Modeling Arterial Wall TransportFor Drug-Eluting Stents

Franz Bozsak

Abdul I. BarakatJean-Marc Chomaz

Laboratoire dHydrodynamique (LadHyX)Ecole Polytechnique, France

"Mechanics and Living Systems Initiative" LadHyX-LMS

COMSOL Conference Stuttgart 2011October 26, 2011

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Why Drug-Eluting Stents?

Initial problem: re-occlusion of Bare-metal stents quickly afterimplantationTodays common solution: Drug-eluting stents (DES) for treatingcoronary atherosclerosis

Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 2 / 17

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Atherosclerosis and Drug-Eluting Stents

Many different DES designshave been proposed.Clinical trials and animalstudies of different stents showdiverse responses of the targetvessel.The underlying causes are notwell understood.

Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 3 / 17

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Modeling the Arterial Wall and Drug Transport

Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 4 / 17

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Modeling the Arterial Wall and Drug TransportModel of the Arterial Wall

Multi-LayerSES and mediadescribed as porouslayersET and IEL expressedas Kedem-Katchalskymembranes (Prosi et al.(2005))Commonly used formacromoleculartransport simulations

Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 4 / 17

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Baseline Model of the Stented Artery

Layers: multi-layer model +Reaction: reversible binding model +Drug: paclitaxel

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Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Baseline Model of the Stented Artery

Implemented in COMSOL Multiphysics 4.2

Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 5 / 17

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Baseline Model of the Stented Artery: Intima

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Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Solute Dynamics Model: Reaction Model

Reaction Model of Specific Binding and Differential Equation Representation

L + Skfkr

B dbdt

= Da2(c (1 b)

forward

bMc0Bp

b reverse

)

b : Concentration of Bound Drug c : Concentration of Free Drug

Da2: 2nd Damkhler number = reactiondiffusion Bp : Binding Potential:hydrophilic drugs: small Bphydrophobic drugs: large Bp

Drug Properties: Paclitaxel vs. Sirolimus

Drug Pe Da1 = reactionconvection Da2 Bp =bmKd

Kd =krkf

[molm3

]bM

[molm3

]Paclitaxel 13.0 0.5 6.8 41 3.1 103 0.127Sirolimus 3.7 33.8 125.0 139 2.6 103 0.366

(Tzafriri et al. (2009))Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 7 / 17

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Solute Dynamics Model: Reaction Model

Reaction Model of Specific Binding and Differential Equation Representation

L + Skfkr

B dbdt

= Da2(c (1 b)

forward

bMc0 Bp

b

reverse

)

b : Concentration of Bound Drug c : Concentration of Free Drug

Da2: 2nd Damkhler number = reactiondiffusion Bp : Binding Potential:hydrophilic drugs: small Bphydrophobic drugs: large Bp

Drug Properties: Paclitaxel vs. Sirolimus

Drug Pe Da1 = reactionconvection Da2 Bp =bmKd

Kd =krkf

[molm3

]bM

[molm3

]Paclitaxel 13.0 0.5 6.8 41 3.1 103 0.127Sirolimus 3.7 33.8 125.0 139 2.6 103 0.366

(Tzafriri et al. (2009))Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 7 / 17

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Solute Dynamics Model: Reaction Model

Reaction Model of Specific Binding and Differential Equation Representation

L + Skfkr

B dbdt

= Da2(c (1 b)

forward

bMc0 Bp

b

reverse

)

b : Concentration of Bound Drug c : Concentration of Free Drug

Da2: 2nd Damkhler number = reactiondiffusion Bp : Binding Potential:hydrophilic drugs: small Bphydrophobic drugs: large Bp

Drug Properties: Paclitaxel vs. Sirolimus

Drug Pe Da1 = reactionconvection Da2 Bp =bmKd

Kd =krkf

[molm3

]bM

[molm3

]Paclitaxel 13.0 0.5 6.8 41 3.1 103 0.127Sirolimus 3.7 33.8 125.0 139 2.6 103 0.366

(Tzafriri et al. (2009))Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 7 / 17

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Study Objectives

Assess the advantages of a multi-layer modelInvestigate the transport dynamics of the two commonly appliedhydrophobic drugs paclitaxel and sirolimus.

