Short symmetric and highly selective asymmetric first and second order gradient modulated offset independent adiabaticity (GOIA) pulses for applications in clinical MRS and MRSI

Abstract

Gradient modulated RF pulses, especially gradient offset independent adiabaticity (GOIA) pulses, are increasingly gaining attention for high field clinical magnetic resonance spectroscopy and spectroscopic imaging (MRS/MRSI) due to the lower peak B₁ amplitude and associated power demands achievable relative to its non-modulated adiabatic full passage counterparts. In this work we describe the development of two GOIA RF pulses: 1) A power efficient, 3.0 ms wideband uniform rate with smooth truncation (WURST) modulated RF pulse with 15 kHz bandwidth compatible with a clinically feasible peak B₁ amplitude of 0.87 kHz (or 20 μT), and 2) A highly selective asymmetric 6.66 ms RF pulse with 20 kHz bandwidth designed to achieve a single-sided, fractional transition width of only 1.7%. Effects of potential asynchrony between RF and gradient-modulated (GM) waveforms for 3 ms GOIA-WURST RF pulses was evaluated by simulation and experimentally. Results demonstrate that a 20+ μs asynchrony between RF and GM functions substantially degrades inversion performance when using large RF offsets to achieve translation. A projection-based method is presented that allows a quick calibration of RF and GM asynchrony on pre-clinical/clinical MR systems. The asymmetric GOIA pulse was implemented within a multi-pulse OVS sequence to achieve power efficient, highly-selective, and B₁ and T₁-independent signal suppression for extracranial lipid suppression. The developed GOIA pulses were utilized with linear gradient modulation (X, Y, Z gradient fields), and with second-order-field modulations (Z2, X2Y2 gradient fields) to provide elliptically-shaped regions-of-interest for MRS and MRSI acquisitions. Both described GOIA-RF pulses have substantial clinical value; specifically, the 3.0 ms GOIA-WURST pulse is beneficial to realize short TE sLASER localized proton MRS/MRSI sequences, and the asymmetric GOIA RF pulse has applications in highly selective outer volume signal suppression to allow interrogation of tissue proximal to extracranial lipids with full-intensity.

Introduction

Proton magnetic resonance spectroscopy (MRS) and spectroscopic imaging (MRSI) are powerful techniques that can measure levels of neurochemicals in the brain, non-invasively (1–3). Moving towards higher magnetic field strengths (> 3 T) provides improved sensitivity, and improved spectral quantification due to increased spectral dispersion as highlighted by the separation of glutamate and glutamine in human brain at 7 T (4). While beneficial for spectroscopic signal acquisition, the increased chemical shift dispersion leads to increased chemical shift displacement (CSD) with spatial localization. CSD artifacts are minimized with the utility of high bandwidth RF pulses at the cost of increased RF power deposition. Frequency offset corrected inversion (FOCI) (5) pulses employ gradient modulation to achieve a ten-fold improvement in CSD and a substantially reduced transition width (TW) ratio, relative to an adiabatic full passage (AFP) hyperbolic secant (HS) counterpart (6), while operating within experimental peak B₁ amplitudes applicable to human brain studies (< 25 μT). Based on the adiabatic condition, Tannus and Garwood developed the Gradient Offset Independent Adiabaticity (GOIA) algorithm (7) for computing a frequency modulation (FM) function for a given amplitude modulation (AM) and gradient modulation (GM) function set. In this seminal work by Tannus and Garwood, a hyperbolic secant modulated GOIA pulse (GOIA-HS) was developed that requires substantially less peak B₁ amplitude and time-average power relative to a FOCI pulse of equal bandwidth, making GOIA pulses highly attractive for MRS (8) and MRSI (9) applications at high magnetic fields.

Wideband uniform rate and smooth truncation (WURST) modulated (10) GOIA pulses (GOIA-WURST,11) is an attractive alternative to GOIA-HS variants that allows: 1) short duration pulses with peak B₁ amplitudes compatible with most clinical systems to realize high BW semi- LASER (localization by adiabatic spin-echo refocusing 12) methods with short TE (3,8,13), and 2) reduce inversion profile smearing of off-resonance spins (due to chemical shift) relative to HS modulated GOIA pulses (8,9,11,14). This originally presented GOIA-WURST (11) pulse (with R = 70, where R = BW.T_p, BW and T_p are the RF pulse bandwidth and length, respectively) however is less efficient at lower R values in the R ≈ 45 range in terms of time-averaged power requirements. In this work a GOIA-WURST variant optimized for R = 45 is investigated, that allows T_p = 3 ms, for short TE sLASER and ECLIPSE (Elliptical localization with pulsed second-order fields 15) based inner volume selection (ECLIPSE-IVS) implementations compatible on clinical systems.

Highly selective RF pulses provide the ability to interrogate tissue types of interest proximal to contaminant regions (e.g., skull lipids adjacent to cortical tissue). In situations where cortical tumors are present, or in pathologies such as Alzheimer’s disease, where cortical tissue atrophy is prominent, the ability to interrogate underlying neurochemistry with minimal extracranial lipid contamination is greatly beneficial. As part of this work, we investigated a highly selective asymmetric GOIA pulse that combines power efficiency of high BW GOIA pulses and high selectivity of asymmetric AFP pulses.

Hardware related time delays can exist between the trigger and start of output waveforms for both RF and gradient amplifiers. Given that gradient modulated RF pulses require synchronized outputs from both gradient and RF systems, time-offsets can lead to distorted localization profiles. The measurement and calibration of such hardware delays from gradient and RF systems have previously been described (16–18), with gradient amplifier delays in the order of 5 – 80 μs and RF amplifier delays in the 2 – 10 μs reported. The effect of such an asynchrony between RF and gradient waveforms on short GOIA-WURST RF pulses was evaluated in this work with simulations and experimentally. Subsequently, a projection-based calibration method was used to synchronize RF and gradient waveforms.

In summary, here we further advance the envelope of capabilities with GOIA pulses by presenting: 1) a power efficient R ≈ 45 GOIA-WURST pulse variant to allow 3 ms long RF pulses with 15 kHz BW for short TE sLASER implementations compatible on > 3 T clinical systems, and 2) a highly selective asymmetrical GOIA pulse that is simultaneously capable of providing Transition width (TW) metrics of 1.7% and 20 kHz BW, allowing interrogation of tissue proximal to lipid contaminants ~ 2 mm away.

