Optimization of the flip angles of narrow-band editing pulses in J-difference edited MRS of lactate at 3T

Abstract

Purpose:

Application of highly selective editing RF pulses provides a means of minimizing co-editing of contaminants in J-difference MRS (MEGA), but it causes reduction in editing yield. We examined the flip angles (FAs) of narrow-band editing pulses to maximize the lactate edited signal with minimal co-editing of threonine.

Methods:

The effect of editing-pulse FA on the editing performance was examined, with numerical and phantom analyses, for bandwidths of 17.6 – 300 Hz in MEGA-PRESS editing of lactate at 3T. The FA and envelope of 46 ms Gaussian editing pulses were tailored to maximize the lactate edited signal at 1.3 ppm and minimize co-editing of threonine. The optimized editing-pulse FA MEGA scheme was tested in brain tumor patients.

Results:

Simulation and phantom data indicated that the optimum FA of MEGA editing pulses is progressively larger than 180° as the editing-pulse bandwidth decreases. For 46 ms long 17.6 Hz bandwidth Gaussian pulses and other given sequence parameters, the lactate edited signal was maximum at the first and second editing-pulse FAs of 241° and 249°, respectively. The edit-on and difference-edited lactate peak areas of the optimized FA MEGA were greater by 43% and 25% compared to the 180°-FA MEGA, respectively. In-vivo data confirmed the simulation and phantom results. The lesions of the brain tumor patients showed elevated lactate and physiological levels of threonine.

Conclusion:

The lactate MEGA editing yield is significantly increased with editing-pulse FA much larger than 180° when the editing-pulse bandwidth is comparable to the lactate quartet frequency width.

INTRODUCTION

Lactate plays important roles in several functions including energy supply and cell signaling for neuronal activities, and changes in brain lactate level are associated with many neurological disorders.^1,2 The ability to detect brain lactate accurately is therefore of clinical value. Recently, Robison et al. reported MEGA-PRESS editing of lactate and threonine in the human brain.³ Using 45.3 ms long 180° editing pulses (bandwidth 17.6 Hz) at 3T, which had negligible effects at resonances 0.15 ppm away from the carrier frequency, the 1.3 ppm resonances of lactate and threonine were differentiated by means of selective inversion of their coupling partners at 4.1 and 4.25 ppm in two edit-on scans, followed by subtraction of an edit-off spectrum from the edit-on data. The lactate edit-on signal from the narrow-band editing pulses was substantially smaller compared to that from large bandwidth editing pulses. Also, the pattern of the lactate 1.3 ppm signal in a threonine edit-on scan was very different than the lactate signal from a PRESS run. These observations were largely associated with the use of the narrow-band editing pulses, whose bandwidth was comparable to the lactate quartet frequency width (~20 Hz).

When the inversion band of editing pulses does not fully cover the frequency range of the transitions between the lactate CH proton energy states, the longitudinal polarization of the CH proton spins is not completely inverted by the editing pulses and consequently the inphase coherence of the 1.3 ppm spin resonance is reduced at the end of the sequence, thereby leading to reduction in the edit-on signal of lactate.³ Part of the longitudinal polarization of the lactate 4.1 ppm resonance may become transverse during the lengthy low-B₁ RF action and may result in production of multiple types of coherences. We hypothesized that the coherence generation depends on the flip angle (FA) of the editing pulses and thus the MEGA editing-pulse FA is linked to the fractional inphase coherence at the end of the edit-on scan when the editing-pulse bandwidth is relatively small. In this paper, we report some numerical and phantom analyses that were conducted to find editing-pulse FAs responsible for maximum MEGA-PRESS edited lactate signal at 3T. Gaussian editing pulses with a wide range of bandwidths have been examined. In vivo data from brain tumor patients, obtained with an optimized editing scheme, are presented.

METHODS

Spectrally-selective RF pulses with Gaussian envelopes were implemented in a MEGA-PRESS sequence to examine the effects of the editing-pulse FA in lactate editing. A Gaussian pulse had truncations at a percentage level β with respect to its maximum RF amplitude and used for spin rotation through θ degrees (Supporting Information Figure S1). The TE of the MEGA PRESS was 144 ms, at which the lactate inphase coherences may be maximum in PRESS.

