scispace - formally typeset

Reference EntryDOI

2‐D MR Spectroscopy Combined with 2‐D/3‐D Spatial Encoding

15 Mar 2016-Vol. 5, Iss: 1, pp 1039-1060

AbstractIn addition to detecting water and lipids in human tissues using magnetic resonance imaging (MRI), a number of metabolite resonances have been recorded noninvasively using one (chemical shift)-dimensional (1-D) proton (1H) magnetic resonance (MR) spectroscopy (MRS) on whole-body MRI scanners (1.5 and 3 T). However, severe overlap of resonances in 1-D MRS limits the unambiguous identification of many metabolites. Different versions of spectral editing sequences allow detection and quantification of selected metabolites. This approach, too, is limited in that it detects only one metabolite per acquisition, and many metabolites still cannot be detected owing to severe overlap. Adding another spectral dimension can overcome this limitation by providing resolution of metabolite resonances along the second dimension, thereby reducing the ambiguity, especially for quantifying J-coupled metabolites. In this article, we review progress with two-dimensional (2-D) MRS such as localized J-resolved spectroscopy (JPRESS) and localized correlated spectroscopy (L-COSY and their multidimensional versions, namely echo-planar-correlated spectroscopic imaging EP-COSI) and echo-planar J-resolved spectroscopic imaging (EP-JRESI), where 2-D spectral encoding is combined with two- or three-dimensional spatial encoding. These ‘4-D’ or ‘5-D’ spectroscopic imaging sequences can be extremely time consuming. However, acquisition using nonuniform undersampling (NUS) strategies and compressed sensing (CS) accelerates their acquisition times. Keywords: magnetic resonance spectroscopy; 2-D J-resolved spectroscopy (JPRESS); localized correlated spectroscopy (L-COSY); echo-planar spectroscopic imaging (EPSI); echo-planar correlated/J-resolved spectroscopic imaging; NAA; creatine; choline; nonuniform undersampling; compressed sensing

Summary (5 min read)

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 spectroscopy (MRS) was introduced in the clinical setting.
  • 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).
  • Furthermore, an inability to separate J-coupling from chemical shift leads to assignment problems that hinder the identification and quantification of metabolites.
  • 21,22 These newer experimental techniques are inherently preferable because they utilize multiple quantum coherences to suppress overlapping signals in a single scan.

30.2.1 2D L-COSY: Theory

  • The last slice-selective 90∘ RF pulse acted also as the coherence transfer pulse, critical for recording the 2D spectrum.
  • 37,47 The spin state after the rotation by the first 90∘ RF pulse along the y-direction (time point 1) is the observable A pure-phase L-COSY spectrum can be recorded using a quadrature detection method along the F1 axis, as described by Brereton et al.

30.2.2 Apodization Filters for 2D L-COSY

  • The 2D L-COSY spectrum will contain peaks along the diagonal that are similar to those of 1D MRS and cross-peaks connecting multiplets of spins that are J-coupled.
  • 37,38 The diagonal-peak intensities follow a cosine dependence, and time-domain cross-peak amplitudes increase from zero at the beginning to a maximum at 1/2 J, with the signal decaying according to the inhomogeneously broadened T2s (T2*).
  • Use of the skewed squared SB filter instead of a conventional exponential filter for processing the 2D spectrum in Figure 30.2 has three major advantages.
  • 52 First, unlike the exponential filter, the SB filter begins with a zero value and can emphasize cross-peaks relative to 2D diagonal peaks that are cosine dependent.
  • Third, truncation errors due to apodization are minimized at the end of the time domain: because of the trailing edge of the SB function, the window function goes smoothly to zero.

30.2.3 Eddy Current (EC) Correction

  • As shown in Figure 30.1, the 2D L-COSY sequence uses three slice-selective RF pulses combined with spatial gradient pulses.
  • 50,51 As with 1D MRS, 2D MRS is also sensitive to time-dependent frequency shifts that typically last a few milliseconds and that are induced by ECs due to switching the gradients on and off.
  • In order to calculate an EC-free spectral signal, the phase calculated from an on-resonance signal can be subtracted from the EC-corrupted signal.
  • The WS and NWS time-domain data were processed using the steps shown in Figure 30.3.
  • Using only the first signal (𝛥t1 = 0) from the NWS array for EC correction results in the L-COSY spectrum shown in Figure 30.4(b).

