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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Magn Reson Imaging. Author manuscript; available in PMC 2009 November 20.
Published in final edited form as:
PMCID: PMC2780361

Echo Combination to Reduce PRF Thermometry Errors From Fat



To validate echo combination as a means to reduce errors caused by fat in temperature measurements with the proton resonance frequency (PRF) shift method.

Materials and Methods

Computer simulations were performed to study the behavior of temperature measurement errors introduced by fat as a function of echo time. Error reduction by combining temperature images acquired at different echo times was investigated. For experimental verification, three echoes were acquired in a refocused gradient echo acquisition. Temperature images were reconstructed with the PRF shift method for the three echoes and then combined in a weighted average. Temperature measurement errors in the combined image and the individual echoes were compared for pure water and different fractions of fat in a computer simulation and for a phantom containing a homogenous mixture with 20% fat in an MR experiment.


In both, simulation and MR measurement, the presence of fat caused severe temperature underestimation or overestimation in the individual echoes. The errors were substantially reduced after echo combination. Residual errors were about 0.3°C for 10% fat and 1°C for 20% fat.


Echo combination substantially reduces temperature measurement errors caused by small fractions of fat. This technique then eliminates the need for fat suppression in tissues such as the liver.

Keywords: thermometry, temperature, proton resonance frequency shift, PRF, fat


Temperature estimation with the PRF method is based on the shift in resonance frequency of water protons of 0.01 ppm/°C (1). The lipid resonance frequencies, however, are not temperature dependent. This poses a problem when the PRF method is used in tissues that contain partial volumes of both water and fat. The presence of lipids modifies the phase difference obtained in the thermometry experiment and thus leads to temperature measurement errors, making temperature quantification difficult.

This is a problem for temperature estimation in the liver, an organ that is frequently targeted for minimally invasive thermal therapy. The fat content of the liver in healthy adults is usually below 10% (2), but can be higher in obese people or patients undergoing chemotherapy. In the diseased condition of hepatic steatosis (fatty liver) the fat content can exceed 30% (3).

For temperature imaging with the PRF method, different techniques to eliminate the signal from fat during signal reception are commonly used. Spectrally selective excitation (also called chemical shift selective excitation) takes advantage of the difference in resonance frequency between water and fat to avoid excitation of the lipid signal (4,5). In spectrally selective lipid suppression, the lipid magnetization is rotated into the transverse plane by a spectrally selective pulse and subsequently dephased by a spoiler gradient (6).

Both, selective excitation and suppression are impractical at low field strength because the small spectral shift between water and fat (approximately 70 Hz at 0.5 T) would require a very homogeneous magnetic field, which is often lacking in interventional MR scanners, and a very long RF pulse. In addition, the PRF change of water with temperature has to be taken into account, when spectrally selective methods are used. For example, a temperature change of 60°C, not uncommon in thermal ablation procedures, causes a PRF shift by -0.6 ppm, reducing the chemical shift difference between water and fat from 3.5 ppm to 2.9 ppm.

Because of these shortcomings, the Dixon water/fat separation technique is often used at low field. The 3-point Dixon (7) technique uses a phase correction for field inhomogeneities. This correction also eliminates the temperature information and the resulting real-valued Dixon water and fat images cannot be used for temperature measurements.

Relaxation rate dependent methods such as short tau inversion recovery (STIR) (8) use the short T1 relaxation time of lipids to null the magnetization of the lipid spins. STIR offers an advantage over spectrally selective lipid suppression techniques, because it is based on the difference in T1 relaxation times between water and fat and not their chemical shift difference. This makes the method insensitive to B0 inhomogeneity and quite effective to suppress lipid signal at low magnetic field strengths. However, waiting for the lipid magnetization to null increases the scan time of STIR sequences and, in addition to fat, a considerable amount of water signal is suppressed, reducing the SNR. In addition, STIR fat suppression is affected by temperature, because T1 of fat changes with temperature (9).

