Compressed sensing effects on quantitative analysis of undersampled human brain sodium MRI

Rapid 2D 23Na MRI of the calf using a denoising convolutional neural network

PURPOSE

23Na MRI can be used to quantify in-vivo tissue sodium concentration (TSC), but the inherently low 23Na signal leads to long scan times and/or noisy or low-resolution images. Reconstruction algorithms such as compressed sensing (CS) have been proposed to mitigate low signal-to-noise ratio (SNR); although, these can result in unnatural images, suboptimal denoising and long processing times. Recently, machine learning has been increasingly used to denoise 1H MRI acquisitions; however, this approach typically requires large volumes of high-quality training data, which is not readily available for 23Na MRI. Here, we propose using 1H data to train a denoising convolutional neural network (CNN), which we subsequently demonstrate on prospective 23Na images of the calf.

METHODS

1893 1H fat-saturated transverse slices of the knee from the open-source fastMRI dataset were used to train denoising CNNs for different levels of noise. Synthetic low SNR images were generated by adding gaussian noise to the high-quality 1H k-space data before reconstruction to create paired training data. For prospective testing, 23Na images of the calf were acquired in 10 healthy volunteers with a total of 150 averages over ten minutes, which were used as a reference throughout the study. From this data, images with fewer averages were retrospectively reconstructed using a non-uniform fast Fourier transform (NUFFT) as well as CS, with the NUFFT images subsequently denoised using the trained CNN.

RESULTS

CNNs were successfully applied to 23Na images reconstructed with 50, 40 and 30 averages. Muscle and skin apparent TSC quantification from CNN-denoised images were equivalent to those from CS images, with <0.9 mM bias compared to reference values. Estimated SNR was significantly higher in CNN-denoised images compared to NUFFT, CS and reference images. Quantitative edge sharpness was equivalent for all images. For subjective image quality ranking, CNN-denoised images ranked equally best with reference images and significantly better than NUFFT and CS images.

CONCLUSION

Denoising CNNs trained on 1H data can be successfully applied to 23Na images of the calf; thus, allowing scan time to be reduced from ten minutes to two minutes with little impact on image quality or apparent TSC quantification accuracy.

Accelerated multiple-quantum-filtered sodium magnetic resonance imaging using compressed sensing at 7 T

PURPOSE

Multiple-quantum-filtered (MQF) sodium magnetic resonance imaging (MRI), such as enhanced single-quantum and triple-quantum-filtered imaging of 23Na (eSISTINA), enables images to be weighted towards restricted sodium, a promising biomarker in clinical practice, but often suffers from clinically infeasible acquisition times and low image quality. This study aims to mitigate the above limitation by implementing a novel eSISTINA sequence at 7 T with the application of compressed sensing (CS) to accelerate eSISTINA acquisitions without a noticeable loss of information.

METHODS

A novel eSISTINA sequence with a 3D spiral-based sampling scheme was implemented at 7 T for the application of CS. Fully sampled datasets were obtained from one phantom and ten healthy subjects, and were then retrospectively undersampled by various undersampling factors. CS undersampled reconstructions were compared to fully sampled and undersampled nonuniform fast Fourier transform (NUFFT) reconstructions. Reconstruction performance was evaluated based on structural similarity (SSIM), signal-to-noise ratio (SNR), weightings towards total and compartmental sodium, and in vivo quantitative estimates.

RESULTS

CS-based phantom and in vivo images have less noise and better structural delineation while maintaining the weightings towards total, non-restricted (predominantly extracellular), and restricted (primarily intracellular) sodium. CS generally outperforms NUFFT with a higher SNR and a better SSIM, except for the SSIM in TQ brain images, which is likely due to substantial noise contamination. CS enables in vivo quantitative estimates with <15% errors at an undersampling factor of up to two.

CONCLUSIONS

Successful implementation of an eSISTINA sequence with an incoherent sampling scheme at 7 T was demonstrated. CS can accelerate eSISTINA by up to twofold at 7 T with reduced noise levels compared to NUFFT, while maintaining major structural information, reasonable weightings towards total and compartmental sodium, and relatively reliable in vivo quantification. The associated reduction in acquisition time has the potential to facilitate the clinical applicability of MQF sodium MRI.

2D sodium MRI of the human calf using half-sinc excitation pulses and compressed sensing

PURPOSE

Sodium MRI can be used to quantify tissue sodium concentration (TSC) in vivo; however, UTE sequences are required to capture the rapidly decaying signal. 2D MRI enables high in-plane resolution but typically has long TEs. Half-sinc excitation may enable UTE; however, twice as many readouts are necessary. Scan time can be minimized by reducing the number of signal averages (NSAs), but at a cost to SNR. We propose using compressed sensing (CS) to accelerate 2D half-sinc acquisitions while maintaining SNR and TSC.

