 anatomical structure segmentation to pathological lesion segmentation, particularly for computed tomography (CT) images and magnetic resonance images (MRI). [23][24][25] Although numerous segmentation algorithms have been developed, there has been little work on SPECT segmentation in general and CNNs for SPECT in particular. This is also true of the non-contract, low-dose CT images that are acquired as part of SPECT/CT acquisitions for attenuation compensation.
This study aimed to develop an automated image segmentation method that can be used for 90 Y SIRT planning using pretreatment simulation based on 99m Tc-MAA SPECT/CT images. For this purpose, we developed and evaluated three CNN-based segmentation algorithms for lung and liver segmentation using non-contrast, low-dose CT images and for liver tumor segmentation using 99m Tc-MAA SPECT images.

MATERIALS AND METHODS
We used three CNN-based segmentation algorithms to segment the lungs, liver, and tumor liver independently. The lung (LungNet) and liver (LiverNet) segmentation networks were trained to segment lungs and whole liver, respectively, from low-dose CT images acquired in the 99m Tc-MAA study. The tumor segmentation network (TumorNet) was trained to segment liver tumors from 99m Tc-MAA SPECT images. The details of the dataset used in this study are explained in Section 2.1. The three networks shared the same network architecture designed to perform segmentation of 99m Tc-MAA SPECT/CT images. The details of network architecture and its implementation are explained in Sections 2.2. and 2.3., respectively.

Image acquisition
We retrospectively collected data from 56 HCC patients who underwent evaluation for 90 Y SIRT at Siriraj Hospital during 2016 and 2019. Each dataset includes 99m Tc-MAA SPECT images, CT images, and corresponding manual lung, liver, and liver tumor segmentation performed by nuclear medicine physicians. Institutional review board approval was obtained, and no informed consent was required for this retrospective analysis. For each patient, a SPECT/CT scan was performed about 1 h after injection of 4-5 mCi of 99m Tc-MAA using either a GE Discovery 670 or 670 pro system (GE Healthcare, USA) with a low-energy high-resolution collimator. SPECT acquisitions were performed in 2 FOVs to encompass the lungs and liver. The acquisition energy windows were set at 140 ± 20% keV and 120 ± 10% keV for window-based scatter correction. Sixty projections in a 128 × 128 matrix size were acquired over a 360 • angular range with a 20-s acquisition duration at each view. SPECT images were reconstructed on a Xeleris workstation (GE Healthcare, USA) using 5 iterations and 10 subsets of OSEM with CT-based attenuation correction, window-based scatter correction, and collimatordetector response modeling. The CT scan was acquired in low-dose mode (80 reference mAs, 120 kVp) during free breathing with a 3.75 mm slice thickness. Reconstructed SPECT and CT images were resampled to have the exact dimensions of 256 × 256 × 256 voxels with an isotropic voxel size of 2.20 mm.

Reference segmentation
Segmentations performed by nuclear medicine physicians served as the reference for comparison in this work. The segmentations were performed using the Dosimetry Toolkit on the Xeleris workstation. These reference segmentations include volume of interest (VOI) definitions for the lungs, liver, and liver tumor. For the lung segmentation,physicians used CT images and intensitybased semi-automatic tools provided in the software to define initial lung VOIs. Manual modification was usually performed to remove the trachea, primary bronchus, and lung base near hepatic dome from the lung VOI. For liver segmentation, the entire liver was generally segmented based on the non-contrast, low-dose CT from the MAA study. Regions of interest (ROIs) were manually drawn on CT slices and stacked to create liver VOIs.
Tumor VOIs were initially created on SPECT images using region-growing and thresholding methods; manual modification was then performed to account for the potential overlooked or over-covered tumor volumes that appeared on the fused SPECT/CT, hepatic angiography, and contrast-enhanced CT. The final segmentation results were regarded as the reference segmentation for the subsequent training and evaluation processes.

