CN113917378B - Magnetic resonance imaging method and magnetic resonance imaging system - Google Patents
Magnetic resonance imaging method and magnetic resonance imaging system Download PDFInfo
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- CN113917378B CN113917378B CN202010655405.4A CN202010655405A CN113917378B CN 113917378 B CN113917378 B CN 113917378B CN 202010655405 A CN202010655405 A CN 202010655405A CN 113917378 B CN113917378 B CN 113917378B
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
- G01R33/48—NMR imaging systems
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
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Abstract
The invention discloses a magnetic resonance imaging method and a magnetic resonance imaging system, wherein the method comprises the following steps: acquiring a target object; applying a two-dimensional selective pulse sequence to the target object to excite nuclear spins of at least two slices of the target object simultaneously, the applying the two-dimensional selective pulse sequence to the target object comprising: applying polarity inversion gradients to the two layers along the phase encoding direction, and applying discrete encoding gradients to the two layers along the layer selecting direction, wherein the application time of the discrete encoding gradients is consistent with the polarity inversion time of the polarity inversion gradients; applying phase encoding gradients along a first direction and a second direction to the two layers to perform phase encoding on nuclear spins of the two layers, and applying readout encoding gradients along a third direction to acquire magnetic resonance signals of the two layers; the magnetic resonance signals are acquired and reconstructed to generate a magnetic resonance image of the target object. The problem of high radio frequency energy absorptivity of the multilayer simultaneous imaging technology is solved.
Description
Technical Field
The embodiment of the invention relates to the field of magnetic resonance imaging, in particular to a magnetic resonance imaging method and a magnetic resonance imaging system.
Background
The nuclear magnetic resonance imaging technology can obtain various contrast parameter images of human bodies in a noninvasive and non-radiative way, and is widely used in clinic. However, the imaging scan time is relatively long, and various acceleration imaging techniques are continuously proposed and perfected for shortening the imaging scan time, including a partial fourier technique, an intra-layer parallel imaging technique, a layer-direction parallel excitation technique, a compressed sensing technique, and the like, or a combination of techniques for achieving a higher acceleration multiple. Among these, there are layer-direction parallel imaging techniques, PINS based on layer-direction encoding, and SMS of simultaneous multi-layer RF synthesis techniques.
Multi-layer simultaneous imaging (SMS) technology utilizes the cooperation of multi-band rf pulses and layer-selective gradients to achieve simultaneous excitation of multiple layers, which typically results in greater radio frequency energy absorption rate (SAR) deposition and requires higher power amplifier systems for magnetic resonance systems. The radio frequency energy absorption rate refers to the radio frequency energy absorbed by a human body in a unit weight in a unit time, namely, how much energy is deposited in the unit weight. When the radio frequency energy absorption rate reaches a certain threshold value, the magnetic resonance imaging system automatically stops scanning until the local absorbed radio frequency energy is released to a safe range, and then the scanning is started again, and the scanning is repeated in such a way, so that the multi-layer simultaneous imaging technology cannot greatly improve the scanning efficiency.
In summary, the multi-layer simultaneous imaging technology of the prior art has lower scanning efficiency due to higher radio frequency energy absorptivity.
Disclosure of Invention
The embodiment of the invention provides a magnetic resonance imaging method and a magnetic resonance imaging system, which solve the problem of higher radio frequency energy absorptivity in the multilayer simultaneous imaging technology in the prior art.
In a first aspect, an embodiment of the present invention provides a magnetic resonance imaging method, including:
acquiring a target object;
applying a two-dimensional selective pulse sequence to a target object to excite nuclear spins of at least two slices of the target object simultaneously, the applying the two-dimensional selective pulse sequence to the target object comprising: applying a polarity inversion gradient to the at least two layers along a phase encoding direction, and applying a discrete encoding gradient to the at least two layers along a layer selection direction, wherein the application time of the discrete encoding gradient is consistent with the polarity inversion time of the polarity inversion gradient;
after the two-dimensional selective pulse sequence is finished, applying phase encoding gradients along a first direction and a second direction to the at least two layers to perform phase encoding on nuclear spins of the at least two layers, and applying readout encoding gradients along a third direction to acquire magnetic resonance signals of the at least two layers;
The magnetic resonance signals are acquired and reconstructed to generate a magnetic resonance image of the target object.
In a second aspect, an embodiment of the present invention further provides a magnetic resonance imaging system, including:
the bed body is used for bearing a target object;
the radio frequency transmitting coil is used for transmitting radio frequency pulses to the target object;
gradient coils for generating gradient fields;
a radio frequency receiving coil for receiving magnetic resonance signals;
a processor for controlling the radio frequency transmit coil to apply a two-dimensional selective pulse sequence to at least two slices of the target object to excite nuclear spins of the at least two slices of the target object simultaneously; during the application of the two-dimensional selective pulse sequence, further for controlling the gradient coils to apply a polarity inversion gradient to the at least two slices in a phase encoding direction and to apply a discrete encoding gradient to the at least two slices in a slice selection direction; and after the two-dimensional selective pulse sequence is finished, controlling the gradient coil to apply phase encoding gradients along the first direction and the second direction to the at least two layers to encode nuclear spins of the at least two layers, thereby generating magnetic resonance signals of the at least two layers; the radio frequency receiving coil is also used for controlling the radio frequency receiving coil to receive the magnetic resonance signals; and is further configured to image reconstruct the received magnetic resonance signals to generate a magnetic resonance image of the target object; wherein the time of application of the discrete encoding gradient coincides with the time of polarity reversal of the polarity reversal gradient.
