What makes this work different from previously published work (37, 45-48, 152) is not the sequence itself, but rather the approach taken in setting acquisition parameters, the efficient use of the imaging time and data generated, and the approach to post- processing of the low resolution, aliased spectral data.
Our simulations and results from phantom studies demonstrate that processing algorithms discussed in this study can measure these frequency shifts with a high degree of accuracy even when the lipid peak is aliased, and that the SM algorithm is useful in overcoming the limitations of conventional windowed Fourier-based methods. The relaxation of the ESP constraint gave us the ability to use lower receiver bandwidths allowing higher SNR. Also, while only a few echoes were used, the relaxed ESP helped maintain reasonable spectral resolution. Additionally, the frequency difference between water and lipid is well known in the range of temperatures used for thermal therapy, so the ESP can be determined and ued to avoid problems with N/2 ghosts associated with bipolar readout gradients and aliasing the lipid peak too close to the water peak.
Another assumption we made was that we could accurately monitor peak shifts using only 16 echoes. While this could be accomplished using windowed Fourier techniques and peak finding routines, we applied a non-Fourier technique based on ARMA analysis of the data in order to provide a more robust method for finding peaks, as well as estimating the T2* and amplitude for each peak. This is in contrast to well-
89 known lipid-water separation techniques where peak amplitude quantification is of primary concern (128, 135, 137).
We observed robust performance of the SM algorithm in accuracy, uncertainty, and secondary peak detection across a range of SNR values for a very low number of echoes. The use of minimal samples represented as a rational polynomial in the z- domain, which has been shown to converge exponentially as the number of echoes increases (118), is important because this allows the acquisition either to run faster with less computational overhead or to facilitate the acquisition of multiple slices within the same TR period. For example, using the minimum TR possible with an ETL=8 and ESP=3.3 at 1.5T, acquisitions could be performed in less than two seconds. Three slices could be encoded in less than six seconds.
In addition to choosing a low number of echoes, the choice of other acquisition parameters, such as the ESP, can affect the accuracy and precision of the measurements. We have shown that choosing ESPs that extend TEmax past the T2* of the tissue increases
the uncertainty in the measurements (Figure 4-4). In low T2* tissues or where there is
low SNR in the later echoes, those echoes should be dropped since an increase in uncertainty has been observed. For instance, in a signal with a T2*=10 ms, TEmax=51.2
ms and SNR=20, sampling 16 echoes gave an uncertainty of 0.0154 ppm whereas sampling 8 echoes reduces the uncertainty to 0.0044 ppm. Therefore, for signals with low SNR (<5) at the later echoes, it is better to exclude those echoes and proceed with a lower ETL than to include them.
90 Theoretical calculation of the CRLB demonstrates that the uncertainty is inversely proportional to the SNR, a relationship corroborated by simulation and phantom measurements. Therefore, MR acquisition parameters, such as the flip angle, should be chosen to increase the SNR of the peak of interest. For instance, in a one-peak system, the flip angle that provides maximum SNR is the Ernst angle. For two-peak systems in which information from both peaks is desired, acquisition parameters should be tailored to help increase the SNR of the secondary peak, which was assumed here to be the smaller of the two. If TR is fixed for optimal timing, the flip angle could be used to provide optimal modulation of the secondary peak signal.
Given adequate SNR, the acquisition used in this work could provide T2* maps of
8-10 slices in a single breathhold (<20 s) using ETL=8, while also providing inherent lipid suppression. A recent study in liver constrained the solution of the estimated tissue- based T2* for water by assuming equivalent T2* values for water and lipid, owing to a
heavy iron overload (138). The authors concluded that this assumption may not be reasonable. The technique investigated here could potentially be used to separate these T2* values directly, without any assumptions on the chemical shift or T2* equivalency,
thereby allowing identification of separate T2* values for water and lipid. Another
potential application is quantitating the distribution of superparamagnetic iron oxides (SPIOs) (153). These particles have been suggested for use in thermal therapy, and such therapies could potentially benefit from the temperature imaging capabilities of our
91 technique as well (154). Our data shows that precision can be maintained through a wide range of SPIO concentrations.
Our simulations and phantom experiments also show that for the same imaging time and parameters, this technique is more precise than current CPD techniques over a wide range of SNR values because it maintains better accuracy and precision across a variety of T2* values and thus improves sensitivity of temperature imaging (Fig. 4-16).
Therefore, our data supports the hypothesis for increased accuracy and precision compared to CPD.
92 Figure 4-16The uncertainty in temperature versus imaging SNR for a signal containing 25% lipid
The simulation (n = 20,000 samples) for evaluating the uncertainty in the signal for water using the SM algorithm (circles) is compared with CRLB results (solid line). Note that our algorithm stays close to the CRLB over a wide range of SNRs. For reference, the CPD results are shown for an optimal TE (TE=T2*) at
the same bandwidth as the 16-echo sequence (black diamonds) and at one half this bandwidth (white diamonds) as would more likely be used. This case also assumes that the CPD can perfectly remove the influence of the lipid signal, which is unlikely; thus, it stands as a "best case" scenario for CPD against our technique. As can be seen, in addition to providing lipid-water separation, the fast CSI approach easily outperforms the CPD approach across a large range of imaging SNR values for the same imaging time. Reprinted with permission from the American Association of Physicists in Medicine, (150).
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