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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. Aneurysk Project. Structure of the project. Clinical Data (DICOM). GEOMETRICAL ANALYSIS.
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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
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,…
Saccular Fusiform 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
Growth: increase on mass Remodelling: change on mechanical properties Microstructural damage Clinical background: cerebral aneurysms Aneurysm Development • Adaptive phenomena (typical of biological tissues) • Degradation phenomena
Growth: increase on mass Remodelling: change on mechanical properties Microstructural damage 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
Aims The goal • To create a numerical tool able to simulate an adaptive process
Aims The goal • To create a numerical tool able to simulate an adaptive process Finite element approach: interaction with CFD simulations
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
State-of-the-art: biomechanics Constitutivemodels: • 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
State-of-the-art: biomechanics Constitutivemodels: • 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
Constitutive model • Cerebral vessel wall behaviour: • Nonlinearity • Viscoelasticity • Anisotropy • Large Deformations with Incompressibility constraint • In vivo prestretch
= Strain Energy Function 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
a Constitutive model • Cerebral vessel wall behaviour: • Nonlinearity • Viscoelasticity • Anisotropy • Large Deformations with Incompressibility constraint • In vivo prestretch
a s e 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)
Perturbation Remodelling Law implementation Remodelling effect Stimulus Adaptive law
Perturbation Stimulus Hypothesis Remodelling Law implementation Remodelling effect Adaptivelaw • Perturbation: pressure, WSS, structural failure
Remodelling effect Perturbation Remodelling Law implementation Stimulus Adaptivelaw • Perturbation: pressure, WSS, structural failure • Definition of the suitable stimulus for remodeling: strain elastic energy of fibers
Perturbation Remodelling Law implementation Remodelling effect Stimulus Adaptivelaw • 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
Physiological condition (step2) Perturbation Perturbation step (step 3) Increase stretch Reference state (step1) Remodelling step (step 4) New equilibrium Remodelling Law implementation Remodelling effect Stimulus • Definition of the effect of remodeling: fiber lenghtening
Perturbation 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
FEM model Mechanical behaviour Adaptive behaviour Strain Energy Function Numerical model 3D Geometry Simplified FEM models for saccular and fusiform aneurysms
FEM model Geometry • Saccularaneurysms
FEM model Geometry • Saccularaneurysms Boundary conditions and loads
FEM model Geometry • Saccularaneurysms Boundary conditions and loads • Encastre
FEM model Geometry • Saccularaneurysms Boundary conditions and loads • Encastre • Pressure Load
FEM model Geometry • Saccularaneurysms Boundary conditions and loads • Encastre • Pressure Load Material • Perpendicular fibers • W: adventitia parameters (Holzapfel et al., 2005)
FEM model Geometry • Saccularaneurysms Boundary conditions and loads • Encastre • Pressure Load Material • Perpendicular fibers • W: adventitia parameters (Holzapfel et al., 2005) Symmetries
Axial displacement (mm) FEM model: results Steps of simulations: Axial direction
Axial displacement (mm) FEM model: results Steps of simulations: Prestretching fibers Physiological pressure
Axial displacement (mm) FEM model: results Steps of simulations: Prestretching fibers Physiological pressure Perturbation peak
Axial displacement (mm) FEM model: results Steps of simulations: Prestretching fibers Physiological pressure Perturbation peak Remodelling
Axial displacement (mm) FEM model: results Steps of simulations: Prestretching fibers Physiological pressure Perturbation peak Remodelling
FEM model: results Steps of simulations: Prestretching fibers Physiological pressure Perturbation peak Remodelling Stability of the phenomenon ?
5.7° FEM model: results Fusiform aneurysms Effect of the geometry
Works in progress Clinical evidence: stability or instability • Not only a single mechanism in remodelling law
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
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
Lumen • Media • Adventitia 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
LaBS Staff involved: • Federica Boschetti • Gabriele Dubini • Dario Gastaldi • Francesco Migliavacca • Giancarlo Pennati • Pasquale Vena Acknowledgements Thank you for your attention……
LaBS Staff involved: • Federica Boschetti • Gabriele Dubini • Dario Gastaldi • Francesco Migliavacca • Giancarlo Pennati • Pasquale Vena Acknowledgements Thank you for your attention……
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