Off-resonance effects (e.g., field inhomogeneity, susceptibility, chemical shift) cause artifacts in MRI (1, 2). The artifacts appear as positional shifts along the readout direction in rectilinearly sampled acquisitions. Usually, they are insignificant because of short readout times in normal spin echo (SE) and gradient echo (GRE) sequences. However, they sometimes appear as severe geometric distortion in echo-planar imaging (EPI) because of the relatively long readout time of these acquisitions (3).
Over the past decade, spiral imaging techniques have gained in popularity due to their short scan time and their insensitivity to flow artifacts. However, off-resonance effects give rise to blurring artifacts in the reconstructed image. Most spiral off-resonance correction methods proposed to date (7–11) are difficult to apply to correct for blurring artifacts that result from fat since the frequency shift between fat and water is typically much greater than that due to main magnetic field (B0) inhomogeneity across the field of view (FOV). As such, off resonance artifacts remain one of the main disadvantages of spiral imaging (4–6).
Currently, off-resonance artifacts from fat are most commonly avoided by using spatially and spectrally selective RF excitation pulses (SPSP pulses). These RF pulses excite only water spins, thereby eliminating the off-resonance fat signals and hence avoid artifact generation (6, 12, 13). Yet, SPSP pulses may not lead to satisfactory fat signal suppression in the presence of large B0 inhomogeneities. Alternatively, excitation of only water spins could be achieved through application of chemical shift presaturation pulses (e.g., CHESS pulses (14)) prior to normal spatially selective excitation. However, the effectiveness of these frequency selective RF excitation pulses is also dependent on homogeneity of the main magnetic field.
Dixon techniques have primarily been investigated for water–fat decomposition in rectilinear sampling schemes. In the original Dixon technique water and fat images were generated by either addition or subtraction of the “in-phase” and “out-of-phase” datasets (15). Water and fat separation is unequivocal using this technique when the magnetic field inhomogeneity is negligible over the scanned object. However, decomposition of fat and water images via the original Dixon technique is inaccurate when B0 inhomogeneity cannot be neglected. Therefore, modified Dixon techniques using three datasets (i.e., three-point Dixon (3PD) technique) or four datasets were developed to correct for B0 inhomogeneity off-resonance effects and microscopic susceptibility dephasing (16–18). New versions of the Dixon technique use two datasets with B0 inhomogeneity off-resonance correction (i.e., two-point Dixon (2PD) technique) (19). The effectiveness of water–fat decomposition is almost equivalent to that of the 3PD technique, although off-resonance frequency estimation of this technique would be unstable for voxels with nearly equal water and fat signal intensities (19). The advantage of these multiple-point Dixon techniques over spectrally excited RF pulses is that unequivocal water–fat separation can be achieved even in the presence of B0 inhomogeneity. This advantage is of notable importance because neither tissue-induced local magnetic field inhomogeneity nor external applied magnetic field inhomogeneity can be completely removed by shimming (16, 17).
In this article, 3PD and 2PD techniques are extended to spiral trajectories for effective water–fat decomposition with B0 inhomogeneity off-resonance correction. The multiple required acquisitions for the Dixon techniques are not a significant limitation in the newly proposed techniques compared to the conventional spiral data acquisitions since conventional spiral acquisitions often require two datasets with slightly different TEs to create a frequency map for off-resonance correction. The newly proposed techniques do not require SPSP pulses and provide effective fat signal suppression and off-resonance blurring correction.
MATERIALS AND METHODS
Spiral Dixon Techniques
The long readout time of spiral trajectories leads to off-resonance signals that blur into neighboring pixels; spins from multiple off-resonance frequencies can all contribute to a voxel signal. However, it can generally be assumed that B0 inhomogeneity is smoothly varying across the FOV (this assumption will be referred to as “assumption (i)” in this article). Thus, the average off-resonance frequency in any pixel is usually close to that corresponding to the true local B0 field strength. This concept is exploited in the conventional method to create an off-resonance frequency map in spiral imaging, in which the phase difference is taken between two images (with different TEs) even though both images are already blurred by off-resonance effects. It is also assumed that: ii) only two chemical shift species (i.e., water and fat), are considered, and their spectra are both sufficiently narrow so that little spectral overlap occurs; and iii) signal intensity differences due to T2* decay among datasets with different TEs are negligible.
