A Tutorial Introduction to Inverse Problems in Magnetic Resonance

Simple MATLAB and Python scripts for multi-exponential analysis

Multi-exponential decay is prevalent in magnetic resonance spectroscopy, relaxation, and imaging. This paper describes simple MATLAB and Python functions and scripts for regularized multi-exponential analysis methods for 1D and 2D data and example test problems and experiments. Regularized least-squares solutions provide production-quality outputs with robust stopping rules in ~5 and ~20 lines of code for 1D and 2D inversions, respectively. The software provides an open-architecture simple solution for transforming exponential decay data to the distribution of their decay lifetimes. Examples from magnetic resonance relaxation of a complex fluid, a Danish North Sea crude oil, and fluid mixtures in porous materials-brine/crude oil mixture in North Sea reservoir chalk-are presented. Developed codes may be incorporated in other software or directly used by other researchers, in magnetic resonance relaxation, diffusion, and imaging or other physical phenomena that require multi-exponential analysis.

Scanning ex situ solid-state magnetic resonance imaging on polymeric films using a static magnetic field gradient by an electromagnet

A new technique for ex situ solid-state nuclear magnetic resonance imaging of polymeric films has been developed. This method uses the static magnetic field gradient generated by a water-cooled copper electromagnet. The imaging process involves scanning the sample in the plane of the film under a static magnetic field gradient. Two-dimensional (2D) 19F MRI measurements are attempted, where the fast Fourier transform (FFT) spectra of the second half of a Hahn echo peak is used for the depth (X-axis) direction, and the sample film is mechanically moved for the Y-axis, which is in-plane with respect to the film surface and normal to the inter-magnetic-pole line (Z-axis). The sample is a poly(tetrafluoroethylene) [PTFE] film with carved stripes on its surface. Furthermore, three-dimensional (3D) measurements of the film surface and thickness orientations were also performed for an analogous PTFE film. For 2D profiling on the film surface, 2D sample-moving was used. For depth profiling, FFT spectrum analysis was undertaken for each voxel situated at a specific (Y, Z) coordinate within the film. As a result, a 3D image of the sample and its corresponding geometry were obtained, although the scanning area was restricted to a part of the sample. Finally, numerical simulations of the spatial distribution of the static magnetic field were performed to confirm the validity of the present method.

Lower Myelin Content Is Associated With Lower Gait Speed in Cognitively Unimpaired Adults

Mounting evidence indicates that abnormal gait speed predicts the progression of neurodegenerative diseases, including Alzheimer's disease. Understanding the relationship between white matter integrity, especially myelination, and motor function is crucial to the diagnosis and treatment of neurodegenerative diseases. We recruited 118 cognitively unimpaired adults across an extended age range of 22-94 years to examine associations between rapid or usual gait speeds and cerebral myelin content. Using our advanced multicomponent magnetic resonance relaxometry method, we measured myelin water fraction (MWF), a direct measure of myelin content, as well as longitudinal and transverse relaxation rates (R1 and R2), sensitive but nonspecific magnetic resonance imaging measures of myelin content. After adjusting for covariates and excluding 22 data sets due to cognitive impairments or artifacts, our results indicate that participants with higher rapid gait speed exhibited higher MWF, R1, and R2 values, that is, higher myelin content. These associations were statistically significant within several white matter brain regions, particularly the frontal and parietal lobes, splenium, anterior corona radiata, and superior fronto-occipital and longitudinal fasciculus. In contrast, we did not find any significant associations between usual gait speed and MWF, R1, or R2, which suggests that rapid gait speed may be a more sensitive marker of demyelination than usual gait speed. These findings advance our understanding on the implication of myelination in gait impairment among cognitively unimpaired adults, providing further evidence of the interconnection between white matter integrity and motor function.

Lower myelin content is associated with more rapid cognitive decline among cognitively unimpaired individuals

INTRODUCTION

The influence of myelination on longitudinal changes in cognitive performance remains unclear.

METHODS

For each participant (N = 123), longitudinal cognitive scores were calculated. Myelin content was probed using myelin water fraction (MWF) or longitudinal relaxation rate (R1 ); both are MRI measures sensitive to myelin, with MWF being specific.

RESULTS

Lower MWF was associated with steeper declines in executive function (p < .02 in all regions) and lower R1 was associated with steeper declines in verbal fluency (p < .03 in all regions). Additionally, lower R1 was associated with steeper declines in executive function (p < .02 in all regions) and memory (p < .04 in occipital and cerebral white matter) but did not survive Bonferroni correction.

DISCUSSION

We demonstrate significant relationships between myelin content and the rates of change in cognitive performance among cognitively normal individuals. These findings highlight the importance of myelin in cognitive functioning and suggest MWF and R1 as imaging biomarkers to predict cognitive changes.

Stabilization of parameter estimates from multiexponential decay through extension into higher dimensions

Analysis of multiexponential decay has remained a topic of active research for over 200 years. This attests to the widespread importance of this problem and to the profound difficulties in characterizing the underlying monoexponential decays. Here, we demonstrate the fundamental improvement in stability and conditioning of this classic problem through extension to a second dimension; we present statistical analysis, Monte-Carlo simulations, and experimental magnetic resonance relaxometry data to support this remarkable fact. Our results are readily generalizable to higher dimensions and provide a potential means of circumventing conventional limits on multiexponential parameter estimation.

PCA denoising and Wiener deconvolution of 31 P 3D CSI data to enhance effective SNR and improve point spread function

Purpose

This study evaluates the performance of 2 processing methods, that is, principal component analysis‐based denoising and Wiener deconvolution, to enhance the quality of phosphorus 3D chemical shift imaging data.

Methods

Principal component analysis‐based denoising increases the SNR while maintaining spectral information. Wiener deconvolution reduces the FWHM of the voxel point spread function, which is increased by Hamming filtering or Hamming‐weighted acquisition. The proposed methods are evaluated using simulated and in vivo 3D phosphorus chemical shift imaging data by 1) visual inspection of the spatial signal distribution; 2) SNR calculation of the PCr peak; and 3) fitting of metabolite basis functions.

Results

With the optimal order of processing steps, we show that the effective SNR of in vivo phosphorus 3D chemical shift imaging data can be increased. In simulations, we show we can preserve phosphorus‐containing metabolite peaks that had an SNR < 1 before denoising. Furthermore, using Wiener deconvolution, we were able to reduce the FWHM of the voxel point spread function with only partially reintroducing Gibb‐ringing artifacts while maintaining the SNR. After data processing, fitting of the phosphorus‐containing metabolite signals improved.

Conclusion

In this study, we have shown that principal component analysis‐based denoising in combination with regularized Wiener deconvolution allows increasing the effective spectral SNR of in vivo phosphorus 3D chemical shift imaging data, with reduction of the FWHM of the voxel point spread function. Processing increased the effective SNR by at least threefold compared to Hamming weighted acquired data and minimized voxel bleeding. With these methods, fitting of metabolite amplitudes became more robust with decreased fitting residuals.