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Keywords:

  • multicoil;
  • parallel imaging;
  • PILS;
  • spiral;
  • multiple-demodulation;
  • broadband

Abstract

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

Multiple receiver-coil data collection is an effective approach to reduce scan time. There are many parallel imaging techniques that reduce scan time using multiple receiver coils. One of these methods, partially parallel imaging with localized sensitivities (PILS), utilizes the localized sensitivity of each coil. The advantages of PILS over other parallel imaging methods include the simplicity of the algorithm, good signal-to-noise ratio (SNR) properties, and the fact that there is no additional complexity involved in applying the algorithm to arbitrary k-space trajectories. This PILS method can be further improved to provide truly parallel broadband imaging with the use of multiple-demodulation hardware. By customizing the demodulation based on each coil's location, the k-space sampling rate can be chosen based on each coil's localized sensitivity region along the readout direction. A simulated demodulation of data from 2D Fourier transform (FT) and spiral trajectories is shown to demonstrate the method's feasibility. Magn Reson Med, 2005. © 2005 Wiley-Liss, Inc.

Image acquisition and reconstruction methods using multiple receiver coils are very effective ways to improve the signal-to-noise ratio (SNR) or reduce scan time. Traditionally, phased-array imaging methods (1) were commonly used to improve SNR (2). In phased-array imaging, SNR is improved by reducing the noise volume of each coil. Recently, various methods designed to decrease scan time using multiple receiver coils (3) were developed under the name of parallel imaging. These methods include sensitivity encoding (SENSE) (4), simultaneous acquisition of spatial harmonics (SMASH) (5), and partially parallel imaging with localized sensitivities (PILS) (6). The main difference between phased-array imaging and parallel imaging is the fact that parallel imaging utilizes the coils' sensitivity pattern as an encoding scheme. The sensitivity provides additional encoding on top of the gradient encoding. This allows the process of encoding to be more parallel since the multiple sensitivity-encoded data are acquired simultaneously using multiple coils.

SENSE is a method that utilizes the precise knowledge of the receiver coils' sensitivity function as spatial encoding information. The sensitivity of the coil is a smooth function that can be measured with low-resolution scans and can then be used as an additional encoding method. By measuring this sensitivity and using it to invert the encoding matrix to reconstruct the image, the number of samples needed for Fourier encoding can be decreased.

The SMASH method is similar to SENSE in that it uses the sensitivity of the coil for encoding; however, SMASH uses this information in a very different way. SMASH relies on making sinusoids out of the coils' sensitivity patterns. Therefore, it tries to fill in the missing k-space lines by making sinusoids that normally would have been generated through gradients. In other words, it tries to interpolate data in k-space by assuming that the sensitivity pattern mimics a sinusoidal pattern.

In contrast, the PILS method is a simpler method that utilizes the fact that each coil can be sensitive to a different region of the imaging FOV, so that images from different coils can be simply cut and pasted together. This method can be treated as a special case of SENSE when the sensitivity of the coils are completely orthogonal to each other.

In this paper, a method to improve the PILS technique is proposed along with a new hardware configuration that will allow such a method to be implemented.

THEORY

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

The PILS algorithm is attractive because it does not require measurements of the coil sensitivity pattern, calibration of the coils, or complicated reconstructions. The PILS algorithm also offers better noise properties than SENSE and SMASH (7), with less artifacts than SMASH in many cases. Another strength of the PILS algorithm is that it enables truly parallel imaging through an acquisition and reconstruction scheme that is completely independent among different coils. Multiple coils can be placed at locations that are of interest and then images can be separately obtained in parallel. Since images from each coil can be reconstructed independently from images from other coils, the technique can also be applied to cases in which multiple coils are located at distant locations. Such cases would include, for example, simultaneous imaging of both breasts or both knees. The PILS method has the added advantage that unlike other parallel imaging techniques, such as SENSE and SMASH, the reconstruction remains computationally simple even when arbitrary k-space trajectories are used.

However, one concern with applying the PILS method is the fact that anti-aliasing filters are applied before the sampling stage. This poses a problem when the method is applied in a general sense. Here we define the problem and provide a solution.

