This study was approved by the Institutional Review Boards of two participating hospitals. Requirement for informed consent was waived due to the retrospective nature of the study.

Diagnostic criteria for PBM and chronic cholangitis

PBM was diagnosed preoperatively based on MRCP or CT showing convergence of the pancreatic and bile ducts outside the duodenal wall and abnormally long common channel (> 5 mm), and confirmed by intraoperative cholangiography (IOC) in all cases [5, 16].

Chronic cholangitis was diagnosed based on chronic inflammation of the bile duct wall on pathological examination under local protocol. Features that were considered included hyperemia, edema, inflammatory infiltration, exfoliation of the mucous epithelium, and proliferation of fibrous tissue [17].

Patients

The initial screening identified a total of 213 PBM children during a period from January 1, 2015 to December 31, 2021.The inclusion criteria were as follows: (1) possession of pathological results from surgical specimens; (2) completion of surgery within 1 month after MR examination; and (3) availability of complete clinical data. The exclusion criteria were as follows: (1) incomplete clinical or pathological information; (2) patients diagnosed by CT scan alone, without MR scan; or (3) patients whose radiomics features could not be successfully extracted from the MR images. In total, 144 cases were included in the final analysis (Fig. 1).

Fig. 1

Patient recruitment and study design

Due to the small number of cases at Xuzhou Children’s Hospital (n = 26), we did not adopt the conventional approach of using cases from one site as training cohort and cases from the other site for external validation. Instead, the 144 cases were randomly split at a 7:3 ratio to a training and a validation cohort. Clinical features considered as candidate variables for the model included sex, age (in years), abdominal pain, jaundice, fever, vomiting, liver dysfunction, pancreatitis, and elevated white blood cell (WBC) count. Liver dysfunction was defined as an elevation in serum aspartate aminotransferase (AST) and serum alanine aminotransferase (ALT) levels, while pancreatitis was defined as a preoperative serum amylase or lipase level of more than threefold the normal upper limit.

Image acquisition, segmentation, and feature extraction

All MR images were retrieved from the picture archiving and communication system (PACS) for further analysis. Regions of interest (ROIs) of the T2W images and radiomics feature extraction were performed using 3D Slicer software (version 4.10.2, https://www.slicer.org). The procedure of MR image acquisition, image segmentation, and feature extraction is described in Additional file 1. The radiomic analysis workflow is shown in Fig. 2.

Fig. 2

Workflow of the radiomics analysis

Imaging analysis

Two pediatric radiologists (L.ZH., with 3 years of experience in pediatric radiology; and Y.Y., with 9 years of experience in pediatric radiology) performed initial analysis of all images. They were blinded to the results of pathological diagnosis of cholangitis. The following MR imaging features of PBM were analyzed: protein plug (present or not), ascites (present or not), Todani classification of congenital biliary dilatation (CBD) (I, IVa), and Komi classification of PBM (I, II, III). Disagreements were resolved by discussion and consensus.

Selection of clinical variables

Univariate logistic regression was used to screen for demographic and clinical variables. Variables with p < 0.1 in the univariate regression were entered into the multivariate regression analysis. Results are shown as odds ratios (ORs) and 95% confidence intervals (CIs).

Selection of radiomics features and Rad‑score building

All imaging features were normalized using z-score normalization before feature extraction. To minimize the impact of dimensionality, selection of features was conducted in 3 steps using the training cohort. First, inter- and intra-observer analyses were used to assess the features’ reliability and reproducibility [18]; those with ICCs < 0.75 were eliminated from further consideration. Second, features with ICCs > 0.75 were tested using one-way analysis of variance (ANOVA) to select potentially important ones. Finally, LASSO regression then was conducted to eliminate redundant and irrelevant features [19]. Additionally, Spearman correlation coefficients were calculated for the features selected by LASSO to avoid the underlying severe linear dependence. When the value is less than 0.9, we considered that there is no correlation between the selected features [20].

In order to achieve a high and robust performance of classification, three machine learning classifiers, logistic regression (LR), support vector machine (SVM), and decision tree (DT), were implemented. The performances of the radiomics signatures that we developed were then validated for both the training and validation cohorts according to the area under the receiver operator characteristic (ROC) curve. The Delong test was used to compare the performance of three different machine learning classifiers.

To simplify the model, a Rad-score (the sum of the products of the selected features and their corresponding coefficients) was used for subsequent analysis.

Model development

Diagnostic models were developed based on clinical features alone, Rad-score alone, and clinical features plus Rad-score. Performance of the models (based on the clinical features alone, Rad-score alone, and combined model) was compared using the area under the receiver operator characteristic (ROC) curve. The Delong test was used to compare the performance of three different models. Hosmer–Lemeshow test was used to assess the goodness-of-fit of the models. Decision curve analysis (DCA) was conducted to assess the clinical and combined models through calculating the net benefit at different threshold probabilities.

Radiomics nomogram building

To provide clinicians with an individualized and easy-to-use tool for the preoperative diagnosis of the occurrence of chronic cholangitis in PBM patients, the combined model was visualized as a radiomics nomogram. A radiomics nomogram score (Nomo-score) was calculated based on the significant clinical features and the Rad-score.

Statistical analysis

Statistical analysis was performed using SPSS 26.0 software (IBM) and the R programming language (ver. 4.1.2, http://www.r-project.org). Clinical characteristics were measured based on the variable type. The Shapiro–Wilk’s test was employed to assess the normality of the distributions, and homogeneity of variance (homoscedasticity) was assessed using Bartlett’s test. Differences in continuous variables were assessed by t-test or Mann–Whitney U test. Categorical variables were analyzed using Chi-squared or Fisher’s exact-probability testing. The clinical characteristics with a p < 0.1 in univariate analysis were included in the multivariate models. The statistical significance level in the final models was set at p < 0.05.

LASSO regression was conducted using the “glmnet” package. The “pROC” package was used to plot the ROC curve. The Spearman correlation analysis was performed using the “corrplot” package. Construction of the model that combines clinical variables and radiomics features was carried out using the “rms” package. The Hosmer–Lemeshow test was conducted using the “Resource Selection” package. Decision curves analysis was performed using the “rmda” package.