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01.12.2015 | Research | Ausgabe 1/2015 Open Access

Journal of Cardiovascular Magnetic Resonance 1/2015

Compressed sensing to accelerate magnetic resonance spectroscopic imaging: evaluation and application to 23Na-imaging of mouse hearts

Journal of Cardiovascular Magnetic Resonance > Ausgabe 1/2015
Mahon L. Maguire, Sairam Geethanath, Craig A. Lygate, Vikram D. Kodibagkar, Jürgen E. Schneider
Wichtige Hinweise

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

MLM designed the study, conducted the simulations and MR experiments, carried out the data analysis, and drafted the manuscript. SG and VK wrote the compressed sensing algorithm. CAL was involved in the study design and in vivo experiments. JES was involved in the design of the study, data analysis and in drafting of the manuscript. All authors read and approved the final manuscript.
Magnetic resonance spectroscopic imaging
Compressed sensing
Signal-to-noise ratio
Echo-planar spectroscopic imaging
Chemical shift imaging
Acceleration/undersampling factor


Magnetic Resonance Spectroscopic Imaging (MRSI) allows non-invasive investigation of regional metabolic processes in vivo, but suffers from long scan-times due to low metabolite concentrations, slow spatial encoding schemes, and low MR sensitivity (for nuclei other than protons). This versatile technique would benefit from a reduction in scan-time in order to make it more clinically applicable. Single- or multi-shot echo-planar spectroscopic imaging (EPSI) sequences [ 1- 6] have been proposed to reduce MRSI scan-time. Indeed, Furuyama et al. have evaluated the performance of CS EPSI based 2D J-resolved spectroscopy [ 7, 8]. However, EPSI is known to provide lower sensitivity compared to classical chemical shift imaging (CSI) [ 7]. Low metabolite concentrations and reduced MR sensitivity limit the applicability of parallel imaging. Conversely, Compressed Sensing (CS) is a technique for accelerating the inherently slow data acquisition process, and is well suited for MRSI due to its intrinsic denoising effect [ 9]. CS has been used to accelerate 1H- [ 10, 11], hyperpolarized 13C- [ 12- 14], 23Na- [ 15], 31P-MRSI [ 16], and multi-dimensional NMR experiments [ 17, 18]. The scan time reductions ranged from 2- [ 15, 13] to 18-fold [ 14]. The application of CS to (pre-) clinical in vivo imaging necessitates thorough examination of the conditions under which it is robust. However, little systematic evaluation of the influence of SNR and spatial resolution on the achievable scan-time reductions and quantification of metabolite signals has been performed to date [ 7, 13, 19]. Whilst the work by Geethanath et al. [ 11] made an important step forward in the use of CS-MRSI, it generated some debate regarding the reliability of its use in the clinic [ 20, 21]. We present a detailed performance evaluation of the CS-reconstruction developed by Geethanath et al. in the context of 1H-MRSI [ 11]. For the first time we then apply CS to 23Na-MRSI on mouse hearts demonstrating the potential of CS for high resolution spectroscopic imaging in vivo.


Synthetic phantom data

An in-silico noise-free phantom containing five compartments and representing a simplified mouse thorax was constructed in the image domain (256 × 256 voxels). Each compartment contained a single Lorentzian resonance at a unique frequency (Fig.  1a,b). This enabled quantification of inter-compartment signal contamination arising from CS reconstruction as the spatial origin of the signal could be determined from its frequency. These data were Fourier transformed (FT) into the time domain and the central N × N  k-space points (N = 16, 24, 32, 48, 64) taken as low-resolution representations. Gaussian noise was added to vary the SNR in the image domain (2, 4, 8, 16, 32, 64, 128, 256 and ∞ (i.e. noise-free)), where SNR was defined as the ratio of peak-height to the standard deviation of the noise of the real part of the spectrum.


