Inverse Problems in Bioelectromagnetism

Data is displayed for the academic year: 2024./2025.

Lecturers

Prof.
Igor Lacković
PhD
Prof.
Darko Vasić
PhD

Course Description

In this course, students acquire knowledge of the theory of electromagnetic fields in biological tissues and solving inverse problems with special emphasis on biomedical engineering. The topics covered are: Electromagnetic characteristics of biological tissues. Electromagnetic fields and waves in biological tissues. Methods of numerical electromagnetism: finite difference method, method of moments, finite element method. Basics of the inverse problem. Linear inverse problems: discretization and methods of solution, regularization, iterative methods. Nonlinear inverse problems. Stochastic approach to inverse problems. Electronic instrumentation for electromagnetic tomography: analog signal preprocessing, interference and shielding, digital acquisition. State of the art: electrocardiography, electro- and magnetoencephalography, methods of electromagnetic tomography: electrical impedance tomography, induction tomography, magnetic resonance electrical impedance tomography.

Study Programmes

University graduate
[FER3-HR] Biomedical Engineering - study
Elective Courses (2. semester)

Learning Outcomes

  1. Apply the theory of electromagnetic fields and waves in biological tissues
  2. Describe the principles of selected methods of computational electromagnetism: integral equations, method of moments, finite difference method, finite element method
  3. Describe the features of inverse problems: uniqueness of the solution, poor conditionality, resolution
  4. Develop algorithms for solving inverse problems: discretization and solving linear inverse problems, regularization methods, iterative methods, nonlinear inverse problems and stochastic methods
  5. Describe the specifics of electronic instrumentation for electromagnetic tomography
  6. Analyze the application of inverse methods in electrocardiography, electro- and magnetoencephalography, and methods of electromagnetic tomography: electrical impedance tomography, induction tomography, magnetic resonance electrical impedance tomography

Forms of Teaching

Lectures

Interactive lectures

Seminars and workshops

Individual work and group case study

Week by Week Schedule

  1. Lectures: Electromagnetic characteristics of biological tissues
  2. Lectures: Electromagnetic fields and waves in biological tissues
  3. Lectures: Methods of numerical electromagnetism: finite difference method
  4. Lectures: Methods of numerical electromagnetism: method of moments
  5. Lectures: Methods of numerical electromagnetism: finite element method
  6. Lectures: Basic characteristics of inverse problems
  7. Lectures: Linear inverse problems: discretization and methods of solving, regularization
  8. Lectures: Midterm exam
  9. Lectures: Iterative methods and nonlinear inverse problems
  10. Lectures: Stochastic approach to inverse problems
  11. Lectures: Electronic instrumentation for electromagnetic tomography: analog signal preprocessing, interference and shielding
  12. Lectures: Electronic instrumentation for electromagnetic tomography: digital acquisition
  13. Lectures: State of the art: Electrocardiography, electro- and magnetoencephalography, electrical impedance tomography
  14. Lectures: State of the art: induction tomography and magnetic resonance electrical impedance tomography
  15. Lectures: Final exam

Literature

(.), Per Christian Hansen: Dicrete Inverse Problems - insights and algorithms, SIAM, Philadelphia, USA, 2010,
(.), Richard C. Aster, Brian Borchers, Clifford H. Thurber: Paramter estimation and inverse problems, 2nd ed., Academic Press, Oxford, UK, 2013,

General

ID 261436
  Summer semester
5 ECTS
L3 English Level
L1 e-Learning
30 Lectures
0 Seminar
0 Exercises
0 Laboratory exercises
0 Project laboratory
0 Physical education excercises

Grading System

Excellent
Very Good
Good
Sufficient

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