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Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2015/2016
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Insegnamento 097661 - BIOMATHEMATICAL MODELING
Docente Ambrosi Davide Carlo
Cfu 8.00 Tipo insegnamento Monodisciplinare

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento
Ing Ind - Inf (Mag.)(ord. 270) - MI (487) MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA*AZZZZ097661 - BIOMATHEMATICAL MODELING

Programma dettagliato e risultati di apprendimento attesi
• Elements of dynamical systems: phase space, equilibrium and stability, bifurcations and limit cycles, homoclines and heteroclines. 
Application of the theory to examples in chemical kinetics and population dynamics. Effective potential and ionic currents: cellular excitation.
The model by Hodgkin and Huxley and the model by FitzHugh and Nagumo. [KS, chapter 5]  • Reaction--diffusion equations. Qualitative analysis: traveling fronts, traveling pulses, spiral waves. Application of the theory to the propagation of electical signals
and to the depolarization of living cells. [KS, chapter 6]
Stability in continuous media. Elements of Fourier analysis, linear stability analysis. Application of the theory to reaction-diffusion systems of equations:
Turing instability and pattern formation. Dynamical patterns. [P, chapter 6] [S, chapter 5.2]
Elements of homogenization theory: two-scales expansion, reaction-diffusion equations with periodic and non-periodic microstructure.
Homogenization of the flow in porous media. [H, chapter 5]
• Mixture theory. Volume fraction, saturation constraint, partial stress tensor, boundary conditions. Porosity and permeability, Darcy equation. Application
of the theory to the growth of cell populations and to the diffusion-degradation of drugs in living tissues. [H2] Growth of a tumor spheroid. [P, chapter 10]
• Inverse problems in biomedicine. Radon transform. Ill-posed problems and regularization. The Tichonov functional, the adjoint operator. Differentiability
according to Frechet and Gateaux derivative. Application to medical images. [K]
• Elements of continuum mechanics. [L, chapters 1-2] Fluid-structure interaction, systems of coordinates and interface conditions. The ALE method.
Application of the theory to the fluid dynamics of large vessels.
• The material symmetry group. Isotropic, transverse isotropic and orthotropic materials: strain invariants and strain energies. The role of fibres
in biomechanics: collagen and cardiac fibres. Cardiac mechanics: the anatomy and physiolgy of the heart, the PV-loop, fibres shortening and torsion,
active stress and active strain. [L, chapter 5]
• Viscoelastic materials. Linear lumped-elements models, dynamic rheometry. Application to biological tissues. [J] Testi [KS] J. Keener and J. Sneyd, ``Mathematical Physiology'', Springer. [P] B. Perthame, ``Growth, reaction, movement and diffusion from biology''. http://www.ann.jussieu.fr/~perthame/ [H] M. Holmes, ``Introduction to Perturbation Methods'', Springer, 1995. [H2] M. Holmes, ``Mixture Theories for the Mechanics of Biological Tissues'', RPI Web Book, 1995. [J] D.D. Joseph, ``Fluid dynamics of viscoelastic liquids'', Springer [S] S.Salsa, F.Vegni, A.Zaretti, P.Zunino, ``Invito alle Equazioni a Derivate Parziali'', Springer Italia, 2009. [L] I-Shih Liu, A Continuum Mechanics Primer On Constitutive Theories of Materials, Lecture Notes (2006). http://www.im.ufrj.br/~liu/ [K] A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, Springer (2011)

Note Sulla Modalità di valutazione

Esame orale su tutto il programma. E' *fortemente* consigliato aver seguito con profitto gli esami di Meccanica Razionale e dei Continui (obbligatorio per la laurea triennale) e il corso di Equazioni Differenziali alle Derivate Parziali EDP1 (facoltativo per alcuni indirizzi della laurea triennale).


Bibliografia

Mix Forme Didattiche
Tipo Forma Didattica Ore didattiche
lezione
50.0
esercitazione
30.0
laboratorio informatico
0.0
laboratorio sperimentale
0.0
progetto
0.0
laboratorio di progetto
0.0

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
schedaincarico v. 1.6.2 / 1.6.2
Area Servizi ICT
04/06/2020