testing of models of flowinduced hemolysis in blood...

Testing of Models of Flow-Induced Hemolysis in BloodFlow Through Hypodermic Needles

Yangsheng Chen, Timothy L. Kent, and M. Keith Sharp

Department of Mechanical Engineering, University of Louisville, Louisville, KY, USA

Abstract: Hemolysis caused by flow in hypodermicneedles interferes with a number of tests on blood samplesdrawn by venipuncture, including assays for metabolites,electrolytes, and enzymes, causes discomfort during dialysissessions, and limits transfusion flow rates. To evaluatedesign modifications to address this problem, as well ashemolysis issues in other cardiovascular devices, computa-tional fluid dynamics (CFD)-based prediction of hemolysishas potential for reducing the time and expense for testingof prototypes. In this project, three CFD-integrated blooddamage models were applied to flow-induced hemolysis in16-G needles and compared with experimental results,which demonstrated that a modified needle with cham-fered entrance increased hemolysis, while a roundedentrance decreased hemolysis, compared with a standard

needle with sharp entrance. After CFD simulation of thesteady-state velocity field, the time histories of scalar stressalong a grid of streamlines were calculated. A strain-basedcell membrane failure model and two empirical power-lawblood damage models were used to predict hemolysis oneach streamline. Total hemolysis was calculated by weight-ing the predicted hemolysis along each streamline by theflow rate along each streamline. The results showed thatonly the strain-based blood damage model correctly pre-dicted increased hemolysis in the beveled needle anddecreased hemolysis in the rounded needle, while thepower-law models predicted the opposite trends. KeyWords: Hypodermic needles—Red blood cell—Blooddamage—Computational fluid dynamics—Fluid stress.

The membranes of red cells can be ruptured byfluid stresses in flows through hypodermic needlesduring venipuncture blood draws, hemodialysis, andblood transfusions. Plasma-free hemoglobin (Hb)released from damaged red cells interferes with anumber of common clinical assays, causing a need forrepeated blood draws to get accurate assays. Suchrepeated blood draws induce extra patient discom-fort, cost additional time and resources, and perhapsdelay diagnosis. Of some concern is that rates of sig-nificant hemolysis appear to be greater in emergencydepartments (1), where timely diagnosis can be par-ticularly important.The threat of plasma-free Hb alsoimposes limits on dialysis and transfusion flow rates.While larger needle bores increase allowable flows

(2), these limits are especially evident in pediatrictransfusions, which must be accomplished throughsmall-bore needles.

In experiments conducted at the University ofLouisville (3), new needle designs with modifiedentrance geometry were evaluated for their potentialto reduce flow-induced red cell damage. Hemolysisfrom three groups of 16-G needles—one standardgroup with sharp entrance, another with beveledentrance, and a third with rounded entrance—wascompared. Plasma-free Hb was measured with aspectrophotometric method. The experimentalresults showed that the rounded entrance reducedhemolysis relative to the standard entrance, but thebeveled entrance produced more.

Directly simulating the motion and deformation ofred cells flowing in a cardiovascular device is chal-lenging because of (i) the large number of cells, (ii)their large motion and deformation, (iii) the complexstress/strain relationship of the cell membrane, and(iv) cell/cell interactions. Until these considerableproblems are solved, continuum-based models of

doi:10.1111/j.1525-1594.2012.01569.x

Received February 2012; revised July 2012.Address correspondence and reprint requests to Professor M.

Keith Sharp, Department of Mechanical Engineering, Universityof Louisville, 200 Sackett Hall, Louisville, KY 40292, USA. E-mail:[email protected]

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© 2013, Copyright the AuthorsArtificial Organs © 2013, International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.

