Coil Combination Using OpTIMUS Results in Improved Signal‐to‐Noise Ratios of In Vivo MR Spectra Acquired at 7 T

ABSTRACT

Magnetic resonance spectroscopy (MRS) enables noninvasive quantification of metabolites, but its utility in vivo can be limited by low signal‐to‐noise ratios (SNRs) and long acquisition times. The use of ultrahigh‐field (UHF) strengths (> 3 T) combined with multichannel phased receive arrays can improve spectral SNR. A crucial step in the use of multichannel arrays is the combination of spectra acquired from individual coil channels. We previously developed a coil combination method at 3 T, optimized truncation to integrate multichannel MRS data using rank‐R singular value decomposition (OpTIMUS), which uses noise‐whitened windowed spectra and iterative rank‐R singular value decomposition (SVD) to combine multichannel MRS data. Here, we evaluated OpTIMUS for combination of MR spectra acquired using a multichannel phased array at 7 T and compared spectral SNR and metabolite quantification with spectra combined using whitened SVD (WSVD), signal/noise squared (S/N²), and the Brown method. Data were acquired from 14 healthy volunteers, including five with data acquired at both 3 and 7 T, and from nine people living with HIV. Spectra combined using OpTIMUS resulted in a higher SNR compared to the three other methods, consistent with our prior results at 3 T. With half the number of averages (N = 32), spectra combined with OpTIMUS had higher SNR compared to spectra using the Brown method with 64 averages. Additionally, spectra combined using OpTIMUS at 7 T were compared to spectra acquired at 3 T with the same number of averages (N = 64) or matched acquisition times (N = 110 averages), and spectral fitting was consistently improved at 7 T even when comparable SNR was obtained at 3 T. The ability to increase SNR and maintain spectral quality by optimizing spectral coil combination has the potential to reduce scan time, a key challenge for routine clinical use of MRS.

• Coil combination with OpTIMUS increases SNR of MR spectra at 7 T compared to well‐established coil combination algorithms without compromising spectral quantification.

• By reducing spectral noise and incorporating the metabolic signal from higher order singular vectors, OpTIMUS has the potential to enable shorter acquisition times compared to the default combination provided by the vendor.

• OpTIMUS implementation for MR spectra acquired from both healthy volunteers and patients supports practical utility across multiple brain regions.

Abbreviations

Cho

choline

Cr

creatine

CRLB

Cramér–Rao lower bound

CV

coefficient of variation

FASTESTMAP

fast automatic shim technique using echo‐planar signal readout for mapping along projections

FWHM

full width at half maximum

GEE

generalized estimating equation

Gln

glutamine

Glu

glutamate

GOIA

gradient offset independent adiabaticity

GSH

glutathione

HIV

human immunodeficiency virus

ICC

intraclass correlation coefficient

IQR

interquartile range

Lac

lactate

LFWM

left frontal white matter

MP2RAGE

magnetization‐prepared two rapid acquisition gradient echoes

MPRAGE

magnetization‐prepared rapid gradient echo

MRI

magnetic resonance imaging

MRS

magnetic resonance spectroscopy

MSE

mean squared error

myo‐I

myo‐inositol

NAA

N‐acetylaspartate

NEX

number of excitations

OpTIMUS

optimized truncation to integrate multichannel MRS data using rank‐R singular value decomposition

OVS

outer volume suppression

PCA

principal component analysis

PCC

posterior cingulate cortex

PLWH

people living with HIV

PRESS

point‐resolved spectroscopy

SD

standard deviation

sLASER

semi‐localized by adiabatic selective refocusing

S/N²

signal/noise squared

SNR

signal‐to‐noise ratio

SVD

singular value decomposition

tCho

total glycerophosphocholine + phosphocholine

tCr

total creatine + phosphocreatine

tNAA

total N‐acetylaspartate + N‐acetylaspartyl‐glutamate

UHF

ultrahigh‐field

VAPOR

variable power radiofrequency pulses with optimized relaxation delays

WSVD

whitened singular value decomposition

1. Introduction

Magnetic resonance spectroscopy (MRS) is a noninvasive technique enabling acquisition of the chemical and molecular profiles of tissues in vivo [1, 2]. MRS is inherently limited by the low signal‐to‐noise ratios (SNRs) of non‐water metabolites, which can result in long acquisition times. MRS benefits from ultrahigh‐field (UHF) strengths (> 3 T), which increase peak separation and SNR, enabling higher spectral resolution and sensitivity, respectively. In vivo MRS at UHF strengths can be challenging due to B₀ and B₁ inhomogeneities, increased power deposition into tissues, shorter T₂ relaxation times, and greater chemical shift displacement errors [3]. Recent expert consensus recommends several strategies for high‐quality MRS data acquisition at UHF strengths, including multichannel transmit and receive array coils for optimal excitation and signal acquisition [4].

The use of multichannel phased receive arrays has been shown to increase SNR, as each individual coil receives data simultaneously from the region of interest [5]. Optimal combination of individual spectra collected from each coil channel is fundamental to exploit the increase in SNR facilitated by multichannel arrays. Several coil combination strategies have been proposed since Roemer's seminal combination method to maximize SNR [5]. Brown developed a combination algorithm building upon Roemer's framework, and a variant of this is embedded into Siemens' in‐line reconstruction [6]. The Brown method determines the individual coil weights using the first point of each signal in the time domain. Signal/noise squared (S/N²) [7] uses the S/N² ratio calculated from the spectra acquired from each coil channel as the weighting factor and is used by several open‐source MRS processing tools [8, 9]. The advantage of the Brown and S/N² methods is their straightforward implementation; however, both assume the noise is uncorrelated between individual coil channels. In practice, this is rarely the case. Rodgers and Robson developed the whitened singular value decomposition (WSVD) method, which uses the noise covariance matrix to first perform noise whitening on individual spectra from each channel, followed by singular value decomposition (SVD) to compute the maximum likelihood combined (rank‐1) spectrum [10]. In theory, if the whitening process completely decorrelates all noise between coil channels, the metabolite signal will be fully represented in the first singular vector. The WSVD approach and related variants outperformed other reconstruction methods for in vivo ³¹P MR spectra acquired from the heart at 3 T [11], including methods using field maps to compute coil sensitivities as well as other data‐driven methods that use spectral information to inform coil combination including generalized least squares, Brown, and S/N². The WSVD approach is currently used as the coil combination method in the spectroscopy software FSL‐MRS [12]. In practice, however, the noise whitening process is imperfect, which can result in the presence of a signal beyond the first singular vector [13]. This motivated the development of the optimized truncation to integrate multichannel MRS data using rank‐R singular value decomposition (OpTIMUS) coil combination method [13]. OpTIMUS is a data‐driven strategy that uses noise‐whitened and windowed spectra and iterative rank‐R SVD to combine multichannel MRS data. The evaluation of a higher rank SVD was shown to maximize SNR by incorporating metabolite signal present in higher order singular vectors due to incomplete noise whitening. OpTIMUS was demonstrated at 3 T using data acquired from both a brain phantom and healthy volunteers, reporting increased SNR compared to several methods including WSVD [13].