30.2.4 Localized Spin-echo Correlated Spectroscopy (L-SECSY)

  • Even though there is no real limitation on the number of complex points along the detected t2 dimension, the resolution along the F1 dimension of COSY is dictated by the total number of t1 increments, which directly affects the acquisition duration.
  • One solution that minimizes this loss is to acquire the data with the t1 increments before the 90∘ RF pulse only (similar to 2D L-COSY) and then impose the phase shift for the second t1 evolution as shown in Figure 30.5.
  • The 2D L-COSY data were acquired using the same acquisition parameters that were used for the brain phantom in Figure 30.4, and the WS L-COSY array was phase-corrected using the EC correction scheme in Figure 30.3, based on the first row of the NWS data.

30.2.6 Apodization Filters for 2D JPRESS

  • The J-coupled multiplets are better resolved along the in t1 dimension than in the detected t2 dimension, as any defocusing linear B0 interactions including the static field inhomogeneity during the first half of t1 are refocused during the second half, resulting in a net zero dependence on the B0 inhomogeneity and other static field interactions.
  • Even though this is a major advantage, the phase-modulated time-domain datasets are transformed into phase-twisted 2D peaks after the double FFT of the 2D JPRESS raw data.
  • Hence, the squared or simple SB filter functions described in Section 30.2.2 can be used before the double FFT.
  • 2D L-COSY spectrum acquired from a 35-year-old healthy human subject: (a) Axial MRI slice showing the voxel location.

30.2.7 Strong Coupling Effects in 2D JPRESS

  • One of the advantages of JPRESS over L-COSY is that the chemical shift and any linear interaction are refocused during the t1 dimension while the J-interaction remains unrefocused.
  • At 3 T or lower B0, this assumption is applicable only for weakly coupled metabolites such as lactate, alanine, and glycine.
  • Most other metabolites have strongly coupled protons where J-coupling is equal to or larger than their chemical shifts (𝛿 < J).
  • Hence, the refocusing 180∘ RF pulse at the center of the t1 evolution does not refocus all chemical shifts and results in more cross-peaks.
  • It has been demonstrated earlier that 2D JPRESS spectra of brain and prostate metabolites contain more cross-peaks than those of weakly coupled ones.

30.2.8 Adiabatic COSY and JPRESS

  • With NMR signal excitation using large body coils, the bandwidths of conventional refocusing RF pulses, such as optimized 180∘ pulses,68 become quite small.
  • A second problem with MRS/MRSI using conventional RF pulses is the difficulty of achieving a uniform RF transmit (B1) field, leading to poor slice-selection profiles.
  • All of these limitations and potential artifacts apply equally to L-COSY and JPRESS.
  • Ramadan et al. implemented an adiabatic localized correlated spectroscopy (AL-COSY) in which the VOI was localized by a 90∘ nonselective adiabatic RF pulse for excitation followed by two pairs of adiabatic HS RF pulses for refocusing and a terminal 90∘ RF sine pulse for the coherence transfer.
  • They showed that an ‘sLASERfirst-COSY’ sequence yielded stronger cross-peaks and higher ratios of cross-peak volumes to diagonal-peak volumes than the ‘sLASER-last-COSY’ sequence in which the nonselective hard 90∘ coherence transfer RF pulse is replaced by a slice-selective 90∘ RF pulse.

30.3.1 MRSI/Echo-planar Spectroscopic Imaging

  • Depending on the desired spatial resolution, traditional 2D or 3D MRSI25–27 with conventional CSI phase-encoding schemes generally lead to intolerable scan times.
  • If the MRSI scan requires multiple averages to achieve adequate SNR, or longer TRs to avoid saturation effects, the resultant total acquisition time can easily render clinical applications impractical.
  • In 1983, Mansfield77,78 proposed the use of an echo-planar readout gradient to simultaneously acquire one spatial and one spectral dimensions during a single readout.
  • Phase encoding of that spatial dimension is not needed.
  • This can reduce total scan time to around 20min.

