# Detection and Localisation of Abnormal Parathyroid Glands: An Explainable Deep Learning Approach
## 2 Materials and Methods
### VGG-Based Three-Path CNN (ParaNet)  
CNNs are capable of portraying high-level abstract representations from non-linear information. CNNs belong to the broader area of deep neural networks [17]. CNNs utilise convolution layers to process and filter the input data distributions. Convolution layers transform the input data distributions and extract many image-related features [18]. Auxiliary layers, such as pooling layers, aid in dimensionality reduction, overfitting prevention, regularisation, and more [19]. In classification problems, the extracted feature maps are commonly processed by densely connected layers that filter out the irrelevant features based on a pre-defined desired outcome.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Information** & **Value** \\ \hline Date & 2010-2021 \\ Total Number of Subjects & 632 \\ Total Number of Abnormal PGs & 545 \\ Male Subjects & 19\% \\ Female Subjects & 81\% \\ Average Age & 57.8 years \\ Primary HPPT & 607 \\ Secondary/tertiary HPPT & 25 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Characteristics of the study’s dataset.  
The problem of abnormal PG identification is addressed by cross-examining three images, as presented earlier. To this end, a three-path CNN is suggested. The MIBI early phase image, MIBI late phase image, and the 99 mTc04 thyroid image are processed independently by the three paths of the network, and the extracted features from each path are fused at the later processing stages. Each path is responsible for extracting meaningful information from a single input image. Therefore, the overall approach contains three independent CNN components.  
For each CNN component, the VGG architecture with 19 convolutional layers (VGG19) is suggested (Figure 1). VGG19 is a very consistent and successful CNN for relevant medical imaging tasks. Initially, this network is designed to perform multi-class classification on non-medical images. However, its uniform architecture and feature extraction capabilities have also made it suitable for medical imaging tasks.  
VGG19 has been employed, with the final layer being trainable. The rest of the layers utilise pre-defined weights defined by initial training on non-medical images [20]. We argue that this conception can reduce the number of trainable parameters significantly. The Triple-VGG19, called ParaNet, contains 3,079,628 trainable parameters and 52,999,836 non-trainable. At the top (the last convolutional layer) of each VGG19 component, a global average pooling layer has been applied. The input image size (350 \(\times\) 350 \(\times\) 1) is incrementally reduced to (21 \(\times\) 21 \(\times\) 512), where 512 represents the number of filters of the last convolutional layer. The output of the average max pooling layer is connected to a dense layer of 750 nodes, which is followed by a dropout layer that randomly disconnects half of the nodes. Next, a dense layer of 256 nodes is connected to the previous layer, and a final densely connected layer of two nodes (as many as the output classes) follows. The entire Python 3.6+ code is available on GitHub ([[https://github.com/apjohndim/Parathyroid-Initiative/blob/main/3P-VGG19-Paper.py](https://github.com/apjohndim/Parathyroid-Initiative/blob/main/3P-VGG19-Paper.py)]([https://github.com/apjohndim/Parathyroid-Initiative/blob/main/3P-VGG19-Paper.py](https://github.com/apjohndim/Parathyroid-Initiative/blob/main/3P-VGG19-Paper.py)) accessed on 11 August 2022). The parameters and the hyperparameters of ParaNet are summarised in Table 2. A visual overview of ParaNet is presented in Figure 1.  
Figure 1: ParaNet topology.