METHOD FOR GENERATING A RADIAL OR SPIRAL MRT IMAGE

Abstract

Disclosed herein is a method for generating an MRI image in which a radial or spiral k-chamber path with a constant angular increment Psi is used to take an MRI image, the angular increment Psi being in the angular range of between 5-55 degrees or being in the corresponding supplementary angle Psi′ and is selected according to the formula Psi.sub.N,M=pi/(N+1/(M+tau−1)). Alternatively, for an angular increment Psi which deviates from the angle increment of the optimal distribution of n radial profiles Psi.sub.opt=180°/n, the minimum scanning efficiency of the angular increment Psi for n>21 profiles is greater than 0.95, the angular increment Psi is in an angular range of 5° to less than 68.7537°, in particular between 5-55 degrees or in the corresponding supplementary angle Psi′. Compared to the arrangement of the radial or spiral profile using the golden angle of 111.24°, the angle increments calculated according to the above formula lead to lower eddy current artifacts, for example during the use of a b-SSFP-pulse sequence.

Claims

1. A method for generating an MRI image comprising generating an MRI image utilizing a radial or spiral k-space path with a constant angle increment Psi, wherein the angle increment Psi lies within the angular range of 5 to 55 degrees or the corresponding supplementary angle Psi′, and is selected according to the formula Psi.sub.N,M=pi/(N+1/(M+tau−1)), ${\psi }_{N,M}=\frac{\pi }{N+\frac{1}{M+\tau -1}}$ wherein N lies from about 3 to about 35, and wherein M lies from about 1 to about 5, and wherein tau=(1+sqrt(5))/2.

2. The method according to claim 1, wherein M=1 and N is at least 3, so that the following formula Psi.sub.N=pi/(tau+N−1) results in the angle increment Psi: ${\psi }_N=\frac{\pi }{\tau +N-1}$ wherein N lies from about 3 to about 35, and wherein tau=(1+sqrt(5))/2.

3. The method according to claim 1, wherein M=2.

4. The method according to claim 2, wherein N is at least 5.

5. The method according to claim 1, further selecting a number n of profiles for further reconstruction processing, wherein the number n is a part of a modified Fibonacci sequence G.sup.N,M with:
G.sup.N,M.sub.1=1+(M−1)N,G.sup.N,M.sub.2=N,G.sup.N,M.sub.n=G.sup.N,M.sub.n-1+G.sup.N,M.sub.n-2.

6. A method for creating an MRI image, comprising utilizing a radial or spiral k-space trajectory with a constant angle increment Psi, wherein an angle increment Psi deviates from the angle increment of the optimum distribution of n radial profiles Psi.sub.opt=180°/n, and the minimum sampling efficiency of the angle increment Psi for n>21 is greater than 0.95, wherein the angle increment Psi lies within an angular range of from 5 to less than 68.7537°.

7. The method according to claim 6, wherein the angle increment Psi is selected such that the minimum sampling efficiency of the angle increment Psi for n>21 profiles is greater than 0.97.

8. The method according to claim 6, wherein at least two profiles are measured per angle position.

9. The method according to claim 6, wherein residual eddy current artifacts are reduced by a “through-slice equilibration” method.

10. The method according to claim 6, wherein a T1-/T2- or a proton density mapping sequence is used for imaging.

11. The method according to claim 6, wherein the MRI image is dynamic.

12. The method according to claim 6, wherein the MRI sequence is executed according to a method of “fully balanced SSFP.”

13. The method according claim 6, wherein a plurality of coils can be used in imaging, and images can be reconstructed using a method based upon parallel imaging.

14. The method according to claim 6, further comprising reconstructing images using a method based upon compressed sensing.

15. The method according to claim 1, wherein at least two profiles are measured per angle position.

16. The method according to claim 1, wherein residual eddy current artifacts are reduced by a “through-slice equilibration” method.

17. The method according to claim 1, wherein a T1-/T2- or a proton density mapping sequence is used for imaging.

18. The method according to claim 1, wherein the MRI image is dynamic.

19. The method according to claim 1, wherein the MRI sequence is executed according to a method of “fully balanced SSFP.”

