Course detail

Modelling of Biological Systems

FIT-MOBAcad. year: 2015/2016

Biological system, description of its characteristics. Planning of experiments with biological systems. Theoretical principles of methods used in modelling of biosystems (compartmental analysis, deterministic chaos, fractals, theory of catastrophes, cellular automata). Description of particular models of biological systems, models of populations, epidemic and psychological models, models of biochemical processes, tissue structure modelling, models of basic subsystems of human organism.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

Ing. Martin Vítek, Ph.D.

Department

Department of Biomedical Engineering (UBMI)

Learning outcomes of the course unit

Basic theoretical knowledge of methods used in the field of biosystem modelling and skills in programming developed models in MATLAB, Simulink software.

Prerequisites

Fundamentals of modelling and simulation of systems, and fundamentals of biology.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

At least 15 points for computer practice and project presentation.

Course curriculum

Syllabus of lectures:
  • Basic vocabulary, definition of biosystem, its specificity and characteristics.
  • Continuous models of single-species populations, analysis of logistic equation, models with delay.
  • Discrete models of single-species populations and their analysis, Leslie model, fundamentals of deterministic chaos theory.
  • Discrete models of single-species models with delay, models of interacting populations.
  • Fractals, basic types of fractals. Fractal morphological structure of biosystems.
  • Multicompartmental analysis, models of biochemical processes.
  • Epidemic models and dynamics of infection diseases, venereal diseases, AIDS.
  • Disrete systems, finite automata, discrete models of cellular structure.
  • Artificial life, cellular automata. Conway's "Life", analysis of cellular automata.
  • Catastrophe theory and its application in behavioral models.
  • Verification and optimizing of implemented models, computer experiments and its evaluation.
  • Human organism as a system, models of subsystems in human body, cardiovascular system.
  • Models of subsystems in human body: model of glucose concentration control, control of biochemical processes in intestinal system.

Syllabus of computer exercises:
  • Continuous models of single-species populations.
  • Single species population models with delay, Leslie's model.
  • Deterministic chaos, bifurcation diagram.
  • Compartmental models of biochemical processes.
  • Celullar automata.
  • Models of cardiovascular system.

Syllabus - others, projects and individual work of students:
  • Discrete models of single-species populations.
  • Models of interacting populations.
  • Fractals.
  • Epidemic models, Venereal diseases, AIDS.
  • Conway's "Life".
  • Models of glucose control.

Work placements

Not applicable.

Aims

The aim is to introduce methods and algorithms used in modelling biological (medical and ecological) systems.

Specification of controlled education, way of implementation and compensation for absences

Without possibility to compensate.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

  • Murray, J.D.: Mathematical Biology, Berlin, Springer Verlag, 1989.
  • van Wijk van Brievingh, R.P., Moeller, D.P.F.: Biomedical Modeling and Simulation on a PC, New York, Springer Verlag, 1993.
  • Rowe, G.W.: Theoretical Models in Biology, Oxford, Oxford Univ. Press, 1994.

Recommended reading

  • Holčík, J.: Modelování biologických systémů, Elektronické texty.

Classification of course in study plans

  • Programme IT-MGR-2 Master's

    branch MBI , any year of study, winter semester, elective
    branch MPV , any year of study, winter semester, elective
    branch MGM , any year of study, winter semester, elective
    branch MSK , any year of study, winter semester, elective
    branch MIS , any year of study, winter semester, elective
    branch MBS , any year of study, winter semester, elective
    branch MIN , any year of study, winter semester, elective
    branch MMM , any year of study, winter semester, elective

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

Ing. Martin Vítek, Ph.D.

Syllabus

  • Basic vocabulary, definition of biosystem, its specificity and characteristics.
  • Continuous models of single-species populations, analysis of logistic equation, models with delay.
  • Discrete models of single-species populations and their analysis, Leslie model, fundamentals of deterministic chaos theory.
  • Discrete models of single-species models with delay, models of interacting populations.
  • Fractals, basic types of fractals. Fractal morphological structure of biosystems.
  • Multicompartmental analysis, models of biochemical processes.
  • Epidemic models and dynamics of infection diseases, venereal diseases, AIDS.
  • Disrete systems, finite automata, discrete models of cellular structure.
  • Artificial life, cellular automata. Conway's "Life", analysis of cellular automata.
  • Catastrophe theory and its application in behavioral models.
  • Verification and optimizing of implemented models, computer experiments and its evaluation.
  • Human organism as a system, models of subsystems in human body, cardiovascular system.
  • Models of subsystems in human body: model of glucose concentration control, control of biochemical processes in intestinal system.

Exercise in computer lab

13 hours, optionally

Teacher / Lecturer

Ing. Martin Vítek, Ph.D.

Syllabus

  • Continuous models of single-species populations.
  • Single species population models with delay, Leslie's model.
  • Deterministic chaos, bifurcation diagram.
  • Compartmental models of biochemical processes.
  • Celullar automata.
  • Models of cardiovascular system.