Today’s AgendaTodayToday’’s Agendas Agenda• Lunch• Sam Hund’s Computational Presentation• The Web Site• Subversion Repository

•• LunchLunch•• Sam Sam HundHund’’ss Computational PresentationComputational Presentation•• The Web SiteThe Web Site•• Subversion RepositorySubversion Repository

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A Multi-Physics Approach for Predicting Platelet-Mediated

Thrombosisfor the Evaluation and Design of Medical Devices

A MultiA Multi--Physics Approach for Physics Approach for Predicting PlateletPredicting Platelet--Mediated Mediated

ThrombosisThrombosisfor the Evaluation and Design of Medical Devicesfor the Evaluation and Design of Medical Devices

Samuel J. HundJames F. Antaki, PhD,

CMU Biomedical EngineeringJune 4th, 2010

Samuel J. HundSamuel J. HundJames F. Antaki, PhD, James F. Antaki, PhD,

CMU Biomedical EngineeringCMU Biomedical EngineeringJune 4June 4thth, 2010, 2010

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MotivationMotivationMotivation

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THROMBOSIS

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Thrombus

CoagulationCascade

Thrombin

ADP PAFvWf

TxA2

fg

FluidShearStress

Foreign Surface

Intrinsic Activation

ActivationvWf binding

Extrinsic Activation(TF)

Fibrinolysis

Repair

PDGF

Injured Vessel

HMWKFV, FXI

Hemolysis

Intricacies of ThrombosisIntricacies of ThrombosisIntricacies of Thrombosis

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Brief Review of My WorkBrief Review of My WorkBrief Review of My Work• Computational Modeling of Blood

Rheological ModelingModeling of HemolysisModeling of Thrombosis

• Computational Optimization

•• Computational Modeling of BloodComputational Modeling of BloodRheological ModelingRheological ModelingModeling of HemolysisModeling of HemolysisModeling of ThrombosisModeling of Thrombosis

•• Computational OptimizationComputational Optimization

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Modified Krieger Model of Blood Viscosity

Modified Krieger Model of Blood Modified Krieger Model of Blood ViscosityViscosity

),(

*1

φγ

φφηη

&N

plwb

−

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

10 ParametersNo discontinuities

Modified KriegerModel

Quemada’sModel

14 Parameters1 or 3 discontinuities

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* **

* **

**

* * * * * ** *

Deformation

Aggregation

1000

100

10

10.01 0.1 1 10 100 1,000

Shear Rate (s-1)

Visc

osity

(cP)

*Experimental DataWhole BloodBlood w/o FgHardened Blood w/o Fg

Viscosity FunctionN = Nagg+Ndef+N∞N=Ndef+N∞N=N∞

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Fahraeus-Lindqvist EffectFahraeusFahraeus--Lindqvist EffectLindqvist Effect

* Data from Haynes, 1960 o Model Prediction

Tube Radius (mm)

App

aren

t vis

cosi

ty (c

P)***

****

o

o

o

o

o o o

1.4

2.0

2.6

3.2

0.0 0.5 1.0 1.5 2.0 2.5San

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RBC TransportRBC TransportRBC Transport

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How do we predict the RBC concentration profile?

How do we predict the RBC How do we predict the RBC concentration profile?concentration profile?

500

1000

150000.100

0.1000.0

0.2

0.40.6

0.8

0

Platelet C

oncentration(x 1000/μl)

Hem

atocrit(V

/V)

Radial P

osition (cm)

Aarts et al, 1988

Goldsmith and Spain, 1984San

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Part 1: Transport Down a Collision Gradient

Part 1: Transport Down a Collision Part 1: Transport Down a Collision GradientGradientDirectional Transport

Velocity

Net

Tra

nspo

rt

Large Velocity Difference

Small Velocity DifferenceSan

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Low Resistance

High Resistance

Net Transport

ViscosityVelocity

Directional Transport

Part 2: Transport Down a Resistance Gradient

Part 2: Transport Down a Part 2: Transport Down a Resistance GradientResistance Gradient

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Fluid ModelFluid ModelFluid Model

( )[ ]THctpDtD uuu

∇+∇⋅∇+−∇= ),(γηρ &

BLOOD

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Steady State Prediction of RBC Concentration

Steady State Prediction Steady State Prediction of RBC Concentrationof RBC Concentration

0.5 0.4 0.3 0.2 0.1 0.0Hematocrit

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Temporal Profile DevelopmentTemporal Profile DevelopmentTemporal Profile Development