Density-matrix simulations were conducted to assess the lactate editing efficacy of the MEGA-PRESS sequences. The density operator evolution was numerically calculated using a product-operator based transformation-matrix algorithm,⁴ programmed in Matlab. Transformation matrices were created for the slice-selective pulses and the Gaussian editing pulses, incorporating the actual RF and gradient pulse envelopes, and used for calculating MEGA edit-on, edit-off, and difference spectra, as described in a prior study⁵. For given RF and gradient pulses, the editing-pulse FAs responsible for maximum lactate edited signal were investigated.

Proton MR experiments were carried out on a Philips Elition 3T human scanner, equipped with a whole-body coil for RF transmission and a 32-channel head coil for reception. Phantom experiments were performed on an aqueous solution with 20 mM lactate and 20 mM N-acetylaspartate (NAA) and another solution with 31 mM threonine and 34 mM NAA, both at pH 7.0. Data were obtained, with 2 s TR and 144 ms TE, from a 20×20×20 mm³ voxel at the center of the spherical phantoms. Lactate MEGA edit-on data were acquired with serial FAs ranging from 90° to 300° (5° increments) for three types of Gaussian editing pulses (bandwidths 17.6, 33.2, and 300 Hz). MEGA data were obtained with lactate-tailored editing-pulse FA and the conventional 180° FA.

In vivo MEGA experiments were performed in two brain tumor patients. The brain tumor MR protocol was approved by the local Institutional Review Board. Written informed consent was obtained from the subjects. The MEGA acquisition parameters included 2 s TR, 144 ms TE, 2.5 kHz sweep width, and 2048 sampling points. FIDs were recorded in multiple blocks, each with 8 averages of water-suppressed FIDs. The MEGA editing pulses were tuned to 4.1, 4.25 and 100 ppm (subscans X, Y and Z) for editing of lactate and threonine. An unsuppressed MEGA water signal was acquired at the beginning of each block and used as reference in multi-channel combination and eddy-current compensation. The water signal was also used to determine and update the reference frequency for the block, followed by real-time frequency-drift correction in each excitation using a vendor-supplied tool. A four-pulse variable-flip-angle method was used for water suppression.⁶ B₁ calibration and up-to-second-order shimming were conducted with vendor-supplied tools. The B₁ of editing pulses was calibrated with MEGA edit-on water signals. An unsuppressed water signal was acquired with TE 14 ms STEAM (TR 15 s) for use as a reference in metabolite quantification.

The in vivo multi-block MEGA data were frequency aligned prior to summation. Data were apodized with a 1-Hz exponential and 1-Hz Gaussian function before Fourier transformation. Spectral fitting of the edit-off and difference spectra was performed with LCModel software⁷. The basis sets for fitting of difference spectra had model spectra of 7 metabolites, which included lactate, threonine, NAA, NAAG, my-inositol, MM14, and MM12. The basis spectra were calculated including the effects of slice-selective RF and gradient pulses, with published chemical-shift and J-coupling constants.^8,9 The spectral fitting was conducted between 0.2 and 4.0 ppm. The metabolite levels were estimated in millimolar units with reference to the STEAM water at 48 M, similarly to prior studies^10,11.

RESULTS

Density-matrix simulations and phantom data showed that the lactate edit-on signal was maximized at editing-pulse FA greater than 180° when the bandwidth of the pulses was relatively small (Figure 1A,B). While a 300 Hz bandwidth editing pulse gave a maximum lactate signal at an FA of 181°, editing pulses with 33.2 and 17.6 Hz bandwidths showed maximum lactate signals at their FAs of 211° and 259°, respectively. The maximum peak areas from the 17.6 and 33.2 bandwidth pulses were 85% and 94% with respect to that from the 300 Hz bandwidth editing pulses, respectively. For an FA of 180°, the lactate peak area ratio between the 17.6, 33.2, and 300 Hz bandwidths was 60:86:100. Good agreement was seen between calculated and phantom spectra (Figure 1C). In addition, simulations with five-bandwidth Gaussian pulses (17.6 – 300 Hz) showed that the lactate edit-on signal is larger at unequal FAs of the first and second editing pulses (θ₁ > θ₂) compared to the equal-FA cases and that the deviation of the FAs from 180° increases progressively as the editing-pulse bandwidth decreases (Supporting Information Figure S2).

