fMRI with high spatiotemporal resolution is beneficial for psychology and neuroscience studies^[1][2], but is limited by various factors. Compressed Sensing (CS) based methods for accelerating fMRI data acquisition have been explored and have great potential^[3][4][5], however, it may be problematic because the over-smoothing effects may contaminate the hemodynamic osculation of fMRI data. Here we developed a new method, Dual Extended TRACER (DUET), based on Temporal Resolution Acceleration with Constrained Evolution Reconstruction (TRACER)^[6], for accelerating fMRI acquisitions using golden angle variable density spiral (VDS). Both numerical simulation and in vivo experiments were conducted to evaluate the performance of DUET.

The CS reconstruction is formulated as follows: $$\hat{x}=arg\ min\left\{\parallel y-PFSx\parallel ^2+\lambda\parallel \psi x\parallel ^2\right\}$$ Where y is the acquired k-space data, P is the k-space projection onto sampling trajectories, F is the Fourier transform operator, S is the sensitivity map, $\lambda$ is the regularization weight, x is the time series images of x-y-t, $\psi$ is a sparse transform, here the temporal total-variation (TTV) is chosen since it has shown high performance in other dynamic MRI and fMRI application^[5][7] .

The proposed method DUET is based on TRACER^[6] which was originally used for 3D liver dynamic imaging. In the original TRACER reconstruction, the current iteration ${x_{n}}$ is kept to be close to the last reconstructed frame ${x_{n-1}}$ , and a limited regularization term is added, shown by the following equation, $$\hat{x_{n}}=arg\ min\left\{\parallel y_{n}-PFSx_{n}\parallel ^2+\lambda\parallel x_{n}-x_{n-1}\parallel ^2\right\}$$ where ${y_{n}}$ is the k-space measurement at time n, and ${x_{n}}$ is the fMRI image at time n. During TRACER reconstruction, errors may be accumulated gradually along the time series. To suppress the error accumulation, the reconstruction is executed one more time by reversing the order of time series, with the reverse reconstruction model shown as follows, $$\hat{x_{n}}=arg\ min\left\{\parallel y_{n}-PFSx_{n}\parallel ^2+\lambda\parallel x_{n}-x_{n+1}\parallel ^2\right\}$$ The results by TRACER and reverse-TRACER are then averaged to form the final images. Therefore, the proposed method is called Dual Extended TRACER (DUET).

VDS is suitable for the CS method and has been successfully used in fMRI^[3][8][9]. Here we used golden angle VDS for the signal acquisition.

$\underline{Simulation}$ To evaluate CS, TRACER and DUET in fMRI images with noise, single-shot EPI data were acquired, with a finger tapping task in 4 min (20s on and 20s off). Other imaging parameters: TE=35ms, TR=2s, FOV=230$\times$230$mm^{2}$, acquisition matrix =96$\times$96. For each dynamic image, 5-shot spiral data were generated as full-sampled k-space data using inverse NUFFT. Images were reconstructed using one spiral interleave (i.e. 5-fold acceleration). To test high under-sampling ratios, 14 spiral interleaves were simulated first and then one interleave was selected for the reconstruction.

$\underline{In\ vivo\ Experiments}$ In vivo fMRI experiment were conducted with visual stimulus and finger tapping tasks, all data were acquired using golden angle VDS on a Philips 3.0T Achieva TX MRI scanner (Philips Healthcare, Best, The Netherlands) using an 32-channel head coil. The stimulus paradigm to induce functional brain activation in the visual cortex was a block design consisting of 20 s of blank screen fixation alternating with 20 s of a flashing and rotating checkerboard at 8 Hz. The stimulus paradigm of finger tapping is same as simulation. Three datasets of different spatial resolution including 2.3$\times$2.3$mm^{2}$, 1.3$\times$1.3$mm^{2}$ and 1$\times$1$mm^{2}$ were acquired. For different resolution, the full sampled data for one frame consist of 4, 8 and 14 interleaves. In the reconstruction, one interleave was used to reconstruct one frame, corresponding to 4-fold, 8-fold and 14-fold undersampling ratio.

$\underline{Data\ Processing}$ Image difference, RMSE, sensitivity (SEN), false positive rate (FPR) and activation maps using, CS temporal TV transform (CS-TTV), TRACER and DUET reconstruction were compared. Functional data were processed using FSL^[10], and FWHM was set to 0 to avoid smoothness.

Fig. 1 shows the reconstruction results for the simulation data. The DUET method can achieve high quality images compared with other methods. The resultant SEN and FPR for different methods are listed in Table 1. Fig. 2 shows the time series from the activated regions in the motor cortex for different reconstruction methods. In comparison, the DUET method provided better matched signals in either 5-fold or 14-fold undersampling.

In the finger tapping in vivo experiment paradigm, DUET provided more reliable activation maps than CS-TTV method (Fig. 3) when signals were 8 fold undersampled. Fig. 4 shows the visual activation maps for different undersampling factors with different spatial resolution.

DUET combined with golden angle VDS sampling can reconstruct hemodynamic signals with high undersampling factors. Compared with the methods investigated, DUET provides better signal fidelity, higher fMRI signal sensitivity and more reliable activation maps.