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Title
2-D MR Spectroscopy Combined with 2-D/3-D Spatial Encoding
Permalink
https://escholarship.org/uc/item/9vk3f6z1
Journal
EMAGRES, 5(1)
ISSN
2055-6101
Authors
Thomas, M Albert
Iqbal, Zohaib
Sarma, Manoj K
et al.
Publication Date
2016
DOI
10.1002/9780470034590.emrstm1459
Peer reviewed
eScholarship.org Powered by the California Digital Library
University of California
Chapter 30
Two-Dimensional NMR Spectroscopy Plus
Spatial Encoding
M. Albert Thomas
1
, Zohaib Iqbal
1
, Manoj K. Sarma
1
,
Rajakumar Nagarajan
1
, Paul M. Macey
1
,and
Amir Huda
1,2
1
University of California, Los Angeles, CA, USA
2
California State University, Fresno, CA, USA
30.1 Introduction 495
30.2 Single-voxel-based 2D MRS 497
30.3 Echo-planar Correlated and J-resolved
MRSI 506
30.4 Accelerated Echo-planar J-resolved MRSI
with Nonuniform Undersampling and
Compressed Sensing 514
30.5 Prior-knowledge Fitting for Metabolite
Quantitation 515
30.6 Future Directions: Clinical
Applications 517
Acknowledgments 517
References 517
Handbook of Magnetic Resonance Spectroscopy In Vivo:
MRS Theory, Practice and Applications.
Edited by Paul A. Bottomley and John R. Grifths
© 2016 John Wiley & Sons, Ltd. ISBN: 978-1-118-99766-6
Also published in eMagRes (online edition)
DOI: 10.1002/9780470034590.emrstm1459
30.1 INTRODUCTION
It is now almost three decades since one-dimensional
(1D; in the chemical shift spectral domain)
single-voxel (SV)-based magnetic resonance spec-
troscopy (MRS) was introduced in the clinical
setting.
1–3
While it has become an integral part of
the diagnostic tools in the clinic for some physicians
and selected medical centers, it is still considered
by others as an ‘investigational technique’.
1,3
1D
SV-MRS has developed to a point where the ve
major cerebral metabolites, myo-inositol (mI), total
choline (Cho), total creatine (Cr; phosphorylated
plus unphosphorylated), glutamine/glutamate (Glx),
and N-acetyl aspartate (NAA), are identied and
quantied accurately with prior-knowledge tting
algorithms such as LC Model, JMRUI, and others
(see Chapters 18, 19, and 20).
4–6
Acquisition times
have also been accelerated by stronger gradients,
and we have arguably now reached a plateau in
terms of what can be further extracted from the 1D
technique.
1
Beyond the ve main cerebral metabolites, approx-
imately 25 others that have been detected in human
brain are not commonly assessed for several reasons.
6
Some are difcult to detect because they have a
weak signal (low concentration or fewer hydrogen
496 Methodology
nuclei) and/or many overlapping peaks, for example,
N-acetylaspartylglutamate (NAAG), aspartate, tau-
rine (Tau), scyllo-inositol, betaine, ethanolamine,
purine nucleotides, histidine, glucose, and glycogen.
Others require the use of ‘special techniques’ to
tease them out because they are obscured by much
larger overlapping signals, for example, glutathione
and 𝛾-aminobutyric acid (GABA).
1–7
Yet others
such as 𝛽-hydroxy-butyrate, acetone, phenylalanine,
galactitol, ribitol, arabitol, succinate, pyruvate, ala-
nine, glycine, and threonine are detected only when
levels are elevated under abnormal or pathological
conditions in various disorders. In addition, some
exogenous compounds that cross the blood–brain
barrier such as ethanol and methylsulfonylmethane
can also be detected by proton MRS.
8–10
The limitations of the 1D SV-MRS methods of
yesteryears still remain to a certain extent.
1–3,7
Over-
lapping of spectra due to the chemical shifts of
metabolites keeps us from identifying the ones with
fewer hydrogen protons and/or lower concentrations.
Furthermore, an inability to separate J-coupling
from chemical shift leads to assignment problems
that hinder the identication and quantication of
metabolites.
11,12
One could, in principle, move to
higher main magnetic eld strengths (B
0
) to better
resolve the peaks and reduce the overcrowding, as
the relative width of the multiplets in ppm varies
inversely with B
0
.