30.3.2 4D Echo-planar Correlated

  • A 4D EP-COSI sequence is shown in Figure 30.8, using two spatial encodings (kx and ky) and two spectral dimensions (t2 and t1).
  • The sequence uses a 90∘–180∘–90∘ scheme for localizing the VOI with crusher gradients surrounding the refocusing 180∘ and coherence transfer 90∘ RF pulses.
  • The ‘n’ subscript along the ADC and Gx axes in Figure 30.8 represents the total number of echo-planar readout pairs (positive and negative) that result in the desired number of t2 spectral points.
  • With a slice-selective 180∘ yields the 4D EP-JRESI sequence.
  • The main difference between the two sequence parameters is that a spectral bandwidth of 1000Hz is used for the indirect dimension in EP-JRESI, whereas EP-COSI uses a spectral bandwidth of 1250Hz for the indirect dimension.

30.3.4 Postprocessing of the 4D EP-COSI/EP-JRESI Data

  • Reconstruction of 4D EP-COSI and EP-JRESI data sets is performed offline using custom MATLAB software macroroutines.
  • The center of the k-space is traversed repeatedly with a constant time interval in an ideal EPSI readout.
  • This misalignment generates spectral ghost artifacts when the echoes are combined.
  • 87 Both the reference NWS scans and WS scans have to be first separated into even and odd subsets and reorganized into kx – ky − t2− (t1 for WS only) matrices.
  • The NWS EP-COSI/EP-JRESI data are used to determine the spatially-dependent resonant frequency shifts owing to local B0 inhomogeneities and ECs from gradient switching.

30.3.5 Multiecho Echo-planar Correlated

  • To record a turbo spin-echo (TSE) or fast spin-echo (FSE) MRI,88–90 multiecho (ME)-encoding schemes have been used to reduce the overall scan duration dramatically.
  • Following the first echo-planar readout (t2), the initial phase encoding is reversed just before the 180∘ pulse, whereupon a different line in k-space is phase encoded after the 180∘ pulse.
  • These two different sets of echoes can be summed together by time-reversing the even-numbered gradient echoes to create a single image.
  • Sarma et al.95 modified the ME-EPSI sequence to implement ME-based echo-planar J-resolved Spectroscopic Imaging (MEEP-JRESI) in the human brain.
  • After the completion of the first EPSI readout, the initial phase encoding is reversed, and the decaying magnetization during the first readout train is refocused using the slice-selective 180∘ pulse.

30.3.7 Data Processing of 4D MEEP-COSI/MEEP-JRESI

  • Reconstruction of the ME-EP-COSI/MEEP-JRESI data sets is done offline using a custom MATLAB software package as shown in Figure 30.11.
  • Because of the opposite directions of the trajectories along kx caused by the alternating readout gradients, the odd (or even) echoes must be reversed during data processing for reasons discussed in Section 30.3.4.
  • Both the reference and water-suppressed scans will first be separated into positive (even) and negative (odd) subsets and reorganized into x-y-t2-(t1 for WS only) matrices.
  • The reorganized spectral points will be interpolated to 1024 points using zero filling in the time domain (t2).
  • A skewed squared SB apodization filter can be used to reduce contamination from extra-voxel signals due to the imperfect PSF in both the non-water-suppressed and water-suppressed scans.

180° pulse

  • Be corrected in theWS scan using the phase differences measured from an NWS reference scan.53–55.
  • A pseudo 4D EP-COSI data recorded in a gray matter brain phantom is considered here, using a sequence employing frequency encoding (kx) only with one phase-encoding gradient along the other spatial dimension (𝛥ky = 0) on a 3 T scanner.
  • It is interesting to note that the second correction method gives almost similar results to the third correction method and implies that the EC corrections do not greatly vary from t1 point to t1 point.
  • Therefore, it is recommended that when performingmultidimensional spectroscopic imaging (with 2 spectral+ spatial dimensions), an NWS scan should be acquired with 𝛥t1 = 0 to use for EC corrections for higher spatial and spectral quality.

30.3.10 Evaluation of EP-COSI and MEEP-COSI in Calf Muscle

  • There has been significant attention focused on the relationships between lipid composition within the skeletal muscle and insulin sensitivity, diabetes and obesity.
  • 99,102–110 Spatially resolved MRS techniques enable quantitation of several metabolites including Cr, Cho groups, carnosine, etc. as well as intramyocellular lipids and extramyocellular lipids .
  • (a) T1-weighted MRI of a human calf muscle in a 26-year-old healthy volunteer overlaid with an MRSI grid with voxels highlighted in the tibia marrow , tibialis anterior (red), and soleus (blue) muscles.
  • 2D spectra with 1D diagonal projections for (b) the marrow, (c) tibialis, and (d) soleus voxels spectra can be obtained using EP-COSI in about 20min of scan time.

