Tom Bruijnen^{1}, Bjorn Stemkens^{1}, Jan J. W. Lagendijk^{1}, Cornelis A. T. van den Berg^{1}, and Rob H. N. Tijssen^{1}

Golden angle radial acquisitions are sensitive to gradient imperfections leading to reduced image quality. Multiple methods are known to compensate for the zeroth and first order gradient waveform imperfections. Here we quantify the effect of these different methods on Philips 1.5T and 3T wide bore Ingenia scanners, and assess four direct correction methods on efficacy. We show that on these systems a gradient delay correction has minimal impact on the image quality, while phase correction provides a considerable improvement.

The 1st-order component of the gradient-imperfection represents effective gradient timing delays, which can be estimated by investigating anti-parallel spokes from a pre-scan^{3} or directly from the imaging data^{4}. The first method, termed the Calibration Method (**CM**), acquires a small number of perpendicular and opposing spokes and performs a cross correlation analysis on the phase of the projections to estimate the shift $$$( \triangle k )$$$ in the x-direction $$$(shift_x)$$$ and y-direction $$$(shift_y)$$$. The second method, termed the Autocalibrated Method (**AC**), computes the shifts by analyzing the phase of all the projections from the imaging and performing a least-squares minimization to the model $$$\triangle k(\theta) = shift_x \cos (\theta) + shift_y \sin (\theta)$$$. Here $$$\theta$$$ is the azimuthal angle of the readout. Subsequently, each line is corrected with an individual phase shift derived from the model.

The gradient-induced phase errors can be estimated using the azimuthal dependency of the accumulated phase $$$\varphi (\theta)$$$(Figure2)^{5}. The phase accumulation of the center point of each radial readout is fitted to the model $$$\varphi (\theta)=\psi_x \cos (\theta) + \psi_y \sin (\theta) + \varphi_o$$$ to extract the compensation coefficients $$$\psi_x$$$ and $$$\psi_y$$$. The correction can be applied by subtracting the accumulated phase from the readout, i.e. multiplying with $$$\exp( -i(\psi_x \cos (\theta) + \psi_y \sin (\theta)))$$$, called the Phase Correction Fit (**PCF**) method. Alternatively, the phase of the central k-point can be subtracted from the readout, i.e. without any underlying model, termed the Phase Correction Zero (**PCZ**) method.

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Figure 1: Estimated gradient delays for both in-plane gradients (A+B) for a range of receiver bandwidths. Gradient delays were estimated with the CM and the AC method.

Figure 2: (**A**) Azimuthal angle dependency of the phase error across multiple channels. Note that the model (orange line) fits the data (blue dots) well for channels 5 and 9, but it performs inferior for channel 8. This can be attributed to the low sensitivity of the channel, as seen in the L_{2}-plot. (**B**) $$$\psi_x$$$ and $$$\psi_y$$$ scale with increasing bandwidth to a maximum of +20 and -60 degree.

Figure 3: Effect of phase corrections and gradient delay corrections on the image quality. First column is without any data correction. Second column is with one of the proposed phase correction methods. Third column is both the phase correction and gradient delay correction. Note that the phantom images are windowed to enhance the appearance of the artefacts, volunteer images are not.

Table 1: Quantification of image quality for the various correction methods. Higher SSIM and lower BSI values indicates better quality.