Theory

Localization metrics

Localization performance achievable with an RF pulse or following a sequence of RF pulses, can be primarily characterized by the fractional transition width defined as the BW to TW ratio; and CSD. The TW is defined here as the frequency span covering −0.9 < M_z/M₀ < 0.9, and 0.05 < M_z/M₀ < 0.95 for inversion and saturation, respectively. The BW is the frequency span where M_z/M₀ = 0 and M_z/M₀ = 0.5 for the two cases. The fractional TW characteristic can be improved, for example, by moving towards lower exponent (n < 1) HS AM functions, or in general moving away from flat top AM functions (19,20). The chemical shift displacement (CSD) is defined as the chemical shift spanning from fat to water (δ = 4.7 – 1.2 ppm) in Hz to BW ratio given by: $CSD\left(B_0\right)=\frac{\delta \cdot B_0}{BW}$, where CSD scales with magnetic field strength (B₀), and can only be reduced by increasing the RF pulse BW.

GOIA-WURST

The GOIA-WURST pulse (11) is generated with the WURST (10) modulation for both amplitude (AM) and gradient modulation (GM) functions, derived from F₁(τ) and F₃(τ) functions as follows:

$${\text{F}}_1(\tau )=\left(1-|\sin (\tau ){|}^n\right)$$ (1)

$${\text{F}}_3(\tau )=\left((1-\text{GF})+\text{GF}|\sin (\tau ){|}^m\right)$$ (2)

Here n and m are AM and GM exponents, $\tau =\frac{\pi }{2}\left(\frac{2\text{t}}{{\text{T}}_p}-1\right)$, 0 ≤ t ≤ T_p, GF = 1 – (1/GA), where GA is the gradient amplification factor.

Hereafter a GOIA pulse will be denoted by the shorthand notation of GOIA-XX(n – m, GA), where XX is the modulation type (HS, WURST). The originally proposed GOIA-WURST pulse (11) can be denoted GOIA-WURST(16–4, 10) with the above notation. Given F₁(τ) and F₃(τ), the frequency modulation function F₂(τ), was computed (7) numerically in MATLAB by solving the GOIA algorithm:

$$\frac{d{F}_2(\tau )}{d\tau }-\frac{F_2(\tau )}{F_3(\tau )}\cdot \frac{d{F}_3(\tau )}{d\tau }=\frac{F_1^2(\tau )}{K}$$ (3)

Here K is a scaling constant to normalize the frequency sweep of F₂(τ) such that A ∙ F₂(τ) spans [-A A], R = BW ∙ T_p = 2A ∙ T_p. The final AM, and GM functions are then given as follows:

$$\text{AM}(\tau )=B_{1(95\%)}{F}_1(\tau )$$ (4)

$$\text{GM}(\tau )=GA\cdot F_3(\tau )$$ (5)

B_1(95%) is defined as the minimum B₁ amplitude required to achieve > 95% inversion efficiency (i.e., M_z/M₀ < - 0.9) throughout the slice and meet a mean M_z/M₀ < - 0.95 throughout the inversion BW. Translation is achieved by modifying the FM function according to

$$\text{FM}(\tau )=A\cdot F_2(\tau )+\Delta v_{RF}\cdot F_3(\tau )$$ (6)

Here Δv_RF, is the frequency offset required for an equivalent BW non-GM RF pulse, that needs to be scaled by the time-dependent function F₃(τ) to maintain the slice position.

We investigated an R = 45 (T_p = 3 ms, BW = 15 kHz) variant of the GOIA-WURST(16–4, 10) pulse constrained to 1) peak B₁ < 0.9 kHz for T_p = 3 ms, considering inversion profile smearing associated with GOIA pulses due to chemical shift, and 2) time-averaged power efficiency compared to a previously utilized GOIA-HS(4–2, 5) pulse (14). Empirically perturbing n, m, and GA, the above criterial were met in simulation with n = 12, m = 4, and GA = 7, with R = 45 (hereafter called the GOIA-WURST(12–4, 7) pulse). RF pulse components of the GOIA-WURST(12–4, 7) and GOIA-HS(4–2, 5) are illustrated in Figure 1A for R = 45.

FIGURE 1.

(A) Modulation functions for the GOIA-HS(4–2, 5) R45, and GOIA-WURST(12–4, 7) R45 pulses with T_p = 3 ms. (i) AM functions for the three pulses, where B₁ amplitudes correspond to the 95% inversion efficiency. (ii) FM function and (iii) GM function for the three pulses. The GM function is normalized to the maximum gradient strength. The GOIA factor for the two pulses being 5, and 7 result in the mid-pulse plateau value to be 1/5, and 1/7, respectively. (B) Comparison of simulated residual M_z/M₀ profiles vs B₁ amplitude for the (i) GOIA-HS(4–2, 5), and (ii) GOIA-WURST(12–4, 7) pulses with R = 45 for on-resonance. (iii-iv) correspond to the residual M_z/M₀ profiles for the two pulses in presented order, for a 300 Hz chemical shift (corresponding to 1.75 ppm at 4 T).

Asymmetric GOIA

The asymmetric GOIA pulse design was inspired by a previously described asymmetric AFP pulse with HS and HT amplitude modulation (AM) functions (20). The AM and gradient modulation (GM) functions of the GOIA HS pulse are:

$${\mathrm{F}}_1(\tau )=\mathrm{s}\mathrm{e}\mathrm{c}h\left(\mathrm{\beta }{\tau }^n\right)$$ (7)

$${\mathrm{F}}_3(\tau )=\left(1-\text{GF}\cdot \mathrm{sech}\left(\mathrm{\beta }{\tau }^m\right)\right)0\le \tau \le 1$$ (8)

For the GOIA based HT pulse,

$${\text{F}}_1(\tau )={[\tanh (\xi \tau )]}^n$$ (9)

$${\text{F}}_3(\tau )=(1-\text{GF})+\text{GF}\cdot {[\tanh (\kappa \tau )]}^m-1\le \tau \le 0$$ (10)

For both cases, $\tau =\left(\frac{2\text{t}}{{\text{T}}_p}-1\right)$, 0 ≤ t ≤ T_p, and AM, FM, and GM functions are as defined in eq (1 and 2).

Optimization of the HS and HT components, and their time-contributions to the overall asymmetric GOIA pulse were determined based on the following requirements and constraints:

1. A TW of < 2% around the transition edge of interest. This characteristic is primarily dependent on the time-contribution of the HS component relative to T_p.

2. The parameters and time-contributions of the two pulse components (specifically the HT component) were constrained to limit the maximum GM function slew rate to be below the system gradient rise times when selective for a 3 cm slab.

3. Asymmetric GOIA pulses tend to have a skewed inversion profile similar to asymmetric AFP pulses (20), thus, produce a non-uniform inversion (at practical B₁ amplitudes) or saturation across the slice. Conversely, highly effective OVS can be achieved with an optimized multiple pulse and delays strategy (21), in the presence of B₁ inhomogeneity and heterogeneous T₁ spin species (22,23). Given the skewed inversion profile of asymmetrical GOIA pulses, an efficient OVS module can be developed by utilizing a power efficient RF pulse capable of achieving saturation (M_z/M₀ < 0) throughout the slab. Thus, the R-values and contributions from HS and HT components was empirically optimized to achieve time-averaged power efficient saturation (M_z/M₀ < 0) throughout the slab.