Off-Center Imaging

During a scan it is often the case that the region of interest (ROI) is not at the center of the magnet (the so-called isocenter). In such cases, the FOV is assigned to be off-center. The difference between having the object of interest at the center of the magnet and having the same object off-center is a simple modulation. The signal received from an object off-center is a modulation of the signal that would be received from the same object if it were located at the center of the magnet. This is illustrated in Fig. 1. If the Fourier transform (FT) of an object m(x, y) is M(kx, ky) (Fig. 1a), the FT of the same object that is shifted off-center, m(x−xo, y−yo), is M(kx,ky)emath image (Fig. 1b).

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Figure 1. Off-center imaging and data modulation. a: FT of an object m(x, y) located at isocenter is M(kx, ky). b: FT of the same object shifted, m(x−xo, y−yo) is M(kx,ky)emath image, a simple phase modulation of the FT of the object at the isocenter. Note that the k-space data are displayed as the real part to show the modulation effect.

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The implication of this relationship in multicoil imaging is very significant. When multiple coils are used to cover different ROIS at the same time, it is likely that the regions covered by each coil will be off-center. This means that signals from multiple coils will be modulated versions of the signals that would have been received if the ROIs were located at isocenter. As long as the data from each coil are demodulated properly, this is as if multiple images are acquired in parallel at the same time. This method was proposed in the original PILS paper (6) in a slightly different context.

Anti-Alias Filtering

In any given situation where analog signals are sampled and digitized, anti-aliasing filters are used. The main purpose of the anti-aliasing filter is obviously to make sure no aliasing (particularly from noise) occurs. The anti-aliasing is performed by filtering out any signal that is outside of the bandwidth supported by the real-time k-space sampling rate. The anti-aliasing filters are normally analog low-pass filters that suppress anything outside of the bandwidth that is supported by the sampling rate, assuming that the frequency content of the signal is centered around zero. Since the anti-aliasing filters are spatial filters in MRI, assuming that the signal frequency is around zero is equivalent to assuming that the object is at isocenter.

In the case of PILS imaging, the use of this anti-aliasing filter with a single demodulation hardware for all receive channels is problematic. Since the FOVs are located off-center with coils centered around each FOV location, unless the signals from all coils are demodulated separately so that their frequency range corresponds to being at isocenter, the anti-aliasing filter will end up filtering out signals of interest.

Figure 2 illustrates the problem with off-center imaging in the presence of anti-alias filtering for the case of 2DFT imaging. This figure demonstrates a case in which the readout is in the kx direction. Since the readout and anti-alias filtering are along a straight line in the kx direction, the filter supports a rectangular region in the x direction. When the FOV of interest is at isocenter (Fig. 2a), no problem exists. When the FOV of interest is off-center in the x direction, a problem arises because the spectral content of the signal of interest lies outside the bandwidth of the filter (Fig. 2b). Therefore, the signal must be demodulated prior to sampling so that its spectral content lies within the bandwidth of the anti-aliasing filter (Fig. 2c).

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Figure 2. Anti-alias filtering and dynamic demodulation for 2DFT trajectories. a: When the object is located at isocenter, the anti-aliasing filter does not have any effect on the signal. b: If the object is located outside of the band region supported by the anti-aliasing filter, the signal of interest will be filtered out. c: Therefore, the signal received from the off-center object must be demodulated before it is anti-alias filtered and sampled.

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With time-varying gradients, such as in the case of spiral imaging, the readout signal bandwidth varies with the readout trajectory. Depending on the readout trajectory, signal bandwidth can be increased beyond the bandwidth of the signal in the Cartesian domain. However, this increase is generally difficult to quantify. Due to such an increase in bandwidth, with a k-space sampling rate that corresponds to the bandwidth in the Cartesian domain, the anti-aliasing filter will distort the signal. Therefore, sampling signals from such trajectories is not a trivial problem. Nevertheless, spiral imaging is often done assuming that such an effect is negligible. The analysis of the spiral imaging presented below is based on such assumptions.

