# ECCENTRIC: a fast and unrestrained approach for high-resolution in vivo
metabolic imaging at ultra-high field MR

Antoine Klausera,b,i,j111Corresponding author, antoine.delattre-
<EMAIL_ADDRESS>Bernhard Strassera,c, Wolfgang Bognerc,
Lukas Hingerlc, Sebastien Courvoisieri,j, Claudiu Schirdad, Mehran Babolia,
Jorg Dietriche, Isabel Arrillaga-Romanye, Julie Millere, Erik Uhlmannf, Daniel
P. Cahillg, Tracy T. Batchelorh, Francois Lazeyrasi,j, Ovidiu C.
Andronesia222Corresponding author<EMAIL_ADDRESS>aAthinoula A.
Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts
General Hospital, Harvard Medical School, Boston  bAdvanced Clinical Imaging
Technology, Siemens Healthcare AG, Lausanne, Switzerland  cHigh‐Field MR
Center, Department of Biomedical Imaging and Image‐guided Therapy, Medical
University of Vienna, Vienna, Austria  dDepartment of Radiology, University of
Pittsburgh School of Medicine,Pittsburgh, Pennsylvania, USA  eDepartment of
Neurology, Massachusetts General Hospital, Harvard Medical School, Boston
fDepartment of Neurology, Beth Israel Deaconess Medical Center, Harvard
Medical School, Boston  gDepartment of Neurosurgery, Massachusetts General
Hospital, Harvard Medical School, Boston  hDepartment of Neurology, Brigham
and Women, Harvard Medical School, Boston  iDepartment of Radiology and
Medical Informatics, University of Geneva, Switzerland  jCIBM Center for
Biomedical Imaging, Switzerland

###### Abstract

A novel method for fast and high-resolution metabolic imaging, called
ECcentric Circle ENcoding TRajectorIes for Compressed sensing (ECCENTRIC), has
been developed and implemented on 7 Tesla human MRI. ECCENTRIC is a non-
Cartesian spatial-spectral encoding method optimized for random undersampling
of magnetic resonance spectroscopic imaging (MRSI) at ultra-high field. The
approach provides flexible and random ($k,t$) sampling without temporal
interleaving to improve spatial response function and spectral quality.
ECCENTRIC needs low gradient amplitudes and slew-rates that reduces
electrical, mechanical and thermal stress of the scanner hardware, and is
robust to timing imperfection and eddy-current delays. Combined with a model-
based low-rank reconstruction, this approach enables simultaneous imaging of
up to 14 metabolites over the whole-brain at 2-3mm isotropic resolution in
4-10 minutes with high signal-to-noise ratio. In 20 healthy volunteers and 20
glioma patients ECCENTRIC demonstrated unprecedented mapping of fine
structural details of metabolism in healthy brains and an extended metabolic
fingerprinting of glioma tumors.

high resolution whole-brain metabolite imaging, 3D magnetic resonance
spectroscopic imaging, non-Cartesian compressed sensing acceleration, Low-
Rank, 2-hydroxyglutarate, isocitrate dehydrogenase mutation, glioma

###### Contents

  1. I Introduction
  2. II Theory
    1. II.1 ECCENTRIC sampling
    2. II.2 Reconstruction of ECCENTRIC data
  3. III Methods
    1. III.1 ECCENTRIC sequence and acquisition parameters
    2. III.2 ECCENTRIC metabolite maps acquisition on healthy volunteers
    3. III.3 Glioma patient metabolite imaging with 3D-ECCENTRIC 1H-FID-MRSI
    4. III.4 Quantitative and Statistical Analysis of Metabolic Imaging
  4. IV Results
    1. IV.1 ECCENTRIC metabolic imaging in healthy volunteers
    2. IV.2 ECCENTRIC metabolic imaging in glioma patients
    3. IV.3 Quantitative analysis of ECCENTRIC metabolic imaging
    4. IV.4 Ultra-high resolution metabolic imaging of human brain using 3D-ECCENTRIC 1H-FID-MRSI
  5. V Discussion
  6. VI Acknowledgments
  7. VII  Supplementary material to ECCENTRIC: a fast and unrestrained approach for high-resolution in vivo metabolic imaging at ultra-high field MR
    1. VII.1 Additional data
      1. VII.1.1 ECCENTRIC imaging on high-resolution phantom
      2. VII.1.2 ECCENTRIC water imaging in healthy volunteers
      3. VII.1.3 Stability and reproducibility of ECCENTRIC metabolic imaging
    2. VII.2 Optimizing ECCENTRIC for high SNR and accelerated high-resolution MRSI

##  I Introduction

Magnetic resonance spectroscopic imaging (MRSI) is a molecular MR imaging
modality that can be used to investigate in vivo metabolism in humans non-
invasively with non-ionizing radiation. In particular, 1H-MRSI can
simultaneously image up to 20 metabolites in the brain and assess their
concentration Maudsley et al. (2020) and the dynamic change of their
concentrations under functional tasks Mullins (2018); Bednarik et al. (2021).
MRSI is capable of measuring intrinsic metabolism without the need of contrast
agents, and can probe metabolic enzymatic rates that are not accessible by
radio-tracer imaging techniques such as PET and SPECT Davis et al. (2020).
Numerous studies have demonstrated the considerable potential of MRSI for
clinical applications, but the performance of current MRSI protocols limits
their use in routine clinical investigations Oz et al. (2014), which is
severely lacking behind other MR modalities.

MRSI at ultra-high field (UHF $\geq$ 7T) using very short echo time ($\approx$
1ms) free induction decay (FID) excitation is a method that is gaining large
popularity due to its high SNR for metabolite imaging Henning et al. (2009);
Boer et al. (2012); Bogner et al. (2012). Nevertheless, a major drawback of
MRSI is low resolution and long acquisition times of the 4D ($k,t$) spatial-
temporal space, resulting in a critical need for imaging acceleration
strategies Bogner et al. (2021). This is particularly relevant for high-
resolution whole-brain MRSI where traditional phase-encoding acquisition
schemes would require several hours. Acceleration of UHF MRSI has been shown
by parallel imaging such as SENSE, GRAPPA and CAIPIRINHA with uniform
undersampling Strasser et al. (2017); Hangel et al. (2018); Nassirpour et al.
(2018a), or by Compressed Sensing (CS) with random undersampling Nassirpour et
al. (2018b), but these techniques generally don’t allow acceleration factors
(AF) above 6-10 for MRSI. Additionally, spatial-spectral encoding (SSE)
techniques enable further acceleration for UHF MRSI. By combining spatial-
spectral encoding with undersampling higher accelerations of UHF MRSI may be
achieved Moser et al. (2019); Saucedo et al. (2021); Ma et al. (2016).

So far, SSE has been demonstrated at ultra-high fields using either Cartesian
(EPSI) An et al. (2018); Nam et al. (2022); Weng et al. (2022) and non-
Cartesian (spirals, rosettes, concentric circles) Chiew et al. (2018); Hingerl
et al. (2019); Moser et al. (2019); Esmaeili et al. (2021) $k$-space
trajectories. Despite their potential benefits, these methods have an
important limitation that requires the use of temporal interleaves to achieve
broad spectral bandwidth and high spatial resolution. As the field strength
increases, this becomes even more challenging. Temporal interleaving prolongs
the acquisition time and creates spectral side-bands from spurious signals
that may overlap with metabolite peaks, ultimately degrading the spectral
quality Bogner et al. (2021).

In the current work, we sought to significantly improve metabolic imaging by
addressing limitations of the current methods in order to maximize the
acceleration, spectral quality and flexibility for high-resolution 4D (k,t)
sampling at ultra-high field. Our first guiding principle was to obtain
advanced metabolic imaging that is feasible and robust for clinical use. In
addition, pushing the spatial-temporal limits of metabolic imaging for state-
of-the-art research protocols formed our second line of thought in the overall
concept.

To accomplish these aims, we developed ECCENTRIC method (ECcentric Circle
ENcoding TRajectorIes for Compressed sensing), which provides several
benefits, including: 1) higher acceleration of MRSI acquisition, 2) improved
pseudo-random sampling for compressed sense with non-Cartesian trajectory, 3)
flexible and optimal sampling of the 4D ($k,t$) space and 4) reduced demand on
the gradient system. Circular trajectories, including rosettes, concentric,
and wave circles, provide several advantages over spiral and echo-planar
trajectories in MRSI and MRI Furuyama et al. (2012); Schirda et al. (2018). By
design, ECCENTRIC’s circular trajectories have reduced diameter produced by
readout gradient wave-forms that: 1) do not need rewinding which eliminates
dead-time and the associated loss in SNR per unit time, 2) permit high matrix
sizes with limited gradient amplitude, 3) have constant and moderate gradient
slew-rate that is not demanding for patients nor gradient hardware, hence
minimizing nerve stimulation and artifacts caused by eddy currents, gradient
warming, field drift and mechanical resonances. Moreover, the implementation
of CS acceleration Donoho (2006); Candes et al. (2006) relies on two
prerequisites. The first is that the signal or image exhibits sparsity in a
known transform domain Michael et al. (2007); Knoll et al. (2011a). The second
is that the data are randomly undersampled, which can be achieved by random
undersampling of the $k$-space in MRI applications. To enable the random
sparse undersampling necessary for Compressed Sensing (CS), we utilized a
novel approach where successive circular trajectories are randomly positioned
in $k$-space, rather than using regular patterns such as rosette, concentric,
or wave circles (Fig.1). The flexibility of the ECCENTRIC design, which
includes a random distribution of circle centers and the ability to choose
circle radii freely provides complete flexibility in selecting the matrix
size, field-of-view (FoV), and spectral bandwidth. This design also ensures
that the gradient hardware’s slew-rate and amplitude limitations are not
exceeded, while simultaneously minimizing acquisition time with CS
acceleration. Furthermore, it enables better fulfillment of the random
undersampling requirement for compressed sensing when compared to echo-planar
Hu et al. (2008a); Otazo et al. (2009); Hu et al. (2010, 2008b); Iqbal et al.
(2016); Santos-Díaz and Noseworthy (2019), spiral Chatnuntawech et al. (2015)
and radial Saucedo et al. (2021) trajectories used in previous accelerated
MRSI studies. To reconstruct ECCENTRIC data into image-frequency space, a low-
rank (LR) model constrained with Total-Generalized-Variation (TGV) was used:
CS-SENSE-LR Klauser et al. (2019, 2021, 2022). In addition to the spatial
regularization which is required for CS acceleration, the CS-SENSE-LR
reconstruction model integrates partial-separability (or low-rank) to further
improve the SNR of UHF MRSI. The performance of the new acquisition-
reconstruction scheme was first investigated by simulations and in structural-
metabolic phantoms, and subsequently evaluated in vivo in healthy subjects and
glioma patients.

##  II Theory

###  II.1 ECCENTRIC sampling

ECCENTRIC is a SSE sampling strategy following a random pattern made of off-
center circles as illustrated in Figure 1. The circle centers’ polar
coordinates $(r_{c},\phi_{c})$ are chosen randomly with a uniform probability
within the ranges $r_{c}\in[0,\max(k_{x,y}^{max}-R,R)]$ and
$\phi_{c}\in[0,2\pi[$. Here, $R$ represents the circle radius, $k_{x,y}^{max}$
is the largest in-plane $k$-space coordinate (assuming the same spatial
resolution along all axial plane directions). The majority of circles are
placed randomly as shown with two successive circles ($c$ and $c+1$) in the
sketch A, but with the constraint to avoid significant overlap between circles
(Fig.1B): the distance between the centers of each circle, $\Delta$, must be
larger or equal to the Nyquist distance (the inverse of the FoV size). There
is partial overlap between circles when $\Delta\><2R$, but this redundant
sampling occurs primarily in the center of $k$-space, which allows to optimize
and increase the SNR. In addition to the random pattern, a small subset of
circles ($<5\%$ of the total number) positioned in rosette fashion is acquired
in the center of $k$-space (Fig.1C). This ensures complete sampling of the
center of $k$-space, which is beneficial for SNR and reconstruction
performance Knoll et al. (2011a); Michael et al. (2007) with negligible effect
on acquisition time. The homogeneous random distribution of circle polar
coordinates results intrinsically in a pseudo-random $k$-space sampling with
density following $1/\|k\|$ outside of the rosette sampled central region.

