Phased-array combination of 2D MRS for lipid composition quantification in patients with breast cancer

Lipid composition in breast cancer, a central marker of disease progression, can be non-invasively quantified using 2D MRS method of double quantum filtered correlation spectroscopy (DQF-COSY). The low signal to noise ratio (SNR), arising from signal retention of only 25% and depleted lipids within tumour, demands improvement approaches beyond signal averaging for clinically viable applications. We therefore adapted and examined combination algorithms, designed for 1D MRS, for 2D MRS with both internal and external references. Lipid composition spectra were acquired from 17 breast tumour specimens, 15 healthy female volunteers and 25 patients with breast cancer on a clinical 3 T MRI scanner. Whitened singular value decomposition (WSVD) with internal reference yielded maximal SNR with an improvement of 53.3% (40.3–106.9%) in specimens, 84.4 ± 40.6% in volunteers, 96.9 ± 54.2% in peritumoural adipose tissue and 52.4% (25.1–108.0%) in tumours in vivo. Non-uniformity, as variance of improvement across peaks, was low at 21.1% (13.7–28.1%) in specimens, 5.5% (4.2–7.2%) in volunteers, 6.1% (5.0–9.0%) in peritumoural tissue, and 20.7% (17.4–31.7%) in tumours in vivo. The bias (slope) in improvement ranged from − 1.08 to 0.21%/ppm along the diagonal directions. WSVD is therefore the optimal algorithm for lipid composition spectra with highest SNR uniformly across peaks, reducing acquisition time by up to 70% in patients, enabling clinical applications.

Lipid composition is a central marker for the pathogenesis of breast cancer 1, 2 , the most commonly diagnosed cancer among women 3 . Conventional magnetic resonance spectroscopy (MRS) of stimulated echo acquisition mode (STEAM) with short echo time can detect lipid spectral peaks in the breast non-invasively on standard clinical scanners 4 , and further enhancement in specificity is valuable for clinical applications. Spectral editing methods of double quantum filtering (DQF), effectively suppress background signals, but only target a single metabolite, such as polyunsaturated fatty acids (PUFA) in 1D MRS 5 . The two dimensional (2D) MRS method of correlation spectroscopy (COSY) 6 resolves lipid composition on a 2D map, but suffers from the dominant water signal and wide peak spread 7 . DQF-COSY, combining the strength of spectral editing and 2D MRS, allows unobscured identification of individual lipid resonances through sharp peak appearance and suppression of water contamination signals 8 . However, both the signal retention of only 25% in DQF-COSY 7 and depleted lipids within breast tumours 59 contribute to low signal to noise ratio (SNR), posing a challenge for accurate quantification. Since DQF-COSY collects a series of 1D spectra demanding a long acquisition time (typical scan time of 15-20 min) 10 , SNR improvement approaches beyond signal averaging are required for clinically viable applications.
Phased-array coils have been widely adopted in routine clinical practice, with signal combination algorithms developed to enhance SNR and reduce acquisition time 11,12 . Adaptively Optimised Combination (AOC) 13 , amongst current combination algorithms developed for 1D MRS (Table 1) [13][14][15][16] , is the optimal approach for spectra acquired in the brain using conventional MRS 13 and PUFA spectra acquired in the breast using spectral editing MRS 17 . The SNR of a single spectral peak has been adopted as the common assessment criteria in the comparison of combination algorithms. However, lipid composition in 2D MRS is determined utilising multiple spectral peaks across the 2D map, demanding an algorithm with uniform improvement. In contrast to spectral editing MRS, DQF-COSY retains the presence of dominant metabolites, at reduced amplitude, for the estimation Scientific Reports | (2020) 10:20041 | https://doi.org/10.1038/s41598-020-74397-y www.nature.com/scientificreports/ of sensitivities and phases of coil elements, potentially eliminating the need to acquire an additional reference spectrum. We hypothesise that AOC is the optimal algorithm to provide maximal SNR improvement uniformly across the 2D lipid composition spectrum in breast cancer. We therefore adapted current algorithms (Table 1), with a particular focus on noise decorrelated algorithms, for 2D MRS and applied on lipid composition spectra acquired using DQF-COSY. The combination algorithms were evaluated on spectra acquired from breast tumour specimens, healthy female volunteers and patients with breast cancer, with data from the tumour and the peritumoural adipose tissue (Fig. 1a). Each algorithm was implemented twice with weighting coefficients derived from the spectrum without water suppression (external reference, denoted by subscript "e") and first signal of the DQF-COSY acquisition (internal reference, denoted by subscript "i") (Fig. 1b). The non-uniformity of SNR improvement across spectral peaks (Table 2) and the direction of non-uniformity was additionally evaluated. The non-uniformity was defined as the coefficient of variance of SNR improvement across spectral peaks. The direction of non-uniformity was quantified as the slopes along the diagonal (bias along the frequency axes) and the off-diagonal (bias along the encoding axes) on a plane regressed to the SNR improvement at the spectral location of each peak.

