Background

3D free-breathing whole-heart MRI is fundamental for the assessment of cardiovascular disease but suffers from long scan times. Several undersampled reconstruction techniques, including parallel imaging and compressed sensing have been proposed to accelerate the acquisition. These approaches achieved limited acceleration factors and they require careful setting of parameters. Recently several deep learning reconstruction approaches have been proposed to overcome these challenges, including end-to-end deep learning motion compensated reconstruction for free-breathing 3D CMRA¹ . However, these approaches rely on large datasets for training. More recently, unsupervised reconstruction using Neural Fields Representation (NFR) have been proposed for 2D radial cardiac cine imaging² . However, feasibility of this approach in 3D Cartesian whole-heart imaging has not been investigated. Here we develop a novel unsupervised undersampled reconstruction approach based on implicit neural field representations for 3D whole-heart Cartesian MRI. This approach considers the complexity of the 3D models and is compatible with a large increase in the dataset size. The proposed approach is evaluated on prospective undersampled multi-coil 3D whole-heart free-breathing CMRA data in comparison to a state-of-the-art reference.

Methods

3D Neural Field Representation Network: Neural Fields is a neural representation of a vector field where the MRI inverse problem’s solution is translated to the training of the network³. Neural fields representations are a fully connected multilayer perceptron (MLP) that takes the spatial coordinate as input and aims to predict the pixel intensity value. Neural fields representations suffer of a well-known spectral bias which can be solved using Fourier Features⁴, a preprocessing step applied to the coordinates before passing them through the MLP.
Reconstruction based on Neural fields representations consists of an initial application of Fourier Features, and a spatial encoder to featurize input coordinates⁴. In the proposed approach (Figure 1), the Fourier feature encoding consists of a linear encoder followed by another, but radial, encoder. The first linear encoder uses a finite number of centered Gaussian vectors independent, to generate hyperplanes for each coordinate. The second encoder consists of composing each linear encoding using two sinusoidal and orthogonal functions, doubling the size of the encoding. The encoded coordinate grid is the input of the fully connected multilayer perceptron (MLP) that takes the spatial coordinate as input and aims to predict the pixel intensity MLP network. For each dense layer, a rectified linear unit (ReLU) activation function is applied, except for the last one. The output of the last layer is the complex value for the image reconstructed at the initial coordinate input.

Training: To simplify the 3D processing, before reconstruction, a one-dimensional Fourier transform is applied in the readout direction to obtain a mixed data set between image space and k-space, allowing to train by batches in the readout dimension. To train the network, at each iteration the image estimated by the network is 2D Fourier Transformed (in the plane orthogonal to the readout direction), weighted by the coil sensitivities and undersampled. The loss function consists in the quadratic mean error between the “hybrid k-space” generated and the obtained from the dataset, in the batch selected, divided by the percent of undersampling. The last rescaling of the loss function value allows us to interpret the value as the real mean error of reconstructing each voxel.

Data: The proposed approach was evaluated on a 3D whole-heart Cartesian MRI dataset. Acquisition was performed at 1.5T (Aera, Siemens Healthineers). Acquisition was performed using image-based (iNAV) navigator⁵ with a 4-fold variable density Cartesian undersampling (VD-CASPR)⁶. iNAV-based foot-head and right-left translational motion was corrected in k-space. Reconstruction was performed with iterative SENSE for comparison purposes.

Results

Reconstructions results for the proposed approach in comparison to iterative SENSE are shown in Figure 2 and Figure 3 for two coronal and transversal slices, respectively. Reconstructions results show similar image quality to the iterative SENSE reference, although with some remaining blurring.

Discussion

3D whole-heart Cartesian MRI undersampled reconstruction with unsupervised neural fields enables 4-fold accelerated acquisition, showing similar image quality to the state-of-the-art reference, holding promise for future clinical evaluation. Future work will focus on parameter optimization to reduce remaining blurring and evaluation in a larger cohort of healthy subjects.