eISSN 2384-1109
Open Access, Peer-reviewed
    J Korean Soc Magn Reson Med. 2012 Apr;16(1):6-15. English.
    Published online Apr 30, 2012.
    https://doi.org/10.13104/jksmrm.2012.16.1.6
    Copyright © 2012 Korean Society of Magnetic Resonance in Medicine
    Original Article

    Background Gradient Correction using Excitation Pulse Profile for Fat and T2* Quantification in 2D Multi-Slice Liver Imaging

    Yoonho Nam,1 Hahnsung Kim,1 Sang-Young Zho,1 and Dong-Hyun Kim1,2
      • 1Department of Electrical and Electronic Engineering, Yonsei University, Korea.
      • 2Department of Radiology, Yonsei University, Korea.
    • Corresponding author: Dong-Hyun Kim, Ph.D., Department of Electrical and Electronic Engineering, Yonsei University, 134 Shinchon-dong, Seodaemun-gu, Seoul 120-749, Korea. Tel. 82-2-2123-5874, Fax. 82-2-313-2879, Email: donghyunkim@yonsei.ac.kr
    Received February 22, 2012; Revised April 06, 2012; Accepted April 13, 2012.

    This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

    Abstract

    Purpose

    The objective of this study was to develop background gradient correction method using excitation pulse profile compensation for accurate fat and T2* quantification in the liver.

    Materials and Methods

    In liver imaging using gradient echo, signal decay induced by linear background gradient is weighted by an excitation pulse profile and therefore hinders accurate quantification of T2* and fat. To correct this, a linear background gradient in the slice-selection direction was estimated from a B0 field map and signal decays were corrected using the excitation pulse profile. Improved estimation of fat fraction and T2* from the corrected data were demonstrated by phantom and in vivo experiments at 3 Tesla magnetic field.

    Results

    After correction, in the phantom experiments, the estimated T2* and fat fractions were changed close to that of a well-shimmed condition while, for in vivo experiments, the background gradients were estimated to be up to approximately 120 µT/m with increased homogeneity in T2* and fat fractions obtained.

    Conclusion

    The background gradient correction method using excitation pulse profile can reduce the effect of macroscopic field inhomogeneity in signal decay and can be applied for simultaneous fat and iron quantification in 2D gradient echo liver imaging.

    Keywords
    Fat quantification; T2* measurement; IDEAL; field inhomogeneity; pulse profile; liver imaging

    INTRODUCTION

    Fatty infiltration of liver is one of the primary features of non-alcoholic fatty liver disease (NAFLD). Hepatic iron overload is also common in many liver diseases. Accurate quantification of the liver fat and iron content is an important factor in detecting hepatic diseases. Liver biopsy has been used for diagnosis of NAFLD, but the use of biopsy has problems such as invasiveness and sampling error. On the contrary, MRI is an efficient noninvasive tool for diagnosis of NAFLD (1, 2). Fat signal fraction can be estimated from chemical shift based multi-echo methods (3, 4) because the chemical shift between water and fat is large enough to separate (about 420Hz at 3.0T). Hepatic iron concentration can be estimated by T2* measurements because iron overload accelerates T2* decay (5, 6).

    A recently developed chemical shift based method, named iterative decomposition of water and fat with echo asymmetry and least squares estimation (IDEAL), provides robust separation of water and fat signal with flexible echo sampling times (7). "T2*-IDEAL" which is based on the IDEAL technique provides T2* measurements as well as water-fat decomposition using complex field map (8). Therefore, T2*-IDEAL allows simultaneous quantification of fat and iron in liver with consideration of local B0 field inhomogeneity.

