4 dimensinal magnetic resonance imaging

• US 20040027127A1
• Filed: 02/20/2003
• Published: 02/12/2004
• Est. Priority Date: 08/22/2000
• Status: Active Grant

• Current Assignee: Randell L. Mills
• Original Assignee: Randell L. Mills
• Inventors: Mills, Randell L
• Granted Patent: US 7,382,129 B2
• Time in Patent Office: Days
• US Class Current: 324/317
• CPC Class Codes: G01R 33/482 using a Cartesian trajectory

Abstract

Provided are apparatus and methods for forming a multidimensional image of inanimate or animate objects which utilize a magnetization source (112) to magnetize a volume of an object to be imaged, a radiation source (118) for applying a radiation field to the object to be imaged, an output signal detector (120) for producing output signals in response to the secondary radiation at a plurality of spatial locations outside of the object as a function of time, processors (126, 126a and 126b) for determining a plurality of Fourier components, for associating the Fourier components due to each voxel (14) by phase, and for converting each set of components into a voxel location, and an image processor (128) for producing an image.

Claims

1. Apparatus for providing a multidimensional image of inanimate or animate objects comprising:

a magnetization source for producing a magnetic field to magnetize a volume of an object to be imaged, the volume comprising a plurality of voxels;

a radiation source for applying a radiation field to the object to be imaged when the object is disposed in the magnetic field to produce a secondary radiation field emanating from the object;

an output signal detector for producing output signals in response to said secondary radiation at a plurality of spatial locations outside of the object as a function of time;

a first processor for determining a plurality of Fourier components, each having the same frequency, an intensity and a phase angle;

a second processor for associating the Fourier components due to each voxel of the object to be imaged by phase to form a set corresponding to a spatial variation of intensity of the secondary radiation due to each voxel at said plurality of spatial locations outside of the object;

a third processor for converting each said set of components into a voxel location; and

an image processor for producing an image based on the secondary radiation intensity from each voxel and the location of each voxel.

2. The apparatus according to claim 1, further comprising a display for displaying the image.

3. The apparatus according to claim 2, characterized in that said display comprises at least one selected from the group consisting of printers, cathode ray tube displays, liquid crystal displays, plasma screens, three dimensional modelers, laser monitors, projections monitors and holographic displays.

4. The apparatus according to any one of the preceding claims, characterized in that one processor handles the processing functions of at least two of said first processor, second processor, third processor and image processor.

5. The apparatus according to any one of the preceding claims, characterized in that one processor handles the processing functions of at least three of said first processor, second processor, third processor and image processor.

6. The apparatus according to any one of the preceding claims, characterized in that the third processor comprises a reconstruction processor.

7. The apparatus according to any one of the preceding claims, characterized in that the image is a magnetic resonance image.

8. The apparatus according to any one of the preceding claims, characterized in that the magnetization source comprises a superconducting magnet.

9. The apparatus according to any one of the preceding claims, characterized in that the radiation source comprises a radio frequency generator and transmitter.

10. The apparatus according to claim 9, characterized in that the radio frequency generator and transmitter comprises an antennae to excite protons in a magnetized volume.

11. The apparatus according to claim 10, characterized in that the antenna comprises two saddle coils driven in parallel to provide a rotating radio frequency field.

12. The apparatus according to any one of the preceding claims, characterized in that the source of radiation produces a component of secondary radiation which is transverse to a direction of magnetization of a volume.

13. The apparatus according to claim 12, characterized in that the secondary radiation which is transverse to the direction of the magnetization of the volume comprises radio frequency dipole radiation.

14. The apparatus according to claim 13, characterized in that the radio frequency dipole radiation comprises near field radiation.

15. The apparatus according to any one of the preceding claims, characterized in that the output signal detector comprises a plurality of detectors.

16. The apparatus according to claim 15, characterized in that each of the detectors comprises an associated antenna.

17. The apparatus according to claim 16, characterized in that the plurality of detectors comprises a three dimensional array of antennas.

18. The apparatus according to claim 17, characterized in that each antenna of the three dimensional array of antennas responds to a secondary radio frequency field as a function of time.

19. The apparatus according to claim 18, characterized in that the plurality of detectors are located at spatial locations outside of an object to be imaged.

20. The apparatus according to any one of the preceding claims, characterized in that the output signal detector produces output signals in response to secondary radiation at a plurality of spatial locations as a function of time samples at a Nyquist rate in time over the proton free induction decay.

21. The apparatus according to any one of the preceding claims, characterized in that the first processor further comprises an analog to digital converter to digitize signals of secondary radiation.

22. The apparatus according to any one of the preceding claims, characterized in that the first processor comprises a time Fourier transform processor to convert secondary signals from the signal output detector over time into Fourier components, each having the same frequency, an intensity and a phase angle.

23. The apparatus according to any one of the preceding claims, characterized in that the plurality of Fourier components each having the same frequency, an intensity and a phase angle are such that the phase of each component is unique.

24. The apparatus according to claim 23, characterized in that the unique phase of each component is provided by a combination of the angle θ

suspended between each spatial location at which the secondary field is detected and a radial vector, a vector from each voxel to each spatial location, and the angle φ

due to a separation distance r between each voxel and each spatial location given by a wavenumber of detected field k times r.

25. The apparatus according to any one of the preceding claims, characterized in that said first processor uses a first component having a phase angle, calculates the phase angle as a function of spatial position of a first spatial position relative to any other spatial location and identifies a component at each spatial location having the calculated phase angle.

26. The apparatus according to claim 25, characterized in that a separate detector samples each separate spatial location.

