsatility index defined

as the difference between the maximum and minimum over the baseline value of the flow rate waveform. Although not a

small perturbation, it is small enough, to assume that the steady baseline flow Lagrangian particle trajectories can yield

useful information that lends support to our hypothesis. The k-ω SST model was utilized to account for turbulence with 5%

turbulence imposed at the inlet of the LVAD and 5% turbulence at the inlet of the ascending aorta. For the outlets, a flow-

split boundary condition was applied to the different arteries assigning a fixed percentage of the total flow to each outlet

boundary with the various flow splits assignments shown in Figure 8.

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Figure 8: AO-IA bypass model with assigned flow splits.

LAGRANGIAN PARTICLE TRACKING MODEL

In order to analyze the trajectory of the blood clots in the different aortic-arch LVAD models, the trajectories of

particles with similar properties to those of thrombi are computed using a mixed Eulerian-Lagrangian approach where

thrombi trajectories are predicted using a Lagrangian model in a Newtonian Fluid. In this approach, the discrete phase

(particles/thrombi) is uncoupled from the continuous phase (carrier/blood). Particles with properties analogous to the

blood clots are introduced in the computational domain (at the LVAD conduit inlet plane) and their trajectories are

governed by the momentum conservation equation (Newton’s second law of motion) in terms of the particle velocity, pV→

,

and sum of the forces acting on the particle:

p

body surfacep

dVm F F

dt

→→ →

= +∑ ∑ (2)

The only body force that is accounted is that due to added mass effect, with the buoyancy force neglected due to the

fact the density ratio between blood and the thrombus particle is ρparticle/ρblood=1.097, with the density of thrombi taken from

the literature to be 1117pρ = kg/m3.

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For a particle of density, pρ , diameter, pd , entrained by a fluid of viscosity, fµ , flowing at a mean velocity, U, within a

conduit of diameter, D, the Stokes number (St) defined as the ratio of the particle response time,

2p p

pf

dρτ

µ= , to the

convective time scale, f

D

Uτ = , that

2

18p p p

f f

d DSt

U

τ ρτ µ

= = . The Stokes number is an indicator as to whether the surface

forces entraining the particle dominate over the particle momentum and the particle essentially follows the streamlines (St

<1) or the momentum of the particle dominates over the forces acting on the particle and the particle can deviate from the

streamlines (St>1) as these bend around an obstacle or in a conduit. With a diameter of 30mm in the ascending aorta

and a total flow of 4 liters/min, the Stokes number for the particles in the range of 1mm-6mm span the ranges of St=0.051-

1.828 while in the VAD conduit with a flow rate of 3 liters/min and a diameter of 12mm, the Stokes number range is

St=0.595-21.45. Thus, in general, the paths of thrombi of size greater than 2mm deviate significantly from the streamlines

in this model.

The main surface force in the model is that due to viscous drag force caused by the relative velocity of the particles

with respect to the continuous phase. The drag force for a given particle is given by:

1

2d d p p s sF C A V Vρ=� � �

(3)

Where Cd is the drag coefficient, Ap is the particle cross section, and the particle slip velocity is sV→

. The drag coefficient

can be estimated using correlations for drag on spherical particles. Such a correlation is available in Fluent, or

alternatively, user defined functions can be utilized to implement a desired correlation. The other surface forces, such as

the Saffman lift force and the Faxen correction due to pressure are neglected as they are not expected to significantly

affect the thrombi trajectories.

There is little about the size distribution of thrombi encountered in VAD-induced thrombi. Clinical experience

however suggests that thrombi encountered in such events have diameters that range from 2mm-5mm. Moreover,

interaction between thrombi and arterial walls are due to a complex set of biochemical and biophysical factors such as

arterial wall roughness, chemical bond formation, surface reactivity, and re-suspension. In our analysis, we assume that

the collisions between thrombi and arterial walls are elastic (restitution coefficients equal to unity). Particles are allowed a

maximum residence time of 300s after which the solver removes them from the computational domain. This would occur

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for instance when a particle is captured in a recirculation zone and unable to deviate from a streamline, in such a case

after 300s such a particle will be removed from the simulation. Three different thrombi diameters were used as the particle

diameters, 2mm, 4mm, and 5mm in the simulation. Ultimately, our model allows us to predict the general pattern as to

what type of thrombus posses a higher chance of flowing into the carotid and vertebral arteries and causing cerebral

embolisms.

