Recent advances in computational methodology for simulation of mechanical circulatory assist devices

Advanced Review

Recent advances in computationalmethodology for simulationof mechanical circulatory assistdevicesAlison L. Marsden,1∗ Yuri Bazilevs,2 Christopher C. Long1

and Marek Behr3

Ventricular assist devices (VADs) provide mechanical circulatory support to offloadthe work of one or both ventricles during heart failure. They are used in theclinical setting as destination therapy, as bridge to transplant, or more recently asbridge to recovery to allow for myocardial remodeling. Recent developments incomputational simulation allow for detailed assessment of VAD hemodynamicsfor device design and optimization for both children and adults. Here, we provide afocused review of the recent literature on finite element methods and optimizationfor VAD simulations. As VAD designs typically fall into two categories, pulsatileand continuous flow devices, we separately address computational challenges ofboth types of designs, and the interaction with the circulatory system with threerepresentative case studies. In particular, we focus on recent advancements infinite element methodology that have increased the fidelity of VAD simulations.We outline key challenges, which extend to the incorporation of biological responsesuch as thrombosis and hemolysis, as well as shape optimization methods andchallenges in computational methodology. © 2014 Wiley Periodicals, Inc.

How to cite this article:WIREs Syst Biol Med 2014. doi: 10.1002/wsbm.1260

CURRENT DEVICES AND CLINICALAPPLICATION

Ventricular assist devices (VADs) provide full orpartial mechanical circulatory support to one or

both ventricles of the heart. They are used clinicallyin a range of adult and pediatric diseases, includingcongenital heart disease, cardiomyopathy, and post-infarction heart failure (HF). They were first developedas a bridge to transplant to prolong life of criticallyill patients awaiting organ availability. However, as

∗Correspondence to: [email protected] of Mechanical and Aerospace Engineering, Universityof California San Diego, La Jolla, CA, USA2Department of Structural Engineering, University of California SanDiego, La Jolla, CA, USA3Computational Analysis of Technical Systems, RWTH AachenUniversity, Aachen, GermanyConflict of interest: The authors have declared no conflicts ofinterest for this article.

designs have evolved to become smaller and even fullyimplantable, they can now be used as destinationtherapy, supporting one or both ventricles. Morerecently, there has also been success, most notablyin pediatric patients, with use of VADs in bridge torecovery scenarios, allowing sufficient offloading formyocardial remodeling and recovery.1

HF is a major source of morbidity and mortalityin the United States, with more than 670,000diagnoses predicted this year.2 HF is typically aprogressive disease with a median survival of only2–3 years after diagnosis.3 Patients with advanced HFhave limited treatment options. While a small numbermay qualify for cardiac transplantation, this is limitedby stringent selection criteria and lack of availabilityof donor hearts. Improvements in technology andpatient outcomes, including development of smallerleft VADs (LVADs) suitable for use in a larger numberof patients, have led to growth in the number of LVAD

© 2014 Wiley Per iodica ls, Inc.

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implants and the number of participating clinicalcenters. Estimates of the number of potential VADrecipients in the United States may be as high as250,000–300,000.4

VAD technology has progressed significantlyover the past two decades. Designs have evolved frompulsatile devices that mimicked the stroke volumeof the human heart to small implantable devicesthat deliver continuous flow. The 2001 RandomizedEvaluation of Mechanical Assistance in the Treatmentof Congestive Heart Failure (REMATCH) trialestablished the superiority of a pulsatile flow VAD tomedical treatment of patients with advanced HF whowere ineligible for cardiac transplantation.5 Because ofthe favorable outcomes demonstrated in REMATCH,the Food and Drug Administration (FDA) approvedthe use of the HeartMate XVE (Thoratec Corporation,Pleasanton, CA) for destination therapy in 2003.

Since that time, numerous alternative VADdesigns have come on the market, and the use ofVADs has expanded to include less critically illpatients, with improved selection leading to betteroutcomes.6 Notably, Thoratec’s HeartMate II device,FDA approved for destination therapy in 2010, isnow among the most predominant continuous flowdevices on the market. It is implanted just belowthe diaphragm and connected to the aorta, leavingthe circulatory system otherwise intact. This device issmaller, quieter, and more portable than most otherdevices, making it easier for patients to remain active.The HeartMate II LVAS Pivotal Study7 began in 2005and evaluated the HeartMate II for two indicationsover an 18-month period: bridge to transplantationand destination therapy. Results showed that patientsdesignated NYHA HF class had significantly improvedafter 6 months of LVAD support compared withthe pre-LVAD baseline, providing early evidence thatcontinuous flow LVADs have advantages in termsof durability and reliability. In addition, the firstHeartAssist5, a modern version of the DeBakey VADweighing only 92 g, was implanted at HeidelbergUniversity Hospital in July 2009. Total artificialhearts, which replace both ventricles, have also comeon the market, including Syncardia’s CardioWestdevice, which was FDA approved in 2004, andAbioMed’s AbioCor device, which was approved forhumanitarian use in 2006.

Despite these advances, there are a number ofongoing clinical complications arising from VAD use.Bleeding is the most common early postoperativecomplication following implantation or explantationof LVADs, necessitating reoperation in up to 60% ofrecipients.8 With increased bleeding comes the needfor blood transfusions, which can in turn increase the

incidence of infection, pulmonary insufficiency, rightHF, allosensitization, and viral transmission, some ofwhich can prove fatal or preclude transplantation.Because VAD devices introduce nonbiologic surfaces,predisposing the blood to clotting, there is generallya need for anticoagulation therapy, together withall of its inherent risks. Other problems includeimmunosuppression, clotting with resultant stroke,and bleeding secondary to anticoagulation. LVADpatients are also at elevated risk of developing vonWillebrand disease, in which large multimers of vonWillebrand factor are destroyed by mechanical stress,increasing the risk of bleeding.

