Combined diffusion-relaxometry microstructure imaging: Current status and future prospects

Abstract

Microstructure imaging seeks to noninvasively measure and map microscopic tissue features by pairing mathematical modeling with tailored MRI protocols. This article reviews an emerging paradigm that has the potential to provide a more detailed assessment of tissue microstructure-combined diffusion-relaxometry imaging. Combined diffusion-relaxometry acquisitions vary multiple MR contrast encodings-such as b-value, gradient direction, inversion time, and echo time-in a multidimensional acquisition space. When paired with suitable analysis techniques, this enables quantification of correlations and coupling between multiple MR parameters-such as diffusivity, $T_1$ , $T_2$ , and $T_2^{\ast }$ . This opens the possibility of disentangling multiple tissue compartments (within voxels) that are indistinguishable with single-contrast scans, enabling a new generation of microstructural maps with improved biological sensitivity and specificity.

Keywords: diffusion; multidimensional MRI; quantitative MRI; relaxometry.

FIGURE 1

The parameter space relevant for combined diffusion‐relaxometry experiments. Diffusion parameters, for example, b‐value and gradient direction, are represented on the x‐axis. The echo times (TE) are on the y‐axis, and the inversion times (TI) on the z‐axis. The green dots represent a conventional diffusion acquisition at fixed TE with multiple diffusion preparations. The red dots illustrate a scan sampling several TEs without diffusion weighting to achieve ${\mathrm{T}}_2$/${\mathrm{T}}_2^{\ast }$ maps. The blue dots illustrate a scan sampling multiple TIs without diffusion weighting to achieve ${\mathrm{T}}_1$ maps. The transparent cyan, yellow and magenta planes depict the acquisition parameter space sampled in hypothethical ${\mathrm{T}}_1$‐diffusion, ${\mathrm{T}}_2$‐diffusion (equivalently ${\mathrm{T}}_2^{\ast }$‐diffusion), and T1‐T2 experiments, respectively

FIGURE 2

Separate diffusion and relaxation experiments can confound distinct tissue microenvironments. A,B, display simplified tissue structures comprising two and three distinct microenvironments, respectively. Each point denotes a distinct microenvironment with fixed ${\mathrm{T}}_2$, diffusivity values, and a percentage volume fraction. The projected ${\mathrm{T}}_2$ and diffusivity distributions are shown on the top and right‐hand sides. The 1D distributions are equivalent for both (A) and (B) despite the different tissue structures, showing that 1D measurements can confound distinct tissue microenvironments. Combined diffusion‐relaxometry can disentangle the contributions from the distinct microenvironments due to its ability to quantify correlations between multiple contrasts

FIGURE 3

Standard pulsed gradient spin echo (PGSE) ssEPI dMRI acquisition. From top down the pulse diagram shows: the excitation and refocusing RF pulses, a standard diffusion preparation in all three directions alongside the EPI read‐out train, and the ${\mathrm{T}}_2$ and ${\mathrm{T}}_2^{\ast }$ decay occurring during the spin echo acquisition. A whole dMRI scan comprises multiple repeats of these PGSE ssEPI blocks, one for each slice and each diffusion preparation used. The repetition time TR is defined as the time required to sample each slice in one stack. $T_{\mathit{RO}}$ denotes the readout time, $G_{max}$ the available gradient strength, $\delta$ the length of the gradient lobe, and $\mathrm{\Delta }$ the separation of the gradient pulses

FIGURE 4

Example ${\mathrm{T}}_2$‐diffusion acquisitions with three existing techniques. Each color represents a distinct excitation of length TR. A, The consecutive approach: repeat diffusion‐prepared scans with different TEs (illustrative acquisition time: 50 TRs). B, Simultaneous approach: applying techniques allowing multiple samples in the parameter space within the same excitation of length TR (illustrative acquisition time: 10 TRs). C, MADCO approach: Fully sampled 1D data are augmented with sparsely sampled multidimensional data (illustrative acquisition time: 23 TRs). While we only show 2D ${\mathrm{T}}_2$‐diffusion (or ${\mathrm{T}}_2^{\ast }$‐diffusion) experiments for convenience, the same principles apply when extending these techniques to 3D and higher

FIGURE 5

Illustration of separate vs integrated acquisition strategies using the example of multiple diffusion‐encoded scans with varying TE, that is, ${\mathrm{T}}_2$‐diffusion. A,B, show separate acquisitions at different TEs, together with the included dead time and change in diffusion preparation. Acquiring (A) and (B) to sample the 2D space is a basic ‘consecutive’ acquisition. Integrated multi‐echo acquisitions are shown in (C) for spin echoes, hence acquiring combined diffusion‐relaxometry data ‘simultaneously’