For spiral imaging, the FOV supported by the sampling is circular. Since the anti-aliasing filter is applied in the readout direction along a spiral shaped trajectory, the anti-aliasing filter also supports a circular FOV. Similarly to the 2DFT imaging case, when the object is at isocenter (Fig. 3a), no problem exists. However, with the object outside the circular region supported by the anti-aliasing filter, the signal is distorted (Fig. 3b). This problem can be avoided by demodulating the signal before anti-alias filtering so that the signal frequency content is within the circular region supported by the bandwidth of the anti-aliasing filter (Fig. 3c).

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Figure 3. Anti-alias filtering and dynamic demodulation for spiral trajectories. a: When the object is located at isocenter, the anti-aliasing filter does not have any effect on the signal. b: If the object is located off-center, the anti-aliasing filter will smear out the signal of interest. c: Therefore, the signal received from the off-center object must be demodulated before it is anti-alias filtered and sampled.

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The anti-alias filtering effects for spiral trajectories (8) are shown in Fig. 4. The anti-aliasing filter gives rise to a space-variant response. Therefore, to appreciate the filter response, the impulse response is plotted for several different locations. Since the filtering effects are radially symmetric for spiral trajectories, four different impulses along the x-axis were used for the demonstration. The input impulse location is shown in Fig. 4a. The FOV region is marked with the circle.

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Figure 4. Impulse response of anti-aliasing filters for spiral trajectories. a: To characterize the shift variant response of a spiral trajectory's anti-aliasing filter, the impulse response is plotted for impulses at four different locations. The four dots along the x-axis show the four impulse locations. b: The cross sections of the four impulse responses along the x-axis are shown. The amplitude decrease as the impulse moves away from the FOV region is clearly demonstrated. c: The cross section along the y-axis at each impulse location is overlaid. The amplitude decrease and the widening of the impulse are observed as the impulse moves away from the FOV region.

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For the simulation of the anti-aliasing filter effects, a 40×40 cm2 FOV and 1×1 mm2 resolution spiral trajectory were used. The spiral trajectory chosen for the experiment consisted of 32 interleaves and 3968 readout points (15.9 ms readout time). The samples were taken from an analytical FT of the impulses. To simulate the anti-alias filtering effect, a digital filter of length 101 and cutoff frequency 0.25 π rad (bandwidth 0.5 π rad) was applied to the data. This emulates an anti-aliasing filter that corresponds to supporting a 10 cm FOV about the isocenter. Then the data were undersampled by a factor of 4 in both the readout and interleave directions, resulting in an eight-interleave, 992 readout point spiral trajectory. This spiral trajectory supports a 10×10 cm2 FOV and 1×1 mm2 resolution.

Figure 4b shows the cross section of the four impulse responses along the x-axis. It is clear that the response of impulses outside of the FOV region is attenuated due to the filtering. Such attenuation is also observed in Fig. 4c, where the cross section of the four impulse responses along the y-axis are overlapped. In the cross section along the y-axis, widening of the impulse response is also observed as the impulse moves away from the FOV. This is due to the decrease in curvature of the spiral trajectory in the outer portions of k-space. Because the impulses were shifted along the x-axis, the signal variation in k-space occurs along the kx direction. The decrease in curvature of spiral trajectories in the outer part of k-space results in more filtering in the direction of the variation (kx) in the outer part of k-space in the ky direction. This results in a weighting in the ky direction that ends up being a convolution in the y direction. Since the weighting becomes narrower as the impulse moves further in the x direction, the impulse response in the y direction correspondingly becomes wider.

Multiple-Demodulation Hardware

In addition to readout functions, gradient performance in terms of strength and speed are driven by the need for short, strong encoding pulses (e.g., for diffusion imaging) and shorter-duration, slice-selective RF pulses at any given slice thickness. The use of ever more powerful amplifiers is one way to increase performance. However, such performance boosts are not in lock step with the A/D conversion rate. Therefore, if the strongest possible gradient is used for readout, the receiver anti-aliasing filter bandwidth supports a small FOV at the isocenter. For example, with a 40 mT/m maximum gradient strength and 4 μs minimum sample interval digital receiver, the supported FOV is only 14.68 cm. Therefore, when the FOV of interest is greater than 14.68 cm, the maximum gradient strength cannot be utilized for readout. Using smaller readout gradients leads to longer readout times, which result in longer minimum TRs and greater off-resonance artifacts.

