The target audience is basic scientists and clinical scientists who are interested in ultrafast imaging and non-Cartesian sampling.Spatiotemporally encoded (SPEN) single-shot MRI is an ultrafast MRI technique proposed recently, which has a great advantage in resisting off-resonance compared to the echo planar imaging (EPI).¹ However, due to insufficient sampling rate, the SPEN images are vulnerable to aliasing artifacts.² Besides, for the Cartesian trajectory, the transition between negative and positive gradient lobes will reduce the acquisition efficiency of SPEN MRI. In this work, a variable density spiral sampling (VDSS) scheme is proposed based on bi-SPEN MRI³ to overcome the above limitations. An optimization algorithm is used to generate sinusoidal gradient waveforms for the SPEN spiral MRI. A non-Cartesian super-resolved (SR) reconstruction method is proposed in combination with a specific gridding algorithm and compressive sensing (CS) to reconstruct the spiral data.The single-shot SPEN MRI spiral sampling pulse sequence is shown in Fig. 1. The 90° chirp pulse and 180° chirp pulse are imposed in y and x direction, respectively. An optimization algorithm is used to design the sinusoidal gradient waveform within limits of gradient magnitude and slew-rate.⁴ The flowchart of SPEN spiral imaging is shown in Fig. 2. Due to the quadratic phase modulation, the phase of acquired signal oscillates severely, as shown in Fig. 2(d). Based on the characteristic of SPEN approach, the oscillating phase can be smoothed by removing the quadratic phase modulation without loss of useful information.^2,3 Since the signal is piecewise smooth after the quadratic phase offset is removed, as shown in Fig. 2(e), gridding can be realized by interpolating the spiral data. CS-based SR reconstruction is employed to retrieve SR image by enforcing the sparsity of the image in transform domain.Experiments were performed on a Varian 7.0 T MRI system using a quadrature-coil probe. The experimental sample was an in vivo rat. The FOV was 45 × 45 mm² and the slice thickness was 2 mm. For Cartesian bi-SPEN MRI, the bandwidths and the durations of the phase-encoding chirp pulse and frequency-encoding chirp pulse were 64kHz/3ms and 8kHz/4ms respectively. The imaging matrix size was 64 × 64, and the spectral width (sw) was 250 kHz, the gradient slew-rate was 156 G/(cm×ms), the acquisition time was 27.14 ms. For SPEN spiral MRI, the bandwidths and the durations of the chirp pulse along the y direction and x direction were 64kHz/3ms and 32kHz/3ms respectively. The number of sampling points was 6991, the circle number was 31, and the acquisition time was 27.96 ms. The results are shown in Fig. 3. The zoom-in region in Fig. 3 proves that the SPEN spiral scheme can provide more details and higher image resolution than Cartesian scheme. As indicated by the yellow arrows in Fig. 3b, there are artifacts in the Cartesian result, whereas the artifacts are obviously reduced in VDSS result.Different from the Cartesian sampling, VDSS is a non-Cartesian sampling scheme. The aliasing artifacts are less coherent and spread out efficiently across the field of view in VDSS, which is favorable for the application of CS to further eliminate the aliasing artifacts. Besides, the profile of readout gradient is smooth overall in VDSS. The quick switching of gradients can be avoided in VDSS. Compared to the Cartesian sampling, VDSS can acquire more points within the same time. Furthermore, VDSS can aggregate the sampling points in signal regions, which is favorable for the spatial resolution of resulting image.A VDSS scheme together with an image reconstruction method is proposed for SPEN MRI. Compared to the Cartesian scheme, VDSS can provide images with less aliasing artifacts and more detail information.