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Introduction to NMR Physics

Introduction to NMR Physics. Terry M. Button, Ph.D. Tiny Magnets. Nucleons behave as small current carrying loops. Such current carrying loops give rise to a small magnetic field. Tiny Magnets. Like nucleons pair such their net magnetic fields cancel.

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Introduction to NMR Physics

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

  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 ħ: • 0, ½, 1, etc… • Nuclear magnetic moment is proportional to I:  = Iħ

  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 N S A current carrying loop (l by w) will experience a torque:  = 2 (w/2) I dl x B  = IA x B  =  x B, where  is the 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. B0

  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). B0 M

  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 B0 B0 90o RF at fL M M

  11. Signal from the Free Induction Decay S exp(-t/T2*) M t

  12. 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.

  13. T1

  14. 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.

  15. T2

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

  17. Relaxation

  18. 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

  19. Spectra long T2* I short T2* f

  20. 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.

  21. Quantum Mechanical E = hfL • Protons moving from low to high energy state require radiofrequency. • Protons moving from high to low energy release radiofrequency.

  22. State Population Distribution • Boltzmann statistics provides population distribution these two states: • N-/N+ = e-E/kT where: • E is the energy difference between the spin states • k is Boltzmann's constant (1.3805x10-23 J/Kelvin) • T is the temperature in Kelvin. • At physiologic temperature approximately only 1 in 106 excess protons are in the low energy state. -.

  23. 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.

  24. In Body • Fat and water have 3.5 ppm shift; at • 1.5 T this amounts to 220 Hz. water I lipid 220Hz f

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

  26. Spin Echo echo 90o 180o TE/2 TE/2 Bo +  Bo -  Bo t = 0 t = TE/2 Echo! t = TE

  27. Multi Echo Decay – T2 exp(-t/T2) exp(-t/T2*)

  28. Introduction to Image Formation

  29. Simple NMR Experiment Bo S I FFT t fL f f

  30. Modify with a Gradient Bo

  31. Linear Gradient - Simple Projection Bo S I FFT t f

  32. Rotating Gradient Provides Projection Data

  33. 2D Filtered Backprojection • Rotating gradient • Difficult to collect projections exactly though the origin. • Artifacts. • Most often 2D FT used in present MR.

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