30.4 ACCELERATED ECHO-PLANAR

  • J-RESOLVED MRSI WITH NONUNIFORM UNDERSAMPLING AND COMPRESSED SENSING.
  • The CS reconstruction attempts to enforce the sparsity, while simultaneously maintaining the fidelity of the original measurements to within the noise.
  • Furuyama et al. and Sarma et al. successfully modified the 4D EP-JRESI sequence to accommodate NUS in the kyt1 plane, 84,116 while using the EPSI readout gradient to encode the spatial (kx) and temporal dimensions (t2).
  • They achieved a twofold acceleration in scan time.
  • The reconstructed data sets show alterations of metabolic features of OSA patients and healthy human brain84 and demonstrate the clinical feasibility of a CS-based 4D EP-JRESI sequence.

30.5 PRIOR-KNOWLEDGE FITTING FOR METABOLITE QUANTITATION

  • A few years ago, Schulte et al. developed a prior-knowledge fitting algorithm based on a linear combination of 2D model spectra and demonstrated the feasibility of quantification of brain and prostate metabolites (see Chapter 20).
  • The corresponding 2D J-resolved spectra extracted from the mid-frontal and left-frontal voxels are shown in (b) and (c), respectively.
  • © American Society of Neuroradiology, 2014) model and JMRUI,4,5 ProFit performs a hybrid timeand frequency-domain fitting using a nonlinear outer loop and an inner linear least-squares fit for obtaining signal amplitudes (proportional to the concentrations) and incorporates the maximum available prior knowledge.
  • The architecture of the fitting process allows for another useful measure of the quality of the fitting of the spectrum by comparing the creatine 3.9 ppm (Cr3.9) to the creatine 3.0 ppm (Cr3.0) signal ratio, which ideally should be 1 because the number of protons (2 and 3, respectively) is already accounted for in their prior-knowledge basis set.

30.6 FUTURE DIRECTIONS: CLINICAL APPLICATIONS

  • Localized 2D MRS has left its infancy and is maturing.
  • In contrast to the decades-old SV-based 2D L-COSY and 2D JPRESS spectroscopic sequences, fully-sampled multivoxel-based 4D EP-JRESI and EP-COSI sequences facilitate the recording of 2D COSY and J-resolved spectra from multiple regions of the brain.
  • Now, recent developments demonstrate that further acceleration is possible using NUS schemes, the end result being the shortening of the total scan time for 4D EP-JRESI and EP-COSI sequences to around 10min or less.
  • At the very least, these techniques clearly demonstrate a rich treasure trove of information linking molecules, metabolism, and function that awaits their investigation.

Did you find this useful? Give us your feedback

...read more

Content maybe subject to copyright    Report

UCLA
UCLA Previously Published Works
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. Grifths
© 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 identied and
quantied 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 difcult 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 bloodbrain
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 identication and quantication 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 difcult 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.
1417
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 (MescherGarwood) that can be combined
with the two popular SV-MRS techniques, STEAM
(stimulated acquisition mode), and PRESS
1820
(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.
2527
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).
2730
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 Prot deal with quantication (see
Chapter 20).
3136
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 difcult, 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
identied and quantied 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.
3846
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
0001
(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
111 1
1 111
11 1 1
100 0
000 0
000 0
0001

498 Methodology
1111
1111
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
+ J2),𝜔
34
∝(𝛿
X
J2),
𝜔
13
∝(𝛿
A
+ J2) and 𝜔
24
∝(𝛿
A
J2) (30.4)
where 𝛿
A
and 𝛿
X
are the chemical shifts of spins A
and X and J represents the indirect spinspin coupling
(in rad s
1
) that is communicated through the covalent
bonds. The direct spinspin 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
0010
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
0010
0 100
10 00
1
2
0 e
i𝜔
(
34
)
𝜏
e
i𝜔
(24)
𝜏
0
e
i𝜔
(34)
𝜏
00e
i𝜔
(13)
𝜏
e
i𝜔
(24)
𝜏
00e
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
111 1
1 111
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

