Teacher: dr. Josip Tambača, professor
- To introduce students to the application of mathematical modelling in the analysis of biomedical systems,
- To show how mathematics, especially partial differential equations and computing can be used in an integrated way to analyse biomedical systems.
Expected learning outcomes
- To have an enhanced knowledge and understanding of mathematical modelling and mathematical methods using ordinary and partial differential equations for the analysis of biological/medical systems,
- To be able to assess biological/medical inferences that rest on mathematical arguments,
- To be aware of the use of ordinary and partial differential equations and computers to assist them in studying biological/medical systems,
- To be able to formulate and analyse dynamical models of reaction kinetics,
- To apply Hodgkin-Huxley model to model ion transport,
- To use partial differential equations to model conservation, convection and diffusion in biomedical systems,
- To derive conclusions in biomedical models from the qualitative properties of the partial differential equations that model the phenomena,
- To formulate and apply models using partial differential equations on moving boundary problems.
- Reaction kinetics. Michaelis-Menten kinetics, sigmoidal kinetics, oscillators and switches.
- Dynamical behaviour of neuronal membranes. Hodgkin-Huxley model, Fitzhugh-Nagumo model.
- Introduction in partial differential equations in biology. Conservation, convection, diffusion and attraction.
- Traveling wave propagation. Fisher’s equation.
- Biological pattern formation. Turing model. A chemical basis for morphogenesis.
- Moving boundary problems. Wound healing, tumour growth.