Multi-exponential Transverse Relaxation Times Estimation from Magnetic Resonance Images under Rician Noise and Spatial Regularization

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.

Quantitative MRI post-processing algorithm and visualization research based on moisture status detection of winter jujube

Quantitative Magnetic Resonance Imaging (qMRI) offers precise measurements of the relaxation characteristics of microstructures, representing a cutting-edge method in non-destructive fruit analysis. This study aims to visualize information on changes in moisture status and distribution at the subcellular level of winter jujube. The 0.5 T nuclear magnetic imaging equipment was utilized to rapidly, non-invasively, and accurately capture the internal relaxation status of the sample with multiple-echo-imaging. By examining the signal and noise data, a simulated dataset was developed to tackle the optimization challenge of estimating parameters for the discrete relaxation model from the multiple-echo-imaging data, especially under conditions of low signal-to-noise ratio (SNR) and in the context of heteroscedastic noise. An optimal weighting factor and the T2NR truncation model have been identified to establish an effective experimental inversion strategy. Subsequently, multiple-echo-imaging can rapidly and stably yielded voxel-level maps under conditions of low signal-to-noise ratio. Utilizing this experimental approach, data from winter jujube was collected and analyzed, facilitating an exploration of water activity (T2 mapping) and associated water content (A2 mapping). Through analyzing winter jujube fruits across two maturity stages, this study elucidates the role of precise quantification and voxel-wise visualization in moisture status detection. The methodology presents an innovative approach for assessing internal moisture distribution in fruits.

Combining variational mode decomposition with regularisation techniques to denoise MRI data

In this paper, we propose a novel method for removing noise from MRI data by exploiting regularisation techniques combined with variational mode decomposition. Variational mode decomposition is a new decomposition technique for sparse decomposition of a 1D or 2D signal into a set of modes. In turn, regularisation is a method that can translate the ill-posed problem (e.g., image denoising) into a well-posed problem. The proposed method aims to remove the noise from the image in two steps. In the first step, the MR imaging data are decomposed by the 2D variational mode decomposition algorithm. In the second step, for effective suppression of Rician noise from MRI data, we used the fused lasso signal approximator with all modes acquired from the medical scan. The performance of the proposed approach was compared with state-of-the-art reference methods based on different metrics, that is, the peak signal-to-noise ratio, the structural similarity index metrics, the high-frequency error norm, the quality index based on local variance, and the sharpness index. The experiments were performed on the basis of both simulated and real images. The presented results prove the high denoising performance of the proposed algorithm; particularly under heavy noise conditions.

Improved myelin water fraction mapping with deep neural networks using synthetically generated 3D data

We introduce a generative model for synthesis of large scale 3D datasets for quantitative parameter mapping of myelin water fraction (MWF). Our model combines a MR physics signal decay model with an accurate probabilistic multi-component parametric T2 model. We synthetically generate a wide variety of high quality signals and corresponding parameters from a wide range of naturally occurring prior parameter values. To capture spatial variation, the generative signal decay model is combined with a generative spatial model conditioned on generic tissue segmentations. Synthesized 3D datasets can be used to train any convolutional neural network (CNN) based architecture for MWF estimation. Our source code is available at: https://github.com/quin-med-harvard-edu/synthmap Reduction of acquisition time at the expense of lower SNR, as well as accuracy and repeatability of MWF estimation techniques, are key factors that affect the adoption of MWF mapping in clinical practice. We demonstrate that the synthetically trained CNN provides superior accuracy over the competing methods under the constraints of naturally occurring noise levels as well as on the synthetically generated images at low SNR levels. Normalized root mean squared error (nRMSE) is less than 7% on synthetic data, which is significantly lower than competing methods. Additionally, the proposed method yields a coefficient of variation (CoV) that is at least 4x better than the competing method on intra-session test-retest reference dataset.

