- 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.
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.
Lesson period: First semester
(In case of multiple editions, please check the period, as it may vary)
- Law of mass action. - 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.
Prerequisites for admission
Basic lectures of the Bachelor degree in Mathematics
Lectures and computer exercises in the laboratory.
- J. Keener and J. Sneyd. Mathematical Physiology. Springer. - N. F. Britton. Essential Mathematical Biology. Springer.
Assessment methods and Criteria
The exam consists of a written test and an oral test.
- The written test consists of a theoretical exercise and two computer exercises, in which mathematical models based on ordinary differential equations that describe some biological systems must be studied qualitatively and numerically simulated.
- Only students who have passed the written test of the same exam session can access the oral exam. During the oral exam the student will be asked to illustrate some of the results of the teaching program, in order to evaluate the knowledge and understanding of the topics covered, as well as the ability to know how to apply them.
The exam is passed if the written and oral tests are passed. The mark is expressed out of thirty and will be communicated immediately at the end of the oral exam.