    T2* decay in gradient echo imaging is not only affected by iron overload, but also by macroscopic field inhomogeneities induced by magnetic field imperfections or susceptibility differences at air-tissue boundaries. This artificial signal decay due to macroscopic field inhomogeneities should be considered because it may disturb accurate quantification. Generally, the scale of macroscopic field inhomogeneities induced by magnetic field imperfections or air-tissue boundaries is larger than the imaging voxel size while that of field inhmogeneities due to iron overload is smaller than the imaging voxel size. In typical 2D liver imaging, the voxel size in the slice-selection direction (i.e., a slice thickness) is larger than that of the in-plane direction. Thus, the effect of macroscopic field inhomogeneities can be approximated by a linear background gradient in the slice-selection direction. Several methods such as reducing the voxel size (9), estimating k-space trajectory (10) or using the tailored RF pulses (11) have been suggested to correct this type of an unwanted signal decay. Postprocessing techniques using a sinc correction which assume a perfect rectangular slice profile, are effective because it doesn't require additional scan time or sequence modification (12, 13). However, the excitation pulse profile and the slice profile have Fourier relationship only when a small flip angle is applied. Signal decay due to linear background gradient is weighted by the time profile of the excitation pulse which is a function of both time and background gradient values (12, 14). Therefore, in reality, the decay depends on the excitation profile the RF pulse used.

    In this study, we examine the effect of linear background gradient on fat and T2* quantification in 2D liver imaging and present a correction algorithm using the excitation pulse profile. The correcting algorithm for linear background gradient is applied to T2*-IDEAL algorithm and demonstrated by phantom and in vivo experiments.

    MATERIALS AND METHODS

    Signal Model

    In the presence of linear background gradient, the signal from a voxel including water and fat in 2D gradient echo images can be represented as (8, 12):

    [1] s(t) = (w + f e i2πΔft ) e i2πψte-t/T2*| A(Gb, t) |

    where w and f are the magnitude of water and fat signals, Δf is the chemical shift difference between fat and water, ψ is the B0 inhomogeneity, A(t) is the time profile of the excitation pulse, and Gb is the linear background gradient in the slice selection direction. A major assumption of this model is that the T2* relaxations are the same for water and fat. This may be resonable when T2* decay is dominated by the presence of iron and fat fraction is relatively small (8, 15). Assuming that phase dispersion and magnitude decay due to Gb are identical for water and fat, the additional signal decay related to the background gradient can be corrected by estimating the Gb values if the excitation pulse profile is given (12).

    Background Gradient Correction and T2*-IDEAL

    The B0 field inhomogeneity (ψ) should first be calculated to estimate the background gradients (Gb) which correct for the signal decay. In a multi-slice scan, Gb can be approximated by linear fitting of ψ in the slice-select direction at each voxel from the phase information of adjacent slices (13). T2*-IDEAL algorithm provides the B0 field inhomogeneities at each voxel along with the fat content, water content, and the T2* values by complex data fitting (8). However, an incorrect ψ can be estimated from T2*-IDEAL when the field inhomogeneity is severe. For example, if the estimated ψ is closer to ψt + Δf (ψt is the real ψ), T2*-IDEAL can result in swapped water and fat signals (16). Therefore, here, the initial field map was calculated from the two unwrapped phase images to prevent false convergence. Two echoes which have similar phase with respect to Δf were chosen for the initial field map to minimize the contamination caused by the chemical shift of water and fat. Phase unwrapping was conducted by applying the automatic phase unwraping algorithm, PRELUDE (17). The B0 field inhomogeneities (ψ) derived from T2*-IDEAL were then used for background gradient estimation at each voxel:

    [2] Gb* = ((ψn+1-ψn) Δz) / (γ(Δz + Δd))

    where ψn is the B0 field inhomogeneity of the nth slice, γ is the gyromagnetic ratio, Δz is the slice thickness, and Δd is the slice gap.

    To minimize the elimination of the effect of the non-macroscopic field inhomogeneities, 2D median filtering was conducted to the calculated background gradient (Gb) maps in the each slice. Afterwards, a pixelwise magnitude correction of the signal is performed by dividing the excitation pulse profile for all echoes:

    [3] scorr(t) = s(t) / | A(Gb*,t) |

    where scorr(t) is the corrected signal for data at t and Gb* is the estimated linear background gradient.