In addition to the rising number of adultsreceiving VAD devices, use in children has alsoincreased. Approximately 1 in 100 children are bornwith some form of congenital heart disease, and ofthose receiving surgery or catheter-based intervention,approximately 85% now survive into adulthood.9

Despite the advances in surgical and managementmethods, some of these patients will develop acuteor chronic HF, requiring heart transplantation and/ormechanical support. It is estimated that approximately10% of Fontan surgery patients will go on toexperience early failure. With the number of availabledonor hearts for children fixed at a relatively constantvalue of ≈500 per year, compared to the nearly1,000,000 people living with congenital heart diseasein the United States, there is a growing need formechanical circulatory support for this population.10

Additionally, there is compelling clinical evidence thatpediatric patients can heal with the help of mechanicalcirculatory support, supporting a bridge-to-recoveryparadigm for VADs.11

Currently, the only FDA-approved VAD forinfants and children is the Berlin Heart EXCORdevice, a pneumatically driven pulsatile flow device,though adult congenital heart disease patients maybe eligible for adult continuous flow devices. Morethan 1000 pediatric patients worldwide have beensupported with a Berlin Heart as a bridge to cardiacrecovery or transplant.12 While survival to transplan-tation is relatively high (63–89%), complications arealso common in patients supported with the EXCORdevice, including thromboembolism (22%), bleedingrequiring reoperation (29%), infection (67%), andadverse neurological events (69%).13–16 Of these mor-bidities, the persistently high rate of stroke remainsa particularly troubling complication associated withVAD support in children. A 2012 study compared theBerlin Heart to extracorporeal membrane oxygena-tion (ECMO) and concluded that a pediatric VADavailable in several sizes as a bridge to heart transplan-tation (such as the Berlin Heart) was associated with


WIREs Systems Biology and Medicine Simulation of mechanical circulatory assist devices

a significantly higher rate of survival when comparedwith ECMO.17

WHY VAD SIMULATIONS?

With the increasing prevalence of VADs in clinicaluse, there is now focus on improving performanceto reduce comorbidities, reducing device size, andallowing patients a more active lifestyle. Numericalsimulations can be used to accelerate the designprocess and optimize current and future designs.In this article, we present a focused review ofselected recent advances in finite element simulationmethodologies applied to VADs. Through threespecific case studies, we illustrate the potential ofsimulations to accelerate the design process, optimizedevice designs, and improve performance. These threecase studies, while by no means an exhaustive reviewof this highly dynamic field, are representative of threekey areas of active research: pulsatile VADs (PVADs),continuous flow VADs, and the interaction of VADswith circulatory physiology. For completeness, we alsoprovide appropriate references to other major workin the field, and the reader is encouraged to refer tothese for a broader view of recent developments.

Simulations offer a promising means to cheaplyand efficiently test and optimize competing deviceprototypes, thereby reducing time to market andidentifying potential performance enhancements.Numerical analysis is an integral part of the designprocess in many industries (e.g., aerospace andautomotive). At Boeing Corporation, for example,computational fluid dynamics (CFD) coupled torigorous optimization algorithms are a crucialand cost-saving part of the design chain for allmajor aircraft.18 Despite its demonstrated success inthese large-scale applications, adoption of simulationtools has lagged behind in the medical deviceindustry, though recently gaining favor. This is inpart due to initial success with designs identifiedthrough trial and error and experimentation, aswell as challenges associated with complicatingfactors of blood biochemistry, mechanobiology,and physiological response that make simulationschallenging. While simulations have been appliedmore recently, particularly in the design of theHeartMate II and HeartAssist 5, there remains a needfor increased adoption of simulation technology andformal design optimization algorithms.

In addition, the significant numerical challengesassociated with VAD simulations can limit theapplicability of commercial CFD solvers, oftenrequiring specialized tool development. Design andsimulation of artificial blood pumps present a

number of unique challenges not encountered in moretraditional industries. The microstructural propertiesof blood affect both the choice of design objectives,such as minimizing blood damage and clotting,and also the possible need to account for non-Newtonian effects.19 Recent work aims to addressthe issue of objective functions that can be correlatedwith the accumulation of blood damage along flowpathlines, and the influence of constitutive model(Newtonian, generalized Newtonian, and viscoelastic)on the resulting optimal shapes. In this review article,we illustrate selected finite element methodologicaladvancements that overcome some of the challengesassociated with VAD simulations through selectedcase studies, and discuss broader remaining challengesand future directions in modeling biological response,including hemolysis and thrombosis, and designoptimization.

PRELIMINARIES OF FINITE ELEMENTMODELING METHODOLOGY

Numerical modeling of blood flow in VADs relies onsolving the Navier–Stokes equations of incompressibleviscous flow. These equations enforce a point-wisebalance of linear momentum and mass for the fluid,and thus allow solution of the unknown fluid velocities(vector quantity) and pressures (scalar quantity), bothas functions of space and time. Analytical solutions ofthe Navier–Stokes equations exist only in a handful ofcases, necessitating the use of CFD for general VADgeometries to predict the hemodynamic phenomenaof interest.

In CFD, the Navier–Stokes equations are solvedapproximately, generating a discrete solution for fluidvelocity and pressure at every point in space in thecomputational domain and at each time of interest.Spatial discretization of the Navier–Stokes equationsfor applications having complex three-dimensional(3D) geometries, such as VAD hemodynamics, istypically handled by means of a finite volume or afinite element method (FEM). FEMs, which are awell-established computational methodology in thefield of structural and solid mechanics, are a relativelynew technology in fluid mechanics, and constitutean area of active research.20 Among the many FEMapproaches in fluid mechanics, the so-called stabilizedand multiscale methods21–23 as well as the morerecent residual-based variational multiscale method,24

and its moving-domain extension called the ALE-VMS method,25,26 have reached the necessary level ofmaturity for general engineering CFD applications.

FEM is a function-based technology with arich theoretical basis and systematic procedures for



achieving higher order solution accuracy for complexgeometries. The weak or variational structure of FEMallows a natural imposition of nonstandard inflowand outflow boundary conditions, robust handling offlows in moving spatial domains, including mechanicalcomponents in relative motion, and straightforwardcoupling with the governing equations of structuralmechanics. These are some of the main simulationchallenges for VADs, which we briefly discuss in whatfollows.

