Ethical approval for this retrospective study was obtained by the Medical Ethics Committee of Henan Provincial People's Hospital [approval number: (2019) No. 68], and the need for written informed consent was waived.

This was a retrospective single-centre study. A total of 239 patients with CRC confirmed by postoperative pathology in Henan Provincial People's Hospital from January 2016 to May 2022 were retrospectively collected. Inclusion criteria were: (1) CRC was confirmed by postoperative pathology, (2) PET/CT was performed within 1 month before surgery, (3) complete preoperative PET-CT images were available. Exclusion criteria were: (1) preoperative neoadjuvant therapy (radiotherapy, chemotherapy or targeted therapy), (2) vascular invasion was not clear in pathology, and (3) combined with other pelvic malignant tumours or poor image quality could not be evaluated.

Clinical information of patients was obtained by searching medical records, including age, sex, serum levels of tumour markers: carcinoembryonic antigen (CEA ≤ 5 ng/ml), carbohydrate antigen 199 (CA199 ≤ 35U/ml), carbohydrate antigen125 (CA125 ≤ 35U/ml), and tumor differentiation degree. Maximum standardized uptake value (SUVmax), mean standardized uptake value (SUVmean), peak standardized uptake value (SUVpeak), metabolic tumor volume (MTV), total lesion glycolysis (TLG), maximum tumour diameter and lymph node metastasis were obtained by PET-CT information.

All patients underwent surgical resection after ¹⁸F-FDG PET-CT examination. All surgical specimens were reviewed by pathologists with more than 6 years of experience in abdominopelvic pathology, specifically to assess for the presence of LVI. LVI was diagnosed when tumour cells or tumour cell thrombi were observed within an endothelium-lined space or if tumour cells had destroyed a lymphovascular wall, as described in a previous study (14).

The imaging equipment used was a Discovery™ VCT PET-CT instrument from GE Company in the United States. ¹⁸F-FDG was synthesized by a GE Minitrace medical cyclotron and FDG automatic synthesis device (Beijing Patte Biotechnology Co., LTD.). The radiochemical purity of ¹⁸F-FDG was >95%. High-performance liquid chromatography was used for quality control. Fingertip blood glucose was collected before the examination, and the blood glucose level was controlled below 11.1 mmol/l. The patients fasted for 6–8 h before the examination, and the dose of ¹⁸F-FDG was 5.55 MBa/kg. After the injection, the patients rested for 40–50 min in a quiet and suitable temperature environment before imaging. The bladder was emptied, and the stomach was filled with 500 ml of water. PET and CT scanning were performed from the head to the feet. CT images were acquired with the following scanning parameters: tube voltage, 120 kV; tube current, 170 mA; field of view, 40 mm; slice thickness, 3.75 mm; tube speed, 0.6 ms/r; pitch, 0.984 mm; scanning time, 13.8 s; and matrix, 256 × 256. Three-dimensional PET scans were performed with 4–6 window levels according to height, and each window level took 3 min to scan. After CT attenuation correction and iterative reconstruction, the fused images of the coronal, sagittal and transverse planes were obtained by Integrated Registration software in the GE 4.6ADW postprocessing station.

The acquired PET-CT original data were imported into the uWS-MR, UIH workstation. The images were processed and analysed by two senior physicians. In cases of disagreement, the result was obtained after discussion. The region of interest (ROI) of CRC lesions was delineated (single-layer ROI was placed, full-layer ROI was automatically traced and delineated, and manual correction was performed), as shown in Figure 1. SUVmax, SUVmean, SUVpeak, MTV, TLG and lymph node status (the current criteria for ¹⁸F-FDG PET/CT diagnosing regional lymph nodes metastasis in CRC were lymph node short diameter ≥1.0 cm or SUVmax ≥2.5) were measured and recorded.

The original PET-CT images of all included patients were obtained from the MedEX System of Nuclear Medicine Workstation of Henan Provincial People's Hospital, and postprocessing was performed based on axial PET and CT sequences. Two radiologists with 5 years of experience applied the ITK-SNAP software (Version 3.8.0 http://www.itksnap.org/) to delineate the ROI layer by layer on rectal cancer lesions and obtain the tumour volume of interest (VOI), as shown in Figure 2. Finally, the VOI of each sequence was saved as a mask file.

Inter- and intra-class correlation coefficients (ICCs) were calculated for evaluation of the inter-reader reliability and intra-reader reproducibility of feature extraction. Radiologist 1 and radiologist 2 randomly selected 30 CT and PET images for radiomics ROI delineation and image feature extraction. Radiologist 1 repeated the segmentations 1 month later. An Intraclass correlation coefficient (ICC) greater than 0.75 indicated good agreement of feature extraction. The ROI segmentation for the remaining cases was performed by radiologist 1.

Radiomics features were calculated and combined for different imaging sequences (PET, CT). The open-source software PyRadiomics (Version 3.0.1, http://github.com/Radiomics/pyradiomics) was used feature extraction and analysis. Feature extraction was performed using filters such as Original, BoxMean and AdditiveGaussianNoise during preprocessing. First Order Statistics (Firstorder), Grey Level Co-occurrence Matrix (GLCM), Shape-based (3D) (Shape), Grey Level Dependence Matrix (GLDM), Neighbouring Grey Tone Difference Matrix (NGTDM), Grey Level Run-Length Matrix (GLRLM), and Grey Level Size Zone Matrix (GLSZM) features were generated from the ROI of image. Finally, 2,264 radiomics features were extracted from each sequence, and the PET-CT features set was generated by means of features stitching.

The dataset was randomly divided into training and validation cohorts at a ratio of 6:4, the training cohort was used for features selection and models construction, and the test cohort was used for models’ evaluation. First, Z score normalization was performed on the extracted features, and then feature selection was performed on the preprocessed data, and the variance threshold method was used to remove the low variance features (P < 0.1). The features with low correlation with the classification label were removed based on the K-best method (F value method, P < 0.05). Finally, the irrelevant or redundant features were removed by the least absolute shrinkage and selection operator (LASSO), and the radiomics signature was constructed according to the weighted linear combination of the selected features and their corresponding regression coefficients. The radiomics score (Rad-score) of each patient was calculated accordingly. Finally, the training model is obtained based on logistic regression classifier.

Univariate logistic regression analysis was used to compare the differences in clinical information between the LVI-positive group and the LVI-negative group, and multivariate logistic regression analysis was used to identify the independent predictors significantly associated with LVI. Four datasets were constructed, and four prediction models were trained based on PET, CT radiomics features and clinical predictors. They were named PET_RS (PET radiomics features), CT_RS (CT radiomics features), PET-CT_RS (PET and CT radiomics features) and clinical radiomics model (with PET-CT radiomics features and clinical predictors).

The predictive ability of the PET_RS, CT_RS, PET-CT_RS and the clinical radiomics models was evaluated based on the Area Under Curve (AUC), sensitivity, and specificity in the training and test cohorts. A radiomics nomogram was constructed by combining the clinical predictors of LVI screened by multivariate logistic regression and the Rad-score of the best model. The calibration of the nomogram was evaluated by drawing the calibration curve between the actual probability of LVI and the predicted probability of LVI. Decision curve analysis (DCA) was used to evaluate the clinical utility of multimodal radiomics by calculating the net benefit at different threshold probabilities.

All statistical analyses were performed using SPSS (version 26.0), R statistical software (version 4.0.2), and MedCalc (version 15.2.2). Measurement data following a normal distribution are represented as x ± s, and comparisons between the two groups were analysed using the two independent sample t test. Measurement data not following a normal distribution are represented as M (P25, P75), and comparisons between the two groups were analysed using the Mann‒Whitney U test. Count data are expressed as cases (%), and the chi-square test was used for comparisons between groups. Univariate and multivariate logistic regression methods (Forward selection) were used to analyse the clinical indicators of patients with CRC. The MedCalc software was used for the ICC test, receiver operating characteristic (ROC) curve drawing and analysis. The nomogram, calibration plots, and DCA were performed using R statistical software (Version 3.3.3, https://www.r-project.org). The “rms” package was used for nomogram and calibration curve drawing, and the “rmda” package was used for decision curve drawing. All statistical tests were two-sided, and P < 0.05 was considered statistically significant.

A total of 95 CRC patients were included in this study after screening, including 54 males and 41 females, with an average age of 62 years. None of the clinical factors significantly differed between the training cohort and the validation cohort (Table 1, P > 0.05). The above information indicates that the distribution of baseline clinical characteristics of patients in the training and validation cohorts was balanced. Among these patients, 44 (46.3%) were pathologically diagnosed to have LVI, and 51 (53.7%) were pathologically diagnosed to be free of LVI. A univariate logistic regression analysis of preoperative colorectal cancer LVI showed that maximum tumour diameter, lymph node metastasis, SUVmax and SUVmean metabolic values were independent risk factors for LVI (Table 2, P < 0.05). Multivariate logistic regression analysis finally included maximum tumour diameter, lymph node metastasis and SUVmean metabolism as independent clinical predictors of LVI (Table 3, P < 0.05).

Taking the clinical radiomics model as an example, firstly, to avoid subjective differences in segmentation of ROI, the radiomics features with both inter- and intra-reader ICCs > 0.75 were retained. Secondly, two PET features and four CT features were selected by variance threshold, K-best and LASSO regression models, and then combined with three clinical predictors, a total of nine features were obtained. The selected features were summed by weighting coefficients to calculate the Rad-score (Figure 3). Finally, the best prediction model was established based on the logistic regression classifier. The Rad-score significantly differed between LVI-positive and LVI-negative patients (P < 0.001). The confusion matrix shown in Figure 4 shows the prediction performance of the training and test set models.

By comparing the area under the ROC curve (AUC), sensitivity, and specificity of each model (Table 4 and Figure 5), the clinical radiomics model (AUC: 0.918, 95% CI 0.782, 0.982) had the best performance, with high sensitivity (87.5%) and specificity (90.9%), which was confirmed to be the best prediction model. We generated a visual nomogram based on the training cohort of the clinical radiomics model (Figure 6A). The calibration curves of both the training cohort and the validation cohort of the nomogram demonstrated good agreement between the predicted LVI and the actual observation (Figures 6B,C). The decision curves of the PET-CT_RS and clinical radiomics models are shown in Figures 6D,E. The results showed that the clinical radiomics model yielded a higher overall net benefit than the PET-CT_RS model.