Artificial Organs 2013, 37(3):256–266

blood damage may be useful. Most popular are themodels of Heuser and Opitz (4) for porcine bloodand Giersiepen et al. (5) for human blood (6), whichare based on a power law of the form IH = Ctatb,where IH is the index of hemolysis, and t and t rep-resent shear stress and exposure time, respectively.The models were based on experiments over a rangeof constant shear stress of 57–255 Pa and exposuretime of 7–700 ms. It was later found that the carbonseals in the Couette system caused significant red celldamage (7), leading to overprediction of hemolysis.Difficulties of application of this formulation includeits prediction of negative hemolysis rate withdecreasing stress when a total time derivative is usedto calculate hemolysis rate (8). While Yeleswarapuet al. (9) point out that the model provides conserva-tive estimates of hemolysis across wide ranges ofstress and exposure time, the degree of conservatismis extreme in some cases. For instance, Goubergritsand Affeld (10) found that following red cells arounda model of the complete human circulation (stressless than about 8 Pa, which is below the range onwhich the model is based) resulted in at least 24¥overprediction. The model has been extended toturbulent flows (11–13). Formulas for sublytic celldamage and damage accumulation have beenhypothesized for the power-law model (10,14), aswell as more generally (9,15,16).

Arora et al. (17) modeled erythrocytes as dropletsand scaled hemolysis with droplet strain. Dropletelasticity was chosen to cause this threshold strain tooccur at a shear rate of 42 000/s. Hemolysis predic-tions were calibrated to Giersiepen et al. (5) by defin-ing an effective shear stress (the steady-state shearstress that would produce a given strain) to insertinto the power-law model. Thus, its accuracy is tied tothat of the underlying empirical prediction, as well asto the linear viscoelastic response of the droplet. Thelatter causes underprediction of cell aspect ratio andoverprediction of major axis angle, both by widemargins, for shear rates below the hemolysis thresh-old, which may cause errors in calculation of strainaccumulation along path lines in more complex flows.

Other models have utilized average flow field char-acteristics rather than path line stress/strain calcula-tions to predict hemolysis (e.g., Arvand et al. [18]).When validated with experimental data for a particu-lar device, these models may be useful for studyingdesign variations in the same device, but extrapola-tion to other devices may require additional valida-tion. Garon and Farinas (16) used a Lagrangian toEulerian transformation of the Giersiepen et al.model to provide a volume-integrated hemolysisindex, which has limited utility for identifying the

specific device features that cause blood trauma.More useful for guiding device modifications mightbe the local damage index, which was an intermediateresult of this work but was not analyzed.

There is potential for reducing the empiricismand increasing the accuracy and design usefulnessof hemolysis models by utilizing a strain-basedapproach that incorporates the observed strainthreshold for red cell membrane failure. A strain-based blood damage model was developed by Chenand Sharp (19) that provides the capability to esti-mate the strain and deformation of red cells underfluid stress and is also amenable to use in the compu-tational fluid dynamics (CFD) analysis of hemolysis.This strain-based model was found to provide animproved fit of experimental hemolysis thresholdresults over a wider range of fluid stress and durationof stress compared with the power-law models and,therefore, may represent another advancementtoward the goal of a hemolysis prediction model uni-versally applicable to complex flows.

Previously, DeWachter and Verdonck (20) calcu-lated hemolysis in 13-, 14-, and 16-G peripheralhemodialysis cannulae with the Giersiepen et al. (5)model and found that the model overpredictedhemolysis by about a factor of two, but successfullyfollowed the expected trend that at equivalent flowrates greater hemolysis occurred in smaller cannulae.In this article, the Chen and Sharp (19) model iscompared with two power-law models in the flowthrough three types of 16-G needles: a standardneedle with sharp entrance and two modified needleswith beveled and rounded entrances. The predictionsof the three red blood cell damage models are alsocompared with experiments.

METHODS

The analysis process included CFD calculation ofthe flow fields and extraction of stress distributionsalong sampled streamlines (CFD simulationssection), and application of the three blood damagemodels to the time histories of fluid stress along eachstreamline to predict the amount of hemolysis foreach model (Blood damage models section). Experi-ments were also conducted to validate the differencesin bulk flow simulated by CFD (Flow measurementssection).

