Uncertainty‐aware physics‐driven deep learning network for free‐breathing liver fat and R₂* quantification using self‐gated stack‐of‐radial MRI

Abstract

Purpose To develop a deep learning‐based method for rapid liver proton‐density fat fraction (PDFF) and R2* quantification with built‐in uncertainty estimation using self‐gated free‐breathing stack‐of‐radial MRI. Methods This work developed an uncertainty‐aware physics‐driven deep learning network (UP‐Net) to (1) suppress radial streaking artifacts because of undersampling after self‐gating, (2) calculate accurate quantitative maps, and (3) provide pixel‐wise uncertainty maps. UP‐Net incorporated a phase augmentation strategy, generative adversarial network architecture, and an MRI physics loss term based on a fat–water and R2* signal model. UP‐Net was trained and tested using free‐breathing multi‐echo stack‐of‐radial MRI data from 105 subjects. UP‐Net uncertainty scores were calibrated in a validation dataset and used to predict quantification errors for liver PDFF and R2* in a testing dataset. Results Compared with images reconstructed using compressed sensing (CS), UP‐Net achieved structural similarity index >0.87 and normalized root mean squared error <0.18. Compared with reference quantitative maps generated using CS and graph‐cut (GC) algorithms, UP‐Net achieved low mean differences (MD) for liver PDFF (−0.36%) and R2* (−0.37 s−1). Compared with breath‐holding Cartesian MRI results, UP‐Net achieved low MD for liver PDFF (0.53%) and R2* (6.75 s−1). UP‐Net uncertainty scores predicted absolute liver PDFF and R2* errors with low MD of 0.27% and 0.12 s−1 compared to CS + GC results. The computational time for UP‐Net was 79 ms/slice, whereas CS + GC required 3.2 min/slice. Conclusion UP‐Net rapidly calculates accurate liver PDFF and R2* maps from self‐gated free‐breathing stack‐of‐radial MRI. The pixel‐wise uncertainty maps from UP‐Net predict quantification errors in the liver.

Accelerated four-dimensional free-breathing whole-liver water-fat magnetic resonance imaging with deep dictionary learning and chemical shift modeling

“…Recently, several algorithms have been proposed for rapid fat and quantification using stack-of-stars MRI, such as model-guided deep learning for water-fat separation (MGDL-WF) ( 36 ), an uncertainty-aware physics-driven DL network (UP-Net) ( 47 ) and multitasking multi-echo MRI (MT-ME) ( 15 ). The MGDL-WF utilizes a U-net in combination with MG reconstruction to accelerate 3D static water-fat imaging.…”

“…The UP-Net utilizes generative adversarial networks (GAN) and U-net to suppress the radial undersampling artifacts, and achieves an acceleration rate around 3 for free-breathing water-fat imaging. Adding k-space DC layers might be helpful for UP-Net to address higher undersampling factors ( 47 ). Instead of using GAN, the proposed HMDDL uses a high-dimensional dictionary learning neural network to reduce the artifacts, and achieved an acceleration rate up to 10.…”

Rapid estimation of 2D relative B1+‐maps from localizers in the human heart at 7T using deep learning

“…The proposed neural network was based on a modified version of the established 2D UNet architecture 34,35 to predict complex, Tx‐channel‐wise, 2D $$$ {\mathrm{B}}_1^{+} $$$‐maps from complex, Rx‐channel‐wise 2D localizer data (Figure 1B). This architecture is suitable for a plethora of applications, for example, image reconstruction, 36,37 quantitative parameter mapping, 38,39 and artifact correction 37,40 . The chosen architecture comprised four encoding stages, each including a 2 × 2 max pooling layer (downsampling) and 2 repetitions of 3 × 3 convolutions, batch normalizations, and LeakyReLU activation functions.…”

A Survey on Uncertainty Quantification Methods for Deep Neural Networks: An Uncertainty Source Perspective

“…To overcome this issue, current research in uncertainty quantification of inverse problems employs conditional deep generative models, such as cVAE, cGAN, and conditional normalizing flow models [2,29,31]. These methods utilize a lowdimensional latent space for image generation but may overlook unique data characteristics, such as structural constraints from domain physics in certain types of image data, such as remote sensing images, MRI images, or geological subsurface images [60,124,127]. The use of physics-informed models may improve uncertainty quantification in these cases.…”