OUTFLOW CONDUIT PLACEMENT OPTIMIZATION

There are several factors that can potentially affect the trajectory of thrombi generated inside the LVAD. For this study,

we consider geometric effects by varying size, position and orientation of the VAD outflow conduit implantation in order to

identify a configuration that minimizes the incidence of carotid, vertebral, and coronary embolism. Moreover, we

numerically analyze the effectiveness of a proposed aortic-to-IA artery bypass graft and an aortic-to-LCA bypass graft in

reducing the incidence of carotid, vertebral, and coronary embolization. Thus, the ultimate goal of this work is to establish

that the orientation of the LVAD conduit significantly affects the incidence of cerebrovascular embolization and to suggest

that there exists an optimal placement and orientation of the LVAD outflow conduit and possibly the addition of an aortic-

to-IA an aortic-to-LCA bypass graft that will significantly reduce the occurrence of thromboembolism in the carotid and

vertebral arteries. We consider three values for the angle, β= 0o, 30o and 60o, and also consider varying the coronal angle

placement, θ. In all cases, we keep the distance of the VAD conduit anastomosis from the IA at δ=15mm. All of these

variations correspond to surgically achievable configurations.

RESULTS AND DISCUSSION

The main objective of the CFD simulations is to determine whether changing the LVAD outflow cannula angle, and/or

adding an aortic bypass significantly affected the trajectory of thrombi emanating from the LVAD conduit. That is we aim to

establish that the geometric configuration of the LVAD conduit anastomoses is an important consideration in determining

eventual stroke events, thus establishing the possibility of searching for an optimal LVAD conduit implantation

configuration that reduces stroke. No study had attempted to study trajectory of thrombi inside the aortic arch bed and

how these trajectories change depending on the implant geometry and thrombi diameter. In our work, we utilized CFD to

investigate the trajectories of representative 2mm, 4mm, and 5mm diameter randomly released particles at the LVAD

cannula inlet plane over a series of 5 trials for each particle diameter. We then computed the percentage of released

particles of a given diameter reaching the critical arteries as well as the pooled statistics.

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We first comment on results from initial studies, reported in part in [35], in which we investigated fifteen geometric

configurations for a simple model that did not include vertebrals or coronaries with a release of a moderate number of

particles (30 per trial). The results obtained in these studies indicate that there is indeed a significant relation between the

LVAD implant geometry configuration and the number of thrombi flowing through the right and left carotid arteries with as

much a 50% (pooled statistic) variation found between configurations. Although the incidence of thromboembolism to the

carotids was never completely eliminated under any one of the considered configurations, the preliminary study

corroborated the hypothesis that there is an optimal LVAD implant configuration that can help reduce the number of

thrombi flowing into the carotid arteries.

Varying the LVAD outflow conduit angle significantly affects the flow field within the aortic arch. Lower values of LVAD

cannula incidence angle β tend to create flows where the cannula outflow jet impinges on the contra-lateral wall of the

ascending aorta, thus creating re-circulation zones and stagnation point zones with low wall shear stresses that have

been associated with platelet activation [9]-[11] and are possible thrombogenic sites.

Figure 9 shows velocity vectors of the Standard LVAD Configuration for values of β of 0o, 30o, and 60o for a sagittal

plane as well as 3D streamlines produced by these flows. Increasing the value of β obviously reduced the impingement on

the contra-lateral wall of the ascending aorta, as well as the observed re-circulation where thrombi have a tendency to get

captured by the large recirculation zones, increasing their potential to be captured by the inflow to the IA. It is also

interesting to note the nature of the complex 3D flow field generated by the confluence of the jet emanating from the LVAD

cannula and the flow ejected by the left ventricle, the complex nature of the impingement flow at the contra-lateral wall of

