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INdAM Fellowship Programs in Mathematics and/or Applications cofunded by Marie Skłodowska-Curie Actions



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Luigi Vergori

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

Project information

Title

Anastomosis: Anastomosis: Biomechanics, Modelling, Instabilities

Outgoing host organisation                                        Return host organisation

National University of Ireland, Galway                             Università  del Salento

University road                                                                       Piazza Tancredi, 7
Galway, Ireland                                                                      73100 Lecce, Italy

http://nuigalway.ie/                                                             http://www.unisalento.it/

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


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