Diffusion-Relaxation Correlation Spectroscopic Imaging (DR-CSI): An Enhanced Approach to Imaging Microstructure

Daeun Kim^{1}, Joong Hee Kim^{2}, and Justin P Haldar^{1}

MR relaxometry and diffusion imaging have each been proposed as methods that can probe microscopic tissue compartments using standard millimeter-scale spatial resolution. For example, relaxometry can be used to estimate the amount of myelin content within a voxel [1,2], while diffusion imaging can be used to quantify the neurite density, the size of the extracellular space, and the presence of edema [3-5]. However, both of these modalities are subject to ambiguities and confounds whenever the diffusion or relaxation parameters of two distinct tissue microenvironments are too similar to one another.

Diffusion-relaxation correlation spectroscopy (DR-COSY) is a (single-voxel, non-imaging) 2D spectroscopic method that encodes diffusion and relaxation parameters jointly, and substantially improves the ability to distinguish different tissue compartments [6-9]. This work proposes and evaluates a novel imaging extension of DR-COSY, which we name diffusion-relaxation correlation spectroscopic imaging (DR-CSI). Enabled by regularization strategies that help to overcome the ill-posedness of the problem, DR-CSI provides a 2D spectrum of information for every voxel. The peaks of this 2D spectrum can be integrated and displayed as spatial maps of the different tissue microcompartments as they vary across the field-of-view. The potential usefulness of DR-CSI is illustrated using ex vivo mouse spinal cord traumatic injury data.

**Diffusion-relaxation
data acquisition:** We acquired 28 different simultaneously diffusion-
and relaxation-encoded images.
Specifically, we acquired 7 different b-values (b = 0, 500, 1000, 2000,
3000, 4000 and 5000 s/mm2), and measured data at 4 different echo
times for each b-value (TE = 40, 80, 120 and 160 ms). We acquired six ex vivo mice spinal cord data sets (three sham controls and three
with traumatic spinal cord injury as described in [10]).

**Diffusion-T2
correlation spectral analysis:** We modeled the measured DR-CSI signal as a mixture
of 2D exponential decays: $$M(x,y,b,TE) =\int \int F(x,y,D,T_{2})~e^{-bD}e^{-\frac{TE}{T_{2}}}~dD~dT_{2}, $$ where $$$M(x,y,b,TE)$$$ is the measured data at spatial position $$$(x,y)$$$, diffusion encoding $$$b$$$, and echo time $$$TE$$$, and $$$F(x,y,D,T_{2})$$$ is the
spatially-varying diffusion-relaxation correlation spectrum as a function of
the diffusion coefficient $$$D$$$ and relaxation parameter $$$T_{2}$$$. Conventionally,
2D inverse Laplace transforms have been used to estimate 2D DR-COSY spectra [11]. However, these approaches typically require a
larger number of diffusion-relaxation encodings and higher SNR, which is only
practical with the large voxel sizes that are common in spectroscopic
applications. To enable DR-CSI with a
smaller number of encodings and lower SNR, we performed regularized 2D spectrum
estimation using the prior information that $$$F(x,y,D,T_{2})$$$ is nonnegative and will exhibit smooth spatial variation. Based on these assumptions, $$$F(x,y,D,T_{2})$$$ was estimated by solving a dictionary-based spatially-regularized
nonnegative least squares optimization problem.
To reduce computational
complexity for this high-dimensional optimization problem, we designed an
efficient reconstruction algorithm based on variable splitting and the
alternating direction method of multipliers [12].

Figure 1 shows spatially-averaged DR-CSI spectra for control and injured spinal cords. The control spectrum has two distinct well-resolved peaks, as well as a third weaker peak in between. In contrast, the spectrum for the injured cord contains an additional peak that was not present in the control spectrum. Importantly, these distinct peaks are only well-resolved in the 2D spectra, while there is considerable ambiguity in the 1D diffusion-only and relaxation-only spectra which resolve substantially fewer peaks.

Figure 2 shows spatial maps of the integrated spectral peaks from Fig. 1. This figure shows that the estimated peaks from Fig. 1 seem to correspond to tissue microenvironments that are consistent with the known anatomy of the spinal cord. Specifically, one of the peaks appears to correspond to white matter (WM), one appears to correspond to ventral gray matter (VGM), one appears to be present in both the dorsal gray matter and the white matter to a lesser degree (DGM), and one seems specific to the injured cords (injury). It should be noted that these spatial maps have considerable spatial overlap, demonstrating that DR-CSI can successfully disentangle partial volume contributions from multiple tissue compartments within the same voxel. This is illustrated even further in Fig. 3, which shows spatially-varying spectra from the WM-GM boundary, as the tissue transitions between WM and VGM.

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Fig.1. DR-CSI-based 2D spectra obtained from (a)
control and (b) injured spinal cords, averaged across all voxels. We also show projected 1D relaxation-only
spectra and 1D diffusion-only spectra along the top and right sides of each 2D
spectrum. Importantly each 2D spectrum
resolves more distinct peaks (corresponding to distinct tissue
microenvironments) than are resolved in the 1D spectra.

Fig.2. Spatial maps of the integrated spectral peaks from the DR-CSI
reconstruction of (top) control and (bottom) injured spinal cords. The spectral regions that were integrated to
obtain each spatial map are indicated in the 2D diffusion-relation correlation
spectra from Fig. 1.

Fig.3. Spatially-varying DR-CSI spectra from the boundary between WM and
VGM in the control cord, corresponding to the black box drawn on the anatomical
image in Fig. 2. DR-CSI successfully
disentangles partial volume effects in the transition region between the two
tissues.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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