the ascending aorta, as well as the rotational flow observed in the descending aorta. A large recirculation zone is

observed on the ventral aortic arch and this feature also has the tendency to trap particles that may subsequently be

ingested by the left carotid or innominate arteries. However, although increasing the angle β helped to reduce the

impingement on the ascending aorta, as well as the re-circulation, this had the negative effect of increasing thrombi flow,

particularly to the LCA as the flow is now directed more towards the take-off of the LCA. As the value of β increased, so

did the number of thrombi flowing into the LCA, as the thrombus were directed preferentially towards the take-off of that

vessel, however, that slight increase was accompanied by a decrease of thrombi reaching the RCA and, consequently, an

overall reduction in the incidence of thrombi reaching critical vessels. It is also worth noting that the level of the

impingement flow at the ascending aorta is reduced with an accompanying reduction in the recirculation close to the IA

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(a) incidence angle β =0o (2D sagittal cutaway with velocity vectors and 3D views of streamlines).

(b)

(b) incidence angle β =30o(2D sagittal cutaway with velocity vectors and 3D views of streamlines).

(c) incidence angle β=60o(2D sagittal cutaway with velocity vectors and 3D views of streamlines).

Figure 9: Close up of the LVAD cannula anastomosis and velocity vectors of the cannula jet for standard LVAD configuration at various incidence angles of: (a) β =0o, (b) β =30o and (c) β =60o.

17 | P a g e

take-off and that the recirculation at the proximal aortic arch is also reduced. At a large angle of β, the features of re-

circulating flow patterns and impingement flow are essentially eliminated.

The possibility of adding an alternative aortic bypass was considered as a way to capitalize on the benefits of higher

values of β, while still reducing the number of thrombi flowing through the RCA and LCA. Models with the IA and LCA

bypasses suggested that it was possible to reduce the number of thrombi flowing into these arteries by routing some of

the blood flow from the aortic root into the IA and LCA, respectively. The advantage of the alternative aortic bypass is that

due to its location, i.e., it mainly feeds from blood being ejected from the heart. This blood has a lower chance of

containing thrombi in comparison to the blood being pumped by the LVAD. However, the addition of the IA Bypass, or the

LCA Bypass did not necessarily reduce overall the number of thrombi flowing through the RCA and LCA. The reason is

that the behavior of thrombi changes greatly as the thrombi diameter changes: smaller thrombi have Stokes numbers

based on the aorta diameter that is less than one and tend to follow the flow, while larger diameter particles have Stokes

numbers that are larger than one and their trajectory can deviate from that of the mean flow as the mean flow changes

direction. Therefore a particular configuration might be an optimum configuration that minimizes 2mm thrombi flow to the

carotid and vertebral arteries, while allowing a large number of 5mm thrombi to flow through these same arteries.

Guided by the results of our previous studies, we focused on a reduced set of configurations that yielded promising

result. These were analyzed for the complete aortic bed model that included both vertebral and coronary arteries. We

used the k-ω SST turbulence model which integrates down to the wall with a high quality mesh consisting of

approximately 2 million tetrahedral elements to ensure proper capture of the boundary layer, see Figure 10 for examples

of the mesh we employed for calculations. We imposed a turbulence intensity of 5% at the cannula inlet plane and the

ascending aorta inlet to model the effect of the wake from the VAD impellers and the turbulence generated by the aortic

valve leaflets. We ensured a y+ value for the first grid point to be less than 5, placing it well within the laminar sublayer in

accordance to the turbulence model requirements. We carried out grid convergence studies to ensure grid independence

of the solution. We compared results for outlet mean pressure and mean velocity using 1.5 million, 2 million, and 4 million

tetrahedral cells for the standard configuration at 00β = . For the velocity, the error was normalized by calculating the

difference between the average velocity magnitudes divided by the difference between the maximum and minimum

velocities of the 4 million cell baseline. Compared to the 4 million cell density grid, results from the 2 million cells were

deemed converged as pressures and velocities were nearly unchanged, while a small deviation was observed for the 1.5

18 | P a g e

million cell grid, see Figure 11 and Figure 12. Similar trends were seen in other configurations. As such, we report the

results from a grid density of nearly 2 million cells in all cases.

