METHOD FOR SUBJECT-SPECIFIC OPTIMIZATION OF A MULTI-BAND RF PULSE

Abstract

A method for optimization of an RF pulse that is multi-band. The RF pulse is a spokes RF pulse including a train of sub-pulses. The method includes using a starting k-space position as a current k-space position, and for each of slices to be excited by the RF pulse, performing: calculating a sub-pulse based on the current k-space position and calculating an expected magnetization after that sub-pulse; calculating an inverse Fourier transform of a difference between an expected magnetization and a target magnetization; and determining an optimal k-space position for a next spoke for this slice to be at a position where an absolute value of the inverse Fourier transform has a maximum. A next k-space position is determined for all slices together based on the optimal k-space positions determined for each slice individually. A multi-band RF pulse is determined based on the determined k-space positions.

Claims

1. A method for subject-specific optimization of an RF pulse for exciting spins within a field-of-view to obtain a target magnetization in a magnetic resonance imaging examination of a subject, the RF pulse being a multi-band RF pulse, wherein the RF pulse is a spokes RF pulse comprising a train of sub-pulses interleaved with gradient blips, wherein the gradient blips are configured to determine a trajectory of a magnetization in transmit k-space so that each sub-pulse is played at a specific position in transmit k-space, and wherein each sub-pulse is configured to excite a predetermined number of slices simultaneously, the method comprising: receiving a starting k-space position and using the starting k-space position as a current k-space position; for each of the slices to be excited by the RF pulse, performing: calculating a sub-pulse based on the current k-space position and calculating an expected magnetization after that sub-pulse; calculating an inverse Fourier transform of a difference between the expected magnetization and the target magnetization; determining an optimal k-space position for a next spoke for the respective slice to be at a position where an absolute value of the inverse Fourier transform has a maximum; determining a next k-space position for all slices together based on the optimal k-space positions determined for each slice individually; and calculating a multi-band RF pulse based on the determined k-space positions.

2. The method of claim 1, further comprising: repeating the performing and the determining of the next k-space position for all slices together with the next k-space position as the current spoke position, until a predetermined number of spokes has been reached, until the difference between the expected magnetization and the target magnetization has reached a minimum, or until a relative change of the expected magnetization between two successive iterations is below a threshold, wherein calculating the multi-band RF pulse is based on the k-space positions determined in the determining of the next k-space position for all slices together and the repeating of the performing and the determining of the next k-space position for all slices together.

3. The method of claim 1, wherein determining the next k-space position for all slices together comprises calculating a weighted mean of the optimal k-space positions determined for each slice individually.

4. The method of claim 3, wherein a weight of each individual slice in the weighted mean is the same.

5. The method of claim 3, wherein a weight of each individual slice in the weighted mean is proportional to a number of tissue pixels in the individual slice.

6. The method of claim 3, wherein a weight of each individual slice in the weighted mean is proportional to an amplitude of the maximum inverse Fourier Transform of that slice.

7. The method of claim 1, wherein determining the next k-space position for all slices together comprises taking the optimal k-space position of the slice that has a largest maximum inverse Fourier transform.

8. The method of claim 1, further comprising receiving a subject-specific B1-field map of the field-of-view, wherein the RF pulse is a parallel transmission pulse, and wherein calculating the sub-pulses of the RF pulse comprises optimizing weights, with which individual channels of a parallel transmission RF coil are driven, based on a B1-field map.

9. The method of claim 1, wherein the starting k-space position is predetermined, is at a center of k-space, or a combination thereof.

10. The method of claim 2, wherein the predetermined number of spokes within the RF pulse is 2 to 6.

11. The method of claim 10, wherein the predetermined number of spokes within the RF pulse is 2 to 4.

12. The method of claim 11, wherein the predetermined number of spokes within the RF pulse is 2 to 3.

13. The method of claim 1, wherein the predetermined number of slices to be excited by the multi-band RF pulse is 2 to 16.

14. The method of claim 13, wherein the predetermined number of slices to be excited by the multi-band RF pulse is 2 to 8.

15. The method of claim 14, wherein the predetermined number of slices to be excited by the multi-band RF pulse is 2 to 4.

16. In a non-transitory computer-readable storage medium that stores instructions executable by a control unit of a magnetic resonance imaging system for subject-specific optimization of an RF pulse for exciting spins within a field-of-view to obtain a target magnetization in a magnetic resonance imaging examination of a subject, the RF pulse being a multi-band RF pulse, wherein the RF pulse is a spokes RF pulse comprising a train of sub-pulses interleaved with gradient blips, wherein the gradient blips are configured to determine a trajectory of a magnetization in transmit k-space so that each sub-pulse is played at a specific position in transmit k-space, and wherein each sub-pulse is configured to excite a predetermined number of slices simultaneously, the instructions comprising: receiving a starting k-space position and using the starting k-space position as a current k-space position; for each of the slices to be excited by the RF pulse, performing: calculating a sub-pulse based on the current k-space position and calculating an expected magnetization after that sub-pulse; calculating an inverse Fourier transform of a difference between the expected magnetization and the target magnetization; and determining an optimal k-space position for a next spoke for the respective slice to be at a position where an absolute value of the inverse Fourier transform has a maximum; determining a next k-space position for all slices together based on the optimal k-space positions determined for each slice individually; and calculating a multi-band RF pulse based on the determined k-space positions.

17. A control unit for a magnetic resonance imaging system, the control unit comprising: a processor configured for subject-specific optimization of an RF pulse for exciting spins within a field-of-view to obtain a target magnetization in a magnetic resonance imaging examination of a subject, the RF pulse being a multi-band RF pulse, wherein the RF pulse is a spokes RF pulse comprising a train of sub-pulses interleaved with gradient blips, wherein the gradient blips are configured to determine a trajectory of a magnetization in transmit k-space so that each sub-pulse is played at a specific position in transmit k-space, and wherein each sub-pulse is configured to excite a pre-determined number of slices simultaneously, the processor being configured for subject-specific optimization of the RF pulse comprising the processor being configured to: receive a starting k-space position and using the starting k-space position as a current k-space position; for each of the slices to be excited by the RF pulse, perform: calculation of a sub-pulse based on the current k-space position and calculation of an expected magnetization after that sub-pulse; calculation of an inverse Fourier transform of a difference between the expected magnetization and the target magnetization; and determination of an optimal k-space position for a next spoke for the respective slice to be at a position where an absolute value of the inverse Fourier transform has a maximum; determine a next k-space position for all slices together based on the optimal k-space positions determined for each slice individually; and calculate a multi-band RF pulse based on the determined k-space positions.

18. A magnetic resonance imaging system comprising: a control unit comprising: a processor configured for subject-specific optimization of an RF pulse for exciting spins within a field-of-view to obtain a target magnetization in a magnetic resonance imaging examination of a subject, the RF pulse being a multi-band RF pulse, wherein the RF pulse is a spokes RF pulse comprising a train of sub-pulses interleaved with gradient blips, wherein the gradient blips are configured to determine a trajectory of a magnetization in transmit k-space so that each sub-pulse is played at a specific position in transmit k-space, and wherein each sub-pulse is configured to excite a pre-determined number of slices simultaneously, the processor being configured for subject-specific optimization of the RF pulse comprising the processor being configured to: receive a starting k-space position and using the starting k-space position as a current k-space position; for each of the slices to be excited by the RF pulse, perform: calculation of a sub-pulse based on the current k-space position and calculation of an expected magnetization after that sub-pulse; calculation of an inverse Fourier transform of a difference between the expected magnetization and the target magnetization; and determination of an optimal k-space position for a next spoke for the respective slice to be at a position where an absolute value of the inverse Fourier transform has a maximum; determine a next k-space position for all slices together based on the optimal k-space positions determined for each slice individually; and calculate a multi-band RF pulse based on the determined k-space positions.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0039] FIG. 1 shows a schematic diagram of an example spokes RF pulse;

[0040] FIG. 2 shows a flow diagram of a method according to an embodiment;

[0041] FIG. 3 shows a graph of root-mean-square errors for different embodiments of the optimization method across six volunteers; and

[0042] FIG. 4 shows a schematic representation of an MRI system according to an embodiment.

DETAILED DESCRIPTION

[0043] FIG. 1 depicts a k-space trajectory of a spokes RF pulse 2. A slice select direction is z, so each sub-pulse 3 is played simultaneously with a slice select gradient in z-direction, and therefore, a trajectory during the sub-pulses 3 runs parallel to a direction k.sub.z in k-space, as depicted in FIG. 1. The depicted spokes RF pulse 2 has five spokes, one at a center of k-space where k.sub.x and k.sub.y are 0. In between the spokes 3, gradient blips in an in-plane direction k.sub.x and k.sub.y are played, resulting in trajectory segments 4 that connect the spokes 3 in the k.sub.x-k.sub.y-plane. According to a method of the present embodiments, an exact position in the k.sub.x-k.sub.y-plane of the spokes 3 (e.g., of the spokes 3 that are not in the center of k-space) is optimized in a patient specific way for multiple slices that are excited with the spokes RF pulse 2 simultaneously.

[0044] An example of an algorithm that embodies a method according to an embodiment is depicted in FIG. 2. The method is applied to optimizing a multi-band RF pulse with an MB factor of N.sub.MB, which is a number of slices excited simultaneously with one RF pulse. If a total number of slices to be imaged is N.sub.sl, there will be a total of N.sub.sl/N.sub.MB=N.sub.slgp slice groups, each requiring an RF excitation pulse. For each slice group, i, where iN.sub.slgp, N.sub.MB slices are to be excited at the same time. The method described may be considered as a workflow for designing an MB pulse for a single slice group.

[0045] In the 1.sup.st step 10, i is set to 1 (e.g., a first spoke). The starting k-space position is taken as a current k-space position (also referred to as spoke position) for i=1; in this case, the starting k-space position is predetermined to be at the center of k-space: ={(0, 0)}

[0046] The next steps 20 to 26 will be repeated for each slice j in the slice group.

[0047] In step 20, the spoke position for the slice j, .sub.j,i is set to equal the current spoke position .sub.i: .sub.j,i=.sub.i.

[0048] In step 22, a sub-pulse is calculated by designing an RF shim based on spoke position, .sub.j, and the resultant expected magnetisation, b, is calculated.

[0049] In step 24, the inverse Fourier transform of the difference between resultant expected magnetization and target magnetization is calculated for slice j: IFFT(bb.sub.target)=IFFT(b.sub.diff).

[0050] In step 26, the optimal new spoke location (k.sub.x,k.sub.y) for slice I is determined by the location coordinates of max(abs(IFFT(b.sub.diff))). The optimal new spoke position for slice j is set to this k-space location .sub.j,i+1={(k.sub.x,k.sub.y)}.

[0051] At 28, if jN.sub.MB, the algorithm increments i by 1 and goes back to step 20, to repeat steps 22 to 28 for the next slice in the slice group.

[0052] If j=N.sub.MB (e.g., if the optimal new spoke location has been determined for all slices), the algorithm proceeds to step 30. In step 30, the next k-space position for all slices together is determined based on the optimal k-space positions for each slice. There are a number of ways of doing this. According to one embodiment, the mean of the optimal new spoke positions for all slices is calculated and used for the final multi-band pulse design:

[00001]${}_{i+1}=\frac{1}{N_{MB}}{.Math.}_{j=1}^{N_{MB}}{}_{j,i+1}.$

[0053] In step 32, the counter i for the spokes is increased by 1 (e.g., i=i+1).

[0054] In step 34, it is determined whether the maximum predetermined number of spokes for the pulse has been reached (e.g., if i=N.sub.sp). If no, the algorithm jumps back to step 20, using the determined optimal new spoke position of all slices .sub.j+1 as the current k-space position.

[0055] This is repeated until i=N.sub.sp, where N.sub.sp spokes is a pre-determined number of spokes of the RF pulse.

[0056] The method then moves on to step 40, in which, for each slice j in the slice group, the RF pulse, P.sub.j, is optimized for N.sub.sp spokes with spoke positions .

[0057] In step 50, the RF pulses P.sub.1 corresponding to each slice j in the slice group are combined P.sub.jj[1,N.sub.MB] to give the final MB pulse, P.

[0058] Step 30 has a number of different embodiments. According to a 2.sup.nd embodiment, the mean of the optimal spokes position in the individual slices is not taken as next spoke position. Rather, the spokes location corresponding to the largest Fourier transform residue in the slice group is taken.

[0059] An example workflow corresponding to this embodiment is described below. [0060] Set i=1 (i.e. the first spoke); and .sub.1={(0, 0)} (Step 10) [0061] repeat [0062] For each slice j in the slice group: [0063] Set .sub.j,i=.sub.i (step 20). [0064] Design RF shim based on spoke positions, .sub.j, and calculate the resultant expected magnetisation, b (step 22). [0065] Calculate the inverse Fourier transform of the difference between current magnetization and target magnetization: IFFT(bb.sub.target)=IFFT(b.sub.diff) (step 24). [0066] New spoke location (k.sub.x,k.sub.y) is determined by the location coordinates of max(abs(IFFT(b.sub.diff))) and .sub.j+i+1={(k.sub.x,k.sub.y)} (step 24). [0067] Alternative step 30: Set .sub.j,i=max(abs(IFFT(b.sub.diff))); [0068] Find

[00002]$J=\underset{j}{\mathrm{argmax}}\left({}_{j,i}\right)$ to determine which slice in the slice group has the largest max(abs(IFFT(b.sub.diff))); [0069] Set .sub.i+1=.sub.J,i+1 [0070] i=i+1 (step 32). [0071] until i=Ns, (step 34). [0072] For each slice j in the slice group: [0073] Optimize RF pulse, P.sub.j, for N.sub.sp spokes with spoke positions (step 40). [0074] Combine P.sub.jj[1,N.sub.MB] to give the final MB pulse, P (step 42).

[0075] Two further embodiments of the MB spokes design algorithms are described below, in which step 30 may be varied as follows.

[0076] According to a third embodiment, an ROI-weighted mean of positions of the spokes are taken across all slices in the slice group, for example, setting

[00003]${}_{i+1}=\frac{1}{N_{MB}}{.Math.}_{j=1}^{N_{MB}}{}_{j,i+1}\frac{W_j}{},$

where W.sub.j is the number of pixels in the image mask for slice j, and =.sub.j=1.sup.N.sup.MBw.sub.j.

[0077] According to a fourth embodiment, the IFFT amplitude-weighted mean of the positions of the spoke across all slices in the slice group is taken, for example, setting

[00004]${}_{i+1}=\frac{1}{N_{MB}}{.Math.}_{j=1}^{N_{MB}}{}_{j,i+1}\frac{{}_{j,i}}{A},$

where W.sub.j is the number of pixels in the image mask for slice j, and A=.sub.j=1.sup.N.sup.MB.sub.j,i.

[0078] The four embodiments for determining the next k-space position based on the optimal k-space positions determined for each slice individually were compared with each other and with the performance of an optimized single-band RF pulse. Magnetic resonance imaging of the brain was performed on six healthy volunteers using the multi-band RF pulses calculated according to the four embodiments, and a single-band RF pulse. The optimization method was performed using whole-brain per-channel B.sub.1.sup.+ and B.sub.0 maps obtained from the six volunteers. The following pulse design parameters were used: MB factor=2; target flip angle (FA)=30; number of spokes=2 (2.56 ms per pulse, Hanning-filtered sinc). No constraints were applied to the overall peak voltage of the pulse.

[0079] The result of the comparison is shown in FIG. 3, which depicts the root-mean-square error (RMSE) across the whole brain for all volunteers across five different optimization methods. Each dot represents a volunteer, while the black crosses and error bars represent the mean and standard deviation RMSE values respectively. Taking the mean spoke locations across the simultaneously excited slices yielded the smallest RMSE values out of the four embodiments of the MB spokes location optimization method. To quantify the differences, especially between the prior art single-band optimization method and the embodiments, four paired Student's t-tests were performed using mean as a reference. There were no significant differences between the single-band optimization method and taking the mean spokes location in MB optimization, implying that it has a good performance.

[0080] In other words, the method of the present embodiments has been shown to have extremely good performance, since the RMSE is comparable to the single-band pulse optimization, which naturally results in RF pulses that require much longer acquisition times, since multi-slice excitation is not possible.

[0081] FIG. 4 shows an embodiment of a magnetic resonance imaging system 60 according to the present embodiments. The magnetic resonance imaging system 60 includes a magnetic resonance scanner 62 and a control unit 64. The control unit 64 is configured to receive B1+ field maps and to perform the multiband RF pulse optimizations described herein. A User may interact with the control unit 64 via a user interface 68, which may include a screen and a keyboard, and the control unit 64 is configured to output information and/or suggestions via an output device of the user interface 68 and to receive user input via a user input device of the user interface 68. A computer program according to the present embodiments may be stored on disc 65 and loaded into the control unit 64.

[0082] The method of the present embodiments extends the iterative inverse Fourier method used in single-band spokes pulse design to multi-band spokes design. According to an embodiment, the method takes the mean of the position of the spokes in the individual slices and uses it for the final MB pulse design.

[0083] The elements and features recited in the appended claims may be combined in different ways to produce new claims that likewise fall within the scope of the present invention. Thus, whereas the dependent claims appended below depend from only a single independent or dependent claim, it is to be understood that these dependent claims may, alternatively, be made to depend in the alternative from any preceding or following claim, whether independent or dependent. Such new combinations are to be understood as forming a part of the present specification.

[0084] While the present invention has been described above by reference to various embodiments, it should be understood that many changes and modifications can be made to the described embodiments. It is therefore intended that the foregoing description be regarded as illustrative rather than limiting, and that it be understood that all equivalents and/or combinations of embodiments are intended to be included in this description.