Introduction to NMR Physics

1. Terry M. Button, Ph.D. Introduction to NMR Physics

2. Tiny Magnets Nucleons behave as small current carrying loops. Such current carrying loops give rise to a small magnetic field.

3. Tiny Magnets Like nucleons pair such their net magnetic fields cancel. Only nuclei with unpaired nucleons have magnetic properties.

4. Nuclear Spin Quantum Number I is quantized in half units of h: 0, �, 1, etc� Nuclear magnetic moment is proportional to I: ? = ?Ih

5. Which nuclei are useful? Not useful for MRI (even-even, I =0): 4 He 12C 16O Useful for MRI (one unpaired): 1H 13C 31P 129Xe

6. Magnetic Moment

7. Effect of Applied Field - Classical An external magnetic field (Bo) causes the proton to precess about it. Larmor (precessional) frequency: fL = gBo/2?. For protons fL is approximately 42 MHz/Tesla.

8. Magnetization A sample of protons will precess about an applied field. The sample will have: a net magnetization along the applied field (longitudinal magnetization). no magnetization transverse to the applied field (transverse magnetization).

9. Classical Picture of Excitation A second field (B1) at the fL and at right angles to Bo will cause a tipping of the longitudinal magnetization. The result is a net transverse component; this is what is detected in MRI. B1 is radiofrequency at fL.

10. RF Excitation for Transverse Magnetization

12. Signal from the Free Induction Decay

13. Longitudinal Relaxation Relaxation of the longitudinal component to its original length is characterized by time constant T1 Spin lattice relaxation time Tumbling neighbor molecules produce magnetic field components at the Larmor frequency resulting in relaxation. following a 90o tip, T1 provides recovery to [1-1/e] or 63% of initial value.

14. T1

15. Transverse Relaxation Relaxation of the transverse magnetization to zero is characterized by time constant T2 Spin-spin relaxation time. following a 90o tip, reduction to 1/e or 37% of initial value. T2* combined dephasing due to T2 and field inhomogeneity.

16. T2

17. In vivo Relaxation T1 > T2 > T2* T1 increases with Bo T2 is not strongly effected.

18. Relaxation

19. Application of FFT to S vs. t FT FFT provides real (a) and imaginary (bi) components at frequencies dictated by Nyquist sampling Magnitude: [a2 + b2]1/2 Phase: arctan (b/a) The magnitude Has center frequency at the Larmor frequency The decay is contained within an exp (-t/T2*) envelope: T2* determines the line width

20. Spectra

21. Effect of Applied Field - Quantum Mechanical Protons can be in one of two state: aligned with the field (low energy) aligned against the field (high energy) The energy separation is: E = h fL.

22. Quantum Mechanical

23. State Population Distribution

24. Chemical Shift Electrons in the molecule shield the nucleus under study: Bobserved = Bapplied - ?B = Bapplied (1 - ?) The chemical shift is measured in frequency relative to some reference: ? = [(fsample � freference )/freference ]x106 ppm Usually freference is tetramethylsilane (TMS) for in vitro. In the body fat and water 3.5 ppm shift.

25. In Body

26. Recovery of Rapid T2* Signal Loss Using Spin-Echo

27. Spin Echo

28. Multi Echo Decay � T2

29. Introduction to Image Formation

30. Simple NMR Experiment

31. Modify with a Gradient

32. Linear Gradient - Simple Projection

33. Rotating Gradient Provides Projection Data

34. 2D Filtered Backprojection Rotating gradient Difficult to collect projections exactly though the origin. Artifacts. Most often 2D FT used in present MR.