Received: 15 January 2020
DOI: 10.1002/mrm.28407
|
Revised: 9 June 2020
|
Accepted: 9 June 2020
NOTE
Artificial neural network for multi-echo gradient echo–based
myelin water fraction estimation
Soozy Jung1
Won-Jun Moon3
|
Hongpyo Lee1 | Kanghyun Ryu1
| Dong-Hyun Kim1
|
Jae Eun Song1
|
|
Mina Park2
1
Department of Electrical and Electronic Engineering, Yonsei University, Seoul, Republic of Korea
2
Department of Radiology, Gangnam Severance Hospital, Yonsei University College of Medicine, Seoul, Republic of Korea
3
Department of Radiology, Konkuk University Medical Center, Konkuk University School of Medicine, Seoul, Republic of Korea
Correspondence
Dong-Hyun Kim, Department of Electrical
and Electronic Engineering, Yonsei
University, 50 Yonsei-ro, Seodaemun-gu,
Seoul 03722, Republic of Korea. Email:
donghyunkim@yonsei.ac.kr
Funding information
National Research Foundation of Korea,
Grant/Award Number:
NRF-2019R1A2C1090635
Purpose: To demonstrate robust myelin water fraction (MWF) mapping using an
artificial neural network (ANN) with multi-echo gradient-echo (GRE) signal.
Methods: Multi-echo gradient-echo signals simulated with a three-pool exponential
model were used to generate the training data set for the ANN, which was designed
to yield the MWF. We investigated the performance of our proposed ANN for various conditions using both numerical simulations and in vivo data. Simulations were
conducted with various SNRs to investigate the performance of the ANN. In vivo
data with high spatial resolutions were applied in the analyses, and results were compared with MWFs derived by the nonlinear least-squares algorithm using a complex
three-pool exponential model.
Results: The network results for the simulations show high accuracies against noise
compared with nonlinear least-squares MWFs: RMS-error value of 5.46 for the nonlinear least-squares MWF and 3.56 for the ANN MWF at an SNR of 150 (relative
gain = 34.80%). These effects were also found in the in vivo data, with reduced SDs
in the region-of-interest analyses. These effects of the ANN demonstrate the feasibility of acquiring high-resolution myelin water images.
Conclusion: The simulation results and in vivo data suggest that the ANN facilitates
more robust MWF mapping in multi-echo gradient-echo sequences compared with
the conventional nonlinear least-squares method.
KEYWORDS
artificial neural network, multi-echo gradient echo, myelin water imaging, T∗2 distribution
© 2020 International Society for Magnetic Resonance in Medicine
Magn Reson Med. 2020;00:1–10.
wileyonlinelibrary.com/journal/mrm
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1
2
| 1
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JUNG et al.
IN TRO D U C T ION
Myelin water fraction (MWF) as a method for measuring
quantitative myelin signals has demonstrated potential to
diagnose various demyelinating diseases such as multiple
sclerosis, schizophrenia, and stroke.1,2 Conventional myelin
water imaging (MWI) uses multi-echo spin-echo acquisition
and nonnegative least-squares estimation,3,4 whereas more
recently multi-echo gradient echo (mGRE) has been suggested.5-9 These methods provide benefits such as faster acquisition time and lower specific absorption rates.
Several studies have proposed methods to acquire
high-quality MWI data using mGRE. Such studies suggest
applying the nonlinear least-squares (NLLS) algorithm to the
acquired signal using a defined model, such as the three-pool
exponential model.8,10 These methods are based on the assumption that the white-matter (WM) water can be reliably
modeled by three-pool exponential components with individual frequency shifts.5,6,8 These methods can be further improved by physiological noise compensation11 and B0 field
inhomogeneity correction.10,12,13
Despite these developments, there are still challenges in
improving the accuracy and robustness of the MWF. The
NLLS (used for estimating MWFs) has been reported to
be inaccurate and unstable, especially at low-to-moderate
SNRs.14-16 This requires high SNR data acquisition for
MWFs, limiting the scans to low resolutions or enforcing
long scan times. Moreover, this method is problematic when
the acquired signals deviate from the established model.
Specifically, the method is sensitive to artifacts such as B0
field inhomogeneities, motion, and Gibbs ringing.10,11
Recently, artificial neural networks (ANNs) have been introduced for parameter mapping in MRI and have shown efficacy to solve ill-conditioned problems17 and robustness to noise
and outliers.18,19 Furthermore, using simulation data sets for
training mitigates the limits from applying MR data with different scan parameters to ANNs. Thus, ANNs may be feasible
for improving the accuracy and robustness of MWF mappings.
