Patients were retrospectively and consecutively recruited from Ruijin Hospital (Shanghai, China) from January 2015 to December 2019. Inclusive criteria were as follows: 1) pathologically confirmed as pT3 or pT4 gastric adenocarcinoma; 2) underwent DECT scan less than one week before confirmed PM by laparoscopy, lavage cytology or surgery; 3) no previous anticancer treatment; 4) no previous abdominal surgery or peritonitis. Exclusive criteria were as follows: 1) undetected primary tumor on CT imaging; 2) unsatisfied quality of images due to insufficient stomach distention or motion artifact; 3) concurrent cancers. A total of 239 patients enrolled in this study (70 females; mean age, 62.9 years old, from 27 to 85). Patients with suspicious peritoneal implants or ascites during surgery were further evaluated by pathologists through biopsy slices or lavage cytology. The ultimate confirmation of PM relied on the consensus between involved pathologists and surgeons, according to the AJCC (American Joint Committee on Cancer) guidelines.

Finally, 65 patients and 174 patients were confirmed as PM and non-PM, respectively. Those patients were divided into a training cohort (n = 160) and a testing cohort (n = 79) at a ratio of 2:1 according to computer random. Baseline clinical factors included location, tumor size (cm) and depth of tumor invasion (cT) of the primary tumor, lymph node status (cN), differentiation status, Bormann type and levels of carcinoembryonic antigen (CEA), carbohydrate antigen 125 (CA125) and carbohydrate antigen 199 (CA199). The definitions for those clinical factors are implemented in Supplementary Material . The flowchart for patient recruitment and framework for the study are presented in Figures 1 and 2 .

All patients underwent DECT scan less than one week before confirmed PM by either of two scanners (Siemens SOMATOM Definition Flash or SOMATOM Force, Siemens Healthineers) after fasting overnight. Images from portal-venous and delayed phases were processed by dual-energy software (Syngo.via, Version VB10, Siemens Healthineers) to acquisition 120-kV equivalent mixed images. The imaging protocol and dual-energy post processing were described in our previous study (27) and detailed information is presented in Supplementary S2 . Then the images were used for post-processing by delivering to a dedicated workstation with dual-energy software (Syngo.via, Version VB20, Siemens Healthineers). Apart from the mixed images, the iodine-uptake (IU) images for portal-venous phase and delayed phase were reconstructed and obtained from the dual-energy datasets (28). The mixed images and the IU images based on both portal-venous phase and delayed phase were ultimately acquired for further delineation and analysis.

For iodine concentration images, iodine quantitation was standardized in an in-house software (iodine standardization, Syngo via). The purpose of iodine standardization was to reduce the influence of technical or physiological differences resulting from variational cardiac output and phase time when loading iodine within tissues (29). A circular ROI inside the abdominal aorta was independently outlined for individuals on the portal-venous phase and delayed phase from the IU images, omitting calcified plaque secondary to atherosclerosis. The rest tissues in this image slice were used as the background to compare with the reference iodine concentration from the abdominal aorta (nIC = ICbackground/ICaorta). The standardized IU images generalized were then used for masking and analyzing.

The segmentation was completed by one senior radiologist with ten years of experience in abdominal imaging, who was aware of the gastric tumor but blinded to the clinical and pathological information. The delineation was performed using an open-source software 3d-slicer (version 4.10.1) on the mixed images on the portal-venous and delayed phases, respectively. Two regions of interest (ROIs), including the peritoneal area and the primary tumor, were independently segmented. For the ROI of the primary tumor, the largest slice of the tumor on the axial image was manually segmented along with the edge of the tumor, avoiding gastric cavity and perigastric fat. For the peritoneal ROI, the delineation was performed according to abdominal regions, which consisted of the upper abdomen, the middle abdomen and the lower abdomen. The anatomical landmarks of the three regions included the upper liver, the lower costal arch, the upper sacroiliac joint and the pubic symphysis. Peritoneal ROIs were segmented at the middle slice of each abdominal region. The peritoneal area on the largest slice of the primary tumor was also included. As a candidate indicator for PM, ascites was also segmented if there was any in the peritoneal cavity. Therefore, the peritoneal ROI for each patient included four slices. The peritoneal ROI was semi-automatically segmented by setting a priori threshold ranging from -150HU to 50HU. The images along with the ROI were in register to the IU images to wipe off potential vessels in the peritoneal area. The ROIs delineated on the mix images were also matched to the IU images, guaranteeing they shared with the same slices. Therefore, for mixed or IU images, each had four ROIs (two on the portal-venous phase and two on the delayed phase).

