Modelling of Biological Systems

Ac.Year:2019/2020 (Not opened)
Language of Instruction:Czech
Completion:credit+exam (verbal)
Type of
Guarantor:Vítek Martin, Ing., Ph.D. (DBME)
Lecturer:Vítek Martin, Ing., Ph.D. (DBME)
Faculty:Faculty of Electrical Engineering and Communication BUT
Department:Department of Biomedical Engineering FEEC BUT
Learning objectives:
  The aim is to introduce methods and algorithms used in modelling biological (medical and ecological) systems.
  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.
Knowledge and skills required for the course:
  Fundamentals of modelling and simulation of systems, and fundamentals of biology.
Learning outcomes and competencies:
  Basic theoretical knowledge of methods used in the field of biosystem modelling and skills in programming developed models in MATLAB, Simulink software.
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.
Fundamental 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.
Study literature:
  • Holčík, J.: Modelování biologických systémů, Elektronické texty.
Controlled instruction:
  Without possibility to compensate.
Progress assessment:
  Presentation of project results on computer prectice (written report max. 15 points and activity during computer practice and oral presentation max. 15 points).
Exam prerequisites:
  At least 15 points for computer practice and project presentation.

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