Welcome to the 4th

European Bifurcation Club 26-27 September 2008 - PRAGUE

Welcome to the 4th

European Bifurcation Club 26-27 September 2008 - PRAGUE

Biomechanical modelling of stent design

Prof. Gabriele DubiniProf. Gabriele Dubini

Laboratory of Biological Structure Mechanics – LaBS

Dept. of Structural EngineeringPolitecnico di Milano

Milan, Italy

Mathematical modelsMathematical models

What is a mathematical model?

A set of mathematical equations that embodies the fundamental concepts and assumptions of a theory

What does it serve to?

It serves to put hypotheses into concise, quantitative forms.Once a mathematical model has been defined, it can be used to:- Calculate the effects of changing any parameter:- Include quantitative relations- Account for a great deal of knowledge- Integrate several different levels of complexity

Computational modelling OR ‘in silico’ experiments

The Finite Element Method (FEM)The Finite Element Method (FEM)

Numerical solution (Computational Fluid Dynamics, CFD)

xxx

zx

yx

xx

x p

z v v

y v v

x v v

t v vF 2∇μ+

∂∂

−=⎭⎬⎫

⎩⎨⎧

∂∂

+∂∂

+∂∂

+⎟⎠⎞

⎜⎝⎛∂∂

ρ

. . . . .

. . . . .

⇒

analytical(continuum)

numerical(discretized)

Stent geometry

Idealized

Etave et al., J Biomechanics, 2001; 34: 1065-75

Realistic

Lally et al., J Biomechanics, 2005; 38: 1574–81

Bedoya et al., J Biomech Eng, 2006; 128: 757-65

Stent geometryStent geometry

Vessel wall geometry

Wu et al., J Biomechanics, 2007; 40: 3034-3040

Walke et al., J Mat Proc Technol, 2005; 164–165: 1263–1268

Ballyk, J Vasc Interv Radiol, 2006; 17: 1139–1145

Idealized

Vessel wall geometryVessel wall geometry

Realistic

Holzapfel and Stadler, J Biomech Eng, 2005; 127: 166-180

LaBS collaboration with ERASMUS Center, Rotterdam, NLBioMedical Engineering OnLine, 2008; 7: 23

Vessel wall geometryVessel wall geometry

Material properties

Material properties: artery, stent, plaque, drug

Holzapfel and Stadler, J Biomech Eng, 2005;127:166-180

Lally, http://www.tcd.ie/bioengineering/researchers/triona_lally%20.htm

Holzapfel et al., Am J Physiol, 2005; 289: H2048-H2058

Material propertiesMaterial properties

Material properties: artery, stent, plaque, drug

Linear elasticElasto-plasticShape memory alloyPolymeric

Absorbable materials?

Strut microstructure

Material propertiesMaterial properties

Material properties: artery, stent, plaque, drug

No difference with arterial wallDeliberately stiffer or softer

Few experimental data on atherosclerotic coronaries. Most are related to peripheral arteries (including the different components of the atherosclerotic plaque)

Holzapfel and Sommer, J Biomech Eng, 2004; 126: 657-665

Lee et al., Circulation, 2001; 103: 1051-1056

Material propertiesMaterial properties

Material properties: artery, stent, plaque, drug

Difficulties to know drug pharmacokineticsSimplified geometrical models

Hose et al., Comput Methods Biomech Biomed Engin, 2004; 7: 257-264

Pressure distribution in the arterial wall (left) and vector field in the region of a stent strut

Migliavacca et al., Comput Methods Biomech Biomed Engin, 2007; 10: 63–73

Material propertiesMaterial properties

Expansion modality, boundary conditions

Possible approaches:- no balloon and force control- no balloon and displacement control- balloon inflation

Pressure load Displacement Balloon inflation

Gervaso et al., J Biomechanics, 2008; 41: 1206-1212

Expansion modality,boundary conditionsExpansion modality,boundary conditions

Fluid dynamics

4 cardiac cycles pulse period = 0.54 s

Inlet Outlet

Velocity profile: parabolic and transient

Constant fixed pressure

Assumptions

- rigid vessel wall- Newtonian fluid (viscosity = 0.0035 kg/(m·s), density = 1060 kg/m3)