In this study, we analyze a simple method for reducing temperature measurement errors with the PRF method in the presence of various amounts of fat. We found that due to the cyclic nature of the error with echo time, temperature images acquired at different echo times can be combined to reduce the measurement error in the individual images. We propose a multiple gradient echo imaging sequence for temperature mapping and subsequent combination of the acquired temperature maps that substantially reduces the error introduced by fat. The image acquisition scheme is similar to that proposed by Mulkern et al. (10), where a number of echoes (4-12 echoes) is acquired and used to determine frequency maps by linear fits to the evolution of phase with TE. In this study, we acquire three echoes at three different echo times and combine them into a single temperature map with predetermined weights. The results show that this echo combination successfully reduces errors caused by low fractions of fat (up to 20% fat), eliminating the need for fat suppressions in tissues such as the liver.


Temperature measurements with the PRF method are affected by the presence of fat, causing possible temperature overestimation or underestimation as a function of echo time. The signal of a two-component system consisting of water and fat, with amplitude a and phase ϕ can be expressed as

equation M1

where the phase of the combined system is given by

equation M2

Figure 1 shows the phase accumulation ϕw of pure water and ϕc of a two-component system with 80% water and 20% fat for different temperatures. The presence of fat causes a phase oscillation around the water phase accumulation.

Fig 1
The phase accumulation versus echo time TE in terms of phase angle between water and fat is plotted for pure water (dotted line) and a two-component system consisting of 80% water and 20% fat (solid line) for different temperature changes. Using the phase ...

The error ε in measuring the water signal phase is defined as the difference between the total signal phase ϕc and the water signal phase ϕw:

equation M3

where a = af/aw and Δϕ = ϕfw. It can be shown that the phase error ε is a cyclic function of Δϕ (6).

In order to measure the temperature change during thermal treatment, the phase difference between a current image and the corresponding baseline image is determined and the temperature change is calculated according to:

equation M4

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 Δ[var phi] is the difference between the phase before and during heating. Because the baseline phase is already modified by the fat signal (see Fig. 1 solid line), the analytic expression of the error for the phase difference becomes more complicated and is not very insightful. However, the behavior of the error can be appreciated in Fig. 1 (dashed line), which shows the oscillation of the error of the phase difference for different temperatures.


Computer Simulation

To investigate the error introduced by a certain percentage of fat in the examined tissue, we simulated the phase difference and resulting temperature measurement errors for temperature changes ranging from -60°C to 60°C and echo times TE from 0 to 30 ms. The simulations were performed for various fat fractions at 0.5 T field strength.

Because measurements at different echo times can cause either an overestimation or an underestimation of the temperature (see Fig. 1), it is possible to combine individual temperature measurements at different TEs in order to reduce the measurement error. We investigated how the echo combination affects the temperature measurement error for various fat fractions. In order to keep the overall imaging time approximately constant to a regular single echo acquisition, all echoes were collected in a single acquisition by increasing the readout bandwidth. With this constraint, the combination of two or three echoes was feasible. For the echo combination, the measured temperatures at the different echo times, determined according to Eq. 4, were combined as a weighted average. Instead of calculating the temperature for all echoes individually and then combining them, the complex images can be combined such that their phase adds with the desired weights. The temperature is then determined from the combined image. Both combination methods avoid phase wraps which could be a problem if the phase images of the echoes were combined. After echo combination, temperature measurement errors were evaluated and compared to errors present in the individual echoes. We also included simulations of the SNR of the temperature measurement when using echo combination and single echo acquisition because both T2* and TE influence the temperature accuracy (11). For this simulation the readout bandwidth of the single echo acquisition was multiplied by the number of echoes to keep the total readout time approximately constant.