100

80

60

40

20

0.00 0.1 0.2 0.3 0.4 0.5

Hei

ght (

mic

rons

)

Normalized Hematocrit

Time0240480720

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Plasma SkimmingPlasma SkimmingPlasma Skimming

Palmer 1965

Flow Division

Profile Develops

Uniform Inlet 0.5

0.4

0.3

0.2

0.1

0.0

Hem

atocrit

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Platelet TransportPlatelet TransportPlatelet Transport

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Transport of RBCs and Pltsin Microchannels

Transport of RBCs and Transport of RBCs and PltsPltsin in MicrochannelsMicrochannels

500

1000

150000.100

0.1000.0

0.2

0.40.6

0.8

0

Platelet C

oncentration(x 1000/μl)

Hem

atocrit(V

/V)

Radial P

osition (cm)

Aarts et al, 1988

Goldsmith and Spain, 1984San

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Theory of RBC-enhanced Platelet Exclusion

Theory of RBCTheory of RBC--enhanced enhanced Platelet ExclusionPlatelet Exclusion

Directional Transport

Isotropic Diffusion

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Extended Convection-Diffusion Model

EExtended xtended CConvectiononvection--DDiffusion iffusion ModelModel

High-ConcentrationSolution

Low-ConcentrationSolution

Mem

bran

e

C1s

C1m

C2s

C2m

ms

ms

CCCC

22

11

ψψ==

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Empirical Results

Sorensen Enhanced Diffusivity Model

Enhanced Convection-Diffusion Model

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0 sec50 sec100 sec150 sec200 sec250 sec300 sec

[Plt]/[Plt]ave

Hei

ght (μm

)

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Aarts et al.1998 ECD

400

800

1200

1600

00 4 8 12 16

Radial Distance (mm)

Pla

tele

t Con

cent

ratio

n (1

000

plt/μ

l)

50,000 plt/μl120,000 plt/μl250,000 plt/μl500,000 plt/μl

[Plt]

Prediction of Margination in Tube Flow

Prediction of Margination Prediction of Margination in Tube Flowin Tube Flow

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Hemolysis (Cell Trauma)Hemolysis (Cell Trauma)Hemolysis (Cell Trauma)

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Hemolysis ModelingHemolysis ModelingHemolysis Modeling

1

212

'][

][

+=

==

βατ

τη

γη

tA

tAtA

HbpfHb

HbpfHb &

Richardson’s Model (from Theory)

Power-Law Model

0.0976+0.2670.0976+0.267ββ3.36+/3.36+/--0.090.09αα(4.07+/(4.07+/--1.39)e1.39)e--99AA’’

(6.9+/(6.9+/--1.2)e1.2)e--88AAValue +/Value +/-- 95%CI95%CIParameterParameter

RMS Values: Richardson Model: 0.791Power-Law Model: 0.7054

•• Is Is ββ+1 significantly +1 significantly different from 1?different from 1?

No pNo p--value = 0.42value = 0.42•• Is Is αα significantly different significantly different

from 2?from 2?No pNo p--value = 0.122value = 0.122

•• The overThe over--all powerall power--law law model is actually model is actually significantly better than significantly better than the Richardson model (p the Richardson model (p value 0.0065), but there value 0.0065), but there is no confidence in the is no confidence in the parameter parameter ββSan

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Prediction of Hemolysis in a Blood Shearing Device

Prediction of Hemolysis in a Blood Prediction of Hemolysis in a Blood Shearing DeviceShearing Device

Inde

x of

Hem

olys

is (%

)

Shear Stress (dyn/cm2)

Exposure Time:

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ADP Release from RBCsADP Release from RBCsADP Release from RBCs

PROPORTIONAL MODELSlope: 0.071 +/- 0.03 μM/mg%

R2:0.89

0 5 10 15 20 25

2.5

2.0

1.5

1.0

0.5

0.0

AD

P (μ

M)

pfHb (mg%)

Data from Alkhamis et al. 1988Best Fit Proportional Line dt

pfHbddtADPd ][][ α=

•Hemolysis can directly lead to platelet activation through the release of ADP•ADP is an often neglected factor in shear induce platelet activation.