27. The apparatus according to claim 26, characterized in that each detector comprises a point detector.

28. The apparatus according to any one of the preceding claims, characterized in that the source of radiation comprises at least one radio frequency generator selected from the group consisting of klystrons, backward wave oscillators, Gunn diodes, and traveling wave tube amplifiers.

29. The apparatus according to any one of the preceding claims, characterized in that the third processor uses a spatial variation of the secondary radiation over a sample volume comprising a plurality of spatial locations at which the radiation is detected to determine a location of the voxels.

30. The apparatus according to claim 29, characterized in that the location of each voxel is determined independently by the third processor.

31. The apparatus according to claim 2, wherein the image processor and display can rotate and display an image from a plurality of desired perspectives.

32. The apparatus according to claim 2, characterized in that the image processor and display can display a reduced dimensional image.

33. The apparatus according to any one of the preceding claims, characterized in that the apparatus provides a two dimensional or three dimensional nuclear magnetic resonance image of inanimate or animate objects.

34. The apparatus according to claim 33, characterized in that the output signal detector comprises a nuclear magnetic resonance detector for detecting a time dependent transverse radio frequency field component as a function of time of over a three dimensional sample volume outside of an object.

35. The apparatus according to claim 34, characterized in that secondary radiation emanating from a magnetized object comprises the transverse, time harmonic nuclear magnetic resonance magnetic dipole radiation.

36. The apparatus according to claim 34, characterized in that the time dependent transverse radio frequency field component comprises a harmonic oscillation of each radio frequency dipole that is equivalent to a dipole rotating in a transverse plane.

37. The apparatus according to claim 34, characterized in that the apparatus can generate an image from a three-dimensional map of a transverse resonant radio frequency magnetic flux external to an object and said nuclear magnetic resonance detector comprises a plurality of detectors at spatial locations, and wherein

a nuclear magnetic resonance signal of each voxel at a given detector gives rise to

a Fourier component with a unique phase angle relative to a Fourier component of other voxels of the object at that detector;

a set of Fourier components that correspond to the nuclear magnetic resonance signal of a given voxel over the detectors is determined; and

an intensity variation of a transverse radio frequency field over space is used to determine a coordinate location of each voxel.

38. The apparatus according to claim 37, characterized in that the each detector is selectively responsive to a component of the secondary field.

39. The apparatus according to claim 38, characterized in that a transverse radio frequency field is a near field which is a dipole that serves as a basis element to form a unique reconstruction.

40. The apparatus according to claim 39, characterized in that the each detector is responsive to a component of radio frequency in a transverse plane.

41. The apparatus according to claim 40, characterized in that each detector is responsive to a component of the radio frequency dipole field parallel to the radio frequency dipole.

42. The apparatus according to claim 41, characterized in that each detector is responsive to the component of the radio frequency dipole field parallel to the radio frequency dipole as a function of time and detects a maximum intensity of the signal during each time harmonic cycle.

43. The apparatus according to any one of the preceding claims, characterized in that the third processor determines a location of a voxel from signals recorded of a transverse dipole radio frequency field.

44. The apparatus according to claim 43, characterized in that a geometric system function corresponding to a dipole determines a spatial intensity variations of the radio frequency field.

45. The apparatus according to claim 44, characterized in that the system function is a band-pass when k_p=k_z, the frequency of spatial variation of the recorded secondary radiation in the rho direction is equal or comparable to that in the z direction of the three dimensional space comprising said plurality of spatial locations.

46. The apparatus according to claim 45, characterized in that each voxel is reconstructed independently in parallel with other voxels using each unique set of components associated by phase such that the scan time is no greater than the nuclear free induction decay time.

47. The apparatus according to claim 46, characterized in that all voxels comprising an image are reconstructed in parallel.

48. The apparatus according to claim 46, characterized in that the apparatus can generate high resolution, three-dimensional, real-time anatomical images and images based on physiological parameters with little or no deterioration from motion artifact.

49. The apparatus according to claim 41, characterized in that at each point in time, each radio frequency dipole rotating in the transverse plane is directed at an angle θ

relative to the direction of detection of each detector.

50. The apparatus according to claim 49, characterized in that the phase angle θ

of the radio frequency dipole relative to the direction of detection axis of the detector gives rise to a phase angle term e<sup>−

iθ</sup>

.

51. The apparatus according to claim 50, characterized in that at each point in time, each radio frequency dipole rotating in the transverse plane with a separation distance r between each voxel and each spatial location at a detector gives rise to an angle φ

given by a wavenumber of the detected secondary radiation k times r directed at the angle θ

relative to a direction of detection of each detector.

52. The apparatus according to claim 51, characterized in that the phase angle φ

of the radio frequency dipole relative to a direction of detection axis of a detector gives rise to a phase angle term e<sup>−

iφ</sup>

directed at angle θ

relative to the direction of detection of each detector and wherein the angle θ

gives rise to a phase angle term e<sup>−

iθ</sup>

.

53. The apparatus according to claim 52, characterized in that a sum of the phase angles, kr and θ

, is unique for each voxel at each detector.

54. The apparatus according to claim 37, characterized in that the unique phase of each component is provided by a combination of

angle θ

suspended between each spatial location at which a secondary nuclear magnetic resonance field is detected and a radial vector from each voxel to each spatial location, and

angle φ

due to a separation distance r between each voxel and each spatial location given by the wavenumber of detected nuclear magnetic resonance field k times r.

55. The apparatus according to claim 37, flier comprising a processor, characterized in that a set of Fourier components that correspond to a nuclear magnetic resonance signal of a given voxel over detectors is determined by the processor using a position of a first detector relative to a different detector to calculated the phase angle of the different detector relative to the first detector.

