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Quantitative mapping of susceptibility and non-susceptibility frequency with DEEPOLE QUASAR

Thomas Jochmann¹, Dejan Jakimovski², Nora Küchler¹, Robert Zivadinov^2,3, Jens Haueisen¹, and Ferdinand Schweser^2,3
¹Department of Computer Science and Automation, Technische Universität Ilmenau, Ilmenau, Germany, ²Buffalo Neuroimaging Analysis Center, Department of Neurology at the Jacobs School of Medicine and Biomedical Sciences, University at Buffalo, The State University of New York, Buffalo, NY, United States, ³Center for Biomedical Imaging, Clinical and Translational Science Institute, University at Buffalo, The State University of New York, Buffalo, NY, United States

Synopsis

Besides magnetic susceptibility, MRI phase contrast is caused by chemical exchange, anisotropic magnetic susceptibility, and anisotropic microstructural compartmentalization. These additional contributions are neglected by conventional QSM. This work presents an improved version of DEEPOLE QUASAR, a phase processing method that accounts for non-susceptibility signal contributions. We present preliminary results from studies on mice, volunteers, and multiple sclerosis (MS) patients.

Introduction

Frequency maps from gradient-recalled echo MRI phase are affected by multiple biophysical contrast mechanisms. Most prominently, the frequency perturbation is explained with voxel-average (bulk) isotropic magnetic susceptibility of the tissue. Besides that, theoretical predictions and experimental evidence exist for additional contributions from (i) chemical exchange,^1–3 (ii) anisotropic magnetic susceptibility,^4,5 and (iii) anisotropic microstructural compartmentalization.^2,6 Neglecting these additional, confounding contributions by assuming bulk isotropic susceptibility as the sole generator of the frequency shift leads to errors in the susceptibility estimates⁴ in quantitative susceptibility mapping (QSM).⁷ These errors are particularly problematic since QSM is increasingly being used in clinical studies^8,9 for its quantitative information. Furthermore, the current simplistic physical model of QSM obscures the highly interesting information about microstructural tissue pathology. The non-susceptibility-contrast bears the potential of a unique and highly sensitive assessment of myelin-related pathology because its sign and magnitude could indicate the type of tissue alteration, even before bulk changes of the chemical tissue composition change the voxel-average magnetic susceptibility. The assumptions in the literature on each non-susceptibility frequency contribution’s individual extend are conflicting.^4,5,10,11 Of all contributions, the isotropic susceptibility presumably causes the strongest non-local field perturbation, described through a convolution (denoted *) with a dipole¹² d. Our recently presented DEEPOLE QUASAR approach¹³ uses this dipole pattern as a hallmark for separating the susceptibility-related frequency contribution, and yields separate maps for the magnetic susceptibility χ versus the other frequency contributions fρ combined, according to the QUASAR model¹⁴ f=d*χ + f_ρ. Here we present an improved version of DEEPOLE QUASAR and preliminary results from studies on mice, volunteers, and multiple sclerosis (MS) patients.

Methods

Deep learning: We set up a U-Net¹⁵ (TensorFlow 2.2.0) to approximate the inverse mapping from f to χ, similar to Bollmann et al.¹⁶ and Yoon et al.,¹⁷ but trained it on synthetic random distributions¹⁸ of f (160³ voxels) that contained non-susceptibility contributions (Fig. 1). We augmented 1200 training samples with complex Gaussian noise,^18,19 set random parts of f to zero (masking), and calculated the loss (mean-squared error) in the unmasked regions. We trained a second network to directly approximate f_ρ. For evaluation, we extended the dataset of the 2019 QSM Reconstruction Challenge²⁰ with a DTI-based microstructure model.^21–24 We explored how signal-to-noise ratio and masking affected the normalized root mean-squared error (nRMSE). Application: We applied the method on (i) volunteer data (N=12, 12 echoes, 3T), (ii) clinical multiple sclerosis data (N=10, 12 echoes, 3T) in comparison with FLAIR, T1, T1 with Gadolinium, and “classical” QSM (HEIDI),⁷ and (iii) on Swiss Jim Lambert (SJL)/J mice (N=23, 9 echoes, 9.4T). In all cases, phase images were acquired with axial 3D multi-echo spoiled gradient recalled echo. The local Ethical Standards Committee approved the human experiments, and a written informed consent form was obtained.

