SEARCH

SEARCH BY CITATION

Keywords:

  • Dixon imaging;
  • water and fat;
  • breath-hold;
  • phase correction;
  • region-growing

Abstract

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. EXPERIMENTS
  5. RESULTS
  6. DISCUSSION AND CONCLUSIONS
  7. Acknowledgements
  8. REFERENCES

A two-point Dixon technique using a novel phase-correction algorithm and commercially available dual-echo fast gradient-echo pulse sequence is presented. The phase-correction algorithm determines the directional rather than phase distribution of signals due to field inhomogeneities. Specifically, a region-growing scheme uses precalculated spatial gradients of the signal phase to guide the growth sequence, so there is no need to manually select the seeds or use an empirical angular threshold. Further, the determination of the signal direction of a given pixel is based on both the amplitude and phase of the surrounding pixels, the direction of which has already been determined. The advantages of this algorithm include its easy implementation, computational efficiency, and robustness in the presence of pixels with large phase uncertainty. The feasibility and usefulness of the technique are demonstrated in vivo with artifact-free water and fat images of an entire abdomen in a single breath-hold. Magn Reson Med 52:415–419, 2004. © 2004 Wiley-Liss, Inc.

The two-point Dixon (2PD) technique was first proposed almost 20 years ago as an imaging method for separating water and fat signals (1). In the original implementation, field inhomogeneities resulted in poor performance of the 2PD technique, just as with the conventional chemical shift fat-saturation technique (2). Unlike the latter case, however, the effect of field inhomogeneities on the 2PD technique could be removed with postprocessing phase correction during image reconstruction. This potential to correct for field inhomogeneities has led to numerous modifications of the original Dixon technique. For example, three-point Dixon (3PD) techniques (3–6) acquire an additional image to correct the phase error distribution. The postprocessing methods used for phase correction range from 2D phase unwrapping (3, 5–7) to statistical global orientation filtering (4). In general, these phase-correction methods rely solely on signal phase, which, unfortunately, is subject to substantial uncertainty for pixels with artifacts or low signal-to-noise ratio (SNR). To minimize failure, most of these methods assume that the phase difference between two neighboring pixels is within an empirical threshold. This is often a serious limitation, as selecting a threshold that is too small will prevent the phase correction in regions of large phase fluctuations, and artificially segment the image into disconnected regions. A threshold that is too large causes phase-correction errors to propagate into, and potentially corrupt, the rest of the image.

This paper presents an efficient and robust 2PD technique that uses a novel phase-correction algorithm and commercially available dual-echo fast gradient-echo data acquisition. In comparison with previous phase-correction methods, the present algorithm does not require phase unwrapping or the use of an empirical threshold for the phase difference between neighboring pixels. Instead, the directional distribution (rather than the actual phase distribution) of the signals is determined by means of an efficient and automated region-growing process. The feasibility and potential utility of the technique are demonstrated in vivo with abdominal water and fat images that are free of respiratory or other postprocessing artifacts.

MATERIALS AND METHODS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. EXPERIMENTS
  5. RESULTS
  6. DISCUSSION AND CONCLUSIONS
  7. Acknowledgements
  8. REFERENCES

Data Acquisition

The pulse sequence used for data acquisition in this study was a commercially available, dual-echo, fast spoiled gradient-echo sequence. After each RF excitation pulse, two gradient echoes with water and fat signals out-of-phase and in-phase, respectively, were collected at the same phase-encode gradient and within the same pulse repetition time (TR). For the 1.5-Tesla field strength at which this study was carried out, the difference between the echo times (TEs) of the out-of-phase and in-phase images was approximately 2.3 ms. The TEs used for the first and second echoes were thus 2.3 and 4.6 ms, respectively. The advantages of the dual-echo, fast gradient-echo acquisition include minimal signal reduction due to tissue relaxation, the ability to examine the entire abdomen in a single-breath-hold, and complete elimination of patient respiratory motion or slice misregistration artifacts.

Image Reconstruction

The in-phase and out-of-phase images were first reconstructed with the use of a fast Fourier transform (FFT). Ignoring tissue relaxation, the two images can be written as follows:

  • equation image(1)
  • equation image(2)

in which water and fat contributions to the signal in a given pixel are represented by W and F, respectively; m and n are the indices for the pixel location along the x- and y-axes, respectively; ϕo is the phase of the image So(m,n), which includes the phase due to the field inhomogeneity and a static phase that may arise from RF penetration and signal delay in the receiver chain; and ϕ represents an additional phase due to the Bo field inhomogeneity accumulated during the time between the first and second echo acquisitions.

