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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:

- to develop a realistic mathematical model theory

in order to account for the fundamental mechanobiological aspects of

anastomosis; - to formulate and analyze fluid-structure

interactions at the anastomotic site, in order to quantify their

effect, or absence thereof, on the stability problem; - to analyze the effect of growth and remodelling

on the occurrence of mechanical instabilities in anastomosed vessels,

and possibly, on their resorption; - 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, UniversitÃ del Salento*2008-2011*: Fellow in Applied Mathematics, UniversitÃ del Salento

#### Publications, preprints, other works

- D. Perrone, L. Vergori,
*Stability of contact metric manifolds and unit*, Bull. Austral. Math. Soc. Vol. 76 (2006)

vector fields of minimum energy

pp. 269-283 - S. Rionero, L. Vergori,
*A note on the nonlinear stability of laminar MHD*, Rend. Acc. Sc. fis. mat. Napoli,

flows in a porous medium in the presence of Brinkman law

Vol. LXXIII, (2006) pp. 387-402 - L. Vergori,
*Spectral geometry for the Jacobi operator of the*, Note di Matematica, vol. 28, n. 1 (2008),

identity map

pp. 29-42 - S. Rionero, L. Vergori,
*Long-time behaviour of fluid motions in porous*, Acta Mechanica 210 (2010), pp. 221-240

media according to Brinkman model - K. R. Rajagopal, G. Saccomandi, L. Vergori,
*On the Oberbeck-Boussinesq approximation for*, Nonlinear Analysis: Real World Applications

fluids with pressure-dependent viscosities

10 (2009), pp. 1139–1150 - K. R. Rajagopal, G. Saccomandi, L. Vergori,
*Stability analysis of the Rayleigh-BÃ©nard*, Zeitschrift für angewandte Mathematik und Physik

convection for a fluid with temperature and pressure dependent

viscosity

60 (2009), pp. 739-755 - K. R. Rajagopal, G. Saccomandi, L. Vergori,
*A systematic approximation for the equations*, Nonlinear Analysis: Real World Applications

governing convection-diffusion in a porous medium

11 (2010), pp. 2366-2375 - G. Saccomandi, L. Vergori,
*Piezo-viscous flows over an inclined surface*, Quarterly Journal of Applied Mathematics

68 (2010), pp. 747-763 - L. Vergori,
*Flows at small Reynolds and Froude numbers*, International Journal of Engineering Science

11 (2010), pp. 1659-1670 - 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 - G. Napoli, L. Vergori,
*Equilibrium of nematic vesicles*, Journal of Physics A 43 (2010) 445207 - K. R. Rajagopal, G. Saccomandi, L. Vergori,
*Stability of Rayleigh-BÃ©nard convection in a*, Zeitschrift für angewandte Mathematik und Physik

porous medium

62 (2011), pp. 149-160 - K. R. Rajagopal, G. Saccomandi, L. Vergori,
*Couette flow with frictional heating in a fluid*, International Journal of Heat and Mass Transfer

with temperature and pressure dependent viscosity

54 (2011) pp. 783-789 - K. R. Rajagopal, G. Saccomandi, L. Vergori,
*Linear stability of Hagen-Poiseuille flow in a*, Computer & Mathematics with Applications 61 (2011)

chemically reacting fluid

pp. 460-469 - G. Napoli, L. Vergori,
*Curvature effects in nematic shells*, Physical Review Letters 108, 207803 (2012) - K. R. Rajagopal, G. Saccomandi, L. Vergori,
*Flow of fluids with pressure and shear dependent*, accepted for publication in Journal of Fluid Mechanics

viscosity down an inclined plane - G. Napoli, L. Vergori,
*Surface free energies for nematic shells*, accepted for publication in Physical Review E.

#### Conferences, schools, other events

*âElasticity Dayâ, 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