Course detail

Biological system modelling

FEKT-NMOBAcad. year: 2009/2010

Biological (medical and ecological) system, desriction of its properties. Planning experiments with biological systems. Theoretical approaches used for modelling biologcial systems (compartmental systems, deterministic chaos, fractals, theory of catastrophes, celular systems). Description of basic biological models - models of population dynamics, epidemiological and psychological models, models of biochemical processes, models of tissue structure, examples of basic models of human organism (cardiovascular system, endocrine system, etc.)

Language of instruction

English

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

doc. Ing. Radovan Jiřík, Ph.D.

Department

Department of Biomedical Engineering (UBMI)

Learning outcomes of the course unit

Capability to analyse function of biological systems and design their models. Implementation of mathematical models in MATLAB and SIMULINK.

Prerequisites

The subject knowledge on the Bachelor´s degree level is requested.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

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

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The aim of the course is to provide students with basic approaches and algorithms used for modelling biological (medical and ecological) systems.

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

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Murray, J.D.:Mathematical Biology,Springer Verlag, Berlin 1989. (EN)
ALLMAN, E.S., RHODES, J.A.: Mathematical Models in Biology: An Introduction. Cambridge University Press, 2004. (EN)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme EEKR-MN Master's

    branch MN-BEI , 1. year of study, summer semester, compulsory
    branch MN-KAM , 2. year of study, summer semester, optional interdisciplinary

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

doc. Ing. Radovan Jiřík, Ph.D.

Syllabus

Modelling and simulation - fundamental terms, aims, consequences. Properties of biological systems and choice of appropriate approaches for their modelling.
Experiments with biological objects. Experiment planning and evaluation.
Continuous models of single species populations, Malthus equation, logistic equation, Hutchinson equation, possibilities for further modifications.
Discrete models of single species populations -Leslie's model, analogons of continuous models, deterministic chaos, delayed discrete models.
Models for interactive populations, predator-prey models, models for competitive and mutualistic populations, Kolmogorov model.
Multicompartmental analysis - principles, models of biochenical processes in human body.
Epidemiological models - SIR models and their analysis, models of veneral diseases, models of AIDS dynamics, geographical models of epidemies.
Discrete models of celular structures - celular automata. Artificial life. Spreading of excitation through tissues of living organisms, models of movement in multimember populations, analysis of celular automata.
Fractals, fundamental terms, principles. Basic fractal models. Morphological biological models - morphology of cardiovascular and respiratory systems.
Theory of catastrophes, fundamental vocabulary, principles. Definitions of basic catastrophes. Behavioral and psychological models.
Models of sybsystems of the human body - cardiovascular system (blood pressure, model of systemic circulation, Windkessel models).
Neurokardiovascular system - models of heart rate variability, baroreflex models. Regulation of gastric acidity regulation.
Models of blood glucose regulation - physiological background, regulation by kidney, regulation by insuline, regulation by glucagon.

Exercise in computer lab

13 hours, optionally

Teacher / Lecturer

doc. Ing. Radovan Jiřík, Ph.D.

Syllabus

MATLAB and SIMULINK, basic features and possibilities
Continuous model of single species populations
Discrete models of single species populations, Leslie's model
Discrete logistic equation and deterministic chaos
Predator-prey models
Epidemic models