R2* Bias Correction for improved χ-Separation
Poster No:
1529
Submission Type:
Abstract Submission
Authors:
Jaewoo Choi1, Jonghyo Youn1, Byeongpil Moon1, Kyeongseon Min1, Chungseok Oh1, Taechang Kim1, Jiye Kim1, Jongho Lee1
Institutions:
1Department of Electrical and Computer Engineering, Seoul National University, Seoul, Korea, Republic of
First Author:
Jaewoo Choi
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Co-Author(s):
Jonghyo Youn
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Byeongpil Moon
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Kyeongseon Min
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Chungseok Oh
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Taechang Kim
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Jiye Kim
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Jongho Lee
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Department of Electrical and Computer Engineering, Seoul National University
Seoul, Korea, Republic of
Introduction:
χ-separation (chi-separation), a novel method currently developed, utilizes R2* maps to differentiate susceptibility sources (Shin et al., 2021). Therefore, obtaining precise R2* mapping in the brain has become essential for accurate susceptibility source separation. However, brain R2* mapping can be erroneous due to B0 field inhomogeneity, vessel flow, and low SNR. To address these issues, several R2* correction techniques have been introduced (Feng et al., 2013; Watanabe & Kubo, 2011; He et al., 2008; Gudbjartsson & Patz, 1995). Given these existing methods, we developed a new R2* bias correction model derived from the truncation method. This approach builds on the truncation method's flexibility in the fitting process, aiming to enhance accuracy in addressing general biases in brain R2* map and χ-separation map results.
Methods:
[Algorithm]
The proposed R2* fitting method (Fig. 1) starts by generating R2* and R-squared maps using Nonlinear Least Squares (NLLS) fitting across all echoes. Voxels with R-squared values below 0.9 are marked for bias correction. NLLS fitting is then repeated, excluding the last echo each time to exceed the 0.9 threshold. If the R-squared value remains below 0.9 after fitting with three echoes, the voxel is masked. The 0.9 threshold was defined by simulation.
[Simulation]
To determine the R-squared threshold for the proposed correction method, we simulated multi-echo GRE signals in various SNRs. In the simulation, the multi-echo GRE signal was assumed as a mono-exponential function with the Rician noise, computed as follows:$$S = M_0 \times e^{-\rm{TE}\times R_2 ^*}+n$$where M0 is the signal magnitude at TE = 0, and n is Rician noise. The first echo was 4 ms, with 6 ms echo spacing, and 6 echoes. Ground-truth values were generated, and Rician noise of varying magntiudes was added. SNR levels varied from 50 to 150 (step size 10), and R2* from 10 to 250 (step size 10). For each SNR-R2* combination, 1000 iterations were performed. R2* fitting used NLLS, and R-squared values were calculated.
[In vivo data]
The method was applied to in vivo multi-echo GRE data from a previous IRB-approved study [1]. Bias correction based on simulation results was evaluated against uncorrected data. Processing was done using the χ-separation toolbox (χ-separation, ver. 1.1.3; SNU-LIST, 2024).
The proposed R2* fitting method (Fig. 1) starts by generating R2* and R-squared maps using Nonlinear Least Squares (NLLS) fitting across all echoes. Voxels with R-squared values below 0.9 are marked for bias correction. NLLS fitting is then repeated, excluding the last echo each time to exceed the 0.9 threshold. If the R-squared value remains below 0.9 after fitting with three echoes, the voxel is masked. The 0.9 threshold was defined by simulation.
[Simulation]
To determine the R-squared threshold for the proposed correction method, we simulated multi-echo GRE signals in various SNRs. In the simulation, the multi-echo GRE signal was assumed as a mono-exponential function with the Rician noise, computed as follows:$$S = M_0 \times e^{-\rm{TE}\times R_2 ^*}+n$$where M0 is the signal magnitude at TE = 0, and n is Rician noise. The first echo was 4 ms, with 6 ms echo spacing, and 6 echoes. Ground-truth values were generated, and Rician noise of varying magntiudes was added. SNR levels varied from 50 to 150 (step size 10), and R2* from 10 to 250 (step size 10). For each SNR-R2* combination, 1000 iterations were performed. R2* fitting used NLLS, and R-squared values were calculated.