Due to the prevalence of lower field strengths (≤ 3 T) in research and clinical settings [3, 14], these combination methods have predominantly been applied to MR spectra acquired at 1.5 or 3 T. Despite the increasing presence of 7 T MR scanners, optimized coil combination methods evaluated using spectra acquired at UHF strengths remain understudied. Increased field inhomogeneities at 7 T can lead to frequency and phase drifts. Higher signals, while typically advantageous, also result in increased noise. Given these factors, coil combination methods must be evaluated at 7 T to leverage the full benefits of UHF strengths. The goal of the present study was to evaluate the OpTIMUS algorithm for the combination of individual spectral data acquired using a multichannel phased array coil at 7 T and compare spectral quality after the combination of spectra acquired at both 3 and 7 T. Spectral SNR, metabolite concentrations, and spectral fitting after combination with OpTIMUS were compared with three other coil combination algorithms, including WSVD [10], S/N² [7], and the Brown method [6, 11], a variant of which is the default method for in‐line spectral combination on Siemens whole‐body MR scanners.

2. Methods

2.1. OpTIMUS Algorithm

OpTIMUS relies on three key steps: noise whitening, spectral windowing, and rank‐R SVD. The OpTIMUS algorithm has been previously reported [13] and is summarized briefly below. The measured MR signal, $S$, is an $M\times N$ matrix, where $M$ corresponds to the number of complex data points and $N$ is the number of coil channels. $S$ can be defined as

$$S=Z{\alpha }^H+E,$$ (1)

where $Z$ is an $M\times 1$ matrix representing the true signal; $\alpha$ is a complex vector of length $N$ and, using the singular vector definition, ${\alpha }^H\alpha =1$ corresponds to the coil sensitivities; $H$ represents the Hermitian transpose; and $E$ is an $M\times N$ complex matrix representing the extrinsic noise.

The complex noise covariance matrix ($\tilde{C}=\frac{1}{M}{E}^{H}E$) can be computed from a noise‐only region of a spectrum or from an acquired noise‐only scan (i.e., transmit voltage set to 0). With the principal component analysis (PCA) approach [15], the noise covariance matrix can be calculated as $\tilde{C}=\tilde{P}\tilde{\Lambda }{\tilde{P}}^H$, where $\tilde{P}$ is a unitary matrix of eigenvectors and $\tilde{\Lambda }$ is a diagonal matrix of eigenvalues. From the eigenvalue decomposition, the noise whitening matrix is calculated as $W=\tilde{P}{\tilde{\Lambda }}^{-1/2}$, which geometrically consists of a rotation determined by $\tilde{P}$, followed by scaling using ${\tilde{\Lambda }}^{-1/2}$. The rotation results in orthogonal components with different variances, and the scaling factor results in whitened data with null mean and unit variance for each coil channel. With this whitening matrix applied to the spectral data, the whitened spectra, $\tilde{S}$, can be calculated as

$$\tilde{S}=\mathit{SW}=Z{\alpha }^H\tilde{P}{\tilde{\Lambda }}^{-1/2}+E\tilde{P}{\tilde{\Lambda }}^{-1/2}.$$ (2)

After whitening, OpTIMUS computes the SVD used for coil combination. In theory, rank‐1 SVD results in optimal spectral combination if the whitening process completely decorrelates the noise between coil channels [10]. In this case, the first singular vector of the whitened spectra will encompass all the metabolite signals. In practice, however, the estimated covariance of the noise is not always equal to the true noise covariance and can lead to the presence of metabolite signal beyond the first singular vector [13]. OpTIMUS addresses this by finding the optimal spectral window for rank‐R SVD, which maximizes the SNR of the final combined spectrum. The algorithm iterates over all possible window sizes, $L$, with the minimum value of $L$ being equal to the number of coils, $N$. For each window size, i.e., $L$, OpTIMUS uses a sliding‐window approach to evaluate all possible $L\times N$ matrices across the whitened spectra. The economy SVD is then performed on each windowed matrix, ${\tilde{S}}_{\mathit{win}}$:

$${\tilde{S}}_{\mathit{win}}={\tilde{U}}_{\mathit{win}}{\tilde{\Sigma }}_{\mathit{win}}{\tilde{V}}_{\mathit{win}}^H$$ (3)

where ${\tilde{U}}_{\mathit{win}}$ is an $L\times N$ matrix of left singular vectors, ${\tilde{\Sigma }}_{\mathit{win}}$ is a diagonal matrix of the singular values of ${\tilde{S}}_{\mathit{win}}$ or the weights for each rank, and ${\tilde{V}}_{\mathit{win}}$ is the $N\times N$ coil combination matrix of right singular vectors. The untruncated (i.e., $M\times N$) whitened spectra, $\tilde{S}$, are combined using the coil weights, ${\tilde{\Sigma }}_{\mathit{win}}$, and combination matrix, ${\tilde{V}}_{\mathit{win}}$, determined from each windowed matrix in an iterative fashion from rank‐1 to rank‐N. This iterative process identifies the combination of rank, window size, and spectral region that maximizes the variance captured by the SVD analysis and the SNR of the combined spectrum. The rank‐R combined spectrum, ${\tilde{S}}_{\mathit{\text{combined}}}$, is calculated as a linear combination,

$${\tilde{S}}_{\mathit{\text{combined}}}={\sum }_{k=1}^R\tilde{S}{\tilde{V}}_{\mathit{win}}\left(:,k\right){\tilde{\Sigma }}_{\mathit{win}}\left(k,k\right).$$ (4)

To estimate the spectral variance represented in the final combination, the percentage of the sum of squared singular values retained in the final combination, ${\mathit{Var}}_{\mathit{est}},$ is defined as:

$${\mathit{Var}}_{\mathit{est}}=\frac{{\sum }_{k=1}^R{\tilde{\Sigma }}_{\mathit{win}}{\left(k,k\right)}^2}{{\sum }_{k=1}^N{\tilde{\Sigma }}_{\mathit{win}}{\left(k,k\right)}^2}\times 100.$$

2.2. MR Experiments

MR imaging (MRI) and MRS data were acquired over the course of ~1 year from the brain of 14 medically healthy volunteers (eight males and six females, mean ± standard deviation [SD] age = 27 ± 10 years) and nine people living with human immunodeficiency virus (HIV) (PLWH) (three males and six females; mean ± SD age = 47 ± 12 years) after approval by the Emory University Institutional Review Board. Written informed consent was obtained from each subject prior to participation. MR data were acquired from all participants using a whole‐body 7 T MR scanner (MAGNETOM Terra, Siemens Healthcare, Erlangen, Germany) with an eight‐channel transmit, 32‐channel phased array receive head coil (Nova Medical Inc., Wilmington, MA, USA). In a subset of five healthy participants (three males and two females), data were also acquired on a whole‐body 3 T MR scanner (MAGNETOM Prisma Fit, Siemens Healthcare, Erlangen, Germany) using a 32‐channel phased array head coil on the same day as 7 T acquisition. The order of the scans was varied (data were acquired at 3 T first for two subjects and 7 T first for three subjects).