In this study, ANN methods were applied for MWF estimations in mGRE acquisitions. Simulated signals were used to
generate the data set, and comparisons between the proposed
ANN and NLLS are presented for both numerical simulations
and in vivo data in terms of noise and various scan parameters.
Additionally, the potential for high-resolution MWI is presented.
2
|
2.1
2.1.1
METHODS
|
Training
|
Training set generation
Simulated signals based on the three-pool exponential model
(Equation 1) were generated for the training data set. Each
compartment consisted of myelin, axonal, and extracellular
waters in the WM,8,20 as shown by the following:
)
(
(
)
(
)
|
|
− T ∗1 +i2𝜋𝛥fbg+my t
− T ∗1 +i2𝜋𝛥fbg+ax t
− T ∗1 +i2𝜋𝛥fbg+ex t |
|
|
|
2,my
2,ax
2,ex
+ Aax e
S (t) = |Amy e
+ Aex e
|
|
|
|
|
)
(
(
(
)
)
|
|
− T ∗1 +i2𝜋𝛥fmy−ex t
− T ∗1 +i2𝜋𝛥fax−ex t
− T ∗1
t|
|
+ Aax e 2,ax
= ||Amy e 2,my
+ Aex e 2,ex ||
|
|
|
|
(1)
where t denotes the time; A denotes the amplitude; Δf denotes
the frequency offset term; and T∗2 denotes the time constant of
each water compartment (my, myelin water; ax, axonal water;
ex, extracellular water).
Artificial MWF for a known ground truth was then determined as the fraction of myelin water amplitude of the total pool.
MWF=
Amy
Amy + Aax + Aex
(2)
For data-set generation, parameters such as T∗2 and Δf were
randomly chosen within plausible ranges, obtained based on
the WM in the in vivo data sets using NLLS (Supporting
Information Figure S1). The in vivo data sets used for observing parameter ranges were not included in the test sets.
The parameters were selected randomly and independently
with the following distributions: MWF ∈ [1, 2, …, 50] %,
T∗2,my ∈ N (10, 1) ms, T∗2,ax ∈ N (72, 10) ms, T∗2,ex ∈ N (48, 6) ms,
Δfmy−ex ∈ U (−10, 20) Hz, and Δfax−ex ∈ U (−10, 10) Hz,
yielding a total of approximately 8,000,000 signals.
To consider perturbation by macroscopic field inhomogeneities, the signal model was multiplied with a sinc function13:
)
(
Δz
S (t) = (Equation1) × sinc 𝛾GZ t
2
(3)
where 𝛾 is the gyromagnetic ratio; GZ is the linear approximation
of the field gradient in the slice-selection direction; and Δz is the
slice thickness. For accurate simulation, Δz was matched to the
actual in vivo data. The range of GZ was randomly chosen based
on the phase information from in vivo data sets (specifically,
GZ ∈ N (0, 30) 𝜇T∕m).
Moreover, white Gaussian noise was added to the signal
to simulate SNR between 100 and 150. The SNR range was
chosen based on actual in vivo data. The signal magnitude
was then used to train the network inputs. While generating
the signal, echo times (TEs) were matched to the imaging
parameters of actual in vivo data.
2.1.2
|
Training procedure
Herein, ANN was used to design the network, which has
four fully connected hidden layers with 250 neurons per
layer. The network was optimized using the analytic
JUNG et al.
phantom results. Furthermore, a rectified linear unit21 was
used for the activation function for each layer except the last
layer. The network input is an n-dimensional signal vector
�p. The network label is a
generated by parameter vector →
1-dimensional MWF:
� �
⎛ S t1
⎛ MWF
⎞
� � ⎟
⎜
� � ⎜ S t2
T2∗
⎟ , where p⃗ = ⎜
S p⃗ ,t = ⎜
⎜
⎟
⎜
⋮
Δf
� � ⎟
⎜
⎜
⎝ S tn
⎠
⎝
GZ
⎞
⎟
⎟
⎟
⎟
⎠
(4)
We used the Adam optimizer22 for parameter updating and
mean-squared error between the label and output as the loss
function. At every epoch, the data set was newly generated
with a size of 40 000. Finally, dropout23 was used to mitigate
overfitting (p = .1). All of the ANN procedures were performed on a GPU workstation (GeForce GTX 1080 TI GPU;
