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Charged particle

Charged particle. Moving charge = current. Associated magnetic field - B. Macroscopic picture (typical dimensions (1mm) 3 ). Consider nucleus of hydrogen in H 2 O molecules: proton magnetization randomly aligned. Macroscopic picture (typical dimensions (1mm) 3 ).

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Charged particle

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  1. Charged particle

  2. Moving charge = current

  3. Associated magnetic field - B

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

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

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

  7. 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

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

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

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

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

  12. 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

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

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

  15. 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

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

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

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

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

  20. 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

  21. MR pulse sequence rf Gz Gx Gy time

  22. 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

  23. MR pulse sequence (centered echo) rf Gz Gx ADC Gy time

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

  25. Gx spins aligned following excitation

  26. Gx dephasing

  27. Gx ADC dephasing

  28. Gx ADC rephasing

  29. Gx ADC echo rephased

  30. Gx ADC

  31. Gx ADC

  32. + + + + + + + + + + + + + + + + + + ADC

  33. + + + + + + + + + + ADC

  34. + + + + + + + + + + ADC

  35. + + + + + + + + + + ADC

  36. + + + + + + + + + + ADC

  37. + + + + + + + + + + ADC

  38. + + + + + + + + + + ADC

  39. + + + + + + + + + + ADC

  40. + + + + + + + + + + ADC FOV

  41. + + + + + + + + + + ADC FOV = resolution N

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