Investig Magn Reson Imaging. 2024 Dec;28(4):174-183. English.
Published online Dec 30, 2024.
Copyright © 2024 Korean Society of Magnetic Resonance in Medicine
Original Article

Reduced Scan Time in Multi-Echo Gradient Echo Imaging Using Two-Stage Neural Network

Ji-Su Yun, Jong-Yun Baek and Dong-Hyun Kim
    • Department of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea.
Received July 23, 2024; Revised September 13, 2024; Accepted October 11, 2024.

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Purpose

Multi-echo gradient echo (mGRE) images are used to acquire and analyze multiple echo signals. As the number of acquired echoes increases, more information on the voxel decay changes can be obtained, facilitating myelin water fraction (MWF) mapping. However, an increase in the acquired echoes leads to an increase in scan time. In this study, we developed a workflow to reduce the scan time using a two-stage neural network approach, which extrapolates additional echo images using mGRE data.

Materials and Methods

In Stage 1, a pseudo-T1 map was estimated using a U-net network combined with a simple signal model to correct the bias between two mGRE acquired with different scan parameters. The pseudo-T1 map was used to generate an initial echo time (TE) image from the mGRE images. In Stage 2, subsequent TE images were predicted from the initial echo image generated using a trained prediction network. The results were quantitatively compared with those obtained using a fitting algorithm. The MWF mapping results were then compared.

Results

The proposed model exhibited better root mean square error, structural similarity index measure, and peak signal-to-noise ratio, as well as a higher correlation with the MWF analysis compared to the fitting algorithm.

Conclusion

These results demonstrate that the proposed network can effectively reduce the scan time for mGRE image acquisition.

Keywords
Artificial neural network; Multi-echo gradient echo; Myelin water fraction; Pseudo-T1 map

Multi-echo gradient echo (mGRE) sequences have been widely used owing to their faster acquisition time, lower specific absorption rate, and lower B1 sensitivity compared to spin echo-based sequences [1, 2]. By utilizing multiple gradient echoes generated after a single radiofrequency excitation pulse, mGRE sequences can efficiently acquire signals at multiple echo times (TE). This capability makes mGRE particularly valuable for quantifying and visualizing properties such as T2* relaxation time, facilitating the precise mapping of the myelin water fraction (MWF) [3, 4, 5, 6], which is a measure used in the monitoring of brain health and development.

However, mGRE has several limitations. While multi-echo signals provide a large amount of information and are useful in signal curve analysis, an increase in the number of acquired echoes leads to an increase in the total scan time. To address this issue, several methods have been proposed to shorten the scan time. Acceleration was achieved through parallel imaging [7, 8] and compressed sensing [9]. Advanced signal processing methods have been proposed to use low-rank and sparse constraints in both spatial and temporal domains [10]. Another method was proposed to fill under-sampled data using deep learning by reconstructing the missing k-space line through joint parallel imaging, reducing errors and increasing fidelity through joint deep learning [11]. Methods that combine dictionary learning and neural networks to utilize spatiotemporal information were also proposed [12]. However, such approaches can induce artifacts and biases, leading to inaccurate MWF mapping [13].

This study presents an alternative method to address these problems, which reduces the scan time by generating a long time of repetition (TR) and numerous echo images with short TR and small echo images. A performance comparison is conducted to assess whether the proposed nonlinear function works correctly. The performances of the proposed method with linear and nonlinear functions were also compared using in vivo data. Finally, the echo images estimated using the proposed method and the acquired images were compared.

Data Acquisition

In vivo sets from nine healthy subjects aged 27–34 years were obtained. A clinical 3-T MRI scanner (Magnetom Tim Trio, Siemens Medical Solution, Erlangen, Germany) with a 64-channel head coil was used. Data from eight of the nine healthy subjects were used in the training dataset, and data from one subject were used in the test dataset. Two consecutive images were acquired for the experiment. Two three-dimensional mGRE sequences were used, with the following scan parameters: 1) Common parameters: bandwidth = 1560 Hz/pixel, flip angle = 20°, field of view (FOV) = 240 mm × 240 mm × 144 mm, spatial resolution = 1.5 mm × 1.5 mm × 1.5 mm; 2) Scan 1 (TR40, short scan time): first TE = 1.71 ms, echo spacing (ES) = 1.04 ms, number of echoes = 8, TR = 40 ms, total scan time = 10 min 16 s; and 3) Scan 2 (TR60, long scan time): first TE = 1.71 ms; ES = 1.04 ms; number of echoes = 28; TR = 60 ms; total scan time = 15 min 23 s.

