Juhyung Park^{1}, Woojin Jung^{1}, Eun-jung Choi^{1}, and Jongho Lee^{1}

^{1}Seoul National University, Korea, Republic of Korea

### Synopsis

A deep neural network, NODDInet, was
developed to generate NODDI parameters (ICVF, ISOVF, OD, and FA) in 1 min. This
network was trained using a computer simulation-generated training dataset
only, and, therefore, is unbiased to experimental data and covers a wide range
of the parameters. For the network input, the diffusion measurements of each shell
were projected onto three 2D plains to reduce the input data size while
preserving the geometric information of the diffusion measurements. The
results demonstrate higher accuracy and faster processing time (x14) than a
previous method (AMICO).

### Introduction

Neurite orientation dispersion
and density imaging^{1} (NODDI) utilizes multi-shell diffusion data to
estimate neurite density and dispersion parameters and has been widely used. However,
the method requires extremely long computation time, taking 17 hours for one
dataset. To shorten the processing time, AMICO^{2} (processing time: ~16
min) was developed at the cost of increased errors. In this study, we developed
a deep neural network to generate NODDI parameters (intra-cellular volume fraction
(ICVF) isotropic volume fraction (ISOVF), orientation dispersion (OD), and fractional
anisotropy (FA)) in 1 min. This network was trained using a computer
simulation-generated training dataset only, and, therefore, is unbiased to
experimental data and cover a wide range of the NODDI parameters. Furthermore,
we designed a new approach of generating a network input dataset that retains
the geometric information of the multi-shell diffusion measurements while
reducing input size. The results demonstrate higher accuracy and faster
processing time (x14) than AMICO.### Methods

**[Diffusion
simulation] **The
training dataset for the network was generated by a Monte-Carlo computer
simulation. A total of 17000 microstructural environments were generated to
cover a wide range of the parameters in NODDI. The environment assumed three
pools, intra-cellular, extra-cellular, and CSF, and the volume fraction of each
pool was determined by ICVF (between 0 to 1) and ISOVF (between 0 to 1). Once
the volume fraction was determined, 2×10^{5} protons were assigned to
each pool by their volume fractions. Protons in CSF performed isotropic
diffusion (3.0×10-3 mm^{2}s^{-1}) whereas protons in
the extra-cellular space performed anisotropic diffusion$$${d'_∥}$$$ = $$$d_{∥}$$$ - $$$d_{∥}$$$ICVF$$$\left(1-{\tau }_1\right)$$$, and $$${d'_⊥}=\ d_{∥\ }-d_{∥\ }ICVF(\left({1+\tau }_1\right)/2)$$$ where $$$d_{\parallel }$$$ = 1.7$$$\mathrm{\times}$$$10$$${}^{-3\ }$$$mm$$${}^{2}$$$s$$${}^{-1}$$$.^{3} Finally, protons in the intra-cellular
space performed hindered diffusion along the axon vectors whose mean direction
was randomly chosen. The axon vectors were dispersed by Watson distribution^{3}.
For the acquisition, the scan parameters were Δ = 46 ms, δ = 33 ms and G =
10.483, 16.031, and 27.032 mT/m for b = 300, 700, and 2000 s/mm^{2}, respectively.
For b = 300, 700, and 2000 s/mm^{2}, 8, 32, and 64 diffusion
directions were applied, respectively. Gaussian noise was added to generate SNR of 50. In total,
108 (= 8+32+64) diffusion measurements were obtained by the computer simulation
for the 17000 microstructural environments.

**[Projection
of 3D multi-shell data]**
The 108 diffusion measurements are sparsely located in a 3D space (Fig. 2a). If
this 3D space is directly inputted to a convolutional neural network (CNN), the
input size can be large, making CNN less efficient. Alternatively, one might
suggest using 108x1 vector as the input for CNN. However, this vector loses
geometric information of the 3D multi-shell diffusion data. In order to retain
the geometric information while reducing the input data size, we projected the diffusion
measurements of each shell onto three 2D plains. Each plain corresponded to a
reference axis (i.e., x-, y-, and z-axis) and the position on the plain was
determined by the spherical coordinate (Θ,Φ) with respectively
the reference axis (Figure 2).
Then each plain was resampled to generate a 20×40 matrix. Hence,
a 20×40×9 matrix was constructed from the 3-shell data while
retaining most of the information in the original 3D space. To demonstrate the importance
of preserving the geometric information, we rearranged the first two dimensions
of the input matrix randomly and trained another network (NODDInet_{random}).

**[Convolutional
neural network]** For
the structure of NODDInet, ResNet^{5} was utilized (Figure 3). Using
the 17000 simulated data, the network was trained to generate ICVF, ISOVF, OD,
and FA. L2 loss and ADAM optimizer were used.

**[Experimental
data]** For the
evaluation of the network performance, five subjects from Ref.6 were used. The
diffusion gradient amplitudes and directions were the same as in the
simulation.

**[Evaluation] **The experimental data were
processed with the four methods: NODDI, NODDInet, NODDInet_{random}, and AMICO. Normalized root-mean-squared error
(NRMSE), structural similarity (SSIM), and correlation coefficient were
calculated with the NODDI results as a reference. An FA map was calculated
using FSL for b = 2000 s/mm2
data and the result was compared to the FA map of the network. ### Results

Figure 4 shows the ICVF, ISOVF,
and OD maps of the three methods and the FA maps. All maps show similar
contrasts. The network results are closer to those of NODDI when compared to the
results of AMICO. The same trends can be found in Figure 5, which summarized
the NRMSE, SSIM, and correlation coefficients. NODDInet_{random}
shows lower performance, demonstrating the importance of preserving the
geometric information. The processing times of NODDI, NODDInet, and AMICO were 17
hours, 1 min 10 sec, and 16 min 12 sec, respectively. Hence, NODDInet is 874
times faster than NODDI, and 14 times faster than AMICO, while providing higher
accuracy than AMICO.### Conclusion & Discussion

In this study, NODDInet was developed.
This new network showed better performances than AMICO in both accuracy and
speed. The newly proposed projection idea helped to retain the geometric
information, which helped to improve accuracy. NODDInet was trained by computer
simulation data, and, therefore, is not biased when compared to the
microstructural environments of the in-vivo data. This may help the network to
be generalized for unseen experimental data. ### Acknowledgements

This research was supported by the National Research Foundation of Korea(NRF) funded by the MSIT(NRF-2018R1A4A1025891) and by the Brain Korea 21 Plus Project in 2019.### References

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