Modelling and Simulation
Code  Completion  Credits  Range  Language 

F7PBBMS  Z,ZK  4  2P+2C  Czech 
 The condition for enrollment in a given course is that the student has successfully completed or at least obtained a credit and has not exhausted all exam dates of the course:
 Introduction to Signals and Systems (F7PBBUSS)
 Garant předmětu:
 Jan Kauler
 Lecturer:
 Jan Kauler
 Tutor:
 Lucie Horáková, Jan Kauler
 Supervisor:
 Department of Biomedical Informatics
 Synopsis:

Basic concepts and consequences of modeling and simulation. Be able to use modeling and simulation methodologies. Emphasis is placed on a thorough understanding of compartmental models, physiological models, pharmacokinetics. Furthermore, continuous and discrete models of population dynamics, epidemiological models, models of venereal diseases.
 Requirements:

Knowledge of differential and integral calculus and the theory of signals and systems.
Credit: Participation in the exercise is mandatory, a maximum of 2 absences are allowed. Exercises can be scored. Points are also awarded for the result of the paper for the 6th and 13th exercises. It is possible to get up to 20 points for each paper. The points obtained in the exercises are counted towards the exam. To be awarded credit, you need to obtain a min. 50 % of possible points.
Exam: The exam has a written and an oral part. Most of the examples are focused on the description of the specified model, i.e. writing the relevant differential (difference) equations, explaining individual terms and drawing time dependencies. Several short multiple choice questions may be added. The maximum number of points earned is 60 points. The overall assessment is given according to the number of points achieved from the credit tests and the examination test according to the ECTS scale.
 Syllabus of lectures:

1. Basic concepts of simulation. Objectives and consequences of modeling and simulation. Methodology of model creation. Parameter identification. Experiments. Objective reality, dynamic system, mathematical and simulation. Models and their description. Informal and formal description. Forms of mathematical description of continuous and discrete systems.
2. Continuous and discrete models of singlespecies populations. Continuous Malthus model. Continuous logistics model with constant and variable parameters. analysis of the properties of its solution. Continuous models of singlespecies populations with delay. Discrete models of singlespecies populations. Discrete variants of Malthus' s and logistic model. Discrete models of singlespecies populations with delay. Models with world structure  Leslie's model.
3. Models of twospecies populations. Predatorprey model. Analysis of the Lotka  Volterry model. Kolmogorov model. Predatorprey model with delay. Models of twospecies populations. Competition models. Models of cooperation
4. Epidemiological models  basic epidemiological models. Model SIR. Kermack  McKendrik model  derivation. Conditions for the spread of the epidemic, estimation of the maximum number of patients, estimation of the number of victims. Models SI, SIS .. Model SIR carriers and vaccinations. SEIR models.
5. Epidemiological models  models of dynamics of venereal diseases. Derivation of the cross model. Analysis of solution properties. AIDS spread model.
6. Detailed block diagram of the process of modeling biological systems. Methodology of model creation. Inverse problemparameter vector optimization.
7. Detailed block diagram of the process of modeling biological systemscompletion. Quality of model parameter estimation, design of a new resp. complementary experiment. The importance of sensitivity functions in the design of a new experiment.
8. Compartment models. Derivation of mathematical description of compartment systems. Creation of compartment models. Examples of the use of compartment systems in biology and medicine.
9. Repetition  examples of using models.
10. Model analysis, sensitivity analysis.
11. Diving and modeling. Pharmacokinetics.
12. Empirical models.
13. Deterministic Chaos.
14. Case Studies (model of glycemic regulation, model of gastric acidity regulation, model of labeled aldosterone kinetics, model of heart rate regulation during physical activity, analysis, use in practice and in the training process)
 Syllabus of tutorials:

1. Introduction to exercises. Motivation to study Modeling and simulations. Repetition of prerequisites. Introduction to SIMULINK environment. Demonstration of graphical programming on simple mathematical models of bacterial growth and physiological system.
2. Biocybernetics. Physiological control. Model building and linearization.
3. Models of singlespecies populations  continuous Malthus model. Analysis. Experiments with model parameters in the MATLABSimulink environment.
4. Implementation of time delay in models of singlespecies populations. Discrete Malhus and logistic model.
5. Discrete model of a singlespecies population by world structure  Leslie's model, simulation and analysis in the Simulink environment.
6. Models of twospecies populations. Predatorprey model; design, simulation and analysis of the Simulink environment.
7. Predatorprey model with delay. Determination of equilibrium states and stability.
8. Test I.
9. Epidemiological models. SIR model; structure design, Simulink environment simulation, model analysis. SIR model with vectors and vaccination. Cross model  model of AIDS spread.
10. Compartment models. Pharmacokinetics.
11. Identification of parameters. Optimization. Least squares method.
12. Sensitivity analysis.
13. Test II.
14. Rehearsal for the exam. Awarding of credits.
 Study Objective:

Students will be able to simulate the evolution of populations over time under different conditions, both in continuous and discrete time, and derive the necessary parameters. Calculate the rate of spread of the disease for different conditions of spread of the disease. To determine the spread of the drug in the body using compartment models, etc.
 Study materials:

Compulsory literature:
[1] KANA, Michel. Tutorial for modeling and simulation of biological processes. Praha: České vysoké učení technické v Praze, Nakladatelství ČVUT, 2010. ISBN 9788001044919.
Recommended literature:
[2]MEURS, Willem van. Modeling and simulation in biomedical engineering: applications in cardiorespiratory physiology. New York: McGraw  Hill, c2011. ISBN 9780071714457
 Note:
 Timetable for winter semester 2022/2023:
 Timetable is not available yet
 Timetable for summer semester 2022/2023:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri  The course is a part of the following study plans:

 Biomedical Technology (compulsory course)