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L. Socci, F. Boschetti, D. Gastaldi, F. Migliavacca, G. Pennati, P. Vena, G. Dubini

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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L. Socci, F. Boschetti, D. Gastaldi, F. Migliavacca, G. Pennati, P. Vena, G. Dubini

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  1. 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

  2. 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,…

  3. 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

  4. 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

  5. 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

  6. Aims The goal • To create a numerical tool able to simulate an adaptive process

  7. Aims The goal • To create a numerical tool able to simulate an adaptive process Finite element approach: interaction with CFD simulations

  8. 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

  9. 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

  10. 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

  11. Constitutive model • Cerebral vessel wall behaviour: • Nonlinearity • Viscoelasticity • Anisotropy • Large Deformations with Incompressibility constraint • In vivo prestretch

  12. = 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

  13. a Constitutive model • Cerebral vessel wall behaviour: • Nonlinearity • Viscoelasticity • Anisotropy • Large Deformations with Incompressibility constraint • In vivo prestretch

  14. 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)

  15. Perturbation Remodelling Law implementation Remodelling effect Stimulus Adaptive law

  16. Perturbation Stimulus Hypothesis Remodelling Law implementation Remodelling effect Adaptivelaw • Perturbation: pressure, WSS, structural failure

  17. 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

  18. 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

  19. 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

  20. 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

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

  22. FEM model Geometry • Saccularaneurysms

  23. FEM model Geometry • Saccularaneurysms Boundary conditions and loads

  24. FEM model Geometry • Saccularaneurysms Boundary conditions and loads • Encastre

  25. FEM model Geometry • Saccularaneurysms Boundary conditions and loads • Encastre • Pressure Load

  26. FEM model Geometry • Saccularaneurysms Boundary conditions and loads • Encastre • Pressure Load Material • Perpendicular fibers • W: adventitia parameters (Holzapfel et al., 2005)

  27. FEM model Geometry • Saccularaneurysms Boundary conditions and loads • Encastre • Pressure Load Material • Perpendicular fibers • W: adventitia parameters (Holzapfel et al., 2005) Symmetries

  28. Axial displacement (mm) FEM model: results Steps of simulations: Axial direction

  29. Axial displacement (mm) FEM model: results Steps of simulations: Prestretching fibers Physiological pressure

  30. Axial displacement (mm) FEM model: results Steps of simulations: Prestretching fibers Physiological pressure Perturbation peak

  31. Axial displacement (mm) FEM model: results Steps of simulations: Prestretching fibers Physiological pressure Perturbation peak Remodelling

  32. Axial displacement (mm) FEM model: results Steps of simulations: Prestretching fibers Physiological pressure Perturbation peak Remodelling

  33. FEM model: results Steps of simulations: Prestretching fibers Physiological pressure Perturbation peak Remodelling Stability of the phenomenon ?

  34. 5.7° FEM model: results Fusiform aneurysms Effect of the geometry

  35. Works in progress Clinical evidence: stability or instability • Not only a single mechanism in remodelling law

  36. 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

  37. 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

  38. 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

  39. LaBS Staff involved: • Federica Boschetti • Gabriele Dubini • Dario Gastaldi • Francesco Migliavacca • Giancarlo Pennati • Pasquale Vena Acknowledgements Thank you for your attention……

  40. LaBS Staff involved: • Federica Boschetti • Gabriele Dubini • Dario Gastaldi • Francesco Migliavacca • Giancarlo Pennati • Pasquale Vena Acknowledgements Thank you for your attention……

  41. 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

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