13
However, currently 3 T remains
the practical limit in the clinical setting.
3
The ‘special techniques’ noted above for teasing
out signal information are often called homonuclear
spectral or J-difference editing techniques.
14,15
They
exploit the J-coupling between coupled spins by se-
lectively perturbing particular resonances on alternate
acquisitions during a spin-echo sequence. J-coupling
results in multiplet signals with distributed peak
intensities (heights) over several peaks, leaving a
broader footprint along the chemical shift axis. For
example, observing GABA, whose concentration is
only 1 mM in the human brain, is difcult because the
signal at 3.0 ppm is coupled to the 1.9 ppm peak and
overshadowed by large signals from NAA, Glx, and
Cr. A frequency-selective pulse, which only directly
affects those signals close to 1.9 ppm, can be added to
the point-resolved spectroscopy sequence (PRESS).
The homonuclear radio frequency (RF) pulse will also
have an indirect effect on GABA signals at 3.0 ppm
because of the coupling, but not on the other uncou-
pled signals. If alternate experiments are performed
with and without this frequency-selective pulse, the
difference will give a spectrum that only contains the
signals affected by the selective perturbation.
14,15
There are a couple of obvious drawbacks to this
technique.
14–17
One is that only one metabolite is
optimized at a time (assuming that the multiplets of
the J-coupled metabolites are well separated). The
second disadvantage is the requirement for subtrac-
tion to remove the strong overlapping signals, which
makes the technique highly vulnerable to subject
movement and to instrumental factors, etc. that can in-
troduce artifacts into the spectrum.
16,17
Mescher et al.
proposed a different metabolite-editing technique
based on subtraction of two measurements, called
MEGA (Mescher–Garwood) that can be combined
with the two popular SV-MRS techniques, STEAM
(stimulated acquisition mode), and PRESS
18–20
(see
Chapter 7). Optimized MEGA-editing sequences
have also been proposed recently.
21,22
These newer
experimental techniques are inherently preferable
because they utilize multiple quantum coherences to
suppress overlapping signals in a single scan.
23,24
Beyond the problems noted above, it has become de-
sirable over the years to obtain multivoxel information
in a reasonable amount of time.
25–27
Chemical shift
imaging (CSI) using 1D MRS has helped satiate this
appetite somewhat but it is performed with sequences
using long echo times (TEs) and hence incurs par-
tial loss of those cerebral metabolites that have low
transverse relaxation times (T
2
s).
27–30
On the other
hand, multidimensional/multivoxel MRS imaging
(MRSI) techniques tackle these problems head-on
during acquisition by unambiguously resolving many
overlapping peaks nonselectively through the addi-
tion of spectral dimensions, while postprocessing
schemes such as Prot deal with quantication (see
Chapter 20).
31–36
These approaches have opened up
the application of MRS to many elds, and this will
lead to new paradigms in the coming decades.
It is important to note that while multidimensional
techniques have been the mainstay in chemistry and
biochemistry for decades, the road to bringing mul-
tidimensionalspectroscopyfrominvitrotoinvivo
applications has been difcult, primarily because
of two major challenges: the B
0
eld strength and
acquisition times. However, current methodologies
have, at least in part, addressed these problems,
and state-of-the-art techniques using clinical MRI
scanners have improved signal-to-noise ratios (SNR)
and reduced acquisition times to clinically practical
durations.
11,12
Two-Dimensional NMR Spectroscopy Plus Spatial Encoding 497
Currently, at least 15 cerebral metabolites can be
identied and quantied using two-dimensional (2D)
localized correlated spectroscopy (L-COSY), which
combines the original COSY sequence described by
Aue et al.
37
and postprocessing algorithms developed
at the University of California in Los Angeles.
35,38
A tool that can bring so much additional information
surely must increase our diagnostic and patient man-
agement capabilities in the clinic. This journey to the
state-of-the art today is described below.
30.2 SINGLE-VOXEL-BASED 2D MRS
30.2.1 2D L-COSY: Theory
Figure 30.1 shows the 2D L-COSY sequence that was
implemented on a 1.5 T MRI/MRS scanner in 2001,
where a combination of three slice-selective RF pulses
(90
∘
–180
∘
–90
∘
) enabled the localization of a volume
of interest (VOI) in a single shot.
