## 2 Materials and Methods
### Nested Model Architectures  
Three models, referred to as UNet, LSTM-UNet, and UNet-LSTM-UNet, were designed and examined. To sequentially evaluate the conferred benefit from each architecture's design, the models were nested such that LSTM-UNet incorporated the UNet architecture, and UNet-LSTM-UNet incorporated the LSTM-UNet architecture. The UNet architecture was selected as a base architecture as is commonly done for medical image segmentation, including for previous OCT and retinal vascular imaging applications [23; 24; 32]. Our standard UNet received a 2D image as input and output a 2D image following a process comprised of an encoder, skip connections, and a decoder. The encoder used convolutional layers to extract features at variable input resolutions. Max-pooling during the encoding process shrank input resolution, further allowing identification of segmentation features at different scales. At each resolution, skip connections were used to concatenate the convolution layer output to a corresponding resolution in the decoding pathway. The decoder uses these convolution outputs along with the up-sampled images as inputs for deconvolution layers to generate the resulting segmentation output following sigmoid activation. The resulting output has two channels, one for vessel activation and one for background activation. Our base model had a network depth of 3 utilizing skip connections at each layer (Figure 1A). We also performed batch normalization and transformation with a leaky rectified linear unit (slope = 0.01) at each convolutional layer. The LSTM-UNet is our proposed 3D-2D deep learning framework that uses bidirectional convolutional LSTM networks to incorporate the 3D context (i.e., inter-slice connectivity) from 3D input slices with unfixed depths to output 2D segmentation maps. LSTM networks are a form of RNNs that extend base RNN's ability to model sequential data by updating a hidden state representation with input-to-state and state-to-state operations, namely an input gate, output gate, forget gate, and cell-state, which can better account for long-term sequential data [33]. Importantly, a LSTM model allows for varying numbers of input slices, which is necessary for our task, as the volumes containing each vessel plexus can vary in size when considering retinal layer thickness variability across patient populations [27, 28]. While the standard LSTM classically uses fully connected layers for language processing applications, for our purposes, we employed a convolutional LSTM, which uses convolutional structures in the input-to-state and state-to-state transitions to more efficiently handle sequential spatial data (Figure 1B) [34]. Furthermore, to incorporate the inter-slice context from both the previous and following slices, we presented slices to two distinct LSTM units in forward (top-to-bottom) and reverse (bottom-to-top) order and concatenated the outputs to generate a bidirectional convolutional LSTM (Figure 1C) [35]. In our LSTM-UNet architecture, we used bidirectional LSTM units at three input resolutions during image encoding (Figure 3). The encoded outputs were concatenated with up-sampled images during decoding, eventually resulting in a single channel 2D output that could be fed into a UNet unit. Figure 1: Architecture schematics (**A**) UNet architecture with a depth of three layers (Conv2d = two-dimensional convolutional operation, batch normalization (BatchNorm), rectified linear activation (ReLU) function) (**B**) convolutional LSTM (cLSTM) unit schematic demonstrating the incorporation of previous cell state memory and output in the generation of current cell state and output (**C**) Bidirectional cLSTM (Bi-cLSTM) architecture schematic with forward and reverse cLSTM as distinct units.