INTRODUCTION

Myocardial first-pass perfusion cardiac MRI (CMR) enables assessment of the functional significance of coronary artery disease. Perfusion CMR is acquired using snap-shot imaging during the passage of a contrast agent, which requires trade-offs between resolution and coverage^1,2. Numerous techniques based on parallel or simultaneous multi-slice (SMS) imaging, and compressed sensing have been proposed to tackle this challenge^3,4. Recently, physics-guided deep learning (PG-DL) has shown exceptional reconstructions at highly accelerated imaging, where conventional methods suffer from residual aliasing and noise^5,6. However, PG-DL faces several challenges on its own. PG-DL struggles to generalize when SNRs/contrasts change between training and testing⁷. A possible solution is to regularize over spatio-temporal (2D+t) domain, but this is prone the temporal blurring, and it is hard to procure large high-quality databases due to changes in contrast dynamics and breathing patterns among subjects. In this work, we tackle these challenges by using structure-encoded maps that capture SNR/contrast changes across dynamics leading to improved generalizability for PG-DL, while reconstructing each dynamic individually. The proposed approach was applied to highly-accelerated myocardial perfusion using self-supervised PG-DL with structure-encoded maps. The proposed method improves on parallel imaging and conventional PG-DL reconstructions.

METHODS

Theory: The inverse problem of MRI reconstruction is given as:

$$\hat{x}_{reg} = \arg \min_{\mathbf{x}} \left\| \mathbf{y}-\mathbf{E}\mathbf{x} \right\|_{2}^{2} + {\cal{R}}(\mathbf{x}), \quad\quad (1)$$


where $$$\mathbf{x}$$$ is the image of interest, $$$\mathbf{y}$$$ is the acquired multi-coil k-space, $$$\mathbf{E}$$$ is the multi-coil encoding operator and $$$\cal{R}(\cdot)$$$ is the regularizer. The encoding operator is formed as $$$\mathbf{E}=[\mathbf{F}_{\Omega}\mathbf{C}_{1};\cdots;\mathbf{F}_{\Omega}\mathbf{C}_{K}]$$$ where $$$\mathbf{F}_{\Omega}$$$ is a partial Fourier operator sampling indices $$$\Omega$$$, and $$$\mathbf{C}_{K}$$$ is the k^th coil map. Conventionally, these maps are generated using ESPIRiT⁸, which leads to normalized maps, i.e. $$$\sum_k \mathbf{C}_{k}^{*}\mathbf{C}_{k}={\bf I}$$$, and these do not inherently capture contrast variations across different dynamics.

As an alternative, we propose to encode contrast/SNR in the coil-maps for PG-DL. Let $$$\mathbf{L}$$$ be an image that contains contrast information for a given dynamic, such as a low-resolution image. We define the structure-encoded coil maps as $$$\mathbf{L}_{K} = \mathbf{C}_{K}\cdot\mathbf{L}$$$. This leads to a reformulated multi-coil operator $$$ \mathbf{H}=\mathbf{E}\mathbf{L}$$$ with the corresponding inverse problem:

$$ \hat{x}_{struct} = \arg \min_{\mathbf{x}} \left\| \mathbf{y}-\mathbf{H}\mathbf{x} \right\|_{2}^{2} + {\cal{R}}(\mathbf{x}). \quad\quad (2)$$
It is easy to show that for the unregularized case⁹,

$$\hat{x}_{reg} = (\mathbf{E}^{*}\mathbf{E})^{-1}\mathbf{E}^{*}\mathbf{y} = \mathbf{L}\cdot\hat{x}_{struct}. \quad\quad (3)$$

The main advantage of the proposed formulation is that the solutions to Eq. 2 have uniform contrast across different dynamics, facilitating generalizability for PG-DL (Fig. 1).

Imaging Experiments: Free-breathing first-pass perfusion CMR was acquired at 3T on 8 subjects with 12-fold acceleration (SMS=3, uniform Cartesian in-plane R=4). A saturation-prepared GRE sequence with slab-selective outer volume suppression¹⁰ was used with resolution=1.7×1.7mm², FOV=360×360mm², temporal resolution=110ms, slice-thickness=8mm. A separate calibration scan was performed with resolution=1.7×5.6mm², FOV= 360×360mm².

Implementation Details: First, ESPIRiT⁸ was used to generate conventional coil sensitivity maps ($$$\mathbf{C}_K$$$) using the central 24×24 region of the calibration scan. Then, split slice-GRAPPA¹¹ was used to generate each dynamic. Note that this step was necessary due to lack of individual k-spaces of the slices due to SMS encoding and would not be needed for single-slice or single-volume imaging. Subsequently, low-resolution images ($$$\mathbf{L}$$$) were estimated using central 24×24 region followed by a ringing filter of each reconstructed dynamic. Finally, $$$\mathbf{C}_K$$$’s from first step were multiplied by $$$\mathbf{L}$$$ to generate the structure-encoded coil maps.

Physics-guided deep learning (PG-DL) training was performed on 4 subjects using self-supervised learning via data undersampling (SSDU), which does not require fully-sampled data¹². Algorithm unrolling based on variable splitting for 10 iterations was used¹². Training was performed over 360 SMS k-spaces using Adam optimizer, learning rate=$$$3\cdot10^{-4}$$$, 100 epochs and normalized $$$\ell_1-\ell_2$$$ loss. Two trainings were performed with same settings, one with conventional ESPIRiT maps and one with proposed structure-encoded coil maps (Fig. 2). Note the structure-encoded network outputs were multiplied with respective low-resolution images ($$$\mathbf{L}$$$) for the final reconstruction, as in Eq. 3.

RESULTS

Fig. 3 shows reconstructed slices from an SMS slice group across different dynamics. Split slice-GRAPPA reconstruction reduces aliasing, but has high noise amplification. PG-DL with conventional encoding operator using ESPIRiT maps reduces noise, but has visible aliasing (yellow arrows). Proposed approach suppresses both aliasing noise amplification.
Fig. 4 depicts reconstructions of the whole heart with 9 slices from 3 SMS groups. Proposed approach shows improved image quality compared to PG-DL with ESPIRiT and split slice-GRAPPA, which suffer from aliasing and noise amplification respectively.

DISCUSSION AND CONCLUSIONS

In this study, we proposed a contrast-aware encoding operator for PG-DL using structure-encoded coil-maps that capture SNR/contrast information across an image series. The proposed structure-encoded maps were used for PG-DL reconstruction of highly accelerated myocardial perfusion, and showed improved image quality compared to conventional ESPIRiT map based encoding operator. ESPIRiT maps do not exhibit variations across dynamics whereas in structure-encoded maps, SNR information is captured in the maps leading a more uniform contrast across dynamics at the network output. This in turn makes it easier for the deep learning reconstruction to generalize for perfusion CMR, when SNR levels fluctuate with inherent physiological processes.

Acknowledgements

Funding: Grant support: NIH R01HL153146, NIH P41EB027061, NIH R21EB028369, NSFCCF-1651825. NWO STU.019.024, 4TU Federation and AHA Predoctoral Fellowship.