This presentation discusses nuclear spin and relaxation in NMR, detailing the structure and properties of protons and neutrons. It explains longitudinal and transverse relaxation processes, their causes, and factors affecting T1 and T2 relaxation times in different tissues. The document also touches on quantum mechanics and the role of spectral density in relaxation phenomena.

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

3. The Atomic Nucleus Proton : mass = 1.67 x 10 -27 kg charge = 1.06 x 10 -19 C spin = ½ Neutron : mass = 1.67 x 10 -27 kg no charge spin = ½

4. The Atomic Nucleus Proton : mass = 1.67 x 10 -27 kg charge = 1.06 x 10 -19 C spin = +½ made up of 3 quarks (2 up, 1 down) Neutron : mass = 1.67 x 10 -27 kg no charge spin = ½ made up of 3 quarks (1 up, 2 down) Q D Q U Q U proton

5. What is Spin?? classical mechanics : spin is the rotation of a body about its own center of mass quantum mechanics : spin refers not to rotation but to the presence of angular momentum. For particles that cannot be broken down into smaller subunits spin is an inherent physical characteristic, just like mass or charge.

6. Nuclear Spin An unpaired neutron or proton will have non-zero spin. Therefore, there is an angular momentum, m (aka the magnetic quantum number) m approximately represents the direction of the angular momentum vector. m ranges from – l to + l , in integer steps, where l is the azimuthal quantum number. m : spin angular momentum h : Planck’s constant γ : gyromagnetic ratio

7. Magnetic Resonance

8. Magnetic Resonance transition energy

9. Magnetic Resonance α β transition energy

10. Relaxation Relaxation describes how a spin returns to equilibrium. * There is no transverse magnetization * There is no phase coherence * The distribution of spins follows the Boltzmann Distribution:

11. Relaxation Two types of relaxation Longitudinal relaxation: along the axis of the external magnetic field Transverse relaxation: perpendicular to the external magnetic field

12. What Causes Relaxation? Magnetic fields are generated within the sample, from 1) spins interacting with other spins 2) spins interacting with the surrounding environment

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

29. Relaxation… In order to cause a single spin to relax, the local spectral density must be equal to the Larmor frequency, At a given frequency , the spectral density is highest when

30. Relaxation… In order to cause a single spin to relax, the local spectral density must be equal to the Larmor frequency, At a given frequency , the spectral density is highest when T 1

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…)

40. Quantum Mechanical Notations There are 4 sets of Quantum Numbers. These describe the energies of electrons in the atom. principal quantum number azimuthal quantum number magnetic quantum number denotes the energy levels available in a subshell spin quantum number