The modified referenceless algorithm presented in this paper allows for temperature estimation in the presence of phase discontinuities between water and fat and takes advantage of both aqueous and adipose tissues present in the frame ROI. The results have shown that in cases without tissue motion temperature measurements with baseline subtraction and modified referenceless reconstructions give similar results that are better than the unmodified referenceless method which performs poorly when phase gaps are present. In situations where tissue motion is present causing temperature measurements with baseline subtraction to fail, the modified referenceless method can still provide reliable temperature measurements.
In the current implementation of the referenceless algorithm, images are reconstructed and displayed off-line in MatLab (MathWorks, MA). Reconstruction times vary with the polynomial order for the phase fit, but are in the order of several seconds, e.g., approximately 3 s for a 5th order polynomial, including the Dixon decomposition, generation of binary maps, phase unwrapping and phase fit for all three echoes. Implementing the referenceless algorithm in C will allow for a decrease in reconstruction time to that required for real-time temperature monitoring.
In the modified referenceless method Dixon decomposed water and fat images are used to create binary maps. For this application,
decay between the echoes was not taken into account for the Dixon decomposition, since it did not affect the binary masks, even in regions of with higher susceptibility changes close to the US applicator. For the binary masks only pixels that exceed a certain water/fat ratio are used; all other pixels are excluded. We used a threshold ratio of 90% in the prostate experiments. This ratio resulted in binary maps that included all pixels in the prostate and most pixels in the frame ROI with the exception of pixels at the water/fat interfaces. Depending on the SNR of the images, the threshold ratio can be adjusted to include a sufficient number of pixels for the polynomial fit. Using a binary map works well in the prostate because the prostate gland and the surrounding fatty and aqueous periprostatic tissue form discrete regions, where the majority of pixels contain only water or fat and little heterogeneity is observed. On the other hand, use of this method in more heterogeneous tissues, where the majority of pixels contain varying amounts of water and fat (e.g. breast tissue) will require further development of the reconstruction algorithm.
For the 3pt-Dixon decomposition used in this work, images are acquired at echo times where the phase angle between water and fat are 2π
, and 4π
, respectively. This means, that although the modified referenceless algorithm can reconstruct images acquired at all echo times, the Dixon decomposition still restricts the choice of TEs. However, another promising water/fat decomposition algorithm allows for a variable choice of echo times [31
]. A more flexible choice of echo times could be used to minimize the uncertainty in the temperature maps by choosing the echo time
or to avoid an echo time where water and fat are out-of-phase, such that the phase unwrapping algorithm does not have to be modified to be able to handle the π
-phase gaps between water and fat.
Since fat and water areas are handled separately in the reconstruction, it is also possible to correct the phase in fatty regions for spatial shift due to chemical frequency shift before the polynomial fit [29
]. With a bandwidth of 12.5 kHz or higher and a maximum of 256 readout samples in our experiments, the chemical shift of fat is less than 0.7 pixels and a correction was not found to be necessary. However, at higher field strength or lower bandwidth, a correction might be useful.
In the in vivo
ablation experiments, the three different echoes were acquired in one or two acquisitions. In both cases, all echoes acquired in the same acquisition are combined into a single temperature map. Measuring the temperature uncertainty of the combined temperature map showed that averaging the echoes compensates for most of the SNR decrease due to the higher bandwidth in the individual echoes. In other words, the temperature uncertainty was comparable with that of a single echo sequence with longer readout time. If two image acquisitions are used to acquire the three echoes necessary for the 3pt-Dixon decomposition, the binary masks are updated every second image. However, since motion experienced during prostate ablation is small from image to image, the same binary mask can be used for the reconstruction of two consecutive temperature maps. Errors introduced by the delayed update of the binary maps are small compared to baseline subtraction errors and do not propagate through the image set. Because temperature measurements can be made from each acquisition, the temporal resolution of the thermal measurements is not compromised. If all three echoes are acquired in a single acquisition as in the fifth in vivo
ablation experiment, the binary maps are updated constantly, but a decrease in readout resolution is necessary due to the limited gradient performance on our system. However, it has been shown that due to the relatively low spatial resolution of the heating distribution it is sufficient to acquire a low resolution image for temperature monitoring (1.7–1.9 mm in plane) [32
], which can easily accomplished with the proposed pulse sequence.
Since the echoes are acquired at different echo times, the temperature uncertainty in images acquired at the three echo times is different. Temperature uncertainty decreases with increasing TE, reaches a minimum at
, then increases again due to decreasing SNR. Depending on the uncertainty in the three echoes, a weighted average results in the lowest uncertainty in the combined image. We currently combine with equal weights, but the weights could be calculated by measuring
or by measuring the temperature uncertainty directly in the pre-heating images.
As described in the reconstruction algorithm section, the frame ROI needs to contain at least a small region of aqueous tissue to determine the phase offset between water and fat. This region of aqueous tissue remains at body temperature and the temperature change is estimated with respect to body temperature. This has to be taken into account when the body temperature changes during anesthesia (which is usually monitored) and corrected to avoid overestimation or underestimation of the temperature change.
The presence of a heating applicator in the treatment area may cause a local magnetic field change and thus a phase variation near the device that results in artifacts in the temperature map. Whereas laser and extra-corporeal focused ultrasound ablation cause little or no artifact in the temperature images, interstitial or transurethral ultrasound applicators and RF-ablation probes may cause artifacts [33
] that could substantially interfere with the temperature estimation. Artifacts created by the presence of the transurethral ultrasound applicators in these experiments made it necessary to correct temperature measurements obtained with referenceless reconstruction. The acquisition of an artifact map from pre-heating images and subsequent subtraction of the artifact during thermal treatment eliminates distortions from the applicator in the temperature maps and recovers the measured temperatures [29
]. Shifting the applicator changes the position of the artifact, but its spatial distribution with respect to the center of the applicator remains identical. Therefore, if motion of the applicator occurs during treatment, tracking of the applicator is needed to correctly subtract the artifact. This might appear to introduce the same problem with motion that the subtraction method suffers from, which could also be corrected for shifts of the image with respect to the baseline image. However, tissue motion not only causes a mis-registration to the pre-heating image, but also changes the background magnetic field non-uniformly. These changes in magnetic field cannot be corrected using the conventional baseline subtraction method, but are detected by the referenceless reconstruction. The phase variation caused by the applicator does not change with translational motion and can, therefore, be eliminated from the images.
The temperature reconstruction method presented in this paper is an extension to the original referenceless method to allow US thermal ablation in the prostate. A limitation of the method is the required user interaction to select the appropriate ROIs before the ablation procedure starts, which is not the case for the baseline subtraction method. Compared to the original referenceless method, the reconstruction proposed here requires the acquisition of additional images to get information about the water and fat composition and needs the temperature reconstruction of three images (including the phase unwrapping of the images); the method is, therefore, computationally more intensive. However, when baseline subtraction fails in the presence of tissue motion, the referenceless method still provides accurate temperature measurements, justifying the more demanding reconstruction algorithm. Although the number of in vivo experiments performed was limited, we believe that the method has advantages in the presence of tissue motion. Additional experiments will be necessary to evaluate if the new method can reliably measure temperature changes in all situations in the prostate.