The developed asymmetric-GOIA pulse adhering to the above requirements, is composed of half an HS pulse with 3600 points (or 82.8% of T_p), and half an HT pulse with 750 points (or 17.2% of T_p). The full passage HS pulse parameters are: β = 5.3, n, m = 1, R = 248, and the full passage HT pulse parameters are: ξ = 5.3, κ = 1.52, n = 1, m = 4, R = 42. Given that tanh(κ) = 0.909, tanh[(κτ)]⁴ spans from 0 to 0.68, F₃(τ) requires normalizing prior to scaling it to span from 1/GA to 1. GA = 8 was used for both pulse components. The asymmetric-GOIA pulse was utilized with T_p = 6.66 ms, with 20 kHz BW. The AM, FM and GM functions of the asymmetric pulse are illustrated in Figure 2.

FIGURE 2.

Modulation functions for the GOIA-asymmetric pulse with T_p = 6.66ms, and BW = 20 kHz. The transition from HT to HS components is marked by the dashed line. (A) Amplitude modulation normalized to 1, (B) Frequency modulation in kHz, (C) Gradient modulation, where the GM function is normalized to the maximum gradient strength required. The amplitude at the lowest point is 1/GA. In the combined RF pulse, the HS and HT component constitutes of 3600 and 750 points (or 0.17T_p and 0.83T_p) respectively.

Practical considerations with GOIA pulses

In comparison to AFP pulses where a static gradient field is maintained during the RF pulse, gradient-modulated pulses require a time-varying gradient field as described above. Notably, AM(τ), FM(τ), and GM(τ) functions experienced within the region of interest (ROI) are required to be reproduced faithfully (distortion-less) and in synchrony. High fidelity can be of concern if the GM waveform slew rate approaches or exceeds the maximum slew rate of the system gradients, and if other imperfections such as gradient oscillations and eddy current effects are present. Furthermore, insufficient sampling with the digital-to-analog (DAC) conversion of the gradient waveform was recently reported to result in compromised localization profiles with spatial offset (24). In this work we limit the practical considerations to asynchronous pulsation of the RF and gradient waveforms. Noting that AM(τ) and FM(τ) functions are part of the RF pulse, an asynchrony can be present between the RF and gradient waveform generation, where the GM function experimentally is

$${\text{GM}}_{exp}(\tau )=\mathrm{GM}(\tau +\delta )$$ (11)

Here δ is defined such that a positive/negative delay corresponds to the gradient waveform leading/lagging the RF pulse, respectively. Considering |δ| > 0, GM_exp(τ) and FM(τ) functions diverge from the theoretical functions, with FM(τ) further deviating with increased RF offsets (Δv_RF) as described in eq (6). Discrepancies between GM_exp(τ) and FM(τ) result in performing an altered frequency sweep (or perturbing an altered spatial slab) which manifests as a distorted localization profile. This principle is exploited to develop a projection-based method to identify and calibrate out a |δ| > 0 situation.

Methods

MR system

All MR experiments were performed on a 4 T magnet (Magnex Scientific Ltd., Yarnton, UK) interfaced to a Bruker Avance III HD spectrometer running ParaVision 6 (Bruker, Billerica, MA, USA). The system contains actively shielded gradients capable of switching 30 mT/m in 1150 μs (26mT/m/ms), and is equipped with a full set of second-order shim coils. A home-built second-order unshielded gradient insert (ECLIPSE) with Z2, X2Y2, and XY spherical order harmonic magnetic fields (15) was used to generate elliptical ROI’s as previously reported (14,15,23). The minimum rise time of the ECLIPSE magnetic fields is 660 μs, but is derated to 1150 μs to match the linear system gradients. A within-brain B₁⁺ optimized, 8-element Tx/Rx volume coil embedded in the ECLIPSE gradient coil was used in a fixed phase configuration. The 8-element Tx/Rx volume coil has a ± 30% and ± 70% B₁ variation within the brain and extracranial region, respectively, with a minimum B₁ amplitude of 1 kHz (~ 24 μT) achievable throughout the brain.

GOIA-WURST pulses for short TE spectroscopy and spectroscopic imaging

The GOIA-WURST(12–4, 7) pulse was compared against an R (= 45) matched GOIA-HS(4–2, 5) pulse operating with T_p = 3 ms. The GOIA-HS(4–2, 5) pulse was used as a reference as it: 1) provides the lowest time-averaged power requirements considering smearing due to off-resonance, compared to other popularly used GOIA pulses at R = 45 (7,9,11,14), and 2) satisfied required metrics (BW, TW, T_p) while operating at compatible peak B₁ and time averaged power values.

An elliptical inner volume-selective, double-spin-echo MRSI method (TE 22.2 ms) using ECLIPSE gradients (here after called ECLIPSE-IVS) (15) executed with GOIA-WURST(12–4, 7) was developed (Figure S1A) preceded with the following: 1) A macromolecular nulling inversion recovery (IR) module (TI = 200 ms) with water suppression (WS), hereafter called IR-MRSI. 2) An 8-pulse VAPOR (variable power RF pulses with optimized relaxation delays, 25,26) module (hereafter termed no-IR-MRSI). The IR + WS and WS modules precedes the IVS module as illustrated in Figure S1A). Timings of the optimized IR-MRSI WS module were: 1763 – 894 – 448 – 224 – 154 – 68 – 39 – 12 ms before the excitation pulse, with relative amplitudes of 1.05α, α, 1.17α, 1.78α, 1.17α, α, 1.35α, 1.78α (pulse sequence diagram is not illustrated). An AFP-HS2 R12 pulse (T_p = 6.66 ms, BW = 1.8 kHz) was used for macromolecule nulling, placed 200 ms before the excitation pulse within this WS module.

