Rotating-frame gradient fields for magnetic resonance imaging and nuclear magnetic resonance in low fields

1. A method of nuclear magnetic resonance (NMR) detection, the method comprising:

a) pre-polarizing a sample by:

applying a prepolarization field B p for a period of time, and

switching the prepolarization field off;

b) providing a static magnetic field B 0 along a first direction;

c) after switching the prepolarization field off, Fourier encoding nuclear spins in the sample by applying a rotating-frame gradient field B G superimposed on the B 0 field, wherein the B G field comprises a vector component rotating in a plane perpendicular to the first direction at an angular frequency ω in a laboratory frame; and

d) detecting a Fourier encoded NMR signal.

2. The method of claim 1 , wherein the B 0 field is inhomogeneous.

3. The method of claim 2 , wherein the degree of inhomogeneity of the inhomogeneous B 0 field is greater than 1 part in 100 over a field of view or imaging volume.

4. The method of claim 1 , wherein the angular frequency w is about at the Larmor frequency of the encoded spins.

5. The method of claim 1 , wherein the rotating-frame gradient field B G comprises a circularly polarized field.

6. The method of claim 5 , wherein the circularly polarized field comprises a superposition of two linearly polarized time-varying fields that are phase-orthogonal to each other.

7. The method of claim 1 , wherein the rotating-frame gradient field B G produces a time-independent component in a rotating frame.

8. The method of claim 1 , wherein the rotating-frame gradient field B G comprises a time-independent z gradient along a transverse direction in a rotating frame.

9. The method of claim 1 , wherein the rotating-frame gradient field B G comprises a time-independent x gradient along a transverse direction in a rotating frame.

10. The method of claim 1 , wherein the rotating-frame gradient field B G comprises a time-independent y gradient along a transverse direction in a rotating frame.

11. The method of claim 1 , wherein the rotating-frame gradient B G is substantially in the form of a(t)(zx+xz)+b(t)(zy+yz), where:

a ( t )= g cos(ω t +φ);

b ( t )= g sin(ω t +φ);

z is a unit vector along the first direction;

x is a unit vector in a laboratory frame that is perpendicular to z;

y is a unit vector in the laboratory frame that is perpendicular to both z and x;

φ is an initial phase angle; and

g is a gradient amplitude.

12. The method of claim 1 , wherein the rotating-frame gradient B G is substantially in the form of a(t)(yx+xy)+εb(t)(−xx−yy+2zz), where:

a ( t )= g cos(ω t +φ);

b ( t )= g sin(ω t +φ);

z is a unit vector along the first direction;

x is a unit vector in a laboratory frame that is perpendicular to z;

y is a unit vector in the laboratory frame that is perpendicular to both z and x;

ε is a scaling factor that can range from −1 to 1;

φ is an initial phase angle; and

g is a gradient amplitude.

13. The method of claim 1 , comprising using the NMR signal for magnetic resonance imaging (MRI) measurement.

14. The method of claim 1 , comprising using the NMR signal for high resolution NMR spectroscopy measurement.

15. The method of claim 1 , comprising using the NMR signal for a gradient diffusion measurement.

16. The method of claim 1 , wherein a ratio (ΔB max /B 0 ) of the maximum amplitude ΔB max of the rotating magnetic gradient field B G over a sample volume to the strength B 0 of the static magnetic field B 0 is greater than 0.1.

17. The method of claim 16 , wherein the ratio ΔB max /B 0 is greater than 25.

18. The method of claim 1 , wherein the B P field is applied while the B 0 field is applied.

19. The method of claim 1 , wherein the B P field is switched off before the B 0 field is applied.

20. The method of claim 1 , wherein the B G field is switched off prior to detecting the NMR signal.

21. A nuclear magnetic resonance (NMR) apparatus comprising:

a pre-polarization magnetic field generator configured to apply a pre-polarization magnetic field B P ;

a switch configured to turn off the pre-polarization magnetic field generator;

a static magnetic field generator configured to generate a static magnetic field B 0 along a first direction;

first and second sets of gradient coils collectively configured to generate a rotating-frame gradient field B G superimposed on the B 0 field;

a current supply module configured to drive a first alternating current in the first set of gradient coils and a second alternating current in the second set of gradient coils, wherein the first and second alternating currents are at least partly out of phase with respect to each other;

a detector configured to detect an NMR signal from a sample placed in the B 0 field;

a switch configured to stop current flowing through the first and second gradient coils; and

a processor configured to actuate the switch prior to detection of the NMR signal with the detector.