Compared with the prior art that nuclear spins of at least two layers of a target object are excited simultaneously by one-dimensional radio frequency pulses, the embodiment of the invention can greatly reduce the intensity of radio frequency pulses by two-dimensional selective pulse sequences, thereby reducing SAR in the target object body, enabling the magnetic resonance imaging system to continuously perform imaging scanning without suspending the imaging scanning because SAR is too high, and thus being beneficial to improving the scanning efficiency of the magnetic resonance imaging system.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a magnetic resonance imaging method according to a first embodiment of the present invention;
FIG. 2A is a sequence diagram of an imaging scan according to a first embodiment of the present invention;
FIG. 2B is a sequence diagram of another imaging scan according to an embodiment of the present invention;
FIG. 2C is a sequence diagram of another imaging scan according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a coding direction according to a first embodiment of the present invention;
FIG. 4A is a schematic diagram of a target object including two levels of localization excited by a spike-encoded gradient provided in accordance with an embodiment of the present invention;
FIG. 4B is a schematic diagram of a target object including a region of interest positioned by polarity inversion gradient excitation according to an embodiment of the present invention;
FIG. 4C is a schematic diagram of an original magnetic resonance image corresponding to magnetic resonance signals acquired without simultaneous application of encoding gradients in a slice selection direction and a phase encoding direction according to an embodiment of the present invention;
FIG. 4D is a schematic diagram of an original magnetic resonance image corresponding to magnetic resonance signals acquired by applying encoding gradients simultaneously in a slice selection direction and a phase encoding direction according to an embodiment of the present invention;
FIG. 4E is a schematic diagram of an original MR image obtained by a conventional simultaneous multi-slice excitation imaging method according to an embodiment of the present invention;
fig. 5 is a schematic diagram of a magnetic resonance imaging system according to a second embodiment of the present invention;
FIG. 6 is a schematic illustration of a third embodiment of the present invention employing a method of the prior art for multi-layer imaging;
FIG. 7 is a schematic illustration of a third embodiment of the present invention employing another prior art method for multi-layer imaging;
Fig. 8 is a schematic diagram of a third embodiment of the present invention for multi-layer imaging using the method shown in fig. 1.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described by means of implementation examples with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
Fig. 1 is a flowchart of a magnetic resonance imaging method according to an embodiment of the present invention. The technical scheme of the embodiment is suitable for the condition of simultaneous multi-layer excited magnetic resonance imaging. The method may be performed by a processor of a magnetic resonance imaging system provided by an embodiment of the present invention. The method specifically comprises the following steps:
s101, acquiring a target object.
The target object may be a living body such as an animal body, a human body, or a water model, or a non-living body, and may be a scanning site such as a tissue or an organ. In this embodiment, the target object includes multiple layers/slices. For example, the target object may include a first deck and a second deck that are spaced apart, and the sizes of the first deck and the second deck may be the same or different.
S102, applying a two-dimensional selective pulse sequence to a target object to excite nuclear spins of at least two layers of the target object simultaneously, wherein the two-dimensional selective pulse sequence is applied to the target object and comprises the following steps: and applying polarity inversion gradients to the at least two layers along the phase encoding direction, and applying discrete encoding gradients to the at least two layers along the layer selecting direction, wherein the application time of the discrete encoding gradients is consistent with the polarity inversion time of the polarity inversion gradients. The two-dimensional selective pulse sequence in the embodiments of the present application may also be referred to as a two-dimensional spatially selective pulse sequence, which may include a radio frequency pulse sequence and a gradient pulse sequence.
An imaging scan sequence diagram provided by an embodiment of the invention as shown in fig. 2A, each scan cycle of magnetic resonance imaging includes an excitation phase (excitation K-space phase) and an acquisition phase (acquisition K-space phase). The excitation phase uses a two-dimensional selective pulse sequence and the acquisition phase uses a gradient echo (GRE) sequence. The excitation K space phase is used for simultaneously exciting nuclear spins of at least two layers respectively. In the excitation K space stage, the radio frequency transmitting coil is controlled to apply a two-dimensional selective pulse sequence to a target object so as to excite at least two layers/local layer range spaces in a layer selection direction (Gss), and simultaneously excite at least two phase surfaces in a phase encoding direction (Gpe), wherein the layer selection direction is perpendicular to the phase encoding direction. The two-dimensional selective pulse sequence may include radio frequency pulses and gradient pulses. The inner envelope or outer envelope of the waveform of the radio frequency pulse may be a two-dimensional selective pulse sequence of gaussian, sinc or SLR waveforms. The sequence diagram of fig. 2A shows a two-dimensional selective pulse sequence with an envelope in the form of a gaussian waveform. It will be appreciated that simultaneous excitation of nuclear spins of at least two slices in this embodiment means that for both slices, nuclear spins of at least two dimensions are excited simultaneously after execution of a two-dimensional selective pulse sequence. At the same time, due to the combined action of the gradient pulses and the radio frequency pulses in the two-dimensional selective pulse sequence, a local/limited area of at least two planes can be selectively excited, which local area is a selected range of parts, but not all, of each slice of the target object.
During the application of the two-dimensional selective pulse sequence, applying discrete encoding gradients to the at least two layers along a layer selection direction, and applying polarity inversion gradients to the at least two layers along a phase encoding direction, wherein the discrete encoding gradients are used for defining/setting excitation and positioning of a layer range, the polarity inversion gradients are used for defining excitation and positioning of a phase interval, so that each discrete encoding gradient and each polarity inversion gradient combination can excite and position a strip-shaped region, the thickness of the strip-shaped region is determined by the total area of each discrete encoding gradient, the width of the strip-shaped region is determined by the polarity inversion gradient area, the set layer thickness corresponding to the discrete encoding gradient is reduced along with the increase of the gradient moment of the discrete encoding gradient, namely, the set layer thickness and the gradient moment of the discrete encoding gradient are in inverse proportion; the set phase interval (range of phase encoding) corresponding to the polarity inversion gradient decreases with an increase in the gradient moment of the polarity inversion gradient, that is, the set phase interval is inversely proportional to the gradient moment of the polarity inversion gradient. The discrete encoding gradient may be arranged as a variety of point (blip) pulses of triangular, trapezoidal, spike, small rectangular, small convex, etc.
As can be seen from fig. 2A, the discrete encoding gradient is set as a spike encoding gradient, and the application timing of the spike encoding gradient coincides with the polarity inversion timing of the polarity inversion gradient, that is, the slice positioning and the phase interval positioning need to be performed simultaneously in the excitation K-space phase. The application time of the peak coding gradient and the polarity inversion time of the polarity inversion gradient are corresponding to the trough of the two-dimensional selective pulse sequence, so that the two-dimensional selective radio frequency pulse is ensured to be applied in the plateau phase of the gradient (the plateau phase coding gradient in the figure). Of course, in other embodiments, for the case where the requirement for the time setting of applying the phase encoding gradient is short, the two-dimensional selective rf pulse may also be applied in a non-plateau phase of the gradient, and the amplitude of the non-plateau phase rf pulse is obtained by an interpolation method, so as to ensure the excitation effect of multiple layers of the target object as much as possible.
