Blind Source Separation for Myelin Water Fraction Mapping Using Multi-Echo Gradient Echo Imaging

Abstract

In conventional gradient-echo myelin water imaging (GRE-MWI), myelin water fraction (MWF) is estimated by fitting the multi-echo gradient recalled echo (mGRE) signal to a pre-assumed numerical model (e.g., multi-component exponential curves or three component exponential curves). However, in mGRE, imaging artifacts (e.g., voxel spread function and physiological noise) and noise render the signal to deviate from the numerical model, leading to misfit of the model parameters. Here, as an alternative to the model-based GRE-MWI, a blind source separation (BSS) technique for the separation of multi-exponential mGRE signal is proposed. Among the various BSS techniques, a modified robust principal component analysis (rPCA) is presented to separate signal sources by enforcing the data-driven properties such as "low rankness" and "sparsity." Considering the signal evolution of T * 2 relaxation (i.e., non-negative exponential decay), low rankness of exponential decay was enforced by nonnegative matrix factorization (NMF) and hankelization. This method provides the separation of slow-decaying, fast-decaying exponential components and artifact components from mGRE images. After the separation, MWF map is reconstructed as the ratio of the fast-decayingcomponent to the total decaying components. The proposed method was demonstrated in numerical simulations and in vivo scans. The method provided a robust estimation of MWF in the presence of statistical noise and imaging artifacts.

Improved estimation of myelin water fractions with learned parameter distributions

“…Interestingly, we also observe that with practical modeling errors the c3e model becomes a lot less robust than the m3e. Because their main difference is whether to model the signal phases, our result implies that the c3e is very sensitive to practical phase errors, consistent with previous studies 16,40 …”

“…For example, the multi‐exponential model was analyzed using numerical simulations under a wide range of noise levels and found to require very high SNR to produce reliable results 12‐14 . Similarly, 3‐exponential models were also found to be rather sensitive to noise, using simulated data with different SNRs and parameter values 15,16 . To address this issue, several methods have been developed to denoise the measured data before parameter estimation by imposing low‐rank constraints 17,18 or sparsity constraints 18 .…”

“…The most widely used models include the multi‐exponential model, 1 which expresses the magnitude signal as a linear combination of preselected or basis functions; the magnitude‐3‐exponential model, 6 which decomposes the magnitude signal into 3 real exponentials; and the complex‐3‐exponential model, 7,8 which decomposes the complex‐valued signal into 3 complex exponentials. However, the exponential model fitting problem is known to be ill‐conditioned, and the fitting results are often highly sensitive to data noise and modeling errors 8‐16 …”

“…However, the exponential model fitting problem is known to be ill-conditioned, and the fitting results are often highly sensitive to data noise and modeling errors. [8][9][10][11][12][13][14][15][16] Several efforts have been made to characterize the effect of measurement noise on MWF estimation. For example, the multi-exponential model was analyzed using numerical simulations under a wide range of noise levels and found to require very high SNR to produce reliable results.…”

Variable flip angle echo planar time-resolved imaging (vFA-EPTI) for fast high-resolution gradient echo myelin water imaging

“…In this study, an extended complex GRE-MWI model with T 1 correction was used as an example of the application of vFA-EPTI for multi-compartment analysis. The proposed acquisition can also be applied to other GRE-MWI models ( Nam et al, 2015b ; Song et al, 2020 ; van Gelderen et al, 2012 ), and to single-pool quantitative mapping as we have shown in Fig. 9 and 10 .…”