Results and Discussion

The in silico results in Fig. 2A-C demonstrated the method’s ability to find valid and accurate solutions for χ and f_ρ. Fig. 2A showed visible estimation errors for χ, but not in the corresponding f_χ, where these contributions (and errors) disappeared due to the magic angle effect. The errors in Fig. 2C are likely related to those contributions from χ and f_ρ that are mathematically inseparable. Fig. 2D shows that nRMSE plateaued at SNR values exceeding 100 and nRMSE drastically increased when offsetting the out-of-brain region with values >0.1, showing the zero-masked training data taught the network to detect masks. Fig. 3 shows in vivo results from mice, where f_ρ was higher in gray matter (GM) than in white matter (WM), identically to our in vivo results from volunteers (Fig. 4).
Fig. 5 shows MS lesions with f_ρ being hypointense, isointense and hyperintense for different lesions, respectively. This could indicate different stages, as well as different types of tissue damage.²⁶ An iron-enhanced rim lesion had a strong susceptibility and a small positive f_ρ, potentially pointing at myelin dysintegration, as opposed to neurofilament (where f_ρ would be decreased).

Conclusion

DEEPOLE QUASAR is the first method for estimating the non-susceptibility frequency without requiring restrictive boundary assumptions. It forms a new MRI contrast and in combination with its improved susceptibility estimates allows assumptions about the microstructural causes of frequency contrast.
Our solutions agree with the existing evidence of iron-caused contrast in deep GM. Our finding of larger non-susceptibility frequency in cortical GM compared to WM might stimulate new theories about the biophysical mechanisms of phase contrast in cortical GM.

Acknowledgements

We thank José P. Marques for providing data and support for the generation of the digital microstructure phantom.

The research reported in this publication was funded by the National Center for Advancing Translational Sciences of the National Institutes of Health under Award Number UL1TR001412 (F.S.). The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH. Furthermore, the research was supported by the German Federal Ministry of Education and Research (BMBF) grant TeleBrain (01DS19009A) and the Free State of Thuringia within the ThiMEDOP project (2018 IZN 0004) with funds of the European Union (EFRE).

References

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Figures

Fig. 1. Physical model for the training data synthesis, examples of the training data, and the neural network architecture for mapping the total frequency contrast f to either of the two source distributions χ or f_ρ.

Fig. 2. In silico evaluation. A) The reconstruction error on synthetic data has small error in χ, which disappears in the corresponding frequencies. B) A simulation without f_ρ proves that the method does not “hallucinate” any f_ρ. C) On a simulation with f_ρ, estimates of χ and f_ρ have visible errors, but the small error of the total field (bottom right) identifies the estimates as valid solutions to the ill-posed problem. D) nRMSE for different noise levels and mask offsets (see text).

Fig. 3. In vivo results from a study on 23 mice. A) Transversal and coronal slices for a representative mouse brain. f_ρ was higher in cortical gray matter than in white matter, similar to our results in humans (see Fig.4). B) Regional mean values and standard deviations.

Fig. 4. Three axial slices from a volunteer (f, 33y.). A) f_ρ has a stronger positive non-susceptibility frequency shift in gray matter than in white matter, and cerebrospinal fluid (CSF) has the smallest shift. CSF was reconstructed homogenously (orange arrow). The iron-rich basal ganglia (B) and dentate nuclei (C) were isointense in f_ρ (blue arrows). Compared to the HEIDI solution, DEEPOLE QUASAR’s χ of the inner capsule was more similar to surrounding white matter (purple arrow).

Fig. 5. Selected lesions from 3 out of 10 multiple sclerosis patients. f_ρ is hypointense only for black hole lesions, but not all black hole lesions are hypointense in f_ρ.

Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)

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