Biomathematics 2

A.Y. 2018/2019
Lesson for
6
Max ECTS
52
Overall hours
SSD
MAT/06 MAT/08
Language
Italian
Learning objectives
- Analysis and numerical simulation of the ordinary differential equations modeling enzyme kinetics.
- Analysis and numerical simulation of the ordinary differential equations modeling the bioelectrical activity of the cellular membrane.
- Analysis and numerical simulation of the partial differential equations modeling the electrical propagation in nerve and cardiac fibers.
- Development and analysis of mathematical models for biological systems.
- Development and analysis of numerical methods for ordinary and partial differential equations.
- Development of matlab codes for the numerical simulation of biological systems.

Course structure and Syllabus

Active edition
Yes
Responsible
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
Laboratories: 24 hours
Lessons: 28 hours
Professor: Scacchi Simone
Syllabus
Mass action law.
- Enzyme kinetics: Michaelis-Menten approximation.
- Enzyme kinetics: outer solution, inner solution, quasi-uniform approximation.
- Enzyme kinetics: inhibition and cooperativity.
- Nernst-Planck equation, Goldman-Hodgkin-Katz current-voltage law, Nernst potential.
- Poisson-Nernst-Planck system: short and long channel limit.
- Cellular membrane and gating variables.
- Hodgkin-Huxley model.
- FitzHugh-Nagumo model.
- Cable equation.
- Homogenization of the cable equation.
- Travelling Wave solutions for the Nagumo equation.
- Travelling pulses in the FitzHugh-Nagumo one-dimensional.
Lesson period
First semester
Lesson period
First semester
Assessment methods
Esame
Assessment result
voto verbalizzato in trentesimi
Professor(s)