Mathemetical software for biomedicine

Lecturer:

Tutor:

Supervisor:

Department of Natural Sciences

Synopsis:

Some physical models application in biomedical processes and their numerical solution with the aid of mathematical SW, partial differential equations and formulation of respective problems, classification of linear 2nd order PDEs, examples of individual types of equations and formulation of problems, numerical solution of the problems by means of the finite difference method.

Requirements:

Maximum 3 absences during the semester for serious reasons like sickness, injury etc. (medical certificate required).

Minimum 50% (i.e. 10 pts) evaluation at each of the 2 tests, each test consisting of 4 tasks, a task evaluated max. 5 pts each (the tests are taken in 6th and 13th week of the semester).

Syllabus of lectures:

1. Mathematical SW as an aid for solving problems - general principles

2. Elementary physical processes and their modeling.

3. Selected models for respiratory system.

4. Selected blood flow processes and their modeling.

5. Population dynamics.

6. Linear 2nd order partial differential equations classification.

7. Formulation of problems for Poisson (Laplace) equation.

8. Finite difference method for solving Dirichlet boundary value problem for Poisson (Laplace) equation in 2D, 3D.

9. Formulation of problems for a heat transfer equationin 1D, 2D.

10. Finite difference method for solving initial and boundary value problem for a heat transfer equation in 1D, 2D.

12. Formulation of problems for a wave equation.

13. Finite difference method for solving initial and boundary value problem for a wave transfer equation in 1D, 2D.

14. Numerical solution of an inverse problem for PDEs.

Syllabus of tutorials:

1. Mathematical SW as an aid for solving problems - general principles.

2. Examples of elementary physical processes their modeling and solving.

3. Examples of selected models for respiratory system.

4. Examples of selected blood flow processes and their models solving.

5. Population dynamics examples.

6. Linear 2nd order partial differential equations classification.

7. Examples of practical use of boundary value problems for Poisson (Laplace) equation.

8. Numerical solution of Dirichlet boundary value problem for Poisson (Laplace) equation in 2D, 3D (finite difference method).

9. Heat transfer equation in 1D, 2D, examples.

10. Numerical solution of the initial and boundary value problem for a heat transfer equation in 1D, 2D.

12. Wave equation in 1D, 2D, examples.

13. Finite difference method for solving initial and boundary value problem for a wave transfer equation in 1D, 2D.

14. Numerical solution of an inverse problem for PDEs.

Study Objective:

The goal of the subject is to introduce to the students models and some methods of solving selected biomedical problems with the aid of mathematical SW.

Study materials:

Studijní materiály

Doňar B., Zaplatílek K., -- MATLAB pro začátečníky, 1. díl, BEN, 2003

Holčík J., -- Modelování a simulace biologických systémů, skriptum ČVUT-- FBMI, 2006

Kvasnica J.,-- Matematický aparát fyziky, Academia, 2. vyd. 1997

Dont M. - Úvod do parciálních diferenciálních rovnic

E. Feuerstein - Řešené příklady z numerické matematiky, pracovní texty

Doporučená literatura:

Doňar B., Zaplatílek K., MATLAB tvorba uživatelských aplikací, 2.díl, BEN, 2006

Moler C.: Numerical computing with MATLAB, Mathworks, PDF

Hannon B., Ruth M. - Modeling Dynamic Biological Systems, Springer, 1999

Hoppensteadt F., Peskin Ch. - Modeling and Simulation in Medicine and the Life Sciences, Springer, 2002

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Navazující magisterský studijní obor Přístroje a metody pro biomedicínu (compulsory elective course)