Spiral 3PD Technique
Suppose that three k-space datasets with TE differences ΔTE (s) are acquired using a normal spatially selective RF pulse for each TR (Fig. 1). As described in the previously proposed rectilinear 3PD techniques (16–18), ΔTE is usually chosen as τ, the time during which fat spins precess by 180° out of phase with respect to water spins. This condition is essential for efficient determination of the frequency map, as briefly explained in the Appendix. With this condition, the signals at each pixel in the reconstructed images (S0, S1, and S2) from these datasets can be expressed as:
where W′ represents water signal blurred by local B0 inhomogeneity off-resonance frequency f (Hz), F′ is fat signal blurred by local B0 inhomogeneity and chemical-shift off-resonance frequencies f + ffat (Hz), and ϕ is the phase shift due to B0 inhomogeneity off-resonance effects during ΔTE. That is,
Figure 2 shows a flow chart of the spiral 3PD technique. Local off-resonance frequencies first need to be determined. 2ϕ is obtained as:
Even though signals blur into neighboring voxels due to the local off-resonance effects in the spiral image, from assumption (i), 2ϕ in Eq.  gives the phase shift due to the true local B0 inhomogeneity off-resonance frequency f at each pixel. Phase unwrapping is then performed to obtain the correct ϕ at each pixel using the region growing method (20) with a manually selected seed point. f can be successively determined from Eq. .
Water–fat signal decomposition is performed at each pixel based on the determined frequency map. From Eqs. –, one obtains:
Deblurring needs to be performed on the W′ and F′ images. This is achieved through the use of the frequency-segmented off-resonance correction method (7). This method reconstructs several images using different demodulation frequencies and selects the most deblurred region from the stack of reconstructed images under the guidance of a frequency map. As shown in Fig. 2, the demodulation frequencies used to deblur W′ are those given by the frequency map. The demodulation frequencies used to deblur F′ are the sum of the chemical-shift off-resonance frequency and the local frequencies given by the frequency map. The use of multiple demodulation frequencies enables deblurred water and fat images, W and F to be reconstructed.
Spiral 2PD Technique
Although the spiral 3PD technique can achieve water–fat separation with off-resonance deblurring, the scan time is prolonged since three datasets are acquired. Here, a newly developed 2PD technique for spiral trajectories is described.
In the spiral 2PD technique, as shown in Fig. 3, the TEs of the first and second data acquisitions are nτ and (n+1)τ, respectively, where n is a positive integer and τ is defined the same as in the spiral 3PD technique.
The signals at each pixel in the reconstructed images (S0 and S1) from these datasets can be expressed as:
where the definitions of W′ and F′ are the same as in the spiral 3PD technique, and ϕ is the phase shift due to B0 inhomogeneity off-resonance frequency f (Hz) during τ (s). That is,
Since it can be assumed that an RF pulse penetration angle into the transverse plane is the same for both water and fat spins in each voxel, their magnetization vectors should be aligned in the transverse plane at the onset of the spiral gradient when TE is an even-integer multiple of τ and opposed phase when TE is an odd-integer multiple of τ. In other words, if W′ and F′ are deblurred by k-space data demodulation with the correct local off-resonance frequencies (the water and fat images obtained this way are defined as W and F, respectively), the orientation of the two vectors W and F will be identical when TE is an even-integer multiple of τ and they will be opposite when TE is an odd-integer multiple of τ.
Figure 4 shows a flow chart of the spiral 2PD technique. For water–fat signal decomposition, several predetermined demodulation frequencies fj (Hz) are substituted into Eqs. , . W′ and F′ are determined for each demodulation frequency fj (defined as Wj′ and Fj′, respectively):
where ϕj = 2πfj · τ.
The deblurred water and fat images Wj and Fj can be obtained after k-space data demodulation with the demodulation frequencies fj and fj + ffat for Wj′ and Fj′, respectively. To determine the correct B0 inhomogeneity off-resonance frequency at each pixel, the orientations of two vectors Wj and Fj are compared. When n is even (odd), the value of fj that makes two vectors Wj and Fj aligned (opposed) is selected as the correct local off-resonance frequency (the correct frequency is defined as fl). As is evident, this process of local off-resonance frequency determination simultaneously reconstructs the final deblurred water and fat images, W and F.
In practice, the vector alignment property described above is difficult to use since some voxels may contain predominantly only water or fat spins. Hence, the following quantity is measured:
The absolute value of the principal value of Eq.  is minimized when the two vectors Wj and Fj are aligned/opposed or when the voxel is predominantly filled with either Wj or Fj. A similar concept was used effectively in an earlier rectilinear 2PD technique (19).
It is difficult to determine the correct frequency in image regions with low SNR. Therefore, here the summation of exp(iΦj) within a small window centered on each pixel is measured and the real part extracted:
Note that the summation in Eq.  is a complex sum. Plocal is expected to be maximized when j = l. However, a plot of Plocal-fj often has more than one peak with their magnitudes close to one another since Φj often shows periodic-like patterns with j; this may occur even in areas with reasonably high SNR. Here, all the values of fj at which Plocal takes local maxima in the Plocal-fj plot are first chosen at every pixel (these fj are defined as fp). Then, the region growing algorithm is performed to select the correct frequency fl: the algorithm is initialized with a manually selected seed point. In other words, the value of fp that is selected is that which is closest to the average local frequency of the neighboring pixels within the frequency-determined region.
Algorithms for the Spiral 3PD and 2PD Techniques With Multicoil Datasets
Multielement surface coils are often used to obtain images with higher SNR than would be achieved with a single larger coil. Each surface coil usually has a small region of signal sensitivity (21, 22). Thus, the image reconstructed from each set of individual coil data shows nonuniform signal intensity over an FOV. The B0 inhomogeneity frequency map derived from an individual coil may not be accurate for the region where the image SNR is low. This subsection describes application of the spiral 3PD and 2PD algorithms when data are acquired from multielement surface coils.
For the spiral 3PD technique, exp(i2ϕ) is first extracted from each coil data using Eq. :
The subscript m represents the m-th coil data. The phase, exp(i2ϕm), is weighted by its signal magnitude, |S0,m| at each pixel. The argument of this value accurately represents twice the phase shift due to the B0 inhomogeneity off-resonance frequency during ΔTE. That is,
where n is the total number of coils. The frequency field map can be determined by the phase unwrapping algorithm described for the spiral 3PD technique. Signal decomposition and frequency demodulation are performed for each coil's data based on the obtained frequency map.
For the spiral 2PD technique, Eq.  is calculated for each coil data at each demodulation frequency fj. Φj are weighted by their signal amplitude and combined at each pixel in the reconstructed images. Hence, Φj is redefined as:
where n is the total number of coils, Wj,m and Fj,m are the water and fat images reconstructed from the m-th coil data with the predetermined demodulation frequency fj. Plocal is computed from Φj defined in Eq.  using the algorithm described for the spiral 2PD technique. The same method to determine the frequency field map is also used.
One-Acquisition Spiral Dixon Techniques Using Variable Density Spiral Trajectories
Ideally, only one acquisition would be needed for fat/water decomposition. An efficient spiral off-resonance correction method with only one acquisition was proposed by Nayak et al. (11). This method is called off-resonance correction using variable density spirals (ORC-VDS). In this method, odd- and even-numbered spiral interleaves have slightly different TEs and the central portion of k-space is oversampled using variable density spiral trajectories. A B0 inhomogeneity field map can be calculated by taking the phase difference between the two low resolution images reconstructed from the data of odd- and even-numbered spiral interleaves.
The extension of this method to the spiral 3PD and 2PD techniques is quite straightforward. Figure 5 shows the spiral trajectories that oversample the inner regions of k-space with three times (Fig. 5a) and twice (Fig. 5b) higher sampling densities than the outer parts. In Fig. 5a, the solid, dashed, and dotted spiral trajectories have three different TEs with their TE differences equal to τ. In Fig. 5b, the solid and dashed spiral trajectories have different TEs, with their TEs equal to nτ and (n+1)τ, respectively. In both cases, off-resonance frequency field maps can be derived from the low spatial frequency data using the same algorithms as the spiral 3PD and 2PD techniques described above. It can be expected that these spiral acquisition schemes enable single acquisition spiral 3PD and 2PD techniques. The Dixon techniques taking advantage of the sampling schemes shown in Fig. 5a,b are referred to as the “variable density spiral 3PD (VDS-3PD) technique” and the “variable density spiral 2PD (VDS-2PD) technique.”
