US RE32712 E Abstract Nuclear magnetic resonance phenomena are employed to generate a two dimensional image of a thin planar slice through a body under investigation. The apparatus herein operates to determine the spin density distribution in a planar slab within the body which typically comprises a biological organism. Each pixel in the resulting image is distinguished by applying time-varying magnetic field gradients so that the frequency history of the spins in each pixel is uniquely distinguishable. Additionally, novel radio frequency excitation means assure selective excitation within the planar slab.
Claims(27) 1. A nuclear magnetic resonance apparatus for determining spin density distribution in a thin planar slab of an object under examination containing nuclear spins, said body being oriented with respect to orthogonal x and y coordinate directions defined therein and also to a z coordinate direction orthogonal to said slab and to said x and y coordinates within said slab, said apparatus comprising:
excitation means for selectively exciting said nuclear spins in said slab, said excitation means including means for applying to said object for a predetermined time period an excitation magnetic field having a gradient in the z-axis direction, said gradient being defined by a function G(t) not having a DC component, said excitation means also including means for applying a pulse of RF energy to said object during the time that said excitation magnetic field is applied, said pulse having an envelope defined by a function h _{1} (t)=h_{1} γG(t)f(K/K.sub. 0)(T_{0} /K_{0}) wherein h_{1} is a constant, T_{0} is a point in time when G(t) is approximately zero, and f is a window function, so that said excited nuclear spins undergo a radiative free induction decay following termination of said excitation and so that nuclear spins in other regions of said object are substantially unexcited;means for applying to said object a spatial differentiation magnetic field H(x,y,t), during at least a portion of the free induction decay of said excited nuclear spins, said magnetic field having the form H _{0} +G_{1} (t)x+G_{2} (t)y;means for receiving radiated electromagnetic energy produced by said free induction decay and converting said energy to a time-varying electric signal representative of the magnitude of said energy; and means for operating on said electrical signal to generate therefrom signals representative of the spin density distribution in said slab. 2. The nuclear magnetic resonance apparatus of claim 1 in which G(t)=G
_{0} ((T_{0} ^{2} -t^{2})/T_{0} ^{2})exp[-(t/T_{0})^{2} /2].3. The nuclear magnetic resonance apparatus of claim 1 in which said receiving means comprises a coil disposed about said object.
4. The nuclear magnetic resonance apparatus of claim 1 in which said radio frequency pulse means includes a transmission coil disposed about the object.
5. The nuclear magnetic resonance apparatus of claim 4 in which said radio frequency pulse transmission coil is the same as the means for receiving radiated electromagnetic energy.
6. The nuclear magnetic resonance apparatus of claim 4 in which said radio frequency pulse transmission coil is disposed within and axially perpendicular to a coil operating as the means for receiving the radiated electromagnetic energy.
7. The nuclear magnetic resonance apparatus of claim 1 in which said functions G
_{1} (t) and G_{2} (t) are selected to produce K-space trajectories which are Lissajous figures.8. The nuclear magnetic resonance apparatus of claim 1 in which said functions G
_{1} (t) and G_{2} (t) are selected to produce K-space trajectories which are rosettes.9. The nuclear magnetic resonance apparatus of claim 1 in which said functions G
_{1} (t) and G_{2} (t) are selected to produce K-space trajectories which are Archimedian spirals.10. The nuclear magnetic resonance apparatus of claim 1 in which said functions G
_{1} (t) and G_{2} (t) are selected to produce K-space trajectories which are concentric circles.11. The nuclear magnetic resonance apparatus of claim 1 in which said spatial differentiation magnetic field H(x,y,t) defines a plurality of K-space trajectories, wherein said trajectories provide a complete and uniform coverage of K-space and wherein the dwell time in each region of K-space is approximately equal so that a detailed image of the entire portion of said object lying in the K-space plane is produced.
12. The nuclear magnetic resonance apparatus of claim 1 in which said spatial differentiation magnetic field H(x,y,t) defines a plurality of K-space trajectories, wherein said K-space trajectories concentrate on and have greater dwell time in selected region of K-space, thus enhancing the image contrast in said selected regions.
13. The nuclear magnetic resonance apparatus of claim 1 wherein the relation of the maximum absolute value G of said function G(t) to the peak amplitude H
_{1} of said function h_{1} (t) is given by the expression (G)(ΔZ)≈H_{1}. .Iadd.14. A nuclear magnetic resonance apparatus for determining spin-density distribution in a thin planar slab of an object under examination containing nuclear spins, said object being positioned in a static magnetic field, H
_{0}, and being oriented with respect to orthogonal x- and y-coordinate directions defined therein and also to a z-coordinate direction orthogonal to said slab and to said x and y coordinates within said slab, said apparatus comprising:excitation means for selectively exciting said nuclear spins in said slab so that said excited nuclear spins undergo a radiative free-induction decay thereby to produce an NMR signal in the form of radiated electromagnetic energy following termination of said excitation and so that nuclear spins in other regions of said object are substantially unexcited; means for applying to said object a spatial differentiation magnetic field H(x,y,t), during at least a portion of the NMR signal produced by said excited nuclear spins, said spatial differentiation magnetic field having the form H _{0} +G_{1} (t)x+G_{2} (t)y, wherein the magnetic-field gradients G_{1} (t) and G_{2} (t) are selected to be continuously varying with time during the NMR signal so as to produce a plurality of trajectories in K-space as parameter t varies, said trajectories being selectable to have variable uniformity and dwell times in predetermined regions of K-space;means for receiving the radiated electromagnetic energy associated with said NMR signal and converting said energy to a time-varying electric signal representative of the magnitude of said energy; and means for operating on said electrical signal to generate therefrom signals representative of the spin-density distribution in said slab. .Iaddend. .Iadd.15. The nuclear magnetic resonance apparatus of claim 14 in which said excitation means comprise: means for