FIGURE 6

Illustration of several alternatives to the conventional PGSE acquisition. A, Replacing the bipolar gradient pair by free waveforms used for q‐space sampling. B, Addition of a global inversion pulse to achieve a set inversion time TI. C, STEAM acquisition including and depicting the mixing time, introducing ${\mathrm{T}}_1$ sensitivity and changing the diffusion time

FIGURE 7

Illustration of estimating 2D diffusion‐relaxation correlation spectra using different kinds of constraints. A, Simulated ground truth spectrum from a single voxel, comprised of three spectral peaks with Gaussian lineshapes. (The simulation is identical to that described in previous work, and we omit the details). B, Simulated noisy combined diffusion‐relaxometry data from one voxel (following, the SNR for the highest‐SNR image was 200). C‐J, Reconstruction results using different kinds of constraints: C, MNLS; D, nonnegative least‐squares using Equation (4); E‐H, regularized solutions using Equation (5), including (E) voxelwise Tikhonov regularization (H is an identity matrix), (F) voxelwise Tikhonov regularization (H computes a finite‐difference approximation of second‐derivatives along the vertical and horizontal dimensions of the spectrum), (G) voxelwise L1‐norm regularization (H is an identity matrix), and (H) spatially regularized reconstruction (assuming the spatial distribution described in previous work ¹⁰⁰ ). We also show fits obtained using Equation (1) with known M and the parametric model from Equation (2) for each component: (I) $M=3$ and (J) $M=4$. Note that these spectra can look very different from one another even though they are all similarly consistent with the measured data (less than 0.4% data error in all cases). This reflects the severe ill‐posedness of the problem and the need to choose constraints carefully. As can be seen, the MNLS reconstruction completely fails to capture the true structure of the data, while the remaining constrained reconstructions have varying levels of correspondence with the ground truth spectrum. Note that it is very hard for any of these methods to estimate the lineshapes of the spectral peaks accurately (some have much sharper peaks while others have much broader peaks), and that aside from (H), the rest of the reconstructions have spectral peaks in the wrong locations and potentially incorrect spectral peak integrals. Despite these mismatches with the ground truth, many of these estimation methods have been shown to produce consistent spectral decompositions of real data that can serve as useful biomarkers for different microstructural characteristics

FIGURE 8

Examples of combined diffusion‐relaxometry in brain and spinal cord applications. A, ${\mathrm{T}}_1$‐diffusion—direction encoded color map ${\mathrm{T}}_1$ maps of tissue in a fiber crossing phantom from Ref. [125]. B, ${\mathrm{T}}_2$‐diffusion—TE‐dependent diffusion imaging (TEdDI) maps for in vivo brain from Ref. [26]. Top row: intra‐ and extra‐axonal ${\mathrm{T}}_2$, and mean ${\mathrm{T}}_2$; bottom row: diffusivity parameters. C, ${\mathrm{T}}_2$‐diffusion—Multi‐TE NODDI parameter maps for in vivo brain from Ref. [29]. Parameters from left to right are: intraneurite fraction, free water volume fraction, and intra‐ and extra‐neurite ${\mathrm{T}}_2$ values. D, ${\mathrm{T}}_2$‐diffusion with b‐tensor encoding—5D diffusion‐relaxation distribution for a selected voxel of in vivo brain scan from Ref. [161]. E, ${\mathrm{T}}_2$‐diffusion—spatially averaged ${\mathrm{T}}_2$‐D distributions and spectral volume fraction maps in control and injured spinal cord samples from Ref. [100]. F, ${\mathrm{T}}_1$‐ ${\mathrm{T}}_2$‐diffusion—spectral signature of microscopic lesions in the human corpus callosum (top: injured, bottom: control). Right panel shows corresponding injury biomarker images, side‐by‐side with histology. Subfigures A, C, and D are reproduced under Creative Commons licenses; subfigures B, E, and F are used with permission

FIGURE 9

Examples of combined diffusion‐relaxometry in the prostate. A, ${\mathrm{T}}_2$‐diffusion—MR‐derived parameter maps and predicted cancer map, and corresponding histologic maps for prostate with Gleason 3+3 cancers. B, ${\mathrm{T}}_2$‐diffusion with varying diffusion time—parameter maps for healthy prostate from [74]. C, ${\mathrm{T}}_2$‐diffusion—and corresponding histology for prostate with Gleason 4+3 cancer from [181]. Subfigures A and C are used with permission, and subfigure B under a Creative Commons license

FIGURE 10

Examples of combined diffusion‐relaxometry in the placenta. A, ${\mathrm{T}}_2$‐diffusion—parameter maps from DECIDE model fit on healthy placenta. B, ${\mathrm{T}}_2^{\ast }$‐diffusion—spatially averaged ${\mathrm{T}}_2^{\ast }$‐D spectra and spectral volume fraction maps in healthy and pre‐eclamptic placentas. Both subfigures are used under a Creative Commons license