In both the VDS-3PD and VDS-2PD techniques, a frequency field map is derived from only low spatial frequency data using the spiral 3PD and 2PD algorithms, respectively. Water–fat decomposition and k-space data demodulation are performed for the low spatial frequency data based on the frequencies indicated in the field map. High spatial frequency data are also demodulated with the frequencies indicated in the frequency field map and will be added to the demodulated low spatial frequency data.
In the VDS-3PD technique, the high-frequency data of three different TEs (defined as Sh0, Sh1, and Sh2) are combined so that their phases are consistent with one another. In other words, when the demodulation frequency is fl (Hz), the high spatial frequency data of the three TEs to be added to the water image, are combined as (defined as Shw):
and those that will be added to the fat image are combined as (defined as Shf):
Similarly, in the VDS-2PD technique the high-frequency data of two TEs (Sh0 and Sh1) to be added to the water image are combined as:
and those to be added to the fat image are combined as:
In both VDS-3PD/2PD techniques, Shw and Shf are demodulated with frequencies fl and fl + ffat, respectively. These demodulated high-frequency data are added to the low-frequency water and fat images that are already demodulated by the same frequencies fl and fl + ffat, respectively.
Both the spiral 3PD and 2PD techniques were implemented for in vivo imaging experiments. All experiments were performed using a 1.5 T Siemens Sonata scanner (Siemens Medical Solutions, Erlangen, Germany). In these experiments, axial brain and pelvis images were acquired from a healthy volunteer using a quadrature head coil and four-element phased array surface coils, respectively. All procedures were done under an institutional review board approved protocol for volunteer scanning.
The following sequence parameters were the same for all the spiral sequences used in the experiments: for the brain image experiments there were 20 spiral interleaves, FOV 240 × 240 mm, slice thickness 10 mm, flip angle 13°, spiral readout time 16 ms, and TR 25 ms. For the pelvis imaging experiments, there were 20 spiral interleaves, FOV 390 × 390 mm, slice thickness 10 mm, flip angle 13°, spiral readout time 15 ms, and TR 25 ms.
For the spiral 3PD technique, TEs were set to 2.2(1st)/4.4(2nd)/6.6ms(3rd) in both the brain and pelvis imaging experiments. For the spiral 2PD technique, TEs were set to 2.2(1st)/4.4ms(2nd) in both the brain and pelvis imaging experiments.
The normal spiral sequences with SPSP pulses were also implemented for comparison. 1-4-6-4-1 binomial pulses were used for excitation. The total flip angle for on-resonance spins was 16°. Two acquisitions were performed for off-resonance correction. TR was 33 ms and TEs were set to 6.0/7.5(ms) in both the brain and pelvis imaging experiments.
The VDS-3PD technique was implemented to acquire an axial image of a volunteer pelvis using a four-element surface coil. The sequence parameters were: 18 interleaved spirals, TE 2.2/4.4/6.6ms (each TE was shared by six interleaves), TR 25 ms, flip angle 13°, FOV 390 × 390 mm, slice thickness 10 mm, and the radius of the oversampled region was 40% of kmax.
For reconstruction of the brain images, k-space data were gridded onto a Cartesian grid. The modified Block Uniform Resampling (BURS) algorithm (23) was used for k-space gridding. Next-neighbor regridding (24) was used to facilitate reconstruction of the multiple k-space datasets pelvis images. The images reconstructed from each coil data was combined using the sum-of-squares method to create either water or fat images (25).
In the spiral 2PD technique, the predetermined demodulation frequencies ranged from –200 Hz to +200 Hz with a frequency resolution of 10 Hz (i.e., 41 demodulation frequencies in total) in both brain and pelvis image reconstructions. The window sizes to compute Plocal were set to 9 × 9 and 5 × 5 pixels for the brain and pelvis image reconstructions, respectively.
