## 2 Materials and Methods
### Training and Internal Testing of the Model
#### 2.2.2 Classification of Segmented Aortic Arch and Supra-Aortic Vessels  
The segmented aortic arch and supra-aortic vessels (for both semiautomatic segmentation and fully automatic segmentation) were processed by the following steps: (i) the three-dimensional (3D) segmentation mask was converted into a 3D mesh; (ii) the 3D mesh was rotated on the longitudinal axis in order to maximize the extension of the aortic arch projection on a two-dimensional (2D) plane; (iii) the 2D projection including the maximum extension of the aortic arch was saved in a 2D square image centered on the aortic arch (square image of the aortic arch, SIAA); and (iv) each SIAA was labeled by radiologists as CILCA or non-CILCA and used as a reference standard to train, tune, and internally test the classification model. Three different CNN architectures were considered for the model: ResNet-50 [27], SqueezeNet [28], and DenseNet-201 [29], three CNNs with deep architecture composed of 50, 18, and 201 layers of neurons, respectively. Each of these CNNs had been previously trained on over a million images from the ImageNet database [30] to classify images into 1000 object categories. During training, such CNNs were able to learn a rich feature representation of the input image classes. Then they can use these feature representationsto classify new images as belonging to one of the input classes' layers. It must be noted that these three CNNs emerged among the best performing pre-trained architectures in a variety of applications in the medical imaging domain, in particular for images with features similar to those used in our study (e.g., [PERSON] et al., 2017; [PERSON] et al., 2020; [PERSON] et al., 2020; [PERSON] et al., 2021; [PERSON] et al., 2020; [PERSON] et al., 2021) [31; 32; 33; 34; 35; 36]. ResNet-50 preprocesses the input image by one convolutional layer (7 \(\times\) 7) and one max pooling layer (3 \(\times\) 3). Then, the preprocessed image is input to four blocks of layers of similar structure, including a different number of 3 \(\times\) 3 convolutional filters providing different features' map size. Each block filters the preprocessed image and sends forward the filtered image to the next block of convolutional filters. Moreover, some blocks skip the preprocessed image to the next block. This operation is called \"skip connection\" and represents one hallmark of ResNet architectures solving the vanishing gradient problem that implies that classifier performance gets saturated rapidly in extremely deep architectures. The last layers of ResNet-50 consist of one average pooling layer and one fully connected layer followed by a support vector machine (SVM) classifier layer. SqueezeNet preprocesses the input image by one convolutional layer (7 \(\times\) 7) and one max pooling layer (3 \(\times\) 3). Then, the preprocessed image is input to nine \"Fire modules\" blocks of similar structure, composed of one 1 \(\times\) 1 convolutional filter feeding into an expand layer that has a mix of 1 \(\times\) 1 and 3 \(\times\) 3 convolution filters. Each block filters the preprocessed image and sends forward the filtered image to the next block of convolutional filters. The last layers of SqueezeNet consist of one convolutional layer (1 \(\times\) 1), one average pooling layer, and one classification layer. DenseNet-201 preprocesses the input image by one convolutional layer (7 \(\times\) 7) and one max pooling layer (3 \(\times\) 3). Then, the preprocessed image is input to 112 blocks of layers of similar structure, grouped in 4 larger \"dense\" blocks (6 blocks in the first dense block, 16 in the second one, 48 in the third one, and 32 in the last one). Each dense block includes a different number of 3 \(\times\) 3 convolutional filters, but dimensions within each dense block are the same, keeping features' map size constant inside the single dense block. Moreover, all the blocks of a dense block have direct access to each other.