Minjun Kim^{1}, Hyeong-Geol Shin^{1}, Chungseok Oh^{1}, Hwihun Jeong^{1}, Sooyeon Ji^{1}, Hongjun An^{1}, Jiye Kim^{1}, Jinhee Jang^{2}, Berkin Bilgic^{3}, and Jongho Lee^{1}

^{1}Seoul National University, Seoul, Korea, Republic of, ^{2}Seoul St Mary’s Hospital, Seoul, Korea, Republic of, ^{3}Harvard Medical School, Boston, MA, United States

The
separation of positive and negative susceptibility source distributions (e.g.,
iron and myelin distributions) has important meanings in neuroscience and
clinic. In this study, a deep learning-based χ-separation method is proposed to
generate high-quality susceptibility source maps. For network training,
multi-orientation head data are utilized, providing artifact-free label data.
For the input data, either R_{2}’ or R_{2}* maps are utilized in
addition to local field and QSM maps, producing two neural networks,
χ-sepnet-R_{2}’ and χ-sepnet-R_{2}* (the latter requires no T_{2}). The results
of χ-sepnets outperformed
the conventional method, revealing details of brain structures both in healthy
volunteers and patients.

The networks had the same 3D U-net

$$\left\|f({R_2}'|{R_2}^*,\Delta f,g(\Delta f))_{pos}-\chi _{pos}\right \|_1+\left \|f({R_2}'|{R_2}^*,\Delta f,g(\Delta f))_{neg}-\chi_{neg}\right\|_1$$

where $$$f$$$ denotes χ-sepnet, for which a R

$$\left\||\triangledown f({R_2}'|{R_2}^*,\Delta f,g(\Delta f))|_{x}-|\triangledown\chi _{pos}|_{x}\right \|_1+\left \||\triangledown f({R_2}'|{R_2}^*,\Delta f,g(\Delta f))|_{y}-|\triangledown\chi_{pos}|_{y}\right \|_1+\left \||\triangledown f({R_2}'|{R_2}^*,\Delta f,g(\Delta f))|_{z}-|\triangledown\chi_{pos}|_{z}\right \|_1$$.

The last loss is model loss that enforces to learn information from local field maps and R

$$\left\||(d*(f({R_2}'|{R_2}^*,\Delta f,g(\Delta f))_{pos}+f({R_2}'|{R_2}^*,\Delta f,g(\Delta f))_{neg}))-\triangle f\right \|_1+\left \|(|f({R_2}',\Delta f,g(\Delta f))_{neg}|)-{R_2}' \right \|_1$$

where $$$d$$$ denotes a dipole kernel. Data augmentation was performed by rotating images by random angles (-30˚ - 30˚) relative to $$$B_0$$$ direction, resulting in a total of 48 datasets for training.

For quantitative evaluation, the test subject results were compared for normalized root-mean-squared error (NRMSE), peak signal-to-noise (PSNR), and structural similarity (SSIM) with χ-sep-COSMOS results as a reference. An ROI analysis was performed in 11 ROIs (Fig. 4), reporting the mean and standard deviation of susceptibility values across head orientation.

Two additional subjects, one multiple sclerosis (MS) patient and the other subject with calcification (IRB-approved), were utilized for the evaluation of the networks in clinical practice.

The three zoomed-in regions reveal well-known structures of the brain, which are the deep gray matters (CN: caudate nucleus, Put: putamen, GP: globus pallidus, Pul: thalamus including pulvinar, ND: nucleus dorsomedialis) and the brainstem regions in Fig. 3. In particular, the hand knob region (HK, orange circles) reveals that the positive susceptibility maps report higher values in the motor cortex (MC) than in the sensory cortex (SC), which is a well-known iron distribution from histology

The ROI analysis results demonstrate consistency in the χ-sepnet measurements, reporting much smaller standard deviation than that of χ-sepnet-MEDI (Fig. 4).

Lastly, MS lesions and calcifications are delineated clearly in the results from χ-sepnets (Fig. 5).

1. Shin, H. G., Lee, J., Yun, Y. H., Yoo, S. H., Jang, J., Oh, S. H., ... & Lee, J. (2021). 𝜒-separation: Magnetic susceptibility source separation toward iron and myelin mapping in the brain. NeuroImage, 240, 118371.

2. Chen, J., Gong, N. J., Chaim, K. T., Otaduy, M. C. G., & Liu, C. (2021). Decompose quantitative susceptibility mapping (QSM) to sub-voxel diamagnetic and paramagnetic components based on gradient-echo MRI data. NeuroImage, 242, 118477.