When the maximum gradient strength jumps ahead of the A/D conversion rate in a scanner that has multiple receiver channels (N), multiple demodulators allow N units of bandwidth to be arbitrarily located in the image domain. These bandwidths can be spliced together into one bandwidth piece that can be the same size as the bandwidth of each piece, N times bigger, or anything in between. This is because the center of the anti-alias filter-supported FOV region can be moved around by means of dynamic analog demodulation. In other words, the demodulation lets one shift the “stuck at isocenter filter bandwidth” to anywhere one desires. By having multiple such demodulators, the center location of the bandwidth can be customized to each coil's center location, which minimizes the need for higher A/D conversion rate.

Therefore, for PILS, centering units of bandwidth on each of the separate coils is a natural approach. By demodulating the signals from each coil separately based on the location of the coil, the k-space sampling rate in the readout direction will not be limited by the FOV size measured from the isocenter. Compared to the case in which PILS imaging is done without such multiple-demodulation hardware (8), readout time can be significantly reduced. This can also lead to a shorter scan time when the scan time is limited by the minimum TR. For k-space trajectories, such as in EPI or spiral imaging, where the readout length is limited by the off-resonance artifacts, for a given readout length the number of excitations can be decreased with new trajectories that can utilize faster gradient speeds.

A block diagram of the proposed multiple-demodulation hardware configuration is shown in Fig. 5. Dynamic demodulation is applied to each coil separately depending on each coil's location, before the anti-alias filtering is applied. For the signal from a coil with the sensitivity region centered at (xi, yi, zi), the demodulation factor is emath image. Note that the demodulation factor is dependent on the center location of the coil as well as the k-space sampling locations, which can be time-varying within a single readout.

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Figure 5. Multiple dynamic demodulation hardware configuration. Dynamic demodulation must be done separately for each coil depending on each coil's location before the anti-aliasing filter is applied. f0 is the Larmor frequency and (xi, yi, zi) (i=1, …, n) indicate the center location of each coil's sensitivity region. Note that the demodulation factor is dependent on the k-space trajectory, which can also be time-varying.

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MATERIALS AND METHODS

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

To demonstrate the proposed method of using multiple-demodulation hardware with PILS, a phased-array coil covering a large FOV (>14.68 cm) with largely separate sensitivity regions was needed. Toward that end, we designed and constructed a four-channel phased-array coil that targeted the lower limb (Fig. 6). When phased-array coils are designed, coils that are in close proximity must be decoupled. One of the most common methods is to overlap the two coil loops so that the coupling will cancel out. However, since in this case the coils were designed so that there would be little overlap between the sensitivity of different coils, the aforementioned method could not be used. The decoupling in this case was performed with the use of additional inductive loops that lay across the adjacent coils. Inductive loops were wound in a figure-eight shape and placed so that the flux from one coil was subtracted in another. This effectively decoupled the coil. Experiments were performed with both a 2DFT trajectory and an interleaved spiral trajectory, implemented on a GE 1.5 T whole-body scanner with a maximum gradient amplitude of 40 mT/m and maximum slew rate of 150 mT/m/ms.

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Figure 6. Four-channel phased-array coil constructed for PILS imaging.

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The experiments were designed to examine the effectiveness of the PILS imaging method as well as to demonstrate the need for multiple dynamic demodulation hardware. One data set was acquired from the scanner with the four-channel phased-array coil and then reconstructed with three different methods. Ideally, three data sets would have been collected separately with different sampling and demodulation schemes. However, since the multiple-demodulation hardware required for the demonstration was not available, the effect was simulated from one data set.

For both 2DFT and spiral imaging, a gradient-echo sequence was used to obtain a 40×40 cm2 FOV and 1.5×1.5 mm2 resolution. The 2DFT trajectory had 256 phase encodes and 256 readout points (1 ms readout time), and the spiral trajectory had 20 interleaves with 2624 readout points (10.5 ms readout time).

