BioMedMath

Modelling with Differential Equations

Teacher: dr. Josip Tambača, professor
Semester: second
ECTS: 6
Required course

  1. To introduce students to the application of mathematical modelling in the analysis of biomedical systems,
  2. To show how mathematics, especially partial differential equations and computing can be used in an integrated way to analyse biomedical systems.
  1. 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,
  2. To be able to assess biological/medical inferences that rest on mathematical arguments,
  3. To be aware of the use of ordinary and partial differential equations and computers to assist them in studying biological/medical systems,
  4. To be able to formulate and analyse dynamical models of reaction kinetics,
  5. To apply Hodgkin-Huxley model to model ion transport,
  6. To use partial differential equations to model conservation, convection and diffusion in biomedical systems,
  7. To derive conclusions in biomedical models from the qualitative properties of the partial differential equations that model the phenomena,
  8. To formulate and apply models using partial differential equations on moving boundary problems.
  1. Reaction kinetics. Michaelis-Menten kinetics, sigmoidal kinetics, oscillators and switches.
  2. Dynamical behaviour of neuronal membranes. Hodgkin-Huxley model, Fitzhugh-Nagumo model.
  3. Introduction in partial differential equations in biology. Conservation, convection, diffusion and attraction.
  4. Traveling wave propagation. Fisher’s equation.
  5. Biological pattern formation. Turing model. A chemical basis for morphogenesis.
  6. Moving boundary problems. Wound healing, tumour growth.

  • Course objectives

    1. To introduce students to the application of mathematical modelling in the analysis of biomedical systems,
    2. To show how mathematics, especially partial differential equations and computing can be used in an integrated way to analyse biomedical systems.

  • Expected learning outcomes

    1. 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,
    2. To be able to assess biological/medical inferences that rest on mathematical arguments,
    3. To be aware of the use of ordinary and partial differential equations and computers to assist them in studying biological/medical systems,
    4. To be able to formulate and analyse dynamical models of reaction kinetics,
    5. To apply Hodgkin-Huxley model to model ion transport,
    6. To use partial differential equations to model conservation, convection and diffusion in biomedical systems,
    7. To derive conclusions in biomedical models from the qualitative properties of the partial differential equations that model the phenomena,
    8. To formulate and apply models using partial differential equations on moving boundary problems.

  • Course content

    1. Reaction kinetics. Michaelis-Menten kinetics, sigmoidal kinetics, oscillators and switches.
    2. Dynamical behaviour of neuronal membranes. Hodgkin-Huxley model, Fitzhugh-Nagumo model.
    3. Introduction in partial differential equations in biology. Conservation, convection, diffusion and attraction.
    4. Traveling wave propagation. Fisher’s equation.
    5. Biological pattern formation. Turing model. A chemical basis for morphogenesis.
    6. Moving boundary problems. Wound healing, tumour growth.
PMF
EU fondovi
UNI-ZG