Fluid2Bio IP 2012

Summer Schools

Intensive Programme "If Fluid Dynamics Turns to Biology"

3 - 15 June 2012, University of L'Aquila

Welcome to the 2012 Intensive Programme (IP) in Fluid2Bio

If Fluid Dynamics Turns to Biology

3 - 15 June 2012, University of L'Aquila

Coordinator: Donatella Donatelli

Coordinating Institution: University of L'Aquila (Italy)

Location: University of L'Aquila (Italy)


Scientific Committee


List of Partner Institutions and Local Coordinators of the IP Fluid2Bio 2013

University of L'Aquila (Italy) - Coordinator, Prof. Donatella Donatelli
University of Genova (Italy) - Prof. Rodolfo Repetto
Politecnico di Milano (Italy) - Prof. Luca Formaggia
University of Trento (Italy) - Prof. Eleuterio F. Toro
Imperial College London (Great Britain) - Prof. Jennifer Siggers
Charles University in Prague (Czech Republic ) - Prof. Josef Malek
Vienna University of Technology (Austria ) - Prof. Ansgar Jüngel
University of Gdansk (Poland) - Prof. Danuta Makowiec
Gdansk University of Technology (Poland) - Prof. Jaroslaw Rybicki


Presentation

With a very suggestive image it has been said: “Mathematics is the lens through which to view the universe”. This IP has the aim to contribute further and to justify in a deeper sense that statement. In the common view of the sciences, physics and chemistry are thought to be heavily dependent on mathematics, while biology is often seen as a science which only in a minor way leans on quantitative methods. In contemporary biology there are many areas which depend heavily on rather advanced mathematics and in particular on fluid dynamics. The development of mathematical methodologies is now considered a major issue in the biological sciences (see the recent advances in mathematical modelling for haemodynamics, or cancer growth).

The Intensive Programme (IP) called "If Fluid dynamics turns to Biology - Fluid2Bio 2012" aims to address those issues and to provide the proper background to PhD and MSc students in order to deal with those problems and situations. Today, mathematicians with expertise as diverse as non-linear partial differential equations, dynamical systems, probability, statistics and stochastic processes, combinatorial mathematics, graphs and networks, and low dimensional topology are engaged in this broad endeavor. In this contest the present project will manly focus on the interplay between fluid dynamics and biological phenomena. Research in physiological fluid mechanics uses the techniques of mathematical modeling, and numerical and asymptotic analysis. Some of the main applications are to blood flow in the cardiovascular system, t fluid dynamics of the eye, growth and development of bacterial biofilms...

The proposed IP  will consist of a set of short courses and seminars and  is addressed mainly to MSc and PhD students in Applied Mathematics, Bioengineering, but also students in Biotechnology. The major target of the program is to contribute to the process of disseminating knowledge and expertise in applied mathematics methods (in particular in the fluid dynamics field) and models in biology, both at a Master and at a PhD level. Based on well- established PhD schools, we aim to provide our students with the possibility of complementary interdisciplinary training at the interface of mathematics, fluid dynamics and biology.

The participation of students and teachers from the partner universities will be supported by the LLP Erasmus Programme. The programme will be held in the period June 3-15, 2012.


Reimbursement

Applicants from partner institutions are eligible for a reimbursement of living and travel expenses.

This contribution is offered by the LLP Italian National Agency. llp erasmus logo

We assume to select:

The contact person of each institution in the Organizing Committee is responsible for the selection of students in their universities.

Details about Reimbursement

Reservation for lodging and contribution for subsistence costs.

Please notice that students and teachers from partner universities will be hosted in university premises free of charge for the whole period of the IP. Unfortunately, the Erasmus agency applies a very low daily amount for subsistence costs of students (24 euro per day, both for lodging and full board). That's why, in addition to the accommodation, we can confirm that we will only be able to offer students free access to the university canteen (open on working days). We hope we'll be able to offer some additional support to students, but we cannot guarantee anything at the moment.


 Lectures

Lecture 1

TITLE

An introduction to fluid dynamic modeling


LECTURER

Vit Prusa, Charles University in Prague, Czech Republic


ABSTRACT

 

The aim of the course is to recall (or briefly introduce) the basic notions in continuum mechanics with an emphasis to notions and concepts useful in modeling the fluids. The first part of the course will be focused on kinematics and dynamics of the fluids, thus on the part of the theory that is universal for any fluid. The most popular fluid model - --- the Navier--Stokes fluid model -- will be discussed in the second part of the course, and it will be shown that the model is, in many cases, not the right one to be applied in technology and medicine. At the end we will return back to the fundamental principles discussed in the first part of the course, and comment how they can be used to introduce several more complicated fluid models.