3. Emmerich, J., Bachert, P., Ladd, M. E., & Straub, S. (2021). On the separation of susceptibility sources in quantitative susceptibility mapping: Theory and phantom validation with an in vivo application to multiple sclerosis lesions of different age. Journal of Magnetic Resonance, 330, 107033.

4. Liu, T., Spincemaille, P., De Rochefort, L., Kressler, B., & Wang, Y. (2009). Calculation of susceptibility through multiple orientation sampling (COSMOS): a method for conditioning the inverse problem from measured magnetic field map to susceptibility source image in MRI. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, 61(1), 196-204.

5. Yoon, J., Gong, E., Chatnuntawech, I., Bilgic, B., Lee, J., Jung, W., ... & Lee, J. (2018). Quantitative susceptibility mapping using deep neural network: QSMnet. Neuroimage, 179, 199-206.

6. Ronneberger, O., Fischer, P., & Brox, T. (2015, October). U-net: Convolutional networks for biomedical image segmentation. In International Conference on Medical image computing and computer-assisted intervention (pp. 234-241). Springer, Cham.

7. Costagli, M., Donatelli, G., Biagi, L., Ienco, E. C., Siciliano, G., Tosetti, M., & Cosottini, M. (2016). Magnetic susceptibility in the deep layers of the primary motor cortex in amyotrophic lateral sclerosis. NeuroImage: Clinical, 12, 965-969.

**Fig. 1** (a) Overview of the four χ-separation
methods applied (χ-sep-COSMOS and χ-sep-MEDI) or developed (χ-sepnet-R_{2}’
and χ-sep net-R_{2}*) in this study. (b) Processing pipeline of χ-sepnet.
The network architecture of χ-sepnet had the same 3D U-net structure as QSMnet.
From a local field map, QSM is reconstructed using QSMnet. Then R_{2}’
(or R_{2}*), local field and QSM maps are concatenated for the input of
χ-sepnet, generating positive and negative susceptibility maps.

**Fig. 2**
(a) Results of the χ-separation methods. The χ_{pos} and χ_{neg} maps from two
χ-sepnets are comparable or even cleaner than reference maps from χ-sep-COSMOS.
The improvements may be from denoising nature of neural networks and
registration issues in χ-sep-COSMOS data. Streaking artifacts are observed in
χ-sep-MEDI maps (yellow arrows) but are less noticeable in other maps. (b)
Quantitative metrics report χ-sepnet-R_{2}’ generates the best results while χ-sepnet-R_{2}* provides good outcomes. χ-sep-MEDI results reveal poor metrics against
reference results.

**Fig. 3** Zoom-in maps of χ-separation methods
at three locations. (a) Deep gray matter
regions (CN, Put, GP, Pul, ND, ALIC, PLIC) clearly delineated in χ_{pos} and χ_{neg} maps. (b) In the brainstem region, SN and RN show high
positive and low negative susceptibility concentrations. (c) In the region
including HK (orange circles), χ-sepnet-R_{2}’ and χ-sepnet-R_{2}*
results show that positive susceptibility maps report higher values in the motor cortex than in the sensory cortex. This finding can be confirmed in the χ-sepnet-COSMOS map.

**Fig. 4** Results of the ROI analysis,
reporting the mean and standard deviation (std) in the five gray matter ROIs
(CN: caudate nucleus, PUT: putamen, GP: globus pallidus, SN: substantia nigra,
RN: red nuclues) and six white matter ROIs (ForcMin: forceps minor, ForcMaj:
forceps major, GENU: genu, CST: corticospinal tract, SPL: superior parietal
lobule, OR: optic radiation) over the six head orientations in one subject.
This result demonstrates consistency in the χ-sepnet measurements, reporting
much smaller std than that of χ-sepnet-MEDI.

**Fig. 5**
Outcomes of χ-sepnets from two clinical data. (a) χ-sepnet results of MS
patient clearly demonstrate lesions with increased paramagnetic and decreased
diamagnetic changes, typical findings of MS lesions on χ-separation (arrows).
(b) Focal diamagnetic hyperintensity in globus pallidus captured in negative
susceptibility maps, which is a common location of calcification. The positive
susceptibility maps of this patient reveal positive susceptibility in the same
region, suggesting our methods can separate two sources, clearly distinguishing
them from conventional QSM.

DOI: https://doi.org/10.58530/2022/2464