CFD simulationsThe geometries of three needles were created by

the three-dimensional (3D) computer-aided design(CAD) tool Solid Edge V13 (Siemens PLM Software,Inc., Plano, TX, USA). Figure 1 shows close-ups of

MODELS OF FLOW-INDUCED HEMOLYSIS 257

Artif Organs, Vol. 37, No. 3, 2013

the geometries of the upstream ends of the standard,beveled, and rounded needles. The standard needlehas an opening formed by a primary bevel thatdefines the angle of the opening with respect tothe axis of the bore and two secondary bevels onthe upstream (lower left in each image) half of theopening for further sharpening the tissue-piercingpoint. The primary bevel creates a sharp downstream(upper right in each image) edge of the opening thatcauses high fluid stresses in blood passing by it. Thebeveled needle is modified with a chamfered edgearound the downstream half of the entrance, and therounded needle is modified with a rounded down-stream edge.

All needles were 16-G stainless steel with innerdiameter Di = 1.219 mm and outer diameterDo = 1.651 mm. The primary bevel angle was 14° foreach. The full length of each needle was 45.19 mm(from the sharp point to the exit end). CAD geom-etries of the needles were imported into GAMBIT(Ansys, Inc., Canonsburg, PA, USA) to generatecomputational grids. FLUENT v6 (Ansys, Inc.) wasused to simulate the incompressible, steady-state,Newtonian, laminar, 3D flow field.

A Newtonian fluid of density r = 1050 kg/m3 andviscosity m = 0.00351 kg/m·s (3.51 cP) was simulatedto flow through the needles. A pressure drop of44.8 kPa (6.50 psig) was applied between the entranceand the exit of the needles to match the experiments.The upstream end of the needle was surroundedby a brick domain of 3 mm ¥ 9 mm ¥ 1.5 mm, inwhich blood flow was drawn into the needle throughthe entrance of the needle. On the faces of the brickdomain, pressure inlet conditions were applied.Because the geometry was symmetric about the mid-plane, only half of the needle was simulated. Figure 2shows the schematic of the initial computationaldomain for the standard needle.

Initially, a coarse grid was applied to simulate thefull length (45.2 mm) of the needle to get the averagevelocity through each type of needle.All the Reynoldsnumbers, based on inner diameter, were less than1220. Note that the velocities were slightly higher inthe modified needles (3.25 m/s in the beveled needle

and 3.34 m/s in the rounded needle) than the standardneedle (3.04 m/s), reflecting the reduction in lossesassociated with the transition of the main stream ofthe flow into the bore of the needle.

Subsequently, fine grids were used to simulate ashorter 24.9 mm length of needle with a velocityboundary condition at its exit. This length of needle,which was verified in preliminary simulations toapproach fully developed flow at its exit, enabled theapplication of higher resolution in the remaininggrid. About 790 000 nodes were used in these simu-lations. Figure 3 shows the schematic of the grid forthe standard needle. Convergent steady solutionswere designated when relative errors of pressure andvelocity components were less than 10-7.

The 3D resultant stress is characterized by the vonMises stress, tvM, which is proportional to the scalarstress ts used in previous literature (12), τ τs vM= 3 .For pure shear flow, the scalar stress is convenientlyequal to the shear stress.

Because the flow is steady, the path line of an arbi-trary particle in the flow is the same as the streamlinethrough the same position. From the CFD solution ofthe velocity field, a grid of streamtubes filling the flowcross section was defined and the time histories of ts

along streamlines central to each streamtube wereextracted.To facilitate the sampling process, the start-ing sample points were located on the circular crosssection of the needle exit and tracked upstream tothe entrance. The sample points were uniformly dis-tributed in the x and z directions across the exit flowcross section. To predict the small value of hemolysis,

FIG. 1. CAD geometries of the upstreamends of three needles.

FIG. 2. Schematic of the initial computation domain for the stan-dard needle.

Y. CHEN ET AL.258


about 48 000 (the exact number is slightly differentfor each needle type) sample points were usedinside the half cross section. To evaluate thediscretization error, another set of sample stream-tubes with about 12 000 sample points was used forcomparison.