To extend ECCENTRIC to 3D $k$-space sampling, a stack of ECCENTRIC is employed
with circles randomly placed in the $k_{x}$-$k_{y}$ planes, while $k_{z}$ is
encoded using Cartesian phase-encoding (Fig.1D). The 3D $k$-space can be
covered using spherical or ellipsoid coverage, where the in-plane $k$-space
boundary is defined as
$k_{x,y}^{max}=\frac{M}{2\>FoV}\sqrt{1-(k_{z}/k_{z}^{max})^{2}}$, with $FoV$
representing the FoV size and $M$ the spatial resolution (matrix, refer to
Fig. 1). To achieve complete sampling in a single $k_{x}$-$k_{y}$ plane, the
number of eccentric circles needed can be derived similar to rosette encoding
that requires $\frac{\pi M}{2}$ circles. To maintain the same number of
sampling points, the total number of eccentric circles required for complete
sampling of a single stack is $\frac{\pi Mk_{x,y}^{max}}{2\>R}$. To achieve
circle encoding with off-center position $(r_{c},\phi_{c})$, a brief gradient
ramp is used to gain an initial momentum $(k_{x},k_{y})$ position and the
necessary velocity. This process is done at the same time as the slab
excitation rewinder overlapped by $z$-phase encoding and does not increase the
echo time, as shown in Fig.1E. To implement CS acceleration, the total number
of ECCENTRIC circles $N_{c}$ is reduced uniformly across the stacks by a
factor of AF.

Figure 1:  (A) circle center positions are parameterized in polar coordinates
$(r_{c},\phi_{c})$ that are chosen randomly in the ranges
$r_{c}\in[0,\max(k_{xy}^{max}-r,r)]$ and $\phi_{c}\in[0,2\pi]$. Two
consecutive circles ($c$ and $c+1$) are shown and must respect the overlap
rule described in (B): the distance between their respective centers,
$\Delta$, must be greater or equal to the Nyquist distance, $\Delta_{Ny}$.
(C), to satisfy a systematic full sampling of the $k$-space center, a small
subset ($<5\%$) of circles is positioned in rosette pattern in each ECCENTRIC
encoding planes. (D), 3D $k$-space sampling is achieved by a stack of
ECCENTRIC encoding planes with variable $k_{x,y}^{max}$ to realize an
ellipsoid coverage. (E) Diagram of the FID-ECCENTRIC 3D sequence. First, a
4-pulse WET water suppression technique is used, preceding the Shinnar–Le Roux
optimized excitation pulse. After the excitation, the Cartesian encoding is
performed along the z-axis, simultaneously to the gradient ramp along the x-
and y-axes to reach the desired $k$-space off-center position and velocity.
Finally, a sinusoidal gradient waveform is applied along the x- and y-axis
during acquisition to produce the circular trajectory.

In Fig.2 a comparison is made between ECCENTRIC, Uniform Wave trajectory
(similar to Wave-CAIPI pattern Bilgic et al. (2015)), concentric circles and
rosette sampling. The trajectory and sampling density in the $k$-space for
each pattern and acceleration factor highlight the differences in sampling
distribution. The density distribution of ECCENTRIC is between the density
profile of rosette/concentric circles that have a high density singularity at
the $k$-space center and the Uniform Wave which has a flatter profile up to
the periphery of the $k$-space. While rosette and concentric circle
trajectories provide a favorable sampling density at the center of $k$-space,
they require temporal interleaving that increase the acquisition time and
create sidebands and spectral artefacts which are detrimental to the
metabolite signal. Uniform Wave has less desirable $k$-space density, but does
not need temporal interleaving similar to ECCENTRIC. Hence, ECCENTRIC provides
a good compromise between the desired high density in the center of $k$-space
to improve SNR and avoiding temporal interleaving.

ECCENTRIC is inherently suited for random undersampling required for good CS
performance Michael et al. (2007), as demonstrated by comparing (Fig.2) the
point spread functions (PSF) of ECCENTRIC, rosette, concentric and Uniform
Wave. The PSF was computed on a $64\times 64$ matrix and obtained from a
single point source Mareci and Brooker (1991) that was encoded in $k$-space
and then reconstructed with Non-uniform Fourier transform with Voronoi’s
partition density compensation Rasche et al. (1999). The PSF reflects the
interference between voxels in image space resulting from undersampling. A PSF
that shows pseudo-random incoherent pattern is more suited for CS
acceleration. Simulations reveal an incoherent pattern for PSF of ECCENTRIC
due to the pseudo random $k$-space sampling, and the PSF pattern spreads with
the increasing acceleration factor but conserve the pseudo-random behavior
with undersampling (Fig.2). In comparison, Uniform Wave, concentric circles,
and rosette trajectories have more compact PSFs for fully sampled
acquisitions, but their PSFs exhibit coherent patterns when undersampling is
applied which is less favorable for CS acceleration.

Figure 2: Top left, $k$-space trajectories for ECCENTRIC, Uniform Wave,
concentric circles and rosette trajectories for a $64\times 64$ encoding
matrix. Red dots indicate the circle center positions. The acceleration
factors AF=$1,2,3$ correspond to ECCENTRIC and Uniform Wave trajectories with
$202$, $101$ and $67$ circles respectively; $31$, $16$ and $11$ concentric
circles; $101$, $51$ and $34$ Rosette circles. Top right, the point spread
function (PSF) calculated for each trajectory and acceleration on a log-scale
highlight the presence of incoherent and coherent aliasing patterns. Bottom,
the sampling density for the same trajectories and AFs, represented in the 2D
$k$-space (left) and along a radial projection (right).

###  II.2 Reconstruction of ECCENTRIC data

The CS-SENSE-LR model reconstruction Klauser et al. (2021, 2022) was used to
reconstruct 4D ECCENTRIC ($k,t$) data into image-frequency spacee. Here, we
adapted this reconstruction to the case of ECCENTRIC data by incorporating the
non-uniform Fourier transform (NUFT).

Defining the discrete MRSI data in image space to be $\rho$ as an
$N_{\mathbf{r}}$ by $T$ array (with $N_{\mathbf{r}}$ the number of spatial
points and $T$ the number of sampling time points), the low-rank hypothesis on
the magnetization assumes that the MRSI data can be separated into a small
number of spatial and temporal components :

$\rho=\mathbf{U}\mathbf{V}$ (1)

where $\mathbf{U}$ is a $N_{\mathbf{r}}$ by $K$ array and $\mathbf{V}$ a $K$
by $T$ array, with $K$ the rank of the low-rank model. These components are
retrieved by CS-SENSE-LR reconstruction solving the inverse problem

$\displaystyle\arg\min_{\mathbf{U},\mathbf{V},\mathbf{L}}$
$\displaystyle\left\|\mathcal{W}\left(\mathbf{s}-\mathcal{FCB}\left(\mathbf{U}\mathbf{V}+\mathbf{L}\right)\right)\right\|^{2}_{2}$
(2) $\displaystyle+\lambda\sum_{c=1}^{K}\text{TGV}^{2}\\{U_{c}\\}\>.$

, where $\mathbf{s}$ the measured data, $\mathcal{F}$ the NUFT encoding
operator, $\mathcal{C}$ the coil sensitivity operator, $\mathcal{B}$ the
$B_{0}$ frequency shift operator and $\mathbf{L}$ represents the lipid signal
($N_{\mathbf{r}}$ by $T$ array) located at the skull that is reconstructed
simultaneously with brain metabolite $\mathbf{U}$ and $\mathbf{V}$ but on a
separate spatial support. $\mathcal{W}$, is a weighting operator of a Hamming
window shape, and decreasing with the distance to the center of the $k$-space
Ban et al. (2019); Klauser et al. (2021). $\text{TGV}^{2}$ is the total
generalized variation cost function with $\lambda$ the regularization
parameter Knoll et al. (2011b). The NUFT encoding operator of ECCENTRIC
$\mathcal{F}$ is a discrete non-uniform Fourier transform of type 1:

$(\mathcal{F}\rho)_{j,t}=\sum_{i}\mathrm{e}^{2\pi\mathrm{i}\mathbf{k}_{j}\cdot\mathbf{r}_{i}}\rho_{i,t}$
(3)

with $\mathbf{r}_{i}$ are the uniform image space coordinates and
${\mathbf{k}_{j}}$ $k$-space sampling-point coordinates located on the
3D-ECCENTRIC circles. The contamination of $\mathbf{U}$ and $\mathbf{V}$ by
skull-lipid signal can be prevented by filtering of the gradient descent
during the reconstruction (eq.2). Lipid signal is removed from each step of
the gradient descent by applying the operator $(\mathbf{1}-\mathbb{P})$ with
$\mathbb{P}$ the lipid subspace projection computed from the estimated lipid
signal at the skull $\mathbf{L}$ Klauser et al. (2019). To remove residual
water signal remaining in measured data, HSVD method for water removal is
applied to the raw data Barkhuijsen et al. (1987). At last, the first order
phase that is inherent to the acquisition delay in FID-MRSI type acquisition,
are removed by predicting the first missing points with an autoregressive
model Nassirpour et al. (2018c).

##  III Methods

###  III.1 ECCENTRIC sequence and acquisition parameters

A 1H-FID-MRSI Henning et al. (2009); Bogner et al. (2012) acquisition was
implemented with 3D spherical stack-of-ECCENTRIC sampling on a 7T scanner
(MAGNETOM Terra, Siemens Healthcare, Erlangen, Germany) running VE12U SP1
software and equipped with a NOVA head coil (32Rx/1Tx). The echo-time (TE) was
set to the minimum possible: $0.9$ ms with a $27$ degree excitation flip-angle
(FA) and $275$ ms repetition-time (TR). A slab selective excitation was
performed with a Shinnar-LeRoux optimized pulse Pauly et al. (1991); Klauser
et al. (2021) with 6.5 kHz bandwidth and was preceded by four-pulses WET water
suppression scheme Ogg et al. (1994); Klauser et al. (2021) (Fig.1E). The FoV
was $220\times 220\times 105$ mm3 (A-P/R-L/H-F) with $85$ mm-thick excited
slab. A voxel size of $3.4\times 3.4\times 3.4$ mm3 (40.5 $\mu l$) was
realized with a $64\times 64\times 31$ matrix. The ECCENTRIC circles radius
$R$ was set to $1/8\frac{n}{FoV}$ which corresponds which corresponds to a
diameter that encompasses a quarter of the width of the $k$-space, with $n$
being the square matrix size. With the chosen radius $R$, each ECCENTRIC
circle sampled 51 points in $k$-space, enabling a spectral bandwidth of 2280
Hz without the need for temporal interleaving. The FID was sampled with 500
time-points, which resulted in a total FID duration of 220 ms. To obtain the
fully sampled (AF=1) spherical 3D Stack-of-ECCENTRIC with these parameters, a
total number of $N_{c}=4072$ circles is required, which corresponds to $18$
min $40$ sec acquisition time (TA). For accelerated acquisitions, we decreased
the number of circles to $N_{c}/AF$, with TA being shortened proportionally.
For instance, with the same encoding parameters, AF=2 needs $N_{c}=2036$ in 9
min 20 sec, AF=3 needs $N_{c}=1357$ in 6 min 16 sec, AF=4 needs $N_{c}=1018$
in 4 min 40 sec, and so on. A very fast water reference data needed for coil
combination, $B_{1}$ and $B_{0}$ field correction ($\mathcal{CB}$ operators in
Eq.2), and image intensity normalization for comparable range of metabolite
concentration values across subjects (in institutional units, I.U.) was
acquired by turning off water suppression and using the same FoV, FA slab
excitation, TR, FID duration and spectral bandwidth, with Rosette sampling at
lower resolution ($23\times 23\times 19$) in $1$ min $16$ sec. The
3D-ECCENTRIC 1H-FID-MRSI data were processed by removing any residual water
and then reconstructed using a TGV regularized model that also includes
simultaneous suppression of scalp lipid signal (Eq. 2).