To solve for W and F, the two terms due to ϕo and ϕ must be eliminated from Eqs. [1] and [2]. Removal of the ϕo term is trivial and can be done as follows:

  • equation image(3)
  • equation image(4)

in which emath image is determined by the ratio of the magnitude of the image So over the image itself:

  • equation image(5)

In the presence of field inhomogeneity, however, ϕ is not zero, and determining the ϕ term is a challenging task. From Eq. [4], ϕ is not solely determined by the phase of the signal Smath image, because the latter also depends on whether water or fat is dominant for a given pixel.

Phase Correction

The phase-correction algorithm used in this study aims at determining eiϕ, which, for the sake of this discussion, shall be called the phase vector. By definition, the phase vector is a unit vector whose direction is defined by the phase ϕ due to the local field inhomogeneity. It is clear from Eqs. [3] and [4] that determining the phase vector without explicitly determining the phase ϕ is sufficient for unambiguous water and fat separation.

Since W-F can be either positive or negative depending on whether water or fat is dominant in the pixel, Eq. [4] can be rewritten as follows:

  • equation image(6)

The phase vector is therefore either parallel or antiparallel to the direction determined by the signal Smath image. With Smath image known, determining the phase vector boils down to selecting either Smath image or −Smath image as the true representation of the phase vector.

Figure 1 presents a flowchart of the phase-correction process. As a preliminary step, two masking flags, Vst and Chk, are set to zero and assigned to each pixel of the image. Separately, multiple initially empty pixel stacks are created and labeled in order. In this study, a total of nine pixel stacks were used, each of which covered an angular range of 10° (see below). To jump start region-growing, an initial seed is placed onto one of the pixel stacks, and its Vst value is set to one. The initial seed can be selected either randomly or with the use of some other convenient criteria. Additionally, two images representing the angular difference between the Smath image of two neighboring pixels along the x- and y-axes, respectively, are calculated as follows:

  • equation image(7)
  • equation image(8)

in which arg(…) and * denote taking the argument and the complex conjugate of a complex variable, respectively. By definition, both Gx and Gy are within the 0–π angular range.

thumbnail image

Figure 1. Flow chart of the phase-correction algorithm used to determine the phase vector distribution.

Download figure to PowerPoint

Since the phase vector is either parallel or antiparallel to Smath image for pixels within water- or fat-dominant regions, Gx and Gy directly represent the angular difference between neighboring pixels for the phase vector. For pixels at the boundaries between a water-dominant region and a fat-dominant region, the angular difference between neighboring pixels for the phase vector is π – Gx and π – Gy, because the direction of the phase vector in the water-dominant region is represented by Smath image and that in the fat-dominant region is represented by −Smath image. For this reason, we replace all pixels with a value of >π/2 in Gx with π – Gx, and all pixels with a value of >π/2 in Gy with π – Gy.

The actual region-growing consists of the following looped processing:

First, a seed pixel is selected from the pixel stack that has the lowest stack order and is not empty. When multiple pixels are on the pixel stack, the seed is selected on a first-in, first-out basis.

As the second step, the four nearest neighbors of the seed pixel are sequentially “visited.” Any of the four neighbors that have not been visited before will be marked as visited by setting their “Vst” flag to one. Additionally, each of these pixels will be placed on one of the nine pixel stacks according to its Gx or Gy value and its position relative to the seed pixel. For example, if the pixel is being visited from the horizontal (or vertical) direction, and its Gx (or Gy) value falls within the range of 0–10°, then the pixel will be placed onto the first pixel stack. Similarly, if its Gx (or Gy) value falls within the range of 20–30°, the pixel will be placed onto the third pixel stack.

As the third step, the value of Smath image, which represents the phase vector of the seed pixel, is determined and the seed pixel is marked as “checked” by setting its pixel value in “Chk” to one. For the initial seed pixel, Smath image assumes the value of Smath image. For all of the other seed pixels, the determination of Smath image is based on the Smath image values of the pixels that are already marked as checked and are located within the neighborhood of the seed pixel. In this study, a simple estimation is as follows:

  • equation image(9)

in which (io, jo) represents the indices for the location of the seed pixel, and summation is performed over a small boxcar region (7 × 7 pixels, for example) centered at the seed pixel. The calculated Smath image is compared with Smath image. If the angular difference between Smath image and Smath image is < π/2, Smath image takes the value of Smath image. Otherwise, Smath image takes the value of −Smath image. After the seed pixel is checked, a new seed is selected from the pixel stacks as in step 1. This three-step process is repeated until all the pixel stacks are empty.