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Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Arterial Wall Dynamics: Drug Transport

Total Drug Concentration

0

2 103

4 103

6 103

8 103

0.0010.01 0.1 1N

orm

.m

ean

concentr

ation

(c c0

)50 100 150

Time (h)

media

SES

Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 9 / 17

VMP_2S_c.aviMedia File (video/avi)

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Effect of Flow Reynolds Number

0

2 103

4 103

6 103

8 103

100 300 500 700 900

Max.

norm

.m

ean

Flow Reynolds number

concentr

ation( c /

c0

)

mediaSES

Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 10 / 17

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Effect of the Choice of Drug

Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 11 / 17

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Arterial Wall Dynamics: Fast- vs. Slow-Release

Fast-release

0

2 103

4 103

6 103

8 103

0.010.1 1

Norm

.m

ean

wall

concentr

ation( c /

c0

)

50 100 150Time (h)

paclitaxel

sirolimus

Slow-release

0

0.5 103

1.5 103

2.5 103

1 103

2 103

0 10 20 30 40 50 60

Norm

.m

ean

wall

Time (d)

concentr

ation( c /

c0

) paclitaxelsirolimus

Drug Pe 1st Da 2nd Da Bp =bmKd

Kd =krkf

[molm3

]bM

[molm3

]Paclitaxel 13.0 0.5 6.8 41 3.1 103 0.127Sirolimus 3.7 33.8 125.0 139 2.6 103 0.366

Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 12 / 17

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Arterial Wall Dynamics: Fast- vs. Slow-Release

Fast-release

0

2 103

4 103

6 103

8 103

0.010.1 1

Norm

.m

ean

wall

concentr

ation( c /

c0

)

50 100 150Time (h)

paclitaxel

sirolimus

Slow-release

0

0.5 103

1.5 103

2.5 103

1 103

2 103

0 10 20 30 40 50 60

Norm

.m

ean

wall

Time (d)

concentr

ation( c /

c0

) paclitaxelsirolimus

Drug Pe 1st Da 2nd Da Bp =bmKd

Kd =krkf

[molm3

]bM

[molm3

]Paclitaxel 13.0 0.5 6.8 41 3.1 103 0.127Sirolimus 3.7 33.8 125.0 139 2.6 103 0.366

Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 12 / 17

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Arterial Wall Dynamics: Fast- vs. Slow-Release

Fast-release

0

2 103

4 103

6 103

8 103

0.010.1 1

Norm

.m

ean

wall

concentr

ation( c /

c0

)

50 100 150Time (h)

paclitaxel

sirolimus

Slow-release

0

0.5 103

1.5 103

2.5 103

1 103

2 103

0 10 20 30 40 50 60

Norm

.m

ean

wall

Time (d)

concentr

ation( c /

c0

) paclitaxelsirolimus

Drug Pe 1st Da 2nd Da Bp =bmKd

Kd =krkf

[molm3

]bM

[molm3

]Paclitaxel 13.0 0.5 6.8 41 3.1 103 0.127Sirolimus 3.7 33.8 125.0 139 2.6 103 0.366

Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 12 / 17

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Arterial Wall Dynamics: Drug BindingPaclitaxel Sirolimus

Occupied Binding Site Fraction

Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 13 / 17

VMP_2S_b.aviMedia File (video/avi)

VMS_2S_b.aviMedia File (video/avi)

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Arterial Wall Dynamics: Transport Modes

PaclitaxelMode I: Transport-dominatedMode II: Competition of transport and reaction (binding)Mode III: Reaction-dominated (unbinding)

SirolimusMode I: Reaction-dominated (binding)Mode II: Competition of transport and reaction (binding)Mode III: Reaction-dominated (unbinding)

Drug Pe Da1 Da2

Paclitaxel 13.0 0.5 6.8Sirolimus 3.7 33.8 125.0

Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 14 / 17

Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Conclusions

MULTI-LAYER MODEL INCREASES SPATIAL RESOLUTIONDifferent properties of intima and media have to be taken intoaccount.

TRANSPORT DYNAMICS DIVIDED IN THREE DISTINCT MODESModes I+II: set distribution pattern and toxicity/efficacy levels.Mode III: determine the efficiency of the stent design.

OPTIMIZATION POTENTIALAdjusting drug properties and release kinetics as part of the stentdesign with the goal of improving drug retention and distributionwithin the arterial wall.

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Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Acknowledgments

PhD Fellowship: Ecole Polytechnique

Sponsor: AXA Research Fund

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Introduction Materials and Methods Results and Discussion Conclusions Epilogue

Thank you for your Attention!

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Numerical Model: Mesh

lumen

arterial wall

polymer

boundary layer elements

300,000 elements

Bozsak (LadHyX) Modeling Arterial Wall Transport COMSOL 2011 10/26/11 1 / 1

IntroductionAtherosclerosis and DES

Materials and MethodsMathematical/Physical ModelReaction Model

Results and DiscussionObjectivesFlowReaction

ConclusionsEpilogueAppendix

conference-button: