On the applications of neural ordinary differential equations in medical image analysis

Abstract Medical image analysis tasks are characterized by high-noise, volumetric, and multi-modality, posing challenges for the model that attempts to learn robust features from the input images. Over the last decade, deep neural networks (DNNs) have achieved enormous success in medical image analysis tasks, which can be attributed to their powerful feature representation capability. Despite the promising results reported in numerous literature, DNNs are also criticized for several pivotal limits, with one of the limitations is lack of safety. Safety plays an important role in the applications of DNNs during clinical practice, helping the model defend against potential attacks and preventing the model from silent failure prediction. The recently proposed neural ordinary differential equation (NODE), a continuous model bridging the gap between DNNs and ODE, provides a significant advantage in ensuring the model’s safety. Among the variants of NODE, the neural memory ordinary differential equation (nmODE) owns the global attractor theoretically, exhibiting superiority in prompting the model’s performance and robustness during applications. While NODE and its variants have been widely used in medical image analysis tasks, there is a lack of a comprehensive review of their applications, hindering the in-depth understanding of NODE’s working principle and its potential applications. To mitigate this limitation, this paper thoroughly reviews the literature on the applications of NODE in medical image analysis from the following five aspects: segmentation, reconstruction, registration, disease prediction, and data generation. We also summarize both the strengths and downsides of the applications of NODE, followed by the possible research directions. To the best of our knowledge, this is the first review regards the applications of NODE in the field of medical image analysis. We hope this review can draw the researchers’ attention to the great potential of NODE and its variants in medical image analysis.