In application to flows with moving mechanicalcomponents, the shear-slip mesh update method(SSMUM)27–29 has been very instrumental. The ideabehind the SSMUM was to restrict the mesh movingand remeshing to a thin layer of elements betweenthe objects in relative motion. The mesh update ateach time step can be accomplished by a ‘shear’deformation of the elements in this layer, followedby a ‘slip’ in node connectivities. The slip in the nodeconnectivities, to an extent, undoes the deformationof the elements and results in elements with bettershapes than those that were shear deformed. Becausethe remeshing consists of simply redefining the nodeconnectivities, both the projection errors and meshgeneration cost are minimized. The SSMUM wasimplemented for objects in fast, rotational relativemotion and applied to computation of flow past arotating propeller27 and flow around a helicopterwith its rotor in motion.28 In this review article, theSSMUM method is used in case study 2, the simulationof the continuous flow VAD.

As an alternative to SSMUM, a sliding interfacetechnique has been proposed29 for flows involvingrotating and stationary components. Because noremeshing or reconnecting at the interface takesplace in this method, the shared sliding cylindricalinterface has nonmatching meshes on each side,and the enforcement of the kinematic and tractioncompatibility conditions at the sliding interface isdone ‘weakly’ using an appropriate modificationof the governing equations of fluid mechanics atthe discrete level. The sliding interface method wasrecently employed for wind-turbine ‘full machine’simulations30,31 to handle the rotor–tower interaction,and is also suitable for continuous flow VADs.Sliding interface finite volume methods have also beendeveloped to simulate ducted propulsors for naval andturbo machinery applications.32

To model PVADs, dynamic interaction of air,blood, and a thin membrane separating the twofluids needs to be considered. Coupled fluid–structureinteraction (FSI) simulations at full scale are essentialfor realistic and accurate modeling of PVADs. Thisis because the motion and deformation of the thin

membrane depends on the flow in the device blood andair chambers, and the flow patterns, in turn, dependon the motion and deformation of the membrane. Asa result, the fluid and structural mechanics equationsneed to be solved simultaneously, with appropriatekinematic and traction coupling at their interface. Thecomputational challenges for FSI of PVADs includelarge buckling motions of a very thin membrane, theneed for periodic remeshing of the fluid mechanicsdomain (owing to the large motions of the membrane,which induce very large changes in the blood andair flow domain geometry during the cycle), andthe necessity to employ tightly coupled FSI solutionstrategies owing to the very strong added structuralmass effect present in the problem. The state-of-the-art in FSI modeling and simulation is able toaddress these challenges (see a recent book on FSI33

and references therein); however, there is currentlyno readily available off-the-shelf commercial softwarewhere these techniques are implemented and that maybe robustly deployed for this class of problems.

To model the structural mechanics of the flexiblemembrane, in recent work34 the authors employeda rotation-free Kirchhoff–Love shell formulation35,36

discretized using isogeometric analysis (IGA)37,38

based on nonuniform rational B-splines (NURBS).39

IGA-based thin shell formulations possess severalaccuracy and efficiency benefits that are discussedat length in recent work,40,41 and, as such, present agood alternative to more standard FEM approaches.

Finally, as the devices supporting bloodcirculation, VADs are connected with the rest ofthe cardiovascular system, and the two subsystemsare coupled. In modeling of VADs, the influence ofthe circulatory system on the VAD hemodynamics istaken into account by the use of the appropriate pumpinlet and outlet boundary conditions. These constitutea significant source of uncertainty in the modeling,and are an area of extensive ongoing research in thecardiovascular simulation community. At the pumpinlet a time-dependent blood flow rate is typicallyprescribed, while at the outlet one typically appliesresistance or RCR-type boundary conditions,42–44

which explicitly relate the flow rate and pressureat a given outlet face. Coupling with a lumpedparameter model of the circulatory system is also anoption that has been employed extensively in patient-specific models of pediatric cardiology and coronaryflows.45–47 In the case of PVADs, on the bloodchamber side, the roles of inlet and outlet boundariesare reversed when the pump switches from the fill tothe eject stage. When the flow reverses through theoutlet boundary, it is essential to ‘stabilize’ the fluidmechanics formulation using an outflow stabilization



technique first proposed by Bazilevs et al.,48 and foundto be minimally invasive in subsequent work.49

EXPERIMENTAL VALIDATION

Validation via in vitro experiments continues to playa crucial role in simulation methods developmentand evolution of pump designs. Experimental studiescomparing and characterizing flow in continuousflow VADs have been performed to identify keyperformance criteria and map the flow fieldsunder different operating conditions.50–52 PVADshave also been extensively evaluated using particleimage velocimetry under a range of operatingconditions, and under conditions representative ofdevice weaning and end-diastolic delay.53–55 The needfor further validation of blood pump components wasillustrated by disparities in results reported in therecent FDA challenge to assess CFD performance,with subsatisfactory agreement compared withexperimental results.56,57 Future validation efforts areneeded not only to demonstrate the reliability of CFDand FSI to accurately characterize the flow field butalso for predictions of blood damage and plateletactivation, as described below.

CASE STUDY 1: A PEDIATRIC PVAD

The results in this section are taken from the originalreference34 where we carried out a simulation of ageneric PVAD. Geometric parameters, such as width,height, and angles of the entrance and exit arms,are consistent with current designs, and are meant tobe a generic representation of current commerciallyavailable devices such as the Berlin Heart. Thecomputational domain of the VAD is shown inFigure 1.