FIGURE 1.

(A) Bloch-simulated inversion profiles of three 180° Gaussian RF pulses are presented for carrier frequency at 4.1 ppm. The pulse duration, truncation percentage, and half-amplitude bandwidth are shown in each subfigure. (B) Green lines and circles represent theoretical and experimental peak areas of a singlet resonance following MEGA edit-on sequences as a function of flip angle (FA) for the three Gaussian editing pulses shown in A. The carrier frequency of the editing pulses was set to a 4.1 ppm artificial singlet resonance in the simulation and to the water resonance in the experiment. Blue lines and circles represent simulated and in-vitro peak areas of the lactate 1.3 ppm resonance following the MEGA edit-on sequence as a function of FA for the three editing pulses shown in A. The carrier frequency of the editing pulses was set at 4.1 ppm in the simulation and experiment. The first editing pulse was identical to the second editing pulse (i.e., θ₁ = θ₂ and β₁ = β₂). Vertical lines are drawn at 181°, 211° and 259°, at which the edit-on lactate peak area was maximum for the three editing pulses. The lactate data from the three editing pulses were normalized to the maximum peak area of the 3.3 ms pulse. The truncation levels β of the three Gaussian envelopes were kept constant for all FAs. (C) Simulated (red line) and phantom (blue line) MEGA edit-on signals of the lactate 1.3 ppm resonance are presented, on top of each other, for the three FAs at which the lactate peak area was maximum. The spectra broadened to singlet FWHM of 6 Hz. Two vertical lines in the top-right subfigure indicate the spectral region (1.215 – 1.415 ppm) of the peak area calculation for the data shown in B.

Seven 46 ms Gaussian pulses were designed for FAs of 180° - 300°, all having a half-amplitude bandwidth of 17.6 Hz (Figure 2A,B). The truncation levels of the envelopes were adjusted for nulling their effects on resonances 0.15 ppm away from the carrier frequency, with the goal of minimizing co-editing of threonine in lactate editing. The truncation level was monotonically decreased as the FA increased (Figure 2C), suggesting that the truncation levels for FAs between the seven FAs can be accurately calculated.

FIGURE 2.

(A) Seven 46 ms long Gaussian RF pulses are shown for flip angles (FA) ranging from 180° to 300°. The numbers in brackets denote the truncation percentages β relative to the maximum B₁ of individual Gaussian pulses. (B) Bloch-simulated inversion profiles of the seven Gaussian pulses are presented for a carrier frequency at 4.1 ppm. A vertical line is drawn at 4.25 ppm (threonine ³CH proton resonance), on which the seven Gaussian pulses all had negligible effects. The lactate ²CH proton quartet and threonine ³CH proton multiplet, broadened to singlet FWHM of 1 Hz, are shown at the top. (C) Open circles represent the FAs and truncation levels of the seven Gaussian envelopes, and the solid line is a cubic spline interpolation of the circled values. Note that the Gaussian pulses defined by the FAs and truncation levels on the interpolated line all had a 17.6 Hz bandwidth at half amplitude.

Gaussian pulses with 17.6 Hz bandwidth, whose envelopes were designed according to the interpolation in Figure 2C, were used for simulating MEGA-edited lactate signals for FAs between 180° and 300° (1° increments for each of θ₁ and θ₂) (Figure 3A). The maximum edit-on and difference-edited lactate peak areas were both observed at (θ₁, θ₂) of (241°, 249°). These Gaussian editing pulses were tested in a phantom solution. MEGA subspectra, obtained with editing-pulse carrier frequencies at 4.1, 4.25, and 100 ppm (subspectra X, Y, and Z, respectively), confirmed the simulated lactate signal intensity and pattern (Figure 3B). Compared to the 180° FA data, editing with the optimized FAs showed lactate peak amplitude and area greater by 44% and 43% in the subspectrum X and by 26% and 25% in (X−Z)/2 difference spectra, respectively (Figure 3B,C). The lactate signal was inverted in the subspectrum Y due to the small effect of the editing pulses on the lactate CH proton spins, resulting in a small lactate signal in the (Y−Z)/2 spectra. The lactate peak amplitude and area in the (Y−Z)/2 spectra were both 22% relative to those in the (X−Z)/2 spectra. Simulation and phantom data showed that the threonine edited signal at 1.3 ppm is similarly enhanced with the lactate-optimized FAs (Supporting Information Figure S3). Compared to 180°-FA MEGA, the optimized-FA MEGA showed threonine edit-on and difference-edited peak areas greater by 39% and 26%, respectively. The threonine peak area ratio between (X−Z)/2 and (Y−Z)/2 spectra were 0.31 and 0.27 for optimized-FA and 180°-FA, respectively.