In healthy subjects and patients shimming of the 85 mm thick whole-brain slab
was performed using the manufacturer methods that adjusted the shim currents
over thirteen spherical harmonics coils: three 1st order, five 2nd order, and
four 3rd order. The global linewidth of the water over the entire 85 mm slab
was between 25-42 Hz across all subjects. In the majority of the subjects the
global water linewidth was between 30-35 Hz. Adjustment of the $B_{1}+$
transmit and water suppression was subsequently performed with manufacturer
methods. The entire adjustment procedure took between 1-2 min for every
subject.

###  III.2 ECCENTRIC metabolite maps acquisition on healthy volunteers

Twenty healthy volunteers (11 female, 9 male, 22-42 years, listed in Table I)
were scanned at Athinoula A. Martinos Center For Biomedical Imaging for this
study. In four volunteers, the 3D-ECCENTRIC 1H-FID-MRSI sequence described
above was acquired with voxel size of $3.4$ mm isotropic at AF= 1,2,3 and 4
successively. In two healthy subjects the performance of 3D-ECCENTRIC 1H-FID-
MRSI was tested at higher resolution with voxel size of $2.5$ mm isotropic
(matrix $88\times 88\times 43$, AF= 4, TA= 10 min 26 sec) and compared to
$3.4$ mm isotropic (matrix $64\times 64\times 31$, AF= 2, TA= 9 min 20 sec).
In the remaining volunteers, the 3D-ECCENTRIC 1H-FID-MRSI was acquired only
with $3.4$ mm isotropic and AF=2 (TA= 9 min 20 sec)

All volunteers were scanned with a $T_{1}$-weighted anatomical MP2RAGE
sequence Marques et al. (2010) (1 mm isotropic, 4300 ms TR, 840 ms & 2370 ms
TI) for positioning of the MRSI FOV and for the generation of skull-masks that
are needed for the lipid suppression during the reconstruction and to exclude
voxels located outside the head volume. The regularization parameter used in
the reconstruction was adjusted to $\lambda=3\times 10^{-4}$ by gradually
increasing it from a low value until the noise-like artifacts in the
metabolite maps disappeared Klauser et al. (2022); Knoll et al. (2011b). The
reconstruction rank, $K$, was determined qualitatively as the minimum number
of components that contain some signal distinguishable from noise. For the 3D
ECCENTRIC reconstruction, $K$ was specifically set to 40.

###  III.3 Glioma patient metabolite imaging with 3D-ECCENTRIC 1H-FID-MRSI

Twenty patients (11 male, 9 female, 28-66 years) were imaged at Athinoula A.
Martinos Center For Biomedical Imaging with 3D-ECCENTRIC 1H-FID-MRSI to assess
the performance for mapping metabolic profile in disease conditions. Seventeen
patients had biopsy confirmed diagnosis: 1) nine patients were diagnosed with
astrocytoma (WHO 2-4), 2) seven patients were diagnosed with oligodendroglioma
(WHO 2-3), and 3) one patient was diagnosed with glioblastoma (WHO 4).
IDH1(R132H) mutation was confirmed in sixteen patients, and 1p/19q codeletion
was confirmed in three patients. In all patients the 3D-ECCENTRIC 1H-FID-MRSI
was acquired with $3.4$ mm isotropic and AF=2 (TA= 9 min 20 sec). In addition,
$2.5$ mm isotropic (AF= 4, TA= 10 min 26 sec) protocol was acquired in two
patients for comparison with the $3.4$ mm isotropic protocol.

###  III.4 Quantitative and Statistical Analysis of Metabolic Imaging

After reconstructing the ECCENTRIC MRSI data, the LCModel software Provencher
(1993) was used to fit the data and quantify the metabolites. A metabolite
basis obtained from quantum mechanics simulations in GAMMA Klauser et al.
(2021) was utilized for quantification, consisting of twenty-one metabolites:
phosphorylcholine (PCh), glycerophosphorylcholine (GPC), creatine (Cr),
phosphocreatine (PCr), gamma-aminobutyric acid (GABA), glutamate (Glu),
glutamine (Gln), glycine (Gly), glutathione (GSH), myo-inositol (Ins),
N-acetylaspartate (NAA), N-acetyl aspartylglutamate (NAAG), scyllo-inositol
(Sci), lactate (Lac), threonine (Thr), beta-glucose (bGlu), alanine (Ala),
aspartate (Asp), ascorbate (Asc), serine (Ser), taurine (Tau).
Phosphorylcholine and glycerophosphorylcholine were combined into total
choline-containing compounds (Cho), while creatine and phosphocreatine were
combined into total creatine (tCr). For the analysis of glioma patients data,
2-hydroxyglutarate (2HG) was also included in the basis. Concentration maps
were then generated for the metabolites included in the simulated basis.

The reconstructed water reference signal was used as quantification reference
by LCModel and the resulting concentration estimates were expressed in
institutional units (I.U.). This allowed for comparisons of metabolite levels
across both subjects and different metabolites. The ultra-short TE used in the
ECCENTRIC MRSI data acquisition meant that $T_{2}$ relaxation correction was
unnecessary for both metabolite and water signals. The results of the LCModel
fitting for each voxel were then used to generate spatial maps of the
concentration of each metabolite. To assess the quality of the MRSI data and
the goodness of fit, quality control maps of Cramer-Rao lower bounds (CRLB),
line-width (FWHM), and signal-to-noise ratio (SNR) were generated. MP2RAGE
images of healthy volunteers were segmented into gray-matter, white-matter and
CSF with Freesurfer version 6.0.0 software Fischl et al. (2002), and cerebral
lobes were identified using a standard atlas Klauser et al. (2022). Tumor
regions of interest (T-ROIs) and healthy contralateral regions of interest
(CL-ROIs) were segmented using ITK-SNAP on FLAIR imaging in glioma patients.
The metabolic tumor contrast-to-noise ratio (CNR
$=\frac{\mu_{T}-\mu_{H}}{\sigma_{H}}$) was computed for all metabolites, where
$\mu_{T,H}$ represent the mean of the metabolite concentrations in tumor and
healthy appearing brain, while $\sigma_{H}$ represents the standard deviation
of the metabolite concentration in the healthy appearing brain. To compare the
metabolite concentrations (IU) in the tumor and tumor CNR across groups, an
ANOVA was carried out, followed by post-hoc multiple comparisons to identify
group means with significant differences. We performed a Wilcoxon signed-rank
test on the metabolite tumor concentrations and CNR with multiple comparison
correction to compare treatment-naïve mutant IDH1 patients with the remaining
patients (treated mutant IDH1 and wild-type IDH1/2 combined). Furthermore, we
conducted a Wilcoxon signed-rank test including all patient data to determine
which metabolite had median CNR values significantly different from zero.

##  IV Results

###  IV.1 ECCENTRIC metabolic imaging in healthy volunteers

Guided by simulations, phantom and water imaging shown in Fig.2 and
Supplementary Fig. S2 and S1, next we investigated ECCENTRIC performance for
whole-brain metabolic imaging in healthy volunteers. 3D-ECCENTRIC 1H-FID-MRSI
was performed with a voxel size of 3.4 mm isotropic using acceleration factors
between 1 to 4. We sought to find whether a metabolic imaging protocol that
provides 3 mm isotropic whole-brain coverage in under 5 minutes ($AF=4$) is
feasible by ECCENTRIC for routine clinical exams. Such performance is similar
to other advanced MR imaging methods such as CEST and perfusion imaging.

Examples of metabolic images for seven metabolites obtained with retrospective
$AF=1-4$ are shown in Fig.3. Very similar structural details and tissue
contrast of metabolic images are obtained for all accelerations compared to
the fully sampled data. This is visible also by inspecting spectra that show
the same metabolic profile across acceleration factors ($AF=1-4$). The CS
accelerations ($AF=2,3,4$) were achieved by retrospectively undersampling the
fully acquired data ($AF=1$). The purpose of this was to solely focus the
analysis on the effects of CS acceleration, while also avoiding any image
differences that could be caused by patient motion during acquisitions with
different accelerations.

Figure 3: 3D-ECCENTRIC 1H-FID-MRSI metabolic images of human brain in healthy
volunteer with $3.4$ mm isotropic voxel size and 1-4 CS acceleration factors.
Top, metabolite maps of seven relevant brain metabolites (NAA, tCre, Cho, Glu,
GABA, GSH, and NAAG) are shown for all acceleration factors (AF). Spectra from
three brain locations indicated by red arrows on the anatomical image. At the
bottom, the left plot displays the correlation coefficients between
accelerated images ($AF=2,3,4$) and fully sampled images ($AF=1$), while the
right plots show the LCModel quantification error (CRLB), linewidth (FWHM),
and SNR.

Visual inspection of metabolic images reveal that: 1) tCre, Glu and GABA have
larger signal in gray matter than white matter, 2) NAA has more signal in gray
than white matter, but with lower gray-white matter contrast compared to tCre,
Glu and GABA, 3) Cho has higher signal in frontal white matter than gray
matter, 4) NAAG has the largest contrast from all metabolites, with much
larger signal in white matter compared to gray matter. Metabolic images
obtained with $AF=1$ and $AF=2$ are largely identical. Minor blurring of fine
structural details starts to become noticeable for $AF\geq 3$, however
adequate delineation of gray-white matter folding is maintained up to $AF=4$.

Quantitative image analysis shows that the correlation between the accelerated
and fully sampled metabolic images is high (R $>$ 0.7) for metabolites that
have a high SNR such as NAA, Cho, tCr, Glu and Ins, while metabolites of lower
SNR such as Gln, GABA, GSH, and NAAG exhibit lower correlations (R =
$0.4-0.7$). The error (CRLB) of metabolite quantification is below 20$\%$ for
all nine metabolites, and it does not degrades with the acceleration factor
except for NAAG and GABA, albeit it does not exceeds the 20$\%$ limit up to
$AF=4$. The SNR shows only a minor decrease between $AF=1$ (SNR=17) and $AF=4$
(SNR=15), while the linewidth does not change. More detailed analysis is
presented in the Table 2 and the following section.

###  IV.2 ECCENTRIC metabolic imaging in glioma patients

Performance of the $3.4$mm isotropic 3D-ECCENTRIC 1H-FID-MRSI was investigated
in twenty patients with glioma brain tumors. Table 1 lists pathology,
molecular diagnosis, treatment history and demographics of the patients.

