Ko Sasaki^{1,2} and Yoshitaka Masutani^{2}

In general, DKI parameters (D and K) are obtained by fitting models to DWI signal values, such as by least-square fitting (LSF) methods. However, when DWI signal values are contaminated by noise of high level, fitting error is often observed especially for diffusional kurtosis K. In this study, we propose a robust method to infer DKI parameters based on deep neural networks trained by only synthetic data to overcome the limitations of real data training. Our experimental results including comparison with LSF showed the potential of our method for robust inference of DKI parameters.

In the first step of our training data synthesis, values of baseline signal $$$S_{０}$$$, diffusion coefficient D, and diffusional kurtosis K are generated as uniform random numbers. Next, DWI signal values for b-factor = 311, 1244, and 2800 are generated by the DKI signal value model . Then, Rician noise is added to $$$S_{０}$$$ and $$$S$$$ so that new value becomes $$$\sqrt{S^2+N(0, \sigma)^2}$$$, where $$$N$$$ shows zero-mean Gaussian noise of standard deviation $$$\sigma$$$. The noise ratio is adjusted for $$$\sigma\diagup S_{0}$$$ with values of 0.0, 0.1, 0.3, 0.5, 0.7, 1.0, and 1.5. For synthetic data test, another dataset is also created with different random number seed. For each dataset for training and test, $$$10^{5}$$$ samples are generated. The synthetic training data is transferred to multi-layer perceptron (MLP) [3] (Fig.1), which uses logarithm of signal decay as input and outputs D or K value. A real dataset is also prepared for test, which is a head DWI dataset of a healthy volunteer with informed consent. DWI is acquired in isotropic voxels of 3 mm, b-factor = 0, 311, 1244, 2800 DWI and MPG direction is AP (0, 1, 0). The LSF results are also obtained for comparison based on the DKI closed-form solution [2].

- Jensen JH, Helpern JA, Ramani A, et al. Diffusional kurtosis imaging: the quantification of non-Gaussian water diffusion by means of magnetic resonance imaging. Magn Reson Med, 2005;53:1432-1440.
- Masutani Y, Aoki S. Fast and Robust Estimation of Diffusional Kurtosis Imaging (DKI) Parameters by General Closed-form Expressions and their Extensions. Magn Reson Med Sci, 2014;13(2):97-115.
- Golkov V, Dosovitskiy A, Sperl IJ, et al. q-Space Deep Learning: Twelve-Fold Shorter and Model-Free Diffusion MRI scans. IEEE Trans. Med. Imag., 2016;35(5):1344-1351.

Figure 1. Structure of deep neural network for DKI parameter inference. A multi-layer perceptron with 3 middle layers of 128 units, activation function of ReLU, and no drop out units was used and was trained with batch size of 100 and 100 epochs.

Figure 2. Synthetic
data test results with nine combinations of training data and synthetic data
with three noise ratios; σ∕S_{0} =0.0, 0.1, and 1.0 for each. The
values with yellow background show the lowest errors for each noise ratio of
test data.

Figure 3. Real
data inference result images for diffusion coefficient:
D
by LSF, and MLPs with seven levels of noise ratio for training.

Figure 4. Real data inference
result images for diffusional kurtosis: K by
LSF, and MLPs with seven levels of noise ratio for training.

Figure 5. Real
data test results for inference of D and K by LSF and MLPs with seven noise
ratios. (a) mean and standard deviation values for whole brain excepting error
voxels for D, (b) those for K, (c) error rates for D within whole brain, and (d)
error rates for K.