FIGURE 3.

(A) The areas of edit-on, edit-off and difference-edited lactate 1.3 ppm signals, simulated with 46 ms long 17.6 Hz bandwidth Gaussian editing pulses, are color mapped for the first and second flip angles (FA), θ₁ and θ₂, between 180° and 300° (1° increments). In the simulation, the truncation level was adjusted for a constant bandwidth of 17.6 Hz for individual FAs according to the interpolated line shown in Figure 2C. The peak area was normalized to the maximum value of the edit-on data. For edit-on and difference subfigures, the maximum value is shown adjacent to a solid circle, which was put at the (θ₁, θ₂) of the maximum value. Dashed lines are drawn for θ₁ of 241° and θ₂ of 249°. The carrier frequency of the editing pulses was set at 4.1 ppm in the edit-on simulations. (B) Simulated and phantom MEGA edited spectra of lactate and NAA for the optimized FAs and truncation levels of 46 ms Gaussian editing pulses (bandwidth 17.6 Hz). The ppm values in brackets (i.e., 4.1, 4.25 and 100 ppm) denote the carrier frequency of the editing pulses. (C) Simulated and phantom MEGA edited spectra of lactate and NAA for 180° FA of 46 ms Gaussian editing pulses (bandwidth 17.6 Hz). In B and C, the spectra were broadened to NAA FWHM of 6 Hz and normalized to the NAA peak amplitude. Simulated spectra were scaled according to the phantom T₂ relaxation times (T₂ = 750 and 1000 ms for lactate and NAA, respectively).

Optimized-FA MEGA data from a brain tumor patient are shown in Figure 4. The patient presented a large T₂-FLAIR hyperintensity volume following surgery and adjuvant chemoradiation therapy. Subspectra, obtained from a non-enhancing T₂-FLAIR volume, showed a spectral pattern that was similar to the normal-brain MRS pattern, but the metabolite signals were much smaller compared to normal brain when normalized to water signal, suggesting that the large FLAIR volume was highly edematous. The concentration estimates of total choline (tCho), total creatine (tCr), and total NAA (NAA+NAAG) were 0.9, 2.7, and 3.9 mM, respectively. A doublet-looking signal was discernible at 1.3 ppm in subspectra X and the signal intensity was clearly higher in optimized-FA MEGA than in 180°-FA MEGA. In the (X−Z)/2 difference spectra, a signal was readily discernible at 1.3 ppm while other metabolite signals were canceled out. The area of the 1.3 ppm peak, returned by LCModel, was larger by 27% in the optimized-FA editing than in the 180°-FA editing, close to what was predicted by simulations and phantom experiments. Spectral fitting of the spectra resulted in similar lactate estimates between the two MEGA methods (1.2 – 1.3 mM, with standard deviations of 2 – 3%), which was as expected since the lactate signal difference between the methods was accounted for in the basis signal preparation. Threonine was not detectable in the (X−Z)/2 spectra, in which threonine co-editing was suppressed. The threonine edited spectra (Y−Z)/2, in which lactate signal was suppressed, showed small signals at 1.3 ppm, suggesting that threonine was unlikely elevated in the lesion and thus a threonine signal in the (X−Z)/2 spectra may be negligible. Fitting of the (Y−Z)/2 spectra resulted in non-zero estimations for both lactate and threonine. The threonine level was estimated to be approximately 0.3 mM. An inverse correlation of −0.164 was observed between lactate and threonine in this difference data while zero correlation was returned by LCModel in the (X−Z)/2 data where the threonine estimates were null (Supporting Information Table S1).

FIGURE 4.