Patient | Age/ | Histological Diagnosis | Molecular Diagnosis |  | MRSI
---|---|---|---|---|---
# | Gender | Grade | Type | IDH1 status | 1p/19q codel | Other | Treatment | quality
01 | 31/M | 2 | Astrocytoma | mIDH1 | not-deleted | ATRX, TP53 | No treatment | Good
02 | 34/F | 3 | Astrocytoma | mIDH1 | not-deleted |  | No treatment | Good
03 | 42/F | 2 | Astrocytoma | mIDH1 | not-deleted |  | PBT 60Gy | Good
04 | 42/M | 2 | Astrocytoma | mIDH1 | not-deleted | ATRX | IMRT 60 Gy + C6-TMZ | Good
05 | 51/M | 3 | Anaplastic Astrocytoma | mIDH1 | not-deleted | ATRX, TP53 | Surgery, PBT 60Gy, C6-TMZ | Good
06 | 66/F | 3 | Oligodendroglioma | mIDH1 | deleted | TP53 | No treatment | Good
07 | 33/F | 2 | Oligodendroglioma | mIDH1 | not-deleted |  | No treatment | Bad
08 | 28/F | 2 | Oligodendroglioma | mIDH1 | not-deleted |  | Surgery | Good
09 | 50/M | 2 | Oligodendroglioma | mIDH1 | not-deleted |  | Surgery, XRT 60 Gy | Good
10 | 57/M | 2 | Oligodendroglioma | mIDH1 | deleted |  | Surgery, C6-TMZ | Good
11 | 52/F | 2 |  | Anaplastic
---
Oligodendroglioma
mIDH1 | not-deleted |  | Surgery, IMRT 60Gy, C11-TMZ | Good
12 | 62/F | 2 |  | Anaplastic
---
Oligodendroglioma
mIDH1 | deleted |  | Surgery, VMAT 60Gy | Good
13 | 28/M | 4 | Astrocytoma | mIDH1 | not-deleted | MGMT | Surgery, XRT 60 Gy, C6-TMZ | Good
14 | 37/M | 4 | Astrocytoma | mIDH1 | not-deleted |  |  | Surgery, IMRT 60 Gy, C4-TMZ,
---
C5-(TMZ+HU), C9-TMZ
Good
15 | 57/F | 2 | Astrocytoma | wtIDH | not-deleted |  | XRT 60Gy + C6-TMZ | Good
16 | 35/M | 3 |  | Anaplastic
---
Astrocytoma
wtIDH | not-deleted |  |  | Surgery, IMRT 60Gy, C18-TMZ,
---
SRS, C4-Bev
Good
17 | 35/M | 4 | Glioblastoma | wtIDH | not-deleted |  | C7/C10, CDK4,
---
EGFR
| VMAT 60Gy, C6-TMZ,
---
C2-BEV
Good
18 | 33/F | ND | Not diagnosed | Not diagnosed | Not diagnosed | Not diagnosed | No treatment | Good
19 | 32/F | ND | Not diagnosed | Not diagnosed | Not diagnosed | Not diagnosed | No treatment | Good
20 | 58/M | ND | Not diagnosed | Not diagnosed | Not diagnosed | Not diagnosed | No treatment | Good

Table 1:  The demographics of the brain tumor patients along with their
histological and molecular diagnoses according to the World Health
Organization guidelines (mIDH1 = IDH1(R132H) mutation, wtIDH = IDH1/2 wild
type). The quality of the MRSI data was rated based on the quality parameters
(CRLB$<20\%$, FWHM$<0.1$ ppm, SNR$>5$) from spectral fitting by LCModel.
Treatment prior to MRSI scan included: PBT = proton beam therapy, IMRT =
intensity modulated radiotherapy, VMAT = volumetric modulated arc therapy, SRS
= stereotactic radiosurgery, TMZ = temozolomide, HU = hydroxyurea, Bev =
bevacizumab. ND = Not Diagnosed by pathology, presumptive diagnosis of glioma
is based on imaging features.

The results of retrospective acceleration on the spatial mapping of metabolite
profiles in tumor and the healthy appearing brain are presented in Fig.4.
Metabolic images from eight metabolites acquired with $AF=2$ and
retrospectively accelerated to $AF=3$ and $4$, are shown. Fully sampled data
($AF=1$) was not acquired in patients due to its long acquisition time
(18min:40s). We demonstrated in both healthy subjects and phantoms that mild
undersampling ($AF=2$) yields metabolic maps that are practically
indistinguishable from those fully sampled ($AF=1$). Hence, in patients we
used $AF=2$ data as ground truth to estimate the performance of higher
accelerations ($AF=3,4$).

Fig.4 shows metabolic images of six important metabolites present in healthy
brain, and additionally two metabolites that are specifically present in
glioma tumors, such as 2HG associated with IDH1,2 mutations and Gly.

Figure 4: ECCENTRIC metabolic imaging in a WHO-3 Astrocytoma patient with
IDH1(R132H) mutation (Patient #2 in Table 1). The performance of 3D-ECCENTRIC
1H-FID-MRSI, acquired at 3.4 mm isotropic resolution with acceleration factors
(AF) of 2, and retrospectively accelerated to 3 and 4, was compared. Top,
metabolic images of eight metabolites for all accelerations. Bottom, spectra
from three brain locations indicated by red arrows on the FLAIR image,
correlation coefficient (R) between $AF=2$ and $AF=3,4$, metabolite
quantification error estimate (CRLB), linewidth (FWHM), and signal-to-noise
ratio (SNR) across AF.

Patient metabolic imaging shows similar performance for different
accelerations, similar to healthy volunteers and phantoms measurements. The
tumor can be visualized with high contrast-to-noise by all metabolites, in
particular NAA, Cho, Glu, Gln, Gly and 2HG. However, the spatial extent and
pattern of metabolic abnormality is different across the eight metabolites,
which is suggestive of tumor heterogeneity as it is typical with glioma.
Examples of spectra from voxels inside and outside the tumor clearly show
different metabolic profiles, which are consistently reproduced by all the
acceleration factors. Seven metabolite maps (NAA, tCre, Cho, Glu, Gln, GABA,
Ins) exhibit high correlation (R $>$ 0.7) between ground truth $AF=2$ and the
higher accelerations ($AF=3,4$). Two metabolites exhibit medium correlation,
2HG (R $\sim$ 0.6) and Gly (R $\sim$ 0.4), which is driven by the low
background outside the tumors. However, no noticeable degradation of the
correlation coefficients is observed for any metabolite with increasing
acceleration, while slight blurriness consecutive to CS acceleration appears
for $AF=4$. The spectral quality metrics CRLB, FWHM, and SNR are also stable
across acceleration factors.

Examples of metabolic images obtained with 3D-ECCENTRIC 1H-FID-MRSI at 3.4 mm
isotropic resolution and $AF=2$ in 9min:20s from five patients, including four
mutant IDH1(R132H) and one wild-type IDH1,2 glioma, are shown in Fig.5. Images
of nine metabolites are shown in comparison to the FLAIR image.

In the the four mutant IDH1 glioma patients five metabolites exhibit positive
contrast for tumor (Cho, Gln, Ins, Gly and 2HG), three metabolites have
negative contrast for the tumor (NAA, Glu and GABA), and one metabolite (GSH)
shows both positive and negative contrast. In the WHO-4 high grade wild-type
IDH1/2 glioblastoma patient all metabolites exhibit negative contrast due to
tumor necrosis, which is corroborated by lack of contrast enhancement and
perfusion imaging. The different spatial extent and pattern of metabolic
abnormality revealed by each metabolite highlights the heterogeneity of glioma
metabolism. This emphasizes the complementarity and value of all metabolites
for glioma imaging. These data demonstrate that an extended metabolic profile
can be imaged at 7T with high quality at high spatial resolution in a
clinically acceptable time in glioma patients.

Figure 5: Metabolic imaging in glioma patients acquired with 3D-ECCENTRIC
1H-FID-MRSI at $3.4$ mm isotropic resolution in 9min:20s accelerated by CS
($AF=2$). The top four patients have mutant IDH1(R132H) glioma: WHO-2
Astrocytoma, WHO-3 Astrocytoma, WHO-3 Oligodendroglioma, and WHO-4 Astrocytoma
(Patients #1, #2, #6, #13 in Table 1). The bottom fifth patient has a necrotic
wild-type IDH1/2 WHO-4 Glioblastoma (Patient #17 in Table 1). Intensity scale
(I.U., institutional units) for each metabolite is the same across all
patients. For each metabolite, we indicate the percentage of voxels inside the
brain and FoV that meet the criteria of acceptable quality (CRLB $<20\%$, FWHM
$<0.07$ppm, SNR $>5$). Percentage on FLAIR indicate the ratio of tumor volume
to the total brain volume.

###  IV.3 Quantitative analysis of ECCENTRIC metabolic imaging

Detailed quantitative analysis including regional metabolite concentrations,
quantification error estimates, and spectral quality metrics is presented in
Table 2 and Fig.6 for healthy volunteers and glioma patients, respectively.

Table 2 presents the regional concentrations of nine metabolites quantified
with respect to the reference water signal and expressed in IU, calculated in
both the gray and white matter of the five major brain lobes across healthy
volunteers. Our results indicate that: 1) six metabolites have higher
concentrations in gray-matter compared to white matter across the brain (GM/WM
= 1.19 tCre, 1.12 NAA, 1.2 Glu, 1.34 Gln, 1.15 GABA, 1.11 GSH); 2) two
metabolites have higher concentrations in white-matter compared to gray-matter
(GM/WM = 0.96 Cho, 0.47 NAAG); 3) one metabolite has region dependent
gray/white-matter ratio (GM/WM = 1.17-0.87 Ins). The largest gray-white matter
contrast is exhibited by NAAG due to its specific compartmentalization in
white matter.

The quality metrics of MRSI data are also listed in Table 2, including the
precision of metabolite quantification by the Cramer-Rao lower bounds, the
signal-to-noise ratio and spectral linewidth. It can be seen that mean CRLB is
below $<20\%$ for all the metabolites across the imaged whole-brain volume. In
particular, mean CRLB is below $<6\%$ for the five metabolites with highest
SNR (NAA, tCre, Cho, Glu and Ins), between $8\%$-$10\%$ for two metabolites
(GABA and GSH) and between $14\%$-$20\%$ for other two metabolites (Glu and
NAAG). Across the brain the mean SNR is larger than 20 and the mean linewidth
is less than 12 Hz (0.04 ppm).

