0923

3D Seiffert spiral k-space trajectories for a functional sodium (²³Na) MRI protocol at 3T

Samuel Rot^1,2, Matthew Clemence³, Bhavana S Solanky^1,4, and Claudia A. M. Gandini Wheeler-Kingshott^1,5,6
¹NMR Research Unit, Queen Square MS Centre, Department of Neuroinflammation, UCL Queen Square Institute of Neurology, Faculty of Brain Sciences, University College London, London, United Kingdom, ²Department of Medical Physics and Biomedical Engineering, University College London, London, United Kingdom, ³Philips Healthcare, Best, Netherlands, ⁴Quantitative Imaging Group, Centre for Medical Image Computing (CMIC), Department of Medical Physics & Biomedical Engineering, University College London, London, United Kingdom, ⁵Department of Brain & Behavioral, University of Pavia, Pavia, Italy, ⁶Digital Neuroscience Centre, IRCCS Mondino Foundation, Pavia, Italy

Synopsis

Keywords: Non-Proton, Non-Proton

Motivation: With advancing hardware, scan durations of ²³Na-MRI have decreased, enabling novel applications that probe dynamic or functional processes; existing sequences, though, may not fully exploit the possible acceleration.

Goal(s): Implement and demonstrate a highly efficient ultrashort echo time non-Cartesian sequence based on 3D Seiffert spirals, for temporally-resolved applications of ²³Na-MRI.

Approach: A possible acquisition protocol for functional brain ²³Na-MRI at a temporal resolution of 47s was tested on a healthy volunteer at rest, at 3T.

Results: Image quality and SNR are high considering the temporal resolution, with compressed sensing successfully reducing noise. Further work will optimise the sequence analytically, ensuring homogeneous k-space sampling.

Impact: Dynamic ²³Na-MRI at 3T is possible at sub-minute temporal resolution with a 3D Seiffert spiral k-space trajectory. Unlike for other sequences, efficient k-space coverage is achieved without downsides of unpleasant acoustic noise, or exciting mechanical resonances of scanner hardware.

Introduction

Sodium (²³Na-)MRI is valued for unique insights into physiology^1,2 and increasingly also dynamic functioning^3–6. Due to rapid transverse relaxation and low MR-sensitivity, ultrashort echo time non-Cartesian sampling is usually employed^7,8. We recently reported⁹ initial simulations of a 3D Seiffert spiral sequence¹⁰ for ²³Na-MRI, characterised by highly efficient, pseudorandom and isotropic (under)sampling of k-space, suited to compressed sensing (CS) reconstruction and dynamic measurements.
This work aims to demonstrate a possible acquisition protocol with 3D Seiffert spirals for in vivo brain functional ²³Na-MRI, an application where time-efficient sampling is essential.

Theory

The theoretical formulism of 3D Seiffert spiral trajectories has been described previously^9–11. Briefly, a spiral waveform is: (i) defined by the Jacobi elliptic functions; (ii) scaled from $$$k_r=0$$$ to $$$k_r=k_{max}$$$; (iii) rotated to fill k-space.
A suitable rotational scheme is essential for complete and homogeneous k-space coverage. With the initial spiral endpoint $$$k_x=k_y=0,k_z=k_{max}$$$, we implemented a three-step $$$zyz$$$ axis rotation with angles $$$\psi,\theta,\phi$$$ (Figure 1); while $$$\theta,\psi$$$ are dictated by the Fibonacci grid endpoint, $$$\psi$$$ is tiny golden angle stepped¹² ($$$\psi$$$=32.03°) around the spiral’s axis.
Elsewhere, the number of readouts was calculated by Nyquist testing random k-space points¹⁰. This is too computationally intensive for online sequence calculations. Instead, we numerically determined the relationship of the Fibonacci point separation with number of points and sphere radius (Figure 1), deriving an upper limit for the number of readouts at which the Nyquist criterion equals the Fibonacci point separation:$$N_r=\frac{1}{UF}\left( 3.24\frac{k_{max}}{\Delta k}\right)^{2.03},[1]$$ where $$$UF$$$ is an undersampling factor, and substituting for nominal resolution: $$$k_{max}=\frac{1}{2\Delta x}$$$, and FOV: $$$\Delta k=\frac{1}{FOV}$$$. Depending on spiral curvature and homogeneity of coverage, varying degrees of undersampling are possible without discernible artifacts.

Methods

Acquisition: a healthy participant (F, 54y) was scanned at rest on a 3T Philips Ingenia CX with a single-tuned ²³Na birdcage head coil (RAPID Biomedical). 3D Seiffert spiral parameters⁹ were: FOV=240x240x240mm³, matrix=60x60x60, TE/TR=0.22/20ms, FA=45°, T_RO=12.9ms, spiral length=20, m=0.025, UF=8, scale=0.75, G_max=10mTm^-1, S_max=100Tm^-1s^-1, bandwidth=140kHz, NSA=2, T_dyn=47s, dynamics=10. Both gradient spoiling and rewinding with RF phase cycling for balanced steady state free precession (bSSFP) were explored. The point spread function (PSF) was simulated with biexponential T₂* attenuation and the sample distribution was visualised by gridding of density compensation factors (DCFs)¹³.
Reconstruction: images were reconstructed offline using a conventional non-uniform FFT¹⁴ (NUFFT) and iterative CS (BART¹⁵) using total variation (TV) and wavelet regularisation, at strengths 0.0–0.005. SNR in NUFFT images was calculated¹⁶ in white matter (WM) and vitreous humour (VH) ROIs.