Nvidia, Santa Clara, CA) with an Intel Core I7-7500 U at
2.70 GHz (Intel, Santa Cruz, CA).
|
2.2
NLLS
To compare the performance between the proposed ANN
and the conventional method, NLLS was implemented using
a complex three-pool exponential model,8 which was constructed as follows:
)
(
(
)
(
−
S (t) = Amy e
1
T∗
2,my
+i2𝜋𝛥fbg+my t
−
+ Aax e
1
T∗
2,ax
+i2𝜋𝛥fbg+ax t
+ Aex
where ∅0 is the B+1 phase offset. The parameters were estimated by minimizing the least-square errors using an iterative nonlinear curve-fitting algorithm. The initial values and
bounds for the NLLS are presented in Supporting Information
Table S1. The NLLS was performed using six CPU cores and
MATLAB R2019b (The MathWorks, Natick, MA).
2.3
|
Testing
We evaluated our method for both numerical simulations and
in vivo data from subjects for different scan parameters.
2.3.1
|
Numerical simulation
Monte-Carlo simulations (200 repetitions for each case)
were performed to investigate the performance between the
estimated MWF map using NLLS (NLLS-MWF) and ANN
|
3
(ANN-MWF). The complex three-pool exponential signals
with SNRs of 200, 150, and 50 were simulated. The MWFs
varied from 3% to 30% in steps of 3%. The model parameters
were sampled randomly based on Gaussian distributions obtained from the in vivo data sets. Details of the signal design
are explained in Supporting Information Figure S2.
The MWF values in the Monte-Carlo simulations were estimated using both the NLLS method10 and the fully trained
ANN. The RMS error (RMSE) and absolute bias between the
MWF values and ground truth were compared. Then, the relative gain in accuracy was calculated as the reduction in RMSE.
Additionally, to demonstrate the proposed ANN performance on unseen data, we used an another MWF signal
model for validation based on multi-exponential relaxometry
signal,9,24 which is different from the signal model used for
training. An analytic phantom was designed with differing T∗2
and MWF values. Details of these simulations are explained
in Supporting Information Figure S3.
|
2.3.2
In-vivo testing
A fully trained ANN was used to estimate the voxel-wise
MWFs of the in vivo data sets. The network generated MWF
from the measured mGRE signals of each voxel. Each signal
was divided by the magnitude of first TE for normalization.25
We acquired mGRE data for various scan parameters.26
Particularly, 1 healthy subject was scanned for different av(
))
− T ∗1 +i2𝜋𝛥fbg+ex t
(5)
e 2,ex
e−i�0
erages to evaluate noise sensitivity. To investigate the feasibility of high-resolution MWI, data with various resolutions
were acquired for another subject with varying resolution
from 2 mm to 1 mm.
For quantitative analysis, the region-of-interest (ROI) analysis was performed in WM for data from 3 healthy subjects
with identical scan parameters. The ROIs were chosen as five
regions: minor forceps, major forceps, splenium and genu
of corpus callosum, and internal capsule. Correspondingly,
the number of voxels for each ROI per subject were approximately 150, 100, 200, 200, and 180. Furthermore, voxel-wise
correlation coefficients were calculated between the ANNMWF and NLLS-MWF.
2.4
|
MRI acquisition
In vivo sets from 17 healthy subjects (age range: 27-30 years)
and 1 patient documented as having subjective cognitive
4
| impairment disease (age 62, subject 2 in Figure 4) were acquired with motion artifact. All human subjects gave consent
to their brain data acquisitions. A clinical 3T MRI scanner
(Magnetom Tim Trio; Siemens Medical Solution, Erlangen,
Germany) was used with 16-channel head coil under the approval of the institutional review board. Eight healthy subjects were used to determine the training data-set parameter
ranges; the remaining 9 subjects (including 1 subjective cognitive impairment patient) were used as the test set.
For MWI, a 3D-mGRE sequence was used with
the following scan parameters: TR = 46 ms, first
TE = 2.28 ms, echo spacing (ES) = 1.7 ms, number of echoes = 18, bandwidth = 780 Hz/pixel, flip
angle = 20°, FOV = 192 × 192 × 144 mm, spatial resolution = 1.5 × 1.5 × 1.5 mm, and scan time = 13 minutes
50 seconds. Based on these default sequence, different TEs,
ES, and spatial resolution were used for a few subjects (see
Supporting Information Table S2).