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Hemolysis in a NozzleHemolysis in a NozzleHemolysis in a Nozzle

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Early PredictionsEarly PredictionsEarly Predictions

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New PredictorsNew PredictorsNew Predictors

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Device DesignDevice DesignDevice Design

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Cannula SimulationCannula SimulationCannula Simulation

Asysimmetric, Laminar FlowNewtonian Flow

Flow Rate: Q = 6 lpmSan

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Platelet Activation in Various Cannula Tips

Platelet Activation in Various Platelet Activation in Various Cannula TipsCannula Tips

215% increase215% increase40% increase40% increase375% increase375% increase

Blunt Tip QVC Blunt Tip

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Flow Deviation AngleFlow Deviation Angle

596159612641264114,45414,454Comparative Index

φ

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Stagnation AreaStagnation AreaStagnation Area

0.23940.23940.05520.05520.77820.7782

skip

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HemoGlide Bearing Strut OptimizationHemoGlideHemoGlide Bearing Strut OptimizationBearing Strut OptimizationDegrees of Freedom

Moving Bezier PointFixed Bezier Point

Maximum Thickness

Chord Length

Distance to Max Thickness

40

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Preliminary ResultsPreliminary ResultsPreliminary Results

41

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Mathematical Model of (Platelet-Mediated) Thrombosis

Mathematical Model of Mathematical Model of (Platelet(Platelet--Mediated) ThrombosisMediated) Thrombosis

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The Role of PlateletsThe Role of PlateletsThe Role of Platelets

TXB2

Anitthrombin III (ATIII)Thombin-Antithrombin (TAT) Heparin (Hep)

PPACK

+

RPkpa AP

Flow and Passive Transport

43

Plt DepositionTXA2Archodonic Acid

Prothrombin (PT)

Thrombin (Thr)

ADPADP

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Sorensen Model of Platelet Deposition

Sorensen Model Sorensen Model of Platelet Depositionof Platelet Deposition

• PlateletsActive: [AP]Resting: [RP]

• AgonistsADP [ADP]TxA2: [TxA2]Thrombin: [Thr]

• Coagulation CascadeProthrombin: [PT]Antithrombin III [AT3]

•• PlateletsPlateletsActive: [AP]Active: [AP]Resting: [RP]Resting: [RP]

•• AgonistsAgonistsADP [ADP]ADP [ADP]TxA2: [TxA2]TxA2: [TxA2]Thrombin: [Thrombin: [ThrThr]]

•• Coagulation CascadeCoagulation CascadeProthrombin: [PT]Prothrombin: [PT]Antithrombin III [AT3]Antithrombin III [AT3]

( ) iiiii SCkCu

tC

=∇∇−∇+∂∂ v

FSuuu=⋅∇−∇+

∂∂ v

t

44

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Reaction Rate ModelsReaction Rate ModelsReaction Rate Models

45

kpa ][RPkS paap =PLATELET

ACTIVATION

ADP ][RPkS paadpadp λ=GRANULERELEASE

( ) ]][3[][][][ ThrATPTRPkAPkS rtatthr Γ−+=

PT Thr

ATIII

TAT

TxA2Archodonic Acid TxB2

]2[][ TxAkAPS txtxtx −= λSURFACEMEDIATEDREACTION San

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Binary Activation ModelBinary Activation ModelBinary Activation Model

⎩⎨⎧

≥ΩΩ<Ω

=

++=Ω

110

*][][

*]2[]2[

*][][

2

pa

ThrTxAADP

k

ThrThrw

TxATxAw

ADPADPw

kpa ][RPkS paap=

Internal SignalingTxA2ADP

Thr

Activation Rate

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Deposition KineticsDeposition KineticsDeposition Kinetics

ΚrsΚr-as

kpa

Κaa

Κaa

Platelet Deposition to Surface Platelet Depositiononto Active platelets

Transport

47

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Weakness of Existing ModelWeakness of Existing ModelWeakness of Existing Model

1. Activation Kinetics2. No Shear Dependent Activation3. Active Cellular Transport4. Valid for Collagen Only5. Lacks Coagulation Cascade6. Lacks Protein Deposition7. Limited Anticoagulation/Plt8. Effect of Growing Thrombus on Flow

1.1. Activation KineticsActivation Kinetics2.2. No Shear Dependent ActivationNo Shear Dependent Activation3.3. Active Cellular TransportActive Cellular Transport4.4. Valid for Collagen OnlyValid for Collagen Only5.5. Lacks Coagulation CascadeLacks Coagulation Cascade6.6. Lacks Protein DepositionLacks Protein Deposition7.7. Limited Anticoagulation/PltLimited Anticoagulation/Plt8.8. EffectEffect of of Growing ThrombusGrowing Thrombus onon FlowFlow

48

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Advanced Activation Kinetics

Advanced Advanced Activation KineticsActivation Kinetics

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Internal SignalingInternal SignalingInternal Signaling

Moer et al., New Perspectives on Drugs, 2004San

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Synergistic Activation of PlateletsSynergistic Activation of PlateletsSynergistic Activation of Platelets

• Platelets are activated by lower levels of agonist when in combination

• Example:Take: [Thr] .025@U and [ADP]@1μMCurrent Model: Ω = .75, hence kpa = 0Experimental Data Shows Activation (Ware et al.)