applying to said object for a predetermined time period an excitation magnetic field directed along said z direction, said excitation magnetic field having an intensity given by H _{0} +zG(t); andmeans for applying a pulse of electromagnetic, radio-frequency energy to said object during the time that said excitation magnetic field is applied, whereby the nuclear spins in said slab are selectively excited to a higher energy state and said nuclear spins in other regions of said object are substantially unexcited. .Iaddend. .Iadd.16. The nuclear magnetic resonance apparatus of claim 14 in which said excitation means operates by applying a time-dependent gradient magnetic field in the z direction together with a radio-frequency pulse. .Iaddend. .Iadd.17. The nuclear magnetic resonance apparatus of claim 14 wherein said excitation means includes means for applying to said object for a predetermined time period an excitation magnetic field having a gradient in the z-coordinate direction, said gradient being defined by a function G(t) not having a DC component, said excitation means also including means for applying a pulse of radio-frequency energy during the time that said excitation magnetic field is applied. .Iaddend. .Iadd.18. The nuclear magnetic resonance apparatus of claim 17 wherein
G(t)=G where G _{0} is a magnitude constant,T _{0} is a point in time when G(t) is substantially zero, andt is a time parameter. .Iaddend. .Iadd.19. The nuclear magnetic resonance apparatus of claim 17 wherein said pulse of radio-frequency energy comprises a pulse having an envelope defined by a function h where h _{1} is a constant,γ is the gyromagnetic ration, and f is a window function in which K(t)=γ∫ .Iadd.20. The nuclear magnetic resonance apparatus of claim 19 wherein the relation of the maximum absolute value G of said function G(t) to the peak amplitude H _{1} of said function h_{1} (t) is given by the expression(G) (ΔZ)≈H where ΔZ is the thickness of the excited slab. .Iaddend. .Iadd.21. The nuclear magnetic resonance apparatus of claim 14 in which said receiving means comprises a coil disposed about said object. .Iaddend. .Iadd.22. The nuclear magnetic resonance apparatus of claim 14 in which said excitation means includes a transmission coil disposed about the object. .Iaddend. .Iadd.23. The nuclear magnetic resonance apparatus of claim 22 in which said radio-frequency pulse transmission coil is the same as the means for receiving radiated electromagnetic energy. .Iaddend. .Iadd.24. The nuclear magnetic resonance apparatus of claim 22 in which said radio-frequency pulse transmission coil is disposed within and axially perpendicular to a coil operating as the means for receiving the radiated electromagnetic energy. .Iaddend. .Iadd.25. The nuclear magnetic resonance apparatus of claim 14 wherein said means for applying a spatial differentiation magnetic field includes means for simultaneously applying magnetic-field gradients G
_{1} (t) and G_{2} (t), such that in the sequential applications thereof said gradients produce K-space trajectories which transverse K-space in a substantially uniform pattern, and wherein the dwell time in each region of K-space is approximately equal so that a detailed image of all spatial frequency components, up to a maximum spatial frequency, of said object is produced. .Iaddend. .Iadd.26. The nuclear magnetic resonance apparatus of claim 14 wherein said means for applying a spatial differentiation magnetic field includes means for simultaneously applying magnetic-field gradients G_{1} (t) and G_{2} (t), such that, in the sequential applications thereof, said gradients produce K-space trajectories which concentrate on and have a greater dwell time in predetermined regions of K-space so as to enhance predetermined qualities in the reconstructed image. .Iaddend. .Iadd.27. The nuclear magnetic resonance apparatus of claim 14 in which said functions G
_{1} (t) and G_{2} (t) are selected to produce a K-space trajectory which is a Lissajous figure. .Iaddend. .Iadd.28. The nuclear magnetic resonance apparatus of claim 14 in which said functions G_{1} (t) and G_{2} (t) are selected to produce a K-space trajectory which is a rosette. .Iaddend. .Iadd.29. The nuclear magnetic resonance apparatus of claim 14 in which said functions G_{1} (t) and G_{2} (t) are selected to produce a K-space trajectory which is an Archimedian spiral. .Iaddend. .Iadd.30. The nuclear magnetic resonance apparatus of claim 14 in which said functions G_{1} (t) and G_{2} (t) are selected to produce K-space trajectories which are concentric circles. .Iaddend. .Iadd.31. The nuclear magnetic resonance apparatus of claim 14 wherein said means for operating includes means for determining the local nuclear spin density μ^{R} (x,y) distribution in said slab by evaluatingμ where V(t) is the voltage induced in a receiver coil sensing the NMR signal, f(t) is a weighting function, -i is the square root of -1, K _{1} (t) and K_{2} (t) are functions defining a point in K-space, andω _{1} is the resonant frequency offset at (x,y). .Iaddend. .Iadd. A nuclear magnetic resonance apparatus for determining spin-density distribution in a region of an object under examination containing nuclear spins, said region being positioned in a static magnetic field, H
_{0}, and being oriented with respect to orthogonal x- and y-coordinate directions defined therein and also to a z-coordinate direction orthogonal to said x and y coordinates within said region, said apparatus comprising:excitation means for exciting said nuclear spins in said region so that said excited nuclear spins undergo a radiative free-induction decay thereby to produce an NMR signal in the form of radiated electromagnetic energy following termination of said excitation; means for applying to said region a spatial differentiation magnetic field H(x,y,t), during at least a portion of the NMR signal produced by said excited nuclear spins, said spatial differentiation magnetic field having the form H _{0} +G_{1} (t)x+G_{2} (t)y, wherein the magnetic field gradients G_{1} (t) and G_{2} (t) are selected to be continuously varying with time during the NMR signal so as to produce a trajectory in K-space, said trajectory being selectable to have variable uniformity and dwell times in predetermined regions of K-space;means for receiving the radiated electromagnetic energy associated with said NMR signal and converting said energy to a time-varying electric signal representative of said energy; and means for operating on said electrical signal to generate therefrom signals representative of the spin-density distribution in said region. .Iaddend. .Iadd.33. The nuclear magnetic resonance apparatus of claim 32 in which said excitation means comprise:
means for applying for a predetermined time period to said object an excitation magnetic field directed along said z direction said excitation magnetic field having an intensity given by H _{0} +zG(t); andmeans for applying a pulse of electromagnetic, radio-frequency energy to said object during the time that said excitation magnetic field is applied, whereby the nuclear spins in said region are selectively excited to a higher energy state and said nuclear spins in other regions of said object are substantially unexcited. .Iaddend. .Iadd.34. The nuclear magnetic resonance apparatus of claim 32 in which said excitation means operates by applying a time-dependent gradient magnetic field in the z direction together with a radio-frequency pulse. .Iaddend. .Iadd.35. The nuclear magnetic resonance apparatus of claim 32 wherein said excitation means includes means for applying to said object for a predetermined time period an excitation magnetic field having a gradient in the z-coordinate direction, said gradient being defined by a function G(t) not having a DC component, said excitation means also including means for applying a pulse of radio-frequency energy during the time that said excitation magnetic field is applied. .Iaddend. .Iadd.36. The nuclear magnetic resonance apparatus of claim 35 wherein
G(t)=G where G _{0} is a magnitude constant,T _{0} is a point in time when G(t) is substantially zero, andt is a time parameter. .Iaddend. .Iadd.37. The nuclear magnetic resonance apparatus of claim 36 wherein said pulse of radio-frequency energy comprises a pulse having an envelope defined by a function h where h _{1} is a constant,γ is the gyromagnetic ration, and f is a window function in which K(t)=γ.sub.∫ ^{t} G(t')dt'. .Iaddend. .Iadd.38. The nuclear magnetic resonance apparatus of claim 37 wherein the relation of the maximum absolute value G of said function G(t) to the peak amplitude H_{1} of said function h_{1} (t) is given by the expression(G) (ΔZ)≈H where ΔZ is the thickness of the excited region. .Iaddend. .Iadd.39. The nuclear magnetic resonance apparatus of claim 32 wherein said excitation means includes means for exciting said region a plurality of times so as to produce a corresponding plurality of NMR signals, and wherein said means for applying includes means for applying a spatial differentiation magnetic field during at least a portion of each of said plurality of NMR signals such that a K-space trajectory produced for at least one of said NMR signals differs from a trajectory produced for another one of said NMR signals by at least one trajectory parameter. .Iaddend. .Iadd.40. The nuclear magnetic resonance apparatus of claim 39 wherein said trajectory parameter comprises at least one of uniformity and dwell time. .Iaddend. .Iadd.41. The nuclear magnetic resonance apparatus of claim 39 wherein said trajectory parameter is selected such that collectively said K-space trajectories traverse K-space in a substantially uniform pattern. .Iaddend. .Iadd.42. The nuclear magnetic resonance apparatus of claim 39 wherein said trajectory parameter is selected so as to vary the dwell time of said trajectories in said K-space. .Iaddend. .Iadd.43. The nuclear magnetic resonance apparatus of claim 32 in which said functions G _{1} (t) and G_{2} (t) are selected to produce a K-space trajectory which is a Lissajous figure. .Iaddend. .Iadd.44. The nuclear magnetic resonance apparatus of claim 32 in which said functions G_{1} (t) and G_{2} (t) are selected to produce a K-space trajectory which is a rosette. .Iaddend. .Iadd.45. The nuclear magnetic resonance apparatus of claim 32 in which said functions G_{1} (t) and G_{2} (t) are selected to produce a K-space trajectory which is an Archimedian spiral. .Iaddend. .Iadd.46. The nuclear magnetic resonance apparatus of claim 32 in which said functions G_{1} (t) and G_{2} (t) are selected to produce K-space trajectories which comprises concentric circles. .Iaddend. .Iadd.47. The nuclear magnetic resonance apparatus of claim 32 wherein said means for operating includes means for determining the local nuclear spin density μ^{R} (x,y) distribution in said region by evaluatingμ where V(t) is the voltage induced in a receiver coil sensing the NMR signal, f(t) is a weighting function, -i is the square root of -1, K _{1} (t) and K_{2} (t) are functions defining a point in K-space, andω _{1} is the resonant frequency offset at (x,y). .Iaddend. .Iadd.48. The nuclear magnetic resonance apparatus of claim 32 wherein said means for applying a spatial differentiation magnetic field includes means for simultaneously applying magnetic-field gradients G_{1} (t) and G_{2} (t), such that in the sequential applications thereof said spatial differentiation magnetic field produces K-space trajectories which collectively traverse K-space in a substantially uniform pattern, and wherein the dwell time in each region of K-space is approximately equal so that a detailed image of all spatial frequency components, up to a maximum spatial frequency, of said object can be produced. .Iaddend. .Iadd.49. The nuclear magnetic resonance apparatus of claim 32 wherein said means for applying a spatial differentiation magnetic field includes means for simultaneously applying magnetic-field gradients G_{1} (t) and G_{2} (t), such that, in the sequential applications thereof, said spatial differentiation magnetic field produces K-space trajectories which collectively concentrate on and have a greater dwell time in predetermined regions of K-space so as to enhance predetermined qualities in the reconstructed image. .Iaddend. .Iadd.50. A nuclear magnetic resonance apparatus for determining spin-density distribution in a thin planar slab of an object under examination containing nuclear spins, said object being positioned in a static magnetic field, H_{0}, and being oriented with respect to first and second orthogonal directions defined therein, said apparatus comprising:excitation means for selectively exciting said nuclear spins in said slab so that said excited nuclear spins undergo a radiative free-induction decay thereby to produce an NMR signal in the form of radiated electromagnetic energy following termination of said excitation and so that nuclear spins in other regions of said object are substantially unexcited; means for applying to said object a spatial differentiation magnetic field H(x,y,t), during at least a portion of the NMR signal produced by said excited nuclear spins, said spatial differentiation magnetic field having the form H _{0} +G_{1} (t)x+G_{2} (t)y, wherein x and y designate, respectively, said first and second directions, and wherein the magnetic-field gradients G_{1} (t) and G_{2} (t) are selected to be continuously varying with time during the NMR signal so as to produce a trajectory in K-space;means for receiving the radiated electromagnetic energy associated with said NMR signal and converting said energy to a