0

0.04

0.08

0.12

0.16

0.2

0 0.1 0.2 0.3 0.4 0.5 0.6

Time [s]

[m/s

]

[ La Disa et al., 2004 ]

Balossino et al., J Biomechanics, 2008; 41: 1053-1061

Fluid dynamicsFluid dynamics

1.1

0.88

0.66

0.44

0.22

0

[Pa]

WSS values alternate across the vessel during the cardiac cycle

2.0

1.6

1.2

0.8

0.4

0

0.65

0.52

0.39

0.26

0.13

0

[Pa][Pa]

Balossino et al., J Biomechanics, 2008; 41: 1053-1061

Fluid dynamicsFluid dynamics

Pietrabissa et al., Med Eng Phys, 1996; 18: 477-484.

SVG, Single Saphenous Vein Graft

SSVG, Sequential Saphenous Vein Graft

IMAG, Internal Mammary Artery Graft

SIMAG, Sequential Internal Mammary Artery Graft

SVG

Fluid dynamic boundary conditions

Fluid dynamic boundary conditions

Stenting bifurcations

View into the side branch at different inflationpressures (p) (balloon not shown), showing the graduallyincreasing cell opening.

Inflation of the side branch balloon results in ainadequate scaffolding of the main branch (indicated bythe arrow).

Mortier et al., Proceeding of the European Society of Biomechanics Workshop, Trinity College, Dublin, 26-28 August 2007

Expansion modalitiesExpansion modalities

CORDIS-like JOSTENT-like PALMAZ-like

SORIN-like MULTILINK-like BIFURCATED

ARTERY-CORDIS-like

Direction of flow

Models of stents and arteriesModels of stents and arteries

ARTERY-JOSTENT-like

CYLINDRICAL CONDUIT

0.08 mm

BIFURCATION simplified model

BIFURCATED: modelsBIFURCATED: models

BIFURCATION with parts of the stent exposed to the blood flow

BIFURCATED: viewsBIFURCATED: views

0.00 7.34 14.7 22.0 29.4 36.7 44.0 51.4 58.7 66.0 73.4 Pa

BIFURCATED: wall shear stress on the wall

BIFURCATED: wall shear stress on the wall

Time: 0.2 sec

- 73.4

- 66.0

- 58.7

- 51.4

- 44.0

- 36.7

- 29.4

- 22.0

- 14.7

- 7.34

- 0.00

Pa

= instants of results visualization

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8

time [s]

velo

city

[m/s

]BIFURCATED: wall shear stress on the stentBIFURCATED: wall shear stress on the stent

- 73.4

- 66.0

- 58.7

- 51.4

- 44.0

- 36.7

- 29.4

- 22.0

- 14.7

- 7.34

- 0.00

Pa

BIFURCATED: wall shear stress between stent struts

BIFURCATED: wall shear stress between stent struts

0.59 0.75 0.15 0.23 0.30 0.38 0.45 0.53 0.60 0.68 0.75 m/s

BIFURCATED: velocity vectors on cutting planes

BIFURCATED: velocity vectors on cutting planes

Simulation of fully-coupled fluid-structure interaction (FSI)

Vascular wall remodellingPlaque evolutionInclusion of the cascade of biological factors

Different time scales, e.g. from the heart beat (≅ 1 s) to drug release (≅ 4 months)

Current limits & challengesCurrent limits & challenges

LABORATORY OF BIOLOGICAL STRUCTURE MECHANICS

www.labsmech.polimi.it

gabriele.dubini@polimi.itFinancial Support

Italian Institute of Technology, Genoa, Italy

Fondazione Cariplo, Milan, Italy

Prof. Francesco Migliavacca

Dr. Lorenza Petrini

Dr. Francesca Gervaso

Dr. Rossella Balossino

Dr. Laura Socci

Dr. Frank Gjisen, Rotterdam

Mr. Claudio Capelli, PhD student, London

Prof. Luca Formaggia

Dr. Paolo Zunino

Dr. Christian VergaraMOX, Dept. of Mathematics,

Politecnico di Milano

AcknowledgementsAcknowledgements