Asymmetric GOIA pulses for outer volume suppression

The HS and HT modulation based asymmetric GOIA pulse (hereafter labelled GOIA-asymmetric) was compared against two reference RF pulses: an AFP pulse with HS2 modulation (R = 40), and a GOIA-HS(4–2, 5) pulse with R = 133. Requirements for the two reference pulses were to: 1) have similar power requirements to achieve saturation, 2) have peak B₁ amplitudes compatible with clinical systems, and 3) provide high TW metrics within its family of pulses The AFP HS2 pulse was chosen as it provides a balance between high TW metrics and peak B₁ requirements relative to HS1 and HS4 variants. The GOIA-HS(4–2, 5) pulse was selected as it provides excellent TW metrics considering off-resonance smearing relative to HS1 and HS2 based GOIA pulses, and serves as a reference to previous work (14). The three pulses were integrated within a 4-pulse OVS configuration (analogous to a WET (21) styled WS method) to achieve B₁ and T₁ independent OVS (Figure S1B). The four pulses in the OVS method are place 1181, 560, 218, and 50 ms before the excitation pulse with relative B₁ amplitudes of 0.64, 0.71, 0.83, and 1, respectively, with interleaved water suppression pulses as previously described (14). Here the n^th RF pulse is followed by a delay τ_n corresponding to the inter-pulse delay (mid points of the n^th and (n+1)^th RF pulses). Since the AM function of the asymmetric-GOIA pulse is skewed to the left, the inter-pulse delay between an asymmetric-GOIA OVS pulse (n^th pulse) and symmetrical RF pulse ((n+1)^th RF pulses) was found to be (τ_n – 2 ms) in simulation. Gradient pre- and post-pulses are placed between each OVS pulse with −50% amplitude to minimize eddy current induced B₀ modulations generated by the unshielded ECLIPSE Z2 gradient coil (14). The negative sign on the GOIA pulse gradient (Figure S1B), realizes a Z2 field (G_Z2) that is positive in the X-Y plane moving away from the origin, given G_Z2 = k_Z2 [2z² – (x² – y²)] (for z = 0), where k_Z2 is the quadratic field amplitude. In this work, the convention of k_Z2 < 0 was used similar to previous work (14,23) such that elliptical lipid ROI radii are smaller than the water ROI radii due to chemical shift.

The sLASER sequence in combination with the asymmetric GOIA OVS method was used to demonstrates localization performance with linear gradients in phantom and was subsequently utilized with ECLIPSE to demonstrate capabilities to interrogate cortical tissue on a curved brain edge proximal to extracranial lipids.

Bloch simulations

1-D Bloch simulations of M_z/M₀ vs B₁ amplitude were used to evaluate: 1) inversion efficiency with regard to time-averaged power and peak B₁ requirements, 2) selectivity metrics (TW and CSD), and 3) inversion profile smearing of GOIA pulses due to chemical shift. For the 3 ms RF pulses compared, inversion profile smearing due to a ± 300 Hz (or ± 1.75 ppm at 4 T) chemical shift was evaluated. Conversely, smearing due to a 600 Hz chemical shift was evaluated for the GOIA-asymmetric pulse within the 4-cycle OVS method for T₁ = 400 ms (characteristic for lipid species at 4 T (23)), since the carrier frequency is set on-resonance for lipids in the OVS method, to be power efficient as described in a previous study (14).

Localization performance of the GOIA-WURST(12–4, 7) pulses due to a δ delay between RF and GM was evaluated in simulation as described in eq (11) above, by extending the Bloch simulations in 2-D (a 40 x 40 mm² in-plane voxel). Localization profiles were generated for five delay settings: δ = −50, −20, 0, +20, +50 μs, and for three y-translations, namely y = 0, 40, and 80 mm, which are achieved with 0, 15, and 30 kHz modulated RF offsets. In each case, δ = 0 for x-selective RF/gradient waveforms.

Phantom experiments

A silicon oil phantom was used to evaluate TW metrics, and a vegetable oil/water phantom was used to evaluate CSD metrics experimentally. A large (~ 100 mm diameter) metabolite phantom and small (~ 10 mm diameter) lipid phantom separated by ~ 2 mm was used to evaluate localization and lipid suppression performance of the asymmetric GOIA-OVS method. Localization profiles due to a δ time delay between the RF and gradient waveforms (described above) were evaluated on a conductivity and permittivity matched sugar/salt mixed water phantom (27) with a B₁ variation of ~ 40% in the region of interest.

Human subjects, acquisition parameters, and data processing

MRSI and MRS acquisitions were validated in vivo on two healthy volunteers with repeat measurements following written informed consent. All procedures were approved by the Yale University Institutional Review Board. Multi-slice gradient-echo MRIs were used to plan MRS/MRSI slice location in the z-direction, and a five-slice gradient-echo MRI was used to interactively plan the elliptical ROI as previously described (14).

For both MRSI methods, an asymmetric Shinnar-Le Roux (SLR, 28) excitation pulse (T_p = 1.4 ms, BW = 4.2 kHz, asymmetry factor = 0.28) selecting a 10 mm axial slab was used for excitation. The MRSI phase encoding gradients were superimposed on the last spoiler gradient, sampling over the elliptical portion of a 17 x 21 matrix (170 x 210 mm² FOV) for a 1 mL nominal volume resolution (TR = 2500 ms, 10.2 min acquisition time). In addition to the MRSI method, the GOIA-WURST(12–4, 7) pulse was also utilized within a sLASER cubical localization sequence with the addition of a highly selective outer volume suppression (OVS) method described next. The sLASER + OVS sequence for MRS was run with a TR/TE = 3500/35 ms, 64 repetitions, resulting in a ~ 3.7 min acquisition. The minimum TE on our Bruker 4 T system was limited to 35 ms primarily due to the slow rise time and maximum amplitude of the system gradients. A separate water reference was acquired for all methods and used for receiver amplitude and phase correction, as well as B₀ eddy current compensation. WS was achieved using Gaussian pulses (10 ms, 200 Hz BW) for all methods.

A home-written MATLAB based software toolkit, NMRWizard (29), was used for data processing. The following steps were employed on all MRS and MRSI datasets. A water reference was used for amplitude- and phase-weightings of each RF coil element and for eddy current correction. Metabolic maps based on spectral integration were obtained over a 0.2 ppm range centered on the respective metabolite peak from the raw spectral data. LCModel (30) was used for spectral fitting of IR and no-IR datasets. The basis sets used were generated using SpinWizard, an in-house developed spin system simulator (31), accounting for RF pulses, gradients and delays. The LCModel fitting included sixteen metabolites (Ala, Asp, Cho, tCr, GABA, Glc, Glu, Gln, GPC, GSH, Lac, Ins, NAA, NAAG, Scyllo, and Tau), one macromolecule at 0.9 ppm for fitting IR spectra, and additional macromolecules (MM09, MM12, MM14, MM17 and MM20) for fitting no-IR spectra.

Results

GOIA RF pulses in simulation

Figure 1B shows the inversion profiles (30 mm slice) for the GOIA-HS(4–2, 5), and GOIA-WURST(12–4, 7) pulses as a function of B₁ amplitude. Figure 1B (i-ii) and (iii-iv) illustrate the on-resonance and 300 Hz off-resonance conditions, respectively. The WURST variant has a more ‘top hat like’ profile relative to the HS modulation on-resonance (Figure 1A(i)), with both pulses demonstrating a smeared inversion profile for a 300 Hz chemical shift. Both pulses have similar TW metrics, with lower time averaged power consumption and B_1(95%) for the GOIA-WURST(12–4, 7) pulse, as summarized in Table 1.