All 23Na-MRSI data were acquired on a horizontal 9.4 T MR system equipped with a VnmrS Direct Drive2 console and 60 mm i.d. 1 T/m imaging gradients (Agilent Technologies, USA). An actively decoupled 23Na quadrature birdcage transmit resonator (i.d. 39 mm) was used in combination with a 14 mm square surface receive coil (Rapid Biomedical, Germany). 1H anatomical images were acquired using a 39 mm quadrature birdcage resonator (Rapid Biomedical, Germany).

Phantom experiments

Validation experiments were conducted on a phantom comprised of two coaxial compartments with the inner compartment (i.d. 3.6 mm, volume ~ 1 ml) containing 20 mM NaCl, and the outer compartment (i.d. 13.5 mm, volume 15 ml) containing 100 mM NaCl (Fig.  1c). The phantom also contained two coaxial concentration references containing 200 and 500 mM NaCl, which, however, were not used for this study. Fully sampled, single average, 2D axial slice-selective MRSI data (60° flip angle, 30 × 30 mm FOV, 2 mm slice, 96 × 96 PE steps, TR/TE = 150/0.50 ms, 9216 FIDs, acquisition time ~24 mins) were acquired and repeated 32 times (total acquisition time: 12.8 h). The central N × N  k-space points (N = 16, 24, 32, 48, 64, 96) from multiple repetitions were combined to give MRSI data sets with varying spatial resolution and SNR.

In vivo experiments

Cardiac 23Na-MRSI experiments were conducted on three female wild-type C57BL/6 mice (body weight 27.5 ± 4.0 g). After induction of anaesthesia (4 % isoflurane in 100 % oxygen), mice were positioned prone in a dedicated animal cradle with the heart centred over the surface coil, and maintained at 37 °C and 1.5–2.0 % isoflurane in 2 L/min oxygen flow throughout the MRSI experiments. Cardiac and respiratory signals were continuously monitored using an in-house developed ECG and respiratory gating device [ 22]. All investigations were approved by the local ethical review committee and conformed to the Animals (Scientific Procedures) Act 1986 (UK) incorporating European directive 2010/63/EU.
Using the same MRSI sequence as for the phantom data, threefold prospectively under-sampled 23Na data were acquired in mouse hearts in vivo in short-axis orientation (FOV 30 × 30 mm, 64 × 64 PE steps, 2 mm slice thickness, 8 averages, 40° flip angle, cardiac triggered, TR/TE = ~125/0.85 ms (i.e. one cardiac cycle), total acquisition time ~23 mins). Under-sampling was carried out as described previously [ 11].

Data analysis

All data were reconstructed and analysed in Matlab2013a (Mathworks, USA). Synthetic and acquired phantom data were retrospectively 1- to 5-fold under-sampled using a pseudo-random sampling scheme and reconstructed using a CS reconstruction described previously [ 11]. Signal amplitudes (i.e. peak maximum of the real component of the complex spectra), and contamination for CS reconstructed data and fully-sampled, FT reconstructed, data were compared. Signal amplitudes obtained from the CS reconstructed data were subject to linear regression analysis with the FT reconstructed fully-sampled data. A p-value of < 0.05 indicated a statistically significant correlation between the datasets. Signal contamination, defined as the total signal amplitude from resonances originating from outside the ROI detected within the ROI divided by the number of voxels in the ROI, was assessed for the synthetic phantom only. The 23Na myocardium/blood-ratio was estimated in vivo by calculating the mean ratio from six pairs of adjacent voxels located in the myocardium and the left ventricular blood-pool. Ratios are quoted as mean ± standard deviation. SNR was calculated for the myocardium by dividing the amplitude of the 23Na resonance in the spectrum by the standard deviation of the real component of the noise between 10–20 ppm, distant from the 23Na resonance; the chemical shift of the 23Na resonance was defined as 0 ppm.


