Modelling and Simulation
- Garant předmětu:
- Jan Kauler
- Jan Kauler
- Lucie Horáková, Jan Kauler
- Department of Biomedical Informatics
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.
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 single-species populations. Continuous Malthus model. Continuous logistics model with constant and variable parameters. analysis of the properties of its solution. Continuous models of single-species populations with delay. Discrete models of single-species populations. Discrete variants of Malthus' s and logistic model. Discrete models of single-species populations with delay. Models with world structure - Leslie's model.
3. Models of two-species populations. Predator-prey model. Analysis of the Lotka - Volterry model. Kolmogorov model. Predator-prey model with delay. Models of two-species 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 problem-parameter vector optimization.
7. Detailed block diagram of the process of modeling biological systems-completion. 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 single-species populations - continuous Malthus model. Analysis. Experiments with model parameters in the MATLAB-Simulink environment.
4. Implementation of time delay in models of single-species populations. Discrete Malhus and logistic model.
5. Discrete model of a single-species population by world structure - Leslie's model, simulation and analysis in the Simulink environment.
6. Models of two-species populations. Predator-prey model; design, simulation and analysis of the Simulink environment.
7. Predator-prey 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:
 KANA, Michel. Tutorial for modeling and simulation of biological processes. Praha: České vysoké učení technické v Praze, Nakladatelství ČVUT, 2010. ISBN 978-80-01-04491-9.
MEURS, Willem van. Modeling and simulation in biomedical engineering: applications in cardiorespiratory physiology. New York: McGraw - Hill, c2011. ISBN 978-0-07-171445-7
- Time-table for winter semester 2023/2024:
- Time-table is not available yet
- Time-table for summer semester 2023/2024:
Lab. robotiky a asis. tech.roomKL:B-520
Lab. umělé inteli. a bioinfor.
Lab. robotiky a asis. tech.
- The course is a part of the following study plans:
- Biomedical Technology (compulsory course)