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Minimally invasive thermal therapy is a promising treatment for a variety of cancers. It is desirable to monitor temperature during such a procedure by magnetic resonance proton resonance frequency (PRF) shift thermometry (1, 2) because it provides quantitative temperature information in near real time. This method uses changes in the phase of gradient-recalled echo (GRE) images to estimate the relative temperature change ΔT, as given by
where α = –0.01 ppm/°C is the PRF change coefficient for aqueous tissue, γ is the gyromagnetic ratio, B0 is the main magnetic field, TE is the echo time, and ϕbaseline is the initial phase before heating. In conventional PRF shift thermometry, phase images acquired prior to heating (i.e., baseline or reference images) are subtracted from phase images acquired during heating. However, when tissue motion is present, images acquired during heating are not registered to the baseline images, and the background magnetic field changes nonuniformly, resulting in erroneous baseline phase elimination and inaccurate temperature measurements.
Many of the target areas for thermotherapy are in the abdomen, where motion is ubiquitous. For example, motion of the liver has an average amplitude of 1.3 cm during normal breathing (3). Because thermal therapy treatments require several minutes to perform, they cannot be performed in a single breath-hold. Furthermore, it is difficult to use multiple breath-holds, because reproducible breath-holding is hard to achieve. Even without respiratory motion, displacement between images can occur. Thermal coagulation leads to structural changes and deformation of the tissue (4, 5), which can even be observed ex vivo without any other contribution to motion. This heating-induced tissue motion is frequently not a simple displacement, and, unlike respiration, it cannot be corrected by a reregistration scheme. Swelling caused by the formation of edema can also contribute to tissue displacement (6), as can changes in bowel-filling and the state of muscles. For example, we have measured shifts in the canine prostate of >5 mm over the course of a 48-min ablation experiment.
In recent studies, investigators have used conventional respiratory gating in animals under general anesthesia and mechanical respiration (7, 8) to overcome the problem of motion in thermal therapy. Others have described motion detection and movement registration with navigator echoes for displacements of ex vivo tissue (9–11). A triggered, navigated, multibaseline method was demonstrated in vivo with variable respiratory motion (12). These methods all use the subtraction of baseline images. The goal of the present work was to develop a temperature-mapping algorithm based on the PRF shift that does not require baseline image subtraction.
We demonstrate a new method whereby the baseline phase is estimated from the acquired phase image itself, so that a separate reference scan is not required. We call this method “referenceless PRF shift thermometry.” Estimating the baseline phase from each temperature map itself eliminates the misregistration of images with the baseline data, and makes the referenceless method inherently robust to frame-to-frame motion. The method was tested in phantoms and investigated for liver and prostate ablation applications.
MATERIALS AND METHODS
In referenceless phase correction, the background phase of the image must be estimated from the image itself. This is possible because in minimally invasive thermal therapy, usually only a small region of the image is affected by the temperature change during thermal treatment. The phase outside this heated region can be used to determine the background phase.
A frame region of interest (ROI) is selected around the area to be heated, as shown in Fig. 1a. In the current implementation of the algorithm, the ROI can be chosen to be rectangular or circular; however, in theory, it can have an arbitrary shape. The inner border is outside the anticipated heating region, and the outer border is well within the object. It is essential to choose the inner ROI outside the heated region because temperature changes within the frame ROI will confound the polynomial fit to the background phase. Potential phase wraps in the image are unwrapped with the use of Goldstein, Zebker, and Werner's algorithm (13, 14). The unwrapped phase in the frame ROI is approximated by a polynomial, and can be written as
The order of the polynomial required for a certain setup is determined in an initialization process at the beginning of each treatment before heating starts, as described in the Initialization section. The polynomial coefficients ai are determined in the least-squares sense, resulting in the phase estimate ϕextrapolated of the selected region. The extrapolation of the fitted phase to locations within the inner ROI border serves as an estimation of the baseline phase. The temperature rise during the treatment is then given by
which only differs from conventional PRF thermometry in that ϕbaseline found from the reference image is replaced by the phase extrapolated to the center of the frame ROI, ϕextrapolated. An example 3D plot of the phase extrapolated to the center of the ROI is shown in Fig. 1b.