38
After the forma-
tion of the Hahn spin echo using the rst 90
∘
and
180
∘
RF pulse pair, an incremental period for the sec-
ond spectral dimension (t
1
) was inserted immediately.
The last slice-selective 90
∘
RF pulse acted also as the
coherence transfer pulse, critical for recording the 2D
spectrum.
37,38
To remove unwanted coherences, this
sequence used refocusing B
0
gradient crusher pulses
around the slice-selective 180
∘
RF pulse, and also
before and after the last 90
∘
RF pulse. In order to im-
prove the SNR from the localized volume, multiple
averages could be used in combination with or without
a multistep RF phase cycling to minimize any artifacts
stemming from improper RF pulses. The 2D L-COSY
sequence has been successfully implemented and eval-
uated on 7, 3, and 1.5 T MRI scanners manufactured by
different vendors.
38–46
To understand the nature of the interactions between
spins during the evolution, mixing, and detection pe-
riods, and how these events modulate the amplitude,
frequency, and phase of the 2D spectral signal array, a
closer look at the time evolution of a weakly coupled
AX type spin-pair system with two protons A and
X, whose chemical shift is large compared to the
J-coupling between them, is considered here. Using
the density matrix formalism, the time course of evo-
lution of coherences and magnetization is presented
at the different time points marked in Figure 30.1 to
describe the spin state before and after each RF pulse,
as well as its evolution during different time intervals.
RF
G
x
G
y
G
z
FID
ADC
0
1
𝜏𝜏t
1
t
2
2
34 5 6
90° 90°180°
Figure 30.1. A schematic diagram of the 2D L-COSY
sequence containing three slice-selective RF pulses (90
∘
,
180
∘
,90
∘
) for volume localization. The B
0
-crusher gradient
pulses were played around the 180
∘
refocusing and the second
90
∘
coherence transfer RF pulses. After the evolution during
2𝜏, there is a formation of the Hahn spin echo. Direct acquisi-
tion along t
2
and indirect detection along t
1
enable encoding
of two spectral dimensions
The weakly coupled AX spin system has four
energy levels that can lead to 4 observable single
quantum (SQ) coherences (𝜔
12
, 𝜔
34
, 𝜔
13
, 𝜔
24
)and
nonobservable multiple quantum (zero and double
quantum) coherences: 𝜔
23
and 𝜔
14
under different
perturbations.
37,47
At time point 0 before the rst
slice-selective 90
∘
RF pulse, the spins are at the
Boltzmann equilibrium, and the spin state is described
by the F
z
matrix as shown below:
𝜌
0
∝
100 0
000 0
000 0
000−1
(30.1)
We assume that the RF pulses are applied along
the y-direction in the rotating frame of reference so
that the RF pulse rotation operators contain only real
numbers. The spin state after the rotation by the rst
90
∘
RF pulse along the y-direction (time point 1) is the
observable F
x
matrix containing nonzero elements for
the four SQ coherences:
𝜌
1
∝ P
y
−1
F
z
P
y
𝜌
1
∝
1
4
1 −1 −11
11−1 −1
1 −11−1
11 1 1
100 0
000 0
000 0
000−1
498 Methodology
1111
−11−11
−1 −111
1 −1 −11
∝
1
2
0110
1001
1001
0110
(30.2)