At 7 T, a T₁‐weighted anatomical image was acquired using the magnetization‐prepared two rapid acquisition gradient echoes (MP2RAGE) [16] sequence (TR = 4300 ms, TE = 2.19 ms, TI₁/TI₂ = 1000/3200 ms, flip angle = 4°, FOV = 240 × 225 mm², slices per slab = 192, voxel resolution = 0.75 mm isotropic), and the combined image from the multiple inversion times [16] was used to position the ¹H MRS voxel. B₀ shimming was performed using the fast automatic shim technique using echo‐planar signal readout for mapping along projections (FASTESTMAP) [17]. The semi‐localized by adiabatic selective refocusing (sLASER) [18] MRS sequence was acquired from the posterior cingulate cortex (PCC) of healthy volunteers and PLWH and from the left frontal white matter (LFWM) only in PLWH using high‐bandwidth gradient offset independent adiabaticity (GOIA) radiofrequency pulses [19] and outer volume suppression (OVS) (TR = 5000 ms, TE = 35 ms, complex data points = 2048, spectral bandwidth = 4500 Hz, PCC nominal voxel size = 2 cm isotropic, LFWM nominal voxel size = 1.5 × 2.5 × 2 cm³, number of excitations [NEX] = 64, excite/refocus pulse durations = 2000/3500 μs, excite/refocus flip angle = 90/180°, gradient ramp time = 210 μs, maximum gradient strength = 80 mT/m at 200 T/m/s, GOIA gradient factor = 0.8 [i.e., the center of the gradient is 0.2 times the maximum gradient value], OVS pulse duration = 5120 μs, OVS slab thickness = 80 mm, acquisition time = 5 min 58 s). Water suppression was performed using variable power radiofrequency pulses with optimized relaxation delay (VAPOR) suppression (bandwidth = 135 Hz, flip angle = 90°). A noise‐only scan (transmit voltage = 0) was acquired after the water‐suppressed scan (NEX = 8, acquisition time = 1 min 8 s). The sLASER [18, 19] and FASTESTMAP [17] sequences were obtained under a C2P agreement from the University of Minnesota.

At 3 T, a T₁‐weighted anatomical image was acquired using the magnetization‐prepared rapid gradient echo (MPRAGE) sequence (TR = 2300, TE = 3.43 ms, TI = 900 ms, flip angle = 9°, FOV = 256 × 256 mm², matrix size = 256 × 256, slices per slab = 160, voxel resolution = 1 mm isotropic) and used to position the ¹H MRS voxel. Single‐voxel MRS data were acquired from the PCC using the sLASER sequence with the same parameters as 7 T except TR = 3000 ms, excite/refocus pulse durations = 2480/3500 μs, gradient ramp time = 140 μs, advanced shim mode instead of FASTESTMAP, without OVS, and VAPOR flip angle = 80° (water‐suppressed acquisition time = 3 min 36 s). An additional single‐voxel MRS scan was also acquired at 3 T with the same parameters but with NEX = 110, resulting in an acquisition time equal to 5 min 57 s to match the acquisition time at 7 T. A single noise‐only scan (transmit voltage = 0) was also acquired using the same settings (NEX = 8, acquisition time = 42 s). The MRSinMRS checklist with full details of MRS acquisition and analysis is provided in Appendix S1 [20].

To evaluate the performance of OpTIMUS on spectra acquired from different relative positions within the scanner, as well as the effect on metabolite concentrations, ¹H MRS data were collected from a spherical brain phantom (GE Braino phantom [21]). The metabolite concentrations in the phantom are 10 mM creatine (Cr), 12.5 mM N‐acetylaspartate (NAA), 3 mM choline (Cho), 7.5 mM myo‐inositol (myo‐I), 12.5 mM glutamate (Glu), and 5 mM lactate (Lac). MRS data were acquired using the same sequence and parameters as for the in vivo experiments and from five different voxel positions: isocenter and 30 mm shifted from the isocenter in anterior, posterior, superior, and inferior directions, with two repeated scans per voxel, yielding 10 spectra per session. After resetting the isocenter, the above acquisition paradigm was repeated. One noise‐only scan was acquired per session.

2.3. Data Processing

2.3.1. In Vivo

Spectral preprocessing and combination algorithms were implemented in MATLAB (vR2023a, Mathworks, Natick, MA, USA). Water‐suppressed spectra acquired from individual coil channels at 7 T from healthy volunteers were combined using all methods and all 64 averages, the first 32 averages, the last 32 averages, and five sets of 16 random averages. Water‐suppressed spectra acquired from PLWH at 7 T were combined using all methods and 64 averages. To evaluate the potential frequency drift at 7 T, consecutive and independent groups of four transients were averaged (for a total of 16 spectra) [22]; zero‐order phase correction was applied, followed by Fourier transform. The position of the total NAA + N‐acetylaspartyl‐glutamate (tNAA) peak was then tracked for two of the coils with the highest SNR in each single‐voxel acquisition. For spectra acquired at 3 T, combination was evaluated using 64 averages and 110 averages for the time‐matched scans. For each set of averages, Siemens twix data for the water‐suppressed and noise‐only scans were loaded into MATLAB using the GannetLoad function in Gannet 3.0 [23]. All corresponding transients (i.e., N = 16, 32, 64, or 110, as applicable) were averaged for each coil channel in the time domain, followed by Fourier transform. Individual spectra from each of the 32 coil channels were then combined using OpTIMUS, WSVD, S/N², and a variant of the Brown method. Zero‐order phase correction was performed on the final combined spectra using the first point of the time domain data.