A stroke volume of 73 mL and an ejectionfraction of 68% were chosen for this device. A beatfrequency of 80 bpm is used for a pump output of5.8 L/min. Each pump cycle may be broken up intotwo components, the fill stage and the ejection stage,lasting 0.45 and 0.3 seconds, respectively. During thepump cycle we prescribe a time-dependent flow rateat the air chamber inlet that is consistent with theabove data, which is within the typical physiologicalrange for adult-sized models. In the blood chamber,we alternate boundary conditions at the inlet andoutlet between the Neumann and Dirichlet conditionsas necessary. We do not directly compute the valvemotion in the simulation. At the outlet we impose twoconditions. During the fill stage we impose a zero-velocity (i.e., no flow) boundary condition. During

12

3

FIGURE 1 | The pulsatile ventricular assist device (PVAD)computational domain, with the blood domain in light color and the airdomain in dark color. The inlet and outlet face of the blood chamber arelabeled 1 and 2, respectively. The air-side inlet/outlet face is labeled 3.

the ejection phase, however, we impose a resistanceboundary condition

p = Crq + p0,

where q is the volumetric flow rate on the outlet face,Cr is a prescribed resistance value, p0 is the distalpressure, and p is the pressure at the outlet face. Forthis simulation we choose p0 to be 65 mmHg, whichenforces a minimum pressure of 65 mmHg duringejection. The resistance value is set to Cr = 183g/(s cm4), which gives a maximum systolic pressure of108 mmHg. The inlet face uses the same boundaryconditions, but, obviously, with opposite phase.

Both air and blood are treated as incompressible,Newtonian fluids. The blood density and dynamicviscosity are set to 1 g/cm3 and 0.04 poise, respectively.The air density and dynamic viscosity are set to1.205 × 10−3 g/cm3 and 2 × 10−4 poise, respectively.Given the VAD geometry, fluid properties, and flowrates employed, the peak Reynolds number is about10,000 in the blood chamber and 7000 in the airchamber. These values are based on the inlet/outletbranch diameters and flow speeds. It is to be notedthat the VAD blood chamber Reynolds number, whichis higher than that in the large blood vessels ofthe human cardiovascular system (e.g., the thoracicaorta), is in the turbulent range. The membrane is aflexible thin sheet commonly made of polyurethane.We use membrane material properties consistent withthose of the Penn State VAD, the LionHeart.58 TheLionHeart membrane has a thickness of 0.38 mm,density of 1.1 g/cm3, and Young’s modulus of 550MPa.58 In our simulation, we use a thinner membraneof 0.25 mm, which is reflective of the smaller device



55.00

41.25

27.50

13.75

0.000

FIGURE 2 | Flow speed (cm/second) in the deformed blood chamberconfiguration at t = 0.15 seconds.

used for the pediatric population, as was provided inprivate communication.54

The VAD simulation was carried out for twotime cycles. All the data presented are gathered fromthe second time cycle, and the time t = 0 in all figuresrefers to the beginning of the second cycle.

Figures 2, 3, and 4 show snapshots ofthe computed blood flow speed and membranedeformation. The simulation captures a very complexmembrane motion, with many folds, clearly seen inFigures 3 and 4. The deformed membrane surface isnotably smooth, with no sharp kinks on the meshedges, which is due to the underlying smoothnessof the NURBS discretization. This buckling motionis smoother than is typically attained using moretraditional methods. Because the structural kinematicsis used to drive the fluid mechanics mesh deformation,the smoother buckling motion ensures that thefluid mechanics mesh at the fluid–structure interfaceremains smooth.

During the fill stage, the inlet jet impinges onthe chamber wall and flows along the wall creatinga strong vortex. The vortex is destroyed early in theeject phase, as seen in Figure 5. This strong vortex isa chief source of the wall shear stress (WSS) and flowstagnation in the center of the device, and may play animportant role in thrombus formation. Strong rotatingflow during filling was also observed experimentally inprior work54 and will be of interest in future validationefforts.

There are a number of other recent studieson development and optimization of pediatric VADtechnology. Mechanical circulatory support basedon an impeller pump design has been proposedfor single ventricle congenital heart patients byRodefeld and coworkers in several recent studies

FIGURE 3 | Top view of the membrane deformed configuration at t= 0.15 seconds. Despite the complex deformation pattern, the wrinkleson the membrane surface are smooth.

combining high fidelity large eddy simulationmodeling with in vitro testing with compellingresults.59–61 Additional promising work in design andoptimization of pediatric VADs includes simulationand optimization of a miniature maglev device. Thiswork incorporates inverse modeling for optimization,geometry parameterization, blood damage models,and the commercial CFD package Star-CD intoa fully automated framework.62,63 Other groupshave investigated design of axial flow pumps forcirculatory support in single ventricle patients in bothsimulation and in vitro models.64 Significant in vitroand animal testing has been reported for the PennState Pediatric pulsatile device.65,66 A number ofgroups have simulated the blood damage and flowpatterns in artificial valves, which are an essentialcomponent of VAD performance.67,68 A recent reportsummarizes the family of devices developed undera recent NIH program for development of pediatriccirculatory support devices.69

CASE STUDY 2: AN ADULTCONTINUOUS FLOW VAD

Simulations of continuous flow devices present adifferent set of challenges owing to their rotatingcomponents and complex geometry. In this example,an axial LVAD similar to the current DeBakey LVADfrom MicroMed Cardiovascular of Houston, Texas isexamined for possible shape modifications in order to



(a)

(c)

(b)

(d)

FIGURE 4 | The membrane deformed configuration at time (a) t = 0 second, (b) t = 0.15 seconds, (c) t = 0.3 seconds, and (d) t = 0.525 seconds.

increase its hemocompatibility.70 Figure 6 shows partof the already discretized surface mesh of the pumpingchamber of the device, with the surface mesh elementsshaded according to the displacements allowed duringthe optimization process. The white elements are notdeformable, and surround the impeller and upstreamregions of the device. Green (light gray) surfaceelements belong to the diffuser portion of the pumpand move as a rigid body along the device axis,controlled by a single shape parameter. Blue (darkgray) surface elements are deformed to accommodatethe axial displacements of the diffuser. The OpenFlipper toolkit71 is used to deform the elements in amanner consistent with the original CAD geometry.Figure 7 shows the dependence of two objectivefunctions, one evaluating the integral of shear rate overthe flow volume (empty markers), which is related toblood damage, and the other measuring the pressurehead across the pump (solid markers), which is relatedto pump hydraulic performance. The optimal shape

parameter will depend on the relative weighting ofthese two quantities. Figure 8 shows the distributionof the scalar shear rate measure for two values of theshape parameter. A trust-region optimization schemeis used effectively in this case to find the optimalparameter values.

