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  1. Free, publicly-accessible full text available April 30, 2025
  2. Abstract Background

    Lung cancer is the deadliest and second most common cancer in the United States due to the lack of symptoms for early diagnosis. Pulmonary nodules are small abnormal regions that can be potentially correlated to the occurrence of lung cancer. Early detection of these nodules is critical because it can significantly improve the patient's survival rates. Thoracic thin‐sliced computed tomography (CT) scanning has emerged as a widely used method for diagnosing and prognosis lung abnormalities.

    Purpose

    The standard clinical workflow of detecting pulmonary nodules relies on radiologists to analyze CT images to assess the risk factors of cancerous nodules. However, this approach can be error‐prone due to the various nodule formation causes, such as pollutants and infections. Deep learning (DL) algorithms have recently demonstrated remarkable success in medical image classification and segmentation. As an ever more important assistant to radiologists in nodule detection, it is imperative ensure the DL algorithm and radiologist to better understand the decisions from each other. This study aims to develop a framework integrating explainable AI methods to achieve accurate pulmonary nodule detection.

    Methods

    A robust and explainable detection (RXD) framework is proposed, focusing on reducing false positives in pulmonary nodule detection. Its implementation is based on an explanation supervision method, which uses nodule contours of radiologists as supervision signals to force the model to learn nodule morphologies, enabling improved learning ability on small dataset, and enable small dataset learning ability. In addition, two imputation methods are applied to the nodule region annotations to reduce the noise within human annotations and allow the model to have robust attributions that meet human expectations. The 480, 265, and 265 CT image sets from the public Lung Image Database Consortium and Image Database Resource Initiative (LIDC‐IDRI) dataset are used for training, validation, and testing.

    Results

    Using only 10, 30, 50, and 100 training samples sequentially, our method constantly improves the classification performance and explanation quality of baseline in terms of Area Under the Curve (AUC) and Intersection over Union (IoU). In particular, our framework with a learnable imputation kernel improves IoU from baseline by 24.0% to 80.0%. A pre‐defined Gaussian imputation kernel achieves an even greater improvement, from 38.4% to 118.8% from baseline. Compared to the baseline trained on 100 samples, our method shows less drop in AUC when trained on fewer samples. A comprehensive comparison of interpretability shows that our method aligns better with expert opinions.

    Conclusions

    A pulmonary nodule detection framework was demonstrated using public thoracic CT image datasets. The framework integrates the robust explanation supervision (RES) technique to ensure the performance of nodule classification and morphology. The method can reduce the workload of radiologists and enable them to focus on the diagnosis and prognosis of the potential cancerous pulmonary nodules at the early stage to improve the outcomes for lung cancer patients.

     
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  3. Abstract

    The anisotropic phase‐field dendritic crystal growth model is a highly nonlinear system that couples the anisotropic Allen–Cahn equation and the thermal equation together. Due to the high anisotropy and nonlinear couplings in the system, how to develop an accurate and efficient, especially a fully decoupled scheme, has always been a challenging problem. To solve the challenge, in this article, we construct a novel fully decoupled numerical scheme which is also linear, energy stable, and second‐order time accurate. The key idea to realize the full decoupling structure is to introduce an ordinary differential equation to deal with the nonlinear coupling terms satisfying the so‐called “zero‐energy‐contribution” property. This scheme is very effective and easy to implement since only a few fully decoupled elliptic equations with constant coefficients need to be solved at each time step. We rigorously prove the solvability of each step and the unconditional energy stability, and perform a large number of numerical simulations in 2D and 3D to demonstrate its stability and accuracy numerically.

     
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