[In vivo data]
The method was applied to in vivo multi-echo GRE data from a previous IRB-approved study [1]. Bias correction based on simulation results was evaluated against uncorrected data. Processing was done using the χ-separation toolbox (χ-separation, ver. 1.1.3; SNU-LIST, 2024).
Results:
[Simulation result]
Fig. 2c-f represent histograms of simulation R-squared values with respect to R2* fitting. Fig. 2c shows that over 99% of voxels have a value above 0.9. In the remaining 0.16 % of cases, this outcome occurred when the estimated echo time points from fitting closely aligned with the average of the true echo time points. Plots in Fig. 2d-f display results for different SNRs. Notably, with the lowest SNR simulation of 50, 97.6% of the voxels maintain an R-squared value above 0.9. As a result, a threshold of 0.9 was defined for robust bias correction, regardless of the SNR variability.
[In-vivo result]
In vivo R2* bias correction results are represented in Fig. 2a-b. Yellow arrows in Fig. 2a indicate regions where signal displacement caused by vessels were corrected through bias correction. The red dashed lines in Fig. 2b show results affected by B0 inhomogeneity, where R2* bias correction reduces the R2* fitting errors. R-squared-based masks were also overlaid on the χ-dia map. Notably, the regions indicated by the yellow arrows were not masked, and B0 inhomogeneity regions were partially masked. This suggests that the voxels after bias correction are being adjusted in a way that tries to best represent the fitting equation.
Fig. 2c-f represent histograms of simulation R-squared values with respect to R2* fitting. Fig. 2c shows that over 99% of voxels have a value above 0.9. In the remaining 0.16 % of cases, this outcome occurred when the estimated echo time points from fitting closely aligned with the average of the true echo time points. Plots in Fig. 2d-f display results for different SNRs. Notably, with the lowest SNR simulation of 50, 97.6% of the voxels maintain an R-squared value above 0.9. As a result, a threshold of 0.9 was defined for robust bias correction, regardless of the SNR variability.
[In-vivo result]
In vivo R2* bias correction results are represented in Fig. 2a-b. Yellow arrows in Fig. 2a indicate regions where signal displacement caused by vessels were corrected through bias correction. The red dashed lines in Fig. 2b show results affected by B0 inhomogeneity, where R2* bias correction reduces the R2* fitting errors. R-squared-based masks were also overlaid on the χ-dia map. Notably, the regions indicated by the yellow arrows were not masked, and B0 inhomogeneity regions were partially masked. This suggests that the voxels after bias correction are being adjusted in a way that tries to best represent the fitting equation.
Conclusions:
Our method improves χ-separation and R2* mapping by correcting and masking regions with inaccurate fitting values. By addressing these biases, it ensures reliable results and enhances data quality, making it a valuable method for R2* and χ-separation analysis.
This work was supported by IITP-2023-RS-2023-00256081, grant funded by the Korea government(MSIT)
This work was supported by IITP-2023-RS-2023-00256081, grant funded by the Korea government(MSIT)
Modeling and Analysis Methods:
Methods Development 1
Other Methods 2
Keywords:
MRI
MRI PHYSICS
Myelin
Statistical Methods
White Matter
Other - Chi-separation, Quantitative Susceptibility Mapping (QSM)
1|2Indicates the priority used for review
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Provide references using APA citation style.
Gudbjartsson, H. (1995). The Rician distribution of noisy MRI data. Magnetic Resonance in Medicine, 34(6), 910–914.
He, T. (2008). A non-subjective method for myocardial T2* curve fitting in thalassemia. Journal of Cardiovascular Magnetic Resonance, 10, 1–4.
Shin, H.-G. (2021). χ-separation: Magnetic susceptibility source separation toward iron and myelin mapping in the brain. NeuroImage, 240, 118371.
SNU-LIST. (2024). chi-separation toolbox (χ-separation, x-separation) Version 1.1.3. GitHub. Retrieved October 14, 2024, from https://github.com/SNU-LIST/chi-separation
Watanabe, Y. (2011). A variable echo-number method for estimating in MRI-based polymer gel dosimetry. Medical Physics, 38(2), 975–982.