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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.Only nuclei with unpaired nucleons have magnetic properties.. . . . . Nucl
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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.