The four-channel phased-array coil was used to collect a coronal image of the lower limbs. The imaging sequence had an FOV that covered the full imaging region even though each individual coil had a smaller sensitivity region. The data were first reconstructed by taking the full data set from each coil. Full-FOV images were reconstructed for all coils, and then a sum-of-squares combination of the images was taken to produce the final image.

Then, to demonstrate how PILS can reduce the image acquisition time, the data were down-sampled by a factor of 2 in all directions. For 2DFT imaging, the down-sampling was in both the readout and phase-encode directions, and for spiral imaging the down-sampling was in both the readout and interleave directions. The factor of 2 decrease in the number of phase encodes and interleaves gives a factor of 2 decrease in scan time. Normally, this would be the only scan time reduction achieved using PILS. However, if the k-space sampling rate is also decreased by a factor of 2 in the readout direction while the temporal sampling rate is kept constant, the resulting decrease in readout time will reduce off-resonance artifacts. Alternatively, for spiral trajectories the trajectory can be redesigned so that the readout length stays the same while an additional reduction in the number of interleaves can be achieved.

The down-sampling was done in two different ways to show the anti-alias filtering effects in two different situations. First, to demonstrate the PILS method without the multiple-demodulation hardware, the data were digitally filtered without any prior demodulation. The filter had a length of 33 and cutoff frequency of 0.5π rad (bandwidth π rad). This filter supports an FOV of 20 cm around the isocenter. The supporting region differs in shape and characteristics depending on the imaging trajectory. For the 2DFT trajectory the filter supports a 20-cm band around the isocenter, whereas for the spiral trajectory the filter supports a 20-cm-diameter circular region around the isocenter. Such filtering simulates the effect of the anti-alias filtering. After filtering was performed, the signal was down-sampled. Then the data were digitally demodulated and reconstructed into quarter-FOV images. The four quarter-FOV images were then cut and pasted together to form a full-FOV image. To simulate the case in which multiple-demodulation hardware is available, the data were first separately demodulated before the same digital filter was applied. After the demodulation, the data were filtered and down-sampled. Then, they were also reconstructed into quarter-FOV images before they were cut and pasted together to produce a full-FOV image.

However, it should be noted that since the experiment was done by undersampling the fully acquired data set, the off-resonance benefit is not demonstrated by this experiment. Because of the lack of multiple-demodulation hardware in our scanner, the proposed imaging scheme can only be shown by simulating the modulation and filtering effects. Under real imaging situations with the proposed hardware in place, off-resonance benefits will be present.

RESULTS

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

Figure 7 shows the results from the 2DFT imaging experiment, and Fig. 8 shows the results from the spiral imaging experiment. In both figures the leftmost images (Figs. 7a and 8a) serve as reference images based on conventional reconstruction without PILS. The simulated PILS images without the multiple-demodulation hardware are shown in the middle (Figs. 7b and 8b). The rightmost images (Figs. 7c and 8c) show the simulated PILS image with the demodulation done before the anti-alias filtering.

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Figure 7. Lower-leg PILS imaging with 2DFT. a: Image reconstructed from full-FOV data sets with sum-of-squares reconstruction. The four coil locations are indicated, with a dotted box around the FOV region covered by each coil. b: PILS reconstruction without the customized demodulation for each coil before the anti-alias filtering. The signal of interest outside of the region supported by the anti-aliasing filter is completely filtered out. The region supported by the anti-aliasing filter is shown with the dotted lines. The dotted arrow points to the anti-alias filtering region. Additional artifacts outside of the filter supported region result from the fact that the anti-aliasing filter failed to filter out unwanted signal while filtering out the signal of interest. Such artifacts are indicated by the solid arrows in the figure. c: PILS reconstruction with the customized demodulation of the signal from each coil before anti-alias filtering. Since customized demodulation is performed for each coil before the anti-alias filtering, the anti-alias filter effectively functions as four different filters with different filtering regions, as indicated by the dotted lines. With the use of this multiple-demodulation scheme, the signal of interest is preserved while off-resonance benefits are obtained due to shorter sampling in the readout direction, in addition to the conventional PILS imaging benefit.

