Use of marginal distributions constrained optimization (MADCO) for accelerated 2D MRI relaxometry and diffusometry

Area of Science:

• Magnetic Resonance Imaging (MRI)
• Nuclear Magnetic Resonance (NMR)
• Porous Media Physics
• Biomedical Imaging

Background:

• Multidimensional relaxation spectra are crucial for NMR and MRI in porous media and biomedical fields.
• Reconstructing these spectra is challenging due to ill-posed Fredholm integral inversion, requiring extensive data.
• Current methods struggle with stability and data demands for accurate 2D spectral analysis.

Purpose of the Study:

• To develop and validate a novel framework for accelerating and enhancing the reconstruction of multidimensional relaxation spectra.
• To introduce a method that leverages 1D spectral projections (marginal distributions) as constraints for improved 2D spectral reconstruction.
• To demonstrate the feasibility of this approach for preclinical and clinical applications.

Main Methods:

• Proposed a novel experimental design and processing framework utilizing a priori information from 1D spectral projections.
• Developed the Marginal Distributions Constrained Optimization (MADCO) methodology.
• Validated the approach using a polyvinylpyrrolidone-water phantom with known 2D D-T1 spectral features and synthetic T1-T2 data.

Main Results:

• The MADCO method significantly improved the accuracy and robustness of 2D spectral reconstruction compared to conventional unconstrained methods.
• The new approach required an order of magnitude less data for accurate estimation of 1D marginal distributions.
• Demonstrated high accuracy and robustness even with subsampled data and in the presence of noise.

Conclusions:

• The MADCO framework offers a substantial advancement in reconstructing multidimensional NMR/MRI relaxation spectra.
• This method overcomes key limitations of existing techniques, enabling more efficient and accurate spectral analysis.
• The generalizability of the framework suggests potential for widespread application in diverse 2D MRI experiments for clinical and preclinical settings.