Table 1:

Comparison of GOIA-HS(4–2,5) and GOIA-WURST(12–4,7) pulse characteristics

Metric	GOIA-HS(4–2, 5) R45	GOIA WURST(12–4, 7) R45
Tp [ms]	3	3
BW [ kHz]	14.8	14.7
TW [%]	13.6	14.7
Minimum1 B1(95%)# amplitude [kHz]	1.02	0.87
Minimum2 Power [au]	1.0	0.80

¹Minimum B_1(95%) amplitude considering a 300 Hz offset

^#B_1(95%) is defined as the minimum B₁ amplitude required to achieve > 95% inversion efficiency, and also meet a mean M_z/M₀ < − 0.95 across the slice. The mean M_z/M₀ < − 0.95 metric was included to standardize signal loss in the presence of inversion profile smearing due to chemical shift.

²Power corresponding to the minimum B_1(95%) amplitude in arbitrary units

GOIA-Asymmetric OVS performance in simulation

Figure 3 illustrates magnetization profiles for the three pulses (HS2, GOIA-HS4, and GOIA-asymmetric) as a function of B₁ amplitude selective for a 30 mm slab. Figure 3 (A-F) are M_z/M₀ profiles, with (A-C) and (D-F) are on-resonance and 600 Hz off-resonance conditions (fat-water separation at 4 T) for the three RF pulses compared. Figure 3 (G-L) illustrate residual magnetization profiles (M_z/M₀) for lipids (T₁ = 400 ms) following the 4-pulse OVS module. Off-resonance results in a translation of the inversion profile for the HS2 pulse as expected, with the GOIA pulses producing a translation and a skewed inversion profile. It must be noted that the ~3.3-fold higher BW of the GOIA pulses result in a ~3.3-fold reduction in CSD relative to the HS2 pulse. While the GOIA-asymmetric pulse is inefficient at achieving full-inversion, it can be used to achieve highly effective saturation across the slice (M_z/M₀ < 0) for both on and off-resonance (Fig. 3I/L). Note that the RF amplitude scale in Figure 3 refers to peak B₁ amplitude. Though the GOIA-asymmetric pulse requires a higher peak B₁ amplitude, the time averaged power requirement for the asymmetric pulse is comparable to the HS and GOIA-HS4 pulses to achieve > 50 – fold in lipid suppression across the slab as summarized in Table 2.

FIGURE 3.

Comparison of simulated residual M_z/M₀ profiles vs B₁ amplitude for the (A) HS2, B) GOIA-HS4, and (C) GOIA-asymmetric pulses, selective for a 30 mm slab. (D-F) M_z/M₀ profiles vs B₁ amplitude for the three pulses considering a 600 Hz chemical shift (fat-water separation at 4 T). (G-L) residual M_z/M₀ profiles for the pulses in the order in (A-F) when utilized within the 4-pulse OVS configuration, simulated for T₁ = 400 ms.

Table 2:

Comparison of HS2, GOIA-HS4 and GOIA-asymmetric pulse characteristics

Metric	HS2	GOIA-HS4	GOIA-asymmetric
Tp [ms]	6.66	6.66	6.66
BW [ kHz]	6	20	20
Minimum B1 amplitude1 [kHz]	0.498	0.4157	0.5843
Minimum power2 [au]	0.93	1	0.92
TW [%]	9.6	4.5	1.73
30 mm slab TW [mm]	2.88	1.35	0.52
30 mm slab CSD (600 Hz @ 4 T) [mm]	3	0.9	0.9

¹Minimum B₁ amplitude to attain M_z/M₀ < 0.02 (>50-fold lipid suppression) throughout the slice with the 4-pulse OVS method

²Power corresponding to the minimum B₁ in arbitrary units

Temporal offset between AM/FM and GM functions in simulation and phantom

In-plane localization profiles (a 40 x 40 mm² in-plane ROI) with 3 ms GOIA-WURST(12–4, 7) pulses within a sLASER were obtained in simulation for a range of temporal offsets between AM/FM and GM functions spanning from −50 μs to +50 μs, is summarized in Figure S2.

Experimental localization profiles with the GOIA-WURST(12–4, 7) pulse with T_p = 3 ms were obtained in phantom for a 40 x 40 mm² voxel (Figure 4), with an 80 mm offset for an array of Δ delays, where Δ corresponds to the delay between initiating gradient and RF components in the pulse sequence. The Δ delay was modified by a variable padding delay between the gradient waveform and RF pulse commands within the pulse sequence. Below each 2D profile, the corresponding x-projection, and y-projection centered around zero are illustrated. Based on a third-order polynomial fit of BW as a function of Δ for the 8 mm offset, Δ was determined to be + 39.5 ± 1.2 μs, specific to the Bruker 4 T system. Similar to the simulation results, the y-projection is reduced for δ < 0 and elongated for δ > 0. The asymmetry in the x and y dimensions for an isotropic voxel (in 2D) as a result of |δ| > 0, can easily be calibrated by comparing x and y projection slice dimensions/BW as illustrated in the lower panel of Figure 4. The inefficient and distorted localization profile with |δ| > 0 can be partially mitigated with increased peak B₁ as illustrated in Figure S3, thus calibration should be performed at a B₁ ~ B_{1, 95%} to maintain sensitivity to the profile distortion.

FIGURE 4.

Localization profiles with the GOIA-WURST(12–4, 7) pulse with T_p = 3 ms, within a sLASER sequence selective for a 40 x 40 mm² in-plane ROI obtained experimentally in phantom. Here an 80 mm offset corresponding to a 30 kHz frequency modulation is used, for varying Δ values. For each case, a ratio image is illustrated where the reference image is obtained with the same sLASER sequence selective for a 300 x 300 mm² ROI with identical B₁ amplitude with a 0 mm offset. All acquisition were based on a 20 mm excitation slab in the z-direction. The ideal ROI edge is illustrated by the square in white color. Below each image, the X and Y projections of the acquired MRI are illustrated, where the Y projection is translated to be centered around zero in space, such that X and Y projections are overlapping when calibrated.