Along each streamline, the time history of ts wasextracted for hemolysis analysis. To reduce errors inhemolysis prediction associated with numericalnoise, a smoothing algorithm was applied to the stresshistories:

ττ τ τ

s jn s j

ns jn

s jn

j m,, , , , ~+ − +=

+ +( )=1 1 1

31 (1)

where m is the end of the index of sampling pointsalong a streamline, n is iteration index, n = 0~20,and τs j

n, represents scalar stress ts at time tj. At

the boundaries, ττ τ

sn s

nsn

,, ,

11 1 22

3+ =

∗ +( ) at j = 1 and

ττ τ

s mn s m

ns mn

,, ,+ −=

+ ∗( )1 1 23

at j = m.

Because the numerical simulations only cover24.88 mm or the first (upstream) half of the needle,the time history of ts along the downstream half wastaken as the constant value for fully developed Poi-seuille flow at each sample point on the exit crosssection.

Blood damage modelsThree blood damage models were applied to the

results of the CFD simulation.A strain-based blood damage model based on

Rand’s (21) viscoelastic membrane model was devel-oped previously (19),

SS

bC C C t C t

cs e= −( ) + − − ⋅( )( ) + ⋅[ ]4

510 1 2 3

ατ τ exp

(2)

where S is the area strain of the membrane andcritical strain Sc for membrane failure is taken asSc = 0.064 (21,22). a is an empirical constant andb = 1.7 mm is the minor radius of deformed red cells.ts is the scalar stress, te = 150 Pa is the stressrequired to elongate the cell to an isoarea ellipsoid(beyond which area dilation ensues), and t is expo-sure time. C0 and C1 are related to the Young’smoduli of the membrane, C2 is related to short-termviscous response, and C3 is related to the viscositythat determines the long-time characteristic of themodel. C0, C1, and C3 were obtained from Rand’smicropipette experiments, C0 = 3.5 ¥ 10-2 cm/dyn,C1 = 3.9 ¥ 10-2 cm/dyn, and C3 = 1.5 ¥ 10-4 cm/dyn·s.a = 39.01 and C2 = 84/s were obtained from optimi-zation based on microscope images of deformed redcells (19).

For CFD analysis of hemolysis, the numericalintegral form of Eq. 2 was applied along each stream-line i:

SS

bC C C t C t

c ii j i j

j

m

si j

⎛⎝⎜

⎞⎠⎟ = + − − ⋅( )( ) + ⋅[ ]{

=∑ 4

510 1 2 3

0

α

τ

exp , ,

, −−( ) + −( )

⋅ ⋅ − ⋅( ) +[ ] −

−τα

τ τsi j si j e

i j i j i

b

C C C t C t t

, ,

, , ,exp

1

1 2 2 3

45

jj−( )}1

(3)

where j = 0~m, j = 0 is the starting time step when thered cell is near the entrance, and j = m is the endingtime step when the cell is at the exit. At any time j, if

(tsi,j - te) < 0, it is reset to (tsi,j - te) = 0.SSc i

⎛⎝⎜

⎞⎠⎟ is the

normalized strain value along streamline i. If along a

particular streamline SSc i

⎛⎝⎜

⎞⎠⎟ > 1, then the red cells

traveling along this streamline i are predicted torupture and flag F is set to indicate this condition,

F

SSi c i=

⎛⎝⎜

⎞⎠⎟ >⎧

⎨⎪

⎩⎪

1 1, ;

.

for

0, otherwise(4)

To estimate the overall percentage of hemolysis forthe total blood flow through the needle, the factor Ffor each streamline was weighted by the flow ratethrough the surrounding streamtube.The overall per-centage of hemolysis (IH) of the blood flow throughthe needle was calculated by

FIG. 3. Schematic of part of the computational grid for standardneedle.



IH CF Q

QC

F A V

A VC

F Ve

i ii

ii

e

i i ii

i ii

e

i ii=

⋅( )

( )=

⋅( ) ⋅

( ) ⋅=

⋅∑

∑

∑

∑

∑Δ

Δ

Δ

Δ VVii

∑(5)

where (DQ)i = (DA)i·Vi is the flow rate through eachstreamtube and (DA)i is the cross-sectional area ofeach streamtube. Because the sample points wereuniformly distributed on the sample plane, (DA)i isconstant except around the boundary of the needlebore. For simplicity, the irregular areas of boundarystreamtubes were taken to be the same as thenonboundary streamtubes. Release of Hb isquantified by the additional factor Ce. Ce = 1 if allintercellular Hb empties into the plasma and Ce = 0 ifnone is released. In this preliminary study, Ce in thestrain-based model was taken as an empiricalconstant for all membrane failures.

