This retrospective as approved by the institutional review board. During this process, the informed consent of the subjects is exempted. We collected information on patients with surgically resected and pathologically confirmed rectal cancer between December 2017 and August 2023. All patients underwent T1WI enhanced examination, including 68 PNI patients and 80 LVI patients. We randomly divided patients into a training group and a validation group in a 7:3 ratio. The PNI training group consisted of 47 patients, the validation group consisted of 21 patients, the LVI training group consisted of 56 patients, and the validation group consisted of 24 patients. Forty-two patients with rectal cancer that were surgically resected and pathologically confirmed between September 2019 and February 2023 at another medical institution were also collected for external validation. These 42 patients met the same inclusion and exclusion criteria. Inclusion criteria: (1) No treatment received before Magnetic Resonance Imaging (MRI) examination and surgery; (2) The tissue biopsy result indicates rectal adenocarcinoma; (3) Perform a complete preoperative MRI enhancement examination; (4) Obtain complete postoperative pathological results. Exclusion criteria: (1) Patients with a history of other tumors; (2) Patients who have received radiotherapy and chemotherapy treatment; (3) Patients with poor image quality; (4) Patients with contraindications to magnetic resonance imaging examination.

All results of nerve and vascular invasion are from the pathology report of our hospital’s pathology department. All rectal cancer samples are diagnosed by pathologists with 5 years of experience in pathological diagnosis. The pathological identification of nerve and vascular invasion generally uses hematoxylin-eosin (H&E) sections. Under a typical nerve invasion microscope, tumor cells can infiltrate any layer of nerve tissue (outer membrane, bundle membrane, and inner membrane), and wrap around at least one-third of the nerve circumference. Typical vascular invasion under endoscopy: (1) Tumor cells directly detach from the walls of blood vessels and/or lymphatic vessels, invading the lumen of blood vessels and lymphatic vessels; (2) Tumor cell clusters can be seen within blood vessels and lymphatic vessels, with tumor cells mixed with red blood cells and lymphocytes, and/or the surface of tumor cell clusters is lined with endothelial cells of blood vessels and lymphatic vessels. Individuals suspected of having vascular and nerve invasion can use immunohistochemistry staining with S-100, CD31, CD34, and D240 to help determine. S-100 causes nerve fibers to turn brown, while CD31, CD34, and D240 cause endothelial cells and lymphatic endothelial cells to turn brown. Then, under a microscope, it is easy to observe whether tumor cells have invaded the nerve and vascular cavities stained brown by immunohistochemistry. Observation of nerve invasion (nerve invasion+); Observed vascular invasion (vascular invasion+).

The patient’s MRI images were collected using a Dutch 3.0T Philips Achieva 3.0T superconducting MRI scanner and scanned using a 16-channel phased array coil on the body surface. All patients were placed in a supine position, with their heads in front, and underwent T1WI enhanced rectal scan. The imaging scheme and parameters are as follows: T1 weighted imaging enhanced scan, TR 600 ms, TE 10 ms, FOV: 240 mm x 240 mm, layer thickness 3 mm, layer spacing 0.5 mm, matrix: 384 × 384.

Through Firevoxel software (https://files.nyu.edu/hr18/public/projects.html) We delineated the region of interest (ROI) on the axial T1WI enhanced image and extracted histogram parameters. Two abdominal and pelvic imaging diagnostic physicians used a double-blind method to draw lines on the magnetic resonance imaging images of each patient. In uncertain circumstances, another radiologist with over 10 years of experience in diagnosing abdominal and pelvic MRI will confirm the specific location of the lesion. The characteristic of rectal cancer is irregular thickening of the rectal wall or pathological changes in the lumen. We directly delineate the ROI along the entire edge of the lesion, and during this process, sagittal T2-weighted images are used as reference standards. We sketch along the inner edge of the rectal wall to avoid gas, water, and other contents inside the cavity. After completing the ROI mapping for all cases, the software automatically generated histogram parameters, as shown in Fig. 1, including mean, variance, skewness, kurtosis, 1st percentile (Perc. 1%), 5th percentile (Perc. 5%), 10th percentile (Perc. 10%), 25th percentile (Perc. 25%), 50th percentile (Perc. 50%), 75th percentile (Perc. 75%), 90th percentile (Perc. 90%), 95th percentile (Perc. 95%), 99th percentile (Perc. 99%).

A 59-year-old woman with rectal cancer. (A) Eccentric thickening of the middle rectal wall. (B) ROI is filled in red for a T1C histogram. (C) T1C histogram of the tumor mass

We conducted a statistical analysis of the data. Firstly, we conducted univariate logistic analysis and LASSO regression analysis on all factors. Next, multiple logistic regression analysis was used to screen for the best predictive factors. Subsequently, we constructed a predictive model using the selected predictive factors in the training group. Finally, we validated the model on the validation group. For the training and validation groups, we plotted receiver operating characteristic (ROC) curves and calculated area under curve (AUC) values, accuracy (ACC), sensitivity (SEN), specificity (SPE), positive predictive value (PPV), and negative predictive value (NPV) to evaluate the performance of the predictive model. In addition, we visualized the presentation by drawing column charts and plotted calibration curves. Finally, we use threshold probability and net profit for decision curve analysis to evaluate the clinical practicality of the model.

The statistical analysis of the data in this study was conducted using R (version 4.1.3) and SPSS (version 28.0) software. Continuous numerical variables that follow a normal distribution are tested using two independent samples t-test, represented by mean ± standard deviation. Continuous variables that do not follow a normal distribution are tested using Mann Whitney U-test and represented as median (Q1, Q3). The categorical variables are tested using chi-square or Fisher’s exact test, expressed as percentages (%). The significance tests are all bilateral tests, and P < 0.05 indicates a statistically significant difference.