Mean across volunteers | Frontal | Limbic | Parietal | Occipital | Temporal | usable voxels
---|---|---|---|---|---|---
(Standard deviation) | WM | GM | WM | GM | WM | GM | WM | GM | WM | GM | mean % (std)
tCre [I.U.] | 3.34 ( 0.34 ) | 3.84 ( 0.04 ) | 3.22 ( 0.35 ) | 4.46 ( 0.28 ) | 3.30 ( 0.28 ) | 3.95 ( 0.28 ) | 3.31 ( 0.30 ) | 3.39 ( 0.19 ) | 3.09 ( 0.25 ) | 3.81 ( 0.19 ) |
tCre CRLB [%] | 3.25 ( 0.24 ) | 3.54 ( 0.41 ) | 3.38 ( 0.31 ) | 3.18 ( 0.30 ) | 3.21 ( 0.33 ) | 3.26 ( 0.26 ) | 3.45 ( 0.62 ) | 3.64 ( 0.62 ) | 3.42 ( 0.37 ) | 3.33 ( 0.26 ) | 73.3 (3.3)
NAA [I.U.] | 4.16 ( 0.98 ) | 4.51 ( 0.66 ) | 4.07 ( 1.01 ) | 5.38 ( 0.90 ) | 4.31 ( 0.96 ) | 4.84 ( 0.88 ) | 4.33 ( 0.98 ) | 4.18 ( 0.85 ) | 3.91 ( 0.84 ) | 4.35 ( 0.73 ) |
NAA CRLB [%] | 3.13 ( 0.34 ) | 3.55 ( 0.64 ) | 3.26 ( 0.33 ) | 3.07 ( 0.36 ) | 2.86 ( 0.26 ) | 3.05 ( 0.37 ) | 3.30 ( 0.54 ) | 3.63 ( 0.64 ) | 3.32 ( 0.39 ) | 3.32 ( 0.34 ) | 73.0 (3.5)
Ins [I.U.] | 3.49 ( 0.52 ) | 3.51 ( 0.35 ) | 3.65 ( 0.60 ) | 4.28 ( 0.48 ) | 3.73 ( 0.66 ) | 3.58 ( 0.29 ) | 3.74 ( 0.65 ) | 3.27 ( 0.57 ) | 3.56 ( 0.65 ) | 3.39 ( 0.51 ) |
Ins CRLB [%] | 5.33 ( 0.64 ) | 6.04 ( 0.94 ) | 5.29 ( 0.52 ) | 5.36 ( 0.42 ) | 5.16 ( 0.42 ) | 5.63 ( 0.52 ) | 5.38 ( 0.48 ) | 5.84 ( 0.50 ) | 5.34 ( 0.33 ) | 5.68 ( 0.40 ) | 73.0 (3.5)
GPC+PCh [I.U.] | 1.03 ( 0.10 ) | 0.93 ( 0.05 ) | 1.10 ( 0.10 ) | 1.24 ( 0.08 ) | 1.06 ( 0.11 ) | 0.95 ( 0.09 ) | 0.94 ( 0.12 ) | 0.79 ( 0.06 ) | 0.99 ( 0.07 ) | 0.98 ( 0.12 ) |
GPC+PCh CRLB [%] | 3.63 ( 0.34 ) | 4.24 ( 0.59 ) | 3.46 ( 0.31 ) | 3.56 ( 0.27 ) | 3.56 ( 0.29 ) | 3.97 ( 0.33 ) | 4.13 ( 0.57 ) | 4.59 ( 0.64 ) | 3.68 ( 0.29 ) | 3.94 ( 0.25 ) | 73.5 (3.3)
Glu [I.U.] | 3.86 ( 0.53 ) | 4.50 ( 0.29 ) | 3.72 ( 0.49 ) | 5.24 ( 0.46 ) | 3.86 ( 0.39 ) | 4.61 ( 0.39 ) | 3.80 ( 0.36 ) | 3.82 ( 0.38 ) | 3.50 ( 0.35 ) | 4.29 ( 0.44 ) |
Glu CRLB [%] | 4.51 ( 0.51 ) | 5.01 ( 0.85 ) | 4.72 ( 0.59 ) | 4.37 ( 0.47 ) | 4.31 ( 0.53 ) | 4.48 ( 0.55 ) | 4.82 ( 1.14 ) | 5.22 ( 1.32 ) | 4.80 ( 0.74 ) | 4.71 ( 0.64 ) | 72.8 (3.8)
Gln [I.U.] | 0.89 ( 0.06 ) | 1.24 ( 0.25 ) | 0.83 ( 0.06 ) | 1.33 ( 0.16 ) | 0.80 ( 0.16 ) | 1.08 ( 0.26 ) | 0.87 ( 0.22 ) | 0.91 ( 0.21 ) | 0.80 ( 0.09 ) | 1.07 ( 0.22 ) |
Gln CRLB [%] | 15.93 ( 2.45 ) | 14.81 ( 2.22 ) | 17.72 ( 2.68 ) | 14.38 ( 2.48 ) | 17.92 ( 4.78 ) | 16.22 ( 3.24 ) | 18.99 ( 5.14 ) | 18.77 ( 4.11 ) | 18.30 ( 2.95 ) | 16.45 ( 2.60 ) | 56.3 (4.6)
GABA [I.U.] | 1.34 ( 0.09 ) | 1.48 ( 0.29 ) | 1.34 ( 0.10 ) | 1.79 ( 0.37 ) | 1.37 ( 0.14 ) | 1.58 ( 0.30 ) | 1.33 ( 0.18 ) | 1.37 ( 0.18 ) | 1.21 ( 0.16 ) | 1.39 ( 0.32 ) |
GABA CRLB [%] | 8.68 ( 1.10 ) | 9.61 ( 1.51 ) | 8.86 ( 1.50 ) | 8.52 ( 1.74 ) | 8.54 ( 2.08 ) | 8.78 ( 1.76 ) | 9.48 ( 2.34 ) | 9.90 ( 2.22 ) | 9.60 ( 2.16 ) | 9.52 ( 2.09 ) | 68.3 (1.5)
GSH [I.U.] | 1.07 ( 0.24 ) | 1.22 ( 0.05 ) | 1.11 ( 0.26 ) | 1.45 ( 0.20 ) | 1.10 ( 0.20 ) | 1.17 ( 0.07 ) | 1.05 ( 0.18 ) | 1.00 ( 0.09 ) | 1.02 ( 0.17 ) | 1.14 ( 0.12 ) |
GSH CRLB [%] | 8.20 ( 0.88 ) | 8.77 ( 1.15 ) | 8.29 ( 0.93 ) | 7.96 ( 0.79 ) | 8.04 ( 1.00 ) | 8.43 ( 0.87 ) | 9.12 ( 2.01 ) | 9.80 ( 1.90 ) | 8.65 ( 1.23 ) | 8.81 ( 1.17 ) | 71.5 (3.1)
NAAG [I.U.] | 0.82 ( 0.14 ) | 0.39 ( 0.12 ) | 0.90 ( 0.13 ) | 0.49 ( 0.17 ) | 0.96 ( 0.17 ) | 0.34 ( 0.13 ) | 0.78 ( 0.16 ) | 0.41 ( 0.12 ) | 0.76 ( 0.11 ) | 0.35 ( 0.10 ) |
NAAG CRLB [%] | 14.11 ( 4.10 ) | 19.02 ( 5.07 ) | 12.43 ( 3.87 ) | 17.35 ( 6.07 ) | 12.01 ( 3.14 ) | 18.03 ( 5.15 ) | 15.51 ( 5.08 ) | 19.40 ( 6.62 ) | 15.36 ( 5.01 ) | 20.13 ( 6.40 ) | 45.3 (11.6)
SNR | 24.64 ( 4.41 ) | 23.67 ( 3.84 ) | 22.92 ( 4.50 ) | 24.53 ( 4.02 ) | 25.64 ( 4.82 ) | 24.73 ( 4.17 ) | 22.48 ( 6.13 ) | 21.32 ( 5.56 ) | 22.07 ( 4.23 ) | 22.40 ( 3.37 ) | $\emptyset$
FWHM [Hz] | 11.43 ( 0.91 ) | 12.09 ( 0.77 ) | 11.28 ( 1.15 ) | 11.13 ( 1.13 ) | 10.21 ( 0.79 ) | 11.02 ( 0.84 ) | 11.64 ( 0.91 ) | 12.33 ( 1.04 ) | 12.26 ( 1.23 ) | 12.38 ( 1.22 ) | $\emptyset$

Table 2: Metabolite concentrations in institutional units (I.U.) relative to
the reference water signal and quantification error estimates by LCModel
(Cramér-Rao lower bound, %) in each brain lobe and tissue type. The values are
calculated as the average (standard deviation) across the healthy volunteers
who were imaged by 3D ECCENTRCIC at 3.4 mm isotropic with $AF=2$ (9min:20s
acquisition time). The two bottom rows in the table present the SNR and FWHM
mean (standard deviation) values. The last column shows the percentage of
voxels inside the brain and FoV that meet the criteria of acceptable quality:
CRLB $<20\%$, FWHM $<0.07ppm$, SNR $>5$.

Stability and reproducibility of metabolite quantification by ECCENTRIC was
investigated by test-retest of repeated imaging in four healthy volunteers.
Results are shown in Supplementary Fig.S3 and Supplementary Tables S1 and S2
obtained at 3.4 mm isotropic resolution acquired in four consecutive 3D
ECCENTRIC scans using AF=1 (18min:40s), AF=2 (9min:20s), AF=3 (6min:16s), and
AF=4 (4min:40s). Across all four scans in all four subjects the metabolite
images appear visually similar, with low ($<7\%$) inter-scan coefficient of
variation for the concentration of the main metabolites.

Fig.6 presents results of metabolite quantification in the glioma patients.
Out of 20 scanned patients (Table 1), the MRSI data quality was good and could
be analyzed in 19 patients, while the MRSI data in one patient was affected by
motion and was excluded from the analysis. The patients with pathology
confirmed diagnosis were grouped in three groups based on their IDH mutation
status and the treatment history: 1) three newly diagnosed mutant IDH1(R132H)
glioma with no prior treatment, 2) eleven mutant IDH1(R132H) glioma with prior
treatment, and 3) three wild-type IDH1/2 glioma with prior treatment. Note,
that two patients were scanned before any diagnosis and found to have high 2HG
levels indicative of mutant IDH1 glioma, which was later confirmed by biopsy.
Three patients have a presumptive diagnosis of glioma based on the imaging
features, however their diagnosis is not confirmed at the moment by
immunohistopathology due to inoperable tumor location and the high risk of
biopsy. Hence, these three patients were not included for statistical analysis
in any of the three groups.

Figure 6:  Group analysis of the metabolites within the tumor region of
interest (ROI) and normal appearing brain in glioma patients. The shape and
color of each point represent the patient group, and the box plots display the
median, 25th, and 75th percentiles for all patients. The A plot shows the mean
values of Cramer-Rao lower bound (CRLB), signal-to-noise ratio (SNR), and
linewidth (FWHM) within the tumor ROI. The B plot shows the mean metabolite
concentration within the tumor ROI in IU. The C plot shows the contrast-to-
noise ratio (CNR) between the tumor ROI and normal appearing brain. ANOVA with
post-hoc multiple comparisons across the three groups was performed for each
metabolite and the dashed ellipses with two linked points indicate groups that
have a significant difference. In B and C, metabolites marked with a $\\#$
indicate a significant difference, as determined by a Wilcoxon sign-rank test
corrected for multiple comparisons, in the tumor concentration or in the
contrast-to-noise ratio (CNR) between treatment-na”ive mutant IDH1(R132H)
patients and other patients. In C, the $*$ denotes metabolites for which the
median CNR value computed over all patients was significantly different from
zero (corrected Wilcoxon signed-rank test). In all plots only the ROI voxels
with CRLB $<30\%$ were included in the analysis.