56. The apparatus according to claim 55, characterized in that the processor determines the set of Fourier components that correspond to the nuclear magnetic resonance signal of a given voxel over the detectors by using the position of each first detector relative to a different detector to calculated the phase angle of the different detector relative to the first detectors, and the process is repeated over all of the detectors to give the set of intensities of the nuclear magnetic resonance signal over the plurality of detectors due to each voxel.

57. The apparatus according to claim 56, characterized in that the set of intensities of the nuclear magnetic resonance signal over the plurality of detectors due to each voxel is processed to determine a coordinate location of each voxel.

58. The apparatus according to any one of the preceding claims, further comprises coils for providing

B₀, a steady primary field,

G_x, a field gradient in an x-axis direction,

G_y, a field gradient in a y-axis direction,

a radio frequency field, and

G_z, a field gradient in a z-axis direction.

59. The apparatus according to claim 58, associated amplifiers for driving the coils and associated control circuits for controlling the coils which provide T₁ and T₂ pulse sequences to alter an intensity of the secondary radio frequency field as a function of time to provide corresponding signals to be processed.

60. The apparatus according to claim 9, characterized in that nuclei present in object are subjected to an additional rotating radio frequency field H₁, which is synchronous with precession and their magnetic moments, and magnetization M is caused to precess about H₁ and rotate away from the primary field H₀ by an angle φ

in a coordinate frame which rotates at the Larmor frequency, the precession about H₁ continues as long as H₁ exists, and a final value of φ

which depends on the strength of H₁, which determines the precession rate, and the time for which it is turned on is such that φ

=90°

that a dipole is perpendicular to a detector array that is responsive to the nuclear magnetic resonance radiation at a plurality of spatial locations external to the object.

61. The apparatus according to any one of the preceding claims, characterized in that the magnetizing source is constructed to provide a magnetic field which permeates the object to be imaged and is confined to a volume to be imaged, and the confined magnetic field limits the source of signal to the volume of interest, characterized in that the volume to be reconstructed is limited to the magnetized volume which sets a limit to required computations and reduces end effects of signal originating outside of edges of the output signal detector.

62. The apparatus according to claim 61, characterized in that the apparatus is constructed to provide a magnetizing field which limits an imaged volume of an object by providing a range of Larmor frequencies and data is rejected at a threshold Larmor frequency.

63. The apparatus according to any one of the preceding claims, characterized in that the apparatus is constructed to provide a magnetizing field which limits an imaged volume of an object by providing a range of Larmor frequencies and data is rejected at a threshold Larmor frequency.

64. The apparatus according to any one of the preceding claims, characterized in that the output signal detector comprises detector elements disposed on a first axis and having corresponding output signals.

65. The apparatus according to claim 64, characterized in that the output signal detector includes detector elements disposed on a second axis and having a corresponding output signal, and the detectors on the second axis are responsive to the corresponding oriented field components of the secondary radiation.

66. The apparatus according to any one of the preceding claims, characterized in that the third processor comprises at least one reconstruction processor selected from the group consisting of a detector processor for processing the detector output signal with an inverse matrix, a reiterative processor, a time Fourier transform processor, a sinc function filter processor for detecting the detector output signals, a space and time Fourier transform processor, and a compensating processor for compensating for a distance from the detector along a detector responsive axis.

67. The apparatus according to any one of the preceding claims, characterized in that the signal output detector further comprises a line or plane of detectors and a drive mechanism that moves the detectors to sample an external secondary radiation over a three-dimensional volume.

68. The apparatus according to claim 67, characterized in that the secondary radiation is a radio frequency magnetic field due to nuclear magnetic resonance of nuclei in a magnetic field produced by the magnetization source and excited by a radiation field from the source of radiation.

69. The apparatus according to claim 68, characterized in that the nuclear magnetic resonance active nuclei are protons.

70. The apparatus according to claim 19, characterized in that each antenna of the three dimensional array of antennas are impedance matched.

71. The apparatus according to claim 70, characterized in that each antenna of the three dimensional array of antennas further comprises superconducting reactance elements which minimize resistive losses.

72. The apparatus according to claim 19, characterized in that cross talk between antennas is ameliorated or eliminated by time multiplexing the signal detection over the array of antennas.

73. The apparatus according to claim 19, characterized in that the signal output detector comprises a synchronous detector wherein the radio frequency field is sampled synchronously so that a phase at any given detector may be related to that at any other detector.

74. The apparatus according to claim 19, characterized in that the signal output detector comprises a synchronous detector wherein the radio frequency field is sampled at known times so that a phase at any given detector may be related to that at any other detector.

75. The apparatus according to claim 19, characterized in that each antenna of the three dimensional array of antennas responds selectively to a component of the secondary radio frequency field at a spatial location outside of the body as a function of time.

76. The apparatus according to claim 19, characterized in that each antenna of the three dimensional array of antennas responds selectively to a parallel component of the secondary radio frequency field at a spatial location outside of an object as a function of time.

77. The apparatus according to claim 19, characterized in that each antenna of the three dimensional array of antennas responds selectively to a perpendicular component of the secondary radio frequency field at a spatial location outside of an object as a function of time.

78. Apparatus for providing a multidimensional image of inanimate or animate objects comprising:

means for producing a magnetic field to magnetize a volume of an object to be imaged, the volume comprising a plurality of voxels;

means for applying a radiation field to the object to be imaged when the object is disposed in the magnetic field to produce a secondary radiation field emanating from the object;

means for producing output signals in response to said secondary radiation at a plurality of spatial locations outside of the object as a function of time;

first processor means for determining a plurality of Fourier components, each having the same frequency, an intensity and a phase angle;

second processor means for associating the Fourier components due to each voxel of the object to be imaged by phase to form a set corresponding to a spatial variation of intensity of the secondary radiation due to each voxel at said plurality of spatial locations outside of the object;

third processor means for converting each said set of components into a voxel location; and

image processor means for producing an image based on the secondary radiation intensity from each voxel and the location of each voxel.