In vivo MEGA edited data from a brain tumor patient, acquired with optimized flip angle (FA) MEGA and 180° FA MEGA, are presented together with LCModel fitting results and voxel positioning in T₂-FLAIR images. The millimolar estimates of lactate and threonine are shown with the LCModel-returned percentage standard deviation values in brackets. The FAs and truncation percentages of the 46 ms Gaussian pulses are shown at the top of each subfigure. The notations of sub and difference spectra are identical to those in Figure 3B,C. Horizontal lines are drawn between spectra from the two MEGA schemes to aid with comparison of lactate signals. The number of signal averages was 64 for each subscan (duration 2.1 min).

Figure 5 shows MEGA-edited data from another brain tumor patient, who presented a large T₂-FLAIR hyperintensity volume after chemoradiation treatment. Spectra from the FLAIR volume also showed relatively low levels of metabolites when normalized to water. Large negative signals were present between 1.2 – 1.5 ppm in all subspectra. These presumably artifactual signals were canceled with the spectral subtraction and as a result, the (X−Z)/2 difference spectra showed a well-defined peak at 1.3 ppm. The LCModel-returned 1.3 ppm peak area was greater by 24% in the optimized-FA MEGA compared to 180°-FA MEGA. Fitting of the (X−Z)/2 spectra returned 2.1 – 2.2 mM lactate and null threonine in both editing methods. A small signal was seen at 1.3 ppm in the (Y−Z)/2 spectra. Spectral fitting resulted in lactate and threonine estimates of 2.1 – 2.4 and 0.4 – 0.5 mM, respectively.

FIGURE 5.

In vivo MEGA edited data from another brain tumor patient, acquired with the two MEGA schemes, are presented in a similar fashion to Figure 4. The number of signal averages was 80 for each subscan (duration 2.7 min).

DISCUSSION

The current paper reports that the MEGA edited signal is maximized at editing-pulse FA larger than 180° when the bandwidth of the editing pulse is not much greater than the multiplet splitting of the J-coupling partner on which the editing pulses act. The deviation of the optimum FA from 180° increases as the editing-pulse bandwidth deceases. In the case of 46 ms Gaussian pulses having bandwidths less than 18 Hz, the bandwidth is smaller than the frequency width of the lactate quartet (~20 Hz) and consequently the lactate edited signal at 1.3 ppm is maximized at FA of 240° - 260°, depending on the truncation level of the pulse envelope and the resulting bandwidth. It is noteworthy that the editing performance can be further improved with differing FAs and envelopes of the two editing pulses in MEGA, as demonstrated in the present study.

A 2D-localizing MEGA-PRESS simulation indicated that the fractional inphase coherence of the optimized-FA MEGA was larger uniformly throughout the 2D space of the localized volume compared to the 180°-FA MEGA. When four compartments were modeled as shown in Supporting Information Figure S4, the increase of the inphase coherence in the edit-on run was 41%, 46%, 49%, and 42% for compartments 1, 2, 3, and 4, respectively. The lactate edit-on signal was larger by similar ratios for individual compartments and for the entire localized volume.

The edit-on signal reduction in narrow-band MEGA editing pulses may be associated with coherence leakage to multiple-quantum coherences that occurs during the editing pulses. A simulation indicated that, for 300 Hz bandwidth editing pulses, the evolution of the lactate 1.3 ppm spin coherences occurs largely between single-quantum coherences throughout the edit-on sequence and a fractional inphase coherence of as high as 93% with respect to the initial coherence may result (Supporting Information Figure S5). In contrast, some zero-/double-quantum coherences may be generated during narrow-band editing pulses, resulting in a signal loss in the edit-on scan. The optimized-FA MEGA preserves the single-quantum coherences to a larger degree throughout the edit-on sequence compared to 180°-FA MEGA, leading to a larger fractional inphase coherence at the end of the sequence. The fractional inphase coherence at the end of the sequence was calculated as 81% and 57% for optimized-FA and 180°-FA MEGA, respectively.

A simulation indicated that, for the slice-selective 180° pulse of the present study (bandwidth 1258 Hz), when the FAs of the first and second editing pulses (both 46 ms long 17.6 Hz bandwidth) are equally varied, the lactate edit-on signal was maximized at an FA of 246°. When the bandwidth of the slice-selective 180° pulse was twice larger (2516 Hz), the maximum edit-on lactate signal occurred at a reduced FA of 237°. For a very large bandwidth slice-selective 180° pulse (e.g., > 100 kHz), the maximum edit-on lactate signal was seen at 235°. This 235° FA was also the case for a non-localized MEGA sequence having very short 90° and 180° pulses (e.g., 1 ns). The increase in optimal FA may therefore be a feature of the MEGA editing scheme, without having much to do with the voxel displacements arising from the finite bandwidths of slice-selective RF pulses.