The algorithm described above performs the least-squares fit using unity weights for all pixels in the frame region. However, this is not generally desirable, because phase measurements in areas of low signal are dominated by noise. We use a weighting that reflects the reliability of the data. The standard deviation (SD) or uncertainty of the phase image (in radians) is given by the inverse of the signal-to-noise ratio (SNR) of the magnitude image (15)
for |I| ≥ 2σ(I0), where σ(I0) is the signal noise. Weighting the phase by the image magnitude squared minimizes the variance of the estimates, since the error in the phase estimate is inversely proportional to the magnitude of the image at each pixel (15).
The order of the polynomial to appropriately approximate the background phase is dependent on the object, the homogeneity of the field, and the chosen ROI. In the initialization step, the order of the polynomial that optimally approximates the background phase in the selected region is determined. This polynomial will be referred to as the best fit. The initialization is performed on the final experimental setup before heating starts. In a thermotherapy experiment using the conventional subtraction method, this would be the baseline acquisition section.
After the frame ROI is selected, polynomials from second to sixth order are tested for their ability to approximate the background phase. Each phase estimate ϕextrapolated is subtracted from the phase ϕ. The phase difference image then allows one to evaluate the quality of the phase estimate. Using Eq.  to calculate the temperature rise ΔT in the inner region should result in a 0° temperature rise, since heating has not started. The SD of the temperature difference ΔT in the inner ROI is compared to the inherent temperature uncertainty σ(T) given by
Unlike the SD in the frame region, which decreases with an increasing number of polynomial terms, the SD in the inner region of the ROI generally displays a minimum for a certain polynomial order. If the order is too low to reliably fit the background phase, residual background phase remains in the temperature maps. Increasing the number of polynomial terms enhances the fit. However, with too many terms, the polynomial tracks the noise in the frame region, which then increases the variance in the phase fit. Plotting the SD of ΔT in the inner region over the polynomial order (as in Fig. 2) shows this minimum. The polynomial that minimizes the variance in the inner region is chosen for the subsequent temperature estimation.
In addition to the variance in the inner region, the mean value of the temperature difference is considered. In only a few cases, the fit results in a low variance but displays a considerable mean offset. Polynomial fits with a mean offset that differs by more than 0.3 times the SD from zero were not selected for the best fit.
Once the ROI is selected and the polynomial order is determined, the background phase is estimated in every image during thermal treatment and subtracted from the actual phase. The temperature rise is calculated according to Eq.  and can be displayed as a color overlay in the corresponding magnitude image.
MRI AND DATA ANALYSIS
Images were acquired on 0.5 T and 1.5 T MRI scanners (Signa SP and Signa CV/i; GE Medical Systems, Milwaukee, WI) and processed with MatLab (MathWorks Inc., Natick, MA). Laser heating was performed with an 800-nm diode laser (Ethicon; Johnson and Johnson, Cincinnati, OH). The human subject protocols were approved by our institutional review board. The animal experiments were performed according to the regulations of our institution's administrative panel on laboratory animal care.
Laser heating was performed on a tofu phantom at 0.5 T with TR/TE = 167/27 ms, flip angle = 60°, BW = ±6.94 kHz, FOV = 12 cm, matrix = 256 × 128, and slice thickness = 6 mm. Fourteen images were acquired during the laser heating. A square inner region (84 × 84 pixels, or approximately 4 × 4 cm) was chosen around the laser fiber. The inner region was surrounded by a frame ROI, as seen in Fig. 3. Due to the shape of the phantom, the width of the frame ROI was 18 pixels (8.4 mm) on two sides and only 3 pixels (1.4 mm) on the other sides. Pixels at the position of the laser fiber were excluded in the calculation of the SD during initialization, because of their low signal amplitude. The first image, acquired before laser heating started, was used for the initialization and also served as the baseline image for the subtraction method, which was used for comparison. The remaining 13 images were used for temperature estimation. We compensated for constant phase drift in the temperature maps generated by the conventional baseline image subtraction method by selecting a reference ROI in the periphery of the tofu phantom.