Algorithms Description
Equal weighting Adding after aligning in phase Signal weighting Aligning in phase and weighting with the signal of reference peak S/N weighting Aligning in phase and weighting with the SNR of reference peak S/N 2 weighting Aligning in phase and weighting with the signal to the noise squared (S/N 2 ) of reference peak nd-comb Noise decorrelation using PCA, then aligning in phase and weighting the noise decorrelated data using the SNR of reference peak WSVD Noise decorrelation using PCA, then aligning in phase and weighting the noise decorrelated spectra using the first left singular vector obtained from the singular value decomposition of the noise decorrelated spectra AOC Phasing and weighting with the signal of reference peak multiplied by the inverted noise correlation matrix  Fig. 2d). Linear algorithms gave lower SNR compared with the noise decorrelated algorithms, and are presented only for information purposes (Table 3). WSVD i improved the SNR by 53.3% (40.3-106.9%) in specimens, 84.4 ± 40.6% in volunteers, 96.9 ± 54.2% in peritumoural adipose tissue and 52.4% (25.1-108.0%) in tumours in vivo, reducing the acquisition time by 50-70% in tumour and adipose tissue respectively. The combined 2D spectra using WSVD i from a specimen, volunteer, peritumoural tissue, and tumour in vivo are shown in Fig. 3.

Discussion
In this work, current combination algorithms, designed for 1D MRS, were adapted and evaluated for lipid composition spectra from breast acquired using 2D MRS, with a particular focus on noise decorrelation algorithms. WSVD i was identified as the most effective signal combination approach in 2D MRS, instead of AOC, the optimal algorithm for 1D MRS 13,17 . WSVD i provided maximal SNR improvement in patients (97% in peritumoural adipose tissue, 52% in tumour) and low non-uniformity of 6% and 21% respectively. WSVD i , eliminating the need for acquiring an additional reference spectrum (typically scan time of 2 min), reduces scan time by 50-70% from 17 to 8 min in tumour and 5 min in peritumoural adipose tissue. Noise decorrelation algorithms outperformed all linear algorithms substantially through the cancellation of correlated noise, as found in 1D MRS studies 13,17 . WSVD performance was not degraded in low SNR spectra acquired from the tumours, in contrast to 1D spectra reported in previous studies 17,18 . In high SNR spectra from adipose tissue, WSVD and AOC yielded comparable SNR and outperformed nd-comb, as observed in 1D PUFA spectra 17 . Among the linear algorithms, S/N 2 Weighting had the best SNR performance, in line with the 1D MRS studies 14,17 .
External reference methods (WSVD e , AOC e and nd-comb e ) showed comparable SNR ex vivo, with the performance of nd-comb e degraded in vivo due to the larger variation in coil weightings associated with the voxel location away from the isocentre 14,15,19 . For internal reference, WSVD i outperformed AOC i and nd-comb i . External reference, with higher SNR than internal reference, is expected to provide more accurate weighting coefficients and in turn higher SNR of combined spectra 20 , as observed in AOC and nd-comb. However, WSVD is less sensitive to the SNR of the reference spectrum as observed in this work, with weighting coefficients generated from the entire spectrum 16 instead of a dominant peak, as in AOC 13 and nd-comb 15 .
WSVD i , in addition to providing maximal SNR, eliminates the need for the acquisition of a reference spectrum, reducing scan time by approximately 2 min. WSVD i improved the SNR by 97% in peritumoural adipose . WSVD e and WSVD i showed better or comparable non-uniformity against other external and internal reference algorithms, with similar performance between WSVD e and WSVD i . WSVD i had non-uniformity of 21% in specimens, 5% in volunteers, 6% in peritumoural adipose tissue and 21% in tumours in vivo, with the variation in non-uniformity reflecting the effects of noise on SNR improvement. The slope along the diagonals further confirmed the observation of non-uniformity, as higher slope (bias in SNR improvement) was associated with lower SNR (observed in spectra from tumours) and lower slope was associated with higher SNR (observed in spectra from adipose tissue). The magnitude of the slop was small in adipose tissue (0.21%/ppm and 0.18%/ ppm in healthy volunteers and 1.08%/ppm and 0.30%/ppm in peritumoural adipose tissue), indicating negligible changes of SNR improvement of 0.92% and 0.79% in healthy volunteers and 4.8% and 1.32% in peritumoural adipose tissue at a maximal frequency gap between peaks of interest (0.9 ppm to 5.3 ppm). However, the slopes found in tumours were noticeably higher with higher improvement towards low frequencies and mixing encoding directions, likely due to the signal elevation closer to contamination water signal stripe along the mixing encoding direction (Fig. 3d). Hence, WSVD i provides minimal non-uniformity for SNR improvement across lipid composition spectra. www.nature.com/scientificreports/ DQF-COSY 8 , similar to STEAM 21 , is composed of three 90° RF pulses, allowing a short echo time and a minimal chemical shift displacement. DQF-COSY, different from STEAM, modulates the evolution time t 1 for 2D spectral encoding and incorporates quantum coherence pathway selection gradients to suppress background signal, allowing enhanced specificity at the expense of a portion of SNR 8 . DQF-COSY directly resolves monounsaturated fatty acids (MUFA) and PUFA through J-coupling sensitivity 8 , while STEAM instead demands a mathematical model 22 . All lipid peaks could be well detected using conventional 1D MRS under reasonable water suppression 23 , while DQF-COSY may have a big advantage for the detection of lipid peaks at 4.1 ppm and 4.25 ppm under challenging conditions for water suppression. Hence, DQF-COSY, supported by its intrinsic minimal chemical shift displacement, high specificity and SNR enhancement from a phased-array combination approach may help studying small lesions or area of interest.
