A powerpoint presentation on relaxation in NMR and MRI, presented at MR journal club on 18 October 2006 in the Texas Medical Center.

1. Relaxation in NMR Rebecca Marsh

2. This presentation can also be found at www.reachforthesky.com A more complete text by James Keeler (from which some of these images were taken) can be found online at http://www-keeler.ch.cam.ac.uk/lectures

7. Magnetic Resonance

8. Magnetic Resonance transition energy

9. Magnetic Resonance α β transition energy

13. Transverse ( spin-lattice ) Relaxation

14. The Dipolar Mechanism H + The overall effect is a property of BOTH nuclei. H + r Amount of interaction is proportional to 1/ r 3 and θ B 0 θ

15. The Dipolar Mechanism H + H +

16. The Dipolar Mechanism H + H +

17. The Dipolar Mechanism H + H +

18. The Dipolar Mechanism H + H +

19. The Dipolar Mechanism The dipolar mechanism acts as a way to transfer energy from spins to the surrounding system. The relaxation that results from dipolar coupling given by: Relaxation is most efficient for nuclei with large

20. A Closer Look at the Spectral Density… spin paramagnetic molecule

21. A Closer Look at the Spectral Density… spin paramagnetic molecule The local magnetic field felt by spin 1 = F 1 (t) 1

22. A Closer Look at the Spectral Density… spin paramagnetic molecule 1 2 The local magnetic field felt by spin 1 = F 1 (t) the local magnetic field felt by spin 2 = F 2 (t) The overall behavior of the system is determined by the average local magnetic field.

23. A Closer Look at the Spectral Density… spin paramagnetic molecule 1 2 The local magnetic field felt by spin 1 = F 1 (t) The local magnetic field at time t+ τ , the magnetic field felt by spin 1 = F 1 (t + τ )

24. A Closer Look at the Spectral Density… spin paramagnetic molecule 1 2 If is very small, then and As gets longer, the spin will have diffused a larger distance, and may be positive or negative. In the limit of very large , approaches zero.

25. A Closer Look at the Spectral Density… spin paramagnetic molecule 1 2 is the correlation time When , is small; when , is large.

26. A Closer Look at the Spectral Density… indicates the amount of motion present at different frequencies.

27. A Closer Look at the Spectral Density… indicates the amount of motion present at different frequencies.

28. A Closer Look at the Spectral Density… large small At a given frequency , the spectral density is highest when

31. Longitudinal Relaxation T 1

32. Why does T 1 vary by tissue? From www.revisemri.com T 1 of fat ~ 250ms ; T 1 of CSF ~ 2000ms “ free” water: pure water, rapidly moving  tumbling frequency > “ structured” water : bound to macromolecules  tumbling frequency ~ “ bound” water: motion restricted by a double bond  tumbling frequency <

33. Why does T 1 vary by field strength? From www.revisemri.com As B 0 increases, T 1 increases.

34. Why do contrast agents affect T 1 ? From www.revisemri.com Increasing the amount of oscillations at the Larmor frequency increases relaxation. Gd 3+ has 7 unpaired electrons, each of which interacts with the external magnetic field.

35. Transverse ( spin-spin ) Relaxation random phase phase coherence MR pulse relaxation disappearing phase coherence

36. Transverse Relaxation disappearing phase coherence Transverse relaxation can be caused by anything that destroys the phase coherence: 1) Local oscillating fields (from transitions between energy states) (This also causes longitudinal relaxation!) 2) Differences in local magnetic fields (not oscillations) which cause them to precess at different Larmor frequencies

37. Transverse Relaxation 2) Differences in local magnetic fields (not oscillations) which cause them to precess at different Larmor frequencies

38. Transverse Relaxation Transverse relaxation (and T 2 ) increases as the correlation time increases Longitudinal relaxation (and T 1 ) as the correlation time increases, the correlation time increases, goes through a maximum, and then decreases

39. Questions? (please be nice…)