Sohae Chung1,2, Dmitry S. Novikov1,2, Pippa Storey1,2, and Yvonne W. Lui1,2
1Center for Advanced Imaging Innovation and Research (CAI2R), Department of Radiology, New York University Grossman School of Medicine, New York, NY, United States, 2Bernard and Irene Schwartz Center for Biomedical Imaging, New York University Grossman School of Medicine, New York, NY, United States
Synopsis
Identification and quantification of imaging biomarkers
sensitive to iron are important in understanding neurodegenerative disorders and
aging. In this study, we introduce a microstructural parameter, $$$\delta\Omega^{2}$$$, the Larmor frequency
variance, measured from the curvature in the logarithm of the signal from a 3D
multiecho gradient echo sequence. Non-monoexponential relaxation originates
from magnetic field perturbations due to the presence of mesoscopic susceptibility
sources such as cellular-level iron. Our results in 26 healthy subjects show a
strong linear correlation between $$$\delta\Omega^{2}$$$ and published values for iron concentration in
deep gray matter regions, suggesting its potential as an imaging biomarker for
iron.
INTRODUCTION
Altered
brain iron is associated with a number of neurodegenerative diseases.1,2
However, characterizing cellular-level iron in vivo is a challenge. Mesoscopic
sources such as iron clusters are primarily responsible for the magnetic field
perturbations that give rise to non-monoexponential transverse relaxation.3,4
Previous work with microbead phantoms has demonstrated that the mesoscopic
contribution to transverse relaxation can be measured using a 3D multiecho
gradient echo (MGRE) sequence.5 Here we measure $$$\delta\Omega^{2}$$$, the Larmor frequency variance, in deep gray
matter nuclei of the normal human brain, including the globus pallidum (GP),
putamen (Pt), caudate (Cd) and thalamus (Th). We correlate the results with reference
values for non-heme iron in normal brain, obtained from histology.THEORY
In the
weak field limit (the Gaussian phase approximation), the MGRE signal is
expressed as a truncated cumulant expansion: $$$\ln S(t) ≈ \ln
S_{0}-R_{2}t-\frac{1}{2}\langle \varphi^{2}(t) \rangle$$$, where the
mesoscopic
contribution to the phase
$$$\varphi(t)=\int_{0}^{t}dt'\Omega(t')$$$
equals
the integral of the local Larmor frequency
$$$\Omega(t) ≡ \Omega(x(t))$$$
experienced
by each spin along its Brownian path
$$$x(t)$$$.4
Assuming
a Gaussian form for the spatial correlation function,
$$$\langle \Omega(x) \Omega(0) \rangle = \delta \Omega^{2} \cdot e^{-x^{2}/l_{c}^{2}}$$$,
the
phase variance can be calculated by averaging over all Brownian paths. This
yields:
$$ \ln S(t) = \ln S_{0}-R_{2}t-2\alpha^{2}(\frac{t}{t_{c}}-2\sqrt{1+\frac{t}{t_{c}}}+2), [1]$$
where $$$\alpha=\delta\Omega \cdot t_{c}$$$, and $$$t_{c}=l_{c}^{2}/D$$$
is the
correlation time to diffuse over a distance equal to the correlation length
$$$l_{c}$$$ of the mesoscopic field $$$\Omega(x)$$$.4
In the
static dephasing regime $$$t « t_{c}$$$,
the
Gaussian phase approximation depends only on the variance of the Larmor
frequency
$$$\delta\Omega^{2}=\langle \Omega(x)^{2} \rangle$$$,
and
the logarithm of the signal varies quadratically with time,
$$$\ln S(t) ≈ \ln S_{0}-R_{2}t-\frac{1}{2}\delta\Omega^{2}·t^{2}$$$.
The curvature
of
$$$\ln S(t)$$$
is a signature
of heterogeneity in
$$$\Omega(x)$$$
within
a voxel. In the opposite, long-time limit
$$$t»t_{c}$$$, the decay of $$$\ln S(t)$$$ is asymptotically linear, $$$\ln S(t) ≈ \ln S_{0}-(R_{2}+2\alpha^{2}/t_{c})t$$$.
METHOD
We
studied 26 normal subjects (age, 37 ± 12, range 23 - 65 years; 9 male). MR imaging was
performed at 3T (Skyra or Prisma, Siemens) using a 3D MGRE sequence with the
following imaging parameters: FOV=220x170x75mm3, 1.25mm isotropic
resolution, 30 monopolar echoes, TE=1.9-69.18ms, TR=92ms, FA=22°, BW/pixel=840Hz. Segmentation of deep gray matter
was performed using FreeSurfer followed by manual correction as needed. Averaged
signal values within the regions-of-interest (ROIs) for each individual were
fitted to the model described by equation [1] using MATLAB R2019b.
The
rationale for using a 3D acquisition is that weak macroscopic gradients in Larmor
frequency $$$\Omega \sim gx$$$ due to imperfect shimming merely shift the 3D
k-space and do not contribute to the signal attenuation.6 RESULTS
We found that
the signal within each of the ROIs exhibited nonmonoexponential decay as a
function of TE (Fig.1). The quadratic and linear behaviors at short and long
times, respectively, are evident in the data.
Fits of
the model [1] to MGRE data provided the following estimates of $$$\delta\Omega^{2}$$$: GP:1939.2±802.7; Pt:1488±888.5; Cd:941.3±489.2; Th:394.3±199.3 $$$s^{-2}$$$. Significant linear correlations were observed
between the average values of $$$\delta\Omega^{2}$$$ and published
non-heme iron concentrations7 in the respective brain regions (Fig.2).DISCUSSION
The signal from
a simple, fast and readily available 3D MGRE sequence contains important
biophysical information regarding susceptibility variations in tissue at a
mesoscopic level. The microstructural parameter $$$\delta\Omega^{2}$$$ can be readily extracted in addition to the
more commonly measured long-time relaxation rate. The high correlation of $$$\delta\Omega^{2}$$$ with documented pathology values from the
literature shows that $$$\delta\Omega^{2}$$$ tracks with non-heme iron. This suggests its
potential applicability in the study of a broad range of neuropathologies, from
Alzheimer’s dementia and Parkinson’s disease to chronic traumatic encephalopathy,
all of which have been associated with abnormalities in cellular-level iron metabolism.1,2
The large standard deviation we observed may be due to the wide age range of the
subjects studied.CONCLUSIONS
Non-heme
iron plays a critical role in brain function and is linked to a variety of
neurodegenerative diseases. Using a simple, fast 3D MGRE sequence, our work
shows the feasibility of mapping non-heme iron concentration via the mesoscopic
contribution to the Larmor frequency variance $$$\delta\Omega^{2}$$$ from microstructural
susceptibility variations in tissue.Acknowledgements
This
work was supported in part by NIH NNDS R01 NS039135, R21 NS090349, R56
NS119767, DoD PT190013, Lowenstein Foundation.References
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