The orientation of the slab was set in the axial direction using spatially selective excitation.

This study was conducted in accordance with the Declaration of Helsinki and approved by the Institutional Review Board of Yonsei University Gangnam Severance Hospital (no: 3-2022-0443). Informed consent was obtained from all participants.

Methods

The workflow of the proposed method is shown in Figure 1 and outlined in Figure 2. Scan 1 mGRE data were obtained and ultimately converted to a scan 2 mGRE dataset. In general, a shorter TE mGRE has different scan parameters than a longer TE mGRE (e.g., different flip angles and TR). To resolve this issue, T1 correction was performed in Stage 1. A U-net structure was used for model fitting. In Stage 2, the extended TE signals were predicted using a trained neural network. The structure and detailed description of the network are provided in the Supplementary Materials. Two images acquired at different TRs were used to train the networks. TR1 had a shorter TE and required a shorter scan time, expressed as S1. TR2 had a longer TE and required a longer scan time. The front TE images are represented as L1 and rear TE images as with L2.

Fig. 1
Workflow of the proposed method. The process consists of two stages. In Stage 1, T1 is estimated and the image contrast of GRE is synthesized with TR = 60 ms (TR60) from GRE with TR = 40 ms (TR40) using the U-Net model. Stage 2 involves an echo-signal prediction process that uses the seq2seq model. GRE, gradient echo; TR, repetition time.

Fig. 2
Summary of terms and procedures used in the study. TR, repetition time.

Stage 1

Although the two acquired images, TR1 (S1) and TR2 (L1, L2), had the same T1 distribution, they appeared different because different TR were used. To correct this difference, a pseudo-T1 map was required. In Stage 1, U-Net was trained using the difference between TR1 and TR2 to form a pseudo-T1 map [14]. Subsequently, differences between the two images were corrected using the generated pseudo-T1 maps. The network structure is shown in Supplementary Figure 1.

Signal Modeling

The mGRE signal model can be characterized by

(1) St=K*M0*sinθ1-e-TR/T11-cosθ*e-TR/T1*e-TE/T2*,

where S(t) denotes the mGRE signal at time TE, K is a scaling factor, M0 is the proton density, and θ is the flip angle. Therefore, dividing the two signals after obtaining front echo signal S1 with TR1 and L1 with TR2 yields

(2) RT1=L1S1=1-cosθ2*e-TR2/T1sinθ21-e-TR2/T1*sinθ11-e-TR1/T11-cosθ1*e-TR1/T1.

According to Eq. (2), L1 can be expressed as the product of S1 and R(T1). This implies that if R(T1) is precalculated, L1^ (an estimate of the true L1) can be estimated using the obtained S1:

(3) L1^=S1×RT1.

Stage 1 in Figure 1 illustrates the workflow used to obtain L1^. U-Net was used to obtain a pseudo-T1 map. Subsequently, Eq. (2) was used to retrieve R(T1). A nonlinear conversion function was used to correct this process.

Nonlinear Conversion Function

To achieve accurate results in Stage 1, pseudo-T1 mapping must be performed correctly, which is described subsequently. In practice, within the evaluation part where the T1 values from the pseudo-T1 map are utilized, areas with the T1 values ranging from 0–4 seconds exhibited an adequate ratio function R(T1). However, in cases where the estimated pseudo-T1 was larger than 4 seconds (e.g., in the region of the cerebral spinal fluid [CSF]), this ratio was not adequate for use. Hence, we use a nonlinear conversion function to compensate for this inadequacy.

To consider various ranges, a nonlinear conversion function (F) was proposed. The formula for F is expressed as follows:

(4) FRT1=0,RT1,−4187.565RT1+1,4492+10.3419,0,T1≤00<T1≤44<T1≤4.54.5<T1

F = R(T1) when T1 < 4 s. However, if T1 > 4 s, F > 1.5, which overcompensates L1^ in Eq. (3). Notably, F is included in the network training and trained simultaneously. Therefore, F acts as a nonlinear activation function. A detailed description of F is provided in Supplementary Figure 2.

