## 2 Materials and Methods
### Radiomics Feature Extraction  
In this study, the tumor features were obtained from 2D and 3D pre-therapy CT slices. Each segmented tumor is depicted on a number of CT slices. The central slice has the largest 2D area, which was identified by radiologists. Accordingly, we first extracted the quantitative features only from the central slice to generate a 2D feature pool. We sequentially added the adjacent slices above and below the central slice until the tumor disappears. After adding one adjacent slice, we will create the corresponding incomplete 3D tumor feature pool (Table 2). We continued the generation of the corresponding incomplete 3D feature pool until the tumor disappears. Before the feature computation, we developed a computer-aided image analysis scheme to segment each individual tumor from the CT images. The tumor segmentation procedure started at the central slice where the tumor was marked by a radiologist according to RECIST criteria [20]. The method then sequentially segmented the tumors on the adjacent slices until the tumor disappeared. For each slice, the tumor was segmented by a hybrid algorithm, which consists of two core algorithms: a region growth approach with adaptive thresholds [21] and a dynamic contour-seeker method [22]. The performance of this algorithm was assessed and validated by a number of our previous studies [23; 24; 25; 26]. Given that metastatic tumors occurred on a number of human organs with high heterogeneity, the automated segmentation may not be able to generate the tumor contour with satisfactory accuracy. Thus, these segmentation results were visually \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Patients’ Characteristics**} & \multicolumn{3}{c}{**6-Month PFS**} & \multirow{2}{*}{_p-Value_} \\ \cline{2-3} \cline{4-4}  & **Responders** & **Non-Responders** & \\ \hline Number of patients & 130 & 58 & \\ \hline Age & 63 \(\pm\) 10 & 61 \(\pm\) 10 & 0.24 \\ \hline Number of tumors & 272 & 133 & \\ \hline Average tumor diameter (mm) & 31.3 \(\pm\) 19.3 & 31.5 \(\pm\) 16.4 & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Information of the patients in our dataset. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Image Type**} & **2D** & **3D** \\ \hline Original & 104 & 110 \\ \hline Exponential & 93 & 93 \\ \hline Gradient Magnitude & 93 & 93 \\ \hline Local binary pattern & 93 & 279 \\ \hline Logarithm & 93 & 93 \\ \hline Square & 93 & 93 \\ \hline Square root & 93 & 93 \\ \hline Wavelet & 741 & 741 \\ \hline Total & 1403 & 1595 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Number of features calculated from original image and other processed versions of the image. evaluated by experienced researchers and were manually corrected if needed. The entire scheme was developed as an ImageJ plugin [27], which was equipped with a user friendly graphical user interface (GUI) to visualize the 2D and 3D tumors. Based on the segmented tumors, we generated the 2D and 3D feature pool using the following methods [11; 12]. The feature computation scheme is based on pyridomics [11], an open source platform that calculates features in accordance with the definitions in the imaging biomarker standardization initiative (IBSI) [12]. The general flowchart of the calculation is described in Figure 1. In this module, the segmented tumor was first processed by a number of operations including exponential, gradient magnitude, local binary pattern (LBP), logarithm (Log), square, square root, and wavelet (Coif1) filters. Next, the radiomics features were then calculated on the processed images as well as the original image. The features can be divided into 3 categories, i.e., geometric, density, and texture features (the details can be found in Supplementary Materials), which describe the tumor in various aspects [28]. Table 2 shows a breakdown of the number of features calculated for each image class, with the number of features per class ranging from 93 to 741.