The following scan parameters were also used for patient MWI: TR = 60 ms, first TE = 1.5 ms, ES = 1.0 ms,
number of echoes = 31, bandwidth = 1560 Hz/pixel, flip
angle = 20°, FOV = 256 × 256 × 100 mm, spatial resolution = 2.0 × 2.0 × 2.5 mm, and scan time = 7 minutes 22
seconds.
In each sequence, bipolar gradient readout and navigator echo were used to reduce ES and compensate for motion
JUNG et al.
artifacts,10,11 respectively. To reduce ringing artifacts, a
Tukey window (parameter = 0.4) was applied to the k-space
of the mGRE data.
MPRAGE images were acquired for anatomical information with the following parameters: TR = 2200 ms, TI = 90 ms,
GRAPPA acceleration factor = 2, FOV = 256 × 256 × 144 mm,
spatial resolution = 1.0 × 1.0 × 1.0 mm, and scan time = 5 minutes 38 seconds.
3
3.1
|
RESULTS
|
Numerical simulation
Figure 1 shows the estimated MWFs and SDs using the
proposed ANN and NLLS in Monte-Carlo simulations.
Each plot indicates results for different SNR conditions to
show noise sensitivity. For various SNRs, the ANN-MWF
presents reduced RMSE than NLLS-MWF (from 5.46 to
3.56 for SNR of 150, relative gain = 34.80%). Absolute
biases and SDs are also reduced for ANN-MWF compared
with NLLS-MWF. Additionally, the results of simulations
using the new signal model with varying SNR and ES are
showed in Supporting Information Figure S4. Supporting
Information Figure S5 shows the effect of various T∗2 in
NLLS and ANN.
F I G U R E 1 Simulated results with respect to various SNR levels. Based on the estimated myelin water fractions (MWFs), the RMS errors
(RMSEs) and absolute bias values were calculated. Abbreviations: ANN, artificial neural network; NLLS, nonlinear least squares
JUNG et al.
3.2
|
In-vivo measurements
Figure 2 shows the in vivo results with respect to number of
averages, with improved performance for ANN. The SNRs of
the in vivo data in Figure 2 were 132, 196, and 271. Figure 2A
shows the estimated MWF map from the in vivo slice with
corresponding MPRAGE image in Figure 2B. To examine
this quantitatively, the mean and SD of the estimated MWF
values from the frontal-lobe ROI (indicated by the blue mask
in Figure 2B) are summarized as follows: 8.67% ± 2.45%
in NLLS-Avg × 1, 8.19% ± 2.00% in NLLS-Avg × 2, and
7.83% ± 1.73% in NLLS-Avg × 4, while the values were
7.85% ± 1.89% in ANN-Avg × 1, 7.96% ± 1.59% in ANNAvg × 2, and 7.58% ± 1.03% in ANN-Avg × 4. The mean
|
5
MWFs are more consistent across the number of averages
using ANN than NLLS. The SDs are reduced for the ANN
compared with NLLS, which agree with the simulation results. Note that the SD of ANN-Avg × 1 shows smaller values than NLLS-Avg × 2. Additionally, the noise robustness
of ANN in low-to-moderate SNRs is illustrated in Supporting
Information Figure S6.
Results from representative in vivo slices of the MWF
map derived from NLLS and ANN are shown in Figure 3A.
The SNR was 132, and the WM area of the ANN shows
clearer visualization than the NLLS, while corresponding
better to the WM structures of the MPRAGE images. Note
that the ANN-MWF shows abnormally high MWF values in
the globus pallidus region (white arrows).