An extended metabolic profile of fourteen metabolites is quantified and
compared in the tumor region-of-interest for the sixteen patients that have
biopsy confirmed diagnosis and good data quality. In the top plot (A) of Fig.6
a mean CRLB $<20\%$ is noted for eight metabolites in the tumor, while the
mean CRLB is $<27\%$ for the remaining six metabolites. In the tumor the mean
SNR of spectra is between 7-17, which is lower than healthy brain due to low
tumor NAA, while the mean FWHM is between 10-18 Hz (0.03-0.06 ppm) comparable
to healthy brain. In the middle plot (B) of Fig.6 the comparison of metabolite
concentration in the tumor indicates that four metabolites have statistically
significant different levels between the three patient groups: 1) tCre is
higher in treatment-naïve mutant IDH1 compared to treated mutant IDH1 (+1.0
IU, $p=0.02$), 2) Cho is higher in treatment-naïve mutant IDH1 compared to
treated mutant (+0.47 IU, p=0.014 ), 3) Gln is higher in treatment-naïve
mutant IDH1 compared to treated mutant and wild-type IDH1/2 (+0.79 IU,
$p<0.002$, +0.64 IU, $p=0.03$), and 4) 2HG is higher in treatment-naïve mutant
IDH1 compared to treated mutant IDH1 (+0.55 IU, p=0.046). In the bottom plot
(C) of Fig.6 the tumor contrast-to-noise ratio (CNR) of metabolites across all
patients indicates that three metabolites (NAA: -1.3, $p<0.001$; Glu: -0.96,
$p<0.001$; GABA: -0.77, $p<0.001$) have statistically significant negative
image contrast between tumor and normal appearing brain. In the three groups
comparison it can be seen that treatment-naïve mutant IDH1 glioma patients
have a CNR for Cho greater (+1.87, $p=0.003$) than treated mutant IDH1, and
that Gln’s CNR is higher in treatment-naïve mutant IDH1 compared to treated
mutant IDH1 (+1.38, $p=0.03$) and wild-type IDH1/2 (+1.95, $p<0.001$) . In
general, it can be seen that the overlap between treated mutant IDH1 and wild-
type IDH1/2 metabolic profiles is larger than between either of these two
groups and the treatment-naïve mutant IDH1 glioma. Standard-of-care has been
shown to reduce significantly the levels of 2HG in mutant IDH1 patients
Andronesi et al. (2016); Choi et al. (2016). Hence, we conducted a two-group
comparison between treatment-naïve mutant IDH1 patients and the remaining
patients (treated mutant IDH1 and wild-type IDH1/2 combined). Upon correction
for multiple comparisons, the analysis revealed significantly higher Gln
concentration in the tumor of treatment-naïve mutant IDH1 patients compared to
the other patients (+0.81 IU, $p=0.05$). Additionally, treatment-naïve mutant
IDH1 patients exhibited a significantly higher tumor CNR compared to the other
patients for three metabolites: 1) Cho: +1.75, $p=0.05$; 2) Gln: +1.90,
$p=0.05$; 3) 2HG: +0.96, $p=0.05$.

###  IV.4 Ultra-high resolution metabolic imaging of human brain using
3D-ECCENTRIC 1H-FID-MRSI

We further explored the performance of 3D-ECCENTRIC 1H-FID-MRSI for ultra-high
resolution metabolic imaging in several healthy volunteers and glioma
patients. Based on the high SNR of the 3.4 mm data we expected that smaller
voxels at higher resolution will still provide sufficient SNR for metabolite
imaging. Fig.7 shows metabolic images obtained at a voxel size of 2.5 mm
isotropic using 3D-ECCENTRIC 1H-FID-MRSI in two glioma patients and two
healthy volunteers.

To achieve a feasible scan time, we used compressed sensing (CS) with $AF=4$.
We demonstrated at the beginning of our work that this AF provides metabolic
maps that are similar to those obtained through fully sampled 3D-ECCENTRIC
1H-FID-MRSI. The $AF=4$ acceleration enabled the acquisition of 3D-ECCENTRIC
1H-FID-MRSI at 2.5 mm isotropic resolution in 10min:26s. For all the subjects
shown in Fig.7 we also acquired the typical 3D-ECCENTRIC 1H-FID-MRSI at 3.4 mm
with CS $AF=2$ acceleration (9min:20s). As readily apparent by visual
inspection, the metabolic maps at higher spatial resolution provide sharper
delineation of the normal brain structure and of the tumor margins. No
compromise is visible for signal-to-noise, contrast-to noise or other data
quality metric at ultra-high resolution compared to typical resolution. We
note that the acquisition time of 3D-ECCENTRIC 1H-FID-MRSI at 2.5 mm with
$AF=4$ is only slightly longer (1 min) than at 3.4 mm with $AF=2$. However,
for the same acceleration factor the acquisition time of 3D-ECCENTRIC 1H-FID-
MRSI at 3.4 mm is 2.2 times faster than with voxel size of 2.5 mm isotropic.

Figure 7: Ultra-high resolution metabolic imaging acquired with 3D-ECCENTRIC
1H-FID-MRSI at $2.5$mm isotropic voxel size ($AF=4$, TA=$10min:26s$) in two
healthy volunteers and two glioma patients (Patients #2 and #13 in Table 1).
The ultra-high resolution metabolic imaging is compared to 3D-ECCENTRIC
1H-FID-MRSI at the typical voxel size of $3.4$mm isotropic ($AF=2$,
TA=$9min:20s$). Two spectra from both spatial resolution and corresponding to
the red arrow location are shown. The blue line represents the MRSI data and
the red line is the fit performed by LCModel.

##  V Discussion

In this work we demonstrated that 3D-ECCENTRIC 1H-FID-MRSI at 7T can
simultaneously image an extended metabolic profile of 10-14 metabolites at
high spatial resolution across whole-brain in clinically acceptable time both
in patients and healthy controls. In particular, we showed that the
acquisition of fast non-Cartesian MRSI can be further accelerated up to four-
fold by CS, allowing metabolic imaging at 3.4 mm isotropic resolution in
4min:40s and at 2.5 mm isotropic resolution in 10min:26s, respectively. The
CS-SENSE-LR reconstruction method produces metabolic images with an effective
voxel size identical to the nominal size Klauser et al. (2021). This may
provide an advantage compared to other filtered reconstructions Hingerl et al.
(2019); Hangel et al. (2020) which increase the effective voxel volume.
ECCENTRIC fully preserves the quality of the metabolite images up to a two-
fold acceleration and even when accelerated up to four-fold, the loss of image
quality is minor and metabolic images still effectively highlight the laminar
structure of the brain and tumor margins. By design ECCENTRIC acquisition and
reconstruction preserves the SNR at high accelerations. This is achieved
through full sampling of the center of k-space and the use of a low-rank
denoising technique.

Here we investigated the performance of 3D-ECCENTRIC 1H-FID-MRSI for two
applications scenarios: 1) high resolution metabolic imaging (3.4 mm in
4min:40s) for routine clinical applications, and 2) ultra-high metabolic
imaging (2.5 mm in 10min:26s) for research applications and more extensive
clinical investigations. Both of these protocols, represent a significant
advancement for imaging human brain metabolism by non-invasive in vivo MRSI.

Results obtained with the clinical 3.4 mm imaging protocol show good
delineation of the brain structure and tumor lesions. At 2.5 mm ultra-high
resolution there is increased gray-white matter contrast of metabolites due to
less partial volume effect that visualise brain structures more clearly than
at 3.4 mm. Several metabolites show particularly high contrast between gray
and white matter in healthy brain, such as the energy buffer tCre, the
neurotransmitter Glu and the dipeptide NAAG. In particular, NAAG is the most
abundant dipeptide in the brain, which is selectively localized in several
regions Pouwels and Frahm (1998) where it neuromodulates the glutamatergic
synapses, and is implicated in neurodegenerative diseases, schizophrenia,
stroke, epilepsy, traumatic brain injury and pain Morland and Nordengen
(2022). 3D-ECCENTRIC 1H-FID-MRSI provides high quality images of the NAAG
brain distribution showing high concentration in parietal white matter. In
addition, good quality metabolic images are obtained for some of the most
important but challenging metabolites such as GABA, Gln, and GSH. The
combination of improved linewidth (FWHM) and generally lower CRLB for GABA,
Gln, and GSH, along with the previous findings reported in 9.4T studies
Nassirpour et al. (2018c); Ziegs et al. (2023) support the reliability of
theses low-concentration metabolite maps obtained here at 7T.

Water images acquired with both fully sampled and accelerated ECCENTRIC
exhibit very high correlation coefficients (Suppl. Figs.S2 and S1). While
correlation coefficients between ground truth and accelerated ECCENTRIC
acquisitions are generally lower for metabolic images (Figs.3-4) than for
water images, visual assessments show that the quality of metabolite mapping
of healthy brain and tumors is preserved across all accelerations. To explain
the discrepancy between results on metabolites and water images, we note that
contrary to the water images where correlation coefficients are determined
straight from the reconstructed images, the correlation coefficients of
metabolic images are influenced also by other pre- and post-reconstruction
steps in the processing pipeline such as water removal, fat removal and
LCModel fitting. These pre- and post-reconstruction steps introduce additional
variability and lower correlation coefficients. In particular, metabolites
that are specific for tumor metabolism such as Gly Ganji et al. (2016) and 2HG
Andronesi et al. (2012) have high signal in the tumors but low background
outside the tumors. The low background levels of 2HG and Gly outside of tumors
have high variability due to noise-like structure, which leads to decreased
correlation coefficients for these metabolites when calculated over the entire
brain image. However, tumors are still mapped well by these metabolites across
all acceleration factors.

The 3D-ECCENTRIC 1H-FID-MRSI clinical protocol showed robust performance in
glioma patients, where 19 patients had good MRSI quality, and only one patient
had low MRSI quality which could not be analyzed due to motion artifacts. The
high quality of the data was achieved through the use of third-order shimming,
which provides more uniform $B_{0}$ field across the brain, as well as the
shortened scan time, which minimized the scanner drift and possibility of
subject motion. The scanner drift typically ranged from 5-10 Hz over a 10min
scan time.

We showed that the oncometabolite 2HG can be imaged by 3D-ECCENTRIC 1H-FID-
MRSI at the highest resolution shown to date in newly diagnosed treatment-
naive mutant IDH1 glioma patients. Compared to previous high resolution 3D
FID-MRSI investigations Hingerl et al. (2019); Hangel et al. (2020) which
exhibited less distinct identification of 2HG in patients with mutant IDH1
glioma, our imaging technique benefited from improved data quality facilitated
by third-order shimming and the CS-SENSE-LR reconstruction. Higher-order
shimming and reconstruction-integrated $B_{0}$ correction helped improve
spectral linewidth, while the low-rank regularized model further enhanced SNR
Klauser et al. (2019, 2021). The increased spectral dispersion at 7T, narrow
linewidth ($<0.05$ ppm) and high SNR, enhances the ability to fit 2HG in
ultra-short TE FID spectra and makes 2HG detection less reliant on particular
spectral patterns generated by long TE spectral editing spin-echo sequences
Esmaeili et al. (2020). Long TE decrease SNR, and spin echo sequences for
spectral editing result in particularly high specific absorption rate at
ultra-high field that impose a long TR and prolongs the acquisition time.
Previously, we showed that narrow linewidth is the primary experimental factor
that determines the precision and accuracy of the 2HG fitting at both 3T and
7T irrespective of spectral editing Esmaeili et al. (2020); Strasser et al.
(2022). High resolution 3D-ECCENTRIC 1H-FID-MRSI allows spectral linewidth
$<0.05$ ppm in glioma tumors. In patients that were treated before the MRSI
scan the chance of 2HG detection is significantly reduced by treatment
regimens combining surgery, radio and chemotherapy, which are very effective
in decreasing the levels of 2HG as shown in previous studies Andronesi et al.
(2016); Choi et al. (2016). However, the pre-operative high resolution 2HG
imaging has high potential and is valuable for image guided therapy of mutant
IDH glioma patients.