Pseudo-T1 Mapping

Through the above process, R(T1), which is composed of T1, was calculated, and the range of the ratio was adjusted. Therefore, to perform this process, an appropriate T1 value must be estimated. In this study, U-Net was used for this task.

S1 is the input to U-Net, which outputs a pseudo-T1 map. This pseudo-T1 map was converted into an appropriate F(R(T1)) through signal modeling and the nonlinear conversion function described above. The processed ratio was multiplied by input S1 to generate L1^. Then, the algorithm learns by reducing the root mean square error (RMSE) of L1 and L1^. Eventually, the value achieved by the training process that reduces the difference between L1^ and L1 is considered the appropriate T1 value, which is learned to produce the same mGRE image as L1.

Stage 2

Stage 2 predicts L2^, which is the echo signal after corrected image L1^ in Stage 1. Each voxel in the mGRE image exhibits a different decay behavior as the echo passes. Hence, voxel-level time-series data processing is required to process these characteristics. Therefore, in Stage 2, the seq2seq model, which is a time-series network, was used to predict the echo signals [15]. The network structure is shown in Supplementary Figure 3.

To improve network performance, as shown in Supplementary Figure 3, the seq2seq model was stacked in multiple layers so that each layer could predict one echo signal at a time. This prevented loss of information, which is otherwise prevalent in models dealing with time-series data, especially when predicting numerous echo signals from a miniscule set of echo signals. Therefore, the (n + 1)th echo signal was generated by inputting the 1st to the nth echo signals in the first layer. In the second layer, the (n + 2)th signal was generated by combining the 2nd to the nth signals and the (n + 1)th signal generated in the 1st layer. Because we aimed to predict a total of 20 echo signals, from the 9th to 28th echo signals, using the initial 1st to 8th echo signals, we set n = 8 to minimize information loss. Thus, we made predictions up to the last signal.

Fitting Algorithm

The proposed framework was compared with a fitting algorithm (‘lsqnonlin’ Matlab function, step tolerance = 1 × 10−5, function tolerance = 1 × 10−5). The fitting algorithm also consisted of two stages identical to those of the proposed framework, with both stages performing the same process. All processes of the fitting algorithm were performed in voxels. In Stage 1, the T1 value that minimized the difference between echo signals S1 and L1 was estimated using Eq. (2). In Stage 2, the myelin water fraction formula was used [4, 5, 6]. First, the parameters that minimized the difference from L1^ were estimated according to the following equation:

(5) Mt-Amye1T2my*t+ Aaxe1T2ax*t+ Aexe1T2ex*t.

Subsequently, L2^ was generated by changing TE, which is the echo time of the generated M(t). The details of the fitting algorithm and parameter set are provided in Supplementary Table 1. A significant difference was observed between the two methods; the proposed method generated L1^ and L2^ using only input S1 in the absence of L1 and L2 as labels, whereas the fitting algorithm required both labels.

The main difference between the fitting algorithm and the proposed framework is that the former requires a specific mathematical model that describes the behavior of data. For instance, Eq. (5) represents a signal that decays exponentially and is defined by six parameters. The fitting algorithm updates these parameters based on the Levenberg–Marquardt algorithm, adapting to the behavior (decay) of the given data by minimizing errors.

Owing to these characteristics, the fitting algorithm provides strong performance and good interpretability under controlled conditions. However, for the same reason, they are inevitably sensitive to noise. As it attempts to minimize the error across all data points, it treats noise as a significant value, thus impacting the results.

Evaluation Methods

For comparison with the proposed method, we used this fitting algorithm. First, the generated pseudo-T1 map and GRE images were compared. To verify the pseudo-T1 map, we compared it with the T1 values from other studies [16, 17, 18, 19, 20, 21]. To evaluate the generated mGRE image, the actual acquired mGRE image was compared using the RMSE, structural similarity index measure (SSIM), and peak signal-to-noise ratio (PSNR) of the region of interest (ROI).

Second, we evaluated whether the generated mGRE images accurately conveyed the information inside the echo signal. After generating the MWF using three mGRE images (acquired and generated by the proposed method and the fitting algorithm), the values were compared [22].

