Biomathematics 2
A.Y. 2026/2027
Learning objectives
Qualitative analysis and numerical simulation of systems of ordinary differential equations describing enzyme kinetics.
Qualitative analysis and numerical simulation of systems of ordinary differential equations describing the electrical activity of the cell membrane.
Qualitative analysis and numerical simulation of systems of partial differential equations describing the propagation of electrical signals in nerve and cardiac fibers.
Qualitative analysis and numerical simulation of systems of ordinary differential equations describing the electrical activity of the cell membrane.
Qualitative analysis and numerical simulation of systems of partial differential equations describing the propagation of electrical signals in nerve and cardiac fibers.
Expected learning outcomes
Development and analysis of mathematical models describing biological processes.
Development and analysis of numerical methods for ordinary and partial differential equations.
Development of MATLAB code for the approximation of mathematical models for biological systems.
Development and analysis of numerical methods for ordinary and partial differential equations.
Development of MATLAB code for the approximation of mathematical models for 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
- Law of Mass Action.
- Two-stage enzyme kinetics: thermodynamic equilibrium approximation, quasi-steady-state approximation.
- Two-stage enzyme kinetics: nondimensionalization, outer solution, inner solution, construction of the uniform approximation.
- Enzyme inhibition and cooperativity.
- Nernst-Planck equation, Goldman-Hodgkin-Katz current-voltage relationship, Nernst equilibrium potential.
- Poisson-Nernst-Planck system: short-channel and long-channel limits.
- Equilibrium potential for multi-ionic fluxes, electrical circuit model of the cell membrane, gating variables.
- Hodgkin-Huxley model.
- FitzHugh-Nagumo model.
- Cable equation.
- Homogenization of the cable equation.
- Traveling wave solutions for the Nagumo equation.
- Traveling pulses in the one-dimensional FitzHugh-Nagumo system.
- Two-stage enzyme kinetics: thermodynamic equilibrium approximation, quasi-steady-state approximation.
- Two-stage enzyme kinetics: nondimensionalization, outer solution, inner solution, construction of the uniform approximation.
- Enzyme inhibition and cooperativity.
- Nernst-Planck equation, Goldman-Hodgkin-Katz current-voltage relationship, Nernst equilibrium potential.
- Poisson-Nernst-Planck system: short-channel and long-channel limits.
- Equilibrium potential for multi-ionic fluxes, electrical circuit model of the cell membrane, gating variables.
- Hodgkin-Huxley model.
- FitzHugh-Nagumo model.
- Cable equation.
- Homogenization of the cable equation.
- Traveling wave solutions for the Nagumo equation.
- Traveling pulses in the one-dimensional FitzHugh-Nagumo system.
Prerequisites for admission
Bachelor program in Mathematics.
Teaching methods
Lectures and practical sessions in the computational laboratory.
Teaching Resources
- J. Keener and J. Sneyd. Mathematical Physiology. Springer.
- N. F. Britton. Essential Mathematical Biology. Springer.
- N. F. Britton. Essential Mathematical Biology. Springer.
Assessment methods and Criteria
The examination consists of submitting a report on the laboratory activities carried out during the course and taking an oral examination. During the oral examination, students will be asked to present their laboratory report and discuss selected results from the course syllabus in order to assess their knowledge and understanding of the topics covered, as well as their ability to apply them. The examination is considered passed if the report is completed and the oral examination is successfully passed. The final grade is expressed on a scale of 30 and will be communicated immediately at the end of the oral examination.
MATH-03/B - Probability and Mathematical Statistics - University credits: 3
MATH-05/A - Numerical Analysis - University credits: 3
MATH-05/A - Numerical Analysis - University credits: 3
Laboratories: 24 hours
Lessons: 28 hours
Lessons: 28 hours
Professor:
Scacchi Simone
Shifts:
Turno
Professor:
Scacchi SimoneProfessor(s)