Typical CS reconstructed data from the virtual phantom (SNR = 32, 32 PE steps) are shown in Fig.  2, demonstrating similar spatial and relative signal intensity distribution to the FT data. Consistent with previous studies [ 13], low SNR (i.e. ≤ 8) resulted in an exaggerated noise floor in the CS reconstructed data preventing the reconstruction from converging; these data were excluded from further analysis. Although absolute signal intensities relative to the fully-sampled noise-free FT reconstructed case were not preserved, CS reconstruction resulted in a linear scaling of the data (right column in Fig.  2). Importantly, all CS reconstructed data demonstrated a high correlation with FT reconstructed noise-free fully-sampled data, with gradients ranging from 1.30 (R = 4, PE = 16, SNR = 16) to 5.73 (R = 1, PE = 64, SNR = 32), R 2 values from 0.80 (R = 4, PE = 16, SNR = 16) to 0.98 (R = 1, PE = 64, SNR = ∞), and p-value always <0.001.
Higher acceleration factor resulted in denoising of the reconstructed spectra, but also in increased blurring of compartment boundaries, particularly at lower resolutions. This is qualitatively illustrated by the boundary of ROI3 (Fig.  3). While the FT reconstruction of the fully sampled data yielded the sharpest transition from signal within ROI3 to the outside, oscillations in signal amplitude outside the compartment are visible as a result of the point-spread-function of the uniformly weighted acquisition. Conversely, CS reconstructions of (R = 1 or 3) reduced these oscillations at the boundary transition, but resulted in an increased near-constant signal-floor outside the compartment, which decreased with improving spatial resolution.
Figure  4 shows the color-coded (a,b; top row) signal amplitude and (c,d; bottom row) contamination for ROI2-4 of the virtual phantom, normalized to the mean signal intensity from ROI1. Data were normalized to the signal from ROI1 as this compartment provided a defined signal and had dimensions similar to those that would be expected from a concentration reference phantom that could reasonably used in murine cardiac in vivo experiments. Data are presented as a function of spatial resolution, acceleration factor, and SNR for the CS- (a, c; left column) and the FT-reconstructions (b, d; right column). Unsurprisingly, the highest contamination, and correspondingly lower signal amplitudes were found for the CS reconstructed data of ROI2 (representing left-ventricular myocardium) at low resolution. Similarly, low amplitudes and high contamination were found for CS reconstructions of all ROIs at lowest SNR and increasing under-sampling factors. Increasing SNR and resolution resulted in CS reconstructions that more closely resembled the FT reconstruction of fully sampled data, while contamination decreased to levels lower than in those for the FT reconstruction.
In Fig.  5, sodium intensity maps from the compartmented phantom are shown for FT reconstructed fully-sampled, and CS-reconstructed data (R = 1, 3 and 5; 32 PE steps). The gradient in signal intensities along the vertical axis of the images reflects the receive profile of the surface coil. Horizontal and vertical profile, correlation plots (normalized FT vs. CS reconstructed data), and Bland-Altman analysis for the amplitudes confirmed the behaviour observed in the virtual phantom: CS reconstruction resulted in a high correlation between CS and FT reconstructed data, in signal denoising, and in increased blurring of compartment boundaries with increased under-sampling.
A prospectively 3-fold under-sampled, CS-reconstructed, myocardial 23Na-map in short-axis orientation obtained in vivo from a mouse overlaid on an anatomical 1H-image, and corresponding spectra, are presented in Fig.  6. Blood/myocardium amplitude ratios of 0.45 ± 0.07, 0.48 ± 0.09, and 0.47 ± 0.08 were obtained in vivo; assuming a blood 23Na concentration of ~79 mM [ 23], myocardial 23Na concentrations of 35.6, 37.9, and 37.1 mM can be estimated for the three experiments. The SNR in the anterior myocardium (close to the surface coil) was 42.1 ± 1.1, 49.2 ± 1.4, and 75.1 ± 1.8 (mean ± SD) whilst in the posterior myocardium (distant from the surface coil) it was 36.6 ± 1.3, 36.5 ± 2.4, and 61.2 ± 1.5 (mean ± SD), respectively.

