INdAM-COFUND Outgoing fellow between 2012-03-06 and 2014-03-05

Project information

Title

Anastomosis: Anastomosis: Biomechanics, Modelling, Instabilities

Abstract

In medicine, the term anastomosis is used to describe the connection of two structures. More specifically, it refers to surgical or pathological connections between blood vessels or between other tubular structures such as loops of the intestine.

Fashioning an anastomosis is typically a complex and time-consuming step in a surgical operation, but proves almost always crucial to the outcome of the procedure. It is not rare that during this surgical operation some complications may occur. There is a propensity for platelets to bind at a native vessel anastomosis, because of subendothelial exposure, of the presence of suture material, and of local flow disturbances that may be generated by alteration of the geometry and topography of the vessel.

The vascular wall reaction to this technique may introduce some mechanical instabilities and deform the vessel in such
a way that the corresponding flow may be severely affected and some major medical problems (such as thrombosis or stenosis) may develop.

The main research objectives of the Project are:

1. to develop a realistic mathematical model theory
   in order to account for the fundamental mechanobiological aspects of
   anastomosis;
2. to formulate and analyze fluid-structure
   interactions at the anastomotic site, in order to quantify their
   effect, or absence thereof, on the stability problem;
3. to analyze the effect of growth and remodelling
   on the occurrence of mechanical instabilities in anastomosed vessels,
   and possibly, on their resorption;
4. to formulate and solve elastic stability
   problems relating to (1) (3), and compare their predictive power with
   available and acquired experimental data.

Fellow information

Research interests

• Stability of harmonic maps
• Linear and nonlinear stability in implicit
  theories of fluid dynamics
• Piezo-viscous fluids
• Mechanics of nematic shells
• Nonlinear elasticity

Previous positions, awards

• 2008-2011: Adjunct Professor of Rational Mechanics, School of Industrial Engineering, Università del Salento
• 2008-2011: Fellow in Applied Mathematics, Università del Salento

Publications, preprints, other works

1. D. Perrone, L. Vergori, Stability of contact metric manifolds and unit
   vector fields of minimum energy, Bull. Austral. Math. Soc. Vol. 76 (2006)
   pp. 269-283
2. S. Rionero, L. Vergori, A note on the nonlinear stability of laminar MHD
   flows in a porous medium in the presence of Brinkman law, Rend. Acc. Sc. fis. mat. Napoli,
   Vol. LXXIII, (2006) pp. 387-402
3. L. Vergori, Spectral geometry for the Jacobi operator of the
   identity map, Note di Matematica, vol. 28, n. 1 (2008),
   pp. 29-42
4. S. Rionero, L. Vergori, Long-time behaviour of fluid motions in porous
   media according to Brinkman model, Acta Mechanica 210 (2010), pp. 221-240
5. K. R. Rajagopal, G. Saccomandi, L. Vergori, On the Oberbeck-Boussinesq approximation for
   fluids with pressure-dependent viscosities, Nonlinear Analysis: Real World Applications
   10 (2009), pp. 1139–1150
6. K. R. Rajagopal, G. Saccomandi, L. Vergori, Stability analysis of the Rayleigh-Bénard
   convection for a fluid with temperature and pressure dependent
   viscosity, Zeitschrift für angewandte Mathematik und Physik
   60 (2009), pp. 739-755
7. K. R. Rajagopal, G. Saccomandi, L. Vergori, A systematic approximation for the equations
   governing convection-diffusion in a porous medium, Nonlinear Analysis: Real World Applications
   11 (2010), pp. 2366-2375
8. G. Saccomandi, L. Vergori, Piezo-viscous flows over an inclined surface, Quarterly Journal of Applied Mathematics
   68 (2010), pp. 747-763
9. L. Vergori, Flows at small Reynolds and Froude numbers, International Journal of Engineering Science
   11 (2010), pp. 1659-1670
10. L. Vergori, Couette and Poiseuille flows in bitumen, Proceedings of the 15th Conference on Waves and
    Stability in Continuous Media, World Scientific, Singapore (2010) ISBN
    981-4317-41-1, pp. 359-364
11. G. Napoli, L. Vergori, Equilibrium of nematic vesicles, Journal of Physics A 43 (2010) 445207
12. K. R. Rajagopal, G. Saccomandi, L. Vergori, Stability of Rayleigh-Bénard convection in a
    porous medium, Zeitschrift für angewandte Mathematik und Physik
    62 (2011), pp. 149-160
13. K. R. Rajagopal, G. Saccomandi, L. Vergori, Couette flow with frictional heating in a fluid
    with temperature and pressure dependent viscosity, International Journal of Heat and Mass Transfer
    54 (2011) pp. 783-789
14. K. R. Rajagopal, G. Saccomandi, L. Vergori, Linear stability of Hagen-Poiseuille flow in a
    chemically reacting fluid, Computer & Mathematics with Applications 61 (2011)
    pp. 460-469
15. G. Napoli, L. Vergori, Curvature effects in nematic shells, Physical Review Letters 108, 207803 (2012)
16. K. R. Rajagopal, G. Saccomandi, L. Vergori, Flow of fluids with pressure and shear dependent
    viscosity down an inclined plane, accepted for publication in Journal of Fluid Mechanics
17. G. Napoli, L. Vergori, Surface free energies for nematic shells, accepted for publication in Physical Review E.

Conferences, schools, other events

• “Elasticity Day”, One-Day Workshop on Mathematical
  Modelling in Solid Mechanics
  organised by Liverpool University, LJMU and
  sponsored by RCMM, 5 May 2012
• Modeling and Simulation in Soft Tissue
  Biomechanics: from Structure to Macroscopic Response.
  Summer School coordinated by Gerhard
  A. Holzapfel and Ray W. Ogden.
  Graz University of Technology, Austria, 3-7 September 2012
• CISM course
  to be held by R. W. Ogden and A. Dorffman, June or July 2013
• Euromech Colloquium
  organised by R. W. Ogden and K. P. Soldatos, September 2013