2.1 Subjects

We retrieved the data of 127 patients with breast cancer, confirmed through pathology, at the Affiliated Tumor Hospital of Guizhou Medical University between 2020 and 2022. The study inclusion criteria encompassed: (1) Female with breast masses suspected through US; (2) Availability of complete clinical data; (3) Underwent breast surgery and had comprehensive immunohistochemical data. The exclusion criteria were: (1) Underwent preoperative therapy; (2) Had multifocal lesions or bilateral disease; (3) Cases involving benign breast lesions or carcinoma in situ; (4) Missing important histopathological findings that would affect data analysis; (5) Insufficient information or incomplete imaging records. Verbal informed consent was obtained from all patients for the use of their data.

2.2 Ultrasonography

The US examination was conducted 1–2 weeks before surgery using an ultrasound scanner equipped with a linear array probe operating at a frequency range of 4–15 MHz. Briefly, the patient assumed a supine position on the examination bed, with arms raised above the head, ensuring full exposure of both breasts and the axillary region. An experienced sonographer systematically scanned all quadrants of the breast, including the nipple, areola, and bilateral axilla, to ensure a comprehensive scanning range without any omissions. In cases where a positive lesion was identified, the lesion area underwent multi-angle and multi-section scanning. The US images capturing the long axis of the mass were acquired and stored in BMP format.

During the examination, we carefully observed and documented various US features of the lesions, including boundary clarity (categorized as clear, still clear or unclear), shape (classified as regular for round and oval shapes and irregular for all others), edge smoothness (categorized as smooth or unsmooth, with unsmooth referring to the presence of microlobulation, angulation or spiculation at the lesion’s edge), lymph node metastasis (noted as yes, no or unclear), blood flow grade (graded as Ⅰ, Ⅱ, Ⅲ or Ⅳ), orientation (described as parallel or vertical), presence of a hyperechoic halo (indicated as yes or no), posterior echo characteristics (categorized as no change, enhancement or attenuation), and the presence or absence of calcification.

2.3 Segmentation of lesions

Accurate object segmentation in medical images is a critical step in medical diagnosis and various applications. However, despite extensive research on automatic segmentation methods, achieving clinically acceptable image quality remains a challenging task [11]. Herein, experienced US imaging diagnostic physicians utilized the ITK-SNAP software (http://www.itksnap.org/pmwiki/pmwiki.php) for manual segmentation. To ensure precision, we opted for manual segmentation, which involved outlining along the tumor boundary and encompassing the entire tumor lesion. To guarantee the robustness and reproducibility of subsequent US image features, another physician skilled in ultrasonographic breast diagnosis was invited to participate. Both physicians were kept unaware of the clinical information and pathology results pertaining to the patients. The region of interest (ROI) for the lesion was meticulously delineated (Fig. 1).

Fig. 1.Delineation of the region of interest on breast cancer ultrasound images. (A,B) The image of a 45 year old female with non-triple-negative breast cancer; (C,D) The images of a 58 year old female with triple negative breast cancer. (A) and (C) show the original images, and (B) and (D) show the segmented images.

2.4 Radiomics features

In this study, we employed the open-source tool PyRadiomics 3.0 [12] for extracting US radiomics features, including: (1) first-order features; (2) three-dimensional (3D) shape features; (3) two-dimensional (2D) shape features; (4) grey-level co-occurrence matrix (GLCM) features; (5) grey-level run length matrix (GLRLM) features; (6) grey-level size zone matrix (GLSZM) features; (7) neighboring grey-tone difference matrix (NGTDM) features; and (8) grey-level dependence matrix (GLDM) features.

2.5 Feature selection

The patient data were divided into training and testing sets based on the chronological order of their examinations. The training set was used for feature screening and model construction, while the testing set was used to validate the model’s performance. The feature selection process consisted of three steps: first, a feature repeatability test, where radiomics features extracted from ROI delineated by two experienced diagnostic physicians were assessed for agreement using the intraclass correlation coefficient (ICC), categorizing reproducibility as poor (ICC <0.40), fair to good (ICC = 0.40–0.75), or excellent (ICC >0.75); second, univariate and multivariate analyses were conducted to identify independent predictors of TNBC, and; third, radiomics feature screening was performed using the RF selection algorithm.

2.6 Model construction and evaluation

In this study, we employed four ML algorithms, LR, SVM, DT and RF, to establish three distinct prediction models. These models included an ultrasonic feature model, a radiomics feature model, and a comprehensive model that integrated both ultrasonic and radiomics features. Briefly, LR is a multiple regression technique utilized for analyzing the relationship between binary or classification outcomes and multiple influencing factors [13]. Comparatively, SVM is a versatile supervised learning model that is applied to classify and regress data [13], DT represents a straightforward and intuitive machine learning approach that introduces sequential nonlinearity of variables [14], and RF is an integrated model that can construct multiple random decision trees using bagging methods [15]. The performance of the three models in predicting TNBC was assessed using metrics such as accuracy, sensitivity, specificity, and the area under the curve (AUC). The complete data analysis process is shown in Fig. 2.

Fig. 2.Flowchart of the radiomics process and analysis.

