Receiver phase alignment using fitted SVD derived sensitivities from routine prescans

Abstract

Magnetic resonance imaging radio frequency arrays are composed of multiple receive coils that have their signals combined to form an image. Combination requires an estimate of the radio frequency coil sensitivities to align signal phases and prevent destructive interference. At lower fields this can be accomplished using a uniform physical reference coil. However, at higher fields, uniform volume coils are lacking and, when available, suffer from regions of low receive sensitivity that result in poor sensitivity estimation and combination. Several approaches exist that do not require a physical reference coil but require manual intervention, specific prescans, or must be completed post-acquisition. This makes these methods impractical for large multi-volume datasets such as those collected for novel types of functional MRI or quantitative susceptibility mapping, where magnitude and phase are important. This pilot study proposes a fitted SVD method which utilizes existing combination methods to create a phase sensitive combination method targeted at large multi-volume datasets. This method uses any multi-image prescan to calculate the relative receive sensitivities using voxel-wise singular value decomposition. These relative sensitivities are fitted to the solid harmonics using an iterative least squares fitting algorithm. Fits of the relative sensitivities are used to align the phases of the receive coils and improve combination in subsequent acquisitions during the imaging session. This method is compared against existing approaches in the human brain at 7 Tesla by examining the combined data for the presence of singularities and changes in phase signal-to-noise ratio. Two additional applications of the method are also explored, using the fitted SVD method in an asymmetrical coil and in a case with subject motion. The fitted SVD method produces singularity-free images and recovers between 95-100% of the phase signal-to-noise ratio depending on the prescan data resolution. Using solid harmonic fitting to interpolate singular value decomposition derived receive sensitivities from existing prescans allows the fitted SVD method to be used on all acquisitions within a session without increasing exam duration. Our fitted SVD method is able to combine imaging datasets accurately without supervision during online reconstruction.

Fig 1. Flow chart of the fitted SVD method.

Images represent example coil sensitivities across the same slice of the brain (four of 32 shown). The four left images are magnitudes of the coil sensitivities, and the four right images are phases of the coil sensitivities. a) Relative coil sensitivities calculated by voxel-wise SVD in prescan space, b) Coil sensitivities after alignment to a virtual reference coil created through minimax optimization across prescan space, c) Fitted coil sensitivities in target image space, d) Combined phase image after alignment with fitted coil sensitivities.

Fig 2. Fitted SVD method in a human using B1+ prescan data from a single subject.

a) Average quality ratio and b) coefficient of variation of quality ratio as a function of fit order and fit mask size. Example convex hull (grey) and voxels included in fit (white) for various mask thresholds c) 10, d) 20, e) 30. f) Example phase image, g) unwrapped phase image, and h) quality ratio map at the selected parameters (order 6, fit mask of 20, minimax mask of 20).

Fig 3. Comparison of phase combination methods.

One example slice is shown for each method. Top row: raw phase image, Middle row: unwrapped phase image for easier visualization (singularities circled in white), Bottom row: quality ratio across a representative slice. a) Complex sum combination, b) VRC c) Fitted SVD method using a low resolution $B_1^{+}$ prescan, d) COMPOSER, e) Voxel-wise SVD combination, f) BCC, g) Fitted SVD method using parameter matched dataset. Single threaded runtime of each method increases left to right and can be found in Table 1. Note: the BCC method applies a rough mask to the region-of-interest during combination and this causes zeros in the exterior of the raw phase image.

Fig 4. Combination quality of an asymmetrical coil.

a) Quality ratio of data collected in an occipital parietal coil when combined with the fitted SVD method, b) Spatially unwrapped phase data after fitted SVD combination.

Fig 5. Phase noise ratios in an asymmetrical coil.

Voxel-wise SVD was used as the reference method. Phase noise ratio combined using a) complex sum, b) VRC, c) BCC, d) the fitted SVD method using the B1+ prescan, and e) the fitted SVD method using the EPI timeseries as input. Hyperintensities correspond with phase singularities in a and b.

Fig 6. Effects of motion on the fitted SVD method.

a) Raw phase image, b) unwrapped phase image, c) quality ratio map created with no motion between the $B_1^{+}$ prescan and the imaging. d) Raw phase image, e) unwrapped phase image, f) quality ratio map created with 3.5 mm motion between the $B_1^{+}$ prescan and the imaging. No singularities were observed.