In vivo liver images of three normal human volunteers, acquired in sets of five images within a breath-hold, were used to determine the accuracy of measuring a 0° temperature rise. Imaging was performed at 1.5 T with TE = 18–20 ms, TR = 30–40 ms, FOV = 24–28 cm, matrix = 256 × 128, and slice thickness = 10 mm. Twenty images were acquired without flow compensation, and 30 images were acquired with flow compensation. Square ROIs were chosen inside the liver. The inner region was 41 × 41 pixels wide (corresponding to 3.8 cm for a 24-cm FOV and 4.4 cm for a 28-cm FOV) and was surrounded by a frame region 12 pixels (1.1 cm and 1.3 cm) wide. To investigate situations in which the treated area was close to the liver border, a rectangular ROI (5.5 × 3.8 cm and 5.9 × 4.5 cm) was chosen near the lung in two sets of images. In these cases, the inner ROI was inside the liver, but the frame ROI extended into the lung.
The first image of each set was used to determine the order of the polynomial for the optimal phase fit. Temperature maps of the other four images were then reconstructed with the referenceless method. In the conventional baseline image subtraction method, the preceding image was used as the baseline for the current image. Every reconstructed image then has a different baseline, and errors that could be introduced by using the same baseline for all images are avoided. Using the phase in the inner region, we corrected the temperature maps of the conventional method for constant and linear phase drift components, which were found to be substantial in some of the images. We then compared the temperature uncertainty σ(T) in the selected region for both methods and compared the results. The mean offset in the referenceless images was also determined.
In the liver images, the theoretically possible temperature uncertainty σ(T) was not calculated from the SNR of the magnitude images as given by Eq. , because the phase uncertainty in a region varied with the number of blood vessels. Regions with many vessels had higher phase uncertainty than regions with few vessels, although the SNR was relatively constant over the whole slice. This was also true for the difference method: flow that is not constant is not eliminated by the subtraction, which results in a higher phase uncertainty in regions with many blood vessels. Therefore, we determined the theoretically possible temperature uncertainty σ(T) from the inner region of the phase difference image itself, after correcting for constant and linear phase components. The resulting temperature uncertainty was divided by √2 to eliminate the increase in noise due to the image subtraction.
Porcine Liver Ablation
The performance of the referenceless reconstruction for interstitial laser ablation was investigated on an image set acquired during in vivo porcine liver ablation at 0.5 T. During the thermal treatment, ventilation was performed manually to simulate free-breathing. The imaging parameters were TR/TE = 60/29 ms, flip angle = 40°, BW = ±8.6 kHz, FOV = 28 cm, and matrix = 256 × 128, and images were acquired with respiratory triggering and without flow compensation. Temperature maps of the images were reconstructed with the referenceless and conventional subtraction methods. The size of the square inner ROI was 40 × 40 pixels (4.4 × 4.4 cm), and the frame region was 10 pixels (1.1 cm) wide.
Canine Prostate Ablation
We studied in vivo prostate ablation in a canine model using a transurethral ultrasound transducer (16). Imaging was performed at 0.5 T with an endorectal coil and TR/TE = 167/30 ms, flip angle = 30°, FOV = 16 × 12 cm, matrix = 256 × 96, and slice thickness = 5 mm. Since all parts of the prostate can be targets for ablation, the inner ROI must include the whole gland, and the periprostatic tissue must be used for the background phase estimation. Images were acquired with echo time (TE) = 30 ms, where water and fat were experimentally found to be in phase.