F I G U R E 2 In vivo results with regard to the different number of averages. A, Representative slice data for the estimated MWF maps from
NLLS and ANN. B, Corresponding MPRAGE image
F I G U R E 3 In vivo results. A, Representative slices for the estimated MWF maps using NLLS and ANN for the corresponding MPRAGE
images. B, Comparison of the MWF values from ANN and NLLS methods in the subjects’ white-matter regions of interest
6
| In Figure 3B, the results for ROI analysis are plotted for NLLS and ANN, demonstrating high correlations
(R = 0.966). The error bars denote intersubject SDs. Note
that the ANN-MWF provides relatively low SD. Supporting
Information Table S3 provides a summary of the MWF in
the five ROIs for NLLS and ANN compared with previous
literature.9,10
Figure 4 presents the results for artifact-corrupted
cases caused by ΔB0 inhomogeneities, motion artifacts,
and ringing artifacts. In Figure 4A, the ANN-MWF shows
clearer delineation at the frontal lobe where ΔB0 inhomogeneity exists (white dashed circle). The abnormally high
values of MWF are reduced more in ANN-MWF than in
NLLS-MWF. Figure 4B shows that the streaking patterns
from motion artifacts seen in NLLS-MWF are reduced
when ANN was applied. Figure 4C indicates that the
Gibbs ringing artifact (white dashed circle) is reduced.
For additional results, refer to Supporting Information
Figure S7.
The results from different resolutions are shown in
Figure 5. In all cases, the ANN-MWF shows improved
image quality. In low-resolution MWF maps, details on the
border between the WM and gray matter are improved more
in the ANN-MWF than in the NLLS-MWF (green box). In
high-resolution MWF maps, ANN-MWF shows enhanced
visualization of WM structures, which is in agreement with
the corresponding MPRAGE image (blue box). Supporting
Information Figure S8 shows the results for specific ROIs.
JUNG et al.
4
|
DISCUSSION
In this work, we applied the ANN method for MWF estimation with simulated training data. Simulation data sets were
generated based on the in vivo parameter ranges using the
three-pool exponential model. The results showed improved
MWF mapping as an alternative to the NLLS method for
mGRE data.
Reduced RMSE over noise was observed in ANN-MWF
during numerical simulation, confirming the robustness
of our method. In the in vivo results, ANN-MWF showed
clear WM delineation, especially in regions near the cortex. Moreover, a statistically significant correlation between
ANN-MWF and NLLS-MWF was reported from ROI analysis. This indicates that the proposed ANN achieves higher
spatial-resolution MWF mapping with high reliability, which
has been challenging thus far, due to smaller voxel sizes and
reduced SNRs.27
The improvements using ANN were also observed in the
in vivo results with high SNRs. This is because in vivo signals entail practical issues such as long ES in the scan parameters and complicated biological tissue characteristics that
could hinder signal quality.10,11,13 Figure 1 and Supporting
Information Figure S4 suggest that these factors affect the
ANN-MWF less than the NLLS-MWF, thus supporting the
benefit of using ANN (Figure 4).
In the conventional NLLS method, when using the threepool exponential model, 10 parameters need to be fitted by
F I G U R E 4 Artifact-corrupted data
from 3 subjects: ΔB0 inhomogeneity (A),
motion artifact (B), and ringing artifact (C).
Abbreviation: mGRE, multi-echo gradient
echo
JUNG et al.
FIGURE 5
|
7
Comparison of MWF maps with various in-plane resolutions for the ANN and NLLS methods
minimizing least-square residuals.8 This causes instability in
the noise and artifacts, which deviate from the model. When applying the ANN to MWI, however, data-driven neural networks
may not fall into local minima with high errors,28-30 thereby
rendering the ANN robust to noise and outliers.31 Moreover,
the ANN is unaffected by initializations and is computationally
more efficient 19,31,32 compared with NLLS, confirming the advantages of applying ANNs in MWF estimations.
In this work, simulated training offers several advantages
to the proposed ANN. Different mGRE signals could be easily generated, showing the potential of applying ANNs to
various scan parameters. Supporting Information Figure S9
presents the representative slices of the MWF maps for four
different scans, confirming the advantage of using simulated
data sets.
Based on the 3D brain data, the processing time of the
proposed ANN was about 3.7 seconds, whereas the NLLS
took 9840 seconds (approximately 2.7 hours). Because the
training required less than 1 hour with the GPU workstation,
training time may not hinder implementation of the proposed
ANN to new data with different TEs.
A recent work33 applied ANN for MWI using multi-echo
gradient and spin-echo data. The network was trained using
the in vivo multi-echo gradient and spin-echo data set and
indicated that the network could be applied to only data with
the same scan parameters as training, showing increased errors for different first TE and ES data. Herein, we could simulate new signals based on the in vivo test set. This could
reduce the cost of collecting in vivo data sets. Additionally,
during acquisition, the long scan times required for sufficient
SNRs might limit the quality of the training data set.