Results

Figure 2 shows PSFs (FWHM=1.75–1.77 voxels) and gridded k-space DCFs. The latter exhibits a sample distribution with fair global homogeneity, but some local inhomogeneities.
Figure 3 displays NUFFT reconstructed images with gradient spoiling and bSSFP for one dynamic and averages of five and ten dynamics. A bar chart also shows SNR, which is the same in WM, but higher in VH for bSSFP compared to gradient spoiling. Image quality is good considering the scan time, although single-dynamic images suffer from structured noise.
Figure 4 contains CS reconstructed images of one dynamic at various regularisation strengths. TV regularisation is more effective at removing noise, at a cost of blurring.
Figure 5 shows five dynamics of a timeseries. Although CS is successful at denoising, coarser noise in low SNR structures like deep grey matter could mimic regionally coherent signal fluctuations.

Discussion and conclusion

We present initial results at 3T of a ²³Na-MRI protocol with 3D Seiffert spirals at sub-minute temporal resolution. Image quality is good and SNR compares favourably with literature (e.g. for 1 dynamic, SNR_WM≈4, and for a 19min 3D cones¹⁶ acquisition, SNR_WM≈7, although the comparison is unfair due to different actual resolutions). Images with bSSFP showed higher SNR in fluids with long T₂ due to T₂/T₁ contrast; this could introduce sensitivity to changes in sodium microenvironment, although modelling is needed. Practical benefits of the trajectory include low-pitched acoustic noise, particularly versus 3D cones (avoiding the “sweep” across mechanical resonances¹⁷). Gradient waveforms are subject to full safety assessments of the scanner software.
Results are encouraging and optimisation will continue, especially to investigate the source of structured noise that could cause misclassification of signal changes as brain activity (Figure 5). Possible culprits are PSF sidelobes and point coherences in k-space (Figure 2). Inhomogeneities in sample distributions can cause noise fluctuations¹⁸ (coloured noise¹⁹) across k-space and should be avoided²⁰.
Ongoing work aims to demonstrate sensitivity to changes in ²³Na concentration accompanying brain function, as well as in phantoms. The sequence will be further optimised analytically, compared to 3D cones, and assessed for quantitative ²³Na-MRI. Finally, other applications of dynamic ²³Na-MRI and acceleration of conventional ²³Na-MRI will be explored.

Acknowledgements

SR: EPSRC-funded UCL Centre for Doctoral Training in Intelligent, Integrated Imaging in Healthcare (i4health) (EP/S021930/1) and the Department of Health’s NIHR-funded Biomedical Research Centre at University College London Hospitals.

CGWK: Horizon2020 (Research and Innovation Action Grants Human Brain Project 945539 (SGA3)), BRC (#BRC704/CAP/CGW), MRC (#MR/S026088/1), Ataxia UK, Rosetrees Trust (#PGL22/100041 and #PGL21/10079). CGWK is a shareholder in Queen Square Analytics Ltd.

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Figures

Figure 1 (a) A representation of the rotational scheme of 3D Seiffert spirals. The overall rotation is composed of three separate rotations of ψ, θ, ϕ around the z, y, z axes. (b) Left, a spherical lattice of 400 evenly spaced Fibonacci points that define the endpoints of Seiffert spiral readouts; right, a plot of the calculated separation of points (black markers) against the number of points and the sphere radius. A fit of the relationship (R²=0.9999), used to derive Equation 1, is represented by the surface plot.

Figure 2 (a) Simulated point spread functions (PSF) of 3D Seiffert spirals in all dimensions, with biexponential T₂^∗ attenuation (T_2s^∗=3ms, T_2l^∗=20ms, 60/40 ratio). (b) 2D projections of the gridded density compensation factors (a.u.), serving as a proxy-measure of the sample distribution in k-space. Black arrows highlight numerous point coherences, clusters (dark) and gaps (bright). Sample density is highest at the k-space centre.

Figure 3 Axial and coronal slices of a volunteer, reconstructed by non-uniform FFT (NUFFT). Image columns show 1 dynamic and averages over 5, 10 dynamics, while rows show acquisitions with gradient spoiling (GR) and balanced steady state free precession (bSSFP), all at the same intensity range. Below is a bar chart of SNR considering vitreous humour (VH) and white matter (WM) ROIs. bSSFP images exhibit higher SNR in fluids, as cross-TR coherences generate T₂/T₁ contrast weighting. SNR and image quality are good, although single-dynamic images inevitably suffer from structured noise.

Figure 4 Gradient spoiled images of a volunteer, reconstructed by compressed sensing. Image rows and columns show varying strengths of wavelet and total variation regularisation respectively. All images are intensity windowed equally, and the colourmap was chosen to better visualise background noise. Total variation regularisation is more effective at denoising, although images at strengths above 0.001 are blotchy or blurred.

Figure 5 A timeseries of 5 gradient spoiled dynamics (t = 1–5) at temporal resolution of 47s, reconstructed with non-uniform FFT (NUFFT) and compressed sensing (CS) using wavelet and total variation regularisation of strength 0.0025. For both reconstruction methods, red arrows indicate regionally coherent signal fluctuations in areas of lower SNR, such as deep grey matter structures.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)

0923

DOI: https://doi.org/10.58530/2024/0923