Discussion and conclusions

MRS(I) provides a unique method for investigation of metabolic processes in living tissue and has been successfully applied in clinical studies of brain and cancer metabolism (e.g. [ 24- 26]). Specifically, 23Na-MRSI has the potential to monitor myocardial ion homeostasis in models of cardiac disease. Widespread application of MRSI remains limited, especially in the clinic, due to significant technical challenges, low sensitivity and associated long scan-times. A reduction in acquisition time without sacrificing accuracy would represent an important step towards making MRSI more widely applicable. The CS algorithm used in this work has been applied previously to study brain and prostate tumours with 1H-MRSI [ 11], however our study offers several novel aspects. By providing a thorough validation of the reconstruction, we sought to determine the (pre-) clinical applicability of CS-accelerated MRSI. The use of synthetic data ensured that the results were generally applicable, independent of organ/tissue and nucleus. It also permitted an assessment of cross-compartment signal contamination, which is not possible with (noise-free model of) clinical data where compartments share similar metabolite populations. To the best of our knowledge, only one study has reported the application of 23Na-MRSI to murine hearts in vivo [ 27]. 23Na-MR spectroscopy commonly utilises only a single resonance arising from both intra- and extra-cellular sodium, which may therefore also be detected with MR imaging. However, we used this nucleus to prove the concept of the technique, with the ultimate aim of combining it with multiple-quantum filters to distinguish intra- from extra-cellular sodium. Thus, application of CS to 23Na-MRSI could significantly reduce scan-time making metabolic data acquisition possible within clinically acceptable times.
There are several technical challenges to be faced in applying CS to 23Na-MRSI of (murine) cardiac tissue: large sodium concentration differences between tissues, and thus MRSI signal intensity variations, lie in close proximity (e.g. blood vs. myocardium vs. lungs), which can be difficult to reconstruct using CS; the influence of SNR and spatial resolution on CS reconstruction fidelity had to be characterized.
Virtual phantom data, which mimicked the appearance and challenges of an in vivo cross-section through a murine thorax, was used to characterize CS performance. For ROI2 (left-ventricular myocardium) this resulted in a wall thickness of between 1 and 3 voxels corresponding to ~0.5-1.5 mm in typical in vivo mouse cardiac MRSI experiment. We found that absolute signal amplitudes following CS reconstruction were not preserved, but correlated linearly with those obtained in the (noise-free) conventional FT reconstruction (i.e. “ground truth”). This finding has two immediate implications. Firstly, linear scaling of the amplitude means relative amplitudes (i.e. metabolite ratios) remain unaffected by CS reconstruction. Consequently, absolute quantification of metabolite concentration relative to a signal from a compartment of known concentration remains accurate. Secondly, the calculation of root-mean-square errors, which are typically used as a measure of data fidelity, would yield high values and not reflect the quality of the reconstruction. Thus reconstructed signal amplitudes and signal contamination, normalized to the mean signal intensity from a defined ROI, were chosen as metrics for this purpose (Fig.  4). For the CS reconstructions, increasing spatial resolution reduced signal contamination (bottom row, Fig.  4) and blurring of compartment boundaries (Fig.  3). Low-resolution FT reconstructed data yielded signal oscillations inside and outside the compartment due to convolution of the image with the FT of a step function. CS reconstruction reduced these oscillations at the cost of near-constant signal level outside the compartment, which increased with higher under-sampling factors and/or decreasing resolution. Whilst there is a straightforward relationship between data sampling and point spread function for FT reconstruction, the relationship is more complex for CS. The CS reconstruction used here assumes that an image consists of regions of approximately homogeneous signal with relatively sharp discontinuities in signal intensity between regions, and that the resulting reconstruction must be consistent with the acquired k-space data. These assumptions give rise to some blurring of the boundaries between homogeneous regions