Water and Fat Separation

Smath image after region-growing can be used directly to calculate the phase vector for phase correction in Eq. [4]. However, we performed two additional processing steps in this study to achieve an optimal solution. The first step was to correct for pixels with phase vectors that were erroneously determined in region-growing. Although no such errors were observed in the images evaluated in this study, the possibility that such mistakes could occur cannot be ruled out, at least theoretically. One way to correct some isolated pixels with incorrectly-assigned phase vectors is to average Smath image within a boxcar (for example, 7 × 7 pixels). This is similar to the operation of a local orientation filter, as described by Xiang and An (4). The averaged Smath image is then compared with the original Smath image for the pixel at the center of the boxcar. If the angular difference between the two is > π/2, the original Smath image for the pixel is replaced with −Smath image. Otherwise, Smath image retains its original value.

The second additional step we used dealt with the fact that for pixels with low signals and artifacts, the phase of Smath image is subject to substantial uncertainty. As a consequence, even the correctly determined Smath image may not be the optimal representation of the direction of the phase vector that is actually due to the field inhomogeneity. To mitigate that problem, another average of Smath image was calculated with a 7 × 7 boxcar. Instead of using Smath image, we used the averaged Smath image to represent the phase vector, which in turn was used for the final phase correction in Eq. [4]. A notable advantage of using the averaged Smath image is that one can effectively mitigate the phase fluctuation for regions of low SNR without affecting the spatial resolution of the final images.

Water and Fat Identification

The data acquisition used in this study sampled the water and fat signals symmetrically (i.e., when the two signals were either parallel or antiparallel). By using the phase information alone, one can only separate water and fat. To identify water and fat from the two output images, additional information (such as the unique spectrum (8) of biological fat, or the image pattern that human eyes use for identification) could be used. For the pulse sequence and the protocol used in this study, we found that the fat-only images always had a distribution of pixels with higher intensity than the water-only images. Consequently, we designated a pixel with intensity that was 70–80% of the maximum image intensity as a fat pixel, and used that as the initial seed for region-growing. Although it was not exploited here, the same histogram information can be used to identify water and fat after the two images are generated with a randomly selected initial seed.

EXPERIMENTS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. EXPERIMENTS
  5. RESULTS
  6. DISCUSSION AND CONCLUSIONS
  7. Acknowledgements
  8. REFERENCES

We collected raw data from five different patients as a part of routine abdominal examinations, using 1.5-Tesla MR scanners (GE Medical Systems, Waukesha, WI) and a four-channel torso phased-array receiver coil. A typical scanning protocol was as follows: sequence TR = 150 ms, TE = 2.2 ms for out-of-phase images, TE = 4.7 ms for in-phase images, receiver bandwidth = ± 62.5 kHz, acquisition matrix = 256 ×, 192, field of view (FOV) = 36 ×, 27 cm, slice thickness = 5–7 mm, and gap = 0–1 mm. With this protocol, a total of approximately 20 slices can be collected in 20 s. Thus, a patient's entire abdomen can usually be covered in a single breath-hold. Institutional review board approval was obtained for all of the human studies.

Reconstruction of the water-only and fat-only images was performed offline on an IBM ThinkPad PC with an Intel processor (x86 family, 896 MHz) operating on the Microsoft Windows 2000 platform. The reconstruction algorithm was implemented in Matlab (The MathWorks, Natick, MA). The length of the code for the entire region-growing algorithm, including variable initiation, was only 75 lines. The phase-correction part of the algorithm was performed on images with data combined from all four receivers (9), and it took approximately 14 s for a 256 × 192 image. After the images were reconstructed, they were transferred via the hospital's network back to the scanners and installed in the image database for archiving and filming. The entire reconstruction process was automatic and required no user intervention except for indicating the name of the raw data file.

For comparison purposes, another region-growing algorithm, originally described by Szumowski et al. (5), was implemented and used to process the same sets of data. Like several other known algorithms, that method of region-growing aims at unwrapping the signal phase using the phase difference between two neighboring pixels. As such, an empirical angular threshold must be chosen. Additionally, that method requires manual selection of seed pixels, and uses a single pixel stack to store the seeds and determine the sequence of region-growing.