The extensive experiments on ex vivo tumour specimens, healthy participants and patients (over 70 datasets from clinical population) encompassed a wide range of physiological environments encountered in a clinical setting. The acquisition voxel was adjusted to the size of the tumour in diseased breast and standardised to 2 × 2 × 2 cm 3 in healthy breast, allowing investigation in both low and high SNR conditions. The comparison among algorithms was comprehensive, covering both internal and external references, with outcome measures extended beyond conventional SNR to non-uniformity. Both standard clinical hardware (scanner and coil) and routine patient imaging procedures were adopted to ensure the immediate clinical translation of the research findings. This study was limited to a single scanner and two different coils, and multi-centre studies on scanners and coils from a range of vendors are required before wider clinical adoption. Patients with invasive breast carcinoma were studied in this work to reduce the confounding factor of experimental setup, however larger patient cohorts with other phenotypes of breast cancer should be investigated in the future.
WSVD, the most effective combination algorithm for 2D MRS, can enhance the sensitivity of inconspicuous lipid constituents found in tumours and accelerate the acquisition in adipose tissue. The extension of single voxel 2D MRS into chemical shift imaging (CSI) of 2D MRS allows the investigation of spatial distribution of lipid composition in tumour but is limited by the voxel size and a demanding acquisition time proportional to the number of voxels acquired. WSVD can potentially allow smaller voxel sizes and reduce acquisition time through trading the enhanced SNR, allowing the investigation of spatially heterogeneous response to neoadjuvant chemotherapy in breast cancer 24 . CSI of 2D MRS, with further support from compressed sensing, can achieve direct lipid composition mapping of the entire breast, for the early detection and prevention of breast cancer, without the need of a mathematical model of lipid amplitudes based on the empirical assumptions made in the Dixon method 25 . However, further investigation is needed to consider the spatial variability in the coil sensitivity and the combination of WSVD with compressed sensing for CSI of 2D MRS.
In conclusion, WSVD i , instead of AOC, is the optimal approach for processing lipid composition spectra acquired using 2D MRS on phased-array coils from the breast. WSVD i not only provides maximal SNR Table 4. Non-uniformity of SNR improvement in 2D lipid composition spectra using DQF-COSY. Data for CV are medians (interquartile range). Slope along the diagonal is positive from (0.9, 0.9) ppm to (5.3, 5.3) ppm. Slope along the off diagonal is positive from reading t 2 /F 2 at (0.9, 5.3) ppm to mixing t 1 /F 1 at (5.3, 0.9) ppm. P-value represents the comparison on CV values between the noise decorrelated algorithms using Wilcoxon signed-rank tests. Results are presented with WSVD i as a reference for comparison. Data with negative SNR improvement were excluded (1 dataset from a healthy volunteer using AOC i , 1 dataset from a healthy volunteer using nd-comb i , and 1 dataset from a tumour in patients using nd-comb i ). AOC = adaptively optimised combination, CV = coefficient of variance, nd-comb = noise decorrelated combination, WSVD = whitened singular value decomposition.    www.nature.com/scientificreports/ improvement without the need of additional reference spectra, but also delivers consistent improvement across lipids with high uniformity. With improved SNR, the acquisition can be achieved at a clinically viable time of 8 min (instead of 17 min), enabling the routine clinical assessment of lipid composition.