time-varying electric signal representative of the magnitude of said energy; and means for operating on said electrical signal to generate therefrom signals representative of the spin-density distribution in said slab. .Iaddend. .Iadd.51. The nuclear magnetic resonance apparatus of claim 50 wherein said means for applying a spatial differentiation magnetic field includes means for simultaneously applying magnetic-field gradients G _{1} (t) and G_{2} (t), such that in the sequential applications thereof said spatial differentiation magnetic field produces K-space trajectories which collectively traverse K-space in a substantially uniform pattern, and wherein the dwell time in each region of K-space is approximately equal so that a detailed image of all spatial frequency components, up to a maximum spatial frequency, of said object can be produced. .Iaddend. .Iadd.52. The nuclear magnetic resonance apparatus of claim 50 wherein said means for applying a spatial differentiation magnetic field includes means for simultaneously applying magnetic-field gradients G_{1} (t) and G_{2} (t), such that, in the sequential applications thereof, said spatial differentiation magnetic field produces K-space trajectories which collectively concentrate on and have a greater dwell time in predetermined regions of K-space so as to enhance predetermined qualities in the reconstructed image. .Iaddend. .Iadd.53. The nuclear magnetic resonance apparatus of claim 50 wherein said excitation means includes means for exciting said region a plurality of times so as to produce a corresponding plurality of NMR signals, and wherein said means for applying includes means for applying a spatial differentiation magnetic field during at least a portion of each of said plurality of NMR signals such that a K-space trajectory produced for at least one of said NMR signals differs from a trajectory produced for another one of said NMR signals by at least one trajectory parameter. .Iaddend. .Iadd.54. The nuclear magnetic resonance apparatus of claim 53 wherein said trajectory parameter comprises at least one of uniformity and dwell time. .Iaddend. .Iadd.55. The nuclear magnetic resonance apparatus of claim 53 wherein said trajectory parameter is selected such that collectively said K-space trajectories traverse K-space in a substantially uniform pattern. .Iaddend. .Iadd.56. The nuclear magnetic resonance apparatus of claim 53 wherein said trajectory parameter is selected so as to vary the dwell time of said trajectories in said K-space. .Iaddend. .Iadd.57. The nuclear magnetic resonance apparatus of claim 50 in which said functions G
_{1} (t) and G_{2} (t) are selected to produce a K-space trajectory which is a Lissajous figure. .Iaddend. .Iadd.58. The nuclear magnetic resonance apparatus of claim 50 in which said functions G_{1} (t) are selected to produce a K-space trajectory which is a rosette. .Iaddend. .Iadd.59. The nuclear magnetic resonance apparatus of claim 50 in which said functions G_{1} (t) and G_{2} (t) are selected to produce a K-space trajectory which is an Archimedian spiral. .Iaddend. .Iadd.60. The nuclear magnetic resonance apparatus of claim 50 in which said functions G_{1} (t) and G_{2} (t) are selected to produce K-space trajectories which comprises concentric circles. .Iaddend. .Iadd.61. The nuclear magnetic resonance apparatus of claim 50 wherein said means for operating includes means for determining the local nuclear spin density μ
^{R} (x,y) distribution in said slab by evaluatingμ where V(t) is the voltage induced in a receiver coil sensing the NMR signal, f(t) is a weighting funcion, -i is the square root of -1, K _{1} (t) and K_{2} (t) are functions defining a point in K-space, andω _{1} is the resonant frequency offset at (x,y). .Iadd.62. A nuclear magnetic resonance apparatus for determining spin-density distribution in a region of an object under examination containing nuclear spins, said region being positioned in a static magnetic field, H_{0}, and being oriented with respect to first and second orthogonal directions defined therein, said apparatus comprising:excitation means for exciting said nuclear spins in said region so that said excited nuclear spins undergo a radiative free-induction decay thereby to produce an NMR signal in the form of radiated electromagnetic energy following termination of said excitation; means for applying to said region a spatial differentiation magnetic field H(x,y,t), during at least a portion of the NMR signal produced by said excited nuclear spins, said magnetic field having the form Ho+G _{1} (t)x+G_{2} (t)y, wherein x and y designate, respectively, said first and second directions, and wherein the magnetic field gradients G_{1} (t) and G_{2} (t) are selected to be continuously varying with time during the NMR signal so as to produce a trajectory in K-space;means for receiving the radiated electromagnetic energy associated with said NMR signal and coverting said energy to a time-varying electric signal representative of said energy; and means for operating on said electrical signal to generate therefrom signals representative of the spin-density distribution in said region. .Iaddend. .Iadd.63. The nuclear magnetic resonance apparatus of claim 62 wherein said means for applying a spatial differentiation magnetic includes means for simultaneously applying magnetic-field gradients G
_{1} (t) and G_{2} (t), such that in the sequential applications thereof said spatial differentiation magnetic field produces K-space trajectories which traverse K-space in a substantially uniform pattern, and wherein the dwell time in each region of K-space is approximately equal so that a detailed image of all spatial frequency components, up to a maximum spatial frequency, of said object can be produced. .Iaddend. .Iadd.64. The nuclear magnetic resonance apparatus of claim 62 wherein said means for applying a spatial differentiation magnetic field includes means for simultaneously applying magnetic-field gradients G_{1} (t) and G_{2} (t), such that, in the sequential applications thereof, said spatial differentiation magnetic field produces K-space trajectories which concentrate on and have a greater dwell time in predetermined regions of K-space so as to enhance predetermined qualities in the reconstructed image. .Iaddend. .Iadd.65. The nuclear magnetic resonance apparatus of claim 62 wherein said excitation means includes means for exciting said region a plurality of times so as to produce a corresponding plurality of NMR signals, and wherein said means for applying includes means for applying a spatial differentiation magnetic field during at least a portion of each of said plurality of NMR signals such that a K-space trajectory produced for at least one of said NMR signals differs from a trajectory produced for another one of said NMR signals by at least one trajectory parameter. .Iaddend. .Iadd.66. The nuclear magnetic resonance apparatus of claim 65 wherein said trajectory parameter comprises at least one of uniformity and dwell time. .Iaddend. .Iadd.67. The nuclear magnetic resonance apparatus of claim 65 wherein said trajectory parameter is selected such that collectively said K-space trajectories traverse K-space in a substantially uniform patterne. .Iaddend. .Iadd.68. The nuclear magnetic resonance apparatus of claim 65 wherein said trajectory parameter is selected so as to vary the dwell time of said trajectories in said K-space. .Iaddend. .Iadd.69. The nuclear magnetic resonance apparatus of claim 62 in which said functions G