79. An apparatus for providing a two dimensional or three-dimensional nuclear magnetic resonance image of an object comprising:

means for generating an image from a three-dimensional map of a transverse resonant radio frequency magnetic flux external to an object having a volume to be imaged, the volume comprising a plurality of voxels; and

processor means for determining the location of each voxel which is a source of the radio frequency field through spatial variations of an intensity of the nuclear magnetic resonance field of a set of components associated by phase.

80. An apparatus for providing a two dimensional or three-dimensional nuclear magnetic resonance image of an object comprising:

a magnetizing source for magnetizing a volume an object in a first direction, the volume comprising a plurality of voxels;

means for causing nuclear magnetic resonance magnetization to rotate into a plane transverse to the first direction;

an output signal detector for detecting the nuclear magnetic resonance field rotated into a transverse plane external to the object at a plurality of spatial locations;

a first processor for determining a set of components of spatial variation of the nuclear magnetic resonance field over a sample volume by association of the components by phase;

a second processor for determining a location of each voxel which is a source of the radio frequency field through each set of components representative of spatial variations of an intensity of the nuclear magnetic resonance field over the sample volume, and

an image processor for displaying the voxel locations representative of anatomical images of the object based on selected physiological.

81. An apparatus for providing a two dimensional or three-dimensional nuclear magnetic resonance image of an object comprising:

means for magnetizing a volume an object in a first direction, the volume comprising a plurality of voxels;

means for causing nuclear magnetic resonance magnetization to rotate into a plane transverse to the first direction;

means for detecting the nuclear magnetic resonance field rotated into a transverse plane external to the object over a sample volume comprising a plurality of spatial locations;

processor means for determining a set of components of spatial variation of the nuclear magnetic resonance field over a sample volume by association of the components by phase;

processor means for determining a location of each voxel which is a source of the radio frequency field through each set of components representative of spatial variations of an intensity of the nuclear magnetic resonance field over the sample volume, and

processor means for displaying the voxel locations representative of anatomical images of the object based on selected physiological parameters.

82. An apparatus for providing a two dimensional or three-dimensional nuclear magnetic resonance image of an object comprising:

means for generating an image from a three-dimensional map of a transverse resonant radio frequency magnetic flux external to an object comprising a volume to be imaged, the volume comprising a plurality of voxels; and

processor means for determining locations of voxels, which is a source of a radio frequency field through spatial variations of an intensity of a nuclear magnetic resonance field of a set of components associated by phase.

83. A method for providing a multidimensional image of inanimate and animate objects comprising the steps of:

placing an object having a volume in a magnetic field, the volume comprising a plurality of voxels;

applying a first source of radiation to the object;

recording a secondary source of radiation emanating from the object at a plurality of spatial locations;

forming components of the spatial variation of the secondary source of radiation external to the object due to voxels of the object;

determining the location of voxels from the intensity variation of the components;

generating and displaying the image from the locations and the intensity of the secondary radiation of each voxel.

84. The method according to claim 83, characterized in that the secondary recorded radiation is a three-dimensional transverse resonant radio frequency magnetic flux external to the object recorded as a function of time.

85. The method according to claim 84, characterized in that the three-dimensional transverse resonant radio frequency magnetic flux external to the object is nuclear magnetic resonance radiation.

86. The method according to any one of claims 84 or 85, further comprising recording the secondary source of radiation emanating from the object at a plurality of spatial locations using a plurality of detectors at each spatial location.

87. The method according to any one of claims 83-86, characterized in that the recorded signals from each voxel contains components each having a unique phase angle relative to other components from different voxels.

88. The method according to any one of claims 83-87, characterized in that a time dependent signal at each detector may be transformed into a series of components having intensity and phase data.

89. The method according to any one of claims 83-88, characterized in that each set of components of the nuclear magnetic resonance signal over a sample volume due to a given voxel is determined from phase data and detector positions.

90. The method according to any one of claims 83-89, characterized in that an intensity variation of a transverse radio frequency field over the sample volume is used to determine the coordinate location of each voxel.

91. The method according to any one of claims 83-90, characterized in that the radio frequency field is a near field which is a dipole that serves as a basis element to form a unique reconstruction.

92. The method according to any one of claims 83-91, characterized in that each volume element is reconstructed independently in parallel with all other volume elements such that a scan time is no greater than a nuclear free induction decay time.

93. The method according to any one of claims 83-92, characterized in that said object is at least one selected from the group consisting of a human body, an animal, and tissue.

97. A method according to any one of claims 83-96, characterized in that a strength and duration of rotating H₁ radio frequency field that is resonant with the protons of the magnetized volume and is oriented perpendicularly to a direction of the magnetizing field is applied such that final precession angle of magnetization is 90°

, φ

_H1=90°

, such that a radio frequency dipole is transverse to a primary magnetizing field and perpendicular to a radio frequency magnetic field detector.

98. The method according to any of claim 83-97, characterized in that nuclear magnetic resonance pulse sequences which provide signals for a T₁ or T₂ image are applied.

99. The method according to claim 98, characterized in that the nuclear magnetic resonance pulse sequences which provide the signals for a T₁ or T₂ image comprises applying a 90°

pulse followed by a series of 180°

pulses.

100. The method according to claim 99, characterized in that the step of applying a 90°

pulse followed by a series of 180°

pulses comprises the Carr-Purcell-Meiboom-Gill sequence.