The above case study illustrates the role ofcustom finite element algorithms to performingdesign parameterization studies on VAD geometries.However, there have been a number of otherkey advances in the simulation of continuous flowdevices and total artificial hearts that should benoted. Bluestein and coworkers performed extensiveanalysis of the Syncardia total artificial heart,which is a pulsatile device intended for adultuse. Their study included platelet reactivity studiesand FSI modeling of both the membrane andvalves using the commercial software ADINA.72

Centrifugal and rotary pumps have been evaluatedin CFD simulations by several groups, primarily using



80.00

60.00

40.00

20.00

0.000

80.00

60.00

40.00

20.00

0.000

(a)

(b)

FIGURE 5 | Blood flow speed (cm/second) at 0.5 cm above the planeseparating the blood and air chambers. In-plane vectors shown during(a) expel stage (t = 0.14 seconds) and (b) fill stage (t = 0.665 seconds).

commercial software to characterize the flow fieldsand stress environment.73,74 A key area of researchrelated to continuous flow VADs is characterizationof hemolysis and thrombotic risk, as discussed insubsequent sections.

CASE STUDY 3: VAD CIRCULATORYSYSTEM INTERACTION

In addition to simulations of internal hemodynamicsin VAD designs, CFD also offers the capability tosimulate vascular hemodynamic conditions followingdevice implantation. Bazilevs et al.48 reported an FSIsimulation of a patient-specific model of the aorta,

FIGURE 6 | Model of a DeBakey left ventricular assist device.Selection of the handle region (green) and the modeling region (blue) inOpen Flipper in order to modify the gap width between impeller anddiffuser.

0.96

0.97

0.98

0.99

1

1.01

1.02

–0.2 –0.1 0 0.1 0.2

Y

X

FIGURE 7 | Modification of the gap width between impeller anddiffuser and resulting objective function values for shear (emptymarkers) and pressure head (solid markers). Values are normalized bythe respective value for the initial design.

A B C D FE

FIGURE 8 | Shear rate (103 second−1) for slices through theDeBakey geometry at t = 88 milliseconds. Two designs are compared:reducing the initial gap width by 0.25 din (top) and increasing the gapwidth by 0.25 din (bottom).

from the aortic valve to the descending thoracic aorta,and including the effect of the Jarvik 2000 LVADimplanted in a descending configuration modeled as anadditional, rigid branch vessel with prescribed inflow



σn = C3q + p0

σn = C2q + p0

σn = C4q + p0

σn = C1q + p0

Inflow withperiod T (s)

Inflow withperiod T (s)

FIGURE 9 | Flow in a patient-specific thoracic aorta with leftventricular assist device (LVAD). Boundary conditions for the fluidmechanics domain. Ca, a = 1, 2, 3, 4, are the resistance constants, σ n isthe normal component of the traction vector, q is the volumetric flowrate, and p0 is responsible for setting the physiological pressure level inthe blood vessels. The LVAD branch is attached on the right side of thevessel, modeling the LVAD implantation in a descending configuration.

boundary conditions (see Figure 9). The simulationwas done using NURBS-based IGA both for the bloodflow and 3D solid vessel wall. The effect of the LVADon hemodynamics is complex and demands a locally3D model of the flow in the aortic valve and aorta,which is evidenced in Figure 10. Three pump settingsare considered: (1) healthy heart and the pump isoff; (2) medium pump setting, where the pump issupplying nearly 50% of the flow; and (3) highpump setting, where the pump is supplying nearly100% of the flow. Figure 11 shows the mean WSSvectors focusing on the aortic arch. In the healthycase, the vectors follow the helical pattern, which isconsistent with the behavior of the blood velocityin this case. For the pump-assisted simulations, themagnitude of the WSS is much lower in the arch, and,furthermore, for the highest pump setting, the WSSvectors point in the direction that is opposite to the

Flow speed (cm/s)

120110100908070605040302010

FIGURE 10 | Flow in a patient-specific thoracic aorta with leftventricular assist device (LVAD). Flow streamlines at peak systole in theLVAD attachment region. LVAD is operating at the highest setting.

conventionally assumed direction. The flow was alsofound to be more or less completely stagnant in thearch for the highest pump setting. Flow stagnationin the aortic arch is the likely source of blood clotformation in this location. Moreover, exposure of thevascular wall to a relatively low WSS may increaseintercellular permeability and consequently increasethe vulnerability of these regions of the vessel toatherosclerosis.

Several other groups have also examined theinteraction between VADs and circulatory physiology.Notably, a recent study aimed to optimize LVADplacement for reduced stroke risk. By adjusting theangle of the cannula during implantation, the riskof emboli migration was quantified probabilistically,and was found to significantly reduce with an optimalchoice of angles.75 Lumped parameter modelingwas used to compare the impact of continuousversus pulsatile flow in a model of mechanicalcirculatory support and physiology. Influences ofcontrol strategies were assessed with regard tophysiological interaction. It was shown that pulsatileflow resulted in increased cardiac index and coronaryflow, and decreased ventricular stroke work and heartrate, with better systemic and coronary perfusion.76

BLOOD DAMAGE ANDTHROMBOEMBOLIC RISK

Blood damage and stroke risk are perhaps the twobiggest challenges arising in the clinical use of VADs.



(a) Pump off (b) 8000 rpm (c) 10 000 rpm

0 5

Mean WSS (dyn/cm2)

>10

FIGURE 11 | Flow in a patient-specific thoracic aorta with left ventricular assist device (LVAD). Mean wall shear stress (WSS) vectors and themagnitude of the mean WSS.

These two adverse phenomena are discussed in thefollowing subsections.

Quantifying the Risk of HemolysisHemolysis in VADs refers to the release of hemoglobinfrom the red blood cells (RBCs) into the plasma.Above a critical level, free hemoglobin is toxic forthe kidneys and can lead to multiple organ failure.Hemolysis can occur when RBCs are deformed andfragmented by shear stress77; however, the relationbetween macroscopic flow characteristics, such asshear stress, and microscopic RBC response, suchas pore formation or fragmentation, is complicatedand not yet fully understood.