When MEGA editing of a resonance can be contaminated by co-edited signals, such as co-editing of threonine in lactate editing and co-editing of macromolecules in GABA editing, a narrow-band editing pulse would provide a means of minimizing the interference from the co-editing, as demonstrated in prior studies.^3,12 The edited signal reduction due to the effect of narrow-band editing pulses can be significantly recovered using editing-pulse FA larger than 180°, as shown in the present study and in a prior study¹³. Since the frequency width of the GABA 1.9 ppm quintet is as large as 30 Hz, for a given editing-pulse envelope the difference of the optimum FA from 180° may be larger in GABA editing compared to lactate editing. Also, an optimum FA for editing of the glutathione 2.95 ppm resonances would deviate from 180° to a lesser degree as the glutathione triplet at 4.56 ppm is as narrow as 12 Hz.

Accurate FA calibration for MEGA editing pulses is important for achieving the optimized edited signal strength. The FA of editing pulses may be accurately calibrated using MEGA edit-on signals of a large singlet. In the present study, the FA of editing pulses was determined with MEGA edit-on water signals prior to lactate editing scans. Also, potential frequency-drift effects were minimized by determining the reference frequency in real time in each excitation. The frequency variations of the choline peak during the 6 – 8 min in-vivo scans were measured to be within ±1.5 Hz.

Using tailored editing-pulse envelopes and FAs in a three-subscan MEGA scheme, the present study has accomplished the first in-vivo observation that, in brain tumor patients, the signal increase at 1.3 ppm is mainly attributed to lactate elevation and the threonine level may not be considerably altered. A major limitation of the present study is the small number of subjects enrolled for in-vivo demonstration of the editing approach. Further study in a large number of brain tumor subjects with various levels of lipids may identify refined subgroups in which the lactate level and the lactate/lipid ratio are clinically informative.

CONCLUSION

While the 180° editing-pulse FA may provide a robust MEGA scan parameter for large editing-pulses bandwidths, the MEGA editing yield is maximized at FAs significantly greater than 180° when the editing-pulse bandwidth is relatively small. For MEGA editing of lactate using editing pulses with a bandwidth of 17.6 Hz, the first and second editing-pulse FAs of 240° - 250° may confer enhancements in lactate edit-on and difference-edited signals by approximately 43% and 25% compared to 180°-FA MEGA, without considerable co-editing of threonine. For given RF pulses, optimum FA of the MEGA editing pulses can be sought for improving the editing performance, in addition to optimization of TE and inter-RF pulse timings¹⁴. Our data from patients provide the first in-vivo evidence that lactate is elevated in brain tumors while threonine is not. Given the prior reports of similar levels of lactate and threonine in the healthy brain,^3,15 the proposed editing approach has potential for reliable measurement of changes in lactate level in brain diseases and/or after interventions, in which alterations in the level are modest.

Supplementary Material

Supporting Information

FIGURE S1. Schematic diagram of the TE 144 ms MEGA PRESS of the present study. Two Gaussian editing RF pulses, which were applied before and after the second 180° slice-selective RF pulse, had a duration of TP, flip angles of θ₁ and θ₂, and truncation levels of β₁ and β₂. The time delay between the editing pulse and the slice-selective pulse was 33.6 ms for both editing pulses. The slice-selective 90° and 180° RF pulses were 9.8 and 13.2 ms long at B₁ of 13.5 μT (bandwidth 4.2 and 1.3 kHz, respectively). The spoiling gradient pulses were 2.4 and 3.4 ms long during the TE₁ and TE₂ periods, respectively (all with 27 mT/m strength).

