1. Charged particle

2. Moving charge = current

3. Associated magnetic field - B

7. Macroscopic picture (typical dimensions (1mm) 3 ) Consider nucleus of hydrogen in H 2 O molecules: proton magnetization randomly aligned

9. Macroscopic picture (typical dimensions (1mm) 3 ) BoBo M Apply static magnetic field: proton magnetization either aligns with or against magnetic field

14. Macroscopic picture (typical dimensions (1mm) 3 ) Can perturb equilibrium by exciting at Larmor frequency  = (  /2  ) B o

15. BoBo M xy Can perturb equilibrium by exciting at Larmor frequency  = (  /2  ) B o With correct strength and duration rf excitation can flip magnetization e.g. into the transverse plane

16. Spatial localization - reduce 3D to 2D BoBo B z y x z

17. z BoBo B rf Spatial localization - reduce 3D to 2D B z y x z

18. z BoBo B B z y x z

19. z B o +G z.z B Spatial localization - reduce 3D to 2D B z y x z

20. z B o +G z.z B Spatial localization - reduce 3D to 2D B z rf resonance condition y x z

21. Spatial localization - reduce 3D to 2D z B o +G z.z B Spatial localization - reduce 3D to 2D B z y x y x z

22. MR pulse sequence B o + G z.z B z GzGz GxGx GyGy rf time

23. Spatial localization - e.g., in 1d what is  (x) ? Once magnetization is in the transverse plane it precesses at the Larmor frequency  = 2  B(x) M(x,t) = M o  (x) exp(-i. .  (x,t)) If we apply a linear gradient, G x,of magnetic field along x the accumulated phase at x after time t will be:  (x,t) = ∫ o t x G x (t') dt' (ignoring carrier term) 

24. Spatial localization - What is  (x) ? x BoBo B  no spatial information object x S(t)

25. Spatial localization - What is  (x) ? x B o +G x x B x object

26. Spatial localization - What is  (x) ? x B o +G x x B  x object S(t)

27. Spatial localization - What is  (x) ? x B o +G x x B x Fourier transform object image x  (x) S(t)

28. For an antenna sensitive to all the precessing magnetization, the measured signal is: S(t) = ∫ M(x,t) dx = M o ∫  (x) exp (-i.( . G x ) x.t) dx therefore:  (x) = ∫ M(x,t) dx = M o ∫ S(t) exp (i. c. x.t) dt

29. MR pulse sequence GzGz GxGx GyGy rf time

30. For NMR in a magnet with imperfect homogeneity, spin coherence is lost because of spatially varying precession Hahn (UC Berkeley)showed that this could be reversed by flipping the spins through 180° - the spin echo In MRI, spatially varying fields are applied to provide spatial localization - these spatially varying magnetic fields must also be compensated - the gradient echo

31. MR pulse sequence (centered echo) GzGz GxGx GyGy rf time ADC

32. MR pulse sequence for 2D GzGz GxGx GyGy rf time ADC

33. GxGx spins aligned following excitation

34. GxGx dephasing

35. GxGx ADC

36. GxGx rephasing ADC

37. GxGx rephased echo ADC

38. GxGx

39. GxGx

41. + + + + + + + + + + + + + + + + + +

42. + + + + + + + + + +

43. + + + + + + + + + +

44. + + + + + + + + + +

45. + + + + + + + + + +

46. + + + + + + + + + +

47. + + + + + + + + + +

48. + + + + + + + + + +

49. + + + + + + + + + + FOV

50. ADC + + + + + + + + + + FOV N = resolution

51. FOV FOV smaller than object

52. FOV

53. FOV smaller than object: - wrap-around artifact

54. MR pulse sequence for 2D GzGz GxGx GyGy rf time ADC

55. MR pulse sequence for 2D GzGz GxGx GyGy rf time ADC phase encoding 128

56. MR pulse sequence for 2D GzGz GxGx GyGy rf time ADC phase encoding 64

57. MR pulse sequence for 2D GzGz GxGx GyGy rf time ADC phase encoding 0

58. MR pulse sequence for 2D GzGz GxGx GyGy rf time ADC phase encoding -64

59. MR pulse sequence for 2D GzGz GxGx GyGy rf time ADC phase encoding -127

60. k-space

62. Fourier

63. Fourier transform(ed)

64. inner k-spaceFourier transform overall contrast information

65. outer k-spaceFourier transform edge information