The OpTIMUS implementation was performed by optimizing the SNR calculated from the raw combined spectra after zero‐order phase correction, as the maximum tNAA peak height divided by the SD of a noise‐only region of 100 data points [13]. The chemical shift range for the noise region was 11.53–12.26 ppm at 7 T and 11.01–12.78 ppm at 3 T. Noise whitening was performed using the noise‐only scan acquired for each subject. To evaluate the need for a subject‐specific noise‐only scan, the first chronological noise‐only scan acquired at 7 T was also used to decorrelate noise for all subsequent healthy volunteers, followed by combination with OpTIMUS. For spectra acquired at 7 T from healthy volunteers, OpTIMUS was also implemented by optimizing a weighted SNR calculated as a weighted signal average of the height of the tNAA, total glycerophosphocholine + phosphocholine (tCho), and total Cr + phosphocreatine (tCr) peaks and the same noise‐only region, as well as by optimizing the SNR of the myo‐I peak and the same noise‐only region to determine if the results were dependent on the peak chosen for SNR optimization and if the choice of a lower SNR peak would compromise coil combination.

WSVD was implemented for each set of averages using the open‐source code as previously reported [11]. Noise decorrelation in WSVD was performed using the same method described above for OpTIMUS. Coil weightings for the S/N² method were determined from the raw spectra using the maximum tNAA peak height and the SD of the same noise‐only regions described above. At 7 T, S/N² was also implemented with N = 64 averages using the SNR from the weighted signal average of the tNAA, tCho, and tCr peaks, and the SNR of the myo‐I peak. For the Brown method [6], individual spectra from each coil channel were weighted using the conjugate of the first point of the corresponding time domain signal from the same coil channel as previously described [11]. All four coil combination methods were implemented in the frequency domain. SNR of the final combined spectra of healthy volunteers and PLWH was compared for all methods, after performing zero‐order phase correction, using the maximum tNAA peak height and the SD of the noise‐only region. Additionally, final spectral SNR at 7 T for healthy volunteers was also compared across methods using the weighted signal average and the myo‐I peak. For methods that use SNR to optimize coil combination, i.e., OpTIMUS and S/N², the reported SNR values correspond to the same peak chosen for optimization, unless otherwise indicated. Representative spectra are normalized to the tNAA peak for display purposes only.

To evaluate the effect of coil combination method on spectral fitting and quantification of data acquired from healthy volunteers at 3 and 7 T, the final spectrum using each combination method was converted into a Siemens rda format in MATLAB, and metabolites were quantified using the LCModel (Version 6.3‐1R) [24] with 3 T and 7 T basis sets of 17 metabolites, four lipids, and five macromolecules. The metabolites included in the basis set are alanine, aspartate, Cr, phosphocreatine, gamma‐aminobutyric acid, glucose, glutamine (Gln), Glu, glycerophosphocholine, phosphocholine, glutathione (GSH), myo‐I, Lac, NAA, N‐acetylaspartyl‐glutamate, scyllo‐inositol, and taurine. Spectral fitting was evaluated with Cramér–Rao lower bounds (CRLBs), and metabolites with CRLBs < 30% were included in the analysis. Metabolites used in the final analysis include tNAA, tCho, myo‐I, Glu, Gln, GSH, and tCr. All metabolites were normalized to tCr to account for differences in radiofrequency gain and performance over the course of ~1 year of data acquisition. To evaluate spectral resolution at 7 T, full width at half maximum (FWHM) of the tNAA peak was calculated from the raw combined spectra after zero‐order phase correction.

2.3.2. In Vitro

Spectra acquired from the braino phantom at 7 T and combined using OpTIMUS and Brown were fitted using the LCModel with the same basis set as for in vivo data, and the mean squared error (MSE) was calculated for NAA, Cho, myo‐I, Glu, and Lac, all normalized to creatine. The coefficient of variation (CV) across repeated measures within and between sessions (four total scans) were calculated for each voxel position and all metabolites.

2.4. Statistical Analysis

All statistical analyses were performed in R. Spectra combined with OpTIMUS at 7 T were compared to spectra combined using WSVD [10], S/N² [7], and the Brown method [6, 11]. Due to non‐normal residuals, generalized estimating equations (GEEs) with subject as the cluster variable and exchangeable working correlation structure were used to compare spectral metrics across combination methods, where SNR (of the tNAA peak or weighted signal average of tNAA, tCho, and tCr peaks, N = 64 averages for both), CRLBs, or metabolite concentration was the response variable and method (OpTIMUS, WSVD, S/N², and Brown method) was the main effect. The fully iterated jackknife variance was used to account for the small sample size. Pairwise SNR comparisons across all methods were performed, and the Tukey method was used to correct for multiple comparisons. Reproducibility of SNR was evaluated with the intraclass correlation coefficient (ICC) using the first 32 averages and last 32 averages for each combination method using a mixed model with a subject random intercept. ICC values were also calculated for metabolite concentrations obtained from spectra combined with OpTIMUS.

To explore the ability of OpTIMUS to maintain high SNR using fewer averages compared to the Brown method, i.e., default coil combination method used by the vendor for in‐line reconstruction [6, 11], with a subsequent reduction in scan time, spectra combined with OpTIMUS using the first 32 averages were compared to spectra combined using the Brown method and all 64 averages using a GEE. Comparisons of spectra combined with OpTIMUS at different field strengths were also performed using separate GEEs, where the SNR of the tNAA peak or CRLBs was the response variable, and the acquisition method (7 T with 64 averages, 3 T with 64 averages, and 3 T with 110 averages to match the 7 T scan time) was the main effect. GEEs were fit using the R package geepack [25], and ICC was calculated using the R package lme4 [26]. Data are reported throughout as the median (interquartile range [IQR]) unless otherwise noted. Significance was determined by p ≤ 0.05.

3. Results

3.1. OpTIMUS Coil Combination Enables Higher SNR of Brain MRS Spectra

Representative MRS voxel positions in the PCC of a healthy volunteer and in the LFWM of a person living with HIV are shown in Figure 1. Representative normalized spectra from a healthy volunteer after combination with each of the four methods are shown in Figure 2.

FIGURE 1.

Representative MR spectroscopy voxel positions (yellow box) in the posterior cingulate cortex of a 26‐year‐old healthy female volunteer (A) and the left frontal white matter of a 34‐year‐old male living with HIV (B), overlaid on axial (left), sagittal (middle), and coronal (right) T₁‐weighted combined images (from two inversion times) acquired at 7 T. Images are displayed in radiological orientation.

FIGURE 2.

Representative in vivo spectra acquired at 7 T from a 21‐year‐old healthy male volunteer and combined using (A) optimized truncation to integrate multichannel MRS data using rank‐R singular value decomposition (OpTIMUS), (B) whitened singular value decomposition (WSVD), (C) signal/noise squared (S/N²), and (D) the Brown method. Spectra are normalized to the total N‐acetylaspartate + N‐acetylaspartyl‐glutamate (tNAA) peak for display. Signal‐to‐noise ratio (SNR) was calculated using the maximum tNAA peak height divided by the standard deviation of a noise‐only region (11.53–12.26 ppm), shown in the inset. au = arbitrary units; ppm = parts per million.