_{1} (t) and G_{2} (t) are selected to produce a K-space trajectory which is a Lissajous figure. .Iaddend. .Iadd.70. The nuclear magnetic resonance apparatus of claim 62 in which said functions G_{1} (t) and G_{2} (t) are selected to produce a K-space trajectory which is a rosette. .Iaddend. .Iadd.71. The nuclear magnetic resonance apparatus of claim 62 in which said functions G_{1} (t) and G_{2} (t) are selected to produce a K-space trajectory which is an Archimedian spiral. .Iaddend. .Iadd.72. The nuclear magnetic resonance apparatus of claim 62 in which said functions G_{1} (t) and G_{2} (t) are selected to produce K-space trajectories which are concentric circles. .Iaddend. .Iadd.73. The nuclear magnetic resonance apparatus of claim 62 wherein said means for operating includes means for determining the local nuclear spin density μ^{R} (x,y)distribution in said slab by evaluatingμ where V(t) is the voltage induced in a receiver coil sensing the NMR signal, f(t) is a weighting funcion, -i is the square root of -1, K _{1} (t) and K_{2} (t) are functions defining a point in K-space, andω _{1} is the resonant frequency offset at (x,y). .Iaddend. .Iadd.74. A nuclear magnetic resonance apparatus for determining spin-density distribution in a region of an object under examination containing nuclear spins, said object being positioned in a static magnetic field, H_{0}, and being oriented with respect to first and second orthogonal directions defined therein, said apparatus comprising:excitation means for applying to said object a time-dependent gradient and a radio frequency pulse, said radio frequency pulse being applied in the presence of said time-dependent gradient, and modulated so as to selectively excite said nuclear spins in said region so that said excited nuclear spins undergo a radiative free-induction decay thereby to produce an NMR signal in the form of radiated electromagnetic energy following termination of said excitation and so that nuclear spins in other regions of said object are substantially unexcited; means for applying to said object a spatial differentiation magnetic field during at least a portion of the NMR signal produced by said excited nuclear spins so as to encode in said NMR signal information of the spin-density distribution of said nuclear spins in said region; means for receiving the radiated electromagnetic energy associated with said NMR signal and converting said energy to a time-varying electric signal representative of the magnitude of said energy; and means for operating on said electrical signal to generate therefrom signals representative of the spin-density distribution in said region. .Iaddend. .Iadd.75. The nuclear magnetic resonance apparatus of claim 74 wherein said first and second orthogonal directions define, respectively, x- and y-coordinate directions, and further including a z-coordinate direction orthogonal to said x and y coordinates, wherein said excitation means comprises: means for applying to said object for a predetermined time period, an excitation magnetic field directed along said z direction, said excitation magnetic field having an intensity given by H _{0} +zG(t); andmeans for applying a pulse of electromagnetic, radio-frequency energy to said object during the time that said excitation magnetic field is applied, whereby the nuclear spins in said region are selectively excited to a higher energy state and said nuclear spins in other regions of said object are substantially unexcited. .Iaddend. .Iadd.76. The nuclear magnetic resonance apparatus of claim 75 wherein said excitation means includes means for applying to said object for a predetermined time period an excitation magnetic field having a gradient in the z-coordinate direction, said gradient being defined by a function G(t) not having a DC component, said excitation means also including means for applying a pulse of radio-frequency energy during the time that said excitation magnetic field is applied. .Iaddend. .Iadd.77. The nuclear magnetic resonance apparatus of claim 76 wherein
G(t)=G where G _{0} is a magnitude constant,T _{0} is a point in time when G(t) is substantially zero, andt is a time parameter. .Iaddend. .Iadd.78. The nuclear magnetic resonance apparatus of claim 75 wherein said pulse of radio-frequency energy comprises a pulse having an envelope defined by a function h where h _{1} is a constant,γ is the gyromagnetic ration, and f is a window function in which K(t)= ∫tG(t')dt'. .Iaddend. .Iadd.79. The nuclear magnetic resonance apparatus of claim 78 wherein the relation of the maximum absolute value G of said function G(t) to the peak amplitude H _{1} of said function h_{1} (t) is given by the expression(G) (ΔZ)≈H where ΔZ is the thickness of the excited slab. .Iaddend. .Iadd.80. The nuclear magnetic resonance apparatus of claim 78 wherein said means for operating includes means for determining the local nuclear spin density μ ^{R} (x,y) distribution in said region is given byμ where V(t) is the voltage induced in a receiver coil sensing the NMR signal, f(t) is a weighting function, -i is the square root of -1, K _{1} (t) and K_{2} (t) are functions defining a point in k-space, andω _{1} is the resonant frequency offset at (x,y). .Iaddend. .Iadd. A nuclear magnetic resonance apparatus for determining spin density distribution in a region of an object under examination containing nuclear spins, said region being positioned in a static magnetic field, H
_{0}, and being oriented with respect to orthogonal x and y coordinate directions defined therein and also to a z coordinate direction orthogonal to said x and y coordinates with said region, said apparatus comprising:excitation means for exciting said nuclear spins in said region so that said excited nuclear spins undergo a radiative free-induction decay thereby to produce an NMR signal in the form of radiated electromagnetic energy following termination of said excitation; means for applying to said region a spatial differentiation magnetic field H(x,y,t), during at least a portion of the NMR signal produced by said excited nuclear spins, said magnetic field having the form H _{0} +G_{1} (t)_{x} +G_{2} (t)_{y}, wherein at least one of the magnetic field gradients G_{1} (t) and G_{2} (t) is chosen to be varying with time during the NMR signal so as to produce a trajectory in K-space, said K-space being the Fourier transform space within which the spatial frequency of the distribution related to the spin density within said region under examination can be specified, and wherein said spatial differentiation magnetic field is chosen such that the frequency history of the spins at each point of said region is distinguishably different from that of every other point;means for receiving the radiated electromagnetic energy associated with said NMR signal and converting said energy to a time-varying electric signal representative of said energy; and means for operating on said electrical signal to generate therefrom, based on the frequency history of the spins, signals representative of the spin density distribution in said region. .Iaddend. .Iadd.82. The apparatus of claim 81 wherein both gradients G
_{1} (t) and G_{2} (t) are varying with time. .Iaddend.Description .Iadd.This application is a continuation of application Ser. No. 814,170, filed 12/23/85 and now abandoned. .Iaddend. This invention relates to a nuclear magnetic resonance apparatus for use in producing two-dimensional images of internal body structures and more particularly it relates to nuclear magnetic resonance apparatus in which two-dimensional spin density distribution is selectively encoded into a rapidly observable time signal whereby the necessary data for image reconstruction is immediately available. Nuclear magnetic resonance is a phenomenon first observed by physicists. When the positively charged and spinning atomic nucleus is placed in a uniform magnetic field, there is a precession of the spin axis of the nucleus. The angular frequency of precession ω depends on the magnetic field strength H and a constant γ which is called the gyromagnetic ratio. The relation between these quantities is given by:
ω=γH. (1) Once the nucleus is set to precessing in such a magnetic field, it is thereafter capable of absorbing electromagnetic radiation at the angular precession frequency. Following absorption of electromagnetic energy, the nucleus reradiates some of the energy which may be subsequently detected and observed. The water molecule is one that is particularly amenable to study by such nuclear magnetic resonance methods. This amenability to study is largely thought to arise from the unpaired hydrogen protons in the water molecule. Because biological cells and tissues comprise water as a major constituent, nuclear magnetic resonance methods are particularly applicable to such specimens. In particular by determining the nuclear spin population density in various portions of a biological specimen, it is possible to generate an image representative of internal body structures. because carcinomic cell structures exhibit a peculiar affinity for water, these structures are well suited for detection by nuclear magnetic resonance imaging methods. A typical value for the above-mentioned gyromagnetic ratio γ is approximately 4.26 KHz/gauss. For a magnetic field strength H of approximately 1.2 kilogauss, equation (1) above implies that a radio frequency electromagnetic field of approximately 5.1 MHz is appropriate for nuclear spin excitation. Following this excitation two separate relaxation times occur during which the sample reradiates. The spin-lattice relaxation time, T Nuclear magnetic resonance imaging as a medical diagnostic method offers significant advantages, the most significant of which being the total noninvasive nature of the procedure. No ionizing radiation is employed as is done in present computerized tomographic imaging systems. However, in spite of apparent efforts to solve the problem, investigators in this field have long been plagued with the problem of exposure time length required to insure that image resolution is adequate. A general requirement for two-dimensional zeugmatographic image reconstruction is that the signal representing the radiation from a particular pixel (picture element) be essentially independent of the signal generated by all nuclear spins except the ones in the physical location corresponding to the pixel position. In some of the nuclear magnetic resonance imaging methods proposed, this pixel identification has been accomplished by operating on one pixel at a time (or one or more lines at a time) and discarding the signals from the remainder of the image. For example, such methods are described in "Image Formation by Nuclear Magnetic Resonance: The Sensitive-Point Method" by W. Hinshaw in Vol. 47, No. 8, pp. 3709-3721 of the Journal of Applied Physics (1975) and also in "Biological and Medical Imaging by NMR" by P. Mansfield and I. L. Pykett in Vol. 29, pp. 355-373 of the Journal of Magnetic Resonance (1978). Others achieved this pixel identification by coherently adding the signals from many separate Fourier Transforms of the object. Such methods are described in "NMR Fourier Zeugmatography" by Kumar, Webti, and Ernst in Vol. 18, pp. 69-83 of the Journal of Magnetic Resonance (1975) and in "Sensitivity and Performance Time in NMR Imaging" by P. Bruner and R. R. Ernst in Vol. 33, pp. 83-106 of the Journal of Magnetic Resonance (1979). Finally, in another method of pixel identification, the images are reconstructed by coherently adding the signal generated in many one-dimensional projections. Such a method is described in "Image Formation by Induced Local Interactions: Examples Employing Nuclear Magnetic Resonance" by P. C. Lauterbur in Nature, Vol. 242, No. 5394, pp. 190-191 (1973). However, while these methods generally accomplish the desired objective, they result in poor signal-to-noise ratio for the reconstructed image unless the data is obtained from a very large number of free induction delays. However, such approaches require a length of time to acquire such data for exceeding the length of time that a patient can be expected to remain immobilized. An alternative approach to this problem is to apply time-varying magnetic field gradients, such that the frequency history of the spins in each pixel is distinguishably different from that of every other pixel. This latter approach taken in the present invention is more particularly described below. In accordance with a preferred embodiment of the present invention, an apparatus for determining nuclear magnetic resonance spin density distributions comprises means for selectively exciting a slab of an object under examination, means for applying to said object a spatial differentiation magnetic field, means for receiving radiated electromagnetic energy from said body, and means for operating on an electrical signal produced by said radiation to generate therefrom other signals representative of the spin density distribution in the slab. For ease of presenting descriptions of the apparatus herein, a coordinate frame of reference having mutually perpendicular x, y and z axes are used, said x and y coordinate axes being within the slab of interest and said z direction axis being perpendicular to said slab. Throughout the data collection period, a constant magnetic field having an intensity H In accordance with another embodiment of the present invention following the above-described excitation for producing free nuclear precession, spatial differention means are engaged for applying to said object a magnetic field having the form H FIG. 1 is a schematic block diagram illustrating the organization of an imaging apparatus in accordance with the present invention. FIG. 2 is a partial cross-sectional side elevation view (looking into the y-z plane) illustrating the relationships between the magnetic field and radio frequency coils to the body under investigation. FIG. 3 is a front elevation view of the apparatus of FIG. 2, that is, looking into the x-z plane. FIG. 4 is a detail drawing of a portion of FIGS. 2 and 3 illustrating the placement of the gradient coils. FIG. 5 is a partial cross-sectional view illustrating an alternate arrangement between the transmitting radio frequency coil and the receiving radio frequency coil. FIG. 6 illustrates several curves which are related to the magnetic excitation signal. FIGS. 7-9 illustrate several possible K-space trajectories. (The concept of K-space is described below). Before a description of the actual apparatus preferably employed in practicing the present invention is described, it is instructive to consider the various stages of the imaging process. In the apparatus of the present invention, there are three such stages: excitation, spatial differentiation, and reconstruction. In the excitation stage, a constant magnetic field H
H(z,t)=H The second stage of image generation is referred to as spatial differentiation. Once having excited a thin slab of spins within the body under investigation by applying a magnetic field such as that given in equation (2) and by concurrently applying a radio frequency radiative source to excite said nuclear spins, the excitation is removed and spin relaxation occurs. During spin relaxation, previously absorbed magnetic radiation is reradiated and typically received by a coil surrounding the body. During this free induction decay time period following excitation, the sample is subjected to a different magnetic field. This second applied magnetic field is given by:
H(x,y,t)=H As is seen above, this spatial differentiation magnetic field does not depend upon z. It is to be particularly noted, to avoid confusion, that the functions of time G
G
G Additionally, two functions, K
Φ(x,y,t)=K The last linear term in ωt corresponds to the free precession frequency ω at the average value of the field, H
V(t)=C where C
V(t)=I(t)+iQ(t) (11) It is also to be noted that in equation (10) T Next considered is the third and last stage of nuclear magnetic resonance image generation produced in accordance with the present invention. The object of reconstruction is to determine μ(x,y) from V(t). These quantities, according to equation (10), are related like Fourier transforms except for the factor exp[-t/T In general, the reconstruction from V(t) takes the following form:
μ where μ
ω where ΔH(x,y) represents slight variations in the H Having considered the three stages of image generation, attention is now turned to the apparatus of the present invention for carrying out the functions associated with each of the above-described stages, namely, excitation, spatial differentiation, and reconstruction. FIG. 1 is a schematic diagram indicating the interrelationship between the various portions of the present nuclear magnetic resonant imaging apparatus. A description of this apparatus is best begun at the object 20 which is the specimen from which an image is generated. This object is subjected to static magnetic field by means of static magnetic field coils 100. These coils are operating during the entire data collection process (excitation and spatial differentiation stages) to generate a constant magnetic field H FIG. 2 is important for an understanding of the relationships between the physical parts of the present apparatus. In FIG. 2 is shown specimen body 20 where thin slab 21 is shown in phantom view. Planar slab 21 has oriented therein x and y coordinate directions. A normal to the slab defines the z coordinate direction so that the x, y, and z axis form the mutually orthogonal directions of a Cartesian coordinate system. Surrounding the body 20 is receiving coil 22. Surrounding receiving coil 22 is transmission coil 24. An alternate configuration of these coils is shown in FIG. 5. The static magnetic field H FIG. 3 is a view of the apparatus shown in FIG. 2 viewed from a direction orthogonal to the x-z plane. Here shown are receiving coil 22 and transmission coil 24 surrounding the specimen 20 with the desired slab 21 therein lying in the x-y plane. Because of the relative strength of the transmitted and received electromagnetic radiation, it is preferred that the receiving coil 22 be located more proximal to the excited slab. An alternate orientation of the receiving coil is shown in FIG. 5. Also shown in FIG. 3 are electromagnetic structures 30 for providing a static and uniform and magnetic field H FIG. 4 illustrates a portion of the apparatus shown in FIGS. 2 and 3. In particular, it illustrates the relationship of the gradient coils to electromagnetic structure 30 in the vicinity of the specimen. Gradient coils 26, 26', 28 and 28' are shown. It is, of course, understood that these conductors are insulated from one another. These current carrying conductors, along with their counterparts 27, 27', 29, and 29', produce the desired magnetic fields within the specimen 20 when driven by appropriate current signals from audio amplifier 124. FIG. 5 illustrates an alternate arrangement of the transmission and receiving coils 24 and 22, respectively. In particular, FIG. 5 describes a portion of the same view seen in FIG. 2. However, in FIG. 5, receiving coil 22 is now oriented orthogonally to the axis of the transmission coil 24, whereas in FIG. 2 the axis of these respective coils are substantially coincident. The configuration shown in FIG. 5 is preferred because this configuration produces minimal interference with the radio frequency pulses during the excitation stage. Next are considered the specific details for proper selective excitation. To achieve the maximal resolution and two-dimensional imaging for a limited bandwidth and fixed scan time, it is necessary to limit the region of excitation to a relatively thin slab. This can be accomplished by providing a spatially dependent ratio frequency field which saturates the spins outside a selected plane, or by low frequency (audio) magnetic field gradients which establish spatially dependent precession frequencies for selective excitation. The latter approach is preferably employed in the present invention. Regardless of the method used to achieve this selective excitation, a truly two-dimensional imaging method prevents the dephasing of adjacent spins on opposite surfaces of the two-dimensional excited region. This implies that the gradient must be greatly reduced during the free induction decay. To insure that nuclear spins at a greater offset z distance than a few Δz are not greatly excited by the radio frequency field, it is required that:
(G)(Δz)≈H where G is the maximum absolute value of G(t) and H If the imaging period is longer than T There are two criteria to be satisfied by spatially adequate selective excitation. The first of these is that the excitation be well confined to a definite physical region, that is the "tails" of the excited region are negligible. Second, the signal from all spins should add coherently, that is, the transverse magnetization points everywhere in the same direction. To satisfy these requirements, it is necessary to apply an audio field gradient orthogonal to the desired plane of excitation and to use long radio frequency pulses with controlled, carefully shaped envelopes determined by the time dependence of the audio field gradient G(t). The function K(t) is defined as follows: ##EQU3## If this is the case, then the relative phase φ' of spin located Δz above the center of the desired slab is:
φ'=-K(t)Δz (16) To achieve a well localized excitation, it is necessary that the radio frequency pulse envelope (which vanishes outside the interval [-K
h wherein h
G(t)=G
K(t)=γG Next is considered specific details associated with the reconstruction stage and the spatial differentiation stage of image generation. Several examples of K-space trajectories are now considered. These include the Lissajous trajectories, the "bull's eye" trajectories, and the rosette trajectories. An example of a Lissajous trajectory is seen in FIG. 7. For a Lissajous trajectory, it is seen that K
K
K where a Another suitable trajectory for K-space is the rosette pattern illustrated in FIG. 8. For the rosette K-space trajectory, suitable choices for K
K
K where K,a
KΔx≈π. (25) For these conditions, Δx is approximately equal to 0.3 cm. The rosette pattern shown in FIG. 8 is rotated by 6° after each reexcitation pulse. This results in complete coverage of a disk in K-space after 20 repetitions of excitation for a period τ followed by relaxation for a period T. In the above example, these 20 repetitions are accomplished in approximately 0.76 secs. This sequence generates data necessary for imaging objects of approximately 30 cm
X(ΔK)≈π (26) where ΔK is the typical spacing between adjacent portions of the trajectory in K-space and X is the diameter of the sample. The rosette trajectory is particularly well suited in its simplicity; the x and y gradient fields are produced with the sum of two sinusoidally varying currents each. Additionally, matched filter reconstruction algorithms for this trajectory lead to closed-form analytical expressions for the point response functions. An additional K-space trajectory is the spiral of Archimedes, r=aθ, expressed parametrically as: ##EQU5## Typical values for the constants in the above equations for the spiral of Archimedes include a value of 6.7×10 Next is considered a set of K-space trajectories referred to herein as the "bull's eye" pattern, the term being obvious from the pattern depicted in FIG. 9. A preferred form of the reconstruction algorithm is given for this pattern. In particular, consider the series of N+1 circles in K-space given by:
K
K for n=0, 1, . . . , N. The form of these trajectories is shown in FIG. 9 for n=1, 2, 3, 4, 5. For n=0, the trajectory is obviously the single point at the origin in the K-space. If the nuclear spins are prepared in the initial state where K
G
G if the spins begin at K
V This may be substituted into equation (37) to yield: ##EQU12## in which K is treated as a continuous variable. The solution of equation (40) is then immediately provided by the Hankel transform inversion formula (see "Tables of Integral Transforms", Vol. 2, page 5 by Erdelyi et al.): ##EQU13## Equation 41 may written as an approximate integral having the following form: ##EQU14## In view of equations (38) and (42), μ(r,θ) is solved for as follows: ##EQU15## The limits on the summation over n in equation (43) are determined by bandwidth of the system as expressed in equation (36). The condition that the effective sampling rate in K-space be equal for the radial and angular directions leads to the condition that M(n) is approximately equal to π(n), which implies that the number of side bands required is proportional to the radius of the circle in K-space. The required bandwidth B is given by:
B=2M∫ It is also noted that in equation (36) the V It is also noted that less esoteric algorithms may be applied to effect an image reconstruction. In particular, it is noted that a matched filter could be provided (algorithmically) for each pixel. Digital filter methods for such operations are well known, but because of the large number of pixels, an algorithmic approach such as this requires a large amount of time to generate an image. From the above, it may be appreciated that the apparatus of the present invention may be operated in a rapid manner to produce images representative of nuclear magnetic resonant spin densities quickly and accurately. The spatial spin density information is encoded into a time-dependent signal. The field gradients employed in the present invention are readily realizable and permit transformation of the spatial information of the object into a temporal dependence which is readily reconstrucible. Straightforward linear reconstruction algorithms are employed. Additionally, the field uniformity requirements of the present invention are significantly better than other methods of nuclear magnetic resonant imaging. Also, the apparatus of the present invention operates to selectively excite a well-defined slab of the specimen. The imaging method of the present invention leads to a greater contrast among the internal organs than is presently available in other nuclear magnetic resonance imaging devices. While the invention has been described with reference to particular embodiments and examples, other modifications and variations will occur to those skilled in the art in view of the above teachings. Accordingly, it should be understood that within the scope of the appended claims, the invention may be practiced otherwise than is specifically described. Patent Citations
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