101. The method according to any one of claims 96-100, characterized in that the step of determining the matrix of Fourier components that correspond to the nuclear magnetic resonance signal of a given voxel over the detectors is achieved by using a first component having a phase angle and calculating the phase angle as a function of spatial position of a first detector relative to any other detector and identifying a component at each detector having the calculated phase angle.

102. The method according to any one of claims 96-100, characterized in that each matrix of components associated by phase comprises the intensity variation over the sample volume of the radio frequency field of bulk magnetization M of each voxel.

150. The method according to claim 87, characterized in that the radio frequency field is sampled synchronously so that the phase at any given detector may be related to that at any other detector.

151. The method according to claim 87, characterized in that the radio frequency field is sampled at known times so that the phase at any given detector may be related to that at any other detector.

94. A method for providing a multidimensional image of inanimate and animate objects comprising the steps of:

magnetizing a volume of an object to be imaged, the volume comprising a plurality of voxels;

applying a radiation field to the object to be imaged when disposed in the magnetic field to produce a secondary radiation field emanating from the object;

producing output signals from a detector in response to said secondary radiation at a plurality of spatial locations outside of the object as a function of time;

determining a plurality of Fourier components each having the same frequency, an intensity and a phase angle;

associating the Fourier components due to each voxel of the object to be imaged by phase to form a set corresponding to the spatial variation of intensity of the secondary radiation due to each voxel at the plurality of spatial locations outside of the object;

converting each set of components into a voxel location; and

producing an image based on an intensity of the secondary radiation from each voxel, the location of each voxel, and plotting the superposition of results for each voxel.

95. A method for providing a two dimensional or three-dimensional nuclear magnetic resonance image of an object comprising the steps of:

generating an image from a three-dimensional map of a transverse resonant radio frequency magnetic flux external to a volume of an object being scanned, the volume comprising a plurality of voxels, characterized in that a nuclear magnetic resonance signal of each voxel at any given detector gives rise to a Fourier component with a unique phase angle relative to the Fourier component of any other voxel of the object at a detector;

a set of Fourier components that correspond to a nuclear magnetic resonance signal of a given voxel over detectors is determined;

an intensity variation of the transverse radio frequency field over space is used to determine a coordinate location of each voxel; and

a superposition of results for each voxel is plotted to provide a total image.

96. A method of providing a multidimensional image of inanimate and animate objects comprising the steps of:

aligning magnetic moments of nuclei of a volume of an object to be imaged using a primary field, the volume comprising a plurality of voxels;

further aligning the magnetic moments by a radio frequency pulse or series of pulses;

recording free induction decay signals;

Fourier transforming time dependent nuclear magnetic resonance signals to give intensity and phase of each Fourier component, characterized in that nuclear magnetic resonance signal of each voxel at any given detector gives rise to a Fourier component with a unique phase angle relative to the Fourier component of any other voxel at that detector;

determining a matrix of Fourier components that correspond to the nuclear magnetic resonance signal of a given voxel over the detectors;

determining matrices for a plurality of voxels;

determining a coordinate location of each voxel from measurements of spatial variations of a transverse radio frequency field of each corresponding matrix; and

processing and displaying the position of each voxel with a representation of the intensity of the nuclear magnetic resonance signal emitted by each voxel.

103. The method according to claim 96, firer comprising reconstructing a multidimensional image representation according to spatial variations of the detected radio frequency magnetic field using at least one of a matrix inversion algorithm, a reiterative algorithm or Fourier transform algorithm.

104. The method according to claim 103, characterized in that a spatial Fourier transform algorithm is used.

105. The method according to claim 104, characterized in that the spatial Fourier transform algorithm is performed on each set of components over the detector array to map each bulk magnetization M corresponding to a voxel to a spatial location of the imaged object.

106. The method according to claims 104 or 105, characterized in that the spatial Fourier transform comprises the steps of:

recording a nuclear magnetic resonance signal at discrete points in the sampling space at position x, y, z as a function of time;

designating each point, x, y, z, as an element in matrix A;

Fourier transforming time dependent signals to give an intensity and phase of each component wherein the nuclear magnetic resonance signal of each voxel at any given detector gives rise to a Fourier component with a unique phase angle relative to the Fourier component of any other voxel of the object at that detector;

determining a matrix of Fourier components that correspond to the nuclear magnetic resonance signal of a given voxel over the detectors;

determining matrices A_n for all of the voxels;

determining a coordinate location of each voxel using the measurements of the spatial variations of the transverse radio frequency field of a given matrix; and

plotting a superposition of results for each voxel to provide a total image.

107. The method according to claim 106, characterized in that the step of determining the coordinate location of each voxel using the measurements of the spatial variations of the transverse radio frequency field of a given matrix comprises the steps of

a.) discrete Fourier transforming each matrix A_n to obtain a matrix B_n;

b.) multiplying each element of each matrix B_n by a corresponding inverse value or reciprocal value of the Fourier transform of a system function which gives the spatial variation of the radio frequency field emitted by each voxel as a function of distance from the voxel to each detector, evaluated at the same frequency as the element of the matrix A_n to form matrix C_n;

c.) generating matrix D_n by taking the discrete inverse Fourier transform of matrix C_n;

d.) multiplying each element of each matrix D_n by the distance squared along the z-axis to which the element corresponds to generate the position of the bulk magnetization M of voxel n which corrects the limitation of the sample volume to z≧

0;

e.) repeating steps a-d for all matrices A_n; and

f) plotting superposition of results for each voxel to provide a total image.