•• Platelets are activated by lower levels of Platelets are activated by lower levels of agonist when in combinationagonist when in combination

•• Example:Example:Take: [Take: [ThrThr] .025@U and [ADP]@1] .025@U and [ADP]@1μμMMCurrent Model: Current Model: ΩΩ = .75, hence k= .75, hence kpapa = 0= 0Experimental Data Shows Activation (Experimental Data Shows Activation (Ware et al.Ware et al.))

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Initial Model of Plt ActivationInitial Model of Plt ActivationInitial Model of Plt Activation

A1

*1

1A

A2

*2

1A

A3

*3

1A

+Activation

Internal Signaling

Internal SignalingTxA2ADP

Thr

Activation Rate

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Expanded Model of Plt ActivationExpanded Model of Plt ActivationExpanded Model of Plt Activation

A1

*1

1A

A2

*2

1A

A3

*3

1A

+

P1(s)

P2(s)

P3(s)

Activation Signal

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Synergy Model of Plt ActivationSynergy Model of Plt ActivationSynergy Model of Plt Activation

A1

A2

*2

1S

A3

*3

1S

+P3(s)

W1

W2

W3

P1(s)

P2(s)

Activation Signal

*1

1S

S21

S31

S1

S2

S3

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Synergy Model of Plt ActivationSynergy Model of Plt ActivationSynergy Model of Plt Activation

A1

A2

*2

~1A

A3

*3

~1A

+Activation Signal

⎟⎟⎠

⎞⎜⎜⎝

⎛−= ∑

≠=

N

jijjjii AAA

,1

0** exp β

*1

~1A

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Synergistic ActivationSynergistic ActivationSynergistic Activation

Experiment

Model Results

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

=Ω⎩⎨⎧

≥ΩΩ<Ω

=

−=

∑

∑≠

=

=

ji

Niii

ojj

Njj

pa

pa

c

k

RPkdtAPd

..1

*

..1

exp

110

][][

ααα

ω

Model was fit to data for ADP, Thrombin, and Epinephrine. Data from Ware et al., J. Clin. Invest, 1987

Agg

rega

tion

Rat

e

Ω Sangri

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ExperimentsExperimentsExperiments• Aggregometry

Gives ATP release and % aggregation as a function of time

• OpticalMorphological changes versus time

• ???

•• AggregometryAggregometryGives ATP release and % aggregation as a Gives ATP release and % aggregation as a function of timefunction of time

•• OpticalOpticalMorphological changes versus timeMorphological changes versus time

•• ??????

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Shear Induced Blood TraumaShear Induced Blood TraumaShear Induced Blood Trauma

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Classic Shear Activation ModelClassic Shear Activation ModelClassic Shear Activation ModelS

hear

Exposure

Serotonin Released (Dense Granules)

PlateletsActivated

“Safe Zone”

1000452.0 == tPSF τ

Data:Hellums et al. 1987PSF:Boreda et al. 1995Jesty et al. 2003

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Damage FunctionDamage FunctionDamage Function

( )

⎪⎩

⎪⎨

⎧

≥

<=

=

+⋅−∇=

1**

1*

0

][,,,,)(

PAFPAF

PAFPAF

PAFPAF

k

S

RPPAFxtSNDtPAFD

pa

T

τ

τ v

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ExperimentsExperimentsExperiments• Validation Case

The FDA/Marina’s Nozzles• Coupling of Stress and Agonists

Linkam Cell• Stress alone (must define activation)• Stress + Agonist

Contracting Micro-channels

•• Validation CaseValidation CaseThe FDA/MarinaThe FDA/Marina’’s Nozzless Nozzles

•• Coupling of Stress and AgonistsCoupling of Stress and AgonistsLinkamLinkam CellCell•• Stress alone (must define activation)Stress alone (must define activation)•• Stress + AgonistStress + Agonist

Contracting MicroContracting Micro--channelschannels

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Surface ReactivitySurface ReactivitySurface Reactivity

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Deposition KineticsDeposition KineticsDeposition Kinetics