Artificial flow devices in particular are capableof producing nonphysiological levels of shear stress.On the basis of the experimental data obtained in aCouette viscometer by Wurzinger et al.,78 Giersiepenet al.79 developed a correlation for steady-shearhemolysis. Previous works attempted to relate the3D flow effects to steady-shear loading through asingle scalar parameter; for example, Bludszuweitproposed a representative stress parameter derivedfrom the six components of the deviatoric stresstensor.80 Models of this kind assume an instantaneousone-to-one relationship between local stress and RBCdeformation; therefore, they can be referred to as‘stress-based’.

Several authors have pointed out the importanceof considering the loading history of the cells.81,82

When integrating the Giersiepen relation along

pathlines, because of its nonlinear dependence in time,this is not taken into account. Two approaches toovercome this deficiency are the definition of a lineardamage fraction83 and the introduction of a virtualtime step.84

Another concern in the long-term use of VADsis that RBCs are repeatedly exposed to mechanicalstraining. The aging of RBCs was incorporated intoa scalar damage accumulation model by Yeleswarapuet al.82 This model requires a damage function, whichis unknown in complex flow situations. To computethe damage of blood cells passing through the devicemore than once, Goubergrits and Affeld define a meanexposure time and mean shear stress.84 A viscoelasticmodel with two time scales of hemolysis has beenproposed recently by Arwatz and Smits.85 Severalof those stress-based models have been evaluatedregarding their blood damage prediction accuracy incomparison to experimental data in a benchmarkapproach by Gu and Smith.86

Most of the blood damage models foundin the literature rely on a stress-based approach.As an alternative to the direct conversion of thestress tensor, a strain-based method was proposed87;using analogies to droplets exposed to shearing, acomparative shear stress is derived based on thedeformation of RBCs in the flow. The deformation of asingle RBC is tracked by solving an evolution equationfor a symmetric, positive definite morphology tensor.The eigenvectors of the tensor represent the half-axes of the droplet. The evolution equation was



adopted from Maffettone and Minale88; details onits enhancement can be found in Arora et al.87

Stress-based models are known to overestimatehemolysis; in contrast, the strain-based approachproduced hemolysis values that were in goodagreement with experimental data.87,89 To furtherimprove the understanding of blood damage inmedical devices and to ease the analysis of large,transient simulation data, we have incorporatedthe strain-based hemolysis model into a virtualenvironment.90 The environment helps to visualizeand identify critical regions inside the device; RBCsare depicted as icons with a transparent hull andregions of high hemolysis are highlighted by the releaseof marker particles. The static overview of one ormore pathlines is used as a metaphor to convenientlynavigate through the transient data set.

In the context of shape optimization, it iscommon practice to define the objective function as avolume integral of quantities directly related to shearstress. As can be expected from the overpredictionseen in stress-based measures, these integrals do notreflect hemolysis adequately. Several modifications,e.g., velocity-weighted variants, of the integrand weretested but results were not satisfactory. Garon andFarinas91 replaced the pathline-based computationof hemolysis based on the Giersepen–Wurzingercorrelation with a volume-based integration, makingit more suitable for shape optimization tasks, andlater included a damage fraction model.83 Recently, avolume-based approach has also been combined withthe RBC morphology tensor computation.92 Efforts tovalidate the existing models with targeted experimentshave also been intensifying.93–96

Quantifying the Risk of ThrombosisAnother concern in LVAD design, arguably moreimportant than hemolysis in short-term applications,is the quantification of the risk of platelet activation,aggregation, and subsequent biochemical processof thrombus formation. Pathological flow patternsoccurring in VADs chronically activate platelets andtrigger thrombus formation. In high-speed rotaryVADs, platelets are exposed to shear stresses upto 8000 dyn/cm2 and extremely high shear stressrates for short durations.97,98 This exposure maybe sufficient to activate platelets and sensitizethem to increased susceptibility in response tosubsequent nonpathological shear stress exposure.99

The optimization of VAD thrombogenic performancerequires the development of flow-induced plateletactivation and biometrical thrombosis cascade modelsthat can be integrated into numerical simulations aspart of the design process.

Because of limitations of computational power,discrete (i.e., individual cell tracking) approachesto modeling thrombosis are generally restrictedto the study of fundamental platelet mechanismsat very small time and length scales (see, e.g.,Ref 100). A few groups have developed cellular-level and multiscale models incorporating individualplatelets and hemodynamics; however, many of thesehave dealt with endothelial, i.e., surface-mediated,injury response rather than shear-induced thrombosisrelevant to VADs. We briefly summarize selectedmodels from both categories, and the reader isreferred to additional detailed reviews focused onthe biochemical and multiscale models of thrombusformation.101,102

Strong et al.103 undertook one of the firstnumerical studies of platelet thrombus growth dueto advection and diffusion in combination with asurface-reaction rate. Although that model was asingle-species model based on significant simplifi-cations, it was helpful in qualitatively describingthe relative effects of advection, diffusion, andsurface reaction on platelet adhesion to polymermaterials. Additionally, methods of platelet diffusivityestimation and computation of free and coveredsurface portions were introduced and later usedby Sorensen et al.104 and others. Sorensen et al.105

proposed to model the distributions of platelets andagonists by an advection–diffusion–reaction equationsystem. Platelet adhesion to surfaces was modeledvia constant shear-independent reaction rates, butaggregate formation and influence of platelets onthe flow was not included. On the other hand,Sorensen’s model did take into account chemicalplatelet activation not only via the platelet-releasedagonist ADP but also via synthesis of thromboxaneA2 from activated platelets and platelet-phospholipid-mediated thrombin generation. Two further equationsdescribing the concentrations of prothrombin and thethrombin-inhibiting substance ATIII are related to thecoagulation cascade. In this manner, Sorensen did notmodel the complete complex cascade but only its laststeps where prothrombin is converted into thrombin.Good agreement was obtained for two-dimensionaltest cases with simple geometries. For application toa 3D test case of a tubular expansion, the agreementwith experimental data was less favorable106 andit was concluded that more complete equations tomodel the transport mechanism would be needed.

