biomechanical modelling of stent design · 2016. 3. 29. · etave et al., j biomechanics, 2001; 34:...
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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
[email protected] 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