Towards Real-time Training of Physics-informed Neural Networks: Applications in Ultrafast Ultrasound Blood Flow Imaging

Physics-informed Neural Network (PINN) is one of the most preeminent solvers of Navier-Stokes equations, which are widely used as the governing equation of blood flow. However, current approaches, relying on full Navier-Stokes equations, are impractical for ultrafast Doppler ultrasound, the state-of-the-art technique for depiction of complex blood flow dynamics \emph{in vivo} through acquired thousands of frames (or, timestamps) per second. In this article, we first propose a novel training framework of PINN for solving Navier-Stokes equations by discretizing Navier-Stokes equations into steady state and sequentially solving steady-state Navier-Stokes equations with transfer learning. The novel training framework is coined as SeqPINN. Upon the success of SeqPINN, we adopt the idea of averaged constant stochastic gradient descent (SGD) as initialization and propose a parallel training scheme for all timestamps. To ensure an initialization that generalizes well, we borrow the concept of Stochastic Weight Averaging Gaussian to perform uncertainty estimation as an indicator of generalizability of the initialization. This algorithm, named SP-PINN, further expedites training of PINN while achieving comparable accuracy with SeqPINN. Finite-element simulations and \emph{in vitro} phantoms of single-branch and trifurcate blood vessels are used to evaluate the performance of SeqPINN and SP-PINN. Results show that both SeqPINN and SP-PINN are manyfold faster than the original design of PINN, while respectively achieving Root Mean Square Errors (RMSEs) of 1.01 cm/s and 1.26 cm/s on the straight vessel and 1.91 cm/s and 2.56 cm/s on the trifurcate blood vessel when recovering blood flow velocities.

Constrained CycleGAN for Effective Generation of Ultrasound Sector Images of Improved Spatial Resolution

Objective. A phased or a curvilinear array produces ultrasound (US) images with a sector field of view (FOV), which inherently exhibits spatially-varying image resolution with inferior quality in the far zone and towards the two sides azimuthally. Sector US images with improved spatial resolutions are favorable for accurate quantitative analysis of large and dynamic organs, such as the heart. Therefore, this study aims to translate US images with spatially-varying resolution to ones with less spatially-varying resolution. CycleGAN has been a prominent choice for unpaired medical image translation; however, it neither guarantees structural consistency nor preserves backscattering patterns between input and generated images for unpaired US images. Approach. To circumvent this limitation, we propose a constrained CycleGAN (CCycleGAN), which directly performs US image generation with unpaired images acquired by different ultrasound array probes. In addition to conventional adversarial and cycle-consistency losses of CycleGAN, CCycleGAN introduces an identical loss and a correlation coefficient loss based on intrinsic US backscattered signal properties to constrain structural consistency and backscattering patterns, respectively. Instead of post-processed B-mode images, CCycleGAN uses envelope data directly obtained from beamformed radio-frequency signals without any other non-linear postprocessing. Main Results. In vitro phantom results demonstrate that CCycleGAN successfully generates images with improved spatial resolution as well as higher peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) compared with benchmarks. Significance. CCycleGAN-generated US images of the in vivo human beating heart further facilitate higher quality heart wall motion estimation than benchmarks-generated ones, particularly in deep regions.

Exploring Concept Contribution Spatially: Hidden Layer Interpretation with Spatial Activation Concept Vector

To interpret deep learning models, one mainstream is to explore the learned concepts by networks. Testing with Concept Activation Vector (TCAV) presents a powerful tool to quantify the contribution of query concepts (represented by user-defined guidance images) to a target class. For example, we can quantitatively evaluate whether and to what extent concept striped contributes to model prediction zebra with TCAV. Therefore, TCAV whitens the reasoning process of deep networks. And it has been applied to solve practical problems such as diagnosis. However, for some images where the target object only occupies a small fraction of the region, TCAV evaluation may be interfered with by redundant background features because TCAV calculates concept contribution to a target class based on a whole hidden layer. To tackle this problem, based on TCAV, we propose Spatial Activation Concept Vector (SACV) which identifies the relevant spatial locations to the query concept while evaluating their contributions to the model prediction of the target class. Experiment shows that SACV generates a more fine-grained explanation map for a hidden layer and quantifies concepts' contributions spatially. Moreover, it avoids interference from background features. The code is available on https://github.com/AntonotnaWang/Spatial-Activation-Concept-Vector.

HINT: Hierarchical Neuron Concept Explainer

To interpret deep networks, one main approach is to associate neurons with human-understandable concepts. However, existing methods often ignore the inherent relationships of different concepts (e.g., dog and cat both belong to animals), and thus lose the chance to explain neurons responsible for higher-level concepts (e.g., animal). In this paper, we study hierarchical concepts inspired by the hierarchical cognition process of human beings. To this end, we propose HIerarchical Neuron concepT explainer (HINT) to effectively build bidirectional associations between neurons and hierarchical concepts in a low-cost and scalable manner. HINT enables us to systematically and quantitatively study whether and how the implicit hierarchical relationships of concepts are embedded into neurons, such as identifying collaborative neurons responsible to one concept and multimodal neurons for different concepts, at different semantic levels from concrete concepts (e.g., dog) to more abstract ones (e.g., animal). Finally, we verify the faithfulness of the associations using Weakly Supervised Object Localization, and demonstrate its applicability in various tasks such as discovering saliency regions and explaining adversarial attacks. Code is available on https://github.com/AntonotnaWang/HINT.

NaviAirway: a bronchiole-sensitive deep learning-based airway segmentation pipeline for planning of navigation bronchoscopy

Navigation bronchoscopy is a minimally invasive procedure in which doctors pass a bronchoscope into a subject's airways to sample the target pulmonary lesion. A three-dimensional (3D) airway roadmap reconstructed from Computer Tomography (CT) scans is a prerequisite for this procedure, especially when the target is distally located. Therefore, an accurate and efficient airway segmentation algorithm is essential to reduce bronchoscopists' burden of pre-procedural airway identification as well as patients' discomfort during the prolonged procedure. However, airway segmentation remains a challenging task because of the intrinsic complex tree-like structure, imbalanced sizes of airway branches, potential domain shifts of CT scans, and few available labeled images. To address these problems, we present a deep learning-based pipeline, denoted as NaviAirway, which finds finer bronchioles through four major novel components - feature extractor modules in model architecture design, a bronchiole-sensitive loss function, a human-vision-inspired iterative training strategy, and a semi-supervised learning framework to utilize unlabeled CT images. Experimental results showed that NaviAirway outperformed existing methods, particularly in identification of higher generation bronchioles and robustness to new CT scans. On average, NaviAirway takes five minutes to segment the CT scans of one patient on a GPU-embedded computer. Moreover, we propose two new metrics to complement conventional ones for a more comprehensive and fairer evaluation of deep learning-based airway segmentation approaches. The code is publicly available on https://github.com/AntonotnaWang/NaviAirway.