Network architecture
We achieved tumor,liver,and lung segmentation by using separate networks for (1) lung segmentation, (2) liver segmentation, and (3) tumor segmentation. All three networks shared the same network architecture (see Figure 1). Each network was comprised of an encoding path to extract features from input data and a decoding path to return to the original resolution. Between the encoding and decoding paths, skip connections were used to forward early-extracted features from encoding directly to the decoding path. The network was designed to receive a small 3D patch as input and produce a small 3D patch as segmentation output. The output patches need to be reassembled into the segmentation result of the original (full-size) image. Typically, fully convolutional network (FCN) architectures (e.g., 3D U-Net, 26 V-Net, 23 DenseVNet 25 ) use full images (or volumes) as inputs and then use pooling/unpooling (or strided convolution/deconvolution in V-Net and DenseVNet) layers to limit the number of parameters and resulting memory requirement. These layers can lead to the loss of spatial information from repeated downsampling operations. Instead, the proposed network uses sub-volumes (3D patches) as inputs. This strategy reduces the memory requirements of the network, thereby removing the need for a pooling layer. More importantly, sampling volumes into small 3D patches substantially increases the number of training examples without the need for data augmentation. Similar to DenseNet and DenseVNet structures, the encoding path contains dense connectivity to support gradient propagation and feature reuse. However, the proposed network does not use pooling layers or strided convolution for downsampling. The decoding path upsampled the feature map using only deconvolution layers (also known as transposed convolution) instead of bilinear upsampling in DenseVnet.
In the encoding path, there are 16 convolutional layers, where each layer was defined as a composite function consisting of 3D convolution, batch normalization (BN), 27 and a Parametric Rectified Linear Unit (PReLU) activation function. 28 The convolution was responsible for producing a feature map by the convolution of the input with the encoder kernel. The kernel contained the weights (also known as learnable parameters) to be learned during the network training. The kernel weights represent the structure or feature that the kernel will detect. The number of kernels in the convolutional layer defines the number of output feature maps. Batch normalization was used to normalize the convolution's feature map to the standard Gaussian distribution. Batch normalization helps in speed up training by allowing use F I G U R E 1 The schematic representation of the proposed convolutional neural network architecture of high learning rates without overfitting. 27 The PReLU activation function was used to increase non-linearity in the output that has been computed using linear operations during the convolution. 28 The encoding path can be divided into four stages. Each stage contains four convolutional layers: one in the convolutional unit and three in the dense block. The convolutional unit allows the network to increase the receptive field of the feature maps being used as input for subsequent layers. The output of the l-layer convolutional unit (C l ) can be expressed as: where C l−1 is the output of the previous layer or the input volume in the first layer, and H l is a composite function consisting of convolution, PReLU activation function, and batch normalization, as previously described.
We designed each convolutional unit to perform convolution using a volumetric kernel of 3 × 3 × 3 voxels with stride one and no padding applied to the input; stride refers to the amount of movement between consecutive applications of the kernel to the input volume. Each convolutional unit had an output size of two voxels smaller and a number of kernels two times larger than the previous stage. The architecture was designed not to include pooling operations to avoid the loss of spatial resolution of the feature map. However, due to memory constraints, we allowed the convolutional unit to gently reduce the feature map's size as the number of feature maps increased during passage through network. The numbers and sizes of kernels for each layer are shown in Table 1. At each stage, following the convolutional unit, we used a dense block to extract further information. Motivated by Gibson et al. 25 and Huang et al., 29 each dense block contained three convolutional layers; the input of each layer was the concatenated output of all preceding layers within the same block. The concatenated feature map helps increase variation in the input of subsequent layers by allowing the feature map learned by different layers to be accessed by subsequent layers. This encourages feature reuse throughout the dense block and leads to a more compact network that is easier to train and highly parameter efficient. 29 The output of the l-th layer within a dense block (D l ) can be expressed as: where [D 0, D 1, …, D l−1 ] refer to the concatenation of the feature maps produced in the preceding layers 0, 1, …, l − 1, and H l is a composite function: convolution, PReLU, and batch normalization. The convolution operation in a dense block was performed using a volumetric kernel of size 3 × 3 × 3 voxels with stride one. However, in contrast to the convolutional unit,where padding was not applied to the input. Instead, each side of the input was zero-padded by one voxel to keep the size of the output feature map the same as its input