1 / 50

Mathematics - ICT - Medicine

Mathematics - ICT - Medicine. Presentation. Per Henrik Hogstad. University of Agder - Mathematics - Statistics - Physics (Main subject: Theoretical Nuclear Physics) - Computer Science - Programming / Objectorienting - Algorithms and Datastructures - Databases

gay-holt
Download Presentation

Mathematics - ICT - Medicine

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

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. MathematicsBachelor / 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 Survey Exam - Physics Comments from the students - 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.

  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. MathematicsParabel

  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 Mathematics - Computer Science - Medicine SINTEF Unimed Ultrasound in Trondheim The Norwegian Radiumhospital in Oslo Sørlandet hospital in Kristiansand / Arendal

  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 OsloLinear Accelerator - Control of the Linear Accelerator - Databases (patient/employee/activity)- Computations of patient positions Patient Database Linear Accelerator Computer

  16. Mathematical Transformation of Medical Images

  17. Detector Metal Detector Mathematics

  18. Image Transformation

  19. Transformation Car Repair Hospital Home

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

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

  22. Analog Digital Music - Digital Ren tone Reell tone Digitalisering Tabell FourierTransform Sammensetn av rene toner Integrasjon Derivasjon

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

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

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

  26. Fourier TransformationFourier Serie N=2 N=10

  27. Analog - DigitalFourier Transformation

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

  29. Wavelet TransformMorlet Wavelet - Non-visible Oscillation

  30. WaveletsNew 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): L2(R )

  32. Wavelet TransformMorlet WaveletFourier / Wavelet Fourier Wavelet

  33. Mammography Seismic The Norwegian RadiumhospitalMammographyMicro-calcificationsWavelet Transformation - Mexican Hat ECG

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

  35. Wavelet TransformMammography - Video

  36. Morlet Osteroporosis External part External part E/I bone edge E/I bone edge

  37. Ultrasound Image - Edge detectionSINTEF – 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. SvevningPiano 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 medøkende frekvens. Svevningstonens frekvens er lik differensen mellom frekvensene til de to pianofrekvensene.

  42. MicrocosmosDifferent parts of microcosmos in our daily life Mobile phone Electricity TV Medicine Magnetic resonance New energy Induction Semiconductor

  43. MicrocosmosLHC - Large Hadron Collider

  44. MRIMagnetic Resonance Imaging

  45. PETEmission 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 imagesthat 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 MedicineSafety Calculator

  48. HeartCirculation

  49. Surgery Simulator

  50. END

More Related