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Whole Brain Source Separation for Neurodegeneration

Alexandra Grace Roberts¹, Mert Sisman¹, Alexey Dimov², Thanh Nguyen², Susan Gauthier³, Pascal Spincemaille², and Yi Wang^2,4
¹Electrical and Computer Engineering, Cornell University, New York, NY, United States, ²Radiology, Weill Cornell Medicine, New York, NY, United States, ³Neurology, Weill Cornell Medicine, New York, NY, United States, ⁴Biomedical Engineering, Cornell University, New York, NY, United States

Synopsis

Keywords: Other Neurodegeneration, Artifacts

Motivation: Cortex and spinal cord tissue are of interest in a variety of neurodegenerative diseases including Multiple Sclerosis (MS), Alzheimer’s Disease (AD), and Amyotrophic Lateral Sclerosis (ALS). These regions are low in signal to noise ratio (SNR) and generate artifacts on quantitative susceptibility maps (QSMs).

Goal(s): To demonstrate the maximum Spherical Mean Value (mSMV) algorithm as a tissue preserving initialization for susceptibility source separation.

Approach: Whole brain source separation enabled by mSMV is applied to patients with MS, AD, and ALS.

Results: The mSMV algorithm reconstructs the whole brain volume in source separations and generates susceptibility maps in agreement with existing methods.

Impact: Whole brain source separation using the maximum Spherical Mean Value (mSMV) algorithm successfully preserves full tissue volume and produces susceptibility map in strong agreement with existing methods.

Introduction

Neurodegenerative disorders such as Multiple sclerosis (MS), Alzheimer’s Disease (AD), and Amyotrophic Lateral Sclerosis (ALS) progressively degrade central and peripheral nervous system functions.¹ In MS, the development of demyelinated lesions² is observed in the brain and spine. For AD, increased susceptibility is witnessed in the frontal cortex.³ For ALS, the motor cortex demonstrates elevated susceptibility.⁴ Increased magnetic susceptibility on quantitative susceptibility maps (QSM) is caused by iron increase or myelin decrease that are most evident on separated paramagnetic and diamagnetic sources. Quantification of iron and myelin sources from complex multi-echo gradient echo (mGRE) data was demonstrated^5-7 by combining magnitude decay modeling and phase to monitor MS disease progression.^8,9 Many QSM reconstruction techniques introduce erosion of the brain mask to reduce shadow and streaking artifacts at voxels with low signal-to-noise ratio (SNR). Here, it is demonstrated that retaining the whole brain volume is particularly relevant for source separation in MS as well as other neurodegenerative pathologies like AD and ALS.

Theory

The bulk susceptibility is decomposed into positive and negative sources by minimizing the cost function⁶ initialized with $$$\chi_0^+$$$ and $$$\chi_0^-$$$ by solving $$\chi_0^{+*},\chi_0^{-*} = \mathrm{argmin}_{\chi_0^+,\chi_0^-} ||A\mathbf{\chi_0}-b||_2^2 \ \ \mathrm{s.t.} \ \ \chi^l_0 \leq \chi_0 \leq \chi_0^u$$
Initial susceptibilities and are obtained from a linear least squares solver minimizing the difference between bulk susceptibility and the dephasing effect of susceptibility. Then, the cost function is solved iteratively using conjugate gradient descent with Gauss-Newton iteratione. Popular reconstruction pipelines^10-13 introduce erosion^14,15 to that removes portions of the occipital lobe, spinal cord, and pathology. Improvement in visualization of the cortex, lobes and pathology with whole brain source separation is demonstrated. Here, the source separation is initialized by $$\chi_{mSMV}(r)=d(r) * b_{mSMV}(r)$$ Where $$$d(r)$$$ is the filtered dipole kernel and $$$b_{mSMV}(r)$$$ is the tissue field estimated from the mSMV algorithm.

