Hanwen Liu^{1,2}, Roger Tam^{3,4}, John K. Kramer^{2,5}, and Cornelia Laule^{1,2,4,6}

The water molecules within a single voxel may
exist in different microenvironments so that the T_{2} relaxation is
considered as a multi-exponential decay. A few quantitative imaging techniques
such as myelin water imaging attempt to extract the short T_{2}
component as a marker specific to myelin. However, decomposition of
multi-exponential T_{2} decay data is an ill-posing problem. Commonly
used non-negative least squares fitting method is slow, complex and unstable,
even with strong regularization and B1 correction. We used synthetic data to
train a single neural network for a better and faster analysis of the
multi-exponential T_{2} decay data.

T_{2} relaxation in brain and spinal cord white matter is governed by the microenvironment of water molecules. Myelin water, the water trapped in myelin bilayers, exhibits shorter T_{2} than that of the intra/extra (IE) cellular water. The T_{2} relaxation curve of each voxel in the white matter is thus considered a multi-exponential decay.^{1} Decomposition of such multi-exponential T_{2} decay curve data is a complex and often unstable process. Non-negative least squares (NNLS) is a commonly used technique which can fit voxel-wise T_{2} decay data to create a T_{2} distribution, from which the myelin water fraction (MWF, the ratio of myelin water signal to the total signal), mean T_{2} of myelin water (MWT_{2}), and mean T_{2} of IE water (IEWT2) can be extracted.^{1,2} The latest NNLS analysis incorporates the extended phase graph (EPG) algorithm to estimate the refocusing flip angle (FA) of each voxel to correct for the effect of stimulated echoes.^{3} However, NNLS analysis is slow due to its complexity and strong regularization for stability.

Machine learning approaches may provide an alternative to NNLS analysis of multi-exponential T_{2} decay data. We previously used synthetic data to train four different neural networks to estimate MWF, MWT_{2}, IEWT_{2}, and FA individually.^{4} Our objective for this study was to **develop a single neural network that is capable of performing multi-exponential T _{2} decay data analysis to estimate** MWF, MWT

** MR data simulation:** 32-echo T

** Neural network models:** A single neural network with 6 fully connected layers (32×32×256×256×32×4) was constructed (activation function: ReLU, optimizer: Adam

** Trained model and NNLS calculation:** The generated 1,000 synthesized 32-echo decay testing data were analyzed by the neural network model and NNLS (in-house software) independently to simultaneously determine MWF, MWT

The neural network model results are plotted against the ground truth labels in **Figure 2**. The mean errors of both methods are presented in **Table 2**. In the predictions of MWF (**Figure 2(A)**) and IEWT_{2} (**Figure 2(C)**), the trained model demonstrated much better agreement with the ground truth than NNLS. The scatter of the points by NNLS calculation illustrates the instability of NNLS and systematical underestimation of MWF and IEWT_{2}. For the estimation of FA (**Figure 2(B)**), both methods performed at a high level of accuracy. Unfortunately, neither of the two methods worked well in the calculation of MWT_{2} (**Figure 2(D)**). However, further training and fine-tuning may improve the performance of the neural network model.

We also applied the neural network model to one example of *in-vivo* MWI data (32 echo, TE/TR=10/1000ms) and compared the resulting MWF with NNLS (**Figure 3**). Although the neural network model reports much higher overall average MWF (0.279) than NNLS (0.082), some similar features between the two MWF maps were observed (**Figure 3**, arrows). Lower *in-vivo* MWF estimated by NNLS was consistent with the underestimation problem that we observed in the simulation study. The neural network model is also undermined by the fact that the training data generated by a two-pool simulation may not be a good representation of *in-vivo* data, possibly causing MWF overestimation. Since there is no ground truth available for the *in-vivo* data, it’s difficult to assess the accuracy of the two methods definitively. Nevertheless, it only takes approximately 20s for the neural network model to perform whole brain analysis while NNLS needs at least 1.5 hours using MATLAB on a CPU processor with 6 cores (3.50GHz).

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2. MacKay A, Whittall K, Adler J, Li D, Paty D, Graeb D. In vivo visualization of myelin water in brain by magnetic resonance. Magn Reson Med. 1994;31(6):673-677.

3. Prasloski T, Mädler B, Xiang Q, MacKay A, Jones C. Applications of stimulated echo correction to multicomponent T2 analysis. Magnetic Resonance in Medicine. 2012;67(6):1803-1814.

4. Liu H, Tam R, Kramer J, Laule C. Myelin water imaging data post-processing: A deep learning approach. Proc. Into. Soc. Mag. Reson. Med, Machine Learning Workshop Part II, 2018.

5. Hennig J. Multiecho imaging sequences with low refocusing flip angles. Journal of Magnetic Resonance. 1988;78(3):397-407.

6. Kingma DP, Ba J. Adam: A method for stochastic optimizaton. arXiv. 2014;1412.6980.