Course detail

Modelling of Biological Systems

FIT-MOBAcad. year: 2009/2010

Biological (medical and ecological) system, desriction of its properties. Theoretical approaches used for modeling of biologcial systems (models based on analogy with elektrotechnical systems, compartment systems). Description of basic biological models - models of population dynamics, epidemiological models, models of biochemical processes, models of tissue structure, examples of basic models of human organism, pharmacokinetic models

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Radovan Jiřík, 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

Requirements for completion of the course are specified by a regulation issued by the lecturer responsible for the course and updated for every.

Course curriculum

1. Organization, overview 1.1. Purpose of modeling 1.2. Classification of models 1.3. Models of static systems 1.4. Models of dynamic systems with lumped parameters 1.5. Models of dynamic systems with distributed parameters 2. Models based on analogy with electrotechnical systems 2.1. Generalized system properties 2.2. Model of cardiovascular system 2.3. Model of airway system 2.4. Model of diffusion in cells 3. Compartment models 3.1. Compartment models in diagnostics 4. Pharmacokinetic models 4.1. Basic pharmacokinetic parameters 4.2. One-compartment pharmacokinetic models 4.3. Multi-compartment pharmacokinetic models 5. Discrete models of single populations 5.1. Malthus model 5.2. Logistic model 5.3. Alternatives to logistic model 5.4. Linear models of structured populations 6. Discrete models of multiple populations 6.1. Predator-prey model 6.2. Further models of multiple populations 7. Continuous models of single populations 7.1. Malthus model 7.2. Logistic model 8. Continuous models of multiple populations 9. Discrete epidemiological models 9.1. SIR models 9.2. SI models 9.3. SIS models 9.4. Furter modifications of epidemiological models

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-MSC-2 Master's

    branch MBI , 0 year of study, summer semester, elective
    branch MBS , 0 year of study, summer semester, elective
    branch MGM , 0 year of study, summer semester, elective
    branch MGM , 0 year of study, summer semester, elective
    branch MIN , 0 year of study, summer semester, elective
    branch MIN , 0 year of study, summer semester, elective
    branch MIS , 0 year of study, summer semester, elective
    branch MIS , 0 year of study, summer semester, elective
    branch MMI , 0 year of study, summer semester, elective
    branch MMM , 0 year of study, summer semester, elective
    branch MPS , 0 year of study, summer semester, elective
    branch MPV , 0 year of study, summer semester, elective
    branch MSK , 0 year of study, summer semester, elective

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Radovan Jiřík, 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

7 hod., optionally

Teacher / Lecturer

doc. Ing. Radovan Jiřík, 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.

Project

6 hod., optionally

Teacher / Lecturer

doc. Ing. Radovan Jiřík, Ph.D.