Figure 6 shows the axial brain images. In Fig. 6a,b are the water and fat images using the spiral 3PD technique, respectively. Figure 6c,d are the water and fat images using the spiral 2PD technique, respectively. Figure 6e is one of the images directly reconstructed from the acquired data (TE 4.4 ms). Figure 6f is one of images reconstructed from the data with SPSP pulses (TE 7.5 ms) after off-resonance correction. Note the uniformity of the signal intensities of the water images (Fig. 6a,c) when compared with Fig. 6f. Figure 7 shows the axial pelvis images. Figure 7a–f were acquired under the same conditions as those in corresponding locations in Fig. 6.
As observed in Fig. 6e and Fig. 7e, the original images are affected by a high level of blurring artifacts in most image regions. However, as noted in Figs. 6 and 7a–d, these blurring artifacts are substantially reduced while simultaneously unambiguous water–fat decomposition is achieved in both the spiral 3PD and 2PD techniques. Figure 7f (SPSP pulses) shows that some areas of fat in the right anterior subcutaneous region are not completely suppressed (Fig. 7f, arrow).
The results of the VDS-3PD technique are shown in Fig. 8a (water image) and Fig. 8b (fat image). As is evident, the water and fat signals are successfully decomposed, and no significant blurring artifacts remain.
Spiral 3PD and 2PD Techniques
As is already clear, the main difference between the spiral Dixon techniques and the earlier rectilinear Dixon techniques is that the spiral Dixon techniques require image deblurring steps in addition to water–fat signal decomposition. Both spiral 3PD and 2PD techniques proposed here successfully perform off-resonance blurring correction with water–fat signal decomposition.
One of the main advantages of the Dixon technique is that uniform fat suppression can be achieved across an image FOV in the presence of B0 inhomogeneity. The frequency maps of the pelvis image (not shown) indicate that local B0 off-resonance frequencies at the right anterior subcutaneous region are quite large (+150 to +180 Hz) compared with other parts due to air–tissue interface susceptibility variations. Thus, the fat signals in this region are not eliminated with SPSP pulses (Fig. 7f, arrow), while the spiral 3PD and 2PD techniques lead to unequivocal water–fat signal decomposition at the corresponding region (Fig. 7a–d). Similarly, Fig. 6f shows wide areas of the left anterior temporal lobe that appear slightly darker (lower homogeneity) than other parts of the brain. This is not seen in Fig. 6a,c. The frequency field maps of the brain image (not shown) indicate that the off-resonance frequencies in the areas of reduced signal amplitude in the left temporal lobes are larger (-90 to -60 Hz) than in other parts of the brain. It can be presumed that water signals in these regions are partly suppressed since SPSP pulses are frequency-sensitive fat suppression techniques. As a consequence, these regions are partially suppressed, as seen in Fig. 6f. As these examples illustrate, both the spiral 3PD and 2PD techniques lead not only to uniform fat suppression but they avoid unwanted water signal suppression when B0 inhomogeneity exists.
Nonuniform fat signal suppression and undesirable water signal suppression could be reduced by the use of SPSP pulses with a sharper transition band between the water and fat frequencies. However, off-resonance frequencies induced by local susceptibility are sometimes as large or even larger than the chemical-shift off-resonance frequency. In such cases, it is impossible to eliminate the above artifacts, independent of the improvement of the applied SPSP pulses.
SPSP pulses often take a relatively long time for excitation. The time duration of SPSP pulses is sometimes even equivalent to the spiral readout time (6, 13). Therefore, the minimum possible TE and TR are determined by the lengths of the SPSP pulses. In contrast, normal slice-selective small flip angle RF pulses can be used in both the spiral 3PD and 2PD techniques, and hence short TEs and TRs can be achieved. A new frequency field map needs to be created for each acquired image when the scan position is changed for each acquisition. Under these conditions, these spiral Dixon techniques can provide a way to reduce imaging scan time if the minimum achievable TR is used.