Mechanistic representations of incomplete Hb lossare reserved for future work. For instance, it has beenobserved that as membrane area stress increases, theprobability of the formation of pores increases,whereas pores smaller than about 10 nm in diameterare stable and tend to reseal (23). Larger pores areunstable and can lead to membrane rupture. If stressis reduced, the hydrophobic pores, regardless of size,tend to reseal. In addition, when cells elongate inresponse to longer duration of uniaxial stress, their

deformation may progress to a dumbbell shape thateventually pinches off in the smaller central section(Fig. 4). Figure 5 shows SEM pictures of red cellssheared between concentric cylinders (24). In theimages for the higher shear rates are such dumbbellshapes, remnants of dumbbells, and only a few cellfragments with openings in the membranes. All thesecell responses tend to reduce Hb loss and supportlower plasma-free Hb prediction, Ce < 1.

For comparison, hemolysis predictions were alsoobtained with two alternate models based on thepower-law equation

ΔHb Hb = Ctasbτ (6)

where Hb is total Hb fraction, DHb is the released Hbfraction, and C = 1.8 ¥ 10-6, a = 0.765, and b = 1.991for the Heuser and Opitz (4) model. For theGiersiepen et al. (5) model, C = 3.62 ¥ 10-5, a = 0.785,and b = 2.416.

Piecewise summation of this equation along astreamline yields

IH C t tsi jb

i j i ja

j

m

= −( )+=∑ τ , , ,1

0(7)

where tsi,j is the scalar stress at step j along streamlinei and (ti,j+1 - ti,j) is the exposure time of the stress tsi,j.

For the Heuser and Opitz (4) and Giersiepen et al.(5) models, the summation along each streamlinepredicts some level of hemolysis on every streamline.However, for the strain-based model, the numericalintegration along each streamline predicts finitehemolysis on streamlines along which the strainthreshold is exceeded and no hemolysis on the rest.Therefore, for flows in which high fluid stress is local-ized, a further discretization criterion was imposed

FIG. 4. Schematic of cell fragmentation with minimal hemoglobinrelease.

FIG. 5. Human red blood cells fixed after4 min of shear flow in concentric cylinderviscometer. Applied shear stress: (a) 10, (b)200, (c) 350, and (d) 450 Pa (from Suteraand Mehrjardi [24]). Used with permissionfrom Elsevier.

Y. CHEN ET AL.260


on the spatial resolution of the high stress region, thatis, that the number of streamlines on which lysis ispredicted is large enough to accurately resolve thehemolysis fraction. This criterion can be approxi-mated as a requirement that the number of blood-damaging streamlines exceeds the reciprocal of thedesired accuracy, for example, for 1% accuracy, atleast 100 hemolytic streamlines should be provided.

Each of the three blood damage models wasapplied to analyze flow-induced hemolysis for eachneedle type. Two C+ + programs were written toprocess the streamline data extracted from theFLUENT simulation and to implement the blooddamage models to obtain the IH.

Hemolysis predictions from all three models werecompared with experimental results (3) obtainedwith a protocol similar to that of Sharp and Moham-mad (25), which found that the needle with roundedentrance produced significantly less hemolysis thanthe standard one, while the one with chamferedentrance produced more. The simulated driving pres-sure and needle size and geometry were set to be thesame as in the experiments.

Flow measurementsExperiments were conducted to measure bulk

flows through the same needles simulated by CFD.The experimental system (25) comprised a 10-mLsyringe housed inside a pressure chamber with asolenoid actuated trigger to release the plunger,forcing blood through the needle in reverse orienta-tion, that is, with the pointed end of the needleinserted through the hub of the syringe and slightlyinto the barrel, so that fluid flowed from the entranceof the needle to its hub, mimicking the flow in veni-puncture blood draws. The shaft of the needle wassealed to the hub of the syringe with an elastic boot.The hub of the needle extended outside the pressurechamber and, thus, was exposed to atmosphericpressure. Similitude was preserved by testing witha water/glycerol (45% by weight) mixture and achamber pressure (45 kPa = 6.5 psig) that causedthe Reynolds numbers to be similar to those of thesimulations.