108. The method according to claims 106 or 107, characterized in that at each sampled external spatial location, x, y, and z in Cartesian coordinates, a magnitude B′

of the transverse radio frequency magnetic flux emitted by the corresponding z-axis aligned magnetic moment m_z of each voxel is given by

109. The method according to any one of claims 106-108, further comprising the step of determining a matrix of Fourier components that correspond to the nuclear magnetic resonance signal of a given voxel over the detectors by using a first component having a phase angle and calculating the phase angle as a function of spatial position of a first detector relative to any other detector and identifying a component at each detector having the calculated phase angle.

110. The method according to claim 109, characterized in that each matrix of components associated by phase comprises the intensity variation over the sample volume of the radio frequency field of the bulk magnetization M of each voxel.

111. The method according to claims 106 or 107, characterized in that a system function as a function of the detector location relative to each voxel in Cartesian coordinates, x, y, z, is by

112. The method according to any one of claims 106-111, further comprising the step of correcting a point spread of each reconstructed voxel by assigning one voxel above a certain threshold with the bulk magnetization M and the other voxels are assigned a zero value.

113. The method according to any one of claims 106-112, further comprising the step of correcting a finite size of each detector by multiplying each numeric value of matrix B_n by the corresponding matrix element of the inverse or reciprocal of the Fourier transform of a waveform representative of a detector geometry.

114. The method according to claim 106-113, characterized in that each matrix element of the inverse or reciprocal of the Fourier transform of a waveform representative of the detector geometry is given by:

115. The method according to any one of claims 106, 107, or 111-114, characterized in that each volume element is reconstructed independently in parallel with all other volume elements such that a scan time is no greater than a nuclear free induction decay time.

116. The method according to any one of claims 106, 107, or 111-115 wherein the Fourier transform of the system function is given by:

117. The method according to any one of claims 106-116, characterized in that each matrix element for the step of multiplying each element of each matrix D_n by the distance squared along the z-axis to which the element corresponds to generate the 15 position of the bulk magnetization M of voxel n which corrects the limitation of the sample volume to z≧

0 is given by;

118. The method according to claim 103, characterized in that the step of reconstructing the multidimensional image uses a matrix inversion reconstruction algorithm.

119. The method according to claim 118, characterized in that the matrix inversion reconstruction algorithm comprises the steps of:

using the geometric system function to determine the spatial intensity variation of the transverse radio frequency field over a detector array to form a corresponding matrix;

inverting the corresponding matrix; and

multiplying the signal over the detector array by the inverted matrix to give voxel sources.

120. The method according to claim 119, further comprising the steps of

a.) determining a coefficient for each voxel mathematically or by calibration which when multiplied by the bulk magnetization M of each voxel is that voxel'"'"'s contribution to the signal at a given detector with the corresponding unique phase at each detector;

b.) repeating step a for every detector;

c.) using the coefficients to determine a matrix which when multiplied by a column vector of the bulk magnetization M values of the voxels, gives the signals at the detectors;

d.) inverting the matrix and storing the result in memory,

e.) recording signals as a function of time over the detector array;

f.) Fourier transforming the signals as a function of time to give the Fourier components each having an amplitude and a unique phase; and

g.) multiplying the components by the inverse matrix to generate a bulk magnetization M map which is displayed.

121. The method according to claim 120, characterized in that the coefficient for each voxel determined mathematically is given by

122. The method according to claim 118, further comprising the steps of

determining a matrix of Fourier components that correspond to the nuclear magnetic resonance signal of a given voxel over the detectors;

determining corresponding matrices for a plurality of voxels;

determining a coordinate location of each voxel from measurements of spatial variations of the transverse radio frequency field of a given matrix wherein each matrix of components associated by phase comprises the intensity variation over the sample volume of the radio frequency field of the bulk magnetization M of each voxel; and

multiplying each matrix of components by the inverse matrix of system function to generate the bulk magnetization M map.

123. The method according to claim 122, further comprising the steps of

a.) correcting a point spread of a reconstructed voxel by assigning one voxel above a certain threshold with the bulk magnetization M;

b.) assigning other voxels with a zero value;

c.) repeating steps a-b for other voxels; and

d.) plotting and displaying the superposition of the separate maps for each voxel which comprises the total bulk magnetization map as a nuclear magnetic resonance image.

124. The method according to claim 103, characterized in that said multidimensional image is reconstructed using a reiterative reconstruction algorithm.

125. The method according to claim 124, characterized in that the reiterative reconstruction algorithm comprises the steps of

a.) using the geometric system function to determine a system of linear equations which gives the intensity, spatial variation, and phase of radio frequency field over a sample volume wherein the system of linear equations gives the signal and phase from each voxel at each detector based on the bulk magnetization M value of each voxel and the position of the voxel relative to the detector;

b.) Fourier transforming the signal as a function of time to give Fourier components each having an amplitude and a unique phase;

c.) determining weighting coefficients based on the linear equations;

d.) determining coefficients for each voxel mathematically or by calibration;

e.) estimating bulk magnetization M for each voxel;

f.) calculating signals at each phase at each detector;

g.) comparing a result of multiplying the bulk magnetization M value of each voxel times its weighting coefficient and its calculated phase at a given detector to a measured signal and phase;

h.) making a correction to M of each voxel to give a second, or recomputed, estimate for M of each voxel;

i.) computing the signal value from this second estimate and making corrections according to steps f-h;

j.) repeating steps f-i until the correction for each reiteration approaches a predefined limit which serves to indicate that the reconstruction is within reasonable limits of error;

k.) repeating steps e-j of the procedure for other detectors; and

l.) plotting and displaying a bulk magnetization map.

126. The method according to claim 125, wherein the coefficient for each voxel determined mathematically is given by

138. The method according to claim 103, further comprising the steps of using the matrix inversion algorithm or the reiterative algorithm in combination with the Fourier Transform Algorithm.