FIGURE S2. The simulated MEGA edit-on lactate peak area is color mapped for five Gaussian editing pulses, whose half-amplitude bandwidth at a flip angle of 180° ranged from 17.6 to 300 Hz. The flip angles of the first and second editing pulses spanned from 90° to 300°, with 1° increments. The peak area was calculated between 1.215 and 1.415 ppm in lactate signals broadened to singlet FWHM of 6 Hz. The peak amplitude and area were normalized respectively to the maximum values of the 3.3 ms editing pulse data and color mapped between 0 and unity for all editing pulses. For each subfigure, the maximum value is shown adjacent to a solid circle, which was put at the (θ₁, θ₂) of the maximum value. Horizontal and vertical lines are drawn at θ₁ = 180° and θ₂ = 180° in each subfigure. The simulation showed that the lactate edit-on peak area was maximum at FAs greater than 180° for all cases. As the editing-pulse bandwidth decreased, the first and second FAs θ₁ and θ₂ responsible for maximum peak area moved progressively further away from (θ₁, θ₂) of (180°, 180°) and the maximum peak area was progressively smaller. The maximum lactate peak area from the 17.6 Hz bandwidth 46 ms Gaussian editing pulse MEGA was observed at (θ₁, θ₂) of (251°, 270°) with magnitude of 85% relative to that of the 300 Hz bandwidth 3.3 ms editing pulse MEGA. The ratio of the maximum peak area to the peak area at (θ₁, θ₂) of (180°, 180°) was progressively larger with decreasing bandwidth.

FIGURE S3. Simulated and phantom MEGA edited spectra of threonine and NAA are presented for the optimized FA and 180° FA MEGA in a similar fashion to Figure 3. The spectra were broadened to NAA FWHM of 6 Hz and normalized to the NAA peak amplitude. Simulated spectra were scaled according to the phantom T₂ relaxation times (T₂ = 750 and 1000 ms for threonine and NAA, respectively).

FIGURE S4. The calculated fractional inphase coherence of the lactate 1.3 ppm spin resonance at the end of the MEGA sequence (i.e., −A_y of the lactate A₃X spin system) is color mapped for the edit-on, edit-off, and difference runs of the optimized editing-pulse flip angle (FA) MEGA (left) and the 180° FA MEGA (right). The simulations were conducted with two slice-selective 180° RF pulses (bandwidth 1258 Hz, duration 13.2 ms, and B₁ 13.5 μT) localizing a 30×30 mm² 2D voxel at the center of a 45×45 mm² 2D volume. The carrier frequency of the slice-selective RF pulses was set at 2.7 ppm, halfway between the lactate resonances (4.1 and 1.3 ppm). The number of slice-selective gradient segments was 150 along each of the x and y axes. For each map, four compartments (red boxes) are labeled 1, 2, 3, and 4, for each of which an average spectrum was calculated. The four mean spectra of the compartments are plotted, on top of each other, in blue, red, green, and black, respectively. The spectra of the entire localized volume are shown below in purple. Horizontal lines are drawn to aid with comparison of the signal strengths between the optimized FA MEGA and the 180° FA MEGA. Shown at the right bottom is the refocusing profile of the slice-selective 180° RF pulse. Note that, for the compartments 3 and 4 of the 180° FA MEGA, the edit-on inphase coherence was notably smaller than the edit-off inphase coherence, resulting in some inphase coherences with opposite polarity in the difference coherence map. The opposite-polarity inphase coherence was markedly reduced in the (X - Z)/2 map of the optimized FA MEGA, leading to difference-edited signal enhancement.

FIGURE S5. The coefficients of the eight transverse coherence terms of the lactate 1.3 ppm spin resonance, which were averaged over the entire 2D localized volume of 1.3 ppm in Supporting Information Figure S4, are plotted for six time points for three types of 2D localizing MEGA schemes. The flip angles θ, truncation percentages β, and half-amplitude bandwidth of the editing pulses are shown at the top for the three MEGA schemes. Vertical lines are drawn between single-quantum coherence and zero/double-quantum coherence terms for each MEGA scheme. Horizontal lines are drawn to aid with comparison of the 1.3 ppm inphase coherence (i.e., −A_y) between the MEGA schemes. In the simulation, the density operator evolution of the lactate A₃X spin system was numerically calculated with the inter-RF pulse timings in Supporting Information Figure S1 after replacing the slice-selective 90° pulse by ρ = −A_y − X_y, where A_y = A_1y + A_2y + A_3y.

TABLE S1. The LCModel-returned correlation coefficients among the estimates of lactate, threonine, MM12, and MM14 are presented for the data from two brain tumor subjects.