T1 was estimated in Stage 1 of the proposed method. Figure 3 and Supplementary Table 1 illustrate the T1 values of the proposed method and fitting algorithm. The top row of Figure 3 shows R(T1) (L1/S1) of the acquired data. According to Eq. (2), the contrast of the ratio map is determined by T1. Therefore, a pseudo-T1 map was used to estimate T1 values of the ratio map. When visually comparing the T1 map from fitting algorithm with the pseudo-T1 map from the proposed method visually, both clearly distinguish the structure of the brain. However, the pseudo-T1 map from the proposed U-net (third row) shows the structural details, albeit with slightly inferior quality than that of the T1 map from the fitting algorithm (second row). For a more accurate numerical analysis, as shown in Supplementary Table 2, the result of the ROI analysis was compared with those in other studies on the white matter, gray matter, and CSF [16, 18, 19, 20, 21]. The values in those studies ranged from 728–1110 ms in terms of white matter, 1165–1615 ms in terms of gray matter, and 3805–4391 ms in terms of CSF. The ROI of the proposed method were 978 ± 45, 1484 ± 51, and 3805 ± 150 ms, and those of the fitting algorithm were 1007 ± 95, 1302 ± 116, and 3839 ± 541 ms, respectively, which lie within the ranges in those studies.

Fig. 3
Ratio images of the two acquired mGRE TR40 (S1) and TR60 (L1). Pseudo-T1 maps generated through the fitting algorithm and the proposed method. mGRE, multi-echo gradient echo.

In Figure 4, the mGRE images generated by the proposed method and fitting algorithm are compared with the actual acquired mGRE images. Four (1, 8, 9, 28) out of the 28 echoes were compared. Examining the difference map, the proposed method exhibits a similar level of difference in the four echoes and a noticeable difference in the outline of the brain. The fitting algorithm shows a similar level of difference in the 1st, 8th, and 9th echoes. However, in the 28th echo, it exhibits a noticeable difference in both the contours and several voxels. This is because the fitting algorithm was more sensitive to noise than the proposed method.

Fig. 4
Acquired TR = 60 ms mGRE, and mGRE images generated by the fitting algorithm and the proposed method. The 1st and 8th echo images are displayed representatively in Stage 1, and the 9th and 28th echo images in Stage 2. Diff*5 images are displayed to clearly demonstrate the difference between the two methods. TR, repetition time; mGRE, multi-echo gradient echo.

In addition, the PSNR of both the proposed method and the fitting algorithm were measured at SNRs of 50, 100, 150, and 200. Figure 5 illustrates the variation in TR60, the proposed method, and the fitting algorithm with the SNR. As shown in Figure 5A, the image obtained using the fitting algorithm contains more artifacts (yellow box) than the other images. By comparing the actual PSNR in Figure 5B, we can observe that the fitting algorithm drastically reduces the PSNR as the SNR decreases, which aligns with the finding that the fitting algorithm is more sensitive to noise.

Fig. 5
Comparison of mGRE images at different SNR levels. A: mGRE image of TR60 by proposed method and fitting algorithm with different SNR. The specific part of the images has been enlarged (yellow box). B: Comparison of PSNR of mGRE for each generated SNR. mGRE, multi-echo gradient echo; TR, repetition time; SNR, signal-to-noise ratio; PSNR, peak signal-to-noise ratio.

Numerical analysis of the generated mGRE images for each echo was conducted. Figure 6 compares the RMSE, SSIM, and PSNR of the proposed method and fitting algorithm in terms of echo. The proposed method exhibits similar performance for each echo with the minimum–maximum values of RMSE, SSIM, and PSNR (red line) being 0.035–0.054, 0.88–0.96, and 25.32–29.08, respectively.

Fig. 6
Comparison of RMSE (A), SSIM (B), and PSNR (C) for accurate numerical analysis. RMSE, root mean square error; SSIM, structural similarity index measure; PSNR, peak signal-to-noise ratio.

However, the fitting algorithm had RMSE, SSIM, and PSNR (blue line) of 0.016–0.095, 0.73–0.98, and 20.36–35.79 (blue line). For the initial echo, the fitting algorithm performed better than the proposed method. However, the performance rapidly deteriorated as the number of echoes increased. This is attributed to the sensitivity of the algorithm to noise (Figure 5).