139. The method according to claim 103, further comprising the steps of using the matrix inversion algorithm and the reiterative algorithm in combination with the Fourier Transform Algorithm.

140. The method according to claim 103, further comprising using the Fourier Transform Algorithm as input for the first reiteration of a reiterative algorithm.

141. The method according to claim 140, further comprising the steps of:

using the Fourier Transform Algorithm to calculate a series of first bulk magnetization images for each matrix of components associated by phase;

detecting at least one peaks or edge of each image by using a cut-off level for the bulk magnetization assigned to a voxel or the value of the derivative of the bulk magnetization as a function of voxel position, respectively;

setting the bulk magnetization of the voxel or voxels corresponding to the peak or edge equal to the peak bulk magnetization and assigning the remaining voxels a zero value;

calculating a signal at each detector using a system function;

comparing each calculated signal to the actual signal and determining a difference or error;

projecting the error over the voxels using the Fourier Transform Algorithm, Matrix Inversion Algorithm, or Reiterative Algorithm;

adding back projected errors to a preceding corrected series of bulk magnetization maps; and

performing the steps reiteratively until it stabilizes.

142. The method according to claim 96, characterized in that a T₁ image is produced by a applying at least one pulse sequence that inverts the magnetization and records the relaxation.

143. The method according to claim 142, further comprising producing a T₁ image by the steps of:

switching on radio frequency receivers to follow a decay following a nuclear excitation comprising a H₁ pulse;

examining M_z(t), a time dependent bulk magnetization in the direction of a primary field H₀, at a time t₀ after an inverting pulse by applying another H₁ pulse equivalent to a rotation by 90°

after waiting the time t₀ following the initial inversion, characterized in that the 90°

pulse puts the z magnetization M_z(t₀) into the transverse plane for observation, and changing the waiting time t₀ to allow for observation of M_z(t) at different times during relaxation.

144. The method according to claim 96, characterized in that a T₂ image is produced by a applying at least one pulse sequence that flips a magnetization vector into a transverse plane and records a transverse relaxation by producing at least one spin-echo.

145. The method according to claim 144, further comprising producing a T₂ image by the steps of

flipping the magnetization initially aligned along the z_R-axis into the transverse plane by applying a H₁ pulse;

recovering the T₂ relaxation from a T₂* FID by applying a 180°

H₁ pulse at time t₀ along the y_R-axis where the T₂* relaxation occurs in time t₀;

recording the T₂ relaxation after an additional time t₀, characterized in that the total time elapsed after the 90°

H₁ pulse is 2t₀=t_E which is the spin-echo time and the dephasing due to the static inhomogeneity of H₀ is canceled out, whereby the relaxation is due to processes that create T₂ relaxation;

applying a plurality of 180°

pulses to form a plurality of spin echoes; and

determining the T₂ relaxation from the envelop of the maximum amplitude of the spin echoes.

146. The method according to claim 145, further comprising a pulse sequence to give the data for a T₂ image known as the Carr-Purcell-Meiboom-Gill sequence comprises applying a 90°

pulse along the x_R-axis followed by a series of 180°

pulses along the y_R-axis at times t₀+2nt₀ where n is an integer including zero.

148. The method according to claim 96, characterized in that the plurality of Fourier components each having the same frequency, an intensity and a phase angle each have a unique phase.

149. The method according to claim 148, characterized in that the unique phase of each component is provided by a combination of

the angle θ

suspended between each spatial location at which the secondary field is detected and a radial vector from each voxel to each spatial location; and

the angle φ

due to a separation distance r between each voxel and each spatial location given by a wavenumber of a detected field k times r.

152. The method according to claim 96, characterized in that the processor which determines a plurality of Fourier components each having the same frequency, an intensity and a phase angle uses a first component having a phase angle and calculates the phase angle as a function of spatial position of the first spatial position relative to any other spatial location and identifies the component at each spatial location having the calculated phase angle.

153. The method according to claim 152, characterized in that the voxels that are on the same axis with a given detector or a plurality of detectors that align vertically with one or more voxels is determined.

154. The method according to claim 153, characterized in that the phase angle is a function of the distance r of the detector from the voxel.

155. The method according to claim 154, characterized in that the components may be identified by the presence of at least one component of a phase given by φ

+kΔ

r where φ

₁ is the phase angle of the first component, Δ

r is the distance of the second detector relative to the first of the detector, and k is the wavenumber of the nuclear magnetic resonance radiation emanating from the object wherein this detector(s) is defined as having a zero angle θ

.

156. The method according to claim 155, characterized in that a phase angle φ

₂ of a second component at a second detector aligned on the detection axis corresponding to a first component at a first detector having a phase angle φ

₁ is given by

φ

₂=φ

₁+kΔ

r

where Δ

r is the distance of the second detector relative to the first of the detector and k is the wavenumber of the nuclear magnetic resonance radiation emanating from the object.

157. The method according to claim 156, characterized in that, from the components identified as coaxial with a detector, the phases of the components from the voxel are determined at the other detectors using the relative position of other detectors of the sample volume relative to the first detector and 0, of the component at the first detector.

158. The method according to claim 157, characterized in that the phase φ

due to a separation distance between a voxel and a detector of r is given by the wavenumber of the radio frequency field k times r,

φ

=kr

where the wavenumber k is given by

159. The method according to claim 158, characterized in that all voxels which have the same radial distance from a given detector will have the same phase φ

.

160. The method according to claim 159, characterized in that at each case that two detectors have the same phase φ

, since the radial distances r of two voxels to a given detector are equivalent, a unique angle θ

suspended between the direction of the detector and the vector along r exists.

161. The method according to claim 160, characterized in that the radio frequency dipoles of all voxels are time synchronous.