22. The apparatus of claim 21 , further comprising a third set of gradient coils disposed with respect to the first and second sets of gradient coils.

23. The apparatus of claim 21 , wherein the first and second sets of gradient coils are disposed geometrically orthogonal to each other.

24. The apparatus of claim 21 , wherein at least one of the first or second sets of gradient coils comprise a Maxwell pair.

25. The apparatus of claim 24 , wherein the Maxwell pair is configured to generate a magnetic field substantially of a form a(−xx−yy+2zz) when driven by the current supply module, wherein:

a is a scalar dependent on geometry and current in the coils;

z is a unit vector along the first direction;

x is a unit vector that is perpendicular to z; and

y is a unit vector that is perpendicular to both z and x.

26. The apparatus of claim 21 , wherein at least one of the first or second sets of gradient coils comprise a saddle coil.

27. The apparatus of claim 21 , wherein at least one of the first or second sets of gradient coils comprise a Golay pair.

28. The apparatus of claim 27 , wherein the Golay pair is configured to generate a magnetic field substantially of a form a(zx+xz) when driven by the current supply module, wherein:

a is a scalar dependent on the geometry of and current in the coils;

z is a unit vector along the first direction; and

x is a unit vector that is perpendicular to z and y.

29. The apparatus of claim 27 , wherein the Golay pair is configured to generate a magnetic field substantially of a form a(zy+yz) when driven by the current supply module, wherein:

a is a scalar dependent on the geometry of and current in the coils;

z is a unit vector along the first direction; and

y is a unit vector that is perpendicular to z and x.

30. The apparatus of claim 27 , wherein the Golay pair is configured to generate a magnetic field substantially of a form a(yx+xy) when driven by the current supply module, wherein:

a is a scalar dependent on the geometry of and current in the coils;

x is a unit vector perpendicular to z, a unit vector along the first direction; and

y is a unit vector that is perpendicular to both z and x.

31. The apparatus of claim 21 , wherein the first set of gradient coils comprise a first Golay pair and the second set of gradient coils comprise a second Golay pair, wherein the first and second Golay pairs are co-axial and geometrically orthogonal to each other, wherein the first Golay pair is configured to generate a magnetic field substantially of a form a(zx+xz) when driven by the current supply module and wherein the second Golay pair is configured to generate a magnetic field substantially of a form a(zy+yz) when driven by the current supply module, wherein:

a and b are scalars dependent on the geometry of and current in the coils;

z is a unit vector along the first direction;

x is a unit vector that is perpendicular to z; and

y is a unit vector that is perpendicular to both z and x.

32. The apparatus of claim 21 , wherein the first set of gradient coils comprise a Golay pair and the second set of gradient coils comprise a Maxwell pair, wherein the axis of the Golay pair is orthogonal to the axis of the Maxwell pair, wherein the Golay pair is configured to generate a magnetic field substantially of a form a(yx+xy) when driven by the current supply module and wherein the Maxwell pair is configured to generate a magnetic field substantially of a form b(−xx−yy+2zz) when driven by the current supply module, wherein:

a and b are scalars dependent on the geometry of and current in the coils;

z is a unit vector along the first direction;

x is a unit vector that is perpendicular to z; and

y is a unit vector that is perpendicular to both z and x.

33. The apparatus of claim 21 , wherein the two alternating currents are phase-orthogonal to each other.

34. The apparatus of claim 33 , wherein the two alternating currents are sinusoidal currents of angular frequency ω that are 90° out of phase with respect to each other.

35. The apparatus of claim 34 , wherein the angular frequency ω is about at a Larmor frequency of a chemical species desired to be detected.