It is suggested that the spiral 2PD technique be used if a shorter total acquisition time is required since it achieves almost the same performance as the spiral 3PD technique. However, as is evident, the spiral 3PD technique algorithm is computationally more efficient than that of the spiral 2PD technique. In the spiral 3PD technique, a frequency field map can be directly computed from Eq.  (with an additional phase unwrapping procedure) and then water–fat signal decomposition and frequency demodulation can be performed based on the obtained frequency map, as shown in Fig. 2. In the spiral 2PD technique, however, a number of predetermined frequencies need to be tested in order to determine the frequency field map. As the off-resonance frequency range of scanned objects is usually unknown a priori, the range of predetermined frequencies must be set sufficiently large to cover off-resonant frequency range in the image. Image reconstruction performed here used 41 predetermined frequencies, covering 400 Hz. On the other hand, the off-resonance frequency ranges that appeared in the computed frequency maps were 300 Hz for the brain image and 240 Hz for the pelvis image (frequency maps not shown). In other words, 10 and 16 extra frequencies were tested in each image reconstruction, although they were actually unnecessary. Unfortunately, without prior knowledge, it is difficult to avoid these extra computations.
As mentioned above, the range of predetermined frequencies must cover all the B0 off-resonance frequencies of scanned objects. Therefore, the center frequency determined in prescan calibrations must be carefully adjusted so that it is near the water peak. This requirement is needed to ensure that the range of predetermined test frequencies spans that associated with B0 off-resonance variation. In our experience, a predetermined frequency range of 400 Hz is sufficient for many cases.
While all the images shown in Figs. 6–8 were reconstructed using MATLAB (MathWorks, Natick, MA), C++ reconstruction code was also developed in v. A1.4 of the ICE software environment found on the scanner's host computer. The computation times of spiral 3PD technique were ∼10 sec and 23 sec when single and four coils were used for the data acquisition, respectively. On the other hand, those of the spiral 2PD technique were ∼80 sec and 132 sec when single coil and four coils were used, respectively.
Another difficulty with the spiral 2PD technique is the determination of the window sizes to calculate Plocal. In the previously proposed two-point rectilinear sampling Dixon technique, off-resonance frequencies were evaluated at each pixel. However, pixelwise frequency evaluation is difficult in low SNR regions and at tissue–lipid boundaries (19). To reduce the errors due to noise in evaluating off-resonance frequencies, we set a small window at each pixel, invoked assumption (i), and assumed that the frequency within the window is almost constant. However, in practice it is difficult to determine appropriate window sizes. For example, observable errors due to noise may still exist in the computed frequency field map if the window size is small. If the window size is large, abrupt changes of local off-resonance frequencies may be difficult to detect even though noise effects can be reduced. In our image reconstruction, relatively large windows (9 × 9 pixels) were used for the brain image since frequency evaluation at the boundaries between postocular fat and neighboring tissues was unstable when a smaller-sized window was used. The inside Arg() of Eq.  may be significantly affected by noise and thus Eq.  may yield inaccurate values for those voxels with comparable water and fat signal magnitudes. In our experiments, voxels in which water (or fat) signal are predominant show only one peak or two in their Plocal-fj plots; if two peaks occur, they typically are sufficiently distinct to allow selection of the correct frequency. In contrast, water–fat equivalent voxels may have many local maxima in the Plocal-fj plots which hinders determination of the correct frequency. Errors were propagated from these locations in the region growing process when a small window was used. However, such errors were reduced as the window size was increased. No apparent error propagations were observed in the brain frequency map when a 9 × 9 window was used.
It is suggested that the frequency map derived for the brain image in the spiral 2PD technique is as accurate as that determined by the spiral 3PD technique since the results from the two methods are comparable. In other words, a 9 × 9 window size is small enough to create an accurate frequency map for the spiral 2PD technique in practice. This result can be understood from the fact that a B0 off-resonance frequency map is often derived from the low-resolution images in the conventional spiral acquisition method (6, 26). This concept was also used advantageously in our VDS-Dixon techniques described below.
