Comparison of optimized intensity correction methods for 23Na MRI of the human brain using a 32-channel phased array coil at 7 Tesla

doi:10.1016/j.zemedi.2019.10.004

Zeitschrift für Medizinische Physik

Volume 30, Issue 2, May 2020, Pages 104-115

https://doi.org/10.1016/j.zemedi.2019.10.004 Get rights and content

Abstract

Purpose

To correct for the non-homogeneous receive profile of a phased array head coil in sodium magnetic resonance imaging (²³Na MRI).

Methods

²³Na MRI of the human brain (n = 8) was conducted on a 7T MR system using a dual-tuned quadrature ¹H/²³Na transmit/receive birdcage coil, equipped with a 32-channel receive-only array. To correct the inhomogeneous receive profile four different methods were applied: (1) the uncorrected phased array image and an additionally acquired birdcage image as reference image were low-pass filtered and divided by each other. (2) The second method substituted the reference image by a support region. (3) By averaging the individually calculated receive profiles, a universal sensitivity map was obtained and applied. (4) The receive profile was determined by a pre-scanned large uniform phantom. The calculation of the sensitivity maps was optimized in a simulation study using the normalized root-mean-square error (NRMSE). All methods were evaluated in phantom measurements and finally applied to in vivo ²³Na MRI data sets. The in vivo measurements were partial volume corrected and for further evaluation the signal ratio between the outer and inner cerebrospinal fluid compartments (CSF_out:CSF_in) was calculated.

Results

Phantom measurements show the correction of the intensity profile applying the given methods. Compared to the uncorrected phased array image (NRMSE = 0.46, CSF_out:CSF_in = 1.71), the quantitative evaluation of simulated and measured intensity corrected human brain data sets indicates the best performance utilizing the birdcage image (NRMSE = 0.39, CSF_out:CSF_in = 1.00). However, employing a support region (NRMSE = 0.40, CSF_out:CSF_in = 1.17), a universal sensitivity map (NRMSE = 0.41, CSF_out:CSF_in = 1.05) or a pre-scanned sensitivity map (NRMSE = 0.42, CSF_out:CSF_in = 1.07) shows only slightly worse results.

Conclusion

Acquiring a birdcage image as reference image to correct for the receive profile demonstrates the best performance. However, when aiming to reduce acquisition time or for measurements without existing birdcage coil, methods that use a support region as reference image, a universal or a pre-scanned sensitivity map provide good alternatives for correction of the receive profile.

Introduction

Sodium ions (Na⁺) play an important role in metabolic processes. The sodium-potassium pump ensures a resting membrane potential between the extra- and intracellular fluid compartments by transporting potassium-ions in and sodium-ions out of the cell. The resting membrane potential guarantees the excitability of cells and thus, the transmission of electrical stimuli. Consequently, changes in extra- and intracellular Na⁺ concentrations – and therefore also of the averaged total Na⁺ concentration – indicate altered metabolic processes. Changed total Na⁺ concentrations can be found in pathological processes in all body parts [1]. Elevated total tissue Na⁺ concentrations (TSC) can be observed in the human brain for several diseases [2], such as multiple sclerosis [3], [4], [5], [6], Alzheimer's disease [7], after stroke [8], [9], [10] and in malignant tumors [11].

Sodium magnetic resonance imaging (²³Na MRI) offers the possibility to non-invasively quantify TSC [1], [12]. However, quantitative measurements require acquisition techniques that enable ultra-short echo times [13] and – depending on the type of the used radiofrequency coil – also correction of the transmit [14] and receive [15] profile. Moreover, due to low in vivo concentrations and low MR sensitivity, ²³Na MRI suffers from a low signal-to-noise ratio (SNR). Different approaches have been developed to increase the SNR of ²³Na MRI data. On the hardware side, the use of ultra-high field systems increases the total spin polarization of the sample and therefore the SNR [16]. In addition, phased array coils (instead of volume coils) can further improve the SNR due to their design consisting of many small receiver elements, which provides a higher SNR efficiency [17], [18], [19]. However, since phased array coils entail a non-homogeneous receive profile, their use hampers straightforward quantification. If the phased array coil is equipped with a homogeneous transmit/receive (Tx/Rx) volume coil (e.g. a birdcage coil), sensitivity maps can be easily calculated and used to correct the receive profile of the phased array coil. Another, more sophisticated method is using the SENSE reconstruction algorithm, which exploits the encoding property of the receiver sensitivity to reconstruct multi-channel raw data sets, but also corrects for the receive profile [20], [21]. Although, SENSE has been applied in a few ²³Na MRI studies [15], [22], [23], these requirements are not broadly available for ²³Na MRI. This might be a reason why phased array coils, despite their mentioned advantages, are used less often in ²³Na MRI as compared to volume coils [15], [22], [24].