The flow rate was estimated by dividing the knownvolume of fluid (6 mL) in the syringe by the elapsedtime of the ejection event found by reviewing videorecorded in Mini-DV, NTSC format. This procedureignores the initial transient acceleration of the flow(25), which could not be quantified by this method.Each condition was repeated 10 times. Statisticalsignificance was tested by analysis of variance(ANOVA).

RESULTS

Measured mean ejection times for the glycerolmixture were 1.192 � 0.0570 (standard deviation),1.126 � 0.0482, and 1.052 s � 0.0480 for the standard,beveled, and rounded entrances, respectively, whichproduced estimates of cross-sectional mean flowvelocities of 4.50, 4.76, and 5.09 m/s. For these condi-tions, the Reynolds numbers were 1463, 1549, and1658, respectively, maintaining laminar flow, whichwas the case for the simulations as well (Reynoldsnumbers of 1109, 1186, and 1219). ANOVA compari-sons showed that all measured differences among theneedle types were significant (P < 0.05).

A comparison of the measured flow rates of themodified needles relative to that of the standardneedle is shown in Fig. 6. The experimental measure-ments exhibit a smaller difference between thebeveled and standard needles than the simulationsand a larger difference between the rounded andstandard needles. However, all trends are the same,including increased velocity in the beveled needlerelative to the standard needle and a further increasein velocity in the rounded needle compared with thebeveled needle.

Figures 7 and 8 show the contour plots of CFD-predicted velocity magnitude and scalar stress nearthe entrance of each of the three types of needles.Figures 9 and 10 show the contour plots of axial (y)velocity and ts of the flow on the cross-sectional planeat 7 mm (5.74 inner diameters) from the downstreamedge of the opening for the three kinds of needles.(To better visualize the scalar stress field in Figs. 8and 10, the color scales on these figures have beenreduced to approximately half of the maximum localstress. Stresses larger than half of the maximum,

FIG. 6. Normalized cross-sectional average velocity measuredexperimentally and simulated by CFD.



which only occur in a small region near the edge ofthe needle, are shown in white.)

Because the flow is steady, the path line of an arbi-trary particle in the flow is the same as the streamlinethrough the same position. From the CFD solution ofthe velocity field, a grid of streamtubes filling the flowcross section was defined and the time histories of ts

along streamlines central to each streamtube wereextracted (Fig. 11). Figure 12 shows an examplesmoothed time history of ts along such a streamline.

Table 1 shows the experimental results and theinitial predicted results for the three models of

hemolysis for each of the three types of needles. Pre-dicted hemolysis was compared for two levels ofspatial resolution to assess the discretization error.The percentage of error was calculated by (IH oflower sample number - IH of higher samplenumber)/IH of higher sample number * 100% foreach set of sample streamtubes. The differences inhemolysis between the two resolution levels were lessthan 5% for all cases.

Table 2 shows that the number of hemolyticstreamlines (for which F = 1 in Eq. 4) for the strain-based model is at least 625 for both levels of spatial

FIG. 7. Contour plots of velocity magnitude (meter per second) on the midplane.

FIG. 8. Contour plots of ts (pascal) on the midplane.

FIG. 9. Contour plots of velocity magnitude (meter per second) on cross-sectional plane 7 mm downstream of the downstream edge ofthe opening of the needle.

Y. CHEN ET AL.262


resolution for a discretization error of no worse than0.16%.

The magnitudes of hemolysis predicted by thepower-law models and by the strain-based modelwith Ce = 1 were much larger than the plasma-freeHb measured in the experiments. The Heuser andOpitz model produced the closest agreement but wasstill roughly an order of magnitude too large. Thestrain-based and Giersiepen et al. models wereroughly two and three orders of magnitude too large,respectively.