In the initialization, it was found that a sixth-order polynomial optimally fit the background phase of the phantom. The temperature uncertainty σ(T) in the inner region of the preheating image was 1.1°C for this polynomial. This is in good agreement with the theoretical temperature uncertainty that was calculated according to Eq. : with an SNR in the magnitude image of approximately 26 over the ROI, the theoretical σ(T) is also 1.1°C. The conventional difference method had a temperature uncertainty of 1.4°C. This is close to its theoretical value, which is √2 times the value from Eq.  due to the subtraction.
Figure 3a shows one slice of the phantom with the laser fiber. Magnified temperature maps of the phantom during heating are shown: one with referenceless (b) and one with conventional (c) processing. The temperature images are essentially identical. A plot of the temperature along a horizontal profile close to the laser fiber is also plotted (d), which shows little difference between the two methods in the heated area.
Figure 4 shows the selected region in the human liver (a), and temperature maps of the region reconstructed from images without (b) and with (c) flow compensation. Quantitative results from the volunteer studies are shown in Table 1. The temperature uncertainty from the conventional subtraction method and the referenceless method are given, as well as the percentage improvement of the referenceless over the conventional subtraction method. The results for cases with and without flow compensation are shown.
Table 1. Comparison of Referenceless and Conventional Subtraction Methods During a Zero Degree Temperature Rise in Human Liver
Inner ROI (cm)
Frame width (cm)
Subtraction σ (T) (°C)
σ (T) (°C)
The table shows the location, size, and annular width of the ROI's for the different image sets, the polynomial order of the best fit, the temperature uncertainty for conventional reconstruction, and temperature uncertainty and maximum mean offset for referenceless reconstruction. The improvement of the referenceless method with respect to the conventional method is given as the reduction in σ(T).
4.5 × 4.5
4.5 × 4.5
3.8 × 3.8
3.8 × 3.8
4.5 × 4.5
4.5 × 4.5
3.8 × 3.8
3.8 × 3.8
4.5 × 4.5
4.5 × 4.5
5.9 × 4.5
5.5 × 3.8
Without flow compensation, the temperature uncertainty of the referenceless images varied from 7% lower to 21% higher than the uncertainty in the difference images, depending on the number of vessels in the ROI. Vessels appear in the temperature map because phase shifts due to flow are interpreted as temperature shifts. In addition, considerable mean offset was found in many of the images without flow compensation. The polynomial for the best fit varied from second to sixth order. With flow compensation, σ(T) decreased by approximately 20–36% compared to the difference images. The maximum mean offset was a fraction of the temperature uncertainty, and the polynomials were between third and fifth order. The temperature map of the flow-compensated image in Fig. 4c shows that phase contributions from the vessels are almost completely eliminated.
In two cases in Table 1, results are given for ROIs that partially overlap the lung to simulate the case in which the lesion is near the diaphragm. In these cases, the frame ROI is effectively U-shaped, since the magnitude squared weighting in the lung reduces the contribution of one side of the square to the polynomial estimation. For these two cases, σ(T) is improved in the referenceless method by approximately 20%.
Porcine Liver Ablation
Figure 5 shows temperature overlays of three frames during porcine liver ablation, reconstructed with the referenceless and conventional subtraction methods. The first time frame was acquired prior to heating, and the other frames were acquired approximately 50 s and 3 min after heating started. Since the images of the porcine liver ablation were acquired without flow compensation, in-plane blood vessels in the inner region are present in the temperature maps, as shown in the preheating image. The pattern of the vessels is similar in all referenceless images. However, despite the corruption by the vessels, the heating region is clearly visible in the temperature maps, and is similar in size and pattern to the heating region in the subtraction images. The temperature maps with conventional subtraction have variable artifacts, depending on the registration of the image to the baseline image. Artifacts from misregistered blood vessels can be seen in some images.