In some embodiments, at the excitation K-space stage, when the two-dimensional selective pulse sequence ends, the spike-encoding gradient and the polarity-reversing gradient also end at the same time, and at this time, the method may further include applying a phase refocusing gradient in the slice-selecting direction and/or the phase-encoding direction of the at least two slices (see fig. 2A), so that the excitation K-space returns to the center of the K-space along the slice-selecting direction and the phase-encoding direction, respectively, and adjusting the magnetization vectors in the multi-slice range of the excited space to return to the uniform direction. In some embodiments, the gradient moment along the polarity inversion gradient in the phase encoding direction may be adjusted. The gradient moment of the polarity inversion gradient affects the size of the region of interest excited by the RF pulse along the phase encoding direction, and by setting the gradient moment of the polarity inversion gradient, a region of interest smaller than the current slice can be selected in the target object, enabling the selection of a small field of view FOV along the phase encoding direction. Correspondingly, a larger acceleration factor can also be obtained along the phase encoding direction.
S103, after the two-dimensional selective pulse sequence is finished, applying phase encoding gradients along a first direction and a second direction to the at least two layers to perform phase encoding on nuclear spins of the at least two layers, and applying readout encoding gradients along a third direction to acquire magnetic resonance signals of the at least two layers.
At the end of the excitation K-space phase, the acquisition K-space phase begins. The acquisition K-space phase is used to encode the nuclear spins of the at least two slices by encoding gradients to generate magnetic resonance signals of the at least two slices.
In this embodiment, the acquisition K-space phase may employ an existing encoding gradient sequence to encode the nuclear spins of at least two slices that have been excited currently, such as a gradient echo sequence GRE (see fig. 2A), a planar echo imaging sequence EPI (see fig. 2B), and a fast spin echo sequence FSE (see fig. 2C). Wherein the encoding gradient is preferably applied to the at least two slices after the phase refocusing gradient.
With continued reference to fig. 2A, the imaging sequence of the excitation phase employs a GRE sequence. The gradient 201 for phase encoding is applied in the Gss direction, the gradient 211 for phase encoding is applied in the Gpe direction, and the two applying timings are the same, with the first direction being the layer selection (Gss) direction in the figure and the second direction being the phase encoding (Gpe) direction in the figure. Further, after the encoding gradient field is applied, a readout gradient field 221 is applied in the readout encoding gradient (Gro) direction, and a pre-dephasing gradient is applied in the Gro direction in front of the readout gradient field. In this embodiment, the magnitudes of the phase-encoded gradient 201 and the phase-encoded gradient 211 are progressively varied, a stronger gradient field may be used before the first magnetic resonance signal is acquired; the phase encoding gradient field is slightly reduced before the acquisition of the subsequent magnetic resonance signals and so on until all signals are phase encoded with different gradient fields. In this embodiment, the phase encoding gradient 211 is used to form a phase difference in the intra-layer phase encoding direction, and the resolution in the intra-layer phase encoding direction is obtained after fourier transform (FFT); the phase encoding gradient 201 in the layer direction makes the multi-layer respective acquisition K-space excited simultaneously generate different linear phases (the magnitude of the linear phase increment is related to the layer off-center distance and the implementation gradient moment), so that the image domain of the multi-layer after acquisition K-space FFT excited simultaneously generates different spatial displacements, thereby reducing the overlapping degree of pixels of different layers, reducing the calculation difficulty of the un-overlapped multi-layer images, and reducing the calculation error between the images after un-overlapping.
As shown in fig. 2B, for an imaging scan sequence diagram of an embodiment of the present application, each scan cycle of magnetic resonance imaging includes an excitation phase (excitation K-space phase) and an acquisition phase (acquisition K-space phase). The excitation phase uses a two-dimensional selective pulse sequence and the acquisition phase uses a plane echo imaging (echo planar image, EPI) sequence. As depicted in fig. 2B, during the 2D multi-slice EPI acquisition phase, which includes a phase encoding gradient field 311 along the Gpe direction and a pre-dephasing gradient applied along the Gro direction in front of an inverted readout gradient/oscillating readout gradient 321. After the small-field 2D multi-layer excitation in this embodiment, the phase encoding gradients 301 and 302 are simultaneously applied along the Gro and Gpe directions at the time corresponding to the polarity change of the inversion readout gradient 321, so that the overlapping degree between the multi-layer images is reduced.