A potential limitation here is that only magnitude information of the signal was used to create the data set. In a previous report, NLLS with complex data provided more reliable
frequency difference mapping of water compartments (eg,
Δfmy−ex) than that with magnitude data.8 This confirms that
the complex signal might better reflect the fiber orientational
dependencies of the signal. The absence of phase information
might cause abnormally high MWF values in iron concentration regions (eg, globus pallidus in Figure 3A).34,35 Further
research using complex-valued signals is necessary for correction of such overestimations.36
Another concern in this work is that an adequate model
for the training data set is crucial for accurate MWF mapping.
Hence, the restricted number of water pools may hamper the
use of ANNs by not reflecting the detailed aspects of practical changes occurring in tissues.9,37,38 However, in previous
studies, the three-pool exponential model showed improved
performance on MWF estimation using mGRE acquisitions.8,26,39 Moreover, because of the increased sensitivity to
physiological noise11 and field inhomogeneities13 in mGRE
acquisitions, multicompartment model application with separable T∗2 amplitudes and frequency offsets for an unknown
number of water pools might be challenging. Thus, only the
three-pool exponential model was considered in this study,
although different signal models could be adopted. However,
this limitation could be improved in future studies using other
models, such as the hollow cylinder fiber40 model.
| 8
JUNG et al.
Finally, the current training data set may not yet reflect
all of the characteristics of in vivo data, such as susceptibility anisotropy,8,41 motion,11,42 and flow.11,42,43 Generating an
adequate training data set is critical, including the range of
input signal parameters. In addition, the range of MWF used
for training should be such as to not reach a class imbalance
problem.44 Further considerations in the training data-set
generation might be required.
Our proposed ANN may be applied to data using parallel
acquisitions,45,46 which are known to contain noise and artifacts that could hamper the quality of MWF maps.47 Using
ANN might overcome these limitations and provide clinically feasible acquisition times for MWF mapping to patients
with demyelination diseases, including multiple sclerosis,48
schizophrenia,49 and stroke.50 However, further validations
are necessary for clinical approaches, because different T∗2
distributions are observed in the demyelinating lesions.37,38
Considering these characteristics to simulate signals could
improve the performance of the ANN.
5
|
CO NC LU S ION
In this study, we demonstrated that ANNs facilitate more robust
MWF mapping compared with the conventional NLLS method.
Using the proposed ANN allowed us to achieve high reliabilities from both simulated and in vivo data. Using the simulation
training data set, the in vivo data from various scan parameters
were easily implemented. However, further validations may be
required for clinical approaches. We therefore conclude that
the proposed ANN shows feasibility for robust mapping during
MWF estimations in mGRE sequences.
ACKNOWLEDGMENTS
This work was supported by the National Research
Foundation of Korea grant funded by the Korea government
(MSIT) (NRF-2019R1A2C1090635).
DATA AVAILABILIT Y STATEMENT
The code supporting the findings of this study is openly
available under [ANN-MWF] at [https://github.com/Yonse​iMILab/].
ORCID
https://orcid.org/0000-0001-8110-5549
Soozy Jung
Kanghyun Ryu
https://orcid.org/0000-0002-6075-5590
Jae Eun Song
https://orcid.org/0000-0002-7616-543X
Dong-Hyun Kim
https://orcid.org/0000-0002-6717-7770
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SUPPORTING INFORMATION
Additional Supporting Information may be found online in
the Supporting Information section.
TABLE S1 Initial values and bounds of the nonlinear leastsquares parameters for simulated and in vivo data according
to previous studies (Nam et al8 and Lee et al10)
Note: In the simulations, ∅0 was omitted; S1 refers to the signal intensity of the first echo data; and ΔB0 refers to the value
of the field map. aRandom refers to initial values that are set
within ±10% from the true values.
TABLE S2 Summary of scan parameters with respect to
number of subjects
Note: A total of eight data sets from scan 4 were used to
determine the parameter ranges of the training data set.
These data sets are excluded from the test set. Scan 1 was
used in Figures 2 and 3 and for region-of-interest analysis;
scans 3, 4, and 8 were used in Figure 4; scans 5-7 were
used in Figure 5; and scans 1-4 were used in Supporting
Figure S9. (The data from scan 8 were used for patient data
acquisition.)
