Biological System Modelling

• 26 hrs lectures
• 13 hrs pc labs

The graduate of the course:
• Is able to identify the basic elements, links and state variables of biological systems
• Can describe the activity of biological systém using set of equations
• Can solve the system of differential equations using Euler's method and Runge-Kutta methods
• Is able to analyze the stability of equilibrium states of the model using the Jacobi matrix
• Can construct an implementation scheme of a model from the system of equations
• Can construct a system of equations from the model implementation scheme
• Is able to implement a computer model in MATLAB and Simulink
• Is able to simulate a computer model in MATLAB and Simulink
• Is able to discuss the results of a computer model simulation

The aim of the course is to provide students the basic knowledge and skills in design of mathematical models of biological systems, their analysis, computer implementation and subsequent simulation.

The student who enters the course should be able to:
• Analyze simple electrical circuits using Ohm's law and Kirchhoff's laws
• Find the analytical solutions of simple differential equations
• Solve the system of equations using matrices
• Create a simple program in MATLAB that contains loops, conditions, and mathematical equations

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

1. Modelling and simulation - fundamental terms, classification of models
2. Modelling and simulation - identification of model parameters, ways of describing the model
3. Mathematical and computer models - analysis of the mathematical model, computer models and simulations
4. Models of single species populations - Malthus, Pearl-Verhulst, Hutchinson and Leslie
5. Models of two species populations - predator-prey, competitive and mutualistic populations
6. Models of cardiovascular system - hemodynamic parameters, Windkessel models
7. Models of action potential impulse - Hodgkin-Huxley model
8. Models of respiratory system - mechanical ventilatory
9. Pharmacokinetical models - compartment model of diffusion, pharmacokinetic parameters, multi compartment models
10. Epidemiological models - models SIR, SEIR, SI a SIS
11. Deterministic chaos - chaos in biological systems, fractals in biological systems
12. Catastrophe theory - basic types of catastrophes, butterfly catastrophe‎
13. Discrete event systems - finite-state automata, models of celular and tissue structures, artificial life

1. Modelling and simulation
2. Models of single species populations
3. Models of two species populations
4. Models of cardiovascular system
5. Pharmacokinetical models
6. Epidemiological models

Computer exercises: 25 points - solving tasks during the exercise, the minimum for the credit and admission to the final examination is to obtain at least 10 points
Final exam: 75 points - exam is written and consists of three parts with 25 points each. The first part verifies the general theoretical knowledge of biological systems modeling, the second part verifies the theoretical knowledge and practical skills in the field of population models and the third part verifies the theoretical knowledge and practical skills in modeling of the human body systems.
For successful completion of the course, it is necessary to obtain from the written exam at least 35 points and in a total at least 50 points.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. Teaching methods include lectures and computer laboratories (modeling in Matlab and Simulink). Course is taking advantage of e-learning (Moodle) systém.

Computer exercises are compulsory, properly excused exercises absences can be substitute at another time after consultation with the teacher.