The overprediction of hemolysis by the power-lawmodels is consistent with previous investigations, asdiscussed earlier. For the strain-based model withCe = 1, the hemolysis prediction is thus far based oncomplete release of Hb from all cells whose mem-branes have been predicted to fail. Now, with experi-mental hemolysis data, it is possible to determine arealistic value of Ce. The Ce value calculated to matchpredicted hemolysis to the experimental plasma-freeHb results for the standard needle, Ce = 9.68 ¥ 10-3,implies that only about 1% of the Hb in cells strainedto membrane failure is actually released to theplasma.

Figure 13 shows the relative experimental and pre-dicted results for the higher spatial resolution ofabout 48 000 sample streamtubes. Only the strain-based model correctly predicted increased hemolysisin the beveled needle and decreased hemolysis in therounded needle. Both the Giersiepen et al. (5) andHeuser and Opitz (4) models incorrectly predicteddecreased hemolysis in the beveled needle andincreased hemolysis in the rounded needle.

The local flow features contributing to the differ-ences in hemolysis among the needles can beexplained in the following figures. Figure 14 showsthe scatter plots of the hemolysis produced in eachstreamtube IHi on a cross-sectional plane at 7 mmfrom the downstream edge of each of the three typesof needles for the strain-based model, whereIH F V Vi i i i

i= ⋅ ∑ for each streamtube i. To simplify

the calculation, streamtubes are represented assquares of the same dimension as initially specified atthe exit of the needle. The center of each square

FIG. 10. Contour plots of ts (pascal) on cross-sectional plane 7 mm downstream of the downstream edge of the opening of the needle.

FIG. 11. Example streamlines along which fluid stress historieswere extracted. FIG. 12. Time history of ts along an example streamline.



marker corresponds to the central position of thestreamtube and its color represents the value of IHi.Four high hemolysis (IH ~ 30 ¥ 10-6) groups ofapproximately 60 streamtubes each appear in theplot for the standard needle and represent theregions of the flow that contribute most to overallhemolysis. For the beveled needle, two high hemoly-sis (IH ~ 30 ¥ 10-6) groups and one large mediumhemolysis (IH ~ 27 ¥ 10-6) group appear higher in thecross section than for the standard needle, and thelow hemolysis (IH ~ 20 ¥ 10-6) regions of moderatehemolysis are slightly more numerous and shifttoward the lower wall of the tube. For the roundedneedle, only two high hemolysis (IH ~ 30 ¥ 10-6)groups appear still higher in the cross section, and theconcentration of low hemolysis (IH ~ 20 ¥ 10-6)streamtubes near the walls is reduced. These plotsconfirm that the strongest contributor to hemolysis isthe high velocity flow past the downstream edge ofthe needle opening, as suggested by the fluid stressplots in Fig. 8.

The high hemolysis regions are further comparedin Fig. 15, which shows 3D plots and time histories ofts of streamlines that pass through the upper righthigh hemolysis (IH ~ 30 ¥ 10-6) region in Fig. 14 foreach needle type. For the standard needle, the peakvalue of ts exceeded 600 Pa. For the beveled needle,the peak value was about 400 Pa, and for the roundedneedle, the peak value was about 300 Pa.

DISCUSSION

This test of hemolysis prediction models in theflows in these needles may appear to be a challengingone, given that the approximately 10% higher bulkflow rate in the rounded needle tends to increasefluid stress across the entire flow cross section. Thishigher flow rate contributed to incorrect predictionsof higher hemolysis in the rounded needle by theGiersiepen et al. and Heuser and Opitz models. Dif-ferences in the potential for hemolysis in theseneedle flows are not readily recognizable from thescalar stress fields (Figs. 8 and 10). For instance, thesmall area of very high stress at the downstream edgeof the beveled needle (Fig. 8) suggests a mechanismby which hemolysis may be larger in the beveledneedle than in the standard needle, but the compari-son of total hemolysis by the entire flow fields foreach needle is not clear. Correctly predicting hemoly-sis differences among the needles apparently dependon accumulating the influences of fluid stress andexposure time along cell paths throughout the wholeflow pattern (Eq. 5). Yet, recognizing such distinc-

