Ultrasound image acquisition

Ultrasound examinations were conducted using the Aiexplorer (SuperSonic Imagine, Aix-en-Provence, Cedex, France) with a linear probe L15-4 (frequency 4–15 MHz) or the Philips EPIQ7 (Philips Healthcare, Amsterdam, The Netherlands) ultrasound system with a linear probe L12-5 (frequency 5–12 MHz). The musculoskeletal imaging mode was selected and optimal depth was adjusted according to the target joint for scanning. All examinations were performed by a single experienced musculoskeletal ultrasonographer blinded to clinical data. The joint with the most pronounced symptoms was assessed in each patient, including the metatarsophalangeal, ankle, knee, elbow, wrist, shoulder and hand joints. Ultrasound examination procedures adhered to EULAR guidelines for musculoskeletal ultrasound. All images meeting inclusion and exclusion criteria were exported from the ultrasound device and reviewed by a musculoskeletal ultrasound expert.

Region of interest delineation

All included ultrasound images were re-sampled to ensure uniform pixel spacing and consistent resolution across all images. Re-sampling adjusted the images to a standardized spatial resolution of 1 mm × 1 mm to reduce variations caused by differences in acquisition settings. The re-sampling process was performed using bi-linear interpolation to preserve image quality and avoid introducing artifacts. Two imaging technicians, certified by the Chinese Academy of Management Science, manually delineated the regions of interest (ROIs) using ITK-SNAP software. These technicians were blinded to the clinical data and ultrasound diagnostic results. Following ROI delineation, the images were analyzed, and relevant features were extracted.

Feature extraction

Radiomic features were automatically extracted using the open-source Python package Pyradiomics ( https://pyradiomics.readthedocs.io/ ). These manually crafted features were divided into three categories: (i) Shape features, which describe the 2-D geometric characteristics of the ROI, such as area, perimeter and compactness; (ii) intensity features, which represent the first-order statistical distribution of pixel intensities within the ROI; and (iii) texture features, which capture patterns and higher order spatial relationships of intensity. Texture features were derived using methods such as Gray-Level Co-occurrence Matrix, Gray-Level Run Length Matrix, Gray-Level Size Zone Matrix and Neighborhood Gray-Tone Difference Matrix.

Feature selection

Statistics. Mann-Whitney U tests were performed on all radiomic features, with only those features achieving a p value < .05 being retained.

Correlation. For highly reproducible features, Spearman’s rank correlation coefficient was used to assess inter-feature correlations. If any two features exhibited a correlation coefficient greater than 0.9, only one of the correlated features was retained. Figure 2 illustrates the percentage of each group of imaging features relative to the total feature set. To maximize the retention of informative features, a greedy recursive deletion strategy was employed, wherein the most redundant feature in the current set was iteratively removed. This process resulted in the retention of 11 features.

Number and ratio of handcrafted features. glcm, Gray‑Level Co-occurrence Matrix; gldm, Gray-Level Dependence Matrix; glrlm, Gray‑Level Run Length Matrix; glszm, Gray‑Level Size Zone Matrix; ngtdm, Neighborhood Gray‑Tone Difference Matrix.

Least absolute shrinkage and selection operator. The least absolute shrinkage and selection operator (LASSO) regression model was applied to the discovery dataset to construct a signature. LASSO penalizes regression coefficients based on a regularization parameter λ, shrinking coefficients toward zero and setting many irrelevant ones to zero. To determine the optimal λ, 10-fold cross-validation using the minimum criteria was conducted, selecting the λ value that minimized cross-validation error. The retained features with non-zero coefficients were used to fit the regression model and combined into a radiomics signature. A radiomics score for each patient was then calculated as a linear combination of the retained features, weighted by their model coefficients. LASSO regression modeling was performed using the Python scikit-learn package.

Radiomics signature

Following LASSO feature selection, the final set of features was input into various machine learning models, including logistic regression (LR), support vector machines (SVM), random forest and XGBoost, to construct risk prediction models. Fivefold cross-validation was employed to derive the final radiomics signature. To assess the added prognostic value of the radiomics signature in conjunction with clinical risk factors, a radiomics nomogram was developed using the validation dataset. This nomogram integrated the radiomics signature with clinical risk factors through LR analysis. A calibration curve was then generated to evaluate concordance between the nomogram’s predictions and actual outcomes.

Clinical signature

The process of constructing the clinical signature mirrored that of the radiomics signature. Initially, clinical features were selected based on baseline statistical analysis, retaining those with p < .05. The same machine learning models used for the radiomics signature were then applied. To ensure a fair comparison, fivefold cross-validation and a fixed test cohort were utilized.

Radiomic nomogram

The radiomic nomogram was developed by integrating radiomics and clinical signatures. The diagnostic performance of the nomogram was assessed in the test cohort, with receiver operating characteristic curves generated to evaluate its diagnostic accuracy. Calibration curves were drawn to assess the nomogram’s calibration efficiency, and the Hosmer-Lemeshow goodness-of-fit test was employed to evaluate its calibration ability. Decision curve analysis (DCA) was conducted to assess the clinical utility of the predictive models.

Data sets

All patients were randomly divided into training and test groups in a 4:1 ratio. The Mann-Whitney U-test, t -test and χ² test were used to compare clinical characteristics between the two groups, identifying any significant differences in patient demographics, clinical presentation and other relevant factors that could influence study outcomes.