Efficient Bayesian inference using physics-informed invertible neural networks for inverse problems

In the paper, we propose a novel approach for solving Bayesian inverse problems with physics-informed invertible neural networks (PI-INN). The architecture of PI-INN consists of two sub-networks: an invertible neural network (INN) and a neural basis network (NB-Net). The invertible map between the parametric input and the INN output with the aid of NB-Net is constructed to provide a tractable estimation of the posterior distribution, which enables efficient sampling and accurate density evaluation. Furthermore, the loss function of PI-INN includes two components: a residual-based physics-informed loss term and a new independence loss term. The presented independence loss term can Gaussianize the random latent variables and ensure statistical independence between two parts of INN output by effectively utilizing the estimated density function. Several numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed PI-INN, including inverse kinematics, inverse problems of the 1-d and 2-d diffusion equations, and seismic traveltime tomography.

Deep learning based automatic segmentation of lumbosacral nerves on non-contrast CT for radiographic evaluation: a pilot study

Background and objective: Combined evaluation of lumbosacral structures (e.g. nerves, bone) on multimodal radiographic images is routinely conducted prior to spinal surgery and interventional procedures. Generally, magnetic resonance imaging is conducted to differentiate nerves, while computed tomography (CT) is used to observe bony structures. The aim of this study is to investigate the feasibility of automatically segmenting lumbosacral structures (e.g. nerves & bone) on non-contrast CT with deep learning. Methods: a total of 50 cases with spinal CT were manually labeled for lumbosacral nerves and bone with Slicer 4.8. The ratio of training: validation: testing is 32:8:10. A 3D-Unet is adopted to build the model SPINECT for automatically segmenting lumbosacral structures. Pixel accuracy, IoU, and Dice score are used to assess the segmentation performance of lumbosacral structures. Results: the testing results reveals successful segmentation of lumbosacral bone and nerve on CT. The average pixel accuracy is 0.940 for bone and 0.918 for nerve. The average IoU is 0.897 for bone and 0.827 for nerve. The dice score is 0.945 for bone and 0.905 for nerve. Conclusions: this pilot study indicated that automatic segmenting lumbosacral structures (nerves and bone) on non-contrast CT is feasible and may have utility for planning and navigating spinal interventions and surgery.