Before feature extraction, all images underwent uniform preprocessing, including resampling and filtering (see Supplementary S3 ). Radiomics features were firstly extracted from the original images and then extracted from the filtering images. Finally, there were 1691 and 1226 radiomics features extracted from the ROI of the peritoneal area and the primary tumor, respectively. All radiomics features were in accordance with the image biomarker standardization initiative (30). Detailed information on feature extraction is implemented in Supplementary S3 .

We performed a reliability test to guaranteeing the reproducibility and robustness of the radiomics features. Sixty patients were randomly selected and one junior radiologist with five years of experience in abdominal imaging repeated the segmentation aforementioned. Given the same ROI of the IU and mixed images, we chose the mixed images for reliability analysis. Intra-class coefficient (ICC) was used to evaluate the reliability between the two radiologists. Radiomics features with ICCs above 0.75 were considered as good reliability.

To overcome potential overfitting, a step-wise process for feature selection was performed in the training cohort. First, Boruta was used to choose relevant features to peritoneal status. Boruta is a wrapper algorithm that selects relevant features by comparing the original importance of attributes, estimated using their permuted copies (31). To avoid randomness, the importance of each feature was calculated with 100 iterations and then a mean importance was generated. Features with the highest mean importance were defined as the confirmed features and remained. The features selected from Boruta would have highly relevant and redundant. Therefore, in the second step, we calculated the Spearman correlation coefficients for those features. Highly correlated features were clustered into the same subgroup using unsupervised clustering algorithm and feature with the highest mean importance in each subgroup was considered as the representative feature for further modeling. Consequently, features selected from the step-wise method would have high contribution and low redundancy and were included in the following modeling.

Radiomics features selected from IU and mixed images were independently used for modeling (the R_IU model and the R_MIX model) to discriminate PM and non-PM in the training cohort. To select the optimal radiomics model, we also built a combined model (the R_comb model) integrating IU and mixed features. Random forest (RF) algorithm with 10-fold cross-validation parameter tuned by grid search approach was implemented for model establishments. The performance of the radiomics models was then validated in the testing cohort. The weight of the features in each radiomics model were evaluated by importance ranking via the Gini impurity using RF.

The optimal radiomics model was in comparison with a clinical model constructed by clinical risk factors. The performance of human experts to assess PM was also recorded for all patients. Two senior radiologists who major in abdominal imaging for more than 10 years of experience independently reevaluated the peritoneal status based on CT imaging. They have informed the patients of GC but aware of the clinical and pathological information. The consensus between the radiologists was recorded and if there was any disagreement, the final decision was made by the discussion. The performance of the radiomics model, the clinical model, human experts was compared in both cohorts.

The goodness of fit for those models was evaluated to observe the agreement between the actual probability and the predicted probability made by those models. Decision curve analysis (DCA) was implemented to show the net clinical benefits of all models to predict peritoneal status.

Continuous variables were compared by independent-sample t-test or Mann-Whitney U test based on their distribution. Categorical variables were compared using χ² or Fisher’s exact test. RF was tuned by Grid search with 10-fold cross validation. Discriminative metrics for peritoneal status included receiver operating characteristic (ROC) curve, area under the curve (AUC), accuracy, sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV). 95% Confidence interval (CI) for each metrics was also recorded. AUCs comparison was examined by the Delong test. The goodness of fit for models was assessed and the deviation was evaluated by the Brier score. The consensus between the radiologists to evaluate peritoneal status was estimated by the kappa coefficient. The strength of kappa coefficients with 0 to 0.20, 0.21 to 0.40, 0.41 to 0.60, 0.61 to 0.80 and 0.81 to 1 was interpreted as slight, fair, moderate, substantial and almost perfect. All statistical analysis was performed with R (version 3.6.0) and Python (version 3.7). Package resources are listed in Supplementary Table S1 . A significant difference was achieved if a two-side p-value < 0.05.

No selective bias was found in terms of the positive rate of PM between the training cohort and the testing cohort (26.9% vs. 27.8%, p = 0.874). Age and gender also presented no significant bias between the two cohorts (p = 0.913 and 0.848, respectively). For patients in the training cohort, gender, ascites, tumor size, differentiation status, and Bormann type showed a significant difference to discriminate the peritoneal status (all p < 0.05). For patients in the testing cohort, age, ascites, tumor size, invasion of tumor depth, and differentiation status showed statistically different to predict the peritoneal status (all p < 0.05). The other clinical factors indicated no significant difference in both cohorts (see Table 1 ). Indices that showed a significant difference in the training cohort were considered as clinical risk factors and were used for modeling using the multivariate logistic regression.

For features extracted from the portal-venous phase, 213 and 138 radiomics features showed robust with an ICC higher than 0.75 for the peritoneal area and the primary tumor, respectively. As for features from the delayed phase, 523 and 189 radiomics features showed robust with an ICC higher than 0.75 for the peritoneal and the primary tumor, respectively. Therefore, for the IU and mixed images, each had 1063 reliable radiomics features for further analysis.

There were 31 and 37 confirmed features after Boruta analysis from IU and mixed images, respectively ( Figures 3A, B ). Given high redundancy among those features, Spearman correlation analysis was performed. Unsupervised clustering indicated 14 and 3 subgroups generated for features from the IU and mixed images ( Figures S1 and S2 ). Finally, 14 and 3 features were selected for each image set by the mean importance of each feature. After tuned by RF, all the 14 radiomics features from IU images were used for RF modeling to construct the R_IU model. Similarly, the three features from mixed images were finally used to establish the R_MIX model through the RF algorithm.

To build the R_comb model, we further integrated the 14 features from the IU images with the three features from the mixed images. The correlation coefficients of those 17 features were also calculated and no redundancy was observed ( Figure S3 ). After tuned by RF, eight features were considered as important and used for modeling the R_comb model.

Consequently, the radiomics features selected by the step-wise method showed little redundant and highly important. For each model, the most important feature was coincidentally from the peritoneal area. The importance ranking of those features in each model are implemented in Figure 4 .

The R_IU model showed power ability to predict PM for the gastric tumor in the training cohort, achieving an AUC of 0.981 (95%CI, 0.961-0.995) and accuracy of 95%. It also presented a considerable sensitivity and specificity (90.7% and 96.6%, respectively). This model showed good generalization by applying it to differentiate peritoneal status in the testing cohort, with an AUC of 0.967 (95%CI, 0.931-1). No overfitting was observed for the R_IU model in the testing cohort (p = 0.528). The other discriminative metrics also demonstrated a good diagnostic value of the R_IU model in the testing cohort. Detailed information on discriminative metrics is implemented in Table 2 .

The R_MIX model showed inferior to the R_IU model in both cohorts. For patients in the training cohort, the R_MIX model reached an AUC of 0.917 (0.860-0.974) and an accuracy of 94.4%. For patients in the testing cohort, the R_MIX model reached an AUC and accuracy of 0.894 (0.800-0.988) and 84.8%, respectively. The R_IU model was significantly better than the R_MIX model to discriminate PM in the training cohort (p = 0.034).

The R_comb model did not improve the performance compared with the R_IU model in both cohorts, with AUCs of 0.955 (95%CI, 0.904-1) and 0.961 (95%CI, 0.918-1), respectively. Other information on discriminative metrics of the R_comb model is implemented in Table 2 .

Overall, we considered the R_IU model as the optimal radiomics model and used it as the representative for further analysis.

ROC curve of each model in both cohorts was visualized in Figures 5 A, B . Gender and ascites were indicated as independent risk factors in the multivariate logistic regression (p = 0.025 and 0.018, respectively). The clinical model showed the significantly poor performance to predict peritoneal status compared with the R_IU model in both cohorts (the training cohort, AUC: 0.847 vs. 0.981, p < 0.001; the testing cohort, AUC: 0.785 vs. 0.967, p = 0.005).

The consensus between the two human experts was almost perfect, with a kappa value of 0.83. There were 10 (5.7%) and 31 (47.7%) patients misclassified by human experts in the non-PM and PM groups, respectively. For patients in the training and testing cohorts, there were 13 and 31 patients demonstrating radiological suggestion of peritoneal metastasis, respectively. The human experts reached AUCs of 0.733 (95%CI, 0.654-0.812) and 0.732 (95%CI, 0.623-0.842) to evaluate PM in the training and testing cohorts, respectively. The sensitivity and specificity of human experts in the training cohort was 53.5% (37.8%-68.5%) and 93.2% (86.6%-96.8%), respectively. The sensitivity and specificity in the testing cohort was 50% (28.8%-71.2%) and 96.5% (86.8%-99.4%), respectively. The R_IU model showed significantly more power to differentiate peritoneal status than the human experts did in both the cohorts (both p < 0.001).

The DCA curve showed similar good clinical benefit for patients if preoperatively diagnosing them using the R_IU model and the R_comb model, which were better than the other models ( Figure 5C ). Analysis of goodness of fit also demonstrated the R_IU model was robust to evaluate peritoneal status in both cohorts (Brier score = 0.051 and 0.055, respectively).