Biomathematics 2
A.Y. 2018/2019
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.
- 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.
Expected learning outcomes
- 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.
- Development and analysis of numerical methods for ordinary and partial differential equations.
- Development of matlab codes for the numerical simulation of biological systems.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course 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.
- 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.
MAT/06 - PROBABILITY AND STATISTICS
MAT/08 - NUMERICAL ANALYSIS
MAT/08 - NUMERICAL ANALYSIS
Laboratories: 24 hours
Lessons: 28 hours
Lessons: 28 hours
Professor:
Scacchi Simone
Professor(s)