20. The method according claim 1, wherein a plurality of coils can be used in imaging, and images can be reconstructed using a method based upon parallel imaging.

21. The method according to claim 1, further comprising reconstructing images using a method based upon compressed sensing.

Description

BRIEF DESCRIPTION OF THE DRAWING

[0047] The method according to the present disclosure will be explained in reference to the drawing. The figures show:

[0048] FIG. 1 A table with angle increments Psi according to the invention for M=1, 2, or 3 and N=3-7;

[0049] FIG. 2 A dynamic image of a temporomandibular joint with a b-SSFP sequence with angles Psi.sub.1 to Psi.sub.8 and a reference image;

[0050] FIG. 3 The distribution of radial profiles P=3, 5, 11, 15, 28, and 61 for angle increments Psi.sub.N where N=1, 3, 5, and 7, and the sampling efficiency SE;

[0051] FIG. 4 The distribution of the minimum sampling efficiency SE over an angle range of 180°;

[0052] FIG. 5 The sampling efficiency SE for Psi.sub.5 in comparison to the angle increment of the golden angle;

[0053] FIG. 6 The sampling efficiency SE for Psi.sub.7 in comparison to the angle increment of the golden angle.

EXEMPLARY EMBODIMENT

[0054] FIG. 1 shows a table with angle increments Psi according to the invention for M=1 and N=3-7, yielding angle increments according to the invention Psi.sub.3 to Psi.sub.7 of 49.75 . . . ° to 23.6281 . . . °.

[0055] The angle increments are irrational; in the specific implementation of the invention, a numeric approximation is used, however. Additional angle increments Psi.sub.N are:

TABLE-US-00001 Psi.sub.N N 20.886434218636708 . . . 8 18.714843408803084 . . . 9 16.952290809269876 . . . 10 15.493154880963477 . . . 11 14.265296809351289 . . . 12 13.217766980806575 . . . 13 12.313557359254249 . . . 14 11.525138191507267 . . . 15 10.831606200941504 . . . 16 10.216803992712247 . . . 17 9.668045514836129 . . . 18 9.175231325586566 . . . 19 8.730221324604273 . . . 20 8.326381580011979 . . . 21 7.958251370987027 . . . 22 7.621294815891128 . . . 23 7.311713034528165 . . . 24 7.026300303881501 . . . 25 6.762332637943018 . . . 26 6.517480573502168 . . . 27 6.289740241092741 . . . 28 6.077378399537631 . . . 29 5.878888241685868 . . . 30 5.692953586679246 . . . 31 5.518419658955621 . . . 32 5.354269082488171 . . . 33 5.199602035704745 . . . 34 5.053619749390260 . . . 35

[0056] For selected values of M>1, in this case M=2 and N=3, 4 angle increments Psi.sub.2,3=53.2235 . . . and 41.0775 . . . result. For M=3 and N=4, an angle increment Psi.sub.3,3 of 54.9385 . . . results

[0057] Moreover, e.g., the following angle increments result for M=2 and N=5-11:

TABLE-US-00002 Psi.sub.N,M N, M 33.445027267682470 . . .  5, 2 28.204474872272382 . . .  6, 2 24.383748140492692 . . .  7, 2 21.474675482864956 . . .  8, 2 19.185744201605331 . . .  9, 2 17.337756625763216 . . . 10, 2 15.814491083709555 . . . 11, 2

[0058] FIG. 2 shows a dynamic image of a temporomandibular joint with a b-SSFP sequence with the known angle increments Psi.sub.1 and Psi.sub.2, and a reference image with an angle Psi=1°, as well as with the angle increments Psi.sub.3 to Psi.sub.8 according to the invention.

[0059] It is evident that the artifacts with decreasing angle increments Psi.sub.1 to Psi.sub.8 are negligible, and an acceptable image quality is reached starting with angle increment Psi.sub.6. The articular disc is easily visualized due to the b-SSFP T1/T2 contrast.

[0060] FIG. 3 shows the distribution of radial profiles P=3, 5, 11, 15, and 28 for angle increments Psi.sub.N where N=1, 3, 5, and 7, and contains the associated sampling efficiency SE under each distribution; accordingly, a sampling efficiency SE of 0.974 results for Psi.sub.5 at n=61 profiles.

[0061] FIG. 4 shows the minimum sampling efficiency SE as a numeric simulation. The minimum sampling efficiency SE between 0.84 and 1.00 is depicted on the Y-axis, and the angle Psi from 0 to 180° with a resolution of 0.002° is depicted on the X-axis. The minimum sampling efficiency was determined for each angle over the range n=(21; 10̂4) (number of profiles). The angle increments Psi.sub.1 to Psi.sub.5 and the supplementary angles Psi.sub.3′ to Psi.sub.5′ are indicated, as well as other suitable angles which are indicated by interrupted lines extending to the top edge. The thick, uninterrupted lines correspond to angle increments Psi.sub.N, wherein each of these angle increments has secondary maxima Psi.sub.N,M depicted by the thinner uninterrupted lines. The diagram is symmetrical to 90°, so that the supplementary angles Psi.sub.3 to Psi.sub.5′ are discernible.

[0062] FIGS. 5 and 6 depict the sampling efficiency SE for Psi.sub.5 and Psi.sub.7 in comparison with the angle increments of the golden angle Psi.sub.1=111.246 . . . . A logarithmic scale is used on the X-axis for the number of profiles n. The maximum sampling efficiency SE is achieved when n is from the modified Fibonacci sequence G.sup.N,M [19].

[0063] In this sequence, the following values of n result for M=1 and N=1 and 5: [0064] G.sup.1,1: 1 1 2 3 5 8 13 21 . . . . [0065] G.sup.5,1: 1 5 6 11 17 28 45 73 . . . .

[0066] It is discernible that for n>2N profiles, the sampling efficiency SE essentially lies between the limit values of the golden angle. For Psi.sub.5, this is the case starting with n=11; for Psi.sub.7, this is the case starting with n=15.

Glossary

[0067] Supplementary angle (English: adjacent angle)

[0068] Two angles are termed supplementary angles (or adjacent angles) when they add up to 180° (see http://de.wikipedia.org/wiki/Winkel#Supplementwinkel oder Ergänz ungswinkel)

ψ′N,M=π−ψN,M

[0069] Each angle generates exactly the same profile distribution as the matching supplementary angle Psi′. This consequently also yields the symmetry with 90° in FIG. 4.

Compressed Sensing MRI

[0070] Compressed sensing [34] is capable of reconstructing the original signal from a small number of measurements that detect random linear combinations of the signal, even when the number of measurements is much less than specified by the Nyquist rate. One possibility of a semi-random sampling of the k-space are radial k-space trajectories with an angle increment that corresponds to the golden angle. With these trajectories and a nonlinear reconstruction algorithm, the methods of compressed sensing can be used for fast MRI imaging [4].

Parallel Imaging

[0071] In the parallel imaging method, the signal is combined from a plurality of coil elements that are arranged in a phased array. Together with the previously determined intensity profiles of the coils, this additional data can then be used to eliminate undersampling artifacts during reconstruction. Known algorithms are based upon either image space (SENSE) or k-space (GRAPPA), or a combination of both methods. By means of the subsampling that this enables, a significant acceleration of MR imaging can be achieved. The combination with compressed sensing [4] and the golden angle enables further acceleration of imaging.

Quantitative Relaxation Parameter Determination

[0072] Inversion recovery sequences consist of an inversion coil in combination with a balanced SSFP sequence, and enable the simultaneous quantification of the relaxation parameters T1, T2 and relative proton density. The combination with a radial k-space trajectory and the golden angle increment enables the relaxation parameter to be determined within a single image [35].

Model-Based Image Reconstruction

[0073] In addition to the methods of parallel imaging, compressed sensing, and quantitative relaxation parameter determination, the described radial profile arrangement can be combined with other components of model-based image reconstruction, such as by including BO maps or trajectory maps [36].

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