Methods
A total of 72 lipid composition spectra were acquired using DQF-COSY from excised human breast tumour specimens, healthy female volunteers and patients with breast cancer (Fig. 1a) Ex vivo study. Seventeen female patients (mean age 61 years, age range 42-78 years) with invasive carcinoma (eight grade II and nine grade III), without prior hormonal therapy or chemotherapy and a tumour size greater than 10 mm in diameter were enrolled. The freshly excised whole tumour at surgery was immediately scanned before formalin treatment using a 32-element phased-array receiver coil for signal detection. Clinical standard T 1 -weighted and T 2 -weighted anatomical images were acquired for voxel localisation. 2D spectra of lipid composition were acquired using DQF-COSY 8  In vivo study. Fifteen healthy female volunteers (mean age 66 years, age range 58-76 years) without previous breast cancer or family history of breast cancer participated in the study. Fifteen patients (mean age 63 years, age range 53-71 years, seven grade II and eight grade III) and a further ten patients (mean age 52 years, age range 36-63 years, one grade II and nine grade III) with invasive carcinoma were enrolled into the study for the acquisition of lipid composition spectra from peritumoural adipose tissue and tumour respectively. Patients with a tumour size greater than 10 mm, without prior chemotherapy or hormonal therapy, and no conditions contraindicative to MRS were eligible. All participants were scanned in the prone position as clinical routine practice using a 16-element phased-array breast receiver coil for signal detection. Standard sagittal T 1 -weighted anatomical images, axial T 2 -weighted anatomical images and diffusion weighted images were acquired for voxel localisation. 2D spectra of lipid composition were acquired using DQF-COSY 8 with TR of 552 ms, initial TE of 25 ms, a t 1 increment of 1 ms, 256 increments (mixing encoding t 1 time domain axis, F 1 frequency domain axis), 256 sampling points (reading encoding t 2 time domain axis, F 2 frequency domain axis), 2 repeats per increment, spectral bandwidth of 1000 Hz, and DQF gradients of 30/40/100 ms mT/m. Reference spectra without water suppression were acquired using single voxel PRESS sequence 26 with TR/TE of 1250/144 ms, 1024 data points, spectral bandwidth of 2000 Hz and 16 averages. In healthy volunteers, data were acquired from both breasts and the voxel size was set to 2 × 2 × 2 cm 3 containing primarily the adipose tissue. In patients, the voxel covering the tumour had a volume ranging from 2.2 to 21 cm 3 for tumours in vivo (10 patients), while a voxel of 2 × 2 × 2 cm 3 was positioned at 1 cm from the tumour for peritumoural adipose tissue (15 patients).
Data processing. All the algorithms were developed in MATLAB (MathWorks, Natick, MA, USA) with the processing flowchart shown in Fig. 1b. The raw data were averaged across repeated acquisitions before signal combination. The averaged signal, organised as a 2D map based on t 1 and t 2 time domain axes for each coil element, was subsequently apodised using squared sine bell along both time domain axes and zero filled to 512 × 512 points. The reference spectrum without water suppression was used as external reference with the maximum peak (either water or lipid) as target metabolite 17 while the first t 1 increment of the DQF-COSY acquisition was used as internal reference with the maximum peak in frequency domain (either residual water or lipid) as the target metabolite. Both external (denoted by subscript "e") and internal (denoted by subscript "i") weighting coefficients, containing weights and phase, were computed using external and internal references respectively for each dataset and for each algorithm. The weighting coefficient derived for a coil element was applied to the apodised and zero filled signals at the corresponding coil element. The combined 2D time domain signal was the summation across all the coil elements, and the combined 2D spectrum was subsequently derived using 2D Fast Fourier transform. The SNR of a spectral peak ( Table 2) was computed as the peak height in the magnitude spectral map divided by the standard deviation of the real part of the noise in the square region covering (F 1 : 6.9-8.4, F 2 : 6.0-7.5) ppm 27 , with the overall SNR quantified at (1.3, 1.3) ppm and SNR improvement referenced to Equal Weighting algorithm 27 . The non-uniformity of SNR improvement across the 2D spectrum was subsequently derived as the coefficient of variance (standard deviation divided by the mean) of the SNR improvement across all the spectral peaks 19 . A 3D scatter plot of SNR improvement at the spectral location of the peak was then created (Fig. 5a). A plane was subsequently regressed onto the 3D scatter plot to derive the direction and degree of bias in frequency along the diagonal (low at (0.9, 0.9) ppm to high at (5.3, 5.3) ppm) and in encoding along the off diagonal (reading t 2 /F 2 at (0.9, 5.3) ppm to mixing t 1 /F 1 at (5.3, 0.9) ppm). Shapiro-Wilk test was performed on the SNR and non-uniformity to assess if the distribution was normal. The SNR across noise decorrelated algorithms was compared using a one-way ANOVA with repeated measures and a Wilcoxon signed-rank test for normally and non-normally distributed data respectively. The SNR of the linear algorithms was also reported for reference purposes. Data with negative SNR improvement for the calculation of the non-uniformity were excluded (1 healthy volunteer using AOC i , 1 healthy volunteer using nd-comb i , and 1 tumour in vivo using nd-comb i ). A p-value < 0.05 was considered statistically significant.

Data availability
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.