Canine Prostate Ablation
Figure 6 shows temperature maps of a single time frame during canine prostate ablation, reconstructed with the conventional and referenceless methods. Even though the heated region was small and close to the urethra, very good agreement between both methods was found. The temperature maps showed a good correlation between the onset and termination of heating, and the direction of the ultrasound beam. Differences in the heating pattern in Fig. 6 can be caused by both methods. The referenceless method is sensitive to phase changes due to susceptibility effects near the ultrasound transducer, and these phase changes will interfere with the temperature estimation. From preheating images, we found that the extent of the region affected by this artifact was small and barely extended outside the signal void around the transducer. Motion of the urethra of approximately 2 mm occurred during the course of treatment, which affected the subtraction method.
The temperature uncertainty σ(T) in the phantom images achieved with the referenceless method was close to the theoretical value calculated from the SNR of the image by the use of Eq. . This shows that the background phase in the inner region can be reliably estimated from the phase in the frame ROI. It also shows that the sixth-order polynomial is sufficient to represent the background phase. Since the referenceless method does not rely on the subtraction of another image corrupted by noise, a theoretical improvement in temperature uncertainty of √2 as compared to the conventional method could be achieved if the polynomial represented the background phase accurately.
Baseline averaging, which is sometimes done in conventional reconstructions to acquire a low-noise baseline image, is not necessary. However, if additional preheating images are acquired, they could be used to verify the chosen polynomial order with the referenceless method. In addition, during treatment, temperature maps acquired with the subtraction method must be corrected for phase drift caused by temporal instability of the reference frequency. This is usually done by calculating the constant and linear components of the phase drift from external reference phantoms (2, 17). Since the referenceless method estimates the phase in the individual images, the need to correct for phase drift is eliminated.
During our initial experiments, we found that polynomials of second to sixth order (most commonly third to fifth order) resulted in reliable fits for the background phase, as seen in the flow-compensated human liver images. Polynomials above sixth order rarely achieved the best fit, and if they did, their temperature uncertainty was very similar to that of the sixth-order polynomial. In addition, higher-order polynomials were less reliable for estimating the background phase in a complete image set. Even if they did achieve the best fit in one image, they often did not perform well in subsequent images, because of their higher sensitivity to changes in the noise. Therefore, we only used polynomials of sixth order or less in our algorithm. The graph in Fig. 2 shows that even if the selected polynomial order deviates by one from the optimal polynomial order, the resulting phase uncertainty is only slightly increased. This ensures robust phase estimation in cases in which the background phase changes due to motion and displacement of tissue. Although other functions, such as sinusoids or splines, could be used to estimate the background phase, we chose polynomials, which were easily implemented into our reconstruction algorithm and resulted in accurate phase representation in our experiments.
In referenceless thermometry, it is important to confine the heated area to the inner region of the ROI. If a temperature change occurs in the frame ROI, the corresponding phase change will be interpreted as background phase, resulting in an underestimation of the actual temperature. It is easier to deal with this constraint in vivo, where the body maintains the frame ROI at body temperature, than ex vivo, where heat eventually dissipates into the frame ROI. If tissue motion is expected, the inner region has to be large enough for the heating area to remain within the inner region in all images.
Phase wraps in the images would inhibit the polynomial fit to the background phase. To avoid phase wraps, all images are unwrapped prior to the polynomial fit. Although phase unwrapping algorithms can fail in some situations, we had no problems with remaining phase wraps in the ROI in any of our images.
A comparison of the volunteer liver images acquired with and without flow compensation showed that flow compensation is necessary to obtain reliable temperature information with the referenceless method. Without flow compensation, flow in the inner region is interpreted as temperature. In addition, phase from vessels in the frame ROI impairs the polynomial fit to the background phase. With flow compensation, these problems were eliminated and the referenceless reconstruction achieved 20–36% lower temperature uncertainty σ(T) than the subtraction method, although it did not quite reach the theoretical improvement of √2. Conventional reconstruction would also benefit from flow compensation. Since phase from blood vessels is different from the background phase, a small displacement with respect to the baseline causes artifacts, as seen in the porcine liver ablation in Fig. 5. With flow compensation, artifacts near the vessels caused by displacement are reduced because the background phase inside the liver is only slowly varying.