Figures (11)
Citations
More filters

Journal ArticleDOI
TL;DR: This work covers terms used to describe all aspects of MRS, starting from the description of the MR signal and its theoretical basis to acquisition methods, processing and to quantification procedures, as well as terms involved in describing results, including those used with regard to aspects of quality, reproducibility or indications of error.
Abstract: With a 40-year history of use for in vivo studies, the terminology used to describe the methodology and results of magnetic resonance spectroscopy (MRS) has grown substantially and is not consistent in many aspects. Given the platform offered by this special issue on advanced MRS methodology, the authors decided to describe many of the implicated terms, to pinpoint differences in their meanings and to suggest specific uses or definitions. This work covers terms used to describe all aspects of MRS, starting from the description of the MR signal and its theoretical basis to acquisition methods, processing and to quantification procedures, as well as terms involved in describing results, for example, those used with regard to aspects of quality, reproducibility or indications of error. The descriptions of the meanings of such terms emerge from the descriptions of the basic concepts involved in MRS methods and examinations. This paper also includes specific suggestions for future use of terms where multiple conventions have emerged or coexisted in the past.

23 citations


Cites methods from "2‐D MR Spectroscopy Combined with 2..."

  • ...In vivo, 2D J-resolved MRS and variants of the COSY(79,82,83) method are most popular.(74,84) For further details, the reader is referred to the literature on high-resolution NMR....

    [...]


Journal ArticleDOI
TL;DR: Preliminary findings indicate that the CovJ method may be used to improve spectral resolution without hindering metabolite quantitation for J‐resolved spectra.
Abstract: Magnetic resonance spectroscopy (MRS) is a powerful tool capable of investigating the metabolic status of several tissues in vivo. In particular, single-voxel-based 1 H spectroscopy provides invaluable biochemical information from a volume of interest (VOI) and has therefore been used in a variety of studies. Unfortunately, typical one-dimensional MRS data suffer from severe signal overlap and thus important metabolites are difficult to distinguish. One method that is used to disentangle overlapping resonances is the two-dimensional J-resolved spectroscopy (JPRESS) experiment. Due to the long acquisition duration of the JPRESS experiment, a limited number of points are acquired in the indirect dimension, leading to poor spectral resolution along this dimension. Poor spectral resolution is problematic because proper peak assignment may be hindered, which is why the zero-filling method is often used to improve resolution as a post-processing step. However, zero-filling leads to spectral artifacts, which may affect visualization and quantitation of spectra. A novel method utilizing a covariance transformation, called covariance J-resolved spectroscopy (CovJ), was developed in order to improve spectral resolution along the indirect dimension (F1 ). Comparison of simulated data demonstrates that peak structures remain qualitatively similar between JPRESS and the novel method along the diagonal region (F1 = 0 Hz), whereas differences arise in the cross-peak (F1 ≠0 Hz) regions. In addition, quantitative results of in vivo JPRESS data acquired on a 3T scanner show significant correlations (r2 >0.86, p<0.001) when comparing the metabolite concentrations between the two methods. Finally, a quantitation algorithm, 'COVariance Spectral Evaluation of 1 H Acquisitions using Representative prior knowledge' (Cov-SEHAR), was developed in order to quantify γ-aminobutyric acid and glutamate from the CovJ spectra. These preliminary findings indicate that the CovJ method may be used to improve spectral resolution without hindering metabolite quantitation for J-resolved spectra.

4 citations


References
More filters

Journal ArticleDOI
TL;DR: Practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference and demonstrate improved spatial resolution and accelerated acquisition for multislice fast spin‐echo brain imaging and 3D contrast enhanced angiography.
Abstract: The sparsity which is implicit in MR images is exploited to significantly undersample k -space. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain–for example, in terms of spatial finite-differences or their wavelet coefficients. According to the recently developed mathematical theory of compressedsensing, images with a sparse representation can be recovered from randomly undersampled k -space data, provided an appropriate nonlinear recovery scheme is used. Intuitively, artifacts due to random undersampling add as noise-like interference. In the sparse transform domain the significant coefficients stand out above the interference. A nonlinear thresholding scheme can recover the sparse coefficients, effectively recovering the image itself. In this article, practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference. Incoherence is introduced by pseudo-random variable-density undersampling of phase-encodes. The reconstruction is performed by minimizing the 1 norm of a transformed image, subject to data

5,802 citations


Journal ArticleDOI
Abstract: The possibilities for the extension of spectroscopy to two dimensions are discussed. Applications to nuclear magnetic resonance are described. The basic theory of two‐dimensional spectroscopy is developed. Numerous possible applications are mentioned and some of them treated in detail, including the elucidation of energy level diagrams, the observation of multiple quantum transitions, and the recording of high‐resolution spectra in inhomogenous magnetic fields. Experimental results are presented for some simple spin systems.

