Charged particle

1. Charged particle

2. Moving charge = current

3. Associated magnetic field - B

7. Macroscopic picture (typical dimensions (1mm)3 ) Consider nucleus of hydrogen in H2O molecules: proton magnetization randomly aligned

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

14. Macroscopic picture (typical dimensions (1mm)3 ) Can perturb equilibrium by exciting at Larmor frequency w = (g /2 p) Bo

15. Can perturb equilibrium by exciting at Larmor frequency w = (g /2 p) Bo Bo Mxy With correct strength and duration rf excitation can flip magnetization e.g. into the transverse plane

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

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

18. z y x Spatial localization - reduce 3D to 2D Spatial localization - reduce 3D to 2D z z B B Bo

19. z y x Spatial localization - reduce 3D to 2D Spatial localization - reduce 3D to 2D z z B B Bo+Gz.z

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

21. z y x Spatial localization - reduce 3D to 2D Spatial localization - reduce 3D to 2D y z z x B B Bo+Gz.z

22. MR pulse sequence z rf Gz Gx B Gy time Bo+ Gz.z

23. Spatial localization - e.g., in 1d what is r(x) ? Once magnetization is in the transverse plane it precesses at the Larmor frequency w = 2 p/g B(x) M(x,t) = Mor(x) exp(-i.g. f(x,t)) If we apply a linear gradient, Gx ,of magnetic field along x the accumulated phase at x after time t will be: f(x,t) = ∫ot x Gx(t') dt' (ignoring carrier term) f

24. Spatial localization - What is r(x) ? S(t) object  x B no spatial information Bo xx

25. Spatial localization - What is r(x) ? object xx B Bo+Gxx xx

26. Spatial localization - What is r(x) ? S(t) object  xx B Bo+Gxx xx

27. Spatial localization - What is r(x) ? S(t) object xx B Fourier transform Bo+Gxx image r(x) xx x

28. For an antenna sensitive to all the precessing magnetization, the measured signal is: S(t) = ∫ M(x,t) dx = Mo∫r(x) exp (-i.(g. Gx) x.t) dx therefore: r(x) = ∫ M(x,t) dx = Mo∫ S(t) exp (i. c. x.t) dt

29. MR pulse sequence rf Gz Gx Gy 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) rf Gz Gx ADC Gy time

32. MR pulse sequence for 2D rf Gz Gx ADC Gy time

33. Gx spins aligned following excitation

34. Gx dephasing

35. Gx ADC dephasing

36. Gx ADC rephasing

37. Gx ADC echo rephased

38. Gx ADC

39. Gx ADC

41. + + + + + + + + + + + + + + + + + + ADC

42. + + + + + + + + + + ADC

43. + + + + + + + + + + ADC

44. + + + + + + + + + + ADC

45. + + + + + + + + + + ADC

46. + + + + + + + + + + ADC

47. + + + + + + + + + + ADC

48. + + + + + + + + + + ADC

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

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