10
| TABLE S3 Summary of myelin water fraction values
(mean ± SD) from our study and previous studies for the five
regions of interest. Note: All reported studies derived the myelin water fraction (MWF) from T∗2 decay in the same manner
as our study. The MWF values from Alonso-Ortiz et al9 are
approximated based on their bar graphs. The results from our
artificial neural network (ANN) were comparable to those in
previous studies and the nonlinear least squares (NLLS) values in our study.
FIGURE S1 Parameter distributions used for simulated signals from eight healthy data sets using scan 4, as summarized
in Supporting Information Table S2. The parameters were
acquired from the NLLS algorithm using the complex threepool exponential model in Equation 5. The red line denotes
fitted distributions in which 𝜇 and 𝜎 are the mean and SD of
the fitted distribution
FIGURE S2 Details of the signal design for the simulations.
A, Complex three-pool exponential signal model multiplied
with sinc function, reflecting perturbation by macroscopic
field inhomogeneities. B, Model parameters for generating
signals
FIGURE S3 An analytic phantom was designed to compare
the performance between NLLS-MWF and ANN-MWF in
differing T∗2 and MWF values. The first TE and last TE were
set to 1 ms and 30 ms, respectively. A, The phantom consisted of 16 squares of size 10 × 10. B,C, The range of T∗2
distribution was varied according to Alonso-Ortiz et al.9 Each
square contains two water pools, including slow-decaying T∗2
(T∗2,s) and fast-decaying T∗2 (T∗2,l). For squares 1-8, T∗2,s and T∗2,l
were set to 10 ms and 60 ms, respectively, and the MWF varied from 3% to 21% in steps of 3%. The MWFs of squares
9-16 were set to 10%. For squares 9-12, the T∗2,s varied from
6 ms to 12 ms in steps of 2 ms, and T∗2,l was set to 60 ms. For
squares 13-16, the T∗2,l varied from 55 ms to 85 ms in steps
of 10 ms, and T∗2,s was set to 10 ms. D, To generate more
realistic biological signals, the two water pools (T∗2,l, T∗2,s) are
Gaussian-distributed in log scale (10% pool width) and centered at each water pool. Here, Gaussian noise was added to
mimic various SNR levels. The SNRs varied from 40 to 200.
The echo spacing (ES) also varied from 1 ms to 3 ms
FIGURE S4 Simulated results of estimated MWFs using
the NLLS method and proposed ANN for various SNRs
JUNG et al.
(ES = 1 ms) and ESs (SNR = 150). The results suggest the robustness of ANN over the NLLS method against SNR and ES
FIGURE S5 Simulated results of estimated MWFs using the
NLLS method and proposed ANN for various T∗2,s and T∗2,l.
The results reveal that the ANN and NLLS methods both
show comparable performance for the various T∗2,s and T∗2,l
FIGURE S6 Results of the ANN and NLLS methods for
various noise situations. Additional artificial noises (noise
SD × 1, SD × 2, and SD × 3) were added to simulate data
with SNRs between 40 and 100. These reveal the noise robustness of ANN for low-to-moderate SNRs
FIGURE S7 Five representative slices of artifact-corrupted
data from subjects (2-mm in-plane resolution). A, ΔB0 inhomogeneity (subject 1). B, Motion artifact (subject 2). C,
Ringing artifact (subject 3). The ANN-MWF shows artifact
reduction in the images compared with the NLLS-MWF
FIGURE S8 Comparison of the MWF maps from ANN and
NLLS methods with various resolutions at specific regions
of interest. A, The ANN-MWF shows clearer visualization of the white matter (WM) structures in the frontal lobe
compared with the NLLS-MWF, regardless of the in-plane
resolution. In particular, the high-resolution ANN-MWF
(1 mm) presents a high-quality MWF map that is in agreement
with the corresponding MPRAGE image. B, High-resolution
MWF maps show finer WM structures, regardless of the
method used. In particular, high-resolution ANN-MWF provides enhanced visualization, which is attributable to the use
of the proposed ANN. The results suggest that high-resolution ANN-MWF maps provide improved image quality
FIGURE S9 In vivo results of various multi-echo gradientecho scan parameters: 1.5-mm isotropic resolution (A,B) and
2.0-mm isotropic resolution (C,D). The ANN was trained
separately using the same TE as the in vivo scan parameters
How to cite this article: Jung S, Lee H, Ryu K, et al.
Artificial neural network for multi-echo gradient
echo–based myelin water fraction estimation.
Magn Reson Med. 2020;00:1–10.
https://doi.org/10.1002/mrm.28407