At 7 T, OpTIMUS yielded significant increases in SNR of spectra acquired in the PCC of healthy volunteers compared to spectra combined with WSVD, S/N², and Brown (p < 0.001 for all) (Figure 3 and Tables 1 and S1). WSVD also yielded significant higher SNR compared to S/N² and Brown (p < 0.001 for both). Differences in SNR between S/N² and Brown were not statistically significant (p = 0.237). Reproducibility of SNR, indicated by ICC values, was high for each combination method (OpTIMUS ICC = 0.964, WSVD ICC = 0.966, S/N² ICC = 0.816, and Brown ICC = 0.880). SNR values for spectra acquired from PLWH were lower than those for spectra acquired from healthy volunteers across all coil combination methods and voxels; however, OpTIMUS consistently yielded spectra with the highest SNR in both cohorts (Figure S1A and Table S2).

FIGURE 3.

Box‐and‐whisker plots of signal‐to‐noise ratio (SNR) values for spectra acquired at 7 T from all subjects and combined with optimized truncation to integrate multichannel MRS data using rank‐R singular value decomposition (OpTIMUS), whitened singular value decomposition (WSVD), signal/noise squared (S/N²), and the Brown method. SNR of spectra combined with OpTIMUS was significantly higher compared to the other three methods. ***p < 0.001; ns = nonsignificant.

TABLE 1.

Signal‐to‐noise ratio (SNR), metabolite concentrations normalized to total creatine + phosphocreatine (tCr), and Cramér–Rao lower bound (CRLB) values for spectra acquired at 7 T using four combination methods.

	OpTIMUS	WSVD	S/N2	Brown
SNRtNAA	249.45 [224.88–272.94]	222.06 [200.60–247.49]	167.05 [149.23–185.88]	145.48 [132.96–176.40]
SNRwSUM	214.25 [192.90–233.17]	191.86 [172.54–211.88]	142.41 [129.32–159.23]	124.50 [114.48–150.81]
SNR myo‐I	66.43 [62.93–71.50]	59.81 [55.69–62.31]	46.25 [39.06–50.00]	41.73 [38.38–43.65]
tNAA
/tCr	1.21 [1.18–1.29]	1.19 [1.15–1.28]	1.21 [1.16–1.29]	1.19 [1.14–1.26]
CRLB	2.00 [2.00–3.00]	2.00 [2.00–3.00]	3.00 [2.00–3.00]	2.00 [2.00–3.00]
tCho
/tCr	0.18 [0.18–0.19]	0.18 [0.18–0.19]	0.19 [0.17–0.19]	0.18 [0.18–0.19]
CRLB	3.00 [3.00–3.00]	3.00 [3.00–3.00]	3.00 [3.00–3.00]	3.00 [3.00–3.00]
myo‐I
/tCr	0.56 [0.54–0.58]	0.57 [0.55–0.58]	0.56 [0.53–0.59]	0.54 [0.52–0.55]
CRLB	5.00 [5.00–5.00]	5.00 [5.00–5.00]	5.00 [5.00–5.00]	5.00 [5.00–5.00]
Glu
/tCr	0.83 [0.81–0.85]	0.81 [0.80–0.85]	0.83 [0.78–0.84]	0.80 [0.78–0.85]
CRLB	3.00 [3.00–3.00]	3.00 [3.00–3.00]	3.00 [3.00–3.00]	3.00 [3.00–3.00]
Gln
/tCr	0.12 [0.11–0.14]	0.12 [0.11–0.14]	0.12 [0.11–0.14]	0.11 [0.10–0.12]
CRLB	17.50 [13.00–20.00]	15.50 [14.00–18.00]	17.50 [15.00–19.00]	18.00 [16.00–21.00]
GSH
/tCr	0.11 [0.11–0.12]	0.12 [0.11–0.12]	0.12 [0.11–0.13]	0.12 [0.11–0.13]
CRLB	10.00 [10.00–11.00]	10.00 [9.00–11.00]	10.00 [9.00–11.00]	10.00 [9.00–10.00]

Note: Values are reported as median [interquartile range], and the units for CRLBs are % standard deviation; for methods that use signal‐to‐noise ratio (SNR) to optimize coil combination, i.e., OpTIMUS and S/N², the reported SNR values correspond to the same peak chosen for optimization; see Table S1 for complete ranges for all values.

Abbreviations: Gln = glutamine; Glu = glutamate; GSH = glutathione; OpTIMUS = optimized truncation to integrate multichannel MRS data using rank‐R singular value decomposition; S/N² = signal/noise squared; SNR _myo‐I = signal‐to‐noise ratio calculated using the myo‐inositol (myo‐I) peak and the standard deviation of a noise‐only region; SNR_tNAA = signal‐to‐noise ratio calculated using the total N‐acetylaspartate + N‐acetylaspartyl‐glutamate (tNAA) peak and the standard deviation of a noise‐only region; SNR_wSUM = signal‐to‐noise ratio calculated using weighted signal average of tNAA, total glycerophosphocholine + phosphocholine (tCho), and total creatine + phosphocreatine (tCr) peaks as the signal and the standard deviation of a noise‐only region; WSVD = whitened singular value decomposition.

Evaluation of frequency drift for the tNAA peak, prior to combination, in spectra acquired in both cohorts revealed a maximum tNAA drift of 0–8.8 Hz. Most of the healthy subjects experienced a maximum drift between ~2 and 5 Hz, while most spectra from the PCC and LFWM of PLWH revealed a maximum drift between ~5 and 6.5 Hz. OpTIMUS produced comparable FWHM to WSVD, S/N², and Brown for spectra acquired in all voxels (Figure S1B and Table S2). FWHM values were generally broader for spectra acquired from the PCC and LFWM of PLWH compared to spectra acquired from healthy volunteers.

Similar increases in SNR with OpTIMUS were obtained when SNR was calculated (for both optimization within OpTIMUS and final SNR calculation) using a weighted signal average of tNAA, tCho, and tCr peaks (p < 0.001 for all methods compared to OpTIMUS, Tables 1 and S1). Spectra acquired from healthy volunteers combined with OpTIMUS using the myo‐I peak to optimize SNR (versus the tNAA peak) yielded an SNR of the myo‐l peak of 66.43 [62.93–71.50] (Tables 1 and S1), higher than the other methods but similar to the SNR of the myo‐I peak from spectra combined using the tNAA peak (65.98 [62.13–66.83]). Notably, the SNR of the myo‐I peak was always the same or higher when myo‐I was used for optimization in OpTIMUS. Similarly, the SNR of the tNAA peak for spectra combined with OpTIMUS when using the myo‐I peak to optimize SNR was not compromised (240.32 [224.88–271.33]).

