BIOMATHEMATICS
Stampa
Enrollment year
2018/2019
Academic year
2019/2020
Regulations
DM270
Academic discipline
MAT/08 (NUMERICAL ANALYSIS)
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Course
MATHEMATICS
Curriculum
PERCORSO COMUNE
Year of study
Period
1st semester (30/09/2019 - 10/01/2020)
ECTS
6
Lesson hours
56 lesson hours
Language
Italian
Activity type
WRITTEN AND ORAL TEST
Teacher
PAVARINO LUCA FRANCO (titolare) - 6 ECTS
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
Regular and singular perturbation theory. Mass action law, biochemical and enzymatic reactions, enzyme kinetics and quasi-steady approximation, cooperative and inhibition phenomena

Population dynamics
Malthusian and logistic models; difference equations in one dimension, stability and biforcations. Interaction in biological systems: pray-predator Lotka-Volterra model, more realistic pray-predator models, models of interaction of two populations, competition and cooperative effects.

Cellular electrophysiology
Nernst potential, electro-diffusion models, approximate current-voltage relationships, dynamics of the ionic currents, ion channels with multiple subunits, voltage-clamping, Hodgkin-Huxley formalism, generation of the action potential of the giant axon of the squid. Approximate two variable excitable models (FitzHugh-Nagumo, Morris-Lecar models): threshold effect and limit cycles.

Introduction to bifurcation involving fixed points and limit cycles in biological systems

Introduction to propagation and reentry in excitable one dimensional ring
Homogenization a 1D arrangement of excitable cells, cable model, threshold, action potential duration, propagation of the excitation.

Introduction to reaction-diffusion systems
Conservation laws; diffusion equation, initial and boundary conditions. Travelling wave solutions; numerical approximation of nonlinear parabolic equations.

Computational Electrocardiology
Anisotropic bidomain model, excitation wavefront propagation, macroscopic structure of the bioelectric cardiac sources, extracellular potential and electrograms.
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.
Assessment methods
Written exam
Further information
Written exam
Sustainable development goals - Agenda 2030