Mechanics

The vessel wall mechanics is described in regime of finite deformations by non linear hyperelastic structural models.

The research is focused on the mathematical and numerical modeling of the arterial wall and celebral aneurysms wall mechanics using hyperelastic materials to describe the biological tissue. 

Another research topic is the computation of deflated vascular geometries starting from patient-specific vascular geometries reconstructed from radiological images,  in order to simulate the prestressed state of arteriesThis allow to obtain the initial reference configuration in view of fluid-structure interaction simulations.

 

 

Comparison among deflated (in blue) and inflated (in grey) human carotid geometries at the inlet section.

Comparison between deflated (in blue) and MRI inflated (in grey) human carotid geometries at the inlet section.

Variation of radial displacement and strain in a vessel.

Variation of radial displacement and strain in a vessel for Linear, St. Venant-Kirchhoff, Neo-Hookean and Exponential materials.

Displacement field in a cerebral aneurysm.

Displacement field in a cerebral aneurysm.

 

 

Publications:

  1. P. Tricerri, L. Dede’, A. Gambaruto, A. Quarteroni and A. Sequeira. A numerical study of isotropic and anisotropic constitutive models with relevance to healthy and unhealthy cerebral arterial tissues, in International Journal of Engineering Science -Pergamon Press-, vol. 101, p. 126-155, 2016.

Thesis:

  1. V. Longinotti – Modelli matematici per il tessuto vascolare – BSc in Mathematical Engineering – Advisor: L. Formaggia – A.Y. ’03-’04
  2. P. Riva – Modelli matematici per il tessuto vascolare – BSc in Mathematical Engineering – Advisor: L. Formaggia – A.Y. ’03-’04
  3. M. De Luca – Mathematical and numerical models for cerebral aneurysm wall mechanics – Ph.D. thesis in Mathematical Engineering – Advisor: A. Veneziani – A.Y. ’08-’09
  4. G. Mengaldo – Nonlinear fluid-structure interaction with application in computational haemodynamics – MSc in Aerospace Engineering – Advisor: L. Formaggia – A.Y. ’10-’11
  5. R. M. Lancellotti – Numerical computations of deflated vascular geometries for Fluid-Structure Interaction in haemodynamics – MSc in Aerospace Engineering – Advisors: C. Vergara, S. De Rosa – A.Y. ’10-’11

 

Projects

MathCard

Aneurisk

 

Links

Modelling the Heart: Mechanics

Clinical Applications: Cerebral Aneurysms

Image Processing: Image Segmentation

Image Processing: Mesh Generation