MR microscopy of samples with translational symmetry

In MR microscopy a signal from an image voxel rapidly decreases with an increase of image resolution. The signal loss can be to some extent compensated by an increase of the MRI scanner's magnetic field, optimization of the MRI probe's filling factor or with signal averaging. The first two options are usually expensive while the third is time consuming. Signal averaging can also be considered differently. Suppose that we have many (N²) identical samples. Then, the samples can be arranged in one larger sample with translational symmetry (where the samples are combined in an N by N matrix). If the samples are small enough the combined sample can be scanned in just one scanner and the acquired image is then split to images of the individual samples which are co-added to perform signal averaging. Since such scanning could take long if the resolution remains high, another approach is proposed here. In this, the combined sample is scanned with a field of view (FOV) identical to the unit cell of the sample. The reduction of FOV (by a factor of N) results in signal aliasing, which normally causes a warp around artifact. However, in this case the artifact is canceled due to the translational symmetry of the sample and with it associated a constructive co-addition of the aliased signals. The so obtained image has a signal identical to the signal obtained by image averaging but a lower noise, which is identical to a noise in the single scan experiment. The proposed method was tested on a test sample with 2D translational symmetry and a unit cell of 8 mm that was repeated on a 3 by 3 matrix. In the center of the cell a 4 mm diameter water-filled tube with was positioned. The sample was scanned in 2D by the spin-echo single point imaging method with parameters: FOV either 24 mm or 8 mm, imaging matrix 256 x 256, TE/TR = 6/200 ms. Figure 1a shows the obtained image of the combined sample with FOV of 24 mm, while Fig. 1b shows an image of the same sample at FOV of 8 mm. The image corresponds to a superposition of all 9 unit cell images and has therefore the same SNR as the original image in Fig. 1a, which is 9 times higher than SNR of a single unit cell image at FOV of 8 mm (Fig. 1c). The proposed method is a powerful alternative to conventional MR microscopy in samples with translational symmetry due to due to SNR preservation at reduction FOV to the size of the unit cell.

Figure 1: Images of a sample with translational symmetry: a) entire sample, b) 3-fold FOV reduction, c) single unit cell.