While spectra appear similar across the four methods, reduced spectral noise after combination with OpTIMUS contributes to higher overall SNR. Comparison of noise correlation between individual coil channels before and after whitening using the noise‐only scan acquired for each healthy volunteer revealed a substantial reduction of correlated noise indicated by reduced values in the off‐diagonal components of the noise correlation matrix (Figure S2A,B); however, noise with nonzero mean values was observed after whitening for some coil channels (e.g., Coils 25, 27, and 31), indicating evidence of incomplete whitening in some subjects (Figure S2C). When OpTIMUS performance was evaluated at 7 T using the first chronological noise‐only scan for all subjects, the SNR of the tNAA peak was 239.22 [221.41–269.82], compared to 249.45 [224.88–272.94] when spectra were combined using the corresponding noise‐only scan acquired for each subject. Similarly, the SNR of the tNAA peak using WSVD and the first chronological noise‐only scan for all combinations was 210.50 [185.38–244.13], compared to 222.06 [200.60–247.49] when using the corresponding noise‐only scan for each subject. The use of a single noise‐only scan for all subjects resulted in a maximum within subject decrease in SNR of ~7% and ~8% for OpTIMUS and WSVD, respectively, when compared to the use of a subject‐specific noise‐only scan. The median SNR values for OpTIMUS and WSVD using the first chronological noise‐only scan remained higher than S/N² and Brown, which do not use noise whitening (Figure S3). Additionally, metabolite quantification from spectra combined using a single noise‐only scan resulted in changes < 5% compared to spectra combined with subject‐specific noise‐only scans for most subjects, metabolite ratios, and both OpTIMUS and WSVD, except for Gln and GSH in some subjects, where the percentage change ranged from 8% to 22%.

3.2. Optimal Rank and Windowing in OpTIMUS

OpTIMUS performs an iterative search to find the spectral window and rank that maximizes the SNR of the combined spectra. For a spectrum of 2048 data points, the algorithm requires ~30 min of computation time (using parallel processing) to evaluate all iterations (2017 window sizes iterated across all spectral regions for a total of 2,035,153 unique windows). Determination of SVD rank required < 0.06 s for every window evaluated. The mean window size (spectral width) across subjects was 1.85 (range: 0.29–5.61) ppm, corresponding to 252 (range: 40–760) data points. Final window sizes and regions for all subjects are overlaid on a representative spectrum in Figure S4A. The majority of spectral regions contained in each window were in the upfield portion of the spectrum, where most of the peaks of interest are located. The evolution of SNR as a function of increasing window size is shown in Figure S4B. A consistent drop in SNR was observed for all spectra when window sizes exceeded 1032 data points, and the choice of window size resulted in SNR decreases as high as 18% of the maximum SNR for each subject. All combined spectra with SNR ≥ 95% of the maximum SNR used window sizes < 1000 data points, and every subject had at least one spectrum with SNR > 95% of the maximum SNR combined using a window size of < 250 data points.

The mean SVD rank across subjects was 18 (range: 5–32), corresponding to a mean estimated spectral variance represented in the final combined spectrum of 92% (range: 73%–100%). A histogram of rank distributions, highlighting the variability of ranks across subjects, is shown in Figure S4C. The relationship between SNR and SVD rank for a fixed window size is represented in Figure S4D. In contrast to window size, there was no clear trend across subjects between SNR and estimated spectral variance with increasing rank. Differences in SVD rank resulted in SNR differences as high as 18%.

3.3. Spectral Fitting and Metabolite Quantification for Spectra Combined With OpTIMUS

No consistent trends in CRLBs for any metabolites were observed between methods, attributed to the relatively low CRLBs (i.e., robust spectral fitting) for most metabolites (Tables 1 and S1). No metabolites were excluded due to CRLBs > 30%. In vivo CRLBs were < 10% for all subjects, methods, and metabolites except for Gln and GSH. Gln CRLBs ranged from 11% to 28%; however, 70% of subjects had Gln CRLB values ≤ 20% for all methods. GSH CRLBs ranged from 9% to 13%. While metabolite ratios were also very similar across methods (Tables 1 and S1), tNAA/tCr was significantly lower after spectral combination with both Brown and WSVD compared to OpTIMUS (p < 0.001 for both). tCho/tCr did not significantly differ between spectra combined with OpTIMUS and any of the three methods. For myo‐I/tCr, significantly lower concentrations were observed after spectral combination with Brown (p = 0.0023) and significantly higher concentrations after combination with WSVD (p = 0.0025) when compared to OpTIMUS. Additionally, Glu/tCr was significantly lower after spectral combination with both Brown and WSVD compared to OpTIMUS (p < 0.001 for both) and Gln/tCr was significantly lower for spectra combined with Brown (p = 0.0016) compared to OpTIMUS. GSH/tCr was significantly higher after spectral combination with WSVD, S/N², and Brown compared to OpTIMUS (p < 0.05 for all).

The mean and variance of in vivo tNAA, tCho, myo‐I, Glu, Gln, and GSH (all normalized to tCr) across spectra quantified using five different sets of 16 random averages for all combination methods are shown in Figure S5. Mean metabolite ratios and variance are similar across methods. Reproducibility analysis resulted in high to moderate ICC values for most metabolites including tNAA/tCr (ICC = 0.79), tCho/tCr (ICC = 0.9), and Glu/tCr (ICC = 0.77) for spectra combined with OpTIMUS.

In vitro, the MSE values for spectra combined with OpTIMUS and Brown (the default method for Siemens in‐line reconstruction), respectively, were 0.0099 and 0.0140 for NAA/Cr, 0.000056 and 0.000039 for Cho/Cr, 0.113 and 0.108 for myo‐I/Cr, 0.192 and 0.200 for Glu/Cr, and 0.012 and 0.015 for Lac/Cr. The CVs for all repeated measures (within and between sessions) for each metabolite and voxel position were < 5%, with more than half of CVs being < 2%.

3.4. Effect of Reducing Averages

Representative spectra acquired from the same subject after combination with OpTIMUS using 32 averages and the Brown method using all 64 averages are shown in Figure 4. Spectra combined with the Brown method had significantly lower SNR (145.48 [132.96–176.40], p < 0.001) compared to spectra combined with OpTIMUS (175.15 [153.47–195.53]), even when using half the number of averages. SNR and CRLBs of spectra combined with all methods and N = 32 averages are reported in Table S3. Notably, the median SNRs achieved with OpTIMUS (N = 32) and WSVD (N = 32) were 20% and 6% higher, respectively, compared to Brown (N = 64), while the median SNR of spectra after combination using S/N² (N = 32) was 20% lower.

FIGURE 4.