After time point 2, the SQ coherences start evolving
during 𝜏 as shown in Figure 30.1 and the density matrix
is
𝜌
2
∝
0e
−i𝜔
(
12
)
𝜏
e
−i𝜔
(13)
𝜏
0
e
i𝜔
(12)
𝜏
00e
−i𝜔
(24)
𝜏
e
i𝜔
(13)
𝜏
00e
−i𝜔
(34)
𝜏
0e
i𝜔
(24)
𝜏
e
i𝜔
(34)
𝜏
0
(30.3)
The evolving SQ coherences are characterized by
𝜔
12
∝(𝛿
X
+ J∕2),𝜔
34
∝(𝛿
X
− J∕2),
𝜔
13
∝(𝛿
A
+ J∕2) and 𝜔
24
∝(𝛿
A
− J∕2) (30.4)
where 𝛿
A
and 𝛿
X
are the chemical shifts of spins A
and X and J represents the indirect spin–spin coupling
(in rad s
−1
) that is communicated through the covalent
bonds. The direct spin–spin dipolar coupling between
the A and X protons communicated through space is
assumed to average to zero due to the tumbling motion
of these spins. After the evolution through crusher gra-
dient pairs and slice-selective refocusing of the 180
∘
RF pulse at the end of 𝜏, the spin state is described by
𝜌
3
∝ R
y
−1
𝜌
2
R
y
∝
1
2
00 01
00−10
0 −100
10 00
0e
−i𝜔
(
12
)
𝜏
e
−i𝜔
(13)
𝜏
0
e
i𝜔
(12)
𝜏
00e
−i𝜔
(24)
𝜏
e
i𝜔
(13)
𝜏
00e
−i𝜔
(34)
𝜏
0e
i𝜔
(24)
𝜏
e
i𝜔
(34)
𝜏
0
00 01
00−10
0 −100
10 00
∝
1
2
0 −e
i𝜔
(
34
)
𝜏
−e
i𝜔
(24)
𝜏
0
−e
−i𝜔
(34)
𝜏
00−e
i𝜔
(13)
𝜏
−e
−i𝜔
(24)
𝜏
00−e
i𝜔
(12)
𝜏
0 −e
−i𝜔
(13)
𝜏
−e
−i𝜔
(12)
𝜏
0
(30.5)
Now, the SQ coherences included in equation (30.5)
will evolve under another period, 𝜏 and at the end of
this period, the rst Hahn spin echo is described by
𝜌
4
∝−
1
2
0e
i
(
𝜔
(
34
)
−𝜔
(12)
)
𝜏
e
i(𝜔
(24)
−𝜔
(13)
)𝜏
0
e
i(𝜔
(12)
−𝜔
(34)
)𝜏
00e
i(𝜔
(13)
−𝜔
(24)
)𝜏
e
i(𝜔
(13)
−𝜔
(24)
)𝜏
00e
i(𝜔
(12)
−𝜔
(34)
)𝜏
0e
i(𝜔
(24)
−𝜔
(13)
)𝜏
e
i(𝜔
(34)
−𝜔
(12)
)𝜏
0
∝−
1
2
0e
−i2πJ𝜏
e
−i2πJ𝜏
0
e
i2πJ𝜏
00e
i2πJ𝜏
e
i2πJ𝜏
00e
i2πJ𝜏
0e
−i2πJ𝜏
e
−i2πJ𝜏
0
(30.6)
It is evident from equation (30.6) that the chemical
shift and any other linear interaction terms are refo-
cused at the time of the Hahn spin echo and that the
spin state contains phase terms with only the bilinear
J-coupling term. The rotation operators P
y
and R
y
used
in equations (30.2) and (30.5) represent the 90
∘
and
180
∘
RF pulses, respectively.
47
The spin state 𝜌
4
is followed by encoding of the
second spectral dimension with a variable time pe-
riod t
1
, meaning that during a series of repeat exper-
iments, t
1
takes on a different set of values that is
similar to phase encoding a second spatial dimension
in MRI. The evolution time (t
1
) is being incremented
here, as opposed to incrementing the amplitude of the
phase-encoding gradient in conventional MRI.
𝜌
5
∝−
1
2
0 Ke
−i𝜔
(
12
)
t
1
Ke
−i𝜔
(13)
t
1
0
K
∗
e
i𝜔
(12)
t
1
00K
∗
e
−i𝜔
(24)
t
1
K
∗
e
i𝜔
(13)
t
1
00K
∗
e
−i𝜔
(34)
t
1
0 Ke
i𝜔
(24)
t
1
Ke
i𝜔
(34)
t
1
0
(30.7)
where K = e
− i2πJ𝜏
and K
*
= e
i2πJ𝜏
.
After the evolution during t
1
, the spins evolve dur-
ing a mixing period in which a slice-selective 90
∘
RF
pulse is applied in the third orthogonal plane, again
sandwiched by gradient crusher pulses:
𝜌
6
∝ P
y
−1
𝜌
4
P
y
∝−
1
8
1 −1 −11
11−1 −1
1 −11−1
1111
0 Ke
−i𝜔
(
12
)
t
1
Ke
−i𝜔
(13)
t
1
0
K
∗
e
i𝜔
(12)
t
1
00K
∗
e
−i𝜔
(24)
t
1
K
∗
e
i𝜔
(13)
t
1
00K
∗
e
−i𝜔
(34)
t
1
0 Ke
i𝜔
(24)
t
1
Ke
i𝜔
(34)
t
1
0