Methods

Multi-echo gradient echo (mGRE) and $$$$T_1$$$-weighted ($$$T_1w$$$) acquisitions were collected for thirty-nine MS patients. The mGRE sequence had echo spacing $$$\Delta TE=4.1ms$$$ with initial echo time $$$TE_1=6.3ms$$$, acquisition matrix $$$260\times320\times56$$$, in-plane resolution of $$$0.75mm^3$$$ and slice thickness $$$3mm$$$. Complex mGRE data was fit¹⁶ and unwrapped using ROMEO.¹⁷ Bulk susceptibility was reconstructed using MEDI-L₁^18-20(regularization parameters $$$\lambda_1=1000, \lambda_2=100$$$ with mSMV²¹ and SMV ($$$5mm$$$ kernel) tissue field filtering. Positive and negative sources were reconstructed and the contrast-to-noise ratio (CNR) was calculated at each lesion with the intersection between a dilated (using a cubic structuring element of the maximum voxel size) lesion label and normal-appearing white matter masks, $$$M_{CNR}$$$(Figure 1). An mGRE sequence for 5 patients with Alzheimer’s Disease (AD) on a $$$3T$$$ MRI scanner with voxel size $$$0.75\times0.75\times3mm^3$$$ and first echo time, $$$TE_1=6.3ms$$$, a repetition time $$$TR=48ms$$$, flip angle of 15°, and a readout bandwidth of $$$260Hz/pixel$$$. Susceptibility sources were reconstructed with the same parameters as the MS patients. The difference between positive and negative sources was calculated for each method. An mGRE sequence⁴ with $$$TE=\Delta TE=TE_1=5ms$$$, 11 echoes, $$$TR=59ms$$$, flip angle 20°, and voxel size of $$$0.75\times0.75\times2mm^3$$$ was acquired for 35 ALS patients and susceptibility sources were reconstructed with the aforementioned parameters.

Results

Strong correlation $$$R=0.98, m=1.04, b\approx0$$$ and agreement $$$[-5.2ppb,5.11ppb]$$$ was found between the mean lesion bulk susceptibilities (Figure 2). Lesions on MS patients eroded on SMV initialized source separations were visible on mSMV initialized source separations (Figure 3). The median CNR for mSMV initialized source separations was significantly higher $$$(p<0.01)$$$than for SMV initialized source separations for both negative ($$$1.34$$$ and $$$1.28$$$, respectively) and positive ($$$0.59$$$ and $$$0.58$$$, respectively) sources. The median gradient at each lesion for whole brain was significantly ($$$p<0.01$$$) higher than for negative ($$$0.0043$$$ and $$$0.0041$$$, respectively) and positive ($$$0.0036$$$ and $$$0.0035$$$, respectively) sources. In AD patients, the mean susceptibility difference between positive and negative sources for both reconstructions was higher for mSMV reconstructions ($$$0.07$$$) than for eroded reconstructions ($$$0.04$$$), $$$p<0.01$$$ with a representative case shown in Figure 4 and a representative ALS case is show in Figure 5.

Conclusion

Whole brain source separation captures previously eroded pathology and improves lesion CNR. Lesion gradients show larger magnitude in whole brain bulk susceptibility, contributing to increased denoising at these voxels from regularization. This results in full brain volume reconstruction and improved lesion visualization. Increased susceptibility source differences were observed in whole brain reconstruction of AD patients, suggesting improved contrast from retaining the full cortex, also relevant for ALS patients.

Acknowledgements

No acknowledgement found.

References

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13. Wei H, Dibb R, Zhou Y, et al. Streaking artifact reduction for quantitative susceptibility mapping of sources with large dynamic range. NMR in Biomedicine. 2015;28(10):1294-1303. doi:10.1002/nbm.3383 14. Roberts A, Spincemaille P, Nguyen T, Wang Y. MEDI-d: Downsampled Morphological Priors for Shadow Reduction in Quantitative Susceptibility Mapping. presented at: International Society for Magnetic Resonance in Medicine; 2021; Vancouver, Canada. https://cds.ismrm.org/protected/21MPresentations/abstracts/2599.html

15. Roberts A, Spincemaille P, Nguyen T, Wang Y. MEDI-FM: Field Map Error Guided Regularization for Shadow Reduction in Quantitative Susceptibility Mapping. presented at: International Society for Magnetic Resonance in Medicine; 2022; London, England. https://archive.ismrm.org/2022/2359.html 16. Liu T, Wisnieff C, Lou M, Chen W, Spincemaille P, Wang Y. Nonlinear formulation of the magnetic field to source relationship for robust quantitative susceptibility mapping. Magnetic Resonance in Medicine. 2013;69(2):467-476. doi:10.1002/mrm.24272

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21. Roberts AG, Romano DJ, Sisman M, et al. Maximum Spherical Mean Value (mSMV) Filtering for Whole Brain Quantitative Susceptibility Mapping. arXiv pre-print server. 2023-04-22 2023;doi:None arxiv:2304.11476

Figures

Figure 1. Creation of lesion-wise CNR masks $$$M_{CNR}$$$ by taking the difference of the lesion label and its dilation $$$\mathcal{D}$$$ (with cubic structuring element of the maximum voxel dimension) and pointwise multiplication with the normal-appearing white matter mask $$$M_{NAWM}$$$.

Figure 2. Correlation and agreement between bulk susceptibility lesion means.

Figure 3. Lesion preserved by whole brain source separation in an MS patient.

Figure 4. Source separation for patient with AD with full cortex preservation.

Figure 5. Lobe preservation in a patient with ALS.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)

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DOI: https://doi.org/10.58530/2024/4370