Modelling in Physiology

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Biomedical Technology

Synopsis:

Computer simulation of physiological systems is an essential tool in the field of biomedicine. When it is not possible to perform experiments for example due to ethical or technical limitations, physiological modeling comes at hand. The use of mathematical models and system simulations involve simplification and conversion of physiological systems, with an extra attention to physical units. The course provides an overview of dynamical systems and compartmental models of cells. We introduce computer software for simulations - Matlab /with Simulink, CAD systems and Mathematica. Using knowledge and basic principles of physiology will enable us to understand basic physiological systems and their functioning - cardiovascular and respiratory system, blood flow through the heart and blood vessels, cardiac revolution and blood ejection, models of the respiratory system. Models of force and energy fields will be studied. Further we will use models of the nervous and hormonal systems, propagation of sensory signals and electrical stimuli, includingsystem response to stimulus. Models of metabolism and energy exchange are anotther domain of this subject.

Requirements:

Proposed classes take place in contact form when possible and the course ends with an oral exam, which is preceded by written test. In case when the number of students is less than 5, classes will take place in the form of guided self-study with consultations. Furthermore, it is required to prepare a written essay on a given topic. The requirement to proceed to the exam is the completion of two laboratory exercises (proven by completing the lab protocol signed by the student, the assistant of the exercises and the course leader). The protocols will be archived in the doctoral student file.

Syllabus of lectures:

Syllabus of lectures:

1. Advantages and limitations of computer simulation.

2. Analytical and symbolic solution of equations, numerical methods.

3. Physical description of the system. Dynamic systems, definitions.

4. Ordinary and partial differential equations.

5. Oscillations, nonlinear problems. Chaotic systems. Synchronization.

6. Approximate solutions, numerical accuracy and error. Stochastic systems.

7. Simulation software: MATLAB, Mathematics, CAD and others.

8. Examples of simulation in biology and physiology: Cardiovascular system.

9. Examples of simulations in biology and physiology: Respiratory system.

10. Elective lecture and conclusions

Syllabus of tutorials:

Syllabus of exercises (block form of 4 teaching hours classes):

1. Modeling of physiological systems in CAD systems: flow models (respiratory system, cardiovascular system), models of force, electric and thermal fields (hyperthermia, modeling of forces in the skeletal system, propagation of excitation by excitable tissues).

2. Modeling of physiological systems in Matlab /Simulink program: model of cardiovascular system, model of nervous system, model of digestive system, model of hormonal control, modeling of metabolism and energy exchange - heat, water, proteins, electrolytes, gases.

Study goals:

Computer simulation of physiological systems is an essential tool in the field of biomedicine, especially, when it is not possible to perform experiments due to ethical or technical limitations. The use of mathematical models and system simulations require the simplification of physiological systems. The course provides a brief overview of dynamical systems and cellular compartmental models. We introduce the basic software for simulations - Matlab /Simulink, CAD systems, Mathematica. Knowledge of general principles of simulation will enable us to understand basic physiological models - cardiovascular and respiratory system, blood flow through the heart and blood vessels, cardiac revolution and blood ejection, respiratory system. Models of force and energy fields, of the nervous and hormonal system, of electrical stimulus propagation and system response to stimulus are studied.

Study Objective:

Study materials:

1] CLAUDIO COBELLI AND EWART CARSON. Introduction to modeling in physiology and medicine. Amsterdam: Academic Press, 2008. ISBN 9780121602406.

Doporučená literatura:

[1] OTTESEN, Johnny T., Mette S. OLUFSEN a Jesper K. LARSEN. Applied mathematical models in human physiology. Philadelphia: Society for Industrial and Applied Mathematics, c2004. ISBN 978-0-89871-539-2

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: