TE
Water Oil
T1
T2
TE
> Two-dimensional NMR data. The 2D nature of T1-T2 maps is highlighted by overlapping signals from the two sets of distributions. The crossplotted signals are at maxima, indicated by the color variation from blue to dark red, in the center and right of this plot. The data converge along the center line in the middle— their agreement indicating similar fluid measurements from both T1 and T2. But, divergence of the longer time components of the two sets of data, resulting from molecular diffusion, moves the plot away from the center line at the right corner. If there were no diffusion effects, the crossplot would be centered along the dividing line.
Water Oil
2 x TE t TE
Diffusion (D)
Transverse relaxation (T2)
> Diffusion editing. With traditional CPMG sequences and short echo spacing (TE), oil (green) and water (blue) signals relax, or decay, at similar rates (top). Lengthening the TE value (middle) enhances the diffusion effect preferentially for the fast-diffusing water compared with slower- diffusing oil. However, long TEs correspond to fewer echoes and a lower signal-to-noise ratio. Diffusion editing (bottom) is a variant of the multi-TE CPMG method, where only the first two echoes are lengthened to enhance the diffusion effect, while maintaining the advantage of the short TE for better signal-to-noise ratio.
are fewer echoes over an equivalent time span, reducing the data density. This also results in more rapid signal decay—T2 times are shorter—because of the diffusion effects. The end result is a reduction in the amount of usable data, and the inversion becomes more challenging because of the lower signal-to- noise ratio.
The diffusion-editing (DE) technique overcomes these limitations by combining two long initial TEs—during which diffusion is effective in reducing the NMR signal— followed by an extended train of short TEs, during which diffusion effects are minimized (above right). A large number of echoes can
be acquired, and the effective signal-to-noise ratio is maximized. Analogous to the T1-T2 measurement described earlier, a 2D experiment can be designed to extract diffusion information.
1. Beyond classical physics, there are other applications that describe four dimensions and beyond. String theory, for example, predicts 10 dimensions, including a zero dimension.
2. The wait time is the time allotted for the alignment of protons within the static magnetic field of the permanent magnet of an NMR logging tool during the measurement cycle.
Rather than acquiring echo trains for a number of sequential WTs, an echo train is acquired with different initial long TEs. The data are subjected to the inversion processing and can then be used to generate D-T2 maps,
3. Song YQ, Venkataramanan L, Hürlimann MD, Flaum M, Frulla P and Straley C: "T1–T2 Correlation Spectra Obtained Using a Fast Two-Dimensional Laplace Inversion,” Journal of Magnetic Resonance154, no. 2 (February 2002): 261–268.
4. Freedman and Heaton, reference 4, main text.
Winter 2008/2009
9
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72