Subsequent studies attempted to model thecascade process in greater detail. Fogelson and Guy107

introduced a mathematical model with elastic linksfor describing adhesion of platelets to the injured walland binding between activated platelets. Furthermore,



many investigators used simplified models for thestudy of platelet reactions under various flowconditions, including works by Affeld et al.,108,109

David et al.,110 and Longest and Kleinstreuer.111

Anand et al.112 developed a viscoelastic thrombusmodel including both rheological properties of thethrombus and multiple biochemical reactions leadingto growth and detachment of mural thrombi. How-ever, none of these early models had yet incorporatedthe effect of the growing thrombus on the flow field.

Development of multiscale models incorpo-rating both hemodynamics and biochemistry of thethrombosis cascade has primarily focused on injury-mediated mechanisms. Of note, the group of Alber andcoworkers developed a discrete cellular Potts model inwhich individual platelets as well as other blood cellsare represented as extended objects with fluctuatingvolumes and boundaries.101,113,114 In this framework,convection and diffusion components of the PDEs forchemical concentrations within blood flow are solved.Then, ODEs representing the coagulation reactionson the surface membrane of each activated platelet are

solved together with the PDE reaction terms to simu-late biochemical reactions. These simulations describethe spatial structure of the developing thrombusboth in time and space. Fogelson and Guy have alsodeveloped coupled multiscale models coupling theimmersed boundary method with biochemistry modelsand flow simulation. At the cellular level, the immersedboundary method models individual platelet behaviorincluding platelet activation by chemical activatorsand subcellular-level platelet–platelet adhesion anddissociation. A microscopic submodel is employed,consisting of a convection–diffusion–reactionequation describing dynamics of the platelet-secretedactivator (e.g., ADP or thrombin) in the fluid. Thismodel can then be combined with more sophisticatedcoagulation submodels that separate coagulationreactions into those occurring on platelet membranesurfaces and those in the solution phase. Thesubmodel describes a finite number of binding sitesfor coagulation zymogens and enzymes on the plateletsurface, which regulates coagulation reactions.

Designmodification

23

4

1

0

0

200

400

Cone-plateCouette

Blood

ω

α

Str

ess

(Pa)

0.05 0.1

Platelet 1

Platelet 2

Platelet 3

Platelet 4

0.15Time (s)

Prototypes built andtested

Activation

Prothrombinase Complex

ProthrombinAcetylated Acetylation

Thrombin

Fibrinogen Fibrin

Agonist Aggregation

Platelet activity state (PAS) assay

Fg, vWF

τ(t)

Xa

– ––

––

–

––

Xa

Xa

XaCa

VaVa

Va

Va

FIGURE 12 | Schematic of the device thrombogenicity emulation (DTE) framework. (Bottom left) Representative platelet trajectories in the flowfield of a ventricular assist device (DeBakey VAD); (bottom right) emulation of stress-loading history of typical platelet trajectories in thehemodynamic shearing device (HSD); (top right) computer-controlled HSD where platelets are exposed to uniform shear stress; (top left) principle ofthe modified prothrombinase assay used to measure the activity state of platelets sampled from the HSD. (Reprinted with permission from Ref 117.Copyright 2012 Public Library of Science)



Of greater relevance to VADs, in which throm-bosis is primarily shear-mediated, the majority ofexisting works use a continuum approach owing to thecomplexity of VAD geometry and cost of CFD simula-tions. Continuum models treat blood as a continuoushomogeneous medium, with the flow described bya form of the Navier–Stokes equations. The solutionfor the blood flow represents the advective term ofadvection–diffusion and advection–diffusion–reactionequation systems. Early models were based onempirical correlations using power law relationshipsfor shear stress during certain exposure times tomeasure propensity for mechanical platelet activation.However, these models do not account for relevantdynamic phenomena, such as loading rate dependenceand platelet sensitization to high stress conditions,which characterize the dynamic flow conditionsin VADs.

Platelet damage due to shear stress activation isa well-known contributor to thrombotic risk. A morecomprehensive phenomenological model for cumula-tive platelet damage was developed by Bluestein andcoworkers to express platelet activation state. Opti-mal model parameter selection was performed usinga genetic algorithm to match experimental data froma hemodynamic shearing device.115 Recent modelsfrom this group have also incorporated activationand sensitization of platelets owing to dynamic stresshistory.116

The concept of device thrombogenicity emu-lation (DTE), combining in silico numerical studieswith in vitro measurements, was also introduced morerecently by Bluestein and coworkers, and is summa-rized in Figure 12.117 This framework aims to (1)overcome limitations of CFD methods that considershear stress alone without consideration of biochem-ical reactions, (2) address the lack of resolution ofplatelet-scale flow features, and (iii) account for stress-loading histories. The aim of DTE is to offer a designloop with multiple integrated steps as follows. First,one performs device optimization in computationalsimulations with FSI, and extracts from these simula-tions the relevant stress-loading histories experiencedby individual platelets, modeled by particle tracking.Second, these histories are emulated in vitro and theresulting platelet activity is measured experimentallyin a hemodynamic shearing device. The design loopis iterated to reduce device thrombogenicity, whichcan then be verified in physical design prototypes.The DTE framework was demonstrated in a proofof concept study with a rotary blood pump VADin a recent study.117 The DTE framework uniquelybridges between simulated platelet stress histories andexperimentally measured platelet activation.

DESIGN AND OPTIMIZATION

Combining the above advancements in finite ele-ment methodology with established hemolysis- orthrombosis-based cost functions, one can set the stagefor optimization of device designs that may mitigateadverse hemodynamic conditions and device throm-bogenicity. When choosing an optimization method,the primary distinction is between gradient-based andderivative-free methods. Factors contributing to thischoice include the availability of cost function gradi-ents, computational cost of the function evaluations,the level of noise and discontinuities in the function,complexity of implementation, the number of designparameters, convergence properties, efficiency, andscalability. In cardiovascular shape optimization, eachcost function evaluation requires a time-dependent,3D solution of the Navier–Stokes equations. Theseproblems are computationally expensive to evaluate,often requiring postprocessing steps.