162. The method according to claim 96, characterized in that the nuclear magnetic resonance pulsing and detection may be synchronized.

163. The method according to claim 96, characterized in that at least one standard dipole may be used as reference phase to set the phases of the radio frequency dipoles of the voxels.

164. The method according to claim 163, characterized in that all voxels that are not collinear with the axis of a detector posses an angle θ

suspended between the direction of the detector and the radial vector from the dipole to the detector.

165. The method according to claim 164, characterized in that since the radio frequency dipoles are time synchronous, at each point in time, the angle corresponds to a phase angle θ

of the radio frequency signal from each voxel at each detector.

166. The method according to claim 165, characterized in that in the case that a two dimensional slice is imaged in the transverse plane, the phase angle θ

is given by

167. The method according to claim 166, characterized in that the total unique phase angle φ

_T of the radio frequency signal from each voxel at each detector is given as the sum of φ and

θ

given by

φ

_T=φ

+θ

.

127. A method of providing a multidimensional image of inanimate and animate objects comprising the steps of:

a.) recording secondary radiation signals corresponding to a transverse radio frequency magnetic field in response to a first radiation applied to a magnetized object over a sample volume comprising a plurality of voxels;

b.) forming a matrix of signals at a plurality of spatial positions each corresponding to a detector element of a detector array;

c.) transforming the matrix numeric values according to a Fourier transform to give an intensity and phase of each component wherein a nuclear magnetic resonance signal of each voxel at any given detector gives rise to a Fourier component with a unique phase angle relative to the Fourier component of any other voxel of the object at that detector;

d.) determining a matrix of Fourier components that correspond to the nuclear magnetic resonance signal of a given voxel over the detectors;

e.) multiplying each numeric value of the transform array by a value which is an inverse or reciprocal of the Fourier transform of a waveform corresponding to an operation performed in step b;

f.) multiplying each numeric value of the discrete spectrum matrix by a value corresponding to an inverse Fourier transform of a function representative of the steps of exciting and detecting and providing a system corrected matrix;

g.) inverse-transforming the system corrected matrix according to a multidimensional discrete inverse Fourier transform providing a voxel location;

h.) correcting each element in the transformed matrix for any asymmetries in the dimensions of the sample volume;

i.) repeating steps c-h for other matrices, each corresponding to a distinct voxel; and

j.) superimposing the results from steps a-h, plotting and displaying the image.

128. The method according to claim 127, characterized in that at each sampled external spatial location, x, y, and z in Cartesian coordinates, the magnitude B′

of the transverse radio frequency magnetic flux emitted by the corresponding z-axis aligned magnetic moment m_z of each voxel is given by

129. The method according to claims 127 or 128, characterized in that the step of determining the matrix of Fourier components that correspond to the nuclear magnetic resonance signal of a given voxel over the detectors is achieved by using a first component having a phase angle and calculating the phase angle as a function of spatial position of a first detector relative to any other detector and identifying the component at each detector having the calculated phase angle.

130. The method according to claim 129, characterized in that each matrix of components associated by phase comprises an intensity variation over the sample volume of the radio frequency field of the bulk magnetization M of each voxel.

131. The method according to any one of claims 127-130, characterized in that a system function as a function of the detector location relative to each voxel in Cartesian coordinates, x, y, z, is given by

132. The method according to any one of claims 127-131, further comprising the step of correcting a point spread of each reconstructed voxel by assigning a voxel above a certain threshold with the bulk magnetization M and other voxels are assigned a zero value.

133. The method according to any one of claims 127-132, further comprising step e of correcting a finite size of each detector by multiplying each numeric value of the matrix formed in step d by the corresponding matrix element of the inverse of the Fourier transform of a waveform representative of a detector geometry.

134. The method according to claim 133, characterized in that each-matrix element of an inverse of the Fourier transform of a waveform representative of the detector geometry is given by formula

135. The method according to any one of claims 127-135, characterized in that each volume element is reconstructed independently in parallel with all other volume elements such that a scan time is no greater than a nuclear free induction decay time.

136. The method according to any one of claims 127-135, characterized in that the step f of multiplying each numeric value of the discrete spectrum matrix by a value corresponding to the reciprocal of the Fourier transform of a function representative of the steps of exciting and detecting and providing a system corrected matrix wherein the discrete values of the Fourier transform of the system function matrix are given by:

137. The method according to any one of claims 127-136, characterized in that the step h of correcting each element in the transformed matrix for any asymmetries in dimensions of the sample volume wherein the discrete values of are given by:

147. A method of providing a multidimensional nuclear magnetic resonance image of an animate or inanimate object comprising the steps of:

placing a volume of an object having nuclei in a static magnetic field H₀, the volume comprising a plurality of voxels, and then subjected them to an additional rotating radio frequency field H₁, which is synchronous with their precession, such that the bulk magnetization M of each voxel of the object precesses about H₁ and rotates away from the primary field H₀ by an angle φ

_H1;

measuring of the intensity of the radio frequency signal over time and space following T₁ and/or T₂ encoding pulses wherein the magnitude of M is a maximum initially and decays with time by emission of the same multipolarity radiation that it absorbed and by transfer of energy to the surrounding lattice and the intensity of the radiation is a function of M and the coordinate position relative to the radio frequency emitting voxel;

Fourier transforming the signal as a function of time at a given detector position to give the components each having an amplitude and a unique phase;

determining each set of components of the nuclear magnetic resonance signal over the sample volume due to a given voxel from the phase data and the detector positions;

determining the location of each voxel through the spatial variations of the intensity of the transverse nuclear magnetic resonance field of the set of components associated by phase; and

superimposing the results of the determination of the location of M of each voxel and the plotting and displaying the resulting image.