The ROIs at the liver/lung border showed that the referenceless reconstruction is also possible when parts of the frame ROI do not contribute to the background phase estimation. This suggests that U-shaped outer ROIs can often suffice for the phase estimation. However, if parts of the frame ROI are missing, or the frame ROI is very narrow compared to the inner region, the reliability of the phase estimate decreases and depends on the degree of background phase variation. Although field inhomogeneities at the liver–lung interface resulted in a more rapidly changing background phase than inside the liver, the phase could still be represented by a low-order polynomial. However, it can be difficult to fit the polynomial near tissue interfaces with more complex phase variations.
In the prostate, the entire gland may be targeted for ablation. If the referenceless method is used to monitor the ablation, the frame ROI must lie wholly or partially in the periprostatic tissue, which contains fat. Fat has a different resonance frequency compared to aqueous tissue, and, therefore, the TE must be chosen such that water and fat are in phase to eliminate phase discontinuities at the water–fat interface within the frame ROI. In our dog study, we experimentally determined the in-phase TE such that phase gaps between water and fat were minimized, since this value is dependent on the animal's body temperature and fat composition. The fact that fat has a PRF-thermal coefficient that is negligible compared to aqueous tissue (18) is irrelevant, because fat is not used to determine a temperature change. It is only needed for background phase estimation and remains at the initial temperature while the prostate is heated. Alternatively, fat suppression can be used, especially at higher field strength. However, fat suppression is difficult to achieve at 0.5 T, and it increases imaging time dramatically. In addition, suppressing the fat will reduce the SNR of the images and the accuracy of the polynomial fit.
In the current experiments, we used magnitude squared weighting of the phase image for the polynomial fit, which achieved a good representation of the background phase. However, magnitude squared weighting might not always achieve the best result for the phase fit (e.g., if the receiver coil sensitivity is highly nonuniform in the region of interest). With magnitude squared weighting, the high signal area would be preferred over the low signal area, which can result in a poor extrapolation to the inner region. In this case, it might be preferable to uniformly weight all pixels in the frame region that are above a noise-dependent threshold. Combinations of magnitude weighting and thresholding can also be applied.
Since the referenceless method estimates the background phase in the inner region, it cannot distinguish between phase changes due to temperature and those introduced by other sources (e.g., by the heating device itself). The field inhomogeneity around the laser fiber was small and inconspicuous in the temperature maps. The ultrasound applicator for prostate ablation, which was roughly parallel to B0, caused only small phase changes that barely extended outside the low signal region of the device. Moreover, temperature estimation in the region close to the heating device itself might not be that important, because many devices are equipped with an integrated temperature sensor. For RF-ablation devices, the field inhomogeneity around the probe is large and causes a distorted temperature map if the referenceless method is used. However, it might be possible to recover the temperature, since the field of the probe can be measured or calculated (19), and subsequently removed from the images.
We have presented a new method that improves the motion insensitivity of minimally invasive temperature mapping by estimating the background phase in each acquired image. This referenceless method eliminates the need for baseline phase subtraction and is therefore robust to changes in the background phase, and to frame-to-frame motion during thermal treatment. Our results show that the referenceless reconstruction provides reliable temperature maps and decreases the temperature uncertainty compared to the conventional subtraction method.
We thank Chris Diederich, William Nau, and Anthony Ross (Department of Radiation Oncology, UCSF) for designing and fabricating the ultrasonic devices used for the canine prostate ablation, and collaborating in the performance of these studies, and Eric Olcott for helpful discussions. We also thank Diane Howard and Wendy Baumgardner for assisting with the animal experiments, and Charles Dumoulin and Ronald Watkins (GE CR&D, Schenectady, NY) for providing the endorectal coil.