In addition to 2HG, several important metabolites for glioma metabolism can be
imaged at high resolution, including Glu, Gln, Gly and GSH Ganji et al.
(2016); Hangel et al. (2022). In particular, Gln metabolism is an alternative
energy source in glioma cells and targeted to induce metabolic vulnerability
in synthetic lethality treatment approaches McBrayer et al. (2018).
Furthermore, NAAG has important clinical applications in many brain diseases
and our data show the highest resolution for NAAG imaging to date. Our
3D-ECCENTRIC data at 2.5 mm isotropic show unprecedented spatial resolution of
3D MRSI metabolic imaging obtained in glioma patients with an acquisition time
of 10min:26s that can still be accommodated in most clinical protocols. At
slightly lower voxel size of 3.4 mm isotropic the patients can be imaged in
4min:40s which is 3 times faster than similar methods used in previous patient
studies Hingerl et al. (2019); Hangel et al. (2020).

ECCENTRIC encoding is highly versatile with flexible choice of FoV, spatial
resolution, spectral bandwidth that can be set to optimize SNR and acquisition
time. The advantage and strength of ECCENTRIC is enabled by the possibility to
freely choose the radius and position of circle trajectories in covering the
k-space: 1) the free choice of circle radius allows freedom in setting FoV,
spatial resolution and spectral bandwidth without the need of temporal
interleaving, 2) the free choice of circle position allows freedom for random
undersampling the k-space to accelerate acquisition by CS. This flexibility is
particularly important for 1H-MRSI at 7T and beyond, due to the increased
spectral bandwidth required which limits the duration of $k$-space
trajectories. In addition, free choice of circle position should enable FoV
with different extent along the axial dimensions for additional time saving,
which cannot be achieved by concentric, rosette and spiral trajectories.

The flexibility in setting FoV, resolution and spectral bandwidth by varying
the circle radius and CS undersampling to optimize SNR and acquisition time is
shown in Supplementary Fig.S4-S6. These results indicate that, when using the
same image resolution and acquisition time, ECCENTRIC provides a higher SNR
for protocols that use smaller circle radii and higher acceleration compared
to protocols using larger circle radii and lower acceleration.

There are some limitations in the current implementation. In particular,
reconstruction time of 3D-ECCENTRIC data requires several hours. For example,
using a $64\times 64\times 31$ matrix size for $3.4$ mm isotropic, the water
removal step took 1 hour, the CS-SENSE-LR reconstruction took 3 hours on a GPU
(or 12 hours on a CPU), and the parallel LCModel fitting took 1 hour on a
high-performance server such as the Dell PowerEdge R7525 (with 64 cores of
2.9GHz and 128M cache, 512 GB RAM, and 3 NVIDIA Ampere A40 GPUs). This
computation time may be considered relatively long for routine clinical
applications. Also, at the moment patient motion or scanner drift is not
corrected during ECCENTRIC acquisition, which may increase the variability of
metabolite quantification. The metabolite concentrations were not provided in
absolute units such as milimolar but expressed in IU relative to the water
reference data that still provides comparable values across subjects and
scanners. We note that for absolute quantification of 1H-FID-MRSI data only
the T1 relaxation correction might be needed. Future improvements of our
method will seek to shorten reconstruction and provide results faster for
clinical use. Also absolute concentrations will be estimated, and the
robustness of data acquisition with regard to motion and hardware instability
will be increased to reduce variability of metabolite quantification.

In conclusion, we developed ECCENTRIC - an advanced MRSI method at ultra-high
field that pushes the spatial and temporal limits of in vivo metabolic
imaging. ECCENTRIC demonstrated high quality performance in healthy volunteers
and patients. We expect that ECCENTRIC will open exciting new avenues in
neuroscience by mapping in great detail the brain neurochemistry in healthy
and disease conditions to answer important questions and enable discoveries in
clinical and research studies.

##  VI Acknowledgments

This work was funded by the U.S. National Institutes of Health through
National Cancer Institute (NCI/NIH) grant R01CA211080 and R01CA255479 (O.C.A),
Swiss National Science Foundation grant IZSEZ0_188859 (A.K.), by NIH/NCI Brain
Cancer Specialized Programs of Research Excellence (SPORE) grant P50 CA165962
(T.T.B. and D.P.C.), and by Austrian Science Fund (FWF): KLI 1106, P 34198 and
J 4124 (B.S, L.H. and W.B.). This research used the imaging equipment at
Athinoula A. Martinos Center for Biomedical Imaging provided by the Center for
Functional Neuroimaging Technologies, P41EB015896, a P41 Biotechnology
Resource Grant supported by the National Institute of Biomedical Imaging and
Bioengineering (NIBIB), National Institutes of Health.

##  VII  Supplementary material to ECCENTRIC: a fast and unrestrained approach
for high-resolution in vivo metabolic imaging at ultra-high field MR

###  VII.1 Additional data

####  VII.1.1 ECCENTRIC imaging on high-resolution phantom

To evaluate the performance of ECCENTRIC sampling, we initially tested it on a
high-resolution structural-metabolic phantom using a 2D FID-MRSI sequence. We
used a custom made phantom with geometry similar to Derenzo molecular imaging
phantom Derenzo et al. (1977) containing 5 sets of tubes with diameters of 2,
4, 6, 8 and 10 mm as shown in Fig.S1). Each set contained 6 tubes of identical
diameter separated by a distance equal to twice the inner diameter positioned
in a triangular configuration. In every set, the six tubes were filled with
metabolite solutions containing 10 mM of creatine. Magnevist (Gd-DTPA) was
added (1 mL/L) in each tube to shorten $T_{1}$ and create $T_{1}$-weighted
contrast for structural MRI. The whole tube structure was inserted in a large
cylindrical container (13.33 cm inner diameter) which was filled with 10 mM
NaCl solution. Further details of phantom manufacturing and chemical
composition are mentioned in Klauser et al. (2021).

Because the phantom has geometric structure only in the axial section we
acquired 2D-ECCENTRIC over a single slice of 10 mm thickness. The 2D-ECCENTRIC
sampling was the same like the central $k$-space partition from 3D-ECCENTRIC.
The 2D-ECCENTRIC was acquired using the same RF-pulse and FA, TE of $1.15$ ms
and TR of $450$ ms to account for the longer $T_{1}$ relaxation times in the
phantom. The FID was measured with a bandwidth of $2000$ Hz over $350$ ms, and
successive acquisitions were performed with increased in-plane resolution. The
circle radius ($R$) was set to $1/8$, $1/8$, $1/9$, and $1/10\frac{M}{FoV}$
for $4.6$, $3.4$, $2.8$, and $2.0$ mm in-plane resolutions, respectively, to
avoid temporal interleaving for any spatial resolution. In addition to
metabolite imaging, to better assess the performance of ECCENTRIC for spatial
encoding we also performed water imaging of the structural phantom at the same
spatial resolutions as metabolites. To achieve this, the 2D ECCENTRIC sequence
without water suppression was utilized with a short TR of $100$ ms and an FA
of $40$ degrees to maximize $T_{1}$-weighted ($T_{1}$w) contrast of the tubes
inside the cylindrical phantom. Following this, the first point of the
acquired timeseries was reconstructed to generate the $T_{1}$-weighted water
image. Both metabolite and water data were acquired with fully sampled
ECCENTRIC. To investigate accelerations, the fully sampled ECCENTRIC data were
retrospectively undersampled for acceleration factors (AF) between $2-12$.

The effect of the acceleration on water and metabolite imaging was evaluated
by analyzing the structural similarity index (SSIM) and correlation
coefficient for all voxels inside the phantom with respect to the fully
sampled data.

Figure S1: ECCENTRIC imaging of water and metabolites in the high-resolution
structural-metabolic phantom. ECCENTRIC performance was tested for spatial
resolutions of 4.6, 3.4, 2.8, 2.0 mm and acceleration factors between 1-12.
Top, examples of water and creatine images are shown for all 4 resolutions and
4 AF: 1,4,8,12. Bottom, SSIM and correlation factors for each resolution and
acceleration are calculated considering as ground truth the fully sampled
image (AF=1).

Water imaging of a single slice showed that 2D ECCENTRIC can resolve the
structural details of the phantom up to the resolution targeted by the imaging
protocol (Fig. S1). Compared to the fully sampled acquisition (AF=1), no
visible difference in image quality can be seen for retrospective
accelerations factors between 1-4, minor changes can be detected for AF
between 4-8, and moderate loss of details for AF 8-12. Considering AF=1 as
ground truth, quantitative analysis reveals that SSIM $\geq$ 0.99 across all
resolutions for accelerations up to AF = 4, and SSIM decreases to 0.97 for the
highest acceleration and resolution tested. Similarly, correlation factors
larger than 0.99 are observed up AF = 4, which decrease to 0.95 for the lowest
resolution and largest acceleration factor. Comparing the different spatial
resolutions, CS acceleration shows better performance for smaller voxel size.

For metabolite imaging, the tCr metabolite was imaged with 2D ECCENTRIC for
the same resolutions and acceleration factors as in the water imaging (Fig.
S1). Similar results are observed: 1) for acceleration factors between 1-4
metabolite maps show similar quality, while 2) for larger acceleration factors
there is a moderate loss of image details and and increase in the noise level.
Considering AF=1 as ground truth, across the entire series of measurements
SSIM range between 0.75-0.89, and correlation factors between 0.79-0.96. In
contrast to the water imaging, the highest SSIM and correlation factors are
not exhibited at the smallest voxel size for accelerated metabolic imaging due
to lower SNR of metabolites compared to water.

In particular, we note that for isotropic voxel size of 3.4 mm and for
acceleration factors up to 4 we obtained the highest SSIM and correlation
factors for metabolic imaging. Hence, we concluded that ECCENTRIC at 3.4 mm
with AF 1-4 represents a good starting protocol to further investigate fast
high resolution metabolic imaging of the human brain.

####  VII.1.2 ECCENTRIC water imaging in healthy volunteers

To assess the validity of ECCENTRIC acquisition with CS-SENSE-LR
reconstruction, three healthy volunteers were scanned with a $T_{1}$w 3D water
acquisition. The same 3D-ECCENTRIC 1H-FID-MRSI sequence described earlier
($3.4$ mm isotropic) was used but with a short TR of $100$ ms, a higher FA of
$40$ degrees, and without water suppression. Reconstructed images were
obtained using the model of Eq. 2, and only the first point of the FID was
used. To test the acceleration performance, we retrospectively undersampled
the $T_{1}$w 3D-ECCENTRIC data by AF $2$, $4$, $6$, $8$, $10$, and $12$. For
qualitative comparison, a $T_{1}$w Cartesian gradient-echo (GRE) imaging
sequence was also scanned on the volunteers with matched spatial resolution,
TR and TE. The performance of the accelerated ECCENTRIC acquisition and CS-
SENSE-LR reconstruction method was assessed with the structural similarity
index (SSIM) and the correlation coefficient of all voxels inside the brain
relative to the non-accelerated ECCENTRIC (Fig. S2). To investigate the
ability of ECCENTRIC to image brain structure, we performed water imaging in
several healthy volunteers using 3D FID-MRSI ECCENTRIC. The water suppression
was turned off, and we used the 3.4 mm protocol with larger FA = 40° and
shorter TR = 100 ms to produce $T_{1}$ weighed images. ECCENTRIC k-space data
were acquired fully sampled (AF=1) and the acceleration was obtained by
retrospective CS undersampling in post-processing. Results in Fig. S2 show
that fully sampled ECCENTRIC images reveal similar brain structure as
$T_{1}$-weighted GRE images acquired with the matched spatial resolution and
tissue contrast. Considering the fully sampled (AF=1) ECCENTRIC as ground
truth, the SSIM $\geq$ 0.99 and correlation factor $\geq$ 0.92 for images
obtained with AF = 1-12. Visually, almost no difference can be observed
between images obtained with AF = 1-4. For AF $\geq$ 8 the noise level
increases, which interferes with fine structural details.

