Presentazione di PowerPoint

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A constituent-based computational model for
vascular remodelling of a growing cerebral
aneurysm
L. Socci, F. Boschetti, D. Gastaldi, F.
Migliavacca, G. Pennati, P. Vena, G. Dubini
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Aneurysk Project
Structure of the project
Clinical Data (DICOM)
GEOMETRICAL ANALYSIS
3D reconstruction and semi-automatic detection of
relevant morphological features
DATA-BASE
NUMERICAL MODELING
STATISTICAL ANALYSIS
Correlation, Functional Data Analysis
3D Simulations, FSI, WSS Computation,
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Aneurysk Project
Structure of the project
Clinical Data (DICOM)
GEOMETRICAL ANALYSIS
3D reconstruction and semi-automatic detection of
relevant morphological features
DATA-BASE
NUMERICAL MODELING
STATISTICAL ANALYSIS
Biomechanics and adaptive features
Correlation, Functional Data Analysis
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Clinical background cerebral aneurysms
Aneurysm Development

• Adaptive phenomena (typical of biological tissues)

• Degradation phenomena

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Clinical background cerebral aneurysms
Aneurysm Development

• Adaptive phenomena (typical of biological tissues)

• elastase activity provides a modification on
  elastin fibers (Canham et al, 1999)
• the stability of mature collagen is altered
  because of the cross-linkage reduction (Gaetani
  et al, 1998)
• apoptosis of smooth muscle cells (Kataoka et al,
  1999)

• Degradation phenomena

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Aims
The goal

• To create a numerical tool able to simulate an
  adaptive process

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Aims
The goal

• To create a numerical tool able to simulate an
  adaptive process

Finite element approach interaction with CFD
simulations
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Aims
The goal

• To create a numerical tool able to simulate an
  adaptive process

The path

• To develop a constitutive model for cerebral
  vascular wall
• To implement an adaptive law to mimic the
  development of aneurysm

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State-of-the-art biomechanics
Constitutive models

• Kyriacou and Humphery (1996) Ryan and Humphrey
  (1999) non linear incompressible isotropic
  strain energy function on a membrane (aneurysms)

• Holzapfel et al. (2005) non linear
  incompressible anisotropic material with matrix
  and fibers (coronaric vessels)

Adaptive and degenerative models

• Watton et al. (2004) microstructural
  recruitment

• Baek et al. (2005 2006) stress-mediated matrix
  turnover on fusiform and saccular aneurysms

• Wulandana and Robertson (2005) an inelastic
  multi-mechanism constitutive model

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State-of-the-art biomechanics
Constitutive models

• Kyriacou and Humphery (1996) Ryan and Humphrey
  (1999) non linear incompressible isotropic
  strain energy function on a membrane (aneurysms)

• Holzapfel et al. (2005) non linear
  incompressible anisotropic material with matrix
  and fibers (coronaric vessels)

Finite element code
Adaptive and degenerative models

• Watton et al. (2004) microstructural
  recruitment

• Baek et al. (2005 2006) stress-mediated matrix
  turnover on fusiform and saccular aneurysms

• Wulandana and Robertson (2005) an inelastic
  multi-mechanism constitutive model

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Constitutive model

• Cerebral vessel wall behaviour
• Nonlinearity
• Viscoelasticity
• Anisotropy
• Large Deformations with Incompressibility
  constraint
• In vivo prestretch

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Constitutive model

• Cerebral vessel wall behaviour
• Nonlinearity
• Viscoelasticity
• Anisotropy
• Large Deformations with Incompressibility
  constraint
• In vivo prestretch

S (second Piola-kirchoff tensor) stress
measure E (Green-Lagrange Tensor) strain measure
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Constitutive model

• Cerebral vessel wall behaviour
• Nonlinearity
• Viscoelasticity
• Anisotropy
• Large Deformations with Incompressibility
  constraint
• In vivo prestretch

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Constitutive model

• Cerebral vessel wall behaviour
• Nonlinearity
• Viscoelasticity
• Anisotropy
• Large Deformations with Incompressibility
  constraint
• In vivo prestretch