2,916 citations


Journal ArticleDOI
TL;DR: Based on the principles of echo imaging, a method is proposed to acquire sufficient data for a 256 × 256 image in from 2 to 40s, and the signal amplitudes of structures with long T2 are nearly the same as those in a conventional 2D FT experiment.
Abstract: Based on the principles of echo imaging, we present a method to acquire sufficient data for a 256 X 256 image in from 2 to 40 s. The image contrast is dominated by the transverse relaxation time T2. Sampling all projections for 2D FT image reconstruction in one (or a few) echo trains leads to image artifacts due to the different T2 weighting of the echo. These artifacts cannot be described by a simple smearing out of the image in the phase direction. Proper distribution of the phase-encoding steps on the echoes can be used to minimize artifacts and even lead to resolution enhancement. In spite of the short data acquisition times, the signal amplitudes of structures with long T2 are nearly the same as those in a conventional 2D FT experiment. Our method, therefore, is an ideal screening technique for lesions with long T2.

1,956 citations


Journal ArticleDOI
TL;DR: DRESS is a simple and versatile localization procedure that is readily adaptable to spectral relaxation time measurements by adding inversion or spin-echo refocusing pulses or to in vivo solvent-suppressed spectroscopy of proton (1H) metabolites using a combination of chemical-selective RF pulses.
Abstract: Spatial localization techniques are necessary for in vivo NMR spectroscopy involving heterogeneous organisms. Localization by surface coil NMR detection alone is generally inadequate for deep-lying organs due to contaminating signals from intervening surface tissues. However, localization to preselected planar volumes can be accomplished using a single selective excitation pulse in the presence of a pulsed magnetic field gradient, yielding depth-resolved surface coil spectra (DRESS). Within selected planes, DRESS are spatially restricted by the surface coil sensitivity profiles to disk-shaped volumes whose radii increase with depth, notwithstanding variations in the NMR signal density distribution. Nevertheless, DRESS is a simple and versatile localization procedure that is readily adaptable to spectral relaxation time measurements by adding inversion or spin-echo refocusing pulses or to in vivo solvent-suppressed spectroscopy of proton (1H) metabolites using a combination of chemical-selective RF pulses. Also, the spatial information gathering efficiency of the technique can be improved to provide simultaneous acquisition of spectra from multiple volumes by interleaving excitation of adjacent planes within the normal relaxation recovery period. The spatial selectivity can be improved by adding additional selective excitation spin-echo refocusing pulses to achieve full, three-dimensional point resolved spectroscopy (PRESS) in a single excitation sequence. Alternatively, for samples with short spin-spin relaxation times, DRESS can be combined with other localization schemes, such as image-selected in vivo spectroscopy (ISIS), to provide complete gradient controlled three-dimensional localization with a reduced number of sequence cycles.

1,333 citations


Journal ArticleDOI
TL;DR: The LCModel method analyzes an in vivo spectrum as a Linear Combination of Model in vitro spectra from individual metabolite solutions using complete model spectra, rather than individual resonances, in order to incorporate maximum prior information into the analysis.
Abstract: The LCModel method analyzes an in vivo spectrum as a Linear Combination of Model in vitro spectra from individual metabolite solutions. Complete model spectra, rather than individual resonances, are used in order to incorporate maximum prior information into the analysis. A nearly model-free constrained regularization method automatically accounts for the baseline and lineshape in vivo without imposing a restrictive parameterized form on them. LCModel is automatic (non-interactive) with no subjective input. Approximately maximum-likelihood estimates of the metabolite concentrations and their uncertainties (Cramer-Rao lower bounds) are obtained. LCModel analyses of spectra from users with fields from 1.5 to 9.4 T and a wide range of sequences, particularly with short TE, are used here to illustrate the capabilities and limitations of LCModel and proton MRS.

1,321 citations


Frequently Asked Questions (1)
Q1. What are the contributions mentioned in the paper "Two-dimensional nmr spectroscopy plus spatial encoding" ?

One-dimensional ( 1D ; in the chemical shift spectral domain ) single-voxel ( SV ) -based magnetic resonance spectroscopy ( MRS ) was introduced in the clinical setting this paper.