Modelling and Simulation

Grading of the course requires grading of the following courses:

Introduction to Signals and Systems (17KBBUSS)

Lecturer:

Tutor:

Supervisor:

Department of Biomedical Informatics

Synopsis:

Modelling and simulation - fundamentals. Compartmental models. Models of population dynamics - single species population, interacting population, continuous models, discrete models. Models with age distribution. Epidemic models - model of SIR structure, criss-cross models, models of venereal diseases.

Requirements:

participation in exercises (max. 5 points)

2 separate processing tasks (20 points)

test - examples, doc. Jiřina (max. 50 points)

exam - theoretical questions, Ing. Potůček (max. 25 points).

Syllabus of lectures:

1st Basic concepts of simulation. Aims and consequences of modeling and simulation. The methodology of model development. Parameter identification. Experiments. Objective reality, dynamical systems, mathematical and simulation. Models and their description. Informal and formal description. Forms of mathematical description of continuous and discrete systems.

2nd Compartmental models. Derivation of the mathematical description compartment systems. Modeling compartmental models. Examples compartmental - use in biology and medicine.

3rd Continuous and discrete models of single populations. Malthus continuous model. Continuous logistic model with constant and variable parameters. Analysis of the solution. Continuous models of single populations of late. Discrete models of single populations. Discrete variants of Malthusian and logistic model. Discrete models of single populations of late. Models with age structure - Leslie's model.

4th Models of interacting populations. Predator-prey model. Analysis model of Lotka - Volterra. Kolmogorov model. Model predator - prey delays. Models of interacting populations. Models of competition. Models of cooperation.

5th Epidemiological models - basic epidemiological models. SIR model. Kermackův - McKendrik model - derivation. Conditions for the spread of the epidemic, estimate the maximum number of patients, estimate the number of victims. SI models, the SIS .. SIR model with vaccination and vector. Models of Seir.

6th Epidemiological models - models of disease dynamics veneral. Derivation of the Cross model. Analysis of the solution. Model the spread of AIDS.

7th Detailed block diagram of the process of modeling biological systems. The methodology of model development. Inverse problem of vector-optimization parameters

8th Detailed block diagram of the process of modeling biological systems-complete. Quality estimation of model parameters, or a new proposal. additional experiment. Importance of the sensitivity function in the design of a new experiment.

9th Pharmacokinetics - linear pharmacokinetic models, examples of models, nonlinear pharmacokinetic models. PHEDSIM, analysis and use.

10th Optimal pharmacotherapy - MWPharm system analysis and application.

11th Kompartmentových modeling systems - a model of kinetics of labeled aldosterone.

12th Model of regulation of heart rate during physical stress, analysis, practical application and training process.

13th Glucose regulation model, a model of control stomach acidity.

Syllabus of tutorials:

1st MATLAB - SIMULINK / PHEDSIM. Familiarization with the environment SIMULINK / PHEDSIM. Demonstration of graphical programming to simple mathematical models.

2nd Ways of creating and analyzing a mathematical model. Demonstration in Simulink. Compartmental models. Build a mathematical model. Simulation in MATLAB-Simulink (model control of food intake).

3rd Models of single populations - Malthus continuous model. Analysis. Experiments with the model parameters in MATLAB-Simulink. Implementation of time delay in models of single populations. Discrete Malhus and logistic model.

4th Discrete model of single-population age structure - Leslie model, simulation and analysis in Simulink.

5th Models of interacting populations. Model predator - prey, design, simulation and analysis in Simulink. Model predator - prey. Determination equilibria and stability.

6th Epidemiological models. SIR model, the structure design, simulation in Simulink, the model analysis. SIR model with vaccination and vector. Cross-model - a model of the spread of AIDS.

7th Ways of creating and analyzing a mathematical model. Demonstration in Simulink / PHEDSIM systems to third Regulations - the most commonly used pharmacokinetic models. Transfer function, určitelnost model.

8th Sensitivity analysis model, a model sensitivity.

9th Pharmacokinetics - linear pharmacokinetic models, examples of models, nonlinear pharmacokinetic models. PHEDSIM, analysis and use.

10th Determine the optimal dose of the specified drugs for healthy and ill patient (MWPharm).

11th Model the kinetics of labeled aldosterone.

12th Physiological models - a model of regulation of heart rate.

13th Physiological models - a model of glucose regulation, regulatory model stomach acidity.

Study Objective:

To provide students with capability to design simple mathematical models of real biological systems and to theoretically analyse their properties, to implement the disigned models in MATLAB and/or SIMULINK, to do basic simulation experiments and to assess results of the experiments.

Study materials:

[1]Murray, J.D.: Mathematical Biology. Berlin, Springer Verlag 1993.

[2]Isham,V., Medley, G.: Models for Infectious Human Diseases. Their Structure and Relation to Data. Cambridge, Cambridge Univ. Press 1999

[3]Carson,E., Cobelli,C.: Modelling Methodology for Physiology and Medicine. San Diego, Academic Press 2001

All teaching materials for this subject are published through e-learning system at http://skolicka.fbmi.cvut.cz

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Bakalářský studijní obor Biomedicínský technik - kombinovaný (compulsory course)