 


TEACHING MATERIAL

Lecture 2

TITLE

Chemotaxis Models


LECTURER

Sabine Hittmeir, Vienna University of Technology


ABSTRACT

1. The Keller-Segel Model (Blow up vs. Global Existence, Travelling Bands)

2. Kinetic Models for Chemotaxis (Diffusion Limit, Hydrodynamic Limit)


TEACHING MATERIAL

Lecture 3

TITLE

Cellular automata approach to model and simulate complex systems


LECTURER

Danuta Makowiec, Gdansk University, Poland


ABSTRACT

 

Cellular automata approach is a  suitable and powerful tool for catching the influence of the microscopic scale to macroscopic properties of  the complex system. During the course we will learn the cellular automata technique anddiscuss its application in

(a)  models of  road traffic

(b)  computational fluid dynamics (the lattice Boltzman method)

(c)  modeling of excitable medium.

 


TEACHING MATERIAL

Lecture 4

TITLE

Mathematical and numerical models for simulating blood flow


LECTURER

Luca Formaggia, Politecnico di Milano, Italy


ABSTRACT

 

We will present the main differential models used to describe blood flow in arteries. We will focus on the numerical solution of Navier-Stokes equations, including the case of compliant arteries, and on the use of reduced models for pulse wave propagation along the arterial tree.

We will also address issues related to the correct imposition of boundary conditions as well as the coupling of the different models.

Bibliography:

Cardiovascular Mathematics. Modeling and simulation of the circulatory system. L. Formaggia, A. Quarteroni, A. Veneziani (Eds). Springer 2009 (mainly Chapters 2, 10 and 11).

 


TEACHING MATERIAL

Lecture 5

TITLE

Fluid dynamics of the eye


LECTURERS

Rodolfo Repetto,  University of Genova, Italy

Jennifer Siggers, Imperial College London, Great Britain

Amabile Tatone, University of L'Aquila, Italy


ABSTRACT

 

The human eye is a complex organ composed of many parts. Good vision depends on the way in which these parts work together. Both solid and fluid mechanics play a fundamental role in the functioning of the eye and in the pathogenesis of common diseases. As most of the eye globe volume is occupied by fluid, many of the problems related with the eye’s functioning are strictly of a fluid dynamic nature. In this course the focus will be on problems involving motion of fluids. In this course we will give an overview of some basic models of the fluid dynamics of the eye. In some cases, more sophisticated analyses have appeared in the literature. The material for this course was selected with the aim of presenting fairly simple, often analytical, mathematical models, which nonetheless allow us to obtain some insight into the physics of the problem. A few experimental results will also be presented and compared with theoretical predictions. The main aim of this course is therefore that of introducing the listener to this fascinating and, in our opinion, underpopulated research area and to show how even very simple mathematical approaches may provide some understanding of the functioning of complex systems. The main topics that will be considered during this course are listed below:

i) motion of the aqueous humour in the posterior and anterior chambers of the eye;

ii) drainage of the aqueous humour through the trabecular meshwork;

iii) motion of the vitreous body induced by eye rotations;

iv) traction on the retina in the presence of posterior vitreous detachment;

v) intracellular flow in optic-nerve axons: a possible mechanism for the pathogenesis of glau- coma;

vi) mechanisms of subretinal fluid displacement;

vii) tear fluid dynamics.

 

References

To the writers’ knowledge the only biomechanics textbook covering the subject of ocular biomechanics is the following:

  • Ethier, C. R. & Simmons, C. A. Introductory Biomechanics - From Cells to Organisms. Chapter 6. (Cambridge Texts in Biomedical Engineering), Cambridge University Press, 2007.

The following papers provide an updated review of the biomechanics works on the eye:

  • Ethier, C. R., Johnson, M. & Ruberti, J. Ocular biomechanics and biotransport. Annu. Rev. Biomed. Eng., 2004, 6, 249-273.
  • Siggers, J. H. & Ethier, C. R. Fluid Mechanics of the Eye. Annu. Rev. Fluid Mech., 2012, 44, 347-372.

An extended bibliography on the topics treated in the course will be provided along with the teaching material.


TEACHING MATERIAL

Lecture 6

TITLE

Earthquakes


LECTURER

Carlo Doglioni, Università Sapienza di Roma, Italy


ABSTRACT

 


TEACHING MATERIAL

Lecture 6

TITLE

Earthquakes


LECTURERS

Carlo Doglioni, Università Sapienza di Roma, Italy


ABSTRACT

 


TEACHING MATERIAL


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