METHODS

Ex vivo and in vivo TSC were compared between 2D spiral sequences with full-sinc (TE = 0.73 ms, scan time ≈ 5 min) and half-sinc excitation (TE = 0.23 ms, scan time ≈ 10 min), with 150 NSAs. Ex vivo, these were compared to a reference 3D sequence (TE = 0.22 ms, scan time ≈ 24 min). To investigate shortening 2D scan times, half-sinc data was retrospectively reconstructed with fewer NSAs, comparing a nonuniform fast Fourier transform to CS. Resultant TSC and image quality were compared to reference 150 NSAs nonuniform fast Fourier transform images.

RESULTS

TSC was significantly higher from half-sinc than from full-sinc acquisitions, ex vivo and in vivo. Ex vivo, half-sinc data more closely matched the reference 3D sequence, indicating improved accuracy. In silico modeling confirmed this was due to shorter TEs minimizing bias caused by relaxation differences between phantoms and tissue. CS was successfully applied to in vivo, half-sinc data, maintaining TSC and image quality (estimated SNR, edge sharpness, and qualitative metrics) with ≥50 NSAs.

CONCLUSION

2D sodium MRI with half-sinc excitation and CS was validated, enabling TSC quantification with 2.25 × 2.25 mm2 resolution and scan times of ≤5 mins.

Recent technical developments and clinical research applications of sodium (23Na) MRI

Sodium is an essential ion that plays a central role in many physiological processes including the transmembrane electrochemical gradient and the maintenance of the body's homeostasis. Due to the crucial role of sodium in the human body, the sodium nucleus is a promising candidate for non-invasively assessing (patho-)physiological changes. Almost 10 years ago, Madelin et al. provided a comprehensive review of methods and applications of sodium (23Na) MRI (Madelin et al., 2014) [1]. More recent review articles have focused mainly on specific applications of 23Na MRI. For example, several articles covered 23Na MRI applications for diseases such as osteoarthritis (Zbyn et al., 2016, Zaric et al., 2020) [2,3], multiple sclerosis (Petracca et al., 2016, Huhn et al., 2019) [4,5] and brain tumors (Schepkin, 2016) [6], or for imaging certain organs such as the kidneys (Zollner et al., 2016) [7], the brain (Shah et al., 2016, Thulborn et al., 2018) [8,9], and the heart (Bottomley, 2016) [10]. Other articles have reviewed technical developments such as radiofrequency (RF) coils for 23Na MRI (Wiggins et al., 2016, Bangerter et al., 2016) [11,12], pulse sequences (Konstandin et al., 2014) [13], image reconstruction methods (Chen et al., 2021) [14], and interleaved/simultaneous imaging techniques (Lopez Kolkovsky et al., 2022) [15]. In addition, 23Na MRI topics have been covered in review articles with broader topics such as multinuclear MRI or ultra-high-field MRI (Niesporek et al., 2019, Hu et al., 2019, Ladd et al., 2018) [16-18]. During the past decade, various research groups have continued working on technical improvements to sodium MRI and have investigated its potential to serve as a diagnostic and prognostic tool. Clinical research applications of 23Na MRI have covered a broad spectrum of diseases, mainly focusing on the brain, cartilage, and skeletal muscle (see Fig. 1). In this article, we aim to provide a comprehensive summary of methodological and hardware developments, as well as a review of various clinical research applications of sodium (23Na) MRI in the last decade (i.e., published from the beginning of 2013 to the end of 2022).

Influence of image contrasts and reconstruction methods on the classification of multiple sclerosis-like lesions in simulated sodium magnetic resonance imaging

PURPOSE

To evaluate the classifiability of small multiple sclerosis (MS)-like lesions in simulated sodium (²³ Na) MRI for different ²³ Na MRI contrasts and reconstruction methods.

METHODS

²³ Na MRI and ²³ Na inversion recovery (IR) MRI of a phantom and simulated brain with and without lesions of different volumes (V = 1.3-38.2 nominal voxels) were simulated 100 times by adding Gaussian noise matching the SNR of real 3T measurements. Each simulation was reconstructed with four different reconstruction methods (Gridding without and with Hamming filter, Compressed sensing (CS) reconstruction without and with anatomical ¹ H prior information). Based on the mean signals within the lesion volumes of simulations with and without lesions, receiver operating characteristics (ROC) were determined and the area under the curve (AUC) was calculated to assess the classifiability for each lesion volume.

