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Nmr relaxation times

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Nmr relaxation times

  1. 1. NMR Relaxation Times Stuart Clare
  2. 2. Review • NMR signal depends on the quantum mechanical properties of nuclei. • Larmor equation relates field to frequency. 0Bγω = • Spins excited by a B1 field, perpendicular to the B0, oscillating at this frequency.
  3. 3. • Time to reach equilibrium is governed by thermal processes. • The return to equilibrium is generally exponential and governed by the equation • T1 is called the spin-lattice relaxation time. The Simplified Bloch Equation 1 0 T MM dt dM zz − =
  4. 4. • The relative populations of the spin states can be altered in a well defined way by the application of a resonant B1 field in the xy- plane. • Any fluctuating magnetic field that has a component in the xy-plane that oscillates at the resonant frequency can induce transitions between the spin states. The T1 Relaxation Process
  5. 5. Lattice Thermal Processes B0 A Xθ r 32 3 cossin r Bxy γ θθ  =
  6. 6. Lattice Thermal Processes • The frequency distribution of the motion of a randomly tumbling molecule is expressed in terms of the spectral density • τc is called the correlation time and is a characteristic time scale of molecular motion. ( ) 22 1 c c J τω τ ω + =
  7. 7. T1 Relaxation Time • It can be shown that where ω0 is the resonant frequency of the spin system. 22 0 2 1 1 1 c c xyB T τω τ + ∝
  8. 8. Recovery Curve time Signal             −−= 1 0 exp1 T t SS
  9. 9. What effect does T1 have on Images? 90° 90° 90° 90° 90° Mz
  10. 10. What effect does T1 have on Images? t = 0 t = 3s t = 6s t = 9s t = 12s
  11. 11. • Assume the steady state has been reached. • Use a flip angle of θ degrees. • Find a condition where the transverse magnetization following the flip is maximized. The Ernst Angle       −= 1 expcos T TR θ
  12. 12. T1-Weighted Images
  13. 13. T1-Weighted Images
  14. 14. T1-Weighted Images
  15. 15. T1-Weighted Images
  16. 16. T1 Mapping • Inversion recovery method. • Invert the magnetization with a 180° pulse. • Wait a period TI and inspect the recovery of the longitudinal magnetization.             −−= 1 0 exp21 T TI SS
  17. 17. Transverse Relaxation • Longitudinal relaxation is driven by field oscillations in the transverse plane. • Transverse relaxation is driven by field oscillations in the longitudinal plane. • Random fluctuations in B0 experienced by a nucleus cause the resonant frequency of that spin to change.
  18. 18. Transverse Relaxation • The return to equilibrium is governed by the Bloch equation. • T2 is called the spin-spin relaxation time 2T M dt dM xyxy −=
  19. 19. Transverse relaxation Rotating frame B0 t
  20. 20. Transverse Relaxation • If the field experienced by the molecule is purely random then the effect would time average to zero. • Correlations in the motion cause a range of frequencies. • In solids where there is no molecular tumbling the range of resonances is very broad.
  21. 21. Transverse Relaxation Long T2 Short T2 frequency
  22. 22. Relating T2 to Spectral Density ( )0 1 2 2 JB T z∝ ( )0 2 1 1 ωJB T xy∝ Transverse relaxation Longitudinal relaxation ( ) cJ τ≈0 ( ) 22 0 0 1 2 c c J τω τ ω + =
  23. 23. Decay Curve time Signal       −= 2 0 exp T t SS
  24. 24. What is T2 * ? • Spin-spin relaxation represents a loss of coherence in the transverse magnetization due to local effects on spin. • Loss of the coherence of the transverse magnetization also occurs as a result of bulk magnetic effects
  25. 25. What is T2 * ?
  26. 26. The Spin Echo
  27. 27. The Spin Echo
  28. 28. The Spin Echo
  29. 29. The Spin Echo
  30. 30. The Spin Echo
  31. 31. The Spin Echo
  32. 32. The Spin Echo • A spin echo can refocus spins that are sitting in a time invariant B0 field. • A spin echo cannot refocus T2 dephasing. • A spin echo cannot refocus spins that have experienced a time varying field, for example diffusing molecules.
  33. 33. What effect does T2 * have on Images? • T2 and T2 * have the same effect on images. • T2 * effects dominate when there is no spin echo. • From now on, we will assume that T2* is more important, since in imaging it often is.
  34. 34. What effect does T2 * have on Images? • Effect of echo time
  35. 35. What effect does T2 * have on Images? • Effect of echo time
  36. 36. What effect does T2 * have on Images? • Effect of echo time
  37. 37. What effect does T2 * have on Images? • Effect of echo time
  38. 38. What effect does T2 * have on Images? × = ⊗ = ⇓ ⇓ ⇓FT FTFT Perfect FID T2 * Decay Actual FID Perfect Image Point Spread Function Actual Image
  39. 39. What effect does T2 * have on Images? × = ⊗ = ⇓ ⇓ ⇓FT FTFT Perfect FID T2 * Decay Actual FID Perfect Image Point Spread Function Actual Image
  40. 40. What effect does T2 * have on Images?
  41. 41. What effect does T2 * have on Images? • Effect of linewidth (point spread function) Acquire Acquire
  42. 42. What effect does T2 * have on Images? • 2DFT imaging – Each line of k-space acquired with a new fid. – No T2 effect in the phase encode direction. (taq= 0) – Small T2 effect in the read direction. (taq≈ 5ms) • EPI – Whole of k-space acquired in one fid. – Small T2 effect in the read direction. (taq≈ 0.5ms) – Large T2 effect in the phase encode direction. (taq≈ 40ms)
  43. 43. T2 Mapping • Acquire a number of images with a different value of echo time. • Fit an exponential decay curve to the pixel values for each TE. • Multiple spin echo technique. TE/2 TE 2 TE 3 TE 90° 180° 180° 180°

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