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Mathematics - ICT - Medicine. Presentation Per Henrik Hogstad University of Agder -Mathematics -Statistics -Physics(Main subject: Theoretical Nuclear.

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Presentation on theme: "Mathematics - ICT - Medicine. Presentation Per Henrik Hogstad University of Agder -Mathematics -Statistics -Physics(Main subject: Theoretical Nuclear."— Presentation transcript:

1 Mathematics - ICT - Medicine

2 Presentation Per Henrik Hogstad University of Agder -Mathematics -Statistics -Physics(Main subject: Theoretical Nuclear Physics) -Computer Science -Programming / Objectorienting -Algorithms and Datastructures -Databases -Digital Image Processing -Supervisor Master Thesis -Research -Mathematics of Wavelets + Computer Application Wavelets / Medicine -SimReal+(SimReal + SimVideo)

3 Mathematics Bachelor / Master Bachelor - Master Fourier / Wavelets Transformation Theory Vector Field - Vector Calculus Linear Algebra - Vector Space Matrix Derivation / Integration Trigonometry Vector Algebra Basic Mathematics University

4 Projects External Projects Mathematics / Physics / Statistics / ICT Internal Projects SimReal+ (SimReal + SimVideo)

5 SimReal+ Interactice Learning Tool in Mathematics / Physics / Statistics / Computer Science Video Lesson / Live Streaming / Video Simulation / Interactive Simulation / Exercise / Applicaction Video Lesson Streaming Video Simulation Interactive Simulation Exercise Application

6 Comments / Results - A great supplement, and very good academic contents - A great way to repeat past lectures - I wish this could be used in all my courses - Enables me to get a better understanding of the subject - Extremely impressive that you have spent all this time to create such a fantastic tool. Survey Exam - Physics Comments from the students

7 SimReal+ - Research Brekke: LICE conference London International Conference on Education Brekke/Hogstad:Journal New teaching methods Using computer technology in physics and mathematics Elira Curri:Master Thesis (UiA, Albania) Ninni Marie Hogstad:Master Thesis (UiA)

8 Mathematics Parabel

9 SimReal+ Calculator - Graph - Function Analysis - Built in Function

10 SimReal+ Calculator - Regression Analysis

11 Projects - SimReal+ External Projects Mathematics / Physics / Statistics / ICT Internal Projects SimReal+ (SimReal + SimVideo)

12 Mathematical Applications

13 External Projects SINTEF Unimed Ultrasound in Trondheim The Norwegian Radiumhospital in Oslo Sørlandet hospitalin Kristiansand / Arendal Mathematics - Computer Science - Medicine

14 The Norwegian Radiumhospital in Oslo -Control of the Linear Accelerator -Databases (patient/employee/activity) -Computations of patientpositions -Mathematical computations of medical image information -Different imageformat (bmp, dicom, …) -Noise Removal -Graylevel manipulation (Histogram, …) -Convolution, Gradientcomputation -Multilayer images -Transformations (Fourier, Wavelet, …) -Mammography -... Wavelet

15 The Norwegian Radiumhospital in Oslo Linear Accelerator -Control of the Linear Accelerator -Databases (patient/employee/activity) -Computations of patient positions Patient Database Computer Linear Accelerator

16 Mathematical Transformation of Medical Images

17 Detector Metal Detector Mathematics

18 Image Transformation

19 Transformation Home Car Repair Hospital

20 Transformation Computing - Addition 4 + 16 = 20 2 + 8 = 10 Room 1 Room 2 Transformation

21 Transformation Computing - Logarithm 8 * 32 = 256 3 + 5 = 8 Rom 1 y Rom 2 x Transformasjon

22 Music - Digital Ren toneReell tone Digitalisering Tabell FourierTransformSammensetn av rene toner IntegrasjonDerivasjon AnalogDigital

23 Transformation Theory Transformasjon f(x) F(u) Room 1Room 2 f(x) = T -1 (F(u)) F(u) = T[f(x)]

24 Transformation Theory Integral Transformation Transformation Theory Integral Transformation f(…) F(…) Room 1Room 2 f(…) = T -1 (F(…)) F(…) = T[f(…)]

25 Transformation Theory Integral Transformation Wavelet - Laplace - Fourier Transformation Theory Integral Transformation Wavelet - Laplace - Fourier f(…) F(…) Fourier Wavelet Laplace

26 N=2 N=10 Fourier Transformation Fourier Serie

27 Analog - Digital Fourier Transformation

28 Transformation Theory x T[f(x)] T -1 [F(a,b)] f(x)F(a,b) a b

29 Wavelet Transform Morlet Wavelet - Non-visible Oscillation

30 Wavelets New mathematical method with many interesting applications Divide a function into parts with frequency and time/position information Signal Processing-Image Processing-Astronomy/Optics/Nuclear Physics Image/Speech recognition-Seismologi-Diff.equations/Discontinuity …

31 Definition of The Continuous Wavelet Transform CWT The continuous-time wavelet transform (CWT) of f(x) with respect to a wavelet  (x): L 2 (R )

32 Wavelet Transform Morlet Wavelet Fourier / Wavelet Fourier Wavelet

33 The Norwegian Radiumhospital Mammography Micro-calcifications Wavelet Transformation - Mexican Hat ECG Mammography Seismic

34 The Norwegian Radiumhospital Mammography Micro-calcifications Diameter Relative contrast Number of microcalcifications Mathematical tranformation of the mammography imaging Mammography phantom Phantom information Transformed image

35 Wavelet Transform Mammography - Video

36 Osteroporosis External part E/I bone edge Morlet

37 Ultrasound Image - Edge detection SINTEF – Unimed – Ultrasound - Trondheim -Ultrasound Images -Egde Detection -Noise Removal -Egde Sharpening -Edge Detection Prosthesis

38 Ultrasound

39 Doppler-effekt Lytter L beveger seg mot / fra lyd-kilden S samtidig som S også beveger seg.

40 Svevning To lyd-kilder med litt avvikende frekvens gir opphav til en resultant-bølge som inneholder varierende amplitude. Frekvensen som resultant-amplituden varierer med kalles svevnings-frekvensen. Svevningsfrekvensen er differensen mellom enkelt-frekvensene

41 Svevning Piano To stk piano spiller samme a-tone med frekvens 440 Hz. Ved å la det ene pianoet endre sin a-tone-frekvens til henholdvis 441 Hz, 442 Hz og 443 Hz, hører vi en svevningstone med økende frekvens. Svevningstonens frekvens er lik differensen mellom frekvensene til de to pianofrekvensene.

42 Microcosmos Different parts of microcosmos in our daily life Electricity Mobile phone TV Induction Semiconductor Medicine Magnetic resonanceNew energy

43 Microcosmos LHC - Large Hadron Collider

44 MRI Magnetic Resonance Imaging

45 PET Emission of Positrons PET radiotracer (18F fluorodeoxyglucose (FDG)) + radioactive fluorine. Natural decay includes emmission of positrons that reach with electrons (annihilaation) in the body produces energy in the form of a pair of photons. The PET skanner, which is able to detect these photons, creates three-dimensional images that show how the FDG is distributed in the area of the body. Areas where a large amount of FDG accumulates, called ’hot spots’ because they appear more intense than surrounding tissue, indicate that a high level of chemical activity or metabolism is occuring there.

46 Infrared camera - Wavelets

47 Calculator in Medicine Safety Calculator

48 Heart Circulation

49 Surgery Simulator

50 END


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