MR Measurements

MR measurements were performed to verify the results of the computer simulation. In this experiment, a vial containing pure water and a vial containing a homogeneous mixture of water and fat (Half and Half, Clover Stornetta Farms, Petaluma, CA) were heated in a water bath to a temperature of 90°C. The vials were then transferred into two insulating chambers and imaged every five minutes while they slowly cooled to ambient temperature. Imaging was performed at 0.5 T scanner (Signa SP, GE Healthcare, Milwaukee, WI). Three echoes were acquired in a single refocused gradient echo acquisition with imaging parameters TR = 120 ms, TE1 = 14.3 ms, TE2 = 21.4 ms, TE3 = 28.6 ms, flip angle = 60°, BW1 = BW2 = BW3 = 15.6 kHz, matrix size = 128×128, FOV = 16 cm and slice thickness = 8 mm.

Temperature images were reconstructed according to Eq. 4 for all three echo times. The last image acquisition after cooling to room temperature was used as a baseline. In addition, phase drift was measured in a reference phantom at room temperature and corrected in all temperature images. Temperatures of the individual echoes and the echo combination in water and the water/fat mixture were compared in a region of interest (ROI) in the sample. To determine the amount of fat in the sample, a 3-point Dixon decomposition (7) was performed at room temperature. Temperature uncertainty and temperature errors were measured and compared to those of a single echo sequence with identical imaging parameters, but with TE = 25 ms and BW = 6.9 kHz, values we commonly use for PRF temperature measurements at 0.5T.


The computer simulations showed that in the presence of lipids, the measured temperature deviates from the ideal temperature and becomes dependent on the echo time. This echo time dependence is illustrated in Fig. 2, which shows the temperature error as a function of TE for 10% and 20% fat in the left and right image, respectively. It can be seen that the temperature measurements can result in overestimation or underestimation depending on the echo time and that the error changes sign with approximately π spacing. Note, that the error plots are not symmetric and that the low error regions between the “error lobes” do not run horizontally, suggesting that no single echo time TE exists, for which the temperature error is minimal for all temperature changes from -60°C to 60°C.

Fig 2
Temperature error for temperature changes from -60 to 60°C as a function of echo time, which is expressed in terms of the phase angle between water and fat. The left image shows the absolute temperature error for a mixture of 90% water and 10% ...

The fact that the sign of the error changes approximately every π, suggests that combining echoes that have a π spacing can reduce the error in the temperature measurement. Combining the phase of three echoes with the following weights

equation M5

substantially reduced the errors for all water and fat ratios. Weighting the echoes is necessary, because in this combination two echoes that underestimate the temperature (for positive temperature changes) and only one echo that overestimates the temperature are combined.

Results of the simulation have shown that the combination of any three echoes with π spacing substantially reduces the temperature error. The error becomes minimal for echo times that are multiples of π/2, for example TE1 = 2π (water and fat in-phase), TE2 = 3π (out-of-phase), and TE3 = 4π (in-phase). (Note, that the fat/water in-phase and out-of-phase condition is only exact at baseline temperature and then changes with a change in temperature.) The results of this particular combination is shown in Fig. 3, which shows plots of temperature errors at the three echo times for different water and fat ratios. In the case of 90% water and 10% fat the error in the individual temperature measurements is larger than 4°C. After echo combination, the error is reduced to less than 0.3°C. For a mixture of 80% water and 20% fat, the error of the combined signal barely extends 1°C, whereas the individual errors reach to up to 10°C. For increasing fat content, the error after echo combination increases as well; for a fat content of 30% the maximum absolute error is still close to 4°C. To set the errors in perspective to the temperature change and fat content, errors and relative errors are plotted in Fig. 4 (lower row) for mixtures containing 10%, 20%, and 30% fat. The relative errors have their maximum at small temperature changes. For 10% fat, the maximum error is less than 1%, for 20% fat the error remains close to 5% and for 30% fat the error is approximately 20%.

