Ing. Martin Vítek, Ph.D.

Department of Biomedical Engineering (UBMI)

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

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

Not applicable.

Not applicable.

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

• 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.

Not applicable.

At least 15 points for computer practice and project presentation.

Czech

Not applicable.

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.

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

Without possibility to compensate.

• Programme IT-MGR-2 Master's

  branch MBI , any year of study, winter semester, 4 credits, elective
  branch MPV , any year of study, winter semester, 4 credits, elective
  branch MGM , any year of study, winter semester, 4 credits, elective
  branch MSK , any year of study, winter semester, 4 credits, elective
  branch MIS , any year of study, winter semester, 4 credits, elective
  branch MBS , any year of study, winter semester, 4 credits, elective
  branch MIN , any year of study, winter semester, 4 credits, elective
  branch MMM , any year of study, winter semester, 4 credits, elective
  

13 hours, optionally

Ing. Martin Vítek, Ph.D.

• 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.