VDS Dixon Techniques
In the conventional spiral acquisition method with SPSP pulses, two datasets with different TEs often need to be acquired to correct for off-resonance blurring artifacts. The need for two datasets diminishes the speed advantages of spiral imaging. The off-resonance correction algorithm may fail in spiral imaging if motion-dependent misregistration between the two images occurs (27). Similarly, accurate water–fat decomposition may not be achieved in the Dixon technique if there is motion-dependent misregistration among the reconstructed images with different TEs. VDS-3PD/2PD techniques have overcome these drawbacks.
As is evident in VDS-3PD/2PD algorithms described above, fat signals in the high-frequency data are also added to the low-resolution water image when the combined high-frequency data of water (Shw: Eqs. , ) are added to the low-resolution water image. This occurs because high-frequency data cannot be separated into water and fat signals. However, the difference between Eqs. ,  and the difference between Eqs. ,  show the phase of fat signals in the high-frequency data from different TEs are inconsistent, while the phase of the water signals in the high-frequency data are consistent. Moreover, the fat signals in the high-frequency data are demodulated not by their demodulation frequency fl + ffat but by the demodulation frequency of water signals fl when the water image is reconstructed. Therefore, the high-frequency components of the fat signals are blurred in the water image. As the total signal amounts of the high-frequency components are usually quite small compared with those of the low-frequency components, the artifacts due to high-frequency components of the fat signals are usually not significant in the water image. Similarly, there are usually no significant artifacts in the fat image caused by the high spatial frequency water signals since water signals in the high-frequency data are spread out in the fat image.
As seen in Fig. 8, water–fat signal decomposition and off-resonance blurring correction are successfully achieved in the VDS-3PD technique. However, the quality of the images in Fig. 8 is degraded when compared with those of the spiral 3PD technique shown in Fig. 7a,b. One of the main reasons for this is that the SNR of the images in Fig. 8 are lower than those in Fig. 7a,b because the images in Fig. 8 were reconstructed from a reduced amount of data compared with Fig. 7a,b. Further, the fine structures in the water image of Fig. 8a (the fat image Fig. 8b) are obscured by the blurred fat signals (water signals) contained in the high-frequency data, as mentioned above. This problem is unavoidable with the VDS-3PD/2PD techniques unless the oversampled k-space region is expanded. As this example suggests, although the VDS-3PD/2PD techniques provide scan time advantages, they may not be suitable when fine structures are of particular interest (e.g., coronary angiography). In such a case, the spiral 3PD/2PD techniques would be recommended.
It has been demonstrated that the Dixon techniques can be extended to spiral data acquisition. The spiral 3PD and 2PD techniques proposed here can achieve not only water–fat signal decomposition but also off-resonance blurring artifact correction. The SPSP pulses commonly used in spiral imaging may not lead to uniform fat suppression and they may also yield undesirable water signal suppression in the presence of B0 inhomogeneity. These disadvantages of SPSP pulses can be overcome by excellently performing techniques we have proposed. One-acquisition spiral Dixon techniques using variable density spiral trajectories have also been shown to be simple extensions of the spiral 3PD and 2PD techniques, thereby avoiding the need for multiple separate acquisitions. The Dixon techniques proposed here offer new and alternative approaches to achieve effective fat signal suppression with reduced scan time in spiral MRI.
The authors thank Bonnie Hami, M.A., for editorial assistance.
Spiral 3PD Technique With Arbitrary ΔTE
As discussed in the previous rectilinear 3PD methods, ΔTE = τ is essential for efficient determination of the frequency field map. This is also the case with the spiral 3PD technique. In this appendix, we briefly describe the derivation of fat and water signals at arbitrary ΔTE, methods to calculate the field map under arbitrary ΔTE conditions, and why ΔTE = τ is important for efficient calculation.
The acquired signals with arbitrary ΔTE can be expressed as:
A quadratic equation with respect to exp(iϕ) can be derived from Eqs. [A1]–[A3] to provide an estimate of the frequency field map:
In practice, it is difficult to select the one appropriate root corresponding to the true B0 inhomogeneity from the two given by Eq. [A6]. Previously, we had attempted to use a region-growing method to select a best guess of the appropriate root from Eq. [A6] based on the spatial continuity of B0 off-resonance frequencies. Yet this method may fail when the two roots are different but close to each other. This problem can be avoided if ΔTE is set to τ because exp(i2ϕ) takes only one value at each location, as described in the text.