(a) close-up of aortic arch mesh with bypass to LCA.

(a) junction of IA, RCA and RVA. (c) cut-away of ascending aorta and cornaries.

Figure 10: Views of the mesh utilized in reported computations: approximately 2 million cells.

Figure 11: Mean pressure measured at outlets as mesh density varies.

19 | P a g e

Figure 12: Mean velocity measured at outlets as mesh density varies.

We randomly released nearly 300 particles at the inlet plane of the LVAD cannula and for each particle diameter, see

Figure 13. This was repeated five times for each particle diameter. The mean and standard deviation of the percentage of

released particles released reaching the LCA, RCA and VA were computed for each diameter using a 95% confidence

level. Moreover, an overall (pooled) static of the mean and standard deviation was also computed so as to better

characterize an overall assessment of a given configuration. If a particular thrombus diameter has a high embolization

probability, this will be reflected in a high overall probability, while a low overall probability will reflect consistently low

embolization probabilities across all thrombus diameters. A time lapse of the particle paths of a subset of 50 particles

taken from the nearly 300 released at the inlet cannula is provided in Figure 14 for 2mm and a subset of 15 particles in

Figure 15 for 5mm diameter particles, while particle paths colored by residence time are provided in Figure 16. The

computed statistics for the predicted rates of embolization of the particles for a given diameter as well as pooled statistics

are provided in Table 2 for several configurations we investigated in this paper.

Figure 13: Cannula inlet plane: location of particle release.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

1350000 1850000 2350000 2850000 3350000 3850000

Vel

ocit

y M

agni

tude

(m

/s)

Number of Cells

Velocity Convergence

ao

cor_one

cor_two

da

lca

lsa

lvad

rca

rsa

va

LVAD

cannula

release

particles

20 | P a g e

Figure 14: A time lapse of the particle paths of a subset of 50 particles from the nearly 300 released at the inlet cannula for 2mm diameter particles.

21 | P a g e

Figure 15: A time lapse of the particle paths of a subset of 15 particles from the nearly 300 released at the inlet cannula for 5mm diameter particles.

22 | P a g e

Figure 16: Particle paths colored by time of residence for a subset of 15 particles from the nearly 300 released at the inlet cannula for 2mm, 4mm, and 5mm diameter particles.

Table 2: Resulting statistics of k-ω SST model for AO bed with vetebrals and coronary arteries with

statistics computed at a 95% level of confidence. Configuration [5% inlet turbulence at LVAD cannula and AO]

2mm Thrombi [% reaching LCA, RCA & VA]



Overall [% reaching LCA, RCA & VA]

Standard β=00, θ=00, no bypass 18.14±3.69 21.24±2.66 25.05±3.18 21.48±3.2

Standard β =200, θ=00, no bypass 24.4±1.1 14.24±0.79 13.3±1.08 17.31±1

Standard β =300, θ=00, no bypass 22.12±1.27 15.37±2.85 14.92±4.71 17.47±3.26

IA Bypass β =300, θ=00 23.8±3.32 16.83±1.87 16.6±0.77 19.07±2.24

LCA Bypass β =300, θ=00 23.25±5.97 12.76±2.88 12.87±1.03 16.28±3.87

LCA Bypass β =300, θ=450 17.86±3.48 15.58±1.75 17.4±4.24 16.94±3.32

Standard β =600, θ=00, no bypass 12.91±1.95 10.45±1.43 9.63±1.13 11±1.54

23 | P a g e

The CFD simulations provide insight into the overall and particular rates of thromboembolization. In what we refer to

as the standard configuration with an angle of β=0, a major feature of the flow is a large recirculation zone and a

stagnation flow region as the jet emanates from the LVAD cannula. Thrombi of all diameters are trapped in that zone and

are susceptible to ingestion at the IA take-off. This is clearly seen in Figure 16 where the predominant path taken by all

thrombi is that leading to the IA and subsequently to the RCA and RVA leading to the highest embolization rates across