RESULTS

Lesions show higher classifiability in ²³ Na MRI than in ²³ Na IR MRI. For typical parameters and SNR of a 3T scan, the voxel normed minimal classifiable lesion volume (AUC > 0.9) is 2.8 voxels for ²³ Na MRI and 19 voxels for ²³ Na IR MRI, respectively. In terms of classifiability, Gridding with Hamming filter and CS without anatomical ¹ H prior outperform CS reconstruction with anatomical ¹ H prior.

CONCLUSION

Reliability of lesion classifiability strongly depends on the lesion volume and the ²³ Na MRI contrast. Additional incorporation of ¹ H prior information in the CS reconstruction was not beneficial for the classification of small MS-like lesions in ²³ Na MRI.

Enhanced detection of paramagnetic fluorine-19 magnetic resonance imaging agents using zero echo time sequence and compressed sensing

Fluorine-19 (19 F) magnetic resonance imaging (MRI) is an emerging technique offering specific detection of labeled cells in vivo. Lengthy acquisition times and modest signal-to-noise ratio (SNR) makes three-dimensional spin-density-weighted 19 F imaging challenging. Recent advances in tracer paramagnetic metallo-perfluorocarbon (MPFC) nanoemulsion probes have shown multifold SNR improvements due to an accelerated 19 F T1 relaxation rate and a commensurate gain in imaging speed and averages. However, 19 F T2 -reduction and increased linewidth limit the amount of metal additive in MPFC probes, thus constraining the ultimate SNR. To overcome these barriers, we describe a compressed sampling (CS) scheme, implemented using a "zero" echo time (ZTE) sequence, with data reconstructed via a sparsity-promoting algorithm. Our CS-ZTE scheme acquires k-space data using an undersampled spherical radial pattern and signal averaging. Image reconstruction employs off-the-shelf sparse solvers to solve a joint total variation and l 1 -norm regularized least square problem. To evaluate CS-ZTE, we performed simulations and acquired 19 F MRI data at 11.7 T in phantoms and mice receiving MPFC-labeled dendritic cells. For MPFC-labeled cells in vivo, we show SNR gains of ~6.3 × with 8-fold undersampling. We show that this enhancement is due to three mechanisms including undersampling and commensurate increase in signal averaging in a fixed scan time, denoising attributes from the CS algorithm, and paramagnetic reduction of T1 . Importantly, 19 F image intensity analyses yield accurate estimates of absolute quantification of 19 F spins. Overall, the CS-ZTE method using MPFC probes achieves ultrafast imaging, a substantial boost in detection sensitivity, accurate 19 F spin quantification, and minimal image artifacts.

Compressed Sensing in Sodium Magnetic Resonance Imaging: Techniques, Applications, and Future Prospects

Sodium (²³ Na) yields the second strongest nuclear magnetic resonance (NMR) signal in biological tissues and plays a vital role in cell physiology. Sodium magnetic resonance imaging (MRI) can provide insights into cell integrity and tissue viability relative to pathologies without significant anatomical alternations, and thus it is considered to be a potential surrogate biomarker that provides complementary information for standard hydrogen (¹ H) MRI in a noninvasive and quantitative manner. However, sodium MRI suffers from a relatively low signal-to-noise ratio and long acquisition times due to its relatively low NMR sensitivity. Compressed sensing-based (CS-based) methods have been shown to accelerate sodium imaging and/or improve sodium image quality significantly. In this manuscript, the basic concepts of CS and how CS might be applied to improve sodium MRI are described, and the historical milestones of CS-based sodium MRI are briefly presented. Representative advanced techniques and evaluation methods are discussed in detail, followed by an expose of clinical applications in multiple anatomical regions and diseases as well as thoughts and suggestions on potential future research prospects of CS in sodium MRI. EVIDENCE LEVEL: 5 TECHNICAL EFFICACY: Stage 1.

Utilizing the Wavelet Transform's Structure in Compressed Sensing

Compressed sensing has empowered quality image reconstruction with fewer data samples than previously thought possible. These techniques rely on a sparsifying linear transformation. The Daubechies wavelet transform is commonly used for this purpose. In this work, we take advantage of the structure of this wavelet transform and identify an affine transformation that increases the sparsity of the result. After inclusion of this affine transformation, we modify the resulting optimization problem to comply with the form of the Basis Pursuit Denoising problem. Finally, we show theoretically that this yields a lower bound on the error of the reconstruction and present results where solving this modified problem yields images of higher quality for the same sampling patterns using both magnetic resonance and optical images.