In this work, basic intensity correction methods were evaluated. The first method utilized a measured birdcage image as reference image to calculate a receive profile that was then used for correction. However, this requires additional acquisition time and not all multi-channel receive coils are equipped with a combined Tx/Rx birdcage coil. Thus, a second method was employed, which approximated the reference image from the combined phased array image [25]. Additionally, a third method, which utilized a universal sensitivity map, obtained by averaging individually calculated receive profiles, was applied. Finally, as fourth and very simple method, a pre-scanned sensitivity map measured from a large uniform phantom was employed. The methods were optimized and evaluated in a simulation study and were applied to ²³Na MRI of the healthy human brain using a 32-channel phased array coil with integrated birdcage coil. The intensity corrected in vivo measurements were partial volume corrected [26] and signal intensities in the inner and outer cerebrospinal fluid (CSF) compartments were compared to each other for further evaluation.

Section snippets

Intensity correction

The measured signal $S (x, y, z)$ of a multi-channel phased array coil is given by multiplying the object magnetization $M (x, y, z)$ with the receive profile $E (x, y, z)$ plus noise $N (x, y, z)$ : $S (x, y, z) = E (x, y, z) \cdot M (x, y, z) + N (x, y, z) .$

Under the assumption E · M ≫ N, the object magnetization can be calculated via $M (x, y, z) = \frac{S (x, y, z)}{E (x, y, z)} .$

To determine the receive profile $E (x, y, z)$ , two methods were implemented and evaluated. Both methods require a homogeneous reference image, where the influence of the receive profile is negligible. First, the

Simulation

In simulation studies, optimized filter parameters for the correction methods using a birdcage image and a support region were determined for each data set (see supplementary material, Table A.1). This was done by minimizing the NRMSE with respect to the GT for different parameter combinations of σ₁ and σ₂ (see supplementary material, Figure A.1). The optimized filter parameters were applied to calculate the receive profile, which was used to correct the phased array image. Additionally, a

Discussion

We analyzed four intensity correction methods for ²³Na MRI with a 32-channel receiver head coil. A birdcage image as well as a support region were employed as reference image to calculate the receive profile. In addition, a universal and a pre-scanned phantom sensitivity map were applied.

The method utilizing a birdcage image performs best. However, the acquisition of the birdcage image requires additional measurement time. This can be avoided by employing a support region as homogeneous

Conclusion

In this work, the inhomogeneous receive profile of a 32-channel head phased array coil was corrected using a measured birdcage image and a support region as homogeneous reference image. Additionally, a universal and a pre-scanned sensitivity map were applied. The proposed correction methods were optimized and evaluated in a simulation study and applied to eight in vivo head data sets acquired at 7T. The method with measured birdcage image yields the best results. However, a support region, a

Declarations of interest

none.