    Generally, a sinc weighted correction algorithm is used which assumed a perfect rectangular slice profile (12, 13). However, a weighting function induced by linear background gradient is not exactly a sinc function when, e.g., windowing is used to achieve a better excitation profile. If a hanning windowed sinc was used for slice selective excitation, then the theoretical weighting function would be

    [4] A(Gb, t) = 0.5 sinc(γGb t) (1 + cos(πγGb t))

    Note that this also depends on the flip angle. Finally, the water content, fat content and T2* were recalculated by T2*-IDEAL algorithm from the corrected signal Scorr(t). A summary of the overall processing is described in Fig. 1. All processing used in this study was done in MATLAB (The MathWorks, Natwick, MA).

    Fig. 1
    Flow chart of the proposed background gradient correction algorithm for quantification of fat, water and T2*. The output variables of each step are given in brackets.

    MRI Experiments

    To examine the validity of the weighting function used for magnitude correction, the actual excitation profiles followed by the applied RF pulses were measured for various flip angles. The identical Hanning windowed sinc pulses were applied to the same scanner used in the phantom and in vivo experiments. The excitation profiles were simply measured by applying the readout gradients in the slice-selection direction without any other directional gradients (Fig. 3). The excitation profiles for five different flip angles (10°, 20°, 30°, 40°, 50°) were measured with identical slice thickness (5 mm) in the phantom experiments.

    Fig. 3
    a. Pulse diagram used to obtain the actual excitation profile. b. The applied excitation pulse profile and the measured excitation profiles for different flip angles.

    To examine the effect of the background gradient in the slice-selection direction on the results of T2*-IDEAL algorithm, phantom studies were performed. Because fat is not soluble in water, aceton was used as an alternative to fat. Gadolinium (Gd) contrast agent of 0.5 mol/L concentration (Dotarem, Guerbet, France) was used to make different T2* values induced by susceptibility differences. The chemical shift between acetone and water was determined to be - 310 Hz by spectroscopy. Four tubes were constructed with the same amount of water and aceton volume, but different Gd volumes (0.25 mL, 0.5 mL, 1 mL, 2 mL). One tube was constructed with only water for reference. Figure 2 illustrates the phantom used in this study. Three different linear background gradients in the slice-selection direction were applied by adjusting the manual shim of the scanner. Imaging was performed by 3 T (Siemens Tim Trio, Erlangen, Germany) using a multi-echo 2D spoiled gradient echo pulse sequence. The Hanning windowed sinc pulse was used for the slice selective excitation. Imaging parameters were as follows: TE = 2.7 ms, 4.8 ms, 6.9 ms, ΔTE = 2.1 ms (θi = 2π/3), TR = 500 ms, flip angle = 20°, bandwidth = 1502 Hz/px, voxel size = 1.8×1.8×5.0 mm3, matrix size = 128×128, 16 interleaved slices with a gap of 2.5 mm, number of averages = 4, applied Gb in the slice-selection direction = 0 µT/m, 50 µT/m, 100 µT/m.

    Fig. 2
    a. The composition of the water and aceton phantom used in this study. Four tubes contain the same volume of water and aceton but different Gd concentrations. b. The signal model of water and aceton determined by -310 Hz chemical shift. The acquired three echoes are pointed by circles.

    In vivo imaging was performed on two healthy volunteers under the approval of the local institutional review board. Twelve transverse slices were obtained using a multi-echo 2D gradient echo pulse sequence on the same scanner. The chemical shift between fat and water used for T2*-IDEAL was assumed to be 420 Hz. Imaging parameters were as follows: Hanning windowed sinc RF (duration = 1 ms), six echoes acquired at TE = 2.1, 3.6, 5.1, 6.6, 8.1, 9.6 ms (θi = 4π/3), TR= 132 ms, flip angle=20°, voxel size = 2.5×2.5×8 mm3, matrix size = 128×128, 12 interleaved slices with a gap of 4 mm, bandwidth = 1502 Hz/px, total scan time = 16.89 s with breath holds.