36. The apparatus of claim 21 , wherein the detector is an induction coil.

37. The apparatus of claim 21 , wherein the detector is a Superconducting Quantum Interference (SQUID) magnetometer.

38. A method of magnetic resonance imaging (MRI), the method comprising:

a) a pre-polarizing a sample by:

applying a prepolarization field B P for a period of time, and

switching the prepolarization field off;

b) providing a static magnetic field B 0 along a z unit vector at the sample;

c) selecting a volume for imaging by applying a frequency-selective pulse in the presence of a rotating-frame magnetic field gradient superimposed on the B 0 field, wherein the rotating-frame gradient comprises a vector component rotating in a plane perpendicular to the z unit vector;

d) spatially encoding nuclear spins in the selected volume; and

e) detecting a spatially encoded nuclear magnetic resonance signal.

39. The method of claim 38 , wherein the selecting comprises applying a hard pulse to excite substantially all spins in the sample and applying a soft pulse to de-excite substantially only those spins within the selected volume.

40. The method of claim 38 , wherein the selecting comprises applying a soft pulse to excite substantially only those spins within the selected volume.

41. The method of claim 38 , wherein the selective pulse comprises a soft pulse intermittently interrupted by one or more coherent hard pulses.

42. The method of claim 41 , wherein each of the hard pulses is selected from a group of hard pulses consisting of:

a) a π y pulse rotating substantially all of the magnetization M into the y direction;

b) a π −y pulse rotating substantially all of the magnetization M into the −y direction;

c) a π z pulse rotating substantially all of the magnetization M into the z direction; and

d) a π −z pulse rotating substantially all of the magnetization M into the −z direction.

43. The method of claim 42 , wherein the selective pulse comprises the sequence:

{2τ−(π y )−τ−(π z )−2τ−(π −z )−τ−(π −y )−2τ} n , wherein:

τ and 2τ indicate delay intervals in which a segment of the soft pulse is applied; and

n is an index indicating n th cycle in repetitive applications of the selective pulse.

44. The method of claim 43 , wherein the delay interval τ is about three orders of magnitude less than the total pulse duration.

45. The method of claim 38 , wherein the spatial encoding comprises Fourier encoding by application of a second rotating-frame magnetic field gradient.

46. The method of claim 38 , wherein the rotating-frame gradient comprises a time-independent z gradient along a transverse direction in a rotating frame.

47. The method of claim 38 , wherein the rotating-frame gradient comprises a time-independent x gradient along a transverse direction in a rotating frame.

48. The method of claim 38 , wherein the rotating-frame gradient comprises a time-independent y gradient along a transverse direction in a rotating frame.

49. A method of performing magnetic resonance imaging (MRI), the method comprising:

a) pre-polarizing a sample by:

applying a prepolarization field B P for a period of time, and

switching the prepolarization field off;

b) providing a static magnetic field B 0 ;

c) selecting a slice for imaging by applying a frequency-selective pulse in the presence of a first rotating-frame gradient superimposed on the B 0 field;

d) performing a plurality of data acquisitions of nuclear magnetic resonance signals from the selected slice, each data acquisition comprising:

Fourier encoding spins within the slice by applying a second rotating-frame gradient superimposed on the B 0 field,

detecting a Fourier encoded nuclear magnetic resonance signal, and

populating a k-space with the detected nuclear magnetic resonance signal;

e) terminating the data acquisitions when the population of the k-space is completed;

f) performing an inverse Fourier transformation on the populated k-space; and

g) displaying an image indicative of local spin density distribution in the selected slice.

50. A magnetic resonance imaging (MRI) system comprising:

a) means for providing a pre-polarization magnetic field;

b) means for providing a static magnetic field;

c) means for generating a first rotating-frame gradient and a second rotating-frame gradient;

d) means for generating a selective pulse applied in the presence of the first rotating-frame gradient;

e) means for phase encoding a plurality of MRI signals by the use of the second rotating-frame gradient;

f) means for performing an inverse Fourier transformation on the phase-encoded MRI signals; and

g) means for displaying an image indicative of local spin density distribution in a slice selected by the selective pulse.