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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], [17], [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).
Volumetric 23Na Single and Triple-Quantum Imaging at 7T: 3D-CRISTINA
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An additional T1-weighted sequence (e.g. the MP2RAGE sequence [23]) acquisition would have helped to provide a GM and WM segmentation. But the MP2RAGE sequence was designed to be employed with a multi-channel receiver coil array, requiring a change of coil which was incompatible with this study [24]. Another clear limitation is the low SQ and TQ signal of phantom vial 7 (4% agar and 50 mM 23Na), further work is needed with standardized fabricated phantoms to explore limitations and rule out phantom ageing problems.
To measure multi-quantum coherence (MQC) ²³Na signals for noninvasive cell physiological information in the whole-brain, the 2D-CRISTINA method was extended to 3D. This experimental study investigated the use and results of a new sequence, 3D-CRISTINA, on a phantom and healthy volunteers.
The 3D Cartesian single and triple-quantum imaging of ²³Na (3D-CRISTINA) was developed and implemented at 7T, favoring a non-selective volume excitation for increased signal-to-noise ratio (SNR) and lower energy deployment than its 2D counterpart. Two independent phase cycles were used in analogy to the 2D method. A comparison of 6-steps cycles and 12-steps cycles was performed.
We used a phantom composed of different sodium and agarose concentrations, 50 mM to 150 mM Na+, and 0–5% agarose for sequence validation. Four healthy volunteers were scanned at 7T for whole brain MQC imaging. The sequence 3D-CRISTINA was developed and tested at 7T.
At 7T, the 3D-CRISTINA acquisition allowed to reduce the TR to 230 ms from the previous 390 ms for 2D, resulting in a total acquisition time of 53 min for a 3D volume of 4 × 4 × 8 mm resolution. The phase cycle evaluation showed that the 7T acquisition time could be reduced by 4-fold with moderate single and triple-quantum signals SNR loss. The healthy volunteers demonstrated clinical feasibility at 7T and showed a difference in the MQC signals ratio of White Matter (WM) and Grey Matter (GM).
Volumetric CRISTINA multi-quantum imaging allowed whole-brain coverage. The non-selective excitation enabled a faster scan due to a decrease in energy deposition which enabled a lower repetition time. Thus, it should be the preferred choice for future in vivo multi-quantum applications compared to the 2D method. A more extensive study is warranted to explore WM and GM MQC differences.
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Since the breast coil does not entail an integrated homogeneous volume coil, a reference image can be approximated by the combined phased array image [39,48]. In addition, the receive profile can be estimated using phantom measurements [39]. Finally, the inhomogeneous receive profile of the phased array image can be corrected by division with the determined receive profile.
To implement and to evaluate a compressed sensing (CS) reconstruction algorithm based on the sensitivity encoding (SENSE) combination scheme (CS-SENSE), used to reconstruct sodium magnetic resonance imaging (²³Na MRI) multi-channel breast data sets.
In a simulation study, the CS-SENSE algorithm was tested and optimized by evaluating the structural similarity (SSIM) and the normalized root-mean-square error (NRMSE) for different regularizations and different undersampling factors (USF = 1.8/3.6/7.2/14.4). Subsequently, the algorithm was applied to data from in vivo measurements of the healthy female breast (n = 3) acquired at 7 T. Moreover, the proposed CS-SENSE algorithm was compared to a previously published CS algorithm (CS-IND).
The CS-SENSE reconstruction leads to an increased image quality for all undersampling factors and employed regularizations. Especially if a simple 2^nd order total variation is chosen as sparsity transformation, the CS-SENSE reconstruction increases the image quality of highly undersampled data sets (CS-SENSE: SSIM_USF=7.2 = 0.234, NRMSE_USF=7.2 = 0.491 vs. CS-IND: SSIM_USF=7.2 = 0.201, NRMSE_USF=7.2 = 0.506).
The CS-SENSE reconstruction supersedes the need of CS weighting factors for each channel as well as a method to combine single channel data. The CS-SENSE algorithm can be used to reconstruct undersampled data sets with increased image quality. This can be exploited to reduce total acquisition times in ²³Na MRI.
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For example, approaches such as sensitivity encoding (SENSE [26]) or generalized autocalibrating partial parallel acquisition (GRAPPA [27]) use sensitivity profiles of phased array coils to speed up the acquisition. Multi-channel phased array coils are also used increasingly for 23Na MRI [28,29], but are not available for every application. Another category of reconstruction algorithms for acceleration, which are applicable for single channel radiofrequency (RF-)coils, are based on compressed sensing [30,31] (CS).
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.
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.
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.
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Original PaperComparison of optimized intensity correction methods for 23Na MRI of the human brain using a 32-channel phased array coil at 7 Tesla

Abstract

Purpose

Methods

Results

Conclusion

Introduction

Section snippets

Intensity correction

Simulation

Discussion

Conclusion

Declarations of interest

Neuroimaging Clin N Am

Neuroimage

Pros and Cons of Ultra-High-Field MRI/MRS for Human Application. Prog Nucl Magn Reson Spectrosc

Neuroimage

Magn Reson Imaging

Med Image Anal

Med Image Anal

J Magn Reson

J Magn Reson

Biomedical applications of sodium MRI in vivo

J Magn Reson Imaging

Imaging of sodium in the brain: a brief review

NMR Biomed

Brain tissue sodium concentration in multiple sclerosis: a sodium imaging study at 3 tesla

Brain

of multiple sclerosis

NMR Biomed

Distribution of brain sodium accumulation correlates with disability in multiple sclerosis: a cross-sectional 23Na MR imaging study

Radiology

Potential of Sodium MRI as a Biomarker for Neurodegeneration and Neuroinflammation in Multiple Sclerosis

Front Neurol

Sodium MR imaging detection of mild Alzheimer disease: preliminary study

Am J Neuroradiol

imaging protocol for stroke management: tissue sodium concentration as a measure of tissue viability in nonhuman primate studies and in clinical studies

Radiology

Relationship Between Sodium Intensity and Perfusion Deficits in Acute Ischemic Stroke

J Magn Reson Imaging

Tissue sodium concentration in human brain tumors as measured with 23Na MR imaging

Radiology

Original Paper
Comparison of optimized intensity correction methods for ²³Na MRI of the human brain using a 32-channel phased array coil at 7 Tesla