    RESULTS

    Figure 3 shows the applied excitation pulse profile and the measured excitation profiles for different flip angles. The measured excitation profiles show very similar shape with the applied excitation pulse profile for small flip angles less than 30°. Although the measured excitation profiles decay faster and zero crossing points appear as the flip angles increase, it is not a problem at the flip angle of 20° used in this study. Note that the faster decay in the measured profile compared to actual profile comes also from transverse magnetization decay.

    Figure 4 shows the estimated linear background gradient, T2* and aceton fraction maps from the phantom experiments. The estimated linear background gradients (Gb) are in good agreement with the actual applied Gb values. While the T2* values changed by applying the linear background gradients, the aceton fractions changed very slightly. In the first row (well-shimmed condition), the aceton fractions are larger and the T2* values are shorter at the higher Gd concentrations. The uncorrected T2* values in the second and third row (artificial 50 µT/m and 100 µT/m background gradients added in the slice-selection direction) are shorter than the well-shimmed condition as the linear background gradients are increased. The corrected T2* values in the second and third row show similar T2* values to those of the well-shimmed condition. However, the aceton fractions in each tube are very slightly changed as compared to the well-shimmed condition. Table 1 shows the numerical results calculated from 60 voxels in each tube. The average ratios of the estimated T2* values to the well-shimmed condition changed from 0.82 to 0.95 for background gradient of 50 uT/m and from 0.61 to 0.96 for that of 100 uT/m with the correction method. The average ratios of the estimated aceton fraction changed from 0.99 to 1.00 for 50 µT/m and from 0.98 to 0.99 for 100 µT/m.

    Fig. 4
    Results from the water and aceton phantom scans with a spatial resolution of 1.8 × 1.8 × 5.0 mm3.

    The estimated linear background gradient (Gb), T2* and aceton fraction maps for different shim conditions.

    Table 1
    The estimated mean±standard deviation of aceton fraction and T2* of 4 tubes before and after applying the correction method for different shim conditions. The numbers in the brackets are the ratio to the uncorrected well-shimmed condition. Bold numbers indicate the corrected values after applying the proposed algorithm

    Figure 5 shows in vivo liver imaging results of the linear background gradient, fat fraction and T2* maps. The calculated Gb map shows large values (up to about 120 µT/m) on the lower-left regions of liver and the uncorrected T2* values of this region are relatively short. The corrected fat fractions, in common with the results from phantom experiments, are similar to the uncorrected fat fractions. Two regions of interest containing 50 voxels were manually selected for each subjects (circle in Fig. 5) to investigate the effect of linear background gradients. The mean Gb of the ROI 2 is larger than the ROI 1 and the uncorrected mean T2* of the ROI 2 is shorter than that of the ROI 1 (ROI 2: 15.6, ROI 1: 19.9 for subject 1 and ROI 2: 12.7, ROI 1: 20.5 for subject 2). However, the corrected mean T2* of the ROI 2 is similar to that of ROI 1 (ROI 2: 22.8, ROI 1: 24.1 for subject 1 and ROI 2: 21.3, ROI 1: 24.9 for subject 2) and the ratio of the ROI 2 and ROI 1 changed from 0.78 to 0.95 for subject 1 and 0.62 to 0.91 for subject 2. Table 2 shows the estimated Gb, fat fraction, T2* values from ROI 1 and ROI 2.

    Fig. 5
    Results from two healthy volunteers (a, b) with a spatial resolution of 2.5 × 2.5 × 8.0 mm3. 5th echo (8.1 ms) magnitude image and its estimated linear background gradient (Gb) , fat fraction and T2* maps.