diameters and in terms of pooled statistics of all the configurations under consideration. Clearly, this is not a desirable

manner to implant the LVAD cannula. As the angle of implantation is increased to 200 and 300, the rate of embolization to

the RCA and RVA are reduced as the recirculation and impingement features of the flow field are reduced with a slight

accompanying increase in embolization to the LCA and LVA due to the redirection of the cannula jet towards the take-off

of the LCA and LSA. Overall, the rate of embolization is reduced by 20% over the standard configuration. Although

embolization rates of 2mm thrombi increased by 16%, the rates for 4mm and 5mm particles decreased by 29% and 40%

respectively. The increase of embolization of 2mm thrombi is due to the reflection of thrombi from the ventral wall of the

ascending aorta preferentially directed towards the intake of the IA as the angle is reduced. These thrombi have a low

Stokes number much smaller than one and thus generally follow the streamlines of the flow. Larger thrombi with Stokes

numbers close to and exceeding one have enough momentum not to be entrained by the mean flow to follow streamlines.

As such, their paths lead them away from the IA as can be clearly seen in Figure 14 - Figure 16, where the reduction of

thrombi reaching the IA, RCA and RVA is evident. With β=30o, with proximal ligation of the IA and with the addition of an

8mm diameter aortic-to-innominate artery bypass graft, with a proximal anastomosis located 10mm below the LVAD

conduit anastomosis, the overall incidence of thromboembolization was not reduced significantly. This is due to the fact

that the recirculation feature, although somewhat reduced, was still present at β=30o and thrombi caught in the

recirculation zone were still prone to be ingested by the inflow to the bypass ultimately reaching the RCA and RVA. An

alternative by-pass to the LCA with ligation of the LCA at the aortic arch did reduce the overall rate of embolization further

down to nearly 25% with slight reduction for 2mm diameter thrombi (<1% reduction) but more significant reduction for

4mm (~38% reduction) and 5mm thrombi (~52% reduction). Locating the LVAD conduit anastomosis to an angle of θ=45o

along the coronal plane with β=30o and with an LCA bypass did not significantly alter the overall thromboembolization rate

reduction obtained by an LCA bypass with β=30o configuration, however, the rates of thromboembolization across all

diameters were more uniformly reduced with an overall reduction of ~20% over the standard configuration.

24 | P a g e

Further increase of the angle of incidence of the cannula anastomosis to β=60o reduced the predicted overall rate of

thromboembolization by 50% with across-the-board reduction in rates of embolization for 2mm diameter thrombi (~28%

reduction), for 4mm (~50% reduction) and 5mm thrombi (~62% reduction). In this configuration, the jet from the cannula is

generally oriented to impinge just past the take-off of the LCA from the dorsal wall of the aorta. Smaller diameter thrombi

with small Stokes numbers are entrained away from the IA and are less subject to ingestion and consequently reaching

the RCA and RVA, while more susceptible to ingestion by the RCA. Overall, this leads to a slight decrease in embolization

of 2mm diameter thrombi. However, larger diameter thrombi with Stokes numbers greater than one adopt a trajectory that

leads them to impinge the dorsal aortic arch at locations between the LCA and RSA take-offs thereby reducing the

incidence of ingestion of these thrombi and leading to a significant overall reduction in predicted thromboembolisms to the

LCA and RVA.

Comparative rates of predicted thromboembolization between the carotids and vertebral arteries provided in Figure 17

reveal that the predicted rates of embolization to the vertebral arteries remain fairly constant over all the configurations

under consideration at a rate of close to 5%. The embolization rates to the carotids are higher ranging from nearly 18% in

the nominal configuration to a low of nearly 7% in the best configuration. Of the two, the predicted embolization to the

carotids is the most affected by the geometric configuration of the LVAD conduit implantation. It can be reasoned that the

embolization to the vertebrals is less sensitive to changes in LVAD implantation configuration is due to their more distal

location relative to the inlet of the IA and LSA, allowing the flow to become more organized, rendering them less prone to

be affected by variations caused in the main flow by cannula orientation. The vertebrals are also smaller diameter vessels

that are oriented nearly normal to the IA or LSA. The carotids on the other hand are fed by flow which directly is affected

by variations of the cannula orientation in the case of the LCA which takes off the lateral wall of the aorta and the RCA

which is affected by the secondary flows present at the take off of the IA and is oriented as a shallow angle presenting a

large acceptance angle to the incoming flow.

