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Myelin Mapping in the Human Brain Using an Empirical Extension of the Ridge Regression Theorem.

Griffin S Hampton, Ryan Neff, Zezheng Song

Biorxiv : the Preprint Server for Biology

|July 14, 2025

Summary

We developed a nonlinear ridge regression (λ -NL-RR) method to improve myelin water fraction (MWF) mapping. This technique enhances parameter estimation accuracy for biexponential signals in MRI, reducing mean square error (MSE).

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Area of Science:

Magnetic Resonance Imaging (MRI)
Biomedical Engineering
Neuroimaging

Background:

Myelin water fraction (MWF) mapping is crucial for central nervous system research.
Estimating parameters from biexponential signals in MWF mapping is often an ill-posed nonlinear problem.
Conventional nonlinear least-squares (NLLS) methods can yield unreliable parameter estimates.

Purpose of the Study:

To present and apply a nonlinear version of the ridge regression theorem (λ -NL-RR) for MWF mapping.
To address the ill-posed nature of parameter estimation in biexponential signal analysis.
To improve the reliability and accuracy of MWF parameter estimates.

Main Methods:

Developed and applied a nonlinear ridge regression (λ -NL-RR) method.
Used generalized cross-validation to define the regularization parameter.
Applied regularization selectively to biexponential signals identified by the Bayesian information criterion.

Main Results:

λ -NL-RR decreased mean square error (MSE) by approximately 10-15% compared to conventional NLLS.
Improvements were most significant under conditions of modest signal-to-noise ratio (SNR) and closely spaced time constants.
Demonstrated effectiveness on both simulated and in vivo MRI brain data.

Conclusions:

Regularization of NLLS parameter estimation for the biexponential model effectively reduces MSE in MWF mapping.
The λ -NL-RR method offers improved accuracy for simulated and in vivo MRI data.
This work provides a generalizable framework for regularizing a wide range of NLLS problems.