# Spider U-Net: Incorporating Inter-Slice Connectivity Using LSTM for 3D Blood Vessel Segmentation
## 1 Introduction
There are attempts to incorporate a recurrent neural network (RNN) into the U-Net baseline to make the model learn additional information through the z-axis [19; 20]. Generally, for 3D medical imaging, the region-of-interest, such as the tumor, lesion, and organ, is spread through several image slices and the nearby images are visually similar to each other. When the 3D volume is interpreted as the image sequence, they form connectivity through the z-axis and it can be extracted by adding an RNN, which is designed to learn features of the consecutive data [21]. A fully convolutional network (FCN)-RNN [20] is a representative architecture for 3D medical image segmentation that arranges arbitrary RNN components after the arbitrary fully convolutional network (FCN) baseline, which is a type of CNN for semantic segmentation with a encoder-decoder structure [22]. FCN-RNN is implemented by adopting convolutional long short-term memory (LSTM) after the customized U-Net. Using an RNN has been demonstrated to be suitable when dealing with 3D medical images achieving a better performance than 2D U-Net and 3D CNN. For 3D BVS, we believe that emphasizing inter-slice connectivity with the RNN could be more effective for the following two reasons. First, the blood vessel in the 3D modality is represented with small cross-sectional areas of less than 1% of an image. This severe lack of information about the blood vessel causes a class imbalance and causes the training stage to be dominated by the non-vessel area, resulting in a tendency to produce false negative pixels [23]. Augmenting information about the blood vessel with adjacent slices would be helpful to alleviate this problem. Second, the blood vessel has the intrinsic characteristic of strong inter-slice connectivity because the prime role of the blood vessel is to convey fluid to the whole body without leakage. An RNN can be effectively trained when dealing with datasets with this characteristic. In this context, we propose Spider U-Net--a novel 2D-based deep learning framework for 3D BVS. It segments blood vessels by emphasizing the inter-slice connectivity using an RNN. Spider U-Net is composed of two paths: the warp path and the weft path. The warp path is formed by stacking several 2D U-Net baselines in parallel to be able to process consecutive axial image slices simultaneously. It extracts spatial features of 2D images one by one. The weft path is implemented by incorporating convolutional LSTM between the encoder and the decoder of the warp path. It additionally learns the connectivity of extracted spatial features through the z-axis. In consequence, the prediction masks are inferred not only by spatial features but also the inter-slice connectivity of adjacent slices. We also suggest a training strategy named striding stencil (SS) to augment data and to train the stable model. Finally, we evaluate Spider U-Net on three 3D BVS datasets that vary in terms of modality and target vessel. Previous representative models re-implemented with an equal baseline are compared with our framework to assess the effectiveness of Spider U-Net.