Representative in vivo spectra acquired at 7 T from a 21‐year‐old healthy male volunteer combined with (left) OpTIMUS using the first 32 averages and (right) the Brown method and 64 averages. Spectra combined with OpTIMUS and half the number of averages yielded significantly higher SNR than spectra combined with the Brown method using twice the number of averages. au = arbitrary units; ppm = parts per million.

3.5. Comparison of OpTIMUS‐Combined Spectra Acquired at 7 and 3 T

Representative combined spectra acquired at 7 T (N = 64 averages) as well as 3 T with the same number of averages (N = 64) and with the same scan time as 7 T (N = 110 averages) are shown in Figure 5. Spectra had significantly higher SNR at 7 T (224.88 [187.32–239.52]) compared to 3 T (159.64 [131.64–170.17], p < 0.001) when the same number of averages were used (N = 64), yielding a median improvement of 1.4× increase in SNR at 7 T compared to 3 T across all subjects. SNR was not significantly different for 7 T with 64 averages (224.88 [187.32–239.52]) compared to 3 T using 110 averages, i.e., with the same scan time as 7 T (216.25 [190.05–251.52], p = 0.86). Spectra acquired at 3 T with 110 averages yielded the highest SNR for two of the five subjects (Figure S6A). Significantly lower CRLBs for Glu were reported at 7 T (3.00% [3.00%–3.00%]) compared to 3 T (6.00% [5.00%–6.25%] and 5.00% [5.00%–5.25%] for 64 and 110 averages, respectively, p < 0.001 for both), indicating improvement in spectral fitting at 7 T even when comparable SNR is achieved at 3 T with matched scan times (Figure S6B).

FIGURE 5.

Representative in vivo spectra acquired from a 32‐year‐old female healthy volunteer at (A) 7 T with 64 averages, (B) 3 T using 64 averages, and (C) 3 T with 110 averages to match the scan time of the 7 T scan. All three spectra were combined using OpTIMUS, and the noise region used for signal‐to‐noise (SNR) calculation is shown in the inset. Spectra acquired at 7 T yielded higher SNR than spectra acquired at 3 T with the same number of averages. With equal scan times for both field strengths, however, two out of five spectra acquired at 3 T (N = 110 averages) had higher SNR than spectra acquired at 7 T (N = 64 averages) (Figure S6A). au = arbitrary units; ppm = parts per million.

4. Discussion

OpTIMUS is a recently reported combination algorithm for multichannel MRS data, originally developed using MR spectra acquired at 3 T with the point‐resolved spectroscopy (PRESS) sequence [13]. In the present study, OpTIMUS resulted in brain spectra with significantly higher SNR at 7 T using the sLASER sequence, compared to other well‐established combination algorithms and consistent with our prior results at 3 T [13]. OpTIMUS does not appear to degrade spectral quality or metabolite quantification and resulted in high reproducibility of SNR. Using half the number of averages, spectra combined using OpTIMUS achieved significantly higher SNR compared to spectra combined using the Brown method and all averages.

4.1. Spectral Improvements at 7 T With OpTIMUS

The increased SNR achieved with OpTIMUS compared to methods that assume uncorrelated noise, i.e., S/N² and Brown, is consistent with previous work demonstrating the improvements in SNR after noise decorrelation for multichannel coil combination [11, 27, 28]. The acquisition time for a noise‐only scan is ~1 min; however, if this is not acquired or available, similar results were reported when noise whitening was performed using the same noise‐only scan for all subjects. Notably, the data in this study were acquired over the course of ~1 year, reinforcing the robustness of the PCA whitening.

In theory, if noise decorrelation is perfect, the variance of the metabolite signal will be best represented by the direction of maximum variance, that is, the metabolite signal will be represented by the first singular vector after SVD [10]. Noise whitening, however, does not always generate fully isotropic noise because the estimated noise covariance is usually not equal to the true noise covariance [13]. In this case, the premise that maximizing the variance also maximizes the SNR no longer holds true, and the metabolite signal is present beyond the first singular vector. OpTIMUS mitigates this by using windowing to reduce the presence of metabolite signal in higher rank singular vectors and rank‐R SVD to recover the full signal, yielding spectra with maximum SNR among all the methods compared.

The results in the present work for spectra acquired at 7 T using sLASER are consistent with previous implementations of OpTIMUS at 3 T for spectra acquired with the PRESS sequence [13] and the sLASER sequence [29]. The increases in SNR while preserving spectral resolution for spectra acquired from both healthy volunteers and PLWH in multiple brain regions highlight the robust nature of OpTIMUS. Additionally, the SNR improvements achieved with OpTIMUS were consistent regardless of the peak chosen for SNR optimization (i.e., tNAA, weighted signal average of tNAA, tCho, and tCr peaks, or myo‐I). The ability of OpTIMUS to optimize coil combination using a low SNR peak, i.e., myo‐I, without compromising other spectral peaks could be beneficial for applications requiring robust signal enhancement in challenging spectral regions or for metabolites with inherently low concentrations. Additionally, we observed the ability for OpTIMUS to retain a high SNR when using a reduced number of averages compared to the Brown method with twice the number of averages. This could have relevant practical applications as this reduction in spectral acquisitions would directly translate to reductions in scan time.

The benefits of using a rank‐R SVD approach have been applied to develop denoising methods that use signal decomposition to separate desired signals from the noise for hyperpolarized ¹³C MR spectroscopy [30, 31] and ³¹P MRS [32], suggesting OpTIMUS may be applicable beyond the proton MR spectra of the brain. Given the larger spectral bandwidths of ¹³C and ³¹P spectra, the performance of OpTIMUS, particularly the effect of spectral windowing, should be evaluated. OpTIMUS was developed as a coil combination method for single‐voxel spectroscopy. While the combination of spectra acquired using MR spectroscopic imaging (MRSI) is an important goal, the direct translation of OpTIMUS is not straightforward given the nature of MRSI acquisition. This is a future area of research.

4.2. Impact of Coil Combination Method on Metabolite Quantification

Differences in quantification of in vivo metabolites with different coil combination methods, despite robust spectral fitting and similar metabolite variance for all methods, highlight the potential effects of coil combination method on concentration estimates, especially when comparing results across different studies. The accuracy and repeatability of metabolite quantification in vitro after spectra were combined with OpTIMUS was comparable to the vendor's in‐line reconstruction method. As expected, MSE values for in vitro spectra acquired at 7 T were lower than those reported at 3 T [13] for metabolites including NAA and Cho. Quantification of myo‐I led to higher errors at 7 T compared to 3 T despite maintaining high reproducibility, suggesting the potential need to optimize the basis set used for quantification for higher resolution phantom spectra.