A general optimization problem may beformulated with linear bound constraints as follows,

minimize J (x)

subject to x ∈ �, (1)

where J : Rn → R is the cost function, and x is thevector of design parameters. The parameter space isdefined by �= {x ∈ R

n|l ≤ x ≤ u}, where l ∈ Rn is a

vector of lower bounds on x and u ∈ Rn is a vector

of upper bounds on x. In a cardiovascular shapeoptimization problem, the function J(x) dependson the solution of the Navier–Stokes equations,and the cost function value is computed in apostprocessing step.

In spite of these challenges, there has beenimportant progress in applying gradient-basedoptimization methods to cardiovascular problems,mostly with 2D geometries and/or steady flow.Non-Newtonian effects in shape optimization havebeen examined by Refs 118 and 119. Optimizationof blood pump components has been carried out byAntaki and coworkers,120,121 and Quarteroni andcoworkers have applied optimization to shape designfor arterial bypasses.122–125 However, applyinggradient methods in a fully time-dependent settingusing unstructured solvers, complex geometries andconstraints, and in the presence of FSI, which arecommon in cardiovascular flow problems, remains achallenge.

Methodologies for gradient and derivative-freeoptimization have been developed and applied tocardiovascular simulations. Recent advances inderivative-free methods will easily translate to VAD



design in future work, as the function evaluations canbe treated as a black box with no restriction on costfunction definition.

Derivative-free optimization methods can offer apromising alternative to gradient-based methods. Thesurrogate management framework (SMF)126,127 is aderivative-free pattern search optimization methodthat relies on surrogates for increased efficiency.Previous work successfully applied SMF to theconstrained optimization of an airfoil trailing edgefor suppression of vortex shedding noise in laminarflow128,129 and for the suppression of broadbandnoise in turbulent flow.130 In addition, the applicationof derivative-approximating trust region methodsto steady flow fluid mechanics problems has beenexplored by Lehnhauser and Schafer.131

The main idea behind the SMF method is toincrease efficiency by using a surrogate functionto ‘stand in’ for an expensive function evaluation,while also benefiting from the convergence propertiesof pattern search methods. In contrast to geneticalgorithms, this class of pattern search methods areamong the only derivative-free methods with estab-lished convergence theory.132–134 Advantages of SMFare its nonintrusive nature, ease of implementation,efficiency, and parallel structure.

The SMF algorithm typically consists of aSEARCH step, employing a Kriging surrogatefunction for improved efficiency, together with aPOLL step to guarantee convergence to a localminimum.135,136 The exploratory SEARCH step usesthe surrogate to select points that are likely to improvethe cost function, but is not strictly required forconvergence. Convergence is guaranteed by the POLLstep, in which points neighboring the current bestpoint on the mesh are evaluated in a positive spanningset of directions to check if the current best point is amesh local optimizer. Recent work has extended theSMF method to incorporate uncertainties in designvariables and model parameters.137,138

These methods have been successfully appliedin the cardiovascular setting to optimize idealizedgeometries, including an end-to-side anastomosis, andvessel bifurcation.139 Sankaran et al. demonstrated ashift in optimal bypass graft anastomosis angles andradius when incorporating uncertainties to performrobust optimization. The SMF method has alsobeen applied in constrained shape optimization of anovel Y-graft conduit design for surgical palliation insingle ventricle congenital heart patients.140,141 Thesemethods should be leveraged for VAD optimization,accounting for uncertainties and constraints, in future

work. For example, they could be nonintrusivelycombined with the DTE framework described aboveto optimize for thrombogenicity reduction in acombined simulation and in vitro setup.

OUTLOOK AND FUTURECHALLENGES

We have reviewed recent significant advancements inboth methodology and approach to finite elementsimulation of VAD hemodynamics. We providedthree case studies illustrating advances in finiteelement methodology for modeling both pulsatileand continuous flow devices for use in adults andchildren. In addition, we outlined recent developmentsin models to quantify the risk of hemolysis andthrombosis, which are the major source of morbidityand mortality associated with VADs. The use of high-fidelity numerical simulations will enable acceleratedidentification of new designs in future work, ultimatelyleading to reduced thrombogenicity and improvedpatient outcomes. We refer the reader to several otherreview articles that provide further perspective onadvances in thrombogenicity, experimental testing,and remaining challenges in the field.102,142–144

Despite recent progress, challenges remain toincrease the relevance and utility of VAD simulationsin the device design process and in the clinic.First, complete modeling of blood biochemistryremains computationally intractable owing to highcomputational cost. Therefore, there is a need forcontinued development and validation of reducedorder models to measure the risks of thrombosisand hemolysis. Second, there is a need forintegration of the advanced simulation and formaloptimization methods outlined above to acceleratethe design process in the presence of constraintsand uncertainties. As the optimization processidentifies new designs, the need will also arise forrapid prototyping of simulation-derived designs forexperimental testing. Third, as simulation methodsmature, there is an increased need for validationof simulated risk of thrombosis and hemolysisagainst clinical data in VAD patients and animalmodels. Finally, one cannot ignore the underlyingphysiology of the patient, and VAD models shouldbe coupled to lumped parameter network modelsof circulatory physiology to elucidate the interplaybetween the device and physiological conditions.This is particularly compelling in pediatric cardiologyowing to the complex physiology and unusualanatomy in congenital heart disease patients.



ACKNOWLEDGMENTS

The authors would like to acknowledge funding from a Burroughs Wellcome Fund Career Award at the ScientificInterface (AM), NSF CAREER awards OCI-1150184 (AM) and OCI-1055091 (YB), the Leducq Foundation,and support from the German Research Foundation under programs SPP 1253 and GSC 111 (MB). Moreover,the authors acknowledge contributions from research associates and doctoral students, in particular Dr. MehdiBehbahani, Dr. Mike Nicolai, and Markus Probst (MB).

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Recent advances in computational methodology for simulation of mechanical circulatory assist devices

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