RESULTS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. EXPERIMENTS
  5. RESULTS
  6. DISCUSSION AND CONCLUSIONS
  7. Acknowledgements
  8. REFERENCES

The image-reconstruction program generates four images per slice: an in-phase image, an out-of-phase image, a water-only image, and a fat-only image. In all of the images (>100) of different patients, our phase-correction algorithm achieved uniform separation and consistent differentiation between water and fat. Figure 2a–b show the water- and fat-only images, respectively, of an exemplary slice from a patient with a healthy liver. No processing artifact is visible, despite the presence of an apparent disconnect along water and fat boundaries, and signal void in the lung and heart regions. In comparison, Fig. 2c–d show the water- and fat-only images, respectively, of the same slice that were processed with the algorithm described in Ref. 5. Despite the use of a ±30° angular threshold in the region-growing, that algorithm failed to obtain correct phase unwrapping, and resulted in erroneous water and fat separation within a large area of the image.

thumbnail image

Figure 2. The water-only (a) and fat-only (b) images of an exemplary slice obtained with our phase-correction algorithm from a patient with a healthy liver. The low-SNR pixels in the lung and heart regions, as well as along the water–fat boundaries are handled well by the phase-correction algorithm. In comparison, the images obtained with a phase unwrapping-based approach (c and d) display incorrect water and fat separation (see arrows).

Download figure to PowerPoint

A notable feature of the water- and fat-only images is their superior SNR as compared to the in-phase and out-of-phase images. Another advantage of separate water and fat images over in-phase and out-of-phase images is the possibility for quantitation. Figure 3 shows the water-only (a) and fat-only (b) images of a slice from a patient with metastatic carcinoid tumor and possible hepatic steatosis. In addition to the clear water and fat separation, an interesting finding is the difference (in comparison with Fig. 2) in the relative fat-to-water content in the two patients. In the images in Fig. 2, the relative fat-to-water signal ratio is < 0.03. In contrast, the relative fat-to-water signal ratio in Fig. 3 is 0.2, which is higher by a factor of 6 than that in the patient in Fig. 2.

thumbnail image

Figure 3. Water-only (a) and fat-only (b) images from a patient with metastatic carcinoid tumor and possible hepatic steatosis. The increased fatty presence in this patient's liver can be appreciated by comparison with the fat-only image in Fig. 2. The fat-to-water signal ratio is 6 times higher in this patient than in the patient of Fig. 2.

Download figure to PowerPoint

DISCUSSION AND CONCLUSIONS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. EXPERIMENTS
  5. RESULTS
  6. DISCUSSION AND CONCLUSIONS
  7. Acknowledgements
  8. REFERENCES

Several region-growing algorithms for phase correction of images acquired with Dixon techniques have been published (4, 5, 10). To the best of our knowledge, all of these methods rely on image phase only, and the presence of low-SNR pixels present special challenges. To prevent unreliable growth, most methods require an empirical angular threshold throughout region-growing. Some further require manual selection of seeds (5), and one approach (4) is specific only to images acquired with 3PD techniques. One possible way to minimize corruption of phase unwrapping due to low-SNR pixels is to use the minimum spanning tree algorithm (11). An apparent drawback of this algorithm is that is requires dynamic sorting of a large number of pixels during the phase-correction process, which renders the technique computationally intensive. In our algorithm, the region-growing sequence is automatically sorted with the use of multiple pixel stacks and precalculated spatial gradients of the signal phase. As such, the growth path follows a pseudo-minimum angular difference between neighboring pixels. Even when the initial seed is selected from a background region, the region-growing can quickly stabilize once it makes contact with a region of good SNR. By using both the phase and amplitude of the signals from a group of neighboring pixels, the reference used to guide the selection of the signal direction for a given pixel is weighted more heavily with pixels of higher amplitude. The signal phase of these pixels is usually more reliable than the signal phase of the pixels of lower amplitude. Consequently, our algorithm can handle low-SNR pixels or pixels along water and fat boundaries more easily.

In conclusion, we have developed an efficient and robust 2PD technique that is capable of automatically generating water and fat images of an entire abdomen in a single breath-hold. Instead of resorting to phase unwrapping, the phase-correction algorithm determines the directional distribution of signals due to field inhomogeneities. The region-growing follows a path of pseudo-minimum angular difference, which is facilitated by the use of multiple pixel stacks. Further, the determination of the signal direction is based on both the amplitude and phase of the surrounding pixels. In vivo water- and fat-only abdominal images that are free of respiratory or other postprocessing artifacts demonstrate the feasibility and potential utility of the technique.

Acknowledgements

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. EXPERIMENTS
  5. RESULTS
  6. DISCUSSION AND CONCLUSIONS
  7. Acknowledgements
  8. REFERENCES

The author thanks Karen F. Phillips, ELS, and Jason Stafford, Ph.D., for their help in editing the manuscript.

REFERENCES

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. EXPERIMENTS
  5. RESULTS
  6. DISCUSSION AND CONCLUSIONS
  7. Acknowledgements
  8. REFERENCES