As shown in fig. 2C, for an imaging scan sequence diagram of an embodiment of the present application, each scan cycle of magnetic resonance imaging includes an excitation phase (excitation K-space phase) and an acquisition phase (acquisition K-space phase). The excitation phase uses a two-dimensional selective pulse sequence and the acquisition phase uses a Fast Spin Echo (FSE) sequence. Which includes a plurality of refocusing radio frequency pulses 401, 402 and more, excited by the RF coil, the flip angle of the refocusing radio frequency pulses may be set to 180 degrees or any other value. Between two adjacent refocusing radio frequency pulses 401, 402, first the phase encoding gradients 411 and 421 are applied simultaneously in the Gro, gpe direction, then the readout gradient field 432 in the Gro direction is applied, and then the dephasing gradient pulses 412, 422 are applied simultaneously in the Gro, gpe direction. A readout pre-preparation gradient pulse 431 in the Gro direction is also applied in this embodiment after the excitation phase and before the first refocusing radio frequency pulse 401 of the acquisition phase. Similarly, a phase encoding gradient 413, 423 may be applied simultaneously in the Gro, gpe direction between the refocusing RF pulse 402 and the subsequent first refocusing RF pulse, followed by a readout gradient field in the Gro direction, followed by a readout gradient field in G The ro, gpe directions apply dephasing gradient pulses 414, 424 simultaneously. It will be appreciated that the amplitude of the gradient pulses applied in the Gro, gpe directions are not the same, but rather are fading variations. In this embodiment, the change of the gradient moment of the encoding in the Gpe direction is the same as that of the conventional FSE phase encoding, and in each acquisition module, after the pulse is focused, the intra-layer phase encoding is completed before the Gro reads the gradient, such as 421, 423 and 425, and the number of encoding gradients and the increment size are related to the FOV and the resolution of the intra-layer phase encoding direction of the graphics layer; furthermore, after each Gro signal acquisition, a refocusing gradient, such as 422, 424, 426, etc., of the phase encoding gradient is applied, of equal and opposite magnitude to the applied phase encoding gradient, before the next refocusing pulse. For 2D multi-layer simultaneous excitation, the embodiment adds the phase encoding in Gss direction before Gro reads out the signals, such as 411, 413, etc., to generate different linear phase changes of K space signals of the multi-layer simultaneous excitation, wherein the gradient moment size of the implementation is determined by the offset distance of the field of view to be generated by the corresponding image and the offset center distance corresponding to the image, and if 1/4FOV offset is required, γ×da is satisfied blip *d offset =pi/2; the corresponding 412, 414, etc. are the refocusing gradients of the layer-direction phase encoding gradients, where: gamma is the magnetic spin ratio and is constant for a particular magnetic nucleus; dA (dA) blip Representing a field of view offset corresponding to the applied phase encoding gradient; d, d offset Representing the distance the sheet is off-center and may be specifically equal to d as shown in fig. 6-8 offcenter 。
In this embodiment, between a first refocusing rf pulse following the refocusing rf pulse 402 and a second refocusing rf pulse following the refocusing rf pulse 402, both the phase encoding gradient and the dephasing gradient pulses applied in the Gss direction are zero; while both the phase encoding gradient 425 and the dephasing gradient pulse 426 applied in the Gpe direction are non-zero. Further, after the second refocusing radio frequency pulse following the refocusing radio frequency pulse 402, both the phase encoding gradient and the dephasing gradient pulse applied along the Gss direction are non-zero; whereas the applied phase encoding gradient 425 and dephasing gradient pulse 426 along the Gpe direction appear as zero moments.
In some embodiments, the nuclear spins of the at least two slices are encoded to generate magnetic resonance signals, such as the GRE encoding gradients in fig. 2A, by simultaneously applying encoding gradients in the slice selection direction and the phase encoding direction of the at least two slices. The gradient coding mode can enable the true phase coding to be along the vector combination direction of the coding gradient in the slice selection direction and the coding gradient in the phase coding direction, so that the aliasing degree of the nuclear spins of all slices excited simultaneously is weakened, the nuclear spins of all slices are further separated in the true phase coding direction, the overlapping degree of the nuclear spin voxels of different slices is reduced, and therefore, the noise amplification is lower during reconstruction and dealiasing, namely the reconstruction g-factor is optimized.
In this embodiment, the phase encoding gradients in the first direction and the second direction may be along the FOVpe direction and the direction perpendicular thereto in the figure, respectively. Referring to fig. 3, the dotted line is the actual phase encoding direction of the layer a, the line is the actual phase encoding direction of the layer B, and the phase encoding of the two layers is the vector sum of the phase encoding gradients of the first direction and the second direction. It can also be seen from fig. 3 that in case of a certain layer spacing, the degree of aliasing of layer a with layer B can be controlled by the coding range of the phase encoding gradient in the phase encoding direction, for example, by reducing the coding range of the phase encoding gradient in the layer selection direction to reduce the degree of aliasing of layer a with layer B or by reducing the coding range of the phase encoding gradient in the phase encoding direction to reduce the degree of aliasing of layer a with layer B. In one embodiment, under the condition of a certain layer spacing, the gradient moment of the phase encoding gradient along the layer selecting gradient direction and the gradient moment of the phase encoding gradient along the phase encoding direction can be adjusted so as to change the aliasing degree between adjacent layers, reduce the aliasing calculation error of the subsequently acquired overlapped signals, reduce the aliasing noise amplification degree and realize multi-layer acceleration imaging. In one embodiment, the first direction is selected to be along the FOVpe direction in fig. 3, the second direction is selected to be along the direction perpendicular to the FOVpe direction in fig. 3, and when the gradient moments of the phase encoding gradients in the first direction and the second direction are equal, the aliasing of the layer a and the layer B is in the direction 45 degrees to the FOVpe direction, and the aliasing area of the two layers may be half of the layer a. In one embodiment, when the gradient moment of the phase encoding gradient in the first direction is smaller than the gradient moment of the phase encoding gradient in the second direction, the aliasing area of the two slices is smaller than half of slice a.
Illustratively, during the excitation K-space phase, the radio frequency transmit coil is first controlled to apply a two-dimensional selective pulse sequence to the target object in fig. 4A to excite nuclear spins of multiple slices simultaneously in the slice selection direction and the phase encoding direction, respectively. During application of the two-dimensional selective pulse sequence, the gradient encoding coil is controlled to apply a spike encoding gradient in a slice selection direction of the plurality of slices while applying a polarity inversion gradient in a phase encoding direction of the plurality of slices. Under periodic excitation of the spike-encoding gradient and co-excitation of the polarity-reversing gradient, small elliptical slices located in the upper half of the target object and large elliptical slices located in the lower half of the target object (see fig. 4A) are located, along with a partial phase interval, i.e., a partial region, of each slice, see the gray portion in fig. 4B. As can be seen from the figure, the gray areas of the two layers have the same size in the phase encoding direction (short axis direction) and the same size in the frequency encoding direction (short axis direction). However, since the small elliptical layers have a smaller dimension in the short axis direction, the dimensions of the two layers in fig. 4C are different in the short axis direction. And when the excitation K space phase is finished, starting to acquire the K space phase. If the nuclear spins of the gray areas of the two layers are encoded by adopting conventional EPI sequence pulses or FSE sequence pulses which do not contain encoding gradients in the layer selection direction in the K space acquisition stage, magnetic resonance signals are generated, and the corresponding original image reconstruction result of the magnetic resonance signals is shown in fig. 4C; if the nuclear spins comprising the gray areas of the two slices are encoded with an encoding gradient in the slice selection direction, magnetic resonance signals are generated, which correspond to the original image reconstruction results as shown in fig. 4D. It can be seen that applying the encoding gradient simultaneously in the slice selection direction and the phase encoding direction can weaken the aliasing degree of the nuclear spins of the adjacent slices excited simultaneously, so that the nuclear spins of the adjacent slices are further separated in the true phase encoding direction, the noise amplification factor of the aliasing reconstruction is reduced, and the more optimized reconstruction g-factor is achieved.
Fig. 4E is a diagram of an original magnetic resonance image corresponding to a magnetic resonance signal acquired using a SMS-sequence pulse or a PINS-sequence pulse of the prior art, from which it can be seen that all slices of the upper and lower slices are excited, a local region of each slice cannot be selected, each slice is excited completely, and the aliasing between adjacent slices is large.
In summary, the present embodiment reduces the excitation range in the phase encoding direction, and reduces the encoding range in the phase encoding direction, thereby reducing the degree of aliasing of the nuclear spins of the adjacent layers that are excited simultaneously, and further separating the nuclear spins of the adjacent layers in the true phase encoding direction. Furthermore, under the condition that the excitation region of interest is reduced, the coding gradient is applied in the layer selection direction and the phase coding direction, so that the coding range of the coding gradient can be reduced, the aliasing degree of the reconstructed original image is further reduced, even the aliasing range is zero, and at the moment, the aliasing and the image reconstruction can be performed without complex algorithm and without consuming more calculation resources of operation algorithm.
S104, acquiring and reconstructing magnetic resonance signals to generate a magnetic resonance image of the target object.
After the magnetic resonance signals are generated, the generated magnetic resonance signals are acquired, and the acquired magnetic resonance signals are subjected to image reconstruction to generate a magnetic resonance image of the target object. The magnetic resonance image of the target object is a small-field image (image corresponding to a partial region) on a plurality of slices, and not all images of each slice.
It should be noted that, in this embodiment, the acquired magnetic resonance signals may be reconstructed by using a magnetic resonance imaging method in the prior art, which is not described herein.
Compared with the prior art, the method and the device for exciting the nuclear spins of at least two layers of the target object in two perpendicular directions through the one-dimensional radio frequency pulse, and the embodiment of the invention realize that the nuclear spins of at least two layers of the target object are excited simultaneously through the two-dimensional selective pulse sequence, so that the intensity of the radio frequency pulse can be greatly reduced, the SAR in the target object is reduced, the magnetic resonance imaging system can continuously perform imaging scanning, and the imaging scanning is not required to be suspended because the SAR is too high, so that the scanning efficiency of the magnetic resonance imaging system is improved.
Example two
An embodiment of the present invention provides a magnetic resonance imaging system, the magnetic resonance imaging system 100 comprising a bed 110, an MR scanner 120 and a processor 130, the MR scanner 120 comprising a radio frequency transmit coil 121, a gradient coil 122 and a radio frequency receive coil 123. The bed 110 is used for carrying a target object 010, the radio frequency transmitting coil 121 is used for transmitting radio frequency pulses to the target object, the gradient coil 122 is used for generating gradient fields, and the gradient fields can be along a phase encoding direction, a layer selecting direction, a frequency encoding direction or the like; the radio frequency receiving coil 123 is used for receiving magnetic resonance signals; the processor 130 is configured to control the radio frequency transmit coil 121 to apply a two-dimensional selective pulse sequence to at least two slices of the target object to excite nuclear spins of the at least two slices of the target object simultaneously; during application of the two-dimensional selective pulse sequence, the gradient encoding coil 122 is further configured to control the gradient encoding coil 122 to apply a polarity inversion gradient to the at least two slices in the phase encoding direction and to apply a discrete encoding gradient to the at least two slices in the slice selection direction; and at the end of the two-dimensional selective pulse sequence, controlling the gradient encoding coil 122 to apply encoding gradients to the at least two slices to encode nuclear spins of the at least two slices to generate magnetic resonance signals of the at least two slices; receiving the magnetic resonance signals through the radio frequency receiving coil 123; image reconstructing the received magnetic resonance signals to generate a magnetic resonance image of the target object; wherein the application time of the spike encoding gradient coincides with the polarity inversion time of the polarity inversion gradient.
As shown in fig. 2A, each acquisition cycle of magnetic resonance imaging includes an excitation K-space phase and an acquisition K-space phase. The excitation K space phase is used for simultaneously exciting nuclear spins of at least two layers respectively. In the excitation K space stage, the processor controls the radio frequency transmitting coil to apply a two-dimensional selective pulse sequence to the target object so as to excite at least two layers in a layer selecting direction (Gss) and simultaneously excite at least two phase surfaces in a phase encoding direction (Gpe), wherein the layer selecting direction is perpendicular to the phase encoding direction. The waveform of the two-dimensional selective pulse train may be a two-dimensional selective pulse train such as a gaussian waveform, a Sinc waveform, or an SLR waveform. The sequence diagram of fig. 2A shows a two-dimensional selective pulse sequence in sinc format. It will be appreciated that simultaneous excitation of nuclear spins of at least two slices in this embodiment means that the nuclear spins of at least two slices are excited simultaneously after the two-dimensional selective pulse sequence is performed. At the same time, due to the combined action of the gradient pulses and the radio frequency pulses in the two-dimensional selective pulse sequence, a local area of at least two layers can be selectively excited, wherein the local area is part of each slice of the target object, but not all of the slices.
During application of the two-dimensional selective pulse sequence, the processor 130 controls the gradient coil 122 to apply discrete encoding gradients to the at least two slices along the slice selection direction, and applies polarity inversion gradients to the at least two slices along the phase encoding direction, wherein the discrete encoding gradients are used for excitation and positioning of the slices, and the polarity inversion gradients are used for excitation and positioning of the phase interval, so that each discrete encoding gradient and each polarity inversion gradient combination can excite and position a strip region, the thickness of the strip region is the set slice thickness corresponding to each discrete encoding gradient, the width of the strip region is the set phase interval corresponding to the polarity inversion gradient, the set slice thickness corresponding to the discrete gradient increases with the increase of the gradient moment of the peak encoding gradient, and the set phase interval corresponding to the polarity inversion gradient increases with the increase of the gradient moment of the polarity inversion gradient. The discrete encoding gradient may be set as a plurality of point (blip) pulses of sharp peaks, small rectangles, small convex shapes, etc.
As can be seen from fig. 2A, the discrete encoding gradient is set as a spike encoding gradient, and the application timing of the spike encoding gradient coincides with the polarity inversion timing of the polarity inversion gradient, that is, the slice positioning and the phase interval positioning need to be performed simultaneously in the excitation K-space phase. The application time of the peak coding gradient and the polarity inversion time of the polarity inversion gradient are corresponding to the trough of the two-dimensional selective pulse sequence, so that the two-dimensional selective radio frequency pulse is ensured to be applied in the plateau phase of the gradient (the plateau phase coding gradient in the figure). Of course, in other embodiments, for the case where the requirement for the time setting of applying the phase encoding gradient is short, the two-dimensional selective rf pulse may also be applied in a non-plateau phase of the gradient, and the amplitude of the non-plateau phase rf pulse is obtained by an interpolation method, so as to ensure the excitation effect of multiple layers of the target object as much as possible.
In some embodiments, at the excitation K-space stage, when the two-dimensional selective pulse sequence ends, the spike-encoding gradient and the polarity-reversing gradient also end at the same time, which may further include applying a phase refocusing gradient in the slice-selection direction and/or the phase-encoding direction of the at least two slices (see fig. 2A) to focus the excitation K-space back to the K-space center in the slice-selection direction, the phase-encoding direction, respectively.
In some embodiments, the gradient moment along the polarity inversion gradient in the phase encoding direction may be adjusted. The gradient moment of the polarity inversion gradient affects the size of the region of interest excited by the RF pulse along the phase encoding direction, and by setting the gradient moment of the polarity inversion gradient, a region of interest smaller than the current slice can be selected in the target object, enabling the selection of a small field of view FOV along the phase encoding direction. Correspondingly, a larger acceleration factor can also be obtained along the phase encoding direction.
At the end of the excitation K-space phase, the acquisition K-space phase begins. The acquisition K-space phase is used to encode the nuclear spins of the at least two slices by encoding gradients to generate magnetic resonance signals of the at least two slices.
In this embodiment, the acquisition K-space phase may employ an existing encoding gradient sequence to encode the nuclear spins of at least two slices that have been excited currently, such as a gradient echo sequence GRE (see fig. 2A), a planar echo imaging sequence EPI (see fig. 2B), and a fast spin echo sequence FSE (see fig. 2C). Wherein the encoding gradient is preferably applied to the at least two slices after the phase refocusing gradient.
In some embodiments, the nuclear spins of the at least two slices are encoded to generate magnetic resonance signals, such as the GRE encoding gradients in fig. 2A, by simultaneously applying encoding gradients in the slice selection direction and the phase encoding direction of the at least two slices. The gradient coding mode can enable the true phase coding to be along the vector combination direction of the coding gradient in the slice selection direction and the coding gradient in the phase coding direction, so that the signal aliasing degree of the nuclear spins of all slices excited simultaneously is weakened, the nuclear spins of all slices are further separated in the true phase coding direction, the more optimal reconstruction g-factor is achieved, and the signal to noise ratio of multi-layer imaging is improved.
In this embodiment, the phase encoding gradients in the first direction and the second direction may be along the FOVpe direction and the direction perpendicular thereto in the figure, respectively. Referring to fig. 3, the dotted line is the actual phase encoding direction of the layer a, the line is the actual phase encoding direction of the layer B, and the phase encoding of the two layers is the vector sum of the phase encoding gradients of the first direction and the second direction. It can also be seen from fig. 3 that, in case of a certain layer spacing, the degree of aliasing of layer a with layer B can be controlled by the coding range of the phase encoding gradient in the phase encoding direction, for example, by reducing the phase encoding layer view range defined by the two-dimensional spatially selective pulse, i.e. by reducing the coding range of the phase encoding gradient in the layer selection direction to reduce the degree of aliasing of layer a with layer B, or by adjusting the vector direction of the phase encoding gradient of the first layer with the second layer in the phase encoding direction to reduce the degree of aliasing of layer a with layer B. In one embodiment, under the condition of certain layer spacing, the gradient moment of the phase encoding gradient along the layer selecting gradient direction and the gradient moment of the phase encoding gradient along the phase encoding direction can be adjusted so as to change the aliasing degree between adjacent layers, reduce the aliasing calculation difficulty of the subsequently acquired overlapping signals and realize multi-layer acceleration imaging. In one embodiment, the first direction is selected to be along the FOVpe direction in fig. 3, the second direction is selected to be along the direction perpendicular to the FOVpe direction in fig. 3, and when the gradient moments of the phase encoding gradients in the first direction and the second direction are equal, the aliasing of the layer a and the layer B is in the direction 45 degrees to the FOVpe direction, and the aliasing area of the two layers may be half of the layer a. In one embodiment, when the gradient moment of the phase encoding gradient in the first direction is smaller than the gradient moment of the phase encoding gradient in the second direction, the aliasing area of the two slices is smaller than half of slice a.
In summary, the present embodiment reduces the excitation range in the phase encoding direction, and reduces the encoding range in the phase encoding direction, thereby reducing the degree of aliasing of the nuclear spins of the adjacent layers that are excited simultaneously, and further separating the nuclear spins of the adjacent layers in the true phase encoding direction. Furthermore, under the condition that the excitation region of interest is reduced, the coding gradient is applied in the layer selection direction and the phase coding direction, so that the coding range of the coding gradient can be reduced, the aliasing degree of the reconstructed original image is further reduced, even the aliasing range is zero, at the moment, the aliasing and the image reconstruction can be completed without complex algorithm or consuming more calculation resources of operation algorithm.
The processor, after acquiring magnetic resonance signals through the radio frequency receiving coil, performs image reconstruction on the acquired magnetic resonance signals to generate magnetic resonance signals of the target object.
Compared with the prior art, the method and the device for exciting the nuclear spins of at least two layers of the target object in two vertical directions through the one-dimensional radio frequency pulse realize that the nuclear spins of at least two layers of the target object are excited simultaneously in two vertical directions through the two-dimensional selective pulse sequence, the intensity of the radio frequency pulse can be greatly reduced, SAR in the target object is reduced, the magnetic resonance imaging system can continuously perform imaging scanning, the imaging scanning is not required to be suspended because SAR is too high, and therefore the method and the device for exciting the nuclear spins of the target object in two vertical directions are beneficial to improving the scanning efficiency of the magnetic resonance imaging system.
As shown in fig. 5, the magnetic resonance imaging system 100 further comprises a controller 140 and an output device 150, wherein the controller 140 can monitor or control the MR scanner 110, the processor 120 and the output device 150 simultaneously. The controller 140 may include one or a combination of several of a central processing unit (Central Processing Unit, CPU), application-specific integrated circuit (ASIC), application-specific instruction processor (Application Specific Instruction Set Processor, ASIP), graphics processing unit (Graphics Processing Unit, GPU), physical processor (Physics Processing Unit, PPU), digital signal processor (Digital Processing Processor, DSP), field-programmable gate array (Field-Programmable Gate Array, FPGA), ARM processor, etc.
An output device 150, such as a display, may display the magnetic resonance image of the region of interest. Further, the output device 150 may also display the height, weight, age, imaging location, and operating status of the MR scanner 110 of the subject. The type of the output device 150 may be one or a combination of several of a Cathode Ray Tube (CRT) output device, a liquid crystal output device (LCD), an organic light emitting output device (OLED), a plasma output device, etc.
The magnetic resonance imaging system 100 may be connected to a local area network (Local Area Network, LAN), wide area network (Wide Area Network, WAN), public network, private network, proprietary network, public switched telephone network (Public Switched Telephone Network, PSTN), the internet, wireless network, virtual network, or any combination thereof.
The MR scanner 110 includes an MR signal acquisition module, an MR control module, and an MR data storage module. The MR signal acquisition module comprises a magnet unit and a radio frequency unit. The magnet unit mainly includes a main magnet generating a B0 main magnetic field and a gradient assembly generating a gradient. The main magnet contained in the magnet unit may be a permanent magnet or a superconducting magnet, the gradient assembly mainly comprises gradient current Amplifiers (AMPs), gradient encoding coils, and the gradient assembly may further comprise three independent channels Gx, gy, gz, each gradient amplifier exciting a corresponding one of the gradient encoding coils in the set to generate gradient fields for generating respective spatial encoding signals for spatially locating the magnetic resonance signals. The radio frequency unit mainly comprises a radio frequency transmitting coil and a radio frequency receiving coil, wherein the radio frequency transmitting coil is used for transmitting radio frequency pulse signals to a person to be detected or a human body, the radio frequency receiving coil is used for receiving magnetic resonance signals acquired from the human body, and the radio frequency coils forming the radio frequency unit can be divided into a body coil and a local coil according to different functions. In one embodiment, the type of body coil or local coil may be a birdcage coil, a solenoid coil, a saddle coil, a helmholtz coil, an array coil, a loop coil, or the like. In one particular embodiment, the local coils are provided as array coils, and the array coils may be provided in a 4-channel mode, an 8-channel mode, or a 16-channel mode. The magnet unit and the radio frequency unit may constitute an open low field magnetic resonance device or a closed superconducting magnetic resonance device.
The MR control module may monitor an MR signal acquisition module, an MR data processing module, comprising a magnet unit and a radio frequency unit. Specifically, the MR control module may receive the information or pulse parameters sent by the MR signal acquisition module; in addition, the MR control module can also control the processing procedure of the MR data processing module. In one embodiment, the MR control module is further connected to a pulse sequence generator, a gradient waveform generator, a transmitter, a receiver, etc., and controls the magnetic field module to execute a corresponding scanning sequence after receiving instructions from the console.
Illustratively, the specific process by which the MR scanner 110 of the present invention generates MR data includes: the main magnet generates a B0 main magnetic field, and atomic nuclei in the subject generate precession frequency under the action of the main magnetic field, wherein the precession frequency is in direct proportion to the intensity of the main magnetic field; the MR control module stores and transmits an instruction of a scan sequence to be executed, the pulse sequence generator controls the gradient waveform generator and the transmitter according to the scan sequence instruction, the gradient waveform generator outputs gradient pulse signals with preset time sequences and waveforms, the signals pass through Gx, gy and Gz gradient current amplifiers, and then pass through three independent channels Gx, gy and Gz in the gradient assembly, and each gradient amplifier excites a corresponding gradient coding coil in the gradient coding coil group to generate a gradient field for generating corresponding spatial coding signals so as to spatially locate magnetic resonance signals; the pulse sequence generator also executes a scanning sequence, outputs data including timing, intensity, shape and the like of radio frequency pulses transmitted by radio frequency, timing of radio frequency reception and length of a data acquisition window to the transmitter, simultaneously the transmitter transmits corresponding radio frequency pulses to a body transmitting coil in the radio frequency unit to generate a B1 field, signals emitted by excited atomic nuclei in a patient body under the action of the B1 field are perceived by a receiving coil in the radio frequency unit, and then transmitted to an MR data processing module through a transmitting/receiving switch, and is subjected to digital processing such as amplification, demodulation, filtering, AD conversion and the like, and then transmitted to an MR data storage module. The scan is completed when the MR data storage module acquires a set of raw k-space data. The raw k-space data is rearranged into separate k-space data sets corresponding to each image to be reconstructed, each k-space data set is input to an array processor for image reconstruction and combined with magnetic resonance signals to form a set of image data.
Example III
By contrast, the present examples provide three different methods for multi-layer imaging at the same time: the first is to use the prior art multi-layer simultaneous imaging method (Simultaneous Multi-Slice, short SMS), allowing several slices to be excited at the same time; the second is the combination of the multi-layer simultaneous imaging method and spike in the prior art; the third is a multi-layer imaging method as shown in fig. 1, which is an embodiment of the present application. FIG. 6 is a schematic diagram of a multilayer imaging using the first method, which includes a center layer, left and right layers, with the left and right layers being offset from the center layer (d offcenter ) The three layers are excited simultaneously, and the corresponding K space of each layer is respectively K1-K3, which are aliased together to form an aliased K space Ksum, the aliased K space Ksum forms a completely aliased magnetic resonance image, and a reference image is required to be additionally acquired for data aliasing. As shown in fig. 7, which is a schematic diagram of multi-layer imaging by adopting the second method, due to the application of spike pulses, magnetic resonance signals acquired by different layers generate certain phase shifts, K-space Ksum' obtained by exciting three layers is subjected to image reconstruction, images of the three layers generate certain shifts, but the images of the three layers are limited by the application of deflection angles of the spike pulses, and certain aliasing still exists among the images of the three layers. Fig. 8 is a schematic diagram of a multi-layer imaging method according to an embodiment of the present application, where images at different layers do not have aliasing, using the method shown in fig. 1. By applying two-dimensional selection The sexual pulse sequence forms a small field of view excitation. According to the fourier transform theorem, between two corresponding domains which can be transformed, the signal of one domain increases the linear phase, and the signal of the domain after fourier transform generates a certain spatial displacement, such as:
when the K-space signals of the 2D multi-layer are simultaneously excited and respectively adjusted by different linear phase increments, signals of different layers in the image domain generate different spatial displacements. In this embodiment, an example is given of a 3-layer simultaneous excited image. The layer-wise phase-encoding gradient causes the layer-wise phase-encoding gradient to be off-centered by an additional different phase increment associated with the distance, if the gradient moment increment of the layer-wise phase-encoding gradient satisfies gamma x dA blip *d offcenter =2pi/3, then the layer image field will produce a displacement of 1/3FOV, where: gamma is the magnetic spin ratio and is constant for a particular magnetic nucleus; dA (dA) blip Representing a field of view offset corresponding to the applied phase encoding gradient; d, d offcenter Indicating the distance the sheet is off-center.
In the embodiment of the application, the range of the excited signal in the layer is constrained through a two-dimensional selective pulse sequence, so that the excited signal is limited in a small visual field range; the layer direction phase coding causes that the layer direction K space signal generates different linear phase accumulation on the basis of original coding at different distances from the center, so that in the signal acquisition stage, images with different center distances of multiple layers are acquired at the same time, different space displacements are generated respectively through Fourier transformation, and the overlapping redundancy degree of the multiple layers of images is reduced. The small-view multilayer excitation combination layer is coded in the direction, and under the combination effect of the small-view multilayer excitation combination layer and the small-view multilayer excitation combination layer, the overlapping redundancy of the multilayer images is greatly reduced, so that the image quality is improved, and the g-factor is improved.
Note that the above is only a preferred embodiment of the present invention and the technical principle applied. It will be understood by those skilled in the art that the present invention is not limited to the particular embodiments described herein, but is capable of various obvious changes, rearrangements and substitutions as will now become apparent to those skilled in the art without departing from the scope of the invention. Therefore, while the invention has been described in connection with the above embodiments, the invention is not limited to the embodiments, but may be embodied in many other equivalent forms without departing from the spirit or scope of the invention, which is set forth in the following claims.
Claims (9)
1. A method of magnetic resonance imaging comprising:
acquiring a target object;
applying a two-dimensional selective pulse sequence to a target object to excite nuclear spins of at least two slices of the target object simultaneously, the applying the two-dimensional selective pulse sequence to the target object comprising: applying a polarity inversion gradient to the at least two layers along a phase encoding direction, and applying a discrete encoding gradient to the at least two layers along a layer selection direction, wherein the application time of the discrete encoding gradient is consistent with the polarity inversion time of the polarity inversion gradient;
After the two-dimensional selective pulse sequence is finished, applying phase encoding gradients along a first direction and a second direction to the at least two layers to perform phase encoding on nuclear spins of the at least two layers, and applying readout encoding gradients along a third direction to acquire magnetic resonance signals of the at least two layers, wherein the first direction is along a layer selection direction, and the second direction is along a phase encoding direction;
the magnetic resonance signals are acquired and reconstructed to generate a magnetic resonance image of the target object.
2. The method of claim 1, wherein the two-dimensional selective pulse train comprises radio frequency pulses and gradient pulses, and wherein the waveforms of the radio frequency pulses comprise one or more of gaussian waveforms, sinc waveforms, SLR waveforms.
3. The method of claim 1, wherein prior to the applying of the phase encoding gradient and after the ending of the polarity inversion gradient, further comprising:
a back-focusing gradient applied along the slice-select direction and/or the phase-encode direction.
4. A method according to any of claims 1-3, wherein the discrete encoding gradient is a spike encoding gradient and the gradient moment of the spike encoding gradient is proportional to the gradient moment of the polarity inversion gradient.
5. The method of claim 4, wherein the polarity reversal gradient excites only a partial region of each layer plane.
6. The method of claim 1, wherein the reconstructing the magnetic resonance signals to generate a magnetic resonance image of the target subject comprises:
performing antialiasing on the magnetic resonance signals to obtain magnetic resonance signals corresponding to each layer;
and reconstructing magnetic resonance signals corresponding to each slice to generate a magnetic resonance image of each slice of the target object.
7. A magnetic resonance imaging system, comprising:
the bed body is used for bearing a target object;
the radio frequency transmitting coil is used for transmitting radio frequency pulses to the target object;
gradient coils for generating gradient fields;
a radio frequency receiving coil for receiving magnetic resonance signals;
a processor for controlling the radio frequency transmit coil to apply a two-dimensional selective pulse sequence to at least two slices of the target object to excite nuclear spins of the at least two slices of the target object simultaneously; during the application of the two-dimensional selective pulse sequence, in particular for controlling the gradient coils to apply a polarity inversion gradient to the at least two slices along a phase encoding direction and to apply a discrete encoding gradient to the at least two slices along a slice selection direction; and after the two-dimensional selective pulse sequence is finished, controlling the gradient coil to apply phase encoding gradients along the first direction and the second direction to the at least two layers to encode nuclear spins of the at least two layers, thereby generating magnetic resonance signals of the at least two layers; the radio frequency receiving coil is also used for controlling the radio frequency receiving coil to receive the magnetic resonance signals; and is further configured to image reconstruct the received magnetic resonance signals to generate a magnetic resonance image of the target object; wherein the application time of the discrete encoding gradient is consistent with the polarity inversion time of the polarity inversion gradient, the first direction is along a layer selection direction, and the second direction is along a phase encoding direction.
8. The system of claim 7, wherein a gradient moment of the discrete encoding gradient is proportional to a gradient moment of the polarity inversion gradient.
9. The system of claim 7, wherein the polarity reversal gradient excites only a partial region of each layer plane.
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