(Holzapfel et al., 2005)
Identification parameters based on experimental
tests histology (a), mechanical tests (m, K1,
K2, r)
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Remodelling
Law implementation
Remodelling effect
Stimulus
Adaptive law
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Remodelling
Law implementation
Remodelling effect
Adaptive law

• Perturbation pressure, WSS, structural failure

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Remodelling
Law implementation
Stimulus
Adaptive law

• Perturbation pressure, WSS, structural failure

• Definition of the suitable stimulus for
  remodeling strain elastic energy of fibers

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Remodelling
Law implementation
Remodelling effect
Stimulus
Adaptive law

• Perturbation pressure, WSS, structural failure

• Definition of the suitable stimulus for
  remodeling strain elastic energy of fibers

• Definition of the effect of remodeling fiber
  lenghtening

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Remodelling
Law implementation
Remodelling effect
Stimulus

• Definition of the effect of remodeling fiber
  lenghtening

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Remodelling
Law implementation
Remodelling effect
Stimulus
Adaptive law

• Perturbation pressure, WSS, structural failure

• Definition of the suitable stimulus for
  remodeling strain elastic energy of fibers

• Definition of the effect of remodeling fiber
  lenghtening

• Definition of the remodeling law linear
  relationship

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FEM model
Mechanical behaviour
Adaptive behaviour
Strain Energy Function
Numerical model
3D Geometry
Simplified FEM models for saccular and fusiform
aneurysms
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FEM model
Geometry

• Saccular aneurysms

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FEM model
Geometry

• Saccular aneurysms

Boundary conditions and loads
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FEM model
Geometry

• Saccular aneurysms

Boundary conditions and loads

• Encastre

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FEM model
Geometry

• Saccular aneurysms

Boundary conditions and loads

• Encastre

• Pressure Load

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FEM model
Geometry

• Saccular aneurysms

Boundary conditions and loads

• Encastre

• Pressure Load

Material

• Perpendicular fibers

• W adventitia parameters (Holzapfel et al., 2005)

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FEM model
Geometry

• Saccular aneurysms

Boundary conditions and loads

• Encastre

• Pressure Load

Material

• Perpendicular fibers

• W adventitia parameters (Holzapfel et al., 2005)

Symmetries
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FEM model results
Steps of simulations
Axial direction
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FEM model results
Steps of simulations

• Prestretching fibers

• Physiological pressure

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FEM model results
Steps of simulations

• Prestretching fibers

• Physiological pressure

• Perturbation peak

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FEM model results
Steps of simulations

• Prestretching fibers

• Physiological pressure

• Perturbation peak

• Remodelling

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FEM model results
Steps of simulations

• Prestretching fibers

• Physiological pressure

• Perturbation peak

• Remodelling

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FEM model results
Steps of simulations

• Prestretching fibers

• Physiological pressure

• Perturbation peak

• Remodelling

Stability of the phenomenon
?
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FEM model results
Fusiform aneurysms
Effect of the geometry
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Works in progress
Clinical evidence stability or instability

• Not only a single mechanism in remodelling law

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Works in progress
Clinical evidence stability or instability

• Not only a single mechanism in remodelling law

• Evolution in perturbation interaction with CFD
  simulations

Pressure contour maps
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Works in progress
Clinical evidence stability or instability

• Not only a single mechanism in remodelling law

• Evolution in perturbation interaction with CFD
  simulations

• Change in boundary conditions

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Works in progress
Clinical evidence stability or instability

• Not only a single mechanism in remodelling law

• Evolution in perturbation interaction with CFD
  simulations

• Change in boundary conditions

• Constitutive parameters identification of
  parameters by experimental tests

Experimental tests
Histological analyses
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Acknowledgements
Thank you for your attention
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Acknowledgements
Thank you for your attention
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Work in progress
Toward stability or instability

• Saccular aneurysm change in geometry and
  boundary conditions

• Change of perturbation interaction with CFD
  simulations

Wall shear stress contour maps