23 Na MRI in ischemic stroke: Acquisition time reduction using postprocessing with convolutional neural networks

Quantitative ²³ Na magnetic resonance imaging (MRI) provides tissue sodium concentration (TSC), which is connected to cell viability and vitality. Long acquisition times are one of the most challenging aspects for its clinical establishment. K-space undersampling is an approach for acquisition time reduction, but generates noise and artifacts. The use of convolutional neural networks (CNNs) is increasing in medical imaging and they are a useful tool for MRI postprocessing. The aim of this study is ²³ Na MRI acquisition time reduction by k-space undersampling. CNNs were applied to reduce the resulting noise and artifacts. A retrospective analysis from a prospective study was conducted including image datasets from 46 patients (aged 72 ± 13 years; 25 women, 21 men) with ischemic stroke; the ²³ Na MRI acquisition time was 10 min. The reconstructions were performed with full dataset (FI) and with a simulated dataset an image that was acquired in 2.5 min (RI). Eight different CNNs with either U-Net-based or ResNet-based architectures were implemented with RI as input and FI as label, using batch normalization and the number of filters as varying parameters. Training was performed with 9500 samples and testing included 400 samples. CNN outputs were evaluated based on signal-to-noise ratio (SNR) and structural similarity (SSIM). After quantification, TSC error was calculated. The image quality was subjectively rated by three neuroradiologists. Statistical significance was evaluated by Student's t-test. The average SNR was 21.72 ± 2.75 (FI) and 10.16 ± 0.96 (RI). U-Nets increased the SNR of RI to 43.99 and therefore performed better than ResNet. SSIM of RI to FI was improved by three CNNs to 0.91 ± 0.03. CNNs reduced TSC error by up to 15%. The subjective rating of CNN-generated images showed significantly better results than the subjective image rating of RI. The acquisition time of ²³ Na MRI can be reduced by 75% due to postprocessing with a CNN on highly undersampled data.

Towards accelerated quantitative sodium MRI at 7 T in the skeletal muscle: Comparison of anisotropic acquisition- and compressed sensing techniques

PURPOSE

To compare three anisotropic acquisition schemes and three compressed sensing (CS) approaches for accelerated tissue sodium concentration (TSC) quantification using ²³Na MRI at 7 T.

MATERIALS AND METHODS

Three anisotropic 3D-radial acquisition sequences were evaluated using simulations, phantom- and in vivo TSC measurements: An anisotropic density-adapted 3D-radial sequence (3DPR-C), a 3D acquisition-weighted density-adapted stack-of-stars sampling scheme (SOS) and a SOS approach with golden-ratio rotation (SOS-GR). Eight healthy volunteers were examined at a 7 Tesla MRI system. TSC measurements of the calf were conducted with a nominal spatial resolution of Δx = (3.0 × 3.0 × 15.0) mm³ and a field of view of (156.0 × 156.0 × 240.0) mm³ for multiple undersampling factors (USF). Three CS reconstructions were evaluated: Total variation CS (TV-CS), 3D dictionary-learning compressed sensing (3D-DLCS) and TV-CS with a block matching prior (TV-BL-CS). Results of the simulations and measurements were compared to a simulated ground truth (GT) or a fully sampled reference measurement (FS), respectively. The deviation of the mean TSC evaluated in multiple ROI (mE_GT/FS) and the normalized root-mean-squared error (NRMSE) for simulations were evaluated for CS and NUFFT reconstructions.

RESULTS

In simulations, the SOS-GR yielded the lowest NRMSE and mE_GT (< 4%) with NUFFT for an acquisition time (TA) of less than 2 min. CS further improved the results. In simulations and measurements, the best TSC quantification results were obtained with 3D-DLCS and SOS-GR (lowest NRMSE, mE_GT < 2.6% in simulations, mE_GT < 10.7% for phantom measurements and mE_FS < 6% in vivo) with an USF = 4.1 (TA < 2 min). TV-CS showed no or only slight improvements to NUFFT. The results of TV-BL-CS were similar to 3D-DLCS.

DISCUSSION

The TA for TSC measurements could be reduced to less than 2 min by using adapted sequences such as SOS-GR and CS reconstruction approaches such as 3D-DLCS or TV-BL-CS, while the quantitative accuracy stays comparable to a fully sampled NUFFT reconstruction (approx. 8 min TA). In future, the lower TA could improve clinical applicability of TSC measurements.