4.3. Strategies for Accelerating OpTIMUS Performance

Given the iterative nature of OpTIMUS, evaluating SNR for every spectral window can yield relatively long computational times. Optimizing the computational efficiency of OpTIMUS is essential for practical implementation. The primary factor influencing the coil combination time is the iterative process of evaluating multiple window sizes and spectral regions. For a spectrum of 2048 data points, OpTIMUS evaluates all windows > 32 data points, i.e., 2017 window sizes, and for each window size, SVD is computed for every possible spectral region, and then rank‐1 to rank‐N coil combination is performed. The final SVD rank for each combined spectrum varied widely between subjects, with different ranks resulting in SNR increases as high as ~20%, suggesting that the rank‐R SVD optimization is clearly beneficial. While the rank‐R determination is relatively fast (< 0.06 s per iteration), the total computational time can become substantial considering this process must be repeated for ~2,000,000 unique spectral windows. As all spectra exhibited a consistent drop in SNR for spectral windows larger than 1032 data points, this threshold could be implemented as a fixed limit to reduce computational time substantially, i.e., the total number of iterations for window sizes > 1032 is 516,636, which corresponds to approximately one‐fourth of the total iterations. For applications where a faster combination is desirable and a small trade‐off in SNR is acceptable, the window size could be further constrained to 250 data points or fewer (see Section 3.2), consequently reducing ~80% of the computational time with a 5% trade‐off in SNR. Additionally, restricting the window search to the upfield part of the spectrum would further reduce iterations and computational time.

4.4. Comparison of OpTIMUS Implementation at 3 and 7 T

In this study, increases in spectral SNR for spectra combined with OpTIMUS at 7 T compared to 3 T for an equal number of excitations are consistent with previous work comparing field strengths [33, 34]. Pradhan et al. compared spectra acquired at 3 and 7 T, equipped with 32‐channel receive head coils, using the sLASER sequence with a similar TE (TE = 32 ms) as the present study (TE = 35 ms). Comparisons across field strengths for three anatomical positions (anterior cingulate cortex, centrum semiovale, and dorsolateral prefrontal cortex) and 32 averages yielded an average SNR improvement for spectra acquired at 7 T of 1.6, 1.2, and 1.6, respectively. Improvements in SNR from 3 to 7 T in the present study for spectra acquired in the PCC using the sLASER sequence are consistent with this prior work; however, improvements were lower than the theoretical linear increase in SNR with increasing field strength.

In comparison, when equal scan times at both field strengths were evaluated in the present study, SNR was higher at 7 T for some subjects but not all. Interestingly, Mekle et al. previously used the spin‐echo full‐intensity acquired localized (SPECIAL) sequence and an ultrashort TE of 6 ms to compare spectra acquired at 7 and 3 T and reported higher SNR for spectra acquired with 64 averages at 7 T compared to spectra with double the number of averages (N = 128) at 3 T [34]. Differences between these results and the present study could be explained by differences in voxel positioning or the use of different acquisition sequences. Nevertheless, spectral fitting of spectra combined with OpTIMUS was not compromised and was improved for glutamate at 7 T, suggesting improved spectral quantification at 7 T compared to 3 T when controlling for scan time and even when SNR is lower at 7 T. Similar to our results, previous work comparing 4 and 7 T also reported improved metabolite quantification at 7 T due to increased chemical shift dispersion even when spectra at both field strengths had equal SNR [35].

4.5. Limitations

We acknowledge several limitations of this study. There were no corrections for phase and frequency drift prior to averaging due to the low SNR of individual transients acquired in some coil channels. For most subjects, a maximum drift of ~2–6.5 Hz was observed over the total acquisition time for the coils with the highest SNR. Despite the acceptable FWHM values of the combined spectra, we acknowledge this is a limitation in the current implementation of OpTIMUS, and in some scenarios (high subject motion), frequency and phase corrections may be required prior to combination. OpTIMUS was evaluated in vivo in a relatively small cohort, and comparisons between field strengths and number of averages were performed on a smaller subset. Additionally, spectra were acquired using a single vendor (Siemens), from two single‐voxel locations in the brain (PCC and LFWM), and using a single sequence (sLASER), the recommended sequence for single‐voxel spectroscopy from recent MRS consensus efforts [4]. Given the challenges with field inhomogeneity at 7 T, further evaluation of OpTIMUS in challenging regions such as deep brain or temporal lobes is needed. Future studies are needed to evaluate the extent of the improvements provided by OpTIMUS for X‐nuclei spectra and organs beyond the brain, as well as the effect of the region of interest and number of coil channels on SNR improvements [36]. Additionally, due to the iterative nature of OpTIMUS, the total computational time may present a limitation for in‐line processing.

5. Conclusions

In conclusion, spectral combination using OpTIMUS results in increased SNR of in vivo MRS spectra at 7 T compared to other well‐established coil combination methods, including WSVD, S/N², and the Brown method, a variant of which is the default method for in‐line spectral combination on Siemens MR scanners. By effectively reducing noise and incorporating the metabolic signal from higher singular vectors, OpTIMUS not only improves spectral quality but has the potential to enable shorter acquisition times, making it a viable tool for clinical MRS applications at UHF strengths.

Supporting information

Figure S1 Signal‐to‐noise ratio (SNR) and full width at half maximum (FWHM) of spectra from healthy volunteers (N = 14) and people living with HIV (PLWH) (N = 9) using four combination methods and in two voxel positions, posterior cingulate cortex (PCC) and left frontal white matter (LFWM).

Figure S2. Noise correlation before and after whitening of spectra acquired at 7 T using a 32‐channel phased array receive head coil.

Figure S3. Impact of the selection of a noise‐only scan used for noise whitening on signal‐to‐noise ratio (SNR) across coil combination methods.

Figure S4. Characterization of the OpTIMUS algorithm.

Figure S5. Effect of the coil combination method on in vivo metabolite quantification.

Figure S6. Comparison of OpTIMUS‐combined spectra acquired at 7 T (N = 64 averages), 3 T (N = 64 averages), and 3 T (N = 110 averages) from five healthy volunteers.

Table S1. Complete data ranges for signal‐to‐noise ratio (SNR), metabolite concentrations normalized to total creatine + phosphocreatine (tCr), and Cramér–Rao lower bounds (CRLBs) for spectra acquired at 7 T using four combination methods.

Table S2. Signal‐to‐noise ratio (SNR) and full width at half maximum (FWHM) calculated from spectra combined with four coil combination methods and acquired from healthy volunteers and people living with HIV (PLWH).

Table S3. Signal‐to‐noise ratio (SNR), metabolite concentrations normalized to total creatine + phosphocreatine (tCr), and Cramér–Rao lower bound (CRLB) values for spectra acquired at 7 T using four combination methods and 32 averages.

Appendix S1. Minimum Reporting Standards for in vivo Magnetic Resonance Spectroscopy (MRSinMRS) checklist.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request and after a data sharing agreement is executed.