25 | P a g e

Figure 17: Comparative rates of embolization to the carotids and vertebral arteries.

Since the levels of free-stream turbulence at the inlet of the LVAD cannula and outlet to the aortic valve are not well

characterized, we also ran some cases using a purely laminar flow model to consider the effect of free-stream turbulence

and the turbulence model on the predicted particle paths, These simulations are reported below in Table 3. It is of interest

to note that the predicted rates of embolization are consistent in trend with those obtained with 5% inlet turbulence and

that the magnitudes of the predicted rates, although slightly different, are also consistent with the turbulence model

predictions.

Table 3: Resulting statistics of laminar flow model for AO bed with vetebrals and coronary arteries arteries with statistics computed at a 95% level of confidence.

Configuration [laminar inlets at LVAD cannula and AO]




Overall [% reaching LCA, RCA & VA]

Standard β =00, θ=00, no bypass 23.45±2.31 21.14±1.79 24.16±3.16 22.91±2.49 Standard β =300, θ=00, no bypass 22.08±0.86 16.04±6.39 17.62±3.99 18.58±4.38 Standard β =600, θ=00, no bypass 13.3±0.71 11.75±1.93 10.8±1.55 11.95±1.48

26 | P a g e

CONCLUSIONS

In summary, CFD models of a representative human aortic arch with a LVAD implant were used to establish that the

geometric configuration of the LVAD conduit implantation affects possible thromboembolic events leading to stroke.

Furthermore, our study establishes that the concept of an optimal LVAD implant configuration that reduces the number of

thrombi flowing through the RCA and LCA is a viable engineering solution to the present problem posed by thrombus

formation in VAD-outfitted patients. By adjusting the angle at which the LVAD outflow cannula is sutured, and the

presence, or lack of an alternative aortic bypass, it was possible to quantify the probability of embolization for 2mm, 4mm,

and 5mm diameter thrombi. In addition, an overall thromboembolization probability was calculated from the individual

probabilities, and used to assess each LVAD implant configuration. Individual results showed that the behavior of 2mm

thrombus differs from the behavior of 4mm, or 5mm thrombi due to the range of Stokes numbers spanned by these

particles over the various flow configurations. For example, configurations that reduce the number of 2mm thrombi flowing

through the carotid arteries might not necessarily reduce the number of 4mm, or 5mm thrombi that flow through the RCA

and LCA. Our simulations on a representative aortic arch geometry reveals that it is possible to reduce the overall rate of

embolization of thrombi by nearly 50% with as much as a 60% reduction of incidence for larger thrombi.

Within the limitations of our model we have established that the LVAD implantation geometry is an important factor

and should be taken into consideration when implanting an LVAD. It is possible that other parameters such as distance of

the LVAD outflow cannula to the root of the IA, could affect the thrombi embolization probabilities. However, the results of

this study suggest that the risk of stoke may be significantly reduced by as much as 50% by tailoring the VAD implantation

by a simple surgical maneuver. We will soon report on ongoing follow-up studies utilizing patient specific aortic arch

anatomies extracted from CT scans, although preliminary results corroborating the findings reported in this paper can be

found in [36]. The results of this line of research may ultimately lead to techniques that can be used to estimate the

optimal LVAD configuration in a patient specific manner by pre-operative imaging.

27 | P a g e

NOMENCLATURE

Ap particle’s projected area

Cd drag Coefficient

Dp particle’s diameter

p pressure

�

V velocity vector

�

V s particle slip velocity vector

Rep particle’s Reynolds number

α LVAD outflow conduit suture angle

ρ blood density

ρp particle’s density

µ blood viscosity

∇ gradient

∇ ⋅ divergence

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