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Figure 8. Lower-leg PILS imaging with spiral trajectories. a: Image reconstructed from full-FOV data sets with sum-of-squares reconstruction. The four coil locations are indicated by the dotted box around the FOV region covered by each coil. b: PILS reconstruction without the customized demodulation for each coil before the anti-alias filtering. The signal outside of the region supported by the anti-aliasing filter is smeared out. The smearing of the signal can be best observed in the regions indicated by the solid arrows. Solid arrows in the other two images indicate the corresponding locations. The region supported by the anti-aliasing filter is indicated by the dotted circle. The dotted arrow points to the filter region. c: PILS reconstruction with the customized demodulation of the signal from each coil before anti-alias filtering. With multiple-demodulation in place, the anti-alias filtering effectively supports four separate regions, each centered about the location of the four separate coils. The anti-alias filtering regions are indicated by the dotted circles. The dotted arrow points to one of the four filter regions. With the use of this multiple-demodulation scheme, the signal of interest is preserved while additional off-resonance or scan-time benefits are obtained due to undersampling in the readout direction.

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With the use of the PILS method, the imaging time can be significantly decreased. However, in the cases in which customized demodulation based on the coil location was not done before the anti-alias filtering (Figs. 7b and 8b), artifacts resulted from the anti-alias filtering. In the 2DFT imaging case (Fig. 7b), signals outside of the half-FOV region along the readout direction are clearly filtered out, resulting in complete loss of signal within the FOV. Additional artifacts are also shown within the FOV region (indicated by the solid arrows). These artifacts arise because the anti-aliasing filter failed to filter out the unwanted part of the signal while it filtered out the signal of interest. In the spiral imaging case (Fig. 8b), smearing of the signal is observed outside of the half-FOV region near the isocenter. The solid arrows in Fig. 8b indicate where the smearing due to the filtering effect is most prominent. On the other hand, in the case in which the customized demodulation for each coil was done before the anti-alias filtering (Fig. 7c and 8c), no such filtering artifacts are observed, while the scan time is significantly reduced. However, all of the images acquired using the PILS method show a reduced SNR compared to the reference images, owing to the shorter data acquisition time.

DISCUSSION

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

The PILS algorithm offers many advantages over other parallel imaging techniques. PILS provides good SNR properties and involves a simple reconstruction that does not require any coil calibration or sensitivity measurement. In addition, there is no added complexity from incorporating arbitrary k-space trajectories. In its simplest form, PILS can be applied to imaging with any k-space trajectory. The proposed modification in the PILS algorithm with the multiple-demodulation hardware provides a further decrease in scan time compared to the original PILS imaging method.

Since PILS imaging relies on the localized sensitivity of each individual coil, the speed-up factor can be potentially smaller in cases in which the multiple coils are located in a geometry with substantial overlap in their sensitivity regions. For instance, this situation can occur when two neighboring coils are located in a right angle with respect to each other. In such cases, other parallel imaging techniques, such as SENSE reconstruction, can be used for two such neighboring coil locations, while PILS technique is used to combine images from blocks of coils that have localized sensitivity regions.

Variable-density sampling methods are known to decrease artifacts from signal outside of the encoding FOV regions (9). Therefore, such methods could also be used with the PILS imaging technique to reduce artifacts due to coupling between different neighboring coils (10).

CONCLUSIONS

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

By reducing the k-space sampling rate in the readout direction to only cover an FOV that each coil supports, one can improve the PILS imaging technique to obtain scan-time or off-resonance benefits. To implement the modified PILS algorithm with a limited bandwidth A/D, a hardware modification is required. Multiple dynamic demodulation hardware is needed for a customized demodulation of each coil. The experiments show that without such demodulation hardware in place, the full speed-up factor cannot be achieved using the PILS algorithm.

Acknowledgements

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

Jin Hyung Lee thanks Steve Conolly and Thomas Grafendorfer for their assistance in constructing the phased-array coil used for the experiments. Jin Hyung Lee is also grateful for generous support from the Korea Foundation for Advanced Studies.

REFERENCES

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