Localization performance of GOIA-asymmetric pulse in phantom

Figure 5 illustrates localization performance in a silicone oil phantom with HS2, GOIA-HS4 and GOIA-asymmetric pulses nested within the 4-cycle OVS module (A-C). 1-D traces along the x-axis for the three cases in (A-C) are overlayed in (D). The experimentally measured mean TW fractions for the HS2, GOIA-HS4, and GOIA-asymmetric pulses are 9.2%, 4.0%, and 1.9%, respectively, which are in close agreement with simulations. CSD evaluated experimentally in an oil/water phantom is illustrated in (E) for the three RF pulse types played out within the 4-cycle OVS method. CSD of 3 mm, 0.9 mm, and 0.9 mm were present over a 30 mm slab. The GOIA-HS4 and GOIA-asymmetric pulses had near identical CSD as expected, due to identical BW of the pulses. Performance metrics of the three pulses are summarized in Table 2.

FIGURE 5:

(A-C) Phantom results illustrating localization performance with the HS2, GOIA-HS4, and GOIA-asymmetric pulses compared, selective for a 70 mm OVS slab, and (D) illustrates traces along the X direction for the cases with a zoomed cut out illustrating the transition profile obtained for the three pulses. Excellent signal suppression throughout the slice (M_z/M₀ < 0.02) and minimal perturbation outside the inversion band is seen for all pulses. (E) CSD from the three pulse types in an oil/water phantom were obtained following a 30 mm slab played out within the 4-cycle OVS method.

A spectroscopic evaluation of the asymmetric OVS module (30 mm OVS slab) further confirms the excellent lipid suppression and edge retention where a small lipid phantom and large metabolite phantom are separated by ~ 2 mm (Figure S4).

In vivo experiments

Figure 6 illustrates IR and no-IR MRSI data acquired in vivo. The metabolic NAA maps based on spectral integration of the NAA methyl spectral region (2.01 ppm) demonstrate excellent extracranial lipid suppression, with a consistent intensity reduction in the 2.0 ppm region of 60 – 70% with the IR method. Circa 36% of the signal reduction is due to IR-related signal losses for NAA, whereas the remaining reduction is due to the removal of overlapping contributions from macromolecular resonances. The 3 x 3 grid of spectra in (D) further illustrate that the signal reduction due to IR is offset by the removal of MM signals leading to a flat baseline. An example of LCModel spectral fits with IR and no-IR methods from the voxel location on the anatomical axial slice are illustrated in Figure S5.

FIGURE 6.

Comparison of MRSI data acquired (TE/TR = 22.2 ms/2500 ms) on a volunteer with the IR and no-IR methods. (A) illustrates the axial slice imaged, with nine voxel regions overlaid. (B-C) illustrate NAA maps with the IR and No-IR methods, respectively, demonstrating effective extracranial lipid suppression with ECLIPSE-IVS. (D) illustrates 9 voxel locations from the 3 x 3 grid illustrated in (A) from the No-IR and IR methods. Both methods demonstrate high quality spectra, even with some reduction of amplitude in the IR data due to inversion recovery. The IR data demonstrate minimal macromolecular resonances evident by the 0.9ppm, and 1.2ppm resonances in the No-IR data, and has a flat baseline compared to the No-IR data.

A single voxel spectroscopic acquisition (35 x 55 x 10 mm³) with sLASER + asymmetric-GOIA obtained from the parietal cortex is illustrated in Figure 7, acquired at 40, and 144 ms TE’s. Localization along the 35 mm and 55 mm dimensions with the GOIA-WURST pulses result in edge-of-voxel TW of 5 mm and 8 mm, respectively, while edge-of-ROI TW of the asymmetric GOIA based ECLIPSE OVS is ~ 0.8 mm. Thus the sLASER ROI was deliberately set to protrude beyond the cortex as illustrated in green in (A), with the asymmetric GOIA-ECLIPSE OVS ROI set aggressively to adhere to the curvature of the cortex as illustrated in white to maximize cortical tissue content, and minimize TW and CSD effects at the ROI edge relative to sLASER localization. Spectra were acquired with OVS turned ON and OFF, illustrated in (C), where substantial lipid contamination is present for the sLASER-only acquisition, and effective lipid suppression in the presence of sLASER + OVS. Furthermore, in the absence of OVS, substantial lipid contamination is present even at 144 ms, though the lipid fraction is small compared to the total voxel size. (D) is a zoomed in version of (C) demonstrating high quality spectra with the OVS + sLASER method at short and long TE’s, and the 144 ms TE spectra illustrates full-intensity spectra throughout the 2 – 3.9 ppm range with OVS + sLASER relative to only sLASER, demonstrating negligible CSD and TW effects with the asymmetric-GOIA based OVS method.

FIGURE 7.

Single voxel spectroscopy acquired using the sLASER + ECLIPSE-OVS methods in the parietal cortex. (A) The sLASER ROI (35 x 55 x 10 mm³) protrudes the cortex (illustrated in green), and partially includes extracranial lipids as illustrated, ECLIPSE-OVS is placed along the curvature of the brain (illustrated in white). (B) An MRI of the OVS + sLASER localization profile is illustrated. (C) Spectra acquired at 40 and 144 ms is illustrated with ECLIPSE-OVS OFF (red spectra) and ON (blue spectra). (D) is a replicate of panel (C) with 6x zoom demonstrating high quality spectra devoid of lipid contaminants with OVS ON.

Discussion

Localized MRS and MRSI based on adiabatic spin-echo refocusing (LASER/sLASER) is highly attractive for clinical applications due to the low CSD, excellent outer volume suppression performance, single-shot localization capabilities, and tolerance to B₁ inhomogeneity. A limitation with (s)LASER, however is the relatively long TE required to accommodate the 4 or 6 adiabatic refocusing pulses with high BW. The GOIA-WURST(16–4, 10) pulse (11) that was originally presented is a SAR efficient and popular choice for sLASER implementations, achievable with short TE’s in the range of 20 – 30 ms (3,8,13). Shorter TE localization methods can see further benefits from T₂-related quantification errors when studying populations with possible alterations of metabolite T₂ values (32), such as in schizophrenia (33), and aging (34), and to minimize SNR losses due to J-modulations and T₂ relaxation. The GOIA-WURST(16–4, 10) pulse with T_p = 3.0 ms however requires a peak B₁ amplitude approaching 1 kHz, making it less robust on clinical systems for sLASER implementations with TE < 20 ms. Conversely, a GOIA-WURST(16–4, 10) pulse with reduced R value (with R ~ 45) has reduced time-averaged power efficiency, considering B₁ compensation required to minimize inversion profile smearing due to CSD. As such, the GOIA-WURST(12–4, 7) pulse variant with R = 45 developed in this wor has a peak B₁ amplitude of 0.87 kHz for T_p = 3 ms, with SAR requirements ~ 20% lower compared to the GOIA-HS(4–2, 5) and GOIA-WURST(16–4, 10) pulses with R = 45. Utilizing this GOIA-WURST(12–4, 7) pulse, would allow TE < 20 ms sLASER sequence implementations (on systems capable of a peak B₁ amplitude of 20 μT), providing full-intensity, single-shot localization with a fractional CSD of 2.9% (or 0.8% per ppm), which is more than 2-fold lower than the maximum recommended CSD based on recent consensus for MRS and 2D MRSI applications (2). Though most clinical systems provide a peak B₁ amplitude of 25 μT with a standard body coil transmitter, some systems have a limited peak B₁ amplitude of 15 μT (3,8). With a 15 μT peak B₁ amplitude limit, the presented GOIA-WURST(12–4, 7) pulse can be utilized with a T_p ~ 4 ms (and BW ~ 11 kHz) to allow sLASER implementations with TE < 30 ms.

