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Accueil > Enseignement > Masters > Archives Master 2 recherche > Programme détaillé du Master 2 recherche 2015-2016 > Multidisciplinary approaches in the study of biological fluids and tissues : mathematical modeling and clinical experience

Multidisciplinary approaches in the study of biological fluids and tissues : mathematical modeling and clinical experience

Giovanna Guidoboni (IUPUI), Chaire Gutenberg 2014/2015

The course will be taught in english

This course covers a variety of mathematical methods for modeling biological fluids and tissues. The basic principles of continuum mechanics for deformable bodies will be reviewed, including conservation laws and constitutive equations, while discussing the mathematical challenges in solving these equations analytically and/or numerically. The use of ordinary and partial differential equations (ODEs and PDEs) will be discussed to model biochemical and biomechanical properties of fluids and tissues. Theoretical concepts will include : Lagrangian/Eulerian description of motion, infinitesimal and finite deformations, PDEs of mixed hyperbolic/parabolic type for fluid flows and solid deformations, multiscale systems of ODEs and PDEs for biophysical applications.

Theoretical concepts will be applied to various areas of anatomy and physiology, with a particular emphasis on the human eye, since Dr. Guidoboni’s main research interest lies in the use of mathematical modeling to elucidate the relationship between eye mechanics, hemodynamics and incidence and progression of ocular diseases. Students will be able to master the class content by working on independent projects that will be selected together with the instructor. Examples include, but are not limited to : Hyperbolic/parabolic nature of fluid-structure interaction problems ; porous media equations for the perfusion of biological tissues ; constitutive modeling of tissue aging and clinical implications ; influence of intraocular pressure on retinal circulation ; analysis of blood velocity in color doppler imaging and clinical interpretation ; modeling the relationship between intraocular pressure, blood pressure and intracranial pressure ; retinal oxygenation : modeling, simulations and comparison with retinal oximetry maps.

This course has been taught by Dr. Guidoboni within the math graduate program at IUPUI in the Spring 2014. Dr. Guidoboni currently holds a joint chair between IRMA and IUPUI and will be present in Strasbourg for the next two years to collaborate with Drs. Prud’homme and Szopos on the modeling of the connection between the eye and the brain (Eye2Brain project), with potential implications on the development of noninvasive ocular biomarkers for the early diagnosis and clinical care of neurodegenerative disorders. The Eye2Brain project is currently funded by the Chaire Gutenberg and the Embassy of France in the United States awarded to one of Dr. Guidoboni’s graduate student, Lucia Carichino, to spend one semester in Strasbourg and advance in her research.

References :
Notes provided by the Instructor
- A. C. Eringen, Mechanics of Continua, 2nd edition, Editore : Robert E. Krieger Publ. Co., Huntington, New York., Anno edizione : 1980
- G. A. Holzapfel, Nonlinear Solid Mechanics : a Continuum Approach for Engineering, Editore : John Wiley & Sons., Anno edizione : 2001
- Fung, YC., Biodynamics : Circulation, Editore : Springer-verlag ; New York, Anno edizione : 1984
- Levick, JR., An introduction to cardiovascular physiology, Editore : Arnold Publishers ; London, Anno edizione : 2003

Dernière mise à jour le 15-09-2015