resulting in an apparent loss of spatial resolution and out-of-voxel signal contamination. Some understanding of the origins of a signal can be inferred from the spatial distribution of the reconstructed signal across a sharp boundary, for example at the edge of a phantom where the signal transitions from that originating from within the phantom to the void surrounding the phantom. Signal present in the void surrounding the phantom indicates of out-of-voxel contamination present in that voxel; Fig.  3 demonstrates this effect of CS and reveals that the out-of-voxel contamination approaches that present in FT reconstructed data as spatial resolution increases. CS can result in low-level signal contamination arising from signals a considerable distance outside the target voxel.
Our findings suggest in agreement with the literature [ 11], that up to 5-fold under-sampling of (pre-)clinical MRSI will be possible without significant impact on data fidelity given modest SNR. This conclusion was subsequently confirmed in retrospectively under-sampled phantom experiments. Prospectively accelerated in vivo data were also acquired. Notably, our murine study was at the lower end of the SNR requirements due to the very high spatial resolution; Neuberger et al. report that a voxel volume of 1 mm 3 could be achieved within ~90 mins [ 27], which was over twice the volume used in our study. Thus, a conservative under-sampling factor of 3 was chosen in vivo. Additionally, the reconstruction of the phantom and in vivo data demonstrated that CS accurately reproduces spatially inhomogeneous signals arising from the receive profile of the surface coil used to acquire the data. The quantified myocardium/blood amplitude ratios agreed well with previously reported values of 0.42 ± 0.15 for mouse [ 27] and 0.57 for humans [ 23]. A 3-fold reduction in scan time to ~23 mins for a single slice makes our protocol suitable for use as part of a multi-parametric MR-phenotyping investigation, or to study severely sick animals by reducing the anaesthetic burden. Assuming that the typical mouse heart is approximately 8 mm in length, full heart coverage using 2D CS-MRSI as described would therefore take ~92 mins; this represents half the voxel volume described by Neuberger et al. within the same scan time. Furthermore, use of through-plane sparsity information in the CS reconstruction should allow further acceleration of 2D multislice or 3D CS-MRSI without loss of reconstruction fidelity. Compressed sensing has undoubtedly a significant role to play in the future of preclinical and clinical MRSI. Increases in total tissue sodium concentration of between 150 and 330 % have been observed for a variety of pathologies [ 28- 31]. Fig.  3 would suggest that for resolutions at or above 32 × 32 PE steps, the level of potential signal contamination in a voxel arising from CS reconstruction would have an approximate upper limit of 20 %. However, in the presence of this level of signal contamination, such pathologies should be detectable. In general, the SNR of the data will fundamentally limit the ability to detect pathological abnormalities; whilst FT performs better than CS at very low SNR, accurate data fitting/quantification under these conditions may prove limiting even for FT reconstruction. Whilst the experimental results presented here focus on MRSI and its application to 23Na, the simulation results apply equally well to 1H, 31P, or 13C MRSI. Prospectively under-sampling data can significantly reduce MRSI data acquisition to a clinically acceptable time, reducing the burden on the patient and increasing scanner throughput without sacrificing diagnostic accuracy.


The authors would like to thank Ms Vicky Thornton for her help with the in vivo experiments. This project was funded by a MRC/EPSRC Grant (G0600829). JES is a British Heart Foundation Senior Basic Science Research Fellow (FS/11/50/29038), and the authors acknowledge the Wellcome Trust Core Award (grant 090532/Z/09/Z).
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Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

MLM designed the study, conducted the simulations and MR experiments, carried out the data analysis, and drafted the manuscript. SG and VK wrote the compressed sensing algorithm. CAL was involved in the study design and in vivo experiments. JES was involved in the design of the study, data analysis and in drafting of the manuscript. All authors read and approved the final manuscript.
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