Short TE MRS/MRSI is associated with macromolecular contributions that affects quantification accuracy of overlapping metabolites (35). Macromolecular targeted inversion recovery (IR) is one approach to null the macromolecular contributions, and also benefits from short TE acquisitions to reduce T₂ and J-modulation related losses for coupled spin systems. A disadvantage of macromolecule-nulling however, is the reduced signal amplitude (and hence SNR) of metabolites due to the lipid T₁ targeted IR component. Preliminary results from a recent study (36) show that fitting of synthetic spectra with LCModel (five included MM’s, a method commonly used with LCModel quantification) to contain a substantial bias in concentration estimates relative to estimates from IR spectra due to the absence of a MM baseline. This result remained true even when IR spectra had 50% less SNR, indicating that though an SNR penalty is associated with IR spectra, accuracy of metabolite quantification estimates to be superior to no-IR data. These results are in agreement with previous findings where an acquired MM baseline included in the fitting is shown to improve metabolite quantification, compared to using the default MM baseline in LCModel (37–39). Future work includes extending this development with IR and no-IR variants in a healthy cohort, to evaluate advantages of experimental nulling of MM signals for metabolite quantification accuracy and precession with short TE MRS/MRSI.

It is beneficial to optimize GOIA pulses with minimized inversion profile skewedness, while being efficient at higher field strengths. A recent study (40) investigated a GOIA-WURST pulse to minimize the skewed inversion profile due to chemical shift at 3T by varying n, m and GA. An extension of this work where n, m, GA, and modulation functions are optimized to achieve shorter T_p pulses (< 3 ms) considering peak B_{1, 95%} time averaged power requirements, inversion profile TW, BW, and skewedness due to off-resonance, tailored for common and emerging clinical field strengths (3 T, 7 T, and 9.4 T) would greatly benefit the broader MR community.

The |δ| > 0 distorted in the localization profile was apparent in all GOIA pulses compared in Table 1. A discrepancy of δ = ± 10 μs between RF and GM waveforms can be easily recognized with 40 x 40 mm² voxel projections acquired at a 30 kHz RF offset (80 mm translation). Uncertainty associated with the δ calculation was ± 1.2 μs, which primarily manifests from experimental uncertainties of the position measurement. A δ measurement (the discrepancy between RF and gradient waveform initiation following a trigger) previously described with 2D RF pulses (16) has a maximum uncertainty of 1.2 μs which is similar to this work. The uncertainties of δ associated with the projection method can be well below 0.5 μs by 1) making the ROI dimensions smaller (20 x 20 mm² for example) with larger RF offsets (an 80 mm translation of a 20 x 20 mm² voxel will require a 60 kHz RF offset) which accentuates the effect observed, 2) set the peak B₁ amplitude at B_1,99% as described in Supplementary Figure S3, and by 3) increasing the readout bandwidth in combination with averaging multiple repetitions to improve SNR. This demonstrates that a projection-based calibration is sensitive and straightforward to implement utilizing short T_p GOIA pulses. Though δ delays of up to ~ 80 μs have been reported on a Varian 3 T system (16), measurements made on clinical Siemens systems is only up to 17 μs (17), both of which can be evaluated and calibrated with the presented method. It must be noted that a delay of δ ~ 50 μs is largely inconsequential on the localization profile using constant gradient based AFP pulses (with T_p > 2 ms), or with GOIA pulses with small RF offsets, and that the δ ~ 40 μs observed on the Bruker 4 T system was undetected in previous studies with GOIA RF pulses with T_p = 6.66 ms (14). Thus it is possible that a clinical or pre-clinical system elsewhere to have a measurable δ delay between RF and gradients, which would not show till very short GOIA pulses are utilized with larger RF offsets, or unless fast k-space trajectory discrepancies are investigated (17).

In addition to the finite δ delays, eddy current effects can also play a role in the fidelity of generated gradient waveforms (17), and subsequently compromise the localization profiles with GOIA pulses. Effects due to eddy currents were not pursued in this work for a few reasons: 1) Given that undistorted and full-intensity localization profiles were achieved following the time calibration between GM and RF waveforms suggest that other gradient related imperfections, especially eddy current effects are minimal. 2) High fidelity of gradient waveforms were maintained by under-utilizing the gradient system. In this work, the gradient amplitudes and slew rates required for the GOIA-WURST pulses selective for a 40 mm slab were ~ 30% and ~ 50% of maximum values of the system gradients, respectively. Furthermore, current monitor waveforms captured on a digital oscilloscope were found to be of high fidelity devoid of artifacts.

Highly selective RF pulses have been previously reported in the form of very selective suppression (VSS) pulses for outer volume suppression (41) and asymmetric adiabatic full passage (AFP) pulses (20) for WS with a fractional TW of ~ 6% and ~ 5%, respectively. However, these highly selective pulses have limited BW, or become peak B₁ intensive for high BW applications. Thus, while RF pulses with high selectivity and high BW can separately be achieved, it is difficult to achieve both features within constrains of SAR and peak B₁ at clinical field strengths. The developed asymmetric GOIA pulse based OVS method is a power efficient alternative, with a fractional TW ~ 1.7% and 20 kHz BW allowing CSD and fractional TW metrics to be < 1 mm for a 30 mm OVS slab. The utility of highly selective asymmetric GOIA-OVS was demonstrated in phantom (Figure 7), where effective lipid suppression was demonstrated with no observable CSD and TW artifacts on metabolite spectra proximal to a lipid phantom ~ 2 mm away. The low fractional TW of the asymmetric GOIA-OVS method can be used in highly selective applications allowing interrogating of cortical tissue proximal to extracranial lipids, and in large (for example ~ 100 mm) OVS slab placements, where the TW will still be negligible (< 2 mm) at the ROI edge of interest. In comparison to a previously developed (14) ECLIPSE-OVS method utilizing GOIA-HS(4 – 2, 5) pulses with 15 kHz BW, the GOIA-asymmetric pulse provides a 33% improvement in CSD and ~ 3.5 -fold reduction in TW, at the cost of a ~ 24% increase in time averaged SAR.