Figure S2: Water imaging of human brain in healthy volunteers using
3D-ECCENTRIC with $3.4$mm isotropic voxel size. Left, images obtained by
$T_{1}$-weighted 3D GRE acquired with matched FA, TR, TE and spatial
resolution. Middle, water images obtained with 3D-ECCENTRIC for acceleration
factors 1-12. Right, SSIM and correlation factors for accelerated ECCENTRIC
water images are calculated considering the fully sampled image (AF=1) as
ground truth.

####  VII.1.3 Stability and reproducibility of ECCENTRIC metabolic imaging

Stability and reproducibility of ECCENTRIC was investigated by test-retest of
repeated imaging in four healthy volunteers. 3D ECCENTRIC 1H-FID-MRSI was
acquired at 3.4 mm isotropic resolution in four consecutive scans using AF=1
(18min:40s), AF=2 (9min:20s), AF=3 (6min:16s), and AF=4 (4min:40s).

Results are shown in Fig.S3 for Glu imaging. Due to high concentration of Glu
in gray mater, Glu images have high gray-white matter contrast and show fine
structural details of brain that can be used to visually assess the stability
and reproducibility of test-retest imaging. It can be seen that across all
four scans in all four subjects the metabolite images appear visually similar.
We note that with repeated measurements some anatomical differences may also
be attributed to slight head motion.

Figure S3: Glu imaging at $3.4$mm isotropic voxel size in four healthy
volunteers scanned with 3D-ECCENTRIC 1H-FID-MRSI in four successive
acquisitions with increasing accelerations AF=1, 2, 3 and 4. Three slices are
shown for each volunteer at each acceleration.

Detailed analysis of the reproducibility of metabolites measurement in healthy
volunteers is presented in Tables S1 and S2. The metabolite data from three
consecutive measurements with AF=3 performed in the 4 subjects were used to
calculate inter-measurement (Table S1) and inter-subject (Table S2)
coefficients-of-variation (COV).

| Inter-measurement COV
---|---
| Frontal | Limbic | Parietal | Occipital | Temporal
| WM | GM | WM | GM | WM | GM | WM | GM | WM | GM
NAA | 0.06 | 0.03 | 0.06 | 0.05 | 0.06 | 0.05 | 0.05 | 0.07 | 0.06 | 0.06
tCr | 0.05 | 0.05 | 0.05 | 0.03 | 0.03 | 0.04 | 0.04 | 0.03 | 0.06 | 0.05
Ins | 0.05 | 0.04 | 0.07 | 0.06 | 0.05 | 0.05 | 0.04 | 0.06 | 0.06 | 0.07
GPC+PCh | 0.04 | 0.03 | 0.03 | 0.04 | 0.04 | 0.06 | 0.03 | 0.04 | 0.03 | 0.05
Glu | 0.05 | 0.03 | 0.05 | 0.05 | 0.07 | 0.07 | 0.07 | 0.07 | 0.06 | 0.07
Gln | 0.14 | 0.10 | 0.15 | 0.11 | 0.12 | 0.12 | 0.12 | 0.07 | 0.14 | 0.08
GABA | 0.07 | 0.11 | 0.05 | 0.07 | 0.09 | 0.12 | 0.05 | 0.11 | 0.06 | 0.11
GSH | 0.12 | 0.10 | 0.14 | 0.13 | 0.13 | 0.13 | 0.13 | 0.10 | 0.14 | 0.11
NAAG | 0.23 | 0.41 | 0.28 | 0.33 | 0.24 | 0.55 | 0.26 | 0.40 | 0.28 | 0.54
Table S1:  The inter-measurement coefficient of variation (COV) for each
metabolite was determined in every lobe and tissue type for the 3D-ECCENTRIC
1H-FID-MRSI acquired at 3.4 mm isotropic resolution in 6min:16sec (AF=3). The
inter-measurement COV was calculated as the standard deviation divided by the
mean of three consecutive measurements for each volunteer and then averaged
across four volunteers. The three AF=3 datasets were obtained from
measurements performed with different accelerations (as shown in Fig. S3), but
retrospectively undersampled by a factor of 3 for AF=1 and 3/2 for AF=2.

Inter-measurement COV smaller than $7\%$ are observed for five metabolites
(NAA, creatine, myo-inositol, choline, glutamate) that are the most abundant
in the brain. COV between $8\%-14\%$ are obtained for glutamine, glutathione
and GABA. NAAG has higher COV in brain regions (gray matter) where its
concentration is low.

| Inter-subject COV
---|---
| Frontal | Limbic | Parietal | Occipital | Temporal
| WM | GM | WM | GM | WM | GM | WM | GM | WM | GM
NAA | 0.21 | 0.15 | 0.23 | 0.17 | 0.23 | 0.17 | 0.24 | 0.23 | 0.23 | 0.22
Cr+PCr | 0.10 | 0.05 | 0.12 | 0.07 | 0.11 | 0.05 | 0.09 | 0.09 | 0.11 | 0.09
Ins | 0.18 | 0.15 | 0.22 | 0.17 | 0.22 | 0.14 | 0.21 | 0.26 | ,0.24 | 0.19
GPC+PCh | 0.06 | 0.07 | 0.07 | 0.06 | 0.10 | 0.10 | 0.12 | 0.14 | 0.11 | 0.15
Glu | 0.19 | 0.13 | 0.20 | 0.16 | 0.20 | 0.15 | 0.18 | 0.18 | 0.18 | 0.20
Gln | 0.16 | 0.25 | 0.12 | 0.16 | 0.18 | 0.21 | 0.21 | 0.23 | 0.17 | 0.18
GABA | 0.37 | 0.33 | 0.39 | 0.38 | 0.36 | 0.36 | 0.38 | 0.39 | 0.37 | 0.40
GSH | 0.13 | 0.09 | 0.15 | 0.11 | 0.13 | 0.07 | 0.11 | 0.13 | 0.11 | 0.12
NAAG | 0.32 | 0.37 | 0.35 | 0.29 | 0.45 | 0.47 | 0.50 | 0.48 | 0.38 | 0.29
Table S2: The inter-subject coefficient of variation (COV) for each metabolite
was determined in every lobe and tissue type for the 3D-ECCENTRIC 1H-FID-MRSI
acquired at 3.4 mm isotropic resolution in 6min:16sec (AF=3). The inter-
subject COV was calculated as the standard deviation divided by the mean of 3
scanned volunteers and then averaged across the three measurements. The three
AF=3 datasets were obtained from measurements performed with different
accelerations(AF=1, AF=2 and AF=3), where AF=1 data was retrospectively
undersampled by a factor of 3 and AF=2 was retrospectively underssampled by a
factor of 3/2.

The inter-subject COV in (Table S2) reflects the biological variability of
metabolite concentrations in the gray and white matter across the group of
subjects.

3D-ECCENTRIC 1H-FID-MRSI had reproducible performance in three repeat
measurements. The method variability (inter-measurement COV) due to the
technical performance of 3D-ECCENTRIC 1H-FID-MRSI (Table S1) is much lower
(2-4 times smaller) than the biological variability (inter-subject COV) of
brain metabolism across individuals (Table S2). The low variability of
ECCENTRIC in repeat measurements indicates high precision of metabolite
quantification and high potential for longitudinal studies to detect
metabolite changes due to disease, treatment and functional tests. The
quantification of the five main metabolites that have the highest SNR in brain
MRSI (NAA, tCre, Cho, Ins, Glu) shows the lowest variability, with a slight
increase in the case of less abundant metabolites (Gln, GABA and GSH). The
highest variability is noticed for NAAG outside of the fronto-parietal white
matter due to its specific localization in this brain area. We note that in-
vivo variability of metabolite quantification in repeat measurements is also
influenced by patient motion and scanner stability in addition to 3D-ECCENTRIC
MRSI, hence methods that reduce the effects of motion and drift Bogner et al.
(2014); Andronesi et al. (2021) are likely to reduce variability.

###  VII.2 Optimizing ECCENTRIC for high SNR and accelerated high-resolution
MRSI

By design, the k-space acquisition by ECCENTRIC is characterized by: the
circle radius (CR), compressed sensing acceleration factor (AF), image matrix
size (MS) and field-of-view (FoV). In addition, acquisition of the time
dimension (FID) for spectroscopy is characterized by the spectral bandwidth
(SW), the dwell-time, and the number of time points. In particular, for
spectral-spatial encoding (SSE) there is a dependency between the spectral
bandwidth, field-of-view and image resolution. Compared to other SSE schemes,
ECCENTRIC allows very high flexibility in the choice of SW, FoV and MS, which
is particularly needed at ultra-high field (7T and beyond) and to operate
within the technical limits of the gradient system minimizing electrical,
mechanical and thermal stress.

Importantly, the ECCENTRIC flexibility can be used to optimize the SNR and
acquisition time while pushing the image resolution. ECCENTRIC parameters have
different impact on the measured signal-to-noise ratio (SNR) and acquisition
time (TA) as highlighted in the following table:

Change \ Effect | SNR | TA
---|---|---
Circle Radius $\nearrow$ | $\searrow$ | $\searrow$
CS Acceleration $\nearrow$ |  $\rightarrow$ (image smoothness $\nearrow$) | $\searrow$
Matrix Size $\nearrow$ | $\searrow$ | $\nearrow$
Table S3:

3D ECCENTRIC MRSI can be optimized by reducing CR and thus increasing the
sampling density in k-space, which can be designed to sample more the center
of k-space to increase SNR. In addition, the CR reduction allows a large range
of spectral windows by controlling the gradient slew rate as needed based on
the image resolution. However, the reduction in CR requires a higher CS
acceleration for an equivalent acquisition time. As we showed, CS acceleration
up to 4 provides high quality metabolite images, and this can be traded to
optimize SNR with lower CR.

To explore the flexibility of ECCENTRIC parameters for SNR optimization, three
acquisitions with the same isotropic resolution (5mm) and acquisition time
(14min) were acquired with different ECCENTRIC circle radii (CR) and CS
acceleration factors: 1) CR = kmax/4 and AF = 1; 2) CR = kmax/8 and AF = 2; 3)
CR = kmax/16 and AF = 4. Sampling patterns of the k-space are shown in Fig.
S4.

Figure S4: ECCENTRIC k-space sampling for various circle radii (CR) and
compressed sensing acceleration (AF).

Metabolite maps obtained in a healthy volunteer are presented in Fig. S5.
Higher SNR can be noticed for the six metabolites as the circle radii is
decreased, while only minor blurring is apparent at the highest acceleration.

Figure S5: Metabolite maps of NAA, total Creatine, total Choline, Glu, Ins and
NAAG produced from 3D 1H-FID-MRSI ECCENTRIC acquisitions at 5 mm isotropic
image resolution in 14 min with various circle radii CR and compressed sensing
AF.

Quantitative analysis in Fig. S6 shows that decreasing CR results in a notable
gain in metabolite SNR of + 30% for kmax/8 and + 40% for kmax/16 relative to
kmax/4, respectively. In the same time, the linewidth is stable across the
different protocols. The increase in SNR enables more precise metabolite
quantification resulting in lower CRLB for spectral fitting, especially for
the low signal metabolites. Among the 3 protocols, the protocol with CR =
kmax/8 and AF = 2 showed the best performance with a marked increase in SNR
and little visible blurring on metabolite maps. These results demonstrate that
CR and AF allow SNR optimization of 3D ECCENTRIC MRSI for a desired image
resolution and acquisition time.

Figure S6: Quantitative analysis of 3D-ECCENTRIC 1H-FID-MRSI acquisitions with
various circle radius CR and compressed sensing AF.

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