In addition, to determine the effect of the nonlinear conversion function, the performance of the proposed algorithm was evaluated with and without the function (green line). When the nonlinear conversion function was not applied, the performance decreased marginally in terms of RMSE, SSIM, and PSNR. Numerically, this is a minor difference; nevertheless, it occurred because the nonlinear conversion function was designed for some voxels corresponding to out-of-distribution data and not the entire data.

The MWF was analyzed to verify if the generated mGRE image contained actual signal information, rather than merely producing predicted values [22]. Figure 7A shows a comparison of the MWF map estimated from the mGRE image generated using the proposed method and the fitting algorithm, and two MWF maps from the acquired mGRE images (TR60 and TR40). Overall, both the fitting algorithm and proposed method exhibited similar characteristics; however, noise artifacts in the fitting algorithm are visually evident. Figure 7B shows the correlation between the proposed method and MWF map of the fitting algorithm with the two maps from the acquired mGRE images (TR60 and TR40). According to the correlation analysis in Figure 7B, the proposed method exhibits a correlation of 0.9506, an RMSE of 2.93%, and a bias of 0.31. The fitting algorithm exhibits a weaker correlation than the proposed method, with a correlation coefficient of 0.9278, an RMSE of 3.99%, and a bias of 1.21.

Fig. 7
Visual and quantitative comparison of MWF maps over various methods. A: MWF maps generated from the acquired TR60 mGRE images with 28 echoes (TR60, the top), the estimated 28 echo images using the proposed method (proposed, the second), fitting method (fitting algorithm, the third), and TR40 mGRE images with 8 echoes (TR40, the bottom). MWF estimated from the mGRE images generated by each method. B: Correlation analysis between TR60, TR40, the proposed, and the fitting algorithm. MWF, myelin water fraction; TR, repetition time; mGRE, multi-echo gradient echo; RMSE, root mean square error.

When the TR40 and TR60 images were compared, the correlation was 0.8402, with an RMSE of 2.87% and a bias of 0.61. By contrast, the comparison between TR40 and the fitting algorithm yielded a higher correlation of 0.9828, a lower RMSE of 1.11%, and a bias of 0.58, indicating a closer alignment between TR40 and the fitting algorithm than with TR60. The relatively low correlation and high bias between TR40 and TR60 can be attributed to the T1 effect, which introduced a minor skew in the scatter plot, leading to a systematic shift in data.

Thus, considering the strong correlation and lower bias between TR60 and the proposed method, along with the high correlation between TR40 and the fitting algorithm, the proposed method effectively reconstructed TR60 images from TR40, outperforming the fitting algorithm.

This paper presents a method for reducing the scan time of the mGRE sequence. The steps in this method included 1) a suitable nonlinear conversion function design, 2) a T1 parameter estimation process for inter-image correction, and 3) prediction of the echo signal. These steps were carried out in two stages. Ideally, the prediction of the mGRE echo signal must be performed in one stage. However, to compensate for the difference between the two mGRE images obtained with different TR, Stage 1 was added. The method was evaluated by comparing the obtained images and analyzing the numerical values using in vivo data. In addition, the MWF from the generated mGRE were analyzed and compared.

In conventional MRI quantitative mapping, T2* is estimated using mGRE, T1 using a variable flip angle, and T2 using spin-echo-based sequences. However, in this study, quantitative mapping of T1 images was possible using mGRE images because the network was trained to estimate T1 by comparing two images acquired with different TR. The output T1 images were compared with fitting algorithms and various other methods. As shown in Figure 3, the brain tissues (white matter, gray matter, and CSF) were delineated. As indicated in Supplementary Table 2, they are in the same range as determined in previous studies. In addition, errors in the out-of-distribution data were mitigated by designing a nonlinear conversion function and allowing the framework to learn it. Finally, mGRE images with more echo information were generated by predicting the echo signals. The scan time is reduced by 20 ms for each TR, and in the data, 15 minutes and 23 seconds was reduced to 10 minutes and 16 seconds by approximately 5 minutes and 7 seconds. Figures 3, 4, 5 confirm that the generated mGRE images have high quality and convey accurate information. Finally, the results of the proposed method (no label) and fitting algorithm (label) showed that the latter performed well in the initial echo; however, the proposed method showed a higher similarity with the acquired mGRE from the back echoes and MWF.