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ExperimentsExperimentsExperiments• Unknowns:

Maximum surface coverageRate of Resting and Active Platelet Deposition onto the SurfaceRate of Active Platelets onto Other Plateletsθ, the “instantaneous effect” or rate at which a material by itself activates plateletsMass transfer rate

•• Unknowns:Unknowns:Maximum surface coverageMaximum surface coverageRate of Resting and Active Platelet Deposition Rate of Resting and Active Platelet Deposition onto the Surfaceonto the SurfaceRate of Active Platelets onto Other PlateletsRate of Active Platelets onto Other Plateletsθθ, the , the ““instantaneous effectinstantaneous effect”” or rate at which a or rate at which a material by itself activates plateletsmaterial by itself activates plateletsMass transfer rateMass transfer rateSan

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Deposition KineticsDeposition KineticsDeposition Kinetics

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ExperimentsExperimentsExperiments• Flow Between Parallel Plates (kaa, kas, krs)

(required) Direct measurement of platelets/areaPossibly platelet morphology

• Maximum surface coverageRocking or submersion testing

• Rate of platelet activation due to the surface

•• Flow Between Parallel Plates (kFlow Between Parallel Plates (kaaaa, k, kasas, , kkrsrs))(required) Direct measurement of (required) Direct measurement of platelets/areaplatelets/areaPossibly platelet morphologyPossibly platelet morphology

•• Maximum surface coverageMaximum surface coverageRocking or submersion testingRocking or submersion testing

•• Rate of platelet activation due to the Rate of platelet activation due to the surfacesurface San

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0 1 2 3 4 5 6 7 8 9 100

200

400

600

800

1000

1200

Example Fit to Experimental Data of Wagner and Hubbell

Example Fit to Experimental Data Example Fit to Experimental Data of Wagner and Hubbellof Wagner and Hubbell

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Cellular Transport ModelsCellular Transport ModelsCellular Transport Models

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Transport ModelsTransport ModelsTransport Models• Challenge: Large Number of Parameters• Cannot be determined from Fully-

Developed, Steady-State flows

•• Challenge: Large Number of ParametersChallenge: Large Number of Parameters•• Cannot be determined from FullyCannot be determined from Fully--

Developed, SteadyDeveloped, Steady--State flowsState flows

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ExperimentsExperimentsExperiments• Channel Flow

Vary flow rate to help isolate lift forcesVary plasma viscosity to isolate drag forcesGet RBC concentration in a 3-Dimensional fieldGet RBC velocity and plasma velocity

•• Channel FlowChannel FlowVary flow rate to help isolate lift forcesVary flow rate to help isolate lift forcesVary plasma viscosity to isolate drag forcesVary plasma viscosity to isolate drag forcesGet RBC concentration in a 3Get RBC concentration in a 3--Dimensional Dimensional fieldfieldGet RBC velocity and plasma velocityGet RBC velocity and plasma velocity

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ExperimentsExperimentsExperiments• Complex Channel Flow•• Complex Channel FlowComplex Channel Flow

Concentrated RBC suspension

Plasma with additives

Track the concentration of RBC,while varying the plasma density

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Cell Scale ModelsCell Scale ModelsCell Scale Models

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ExperimentsExperimentsExperiments• Still taking suggestions

Cell settling and wall interactionsCell-Cell interactions (dilute interactions)Cell-Cell interactions (dense suspensions)Effect of changing internal pressure

•• Still taking suggestionsStill taking suggestionsCell settling and wall interactionsCell settling and wall interactionsCellCell--Cell interactions (dilute interactions)Cell interactions (dilute interactions)CellCell--Cell interactions (dense suspensions)Cell interactions (dense suspensions)Effect of changing internal pressureEffect of changing internal pressure

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HemoGlide Bearing TestHemoGlideHemoGlide Bearing TestBearing Test

CENTRIFUGAL PUMPROTOMETER

Pressure Taps

30oFLOW CHAMBER

PRESSURE TAPS

DIRECTION OF FLOWLC SENSOR

TEST SECTION

75mm

100mmFLOW STRAIGHTENER

ROI

Y

X

(b)

Z

X

(a)

DIRECTION OF FLOWLC SENSOR

TEST SECTION

75mm

100mmFLOW STRAIGHTENER

ROI

Y

X

(b)

Z

X

(a)

Test Section

74

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Web SiteWeb SiteWeb Site

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SVN with TortoisSVNSVN with SVN with TortoisSVNTortoisSVN

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