2.7 Statistical analysis

The analysis of breast tumor US features and statistical procedures was conducted using the Python 3.10 statistical software (https://www.python.org) and packages, such as pandas, numpy, sklearn.metrics and matplotlib.pyplot as the primary tools for data analysis and figure plotting. Quantitative data are presented as mean values with corresponding standard deviations, while categorical variables are presented as percentages (n %). Differences among categorical variables were assessed via Chi-square tests, and features demonstrating significance in the univariate analysis were subsequently integrated into the multivariate Logistic Regression (LR) model. A significance level of p < 0.05 is considered statistically significant.

3.1 Demographics

The study comprised a total of 127 patients with breast tumors. Among them, 39 patients had TNBC, with an average age of 51.18 ± 10.72 years, while 88 patients had non-TNBC, with an average age of 48.86 ± 8.88 years. These 127 breast lesions were randomly divided into two groups: a training set (n = 88; average age of 49.70 ± 9.92 years) and a testing set (n = 39; average age of 49.28 ± 8.58 years). Their additional basic data is shown in Supplementary Table 1.

3.2 Consistency check

Consistency check analysis indicated that the two senior US diagnostic physicians demonstrated excellent agreement in feature assessments, as indicated by high intraclass correlation coefficients (ICC = 0.78–0.99; p < 0.001) (Supplementary Table 2).

3.3 Univariate and multivariate analysis of US features of breast tumors

To identify independent predictors for TNBC, we conducted univariate analysis on the US features of the breast masses. The results revealed significant differences in terms of tumor boundary and posterior echo in the training set (p < 0.05), which were included in the multivariate LR analysis. The results revealed that both the tumor margin (OR 0.296; 95% CI 0.127–0.692; p = 0.005) and posterior echo (OR 0.323; 95% CI 0.112–0.930; p = 0.036) were independent influencing factors for predicting TNBC (Table 1 and Supplementary Table 3).

3.4 Radiomics feature extraction and screening

The PyRadiomics software was used to extract US image features from the ROIs. Each image yielded a total of 105 radiomics features, encompassing first-order features (18), shape features (12), GLCM features (24), GLSZM features (16), GLRLM features (16), GLDM features (14), and NGTDM features (5). Due to variations in the calculation methods for each feature and the differing magnitudes of feature values across dimensions, the Z-score method was used for standardization.

The RF method was used for feature screening, resulting in the selection of 14 radiomics features that exhibited the highest relevance to breast tumor classification. These selected features comprised 2 first-order features, 6 shape features and 6 texture features, which included 1 from GLSZM, 2 from GLRLM, and 3 from NGTDM (Supplementary Table 4).

3.5 Prediction model through LR

After the above screening of radiomics and US features, these selected features were integrated into the ML model for model construction and subsequent prediction. The ROC curves for the LR-based ML models, which include the US feature model, radiomics feature model and comprehensive model, are shown in Fig. 3. In the training set, the AUC values were 0.73 (0.62, 0.74), 0.78 (0.75, 0.89) and 0.85 (0.79, 0.90), respectively, while in the testing set, the AUC values were 0.58 (0.50, 0.79), 0.68 (0.54, 0.84) and 0.64 (0.56, 0.86), respectively. Additional details regarding accuracy, specificity and sensitivity are shown in Table 2.

Fig. 3.ROC curves of each prediction model based on the LR algorithm. (A) training set; (B) testing set.

3.6 Prediction model through SVM

The ROC curves for the SVM-based ML models, including the US feature model, image feature model and comprehensive model, are presented in Fig. 4. In the training set, the AUC values were 0.54 (0.56, 0.77), 0.80 (0.76, 0.93) and 0.92 (0.87, 0.96), respectively, and in the testing set, they were 0.82 (0.41, 0.83), 0.55 (0.47, 0.78) and 0.69 (0.52, 0.80), respectively. Further details regarding accuracy, specificity and sensitivity are shown in Table 3.

Fig. 4.ROC curves of each prediction model based on the SVM algorithm. (A) training set; (B) testing set.

3.7 Prediction model through DT

The ROC curves for DT-based ML models, including the US feature model, image feature model and comprehensive model, are illustrated in Fig. 5. In the training set, the AUC values were 0.73 (0.64, 0.77), 0.84 (0.69, 0.88) and 0.78 (0.70, 0.83), respectively, while in the testing set, they were 0.59 (0.52, 0.75), 0.71 (0.43, 0.78) and 0.63 (0.42, 0.73), respectively. Further details regarding accuracy, specificity and sensitivity are shown in Table 4.

Fig. 5.ROC curves of each prediction model based on the DT algorithm. (A) training set; (B) testing set.

3.8 Prediction model through RF

The ROC curves for the RF-based ML models, including the US feature model, image feature model, and comprehensive model, are displayed in Fig. 6. In the training set, the AUC values were 0.73 (0.63, 0.74), 0.95 (0.89, 0.96) and 0.92 (0.86, 0.96), respectively, and in the testing set, they were 0.60 (0.55, 0.79), 0.65 (0.45, 0.77) and 0.76 (0.43, 0.77), respectively. Further details regarding accuracy, specificity and sensitivity are shown in Table 5.

Fig. 6.ROC curves of each prediction model based on the RF algorithm. (A) training set; (B) testing set.