Characterization of Potato Tuber Tissues Using Spatialized MRI T2 Relaxometry

Magnetic Resonance Imaging is a powerful non-destructive tool in the study of plant tissues. For potato tubers, it greatly assists the study of tissue defects and tissue evolution during storage. This paper describes the MRI analysis of potato tubers with internal defects in their flesh tissue at eight sampling dates from 14 to 33 weeks after harvest. Spatialized multi-exponential T2 relaxometry was used to generate bi-exponential T2 maps, coupled with a classification scheme to identify the different T2 homogeneous zones within the tubers. Six classes with statistically different relaxation parameters were identified at each sampling date, allowing the defects and the pith and cortex tissues to be detected. A further distinction could be made between three constitutive elements within the flesh, revealing the heterogeneity of this particular tissue. Relaxation parameters for each class and their evolution during storage were successfully analyzed. The work demonstrated the value of MRI for detailed non-invasive plant tissue characterization.

Gradient-Based Pulsed Excitation and Relaxation Encoding in Magnetic Particle Imaging

Magnetic particle imaging (MPI) is a radiation-free vessel- and target-imaging modality that can sensitively detect nanoparticles. A static magnetic gradient field, referred to as a selection field, is required in MPI to provide a field-free region (FFR) for spatial encoding. The image resolution of MPI is closely related to the size of the FFR, which is determined by the selection field gradient amplitude. Because of the limitations of existing gradient coil hardware, the image resolution of MPI cannot satisfy the clinical requirements of human in vivo imaging. Pulsed excitation has been confirmed to improve the image resolution of MPI by breaking down the 'relaxation wall.' This work proposes the use of a pulsed waveform magnetic gradient from magnetic resonance imaging to further improve the image resolution of MPI. Through alignment of the gradient direction along the field-free line (FFL), each location on the FFL is able to have a unique excitation field strength that generates a specific relaxation-induced decay signal. Through excitation of nanoparticles on the FFL with many gradient profiles, a high-resolution, one-dimensional (1D) image can be reconstructed on the FFL. For larger magnetic nanoparticles, simulation results revealed that a pulsed excitation field with a greater flat portion generates a 1D bar pattern phantom image with a higher correlation and spatial resolution. With parallel FFL and gradient coil movements, high-resolution, two-dimensional (2D) Shepp-Logan phantom and brain vessel maps were reconstructed through repetition of the spatially resolved measurement of magnetic nanoparticles on the FFL.

Quantitative MRI analysis of structural changes in tomato tissues resulting from dehydration

A quantitative magnetic resonance imaging (MRI) analysis at 1.5T of the effects of different dehydration regimes on transverse relaxation parameters measured in tomato tissue is presented. Multi-exponential T₂ maps have been estimated for the first time, providing access to spatialized microstructural information at voxel scale. The objective was to provide a better understanding of the changes in the multi-exponential transverse relaxation parameters induced by dehydration in tomato tissues and to unravel the effects of microstructure and composition on relaxation parameters. The results led to the hypothesis that the multi-exponential relaxation signal reflects cell compartmentation and tissue heterogeneity, even at the voxel scale. Multi-exponential relaxation times provided information about water loss from specific cell compartments and seem to indicate that the dehydration process mainly affects large cells. By contrast, total signal intensity showed no sensitivity to variations in water content in the range investigated in the present study (between 95% [fresh tissue] and 90% [after dehydration]). The variation in relaxation times resulting from water loss was due to both changes in solute concentration and compartment size. The comparative analysis of the two contrasted tissues in terms of microporosity demonstrated that magnetic susceptibility effects, caused by the presence of air in the placenta tissue, significantly impact the effective relaxation and might be the dominant effect in the variations observed in relaxation times in this tissue.

Multi-exponential MRI T2 maps: A tool to classify and characterize fruit tissues

The estimation of multi-exponential relaxation time T₂ and their associated amplitudes A₀ at the voxel level has been made possible by recent developments in the field of image processing. These data are of great interest for the characterization of biological tissues, such as fruit tissues. However, they represent a high number of information, not easily interpretable. Moreover, the non-uniformity of the MRI images, which mainly directly impacts A₀, could induce interpretation errors. In this paper, we propose a post-processing scheme that clusters similar voxels according to the multi-exponential relaxation parameters in order to reduce the complexity of the information while avoiding the problems associated with intensity non-uniformity. We also suggest a data representation suitable for the visualization of the multi-T₂ distribution within each tissue. We illustrate this work with results for different fruits, demonstrating the great potential of multi-T₂ information to shed new light on fruit characterization.