Previously, scan time reduction was performed through under-sampling of the x- and y-planes in the k-space and image domains [23]. However, these methods have limitations because it is impossible to acquire all k-spaces. As this study was conducted based on the echo axis of an mGRE image, the scan time can be potentially reduced. In addition, the study reduced the scan time while expanding the echo information. Owing to the characteristics of the mGRE image, the signal change according to the echo plays an important role in decay analysis. Therefore, more detailed echo-signal information can provide more stable analytical results. Thus, increased echo information can improve the accuracy of mGRE image utilization.

This study has limitations. First, a simple modification was made to the method for out-of-distribution data processing using Eq. (4). However, actual in vivo data exhibit more complex relationships. Therefore, precise tuning of the nonlinear conversion function used for network training is required. As shown in Figure 5, the nonlinear conversion function reduces the error in out-of-distribution data, but does not eliminate it. This is attributed to spatial artifacts that occur when multiple tissues overlap within a single voxel. Therefore, in addition to the corresponding nonlinear conversion function, spatial artifacts must be considered, and a more sophisticated design must be proposed. Moreover, the use of only two instances in the testing process suggests that the results may not be valid for all cases in practice.

Second, the validation method primarily focused on the estimation of MWF as a key metric. This approach may not fully capture the complexity of individual component analyses. Future studies should expand this work by analyzing individual component amplitudes and T2* values.

Third, simplified signal equations were used to determine the feasibility of the proposed modeling approach. However, flip-angle inhomogeneity leads to limitations in the accuracy of T1 estimation and is closer to the apparent T1. Methods such as the dual-flip-angle technique should be employed to achieve greater robustness.

Finally, the tri-exponential model does not consider the minor frequency differences between components. While this model focuses on magnitude-based analysis, incorporating frequency considerations could improve its accuracy. Future research should explore complex fitting techniques to consider these differences, potentially offering a more accurate representation of data.

In conclusion, this study introduced a practical approach to reduce MRI scan time using the echo axis in mGRE images by incorporating T1 estimation, a nonlinear conversion function design, and echo signal prediction. Validated with in vivo data and MWF mapping, the approach is an efficient alternative to current methods as it improves scan efficiency while maintaining accuracy, which is essential for rapid diagnosis and improving patient experience in clinical settings.

The Supplement is available with this article at https://doi.org/10.13104/imri.2024.0018.

Supplementary Fig. 1

Detailed structure of U-Net used in Stage 1.

Supplementary Fig. 2

Application of a nonlinear function to extend the range of R(T1) for T1 values beyond the initial constraints. A: Range of R(T1) according to T1 change (before applying the nonlinear function). B: Proposed nonlinear function. C: Range of F(R(T1)) according to T1 change (after applying the nonlinear function).

Supplementary Fig. 3

Detailed structure of the model used in Stage 2. The structure of the seq2seq model, which is the basic structure (red box). Overall model structure (green box) built by stacking seq2seq models.

Supplementary Table 1

Range of parameters used in the fitting algorithm

Supplementary Table 2

T1 relaxation time in white matter, gray matter, and cerebrospinal fluid

Click here to view.(1M, pdf)

Notes

Conflicts of Interest:The authors have no potential conflicts of interest to disclose.

Author Contributions:

  • Conceptualization: Ji-Su Yun.

  • Data curation: Ji-Su Yun.

  • Formal analysis: Ji-Su Yun.

  • Investigation: Ji-Su Yun.

  • Methodology: Ji-Su Yun.

  • Project administration: Dong-Hyun Kim.

  • Resources: Ji-Su Yun.

  • Software: Ji-Su Yun.

  • Supervision: Dong-Hyun Kim.

  • Validation: Ji-Su Yun.

  • Visualization: Ji-Su Yun, Jong-Yun Baek.

  • Writing—original draft: Ji-Su Yun.

  • Writing—review & editing: Jong-Yun Baek.

Funding Statement:None

The datasets generated or analyzed during the study are not publicly available because they are part of an ongoing study but are available from the corresponding author upon reasonable request.

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