TABLE 1. Comparison of hemolysis from experiments (3) and models with two different spatial resolutions

Needle

Experimental Number ofsample

streamtubes

Strain-based model Heuser and Opitz model Giersiepen et al. modelΔHbHb (%) IH (%) Error (%) IH (%) Error (%) IH (%) Error (%)

Standard needle 0.029 47 753 2.92 -4.10 0.1399 0.43 21.1 0.0311 981 2.80 0.1405 21.1

Beveled needle 0.040 47 752 3.33 0.81 0.1372 -2.19 21.5 -1.7011 979 3.36 0.1342 21.1

Rounded needle 0.019 47 747 2.73 0.99 0.1623 0.74 24.4 1.8211 980 2.75 0.1635 24.9

TABLE 2. Number of hemolytic streamlines forstrain-based model

Needle

Number ofsample

streamtubes

Number ofhemolytic

streamlines

Standard needle 47 753 255811 981 625

Beveled needle 47 752 288611 979 722

Rounded needle 47 747 252411 980 635 FIG. 13. Hemolysis predictions relative to the standard needle

(experimental results from Kommidi [3]).

Y. CHEN ET AL.264


tions are of fundamental importance, as the modifi-cations made to these needles are representative ofthe changes that might be considered in refining awide range of cardiovascular devices to reducehemolysis. Changes in the leading edge of the impel-ler in a centrifugal blood pump and smoothing ofinlet and outlet ports in a ventricular assist device areexamples of design alternatives with analogous localimpact on an otherwise similar bulk flow. Keys to theoptimization of device design are not only accuratehemolysis results but also the interpretation of theinfluence of design changes that CFD and a mecha-nistic hemolysis model can provide.

With plots of parameters IHi and ts from the strain-based model, a developer of cardiovascular devicescan evaluate the flow region that is critical to reducehemolysis. When a modified design for the geometryof a cardiovascular device is formulated, these tools

can be used to evaluate the resulting IH and explainhow the change in flow pattern may help to reducehemolysis.

CONCLUSIONS

The correct prediction of hemolysis trends amongthe different needle entrance geometries is a signifi-cant, though tentative, step toward providing ahemolysis prediction model for complex blood flows.The current strain-based model requires, in particu-lar, an empirical factor Ce that represents only about1% Hb release from the characteristic membranefailure in this flow. The magnitude of this factor indi-cates that significant aspects of the mechanics ofrelease of Hb from red cells have not yet been incor-porated into the model. Nonetheless, the results showthat the strain-based blood damage model has the

FIG. 14. The scatter plots of IHi on cross-sectional plane from the strain-based model.

FIG. 15. Time histories of ts along streamlines with high hemolysis. Left: standard needle, middle: beveled needle, right: rounded needle.



potential to be an effective tool in the applicationof CFD analysis to hemolysis. With further verifica-tion in a range of flows, the model may facilitate thedevelopment of cardiovascular devices by reducingthe need for physical testing of prototypes forhemolysis.

Another limitation of this model is that it does notapply well to exposure times less than about 0.1 ms(19). For many applications in cardiovasculardevices, which have exposure times longer than 1 ms,this is not a problem. However, for bubble andshockwave flows (e.g., cavitation and shockwavelithotripsy, respectively), the inertial effect may bedominant and a mass term may be needed toprovide better fits. Therefore, one of the futureimprovements for this model may be to add a massterm into the current Maxwell/Voigt mechanicalmodel. Another related improvement may be toinvestigate and incorporate the time dependence ofte in the model, representing the variability of thestress threshold to reach the limiting isoarea ellip-soidal shape, which may also improve the perfor-mance of the model for short exposure times. It isalso worth reiterating that in continuum modelssuch as this, it is challenging to represent influencesat the cellular level, such as cell-to-cell and cell-to-boundary interactions. The paths of cells may alsodeviate from streamlines calculated for continuumflow due to momentum and transverse lift (26–28).These factors are presently not included, nor is theimpact of neglecting them certain.

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