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

Abstract

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.

Keywords: 23Na MRI; UTE; compressed sensing; half-sinc; sodium.

FIGURE 1

Pulse sequence diagrams for 2D sodium imaging with a center‐out spiral k‐space trajectory and a single‐lobe full‐sinc excitation pulse (left) or a half‐sinc excitation pulse (right). The TE is reduced from 0.73 ms with the full‐sinc pulse, and to 0.23 ms with the half‐sinc pulse; however, with the half‐sinc pulse it is necessary to acquire data across two acquisitions, with slice‐select gradients of opposite polarity. These two acquisitions are summed to give the same slice profile as the full‐sinc. G_Z/G_X/G_Y, magnetic field gradients applied along the Z, X, and Y axes, respectively, where Z is the slice‐select axis and X and Y lie in the plane of the imaging slice; RF, radiofrequency excitation pulse.

FIGURE 2

(A) Example ex vivo aTSC maps quantified from a 3D acquisition‐weighted stack‐of‐spirals sequence and 2D acquisitions with full‐sinc and half‐sinc excitation. (B) Ex vivo muscle aTSC quantification. Values are presented without relaxation correction (circles, left) and with relaxation correction (triangles, right) for three samples, plus one repeated sample. (C) Boxplots showing in vivo aTSC in the muscle and skin, quantified from 2D acquisitions with full‐sinc and half‐sinc excitation (N = 10, NSAs = 150). p‐value calculated between full‐sinc and half‐sinc data using a paired t‐test. (D) In silico modeling of signal relaxation in sodium phantoms and muscle tissue (using literature values). Solid lines indicate signal decay based on median relaxation parameters, and the shaded regions indicate possible relaxation across the range of reported T₁ and T₂ values. (E) Signal ratio between sodium phantoms and muscle tissue. Reducing the TE from 0.73 ms (full‐sinc acquisition) to 0.23 ms (half‐sinc acquisition, vertical lines) would be expected to result in a 2.5%–13.7% increase in calculated muscle aTSC. aTSC, apparent tissue sodium concentration.

FIGURE 3

(A) Example in vivo NUFFT reference image (150 NSAs) and images retrospectively reconstructed with 75 and 50 NSAs using NUFFT and CS (with optimal regularization weighting factor). (B) Corresponding aTSC maps. Equivalent T_acq (min:s) are provided for each NSA. CS, compressed sensing; NUFFT, nonuniform fast Fourier transform; NSA, number of signal averages; T_acq, acquisition times.

FIGURE 4

(A) Example in vivo images with 15 NSAs reconstructed with CS, showing the effect of different levels of $\lambda$. Unregularized reconstruction ($\lambda$ = 0.0) produces images with extremely high levels of noise, which can be reduced with increasing $\lambda$ (optimal $\lambda$ = 3.2). However, the images become over‐smoothed with very high $\lambda$ ($\lambda$ = 5.0). (B) Histogram plots showing distribution of aTSC across pixels within the muscle ROI for images shown in A (blue) and the reference image (red, 150 NSAs, NUFFT). With low regularization, the distribution of pixels is broader than the reference image (SD_CS/SD_Ref > 1) due to the high levels of noise. The distribution narrows as $\lambda$ increases, and subsequently becomes narrower than the reference as the image becomes over‐smoothed (SD_CS/SD_Ref < 1), while also introducing a bias in the mean aTSC. (C) Matrix showing ratio of SD of calculated aTSC in the muscle, between CS maps (SD_CS), reconstructed with different NSAs and $\lambda$, and the reference map (SD_Ref). Dashed lines indicate the optimal $\lambda$ for a given NSAs (chosen where SD_CS/SD_Ref ≈ 1). $\lambda$, regularization weighting parameter; Ref, reference; ROI, region of interest.