    Table 2
    The estimated mean±standard deviation of Gb, fat fraction and T2* from ROI 1 and ROI 2 of two subjects (Fig. 5). Arrow indicates the uncorrected (the left side of the arrow) and the corrected (the right side of the arrow) values by the proposed algorithm

    DISCUSSION

    In this study, we have applied the correction method for background gradients in slice-selection direction to T2*-IDEAL for 2D liver imaging. The proposed method can be helpful for more accurate T2* quantification in liver by separating the additional signal decay induced by macroscopic field inhomogeneities from the decay caused by iron. It is difficult to ignore the additional signal decay due to background gradients in the slice-selection direction reducing the slice thickness can have problems in covering the whole 3D volume in a single breath-hold. The fat fraction, however, calculated by T2*-IDEAL did not change significantly after applying correction methods. Assuming the effect of macroscopic field inhomogeneity is identical to water and fat, this result is resonable because the correction algorithm only corrects magitude information.

    Using an excitation pulse profile for magnitude correction is an essential part of this study but its limitation should also be considered. It is correct that signal decay due to a linear background gradient is weighted by an excitation pulse shape under the assumption of Fourier relationship between the excitation pulse and slice profile. However, this assumption is derived from the Bloch equation when the flip angle is sufficiently low. As seen in Fig. 3, the disagreement between the actual profile and the applied profile becomes larger as the applied flip angle increase. Therefore, the effect of transmit RF field inhomogeneity should be considered when a large flip angle is used. In addition, when the object is nonuniform through-slice, the signal is not simply multiplied by the excitation pulse profile. But, rather the spatial-frequency components of the slice are convolved with Fourier transform of the excitation profile. This is not a practical problem in most liver imaging because a low flip angle is typically used for minimizing T1 effects and slice structure does not prevail. However, it should be also considered for more accurate quantification, especially when a large flip angle is used.

    B0 field map (ψ) estimation in each slice is also an important step in obtaining accurate linear background gradients. When the field inhomogeneity exceeds the maximum frequency determined by echo spacing, phase wrapping occurs. As a result, an incorrect ψ was estimated in T2*-IDEAL algorithm when the initial ψ0 is inappropriate. In this study, a phase unwrapping algorithm was used to obtain the initial field map close to the true field map. While this may reduce an incorrect convergence of T2*-IDEAL, it is complex to implement and time consuming. To resolve these problems, other field map estimation methods such as a region growing method (16), a multiresolution method (18) can be used for efficient quantification.

    In our phantom experiments, fat fractions are large at higher Gd concentrations although the actual fat fractions of all the tubes were the same. We suspect that the increased fat fraction at higher Gd concentration is related to the signal model used for quantification. A recent study regarding signal models for fat quantification using SPIO showed similar results when the signal model assumed identical T2* between water and fat (15, 19). However, the fat fraction didn't increase much at higher SPIO concentration in the signal model which has independent T2* of water and fat (15). They guessed that SPIOs preferentially accelerate the signal decay of water more than that of fat because water and fat have different solubilities, so the fat fraction is overestimated at higher SPIO concentrations. Accordingly, independent estimation of T2* of water and fat will be needed when iron overload is severe. However, the independent T2* estimation remarkably increases the complexity of the algorithm and computing time (15).

    In conclusion, this study investigated the effect of background gradient in the slice-selection direction and demonstrated a correction method using excitation pulse profile for simultaneous fat and T2* quantification in 2D multi-slice liver imaging. It is anticipated that this correction method will be helpful for the quantification of fat and T2* in the presence of macroscopic field inhomogeneity.

    Acknowledgements

    This study was supported by a grant of the Korean Health Technology R&D Project, Ministry for Health, Welfare & Family Affairs, Republic of Korea (A110035-1101-0000200).

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    MeSH Terms
    Compensation and Redress
    Iron
    Liver
    Magnetics
    Magnets
    Metrics
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