Introduction

Multi-echo fMRI has the potential to improve the accuracy of fMRI measurements and extract multi-quantitative maps by utilizing the extra echo information¹. Nevertheless, the relatively long readout poses a challenge in integrating multi-echo acquisition into fMRI due to its time constraints. One potential solution to circumvent this challenge involves employing parallel imaging². However, conventional parallel imaging methods, such as compressed sensing^3-6, may struggle to maintain optimal image quality when the under-sampling rate is excessively high.
In recent years, deep learning (DL) has emerged as a promising approach for image reconstruction^7-9, particularly at high accelerations. In this study, we implemented a spiral multi-echo sequence along with a self-supervised physics-driven DL reconstruction to get multi-echo fMRI data with an under-sampling rate of ten, and investigated its utility for BOLD analysis.

Methods

Image Acquisition: A prototype multi-echo 2D GRE sequence was used (Fig.1). The experiments were comprised of two acquisitions. First, training data for the DL algorithm was collected from four healthy subjects. The multi-echo dataset for training was acquired with flip angle 20°, TR=4464ms. TEs=[3.4,9.5,15.6,21.8,27.9,34.1]ms. 72 slices were collected with in-plane FOV=240$$$\times$$$240mm², isotropic resolution2$$$\times$$$2$$$\times$$$2mm³. A corresponding fully sampled dataset with the same parameters was acquired to generate the coil maps for training. This data did not include a time-series.
Subsequently, in-vivo fMRI experiments were performed on another subject using the 2D multi-echo sequence and a standard single-echo spiral sequence for comparison. The protocol for the multi-echo sequence was set similar to the training dataset with same flip angle, TEs and in-plane FOV, but different TR was used by acquiring 24 slices within 1488ms to fulfill the fine time resolution for fMRI while also covering the visual cortex. The single-echo spiral sequence was using flip angle 20°, TE/TR=27.91/1920ms, in-plane FOV=240$$$\times$$$240mm², resolution3$$$\times$$$3$$$\times$$$2mm³. The longer TR value is necessary to accommodate a lengthier spiral readout.
The fMRI tasks consisted of six blocks of 20sec flickering checkerboard for visual stimulation, separated by 20sec resting periods leading to a paradigm duration of 4:20 min. BOLD analyses were carried out using a general linear model with a canonical hemodynamic response function after removal of first and second order temporal trends in the data. We used weighted echo summation¹⁰ based on the local T2* (the T2* map was extracted from the fully sampled multi-echo data) to prepare the multi-echo data for BOLD analyses. All scans were acquired on a 3T Siemens Prisma scanner.

Image Reconstruction: We extended multi-mask self-supervision via data undersampling(SSDU)¹¹ method for non-Cartesian MRI(Fig.2). Specifically, physics-driven DL solves:$$arg\min_{\bf{x}}{||\sqrt{\bf{W}_{\Omega}}(\bf{{E_\Omega}x-y_{\Omega}})||}^2_2+{\mathcal{R({\bf{x}})}}$$where $$$\bf{x}$$$ is the image to be reconstructed, $$$\bf{y_{\Omega}}$$$ is the acquired non-Cartesian k-space samples,$$$\bf{E_\Omega}$$$is the forward operator that incorporates non-uniform fast Fourier transform¹²(NUFFT) and coil sensitivities.$$$\bf{W_\Omega}$$$refers to density compensation¹³ in $$${\Omega}$$$, and$$${\mathcal{R({\cdot})}}$$$is a regularizer. Using variable splitting with quadratic penalty (VSQP)^7,8,14, the problem is solved via algorithm unrolling that alternate between DC and a proximal operator. In DL the proximal operator is implicitly solved via neural networks.
Multi-mask SSDU¹¹ allows training the network with only subsampled points by splitting $$${\Omega}$$$ into multiple pairs of disjoint sets $$$\bf{\Theta_{\it{j}}}$$$and$$$\bf{\Lambda_{\it{j}}}$$$. Here we modify the training loss of multi-mask SSDU into a form amenable to the use of the Toeplitz decomposition^6,15 in non-Cartesian MRI:$$\min_{\bf{\theta}}\sum_{\it{n}}\sum_{\it{j}}\mathcal{L}(\bf{E_{\Lambda_{\it{j}}}^{\it{H}}W_{\Lambda_{\it{j}}}E_{\Lambda_{\it{j}}} {\it{f_{\bf{\theta}}}}(z_{\Theta_{\it{j}},{\it{n}}}),r_{\Lambda_{\it{j}},{\it{n}}}})$$where$$${\mathcal{L}({\cdot},{\cdot})}$$$is the loss function, $$${f_{\bf{\theta}}}$$$is the unrolled network with parameters $$${\bf{\theta}}$$$, $$$\bf{z_{\Theta_{\it{j}},{\it{n}}}}={E_{\Theta_{\it{j}},{\it{n}}}^{\it{H}}}{W_{\Theta_{\it{j}},{\it{n}}}}{y_{\Theta_{\it{j}},{\it{n}}}}$$$ is zero-filled image with acquisition $$$\bf{\Theta_{\it{j}}}$$$for n^th slice, $$$\bf{r_{\Lambda_{\it{j}},{\it{n}}}}={E_{\Lambda_{\it{j}},{\it{n}}}^{\it{H}}}{W_{\Lambda_{\it{j}},{\it{n}}}}{y_{\Lambda_{\it{j}},{\it{n}}}}$$$ is zero-filled image with acquisition $$$\bf{\Lambda_{\it{j}}}$$$for n^th slice. Note loss is calculated in image domain instead of k-space to avoid using NUFFT that slows down the training. Instead$$$\bf{E_{\Lambda_{\it{j}}}^{\it{H}}}{W_{\Lambda_{\it{j}}}}{E_{\Lambda_{\it{j}}}}$$$are implemented using Toeplitz decomposition. The testing is then performed using all available$$${\Omega}$$$.

Results

As shown in Fig.3, the images reconstructed by CG-SENSE are clearly not applicable for BOLD analysis. SSDU show decent quality images however there are some residual artifacts which may be caused by the mismatch of the TR lengths between the training data and the fMRI data. BOLD signal has been well contained with SSDU reconstruction as shown in Fig.4. The BOLD sensitivity from SSDU results was not as strong as the single shot fMRI as a result of the difference between the under-sampling rate and the resolution. The SNR of the single spiral fMRI is about 4.7($$$=\sqrt{10}\times\frac{3}{2}$$$) times higher than the SSDU, not to mention it has a longer TR.

Discussion& Conclusion

The SSDU reconstruction has not only enabled the possibility for multi-echo spiral fMRI to use a short readout time, but also preserved the BOLD sensitivity with the highly under-sampled data. Future plans include optimization of the acquisition parameters and fine tune the DL model using more rigorous training/testing datasets, in order to improve the performance of the DL methods.

Acknowledgements

Acknowledgment: NIH R01EB028627, NIH R01EB032830, NIH P41 EB027061, NIH 1P20GM139753-01A1. The first three authors contributed equally.