Enrollment year
2020/2021
Academic discipline
MAT/08 (NUMERICAL ANALYSIS)
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Curriculum
PERCORSO COMUNE
Period
1st semester (01/10/2020 - 20/01/2021)
Lesson hours
56 lesson hours
Activity type
WRITTEN TEST
Prerequisites
Basic mathematical courses of the "laurea triennale" (undergraduate) + the course Dynamical systems: theory and numerical methods
Learning outcomes
The course proposes an introduction to the mathematical modeling and simulation of physiological systems in biological sciences (cellular physiology dynamics of excitable cells) providing the main analytical and numerical methods for the investigation of the mathematical models and the interpretation of the simulated results
Course contents
The course proposes an introduction to the mathematical modeling and simulation of some physiological systems: enzyme kinetics, dynamics of excitable cells, reaction-diffusion systems, bioelectric cardiac processes.
- Models of cellular physiology.
- Mass action law, biochemical and enzymatic reactions, enzyme kinetics and quasi-steady approximation, cooperative and inhibition phenomena.
- Cellular electrophysiology, Nernst potential, electro-diffusion models, approximate current-voltage relationships.
- Ionic currents, ion channels with multiple subunits, voltage-clamping, Hodgkin-Huxley formalism.
- Approximate two variable excitable models, FitzHugh-Nagumo model: threshold effect and limit cycles.
- Hodgkin - Huxley model for the action potential, threshold effects, refractoriness, bifurcation diagrams.
- Introduction to reaction - diffusion models, balance laws, diffusion equation. Reaction and transport terms. Initial and boundary conditions.
- Numerical approximation of evolution problems.
- Introduction to propagation in excitable media.
- Cable equation, bistable equation, traveling waves.
- Computational Electrocardiology. Anisotropic bidomain model, excitation wavefront propagation, reentry phenomena.
Teaching methods
Lectures + Matlab laboratory
Reccomended or required readings
F. Britton. Essential Mathematical Biology. Springer-Verlag, Heidelberg, 2003.
J.P. Keneer, J. Sneyd. Mathematical Physiology. Springer-Verlag, New York, 1998.
J.P. Keneer, J. Sneyd. Mathematical Physiology I: Cellular Physiology. Springer-Verlag, New York, 2009.
J.P. Keneer, J. Sneyd. Mathematical Physiology II: System Physiology. Springer-Verlag, New York, 2009.
P. Colli Franzone, L. F. Pavarino, S. Scacchi. Mathematical Cardiac Electrophysiology. Springer, 2014
Assessment methods
Written exam
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