Fig 3
Upper row: Temperature errors as a function of temperature change for three different echo times and fat contents of 10%, 20%, and 30%. The black and gray solid lines correspond to the in-phase echo times of 2π and 4π, respectively, and ...
Fig 4
MRI temperature measurements during cooling of pure water and a mixture of water and fat. Whereas the measurements in water are very similar at all echo times, measurements in the water/fat mixture are echo time dependent. Combination of the echoes (dotted ...

Combining 2 echoes (TE1 = 2π and TE2 = 3π or TE2 = 3π and TE3 = 4π) also reduce the error caused by fat compared to the single echo, but the errors are higher than that of the three echo combination, especially at higher temperature changes. In this case the two echoes would need to be combined with equal weights.

We calculated the theoretical SNR in the temperature image of the three echo combination (using TE1 = 2π, TE2 = 3π, and TE3 = 4π) for different T2* values and compared it to a single echo acquisition. For this, we used a three times higher BW for the echo combination method, such that the total imaging time remained the same. Because the weighting for the different echoes in Eq. 5 is not equal, the maximum possible SNR after echo combination is approximately 94% of that of a single echo acquisition. Due to T2* the actual values are slightly lower with a minimum value for T2* = 2π (corresponding to 21 ms at 0.5T) of 91.6%.

Results of the MR measurements are shown in Fig. 4. The graph displays the temperature change measured in pure water and in the homogeneous water/fat mixture at three different echo times. The measurements in water are consistent in all echoes. Measurements in the water/fat mixture show a temperature dependence as predicted by the computer simulation. Both in-phase measurements show a temperature underestimation with lowest values in the first echo; the out-of-phase measurement overestimates the temperature. Echo combination substantially reduces the error of the individual measurements and the resulting temperature is very similar to that measured in pure water. The slightly different slope of the curves of pure water and the combined signal can be explained by different cooling rates in the two insulating containers which was confirmed by fiberoptic temperature measurements (Luxtron Model 790, Luxtron Corporation, Santa Clara, CA). The Dixon decomposition showed a fat content of approximately 20% in the water/fat mixture, which is in agreement with the measured and predicted errors.

Measuring the temperature uncertainty of the three echo sequence showed that the signal averaging of the echoes compensates for most of the signal decrease due to the higher bandwidth in the individual echoes. Temperature uncertainty measured in water was σT = 2.3, 1.6 and 1.4 for the individual echoes and σT = 1.0 after echo combination, which was identical to the temperature uncertainty measured in the single echo acquisition.


The results have shown that the combination of temperature maps acquired at three different echo times substantially reduces measurement errors present in the individual images. Residual errors for small amounts (< 20%) of fat are 1°C or below, which is tolerable for temperature measurements with the PRF. For larger amounts of fat, echo combination still reduces the error considerable. However, the remaining errors are still large, i.e. the relative error exceeds 20% for a fat content of 30%, which is not tolerable for monitoring thermal ablation therapies. Therefore, echo combination in tissues with more than 20% lipids is not sufficient to obtain an acceptable temperature accuracy and it has to be replaced by or combined with fat suppression.

The method is robust to field inhomogeneities as exact in-phase and out-of-phase echo times are not required. Because water and fat in the same pixel experience the same field inhomogeneity, their frequency difference and the π spacing between in-phase and out-of-phase echo time is essentially unchanged. Even for deviations from the π spacing between echoes, the method performs well.

Although computer simulations and experimental verification were performed at 0.5 T field strength, the echo combination method performs equally well at higher field strength. Because echo spacing for water/fat in-phase and out-of-phase decreases at higher field, additional echo combination schemes are feasible within a reasonable range of echo times and with similar amounts of error reduction.

This method requires the acquisition of three echoes. Since the TE in temperature imaging with the PRF method is usually relatively long (equal to T2* of the tissue for lowest temperature uncertainty), it is possible to acquire three echoes in approximately the same readout time by increasing the readout BW. Therefore, there is no apparent penalty in imaging time with the echo combination method. This allows the method to be combined with existing in vivo imaging strategies that address issues with organ motion (12).


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