• Biomedical Engineering, Semester 1, position 5

The goal of this subject is to teach a student to apply fractal and multi-fractal system theory in a field of biomedical engineering; to learn to use mathematical apparatus of fractal analysis and modelling; to master fractal image processing and fractal signal analysis; to learn to define diagnostic parameters, algorithms and instruments for determining functional conditions of organs and organism (normal conditions and pathological conditions).

Upon successful completion of this course, students will be able to: •Assess whether the objects have fractal properties and describe the fractal behavior of the systems by properly chosen method of fractal analysis •Create fractal algorithms for image analysis and signal analysis •Perform calculation of the fractal dimension using modern methods •Define diagnostic parameters for determining the functional states of tissues, organs and organism based on fractal dimension

Fundamentals of classic and quantum physics. Fundamentals of classical and quantum information. Cantor's diad-triad set. Laws of big numbers. Deterministic chaos. Mathematical basis of fractal and multifractal theory. Fractals and fractal dimensions. Fractal analysis of signals and images. Applications of fractal analysis in biomedical engineering. Applications of fractal analysis in cancer diagnostics. Applications of fractal analysis in mechanical engineering.

Fractal dimension and lacunarity calculus for mathematically generated fractal object. Fractal dimension and lacunarity calculus applications for medical images of skin lesions.

Defined by the study curriculum of Biomedical engineering module learning resources

Koruga,Dj., Matija, L., Munćan, J., Written course material (handouts)

Total assigned hours: 75

New material: 25
Elaboration and examples (recapitulation): 5

Auditory exercises: 14
Laboratory exercises: 6
Calculation tasks: 2
Seminar paper: 4
Project: 2
Consultations: 0
Discussion/workshop: 2
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 6
Review and grading of the project: 0
Test: 0
Test: 4
Final exam: 5

Activity during lectures: 5
Test/test: 30
Laboratory practice: 0
Calculation tasks: 10
Seminar paper: 15
Project: 0
Final exam: 40
Requirement for taking the exam (required number of points): 40

Koруга, Ђ.,Фрактална механика: Класично-квантни феномени у природи, биологији и инжењерству, DonVas, Београд, 2013; Brown, C., & Liebovitch, L. (2010). Fractal analysis (Vol. 165). Sage.; Manddelbrot, B.B., The Fractal geometry of nature, W.H.Freeman and Co., New York, 1983; Rangayyan, R. M. (2004). Biomedical image analysis. CRC press.; Nonnenmacher, T. F., Losa, G. A., & Weibel, E. R. (Eds.). (2013). Fractals in biology and medicine. Birkhäuser.