For the GOIA-asymmetric pulse, setting the HT component first was an arbitrary decision. However, minor benefits/drawbacks can be attained by switching the order of HT and HS components. Placing the HT component first results in the highest slew rate gradient component to be at least 5ms further away from a WS pulses to follow in comparison to its time-revered pulse (Figure 2C). This could be beneficial to minimize potential B₀ modulations due to induced eddy currents. However, given that the temporal mid-point of the RF pulses is biased towards the HT component, placing the HT component last allows the last OVS pulse to be placed closer to proceeding WS pulses for potentially improved OVS performance.

The slew rate of the current system gradients (26 mT/m/ms) was a limiting factor that had to be considered for the GOIA-asymmetric pulse design. Higher R valued GOIA-asymmetric pulses with further improved TW are possible with faster gradients, typically available on modern clinical 3T systems. The 4-cycle GOIA-asymmetric OVS method previously reported, was repurposed for this work as it provides effective lipid suppression over a large T₁ and B₁ span. However, the OVS method can be further improved in terms of TW and reduced total power by increasing the cycle count (a 6-cycle OVS method, for example).

Conclusions

Gradient-modulated RF pulses, especially the GOIA family of RF pulses, are gaining popularity for high field applications due to the high BW that can be achieved with clinically compatible peak B₁ and SAR limitations relative to equivalent AFP pulses. In this work we explore two avenues of improving GOIA pulses: 1) a clinically compatible 3 ms GOIA-WURST RF pulse (BW = 15 kHz) variant for applications in short TE sLASER localization methods, and 2) a 6.66 ms asymmetric-GOIA RF pulse that is simultaneously capable of providing TW metrics of 1.7% and 20 kHz BW, that is unparalleled by any previously described RF pulse. Performance of the developed RF pulses were rigorously tested in simulation, in phantoms, and in human volunteers. Phantom and in vivo measurements demonstrate that the asymmetric GOIA pulse allows clear detection of metabolites in cortical tissue near the edge-of-the brain (~ 2mm away from extracranial lipids), which has been challenging historically, and is important for many clinical and research applications in the brain.

Supplementary Material

Supplimentary Figure 1

FIGURE S1. (A) The ECLIPSE-IVS pulse sequence with TE/TR = 22.2/2500 ms. The excitation selects a 10 mm axial slice, followed by an adiabatic double spin-echo selective for an elliptical ROI utilizing ECLIPSE (labeled ECL). The ECLIPSE gradients were also used to supplement the system gradient spoiling following each GOIA pulse for an additional 1.5 ms. (B) The 4-cycle OVS method used with ECLIPSE and linear gradients for slab selection with interleaved seven-pulse VAPOR-style WS pulses (shaded). OVS pulses (unshaded) with relative amplitudes of 0.64, 0.71, 0.83 and 1.00 are placed 1179, 558, 216 and 48 ms before the slice-selective excitation pulse, respectively. Similarly, the WS pulses have relative flip angles of α, α, 1.78α, α, 1.78α, α and 1.78α, which are placed 280, 265, 250, 170, 98, 28 and 13 ms before the slice-selective excitation pulse.

Supplimentary Figure 2

FIGURE S2. Simulated localization profiles with the GOIA-WURST(12–4, 7) pulse with T_p = 3 ms, within a sLASER sequence selective for a 40 x 40 mm² in-plane ROI. Here simulations are repeated for 0, 4, and 80 mm offsets (rows), and δ delays at −50, −20, 0, +20, and +50 μs (columns). The δ delays are applied only between the RF and gradient waveforms for the Y-selective pair of pulses, with δ = 0 for the X-selective pair of pulses. In each case, the excitation pulse globally rotates magnetization in the x-direction, and a 32-step phase cycle was used to cancel out undesired coherences.

Supplimentary Figure 3

FIGURE S3. Simulated localization profiles with the GOIA-WURST(12–4, 7) pulse with T_p = 3ms, within a sLASER sequence selective for a 40 x 40 mm² in-plane ROI. Here δ = −50 μs, with an 80 mm translation along the y-axis. In the four panels starting from the left, B₁ = 0.9 kHz ~ B_{1, 95%}, produces a distorted localization profile similar to column 2, row 3 sub panel in Figure 6 as expected. With increasing B₁ amplitude up to 2 kHz, inversion performance is improved, though slab thickness along the y-axis remains ~ 35% reduced.

Supplimentary Figure 4

FIGURE S4. A 5 x 5 mm² in-plane resolution, 10 mm slab MRSI experiment to evaluate localization with the GOIA-asymmetric pulse with a lipid phantom placed ~ 2 mm away from a metabolite phantom. Ratio MRI’s between a 30 mm slab with a (A) 0 mm offset and (B) 74 mm offset, relative to a reference MRI. No observable signal loss is present in (B) demonstrating negligible CSD and TW effects. (C) MRI illustrates the lipid phantom and OVS slab, and (D) zoomed in view. (E) Spectra from the 4 x 4 grid in (D) with and without the OVS slab. Excellent lipid suppression for voxels within the phantom are seen, with no apparent signal losses due to CSD or TW at edge-of-ROI voxels. The OVS slab was placed such that the lactate ROI is immediately adjacent to the metabolite phantom edge to achieve chemical shift displacement free spectra on voxels proximal to the lipid phantom.

Supplimentary Figure 5

FIGURE S5. Example LCModel fitting of in vivo MRSI (TE/TR = 22.2 ms/2500 ms) data in Figure 4 following LCModel fitting of the IR and No-IR data. Five prominent metabolite contributions, namely NAA, tCho, tCr, Glx (Glu + Gln), and Ins (myo-inositol) are illustrated. Fitting of IR data included 16 metabolites and a MM at 0.9 ppm, while fitting of No-IR spectra further includes five macromolecules and a spline baseline. In both cases excellent fitting is observed with minimal lipid contamination from a voxel location proximal to extracranial lipids.

Abbreviations:

AFP

adiabatic full passage

AM

amplitude modulation

BW

bandwidth

CSD

chemical shift displacement

ECLIPSE

elliptical localization with pulsed second order fields

FM

frequency modulation

FOCI

frequency offset corrected inversion

GA

gradient amplification factor

GM

gradient modulation

GOIA

gradient offset-independent adiabaticity

HS

hyperbolic secant

HT

hyperbolic tangent

IVS

inner volume selection

LASER

localization by adiabatic selective refocusing

OVS

outer volume suppression

RF

radio frequency

ROI

region of interest

SAR

specific absorption rate

T_p

RF pulse length

TW

transition width

WS

water suppression

WURST

wideband uniform rate with smooth truncation