Abstract
Introduction
In patients with invasive breast cancer (IBC), the presence of lymphovascular invasion (LVI) is strongly associated with elevated risks of local recurrence, tumor metastasis, and poor prognosis. In this study, we aimed to develop a prior-radiomics-guided multiscale feature extraction network (PRM-Net) for predicting LVI in IBC using preoperative magnetic resonance imaging (MRI).
Methods
This retrospective study involved a cohort of 303 female patients with IBC who underwent MRI and surgical resection at our hospital between January 2019 and December 2023. The enrolled patients were randomly split into training and validation cohorts at a 7:3 ratio, with the training set used for model development and the validation set reserved for performance evaluation. Four predictive models were developed: 1) a diagnostic imaging hallmark model using logistic regression to analyze MRI morphological features; 2) a radiomics classifier incorporating feature engineering and operator-based feature selection; 3) a multiscale feature extraction deep learning network (M-Net), designed for end-to-end extraction of multiscale features from MRI scans; and 4) PRM-Net, which integrated deep learning and radiomics by the fusion of multiscale deep features and engineered radiomic features.
Results
PRM-Net achieved the highest diagnostic accuracy for LVI prediction [area under the curve (AUC) = 0.854, 95% confidence interval (CI): 0.779–0.929], outperforming M-Net (AUC = 0.816, 95% CI: 0.732-0.901), radiomics classifiers (AUC = 0.771, 95% CI: 0.648-0.894), and traditional imaging hallmarks (AUC = 0.761, 95% CI: 0.655-0.866).
Conclusions
These findings highlight the potential of PRM-Net in the preoperative prediction of LVI in patients with IBC and underscore the value of combining advanced radiomics with deep learning in clinical oncology. This approach may facilitate the identification of optimal surgical strategies tailored to individual patient needs.
Keywords
Introduction
Invasive breast cancer (IBC) remains the most common and lethal malignancy among women globally, largely due to its propensity for recurrence and metastatic dissemination. 1 A critical step in metastasis involves tumor cell intravasation into blood or lymphatic vessels, with lymphovascular invasion (LVI) serving as the predominant mechanism, while perineural and neural invasion contribute to a lesser extent. 2 The presence of LVI is an established prognostic indicator in IBC, strongly correlated with increased risks of locoregional recurrence, distant metastasis, and reduced survival, particularly in node-positive, operable IBC.3–5 Moreover, LVI status significantly influences therapeutic decision-making in early-stage breast cancer, guiding adjuvant chemotherapy recommendations and the necessity for radiotherapy.6,7 Thus, precise preoperative determination of LVI is essential for optimizing treatment strategies.
Breast magnetic resonance imaging (MRI) is a powerful, noninvasive technique for evaluating the biological behavior of IBC, offering superior soft-tissue contrast, high spatial resolution, and multiparametric capabilities. Several MRI-derived morphological features, including dynamic contrast-enhanced (DCE) kinetics, peritumoral edema, adjacent vascular signs, diffusion-weighted imaging (DWI) rim enhancement, ipsilateral vascular prominence, and intratumoral/peritumoral apparent diffusion coefficient (ADC) values, have been identified as potential imaging biomarkers of LVI.8–11 However, conventional MRI interpretation remains subjective, with variability in the diagnostic accuracy and reproducibility due to reliance on qualitative assessment and operator expertise. Consequently, there is a pressing need for more objective and standardized diagnostic approaches to improve LVI detection.
Radiomics is a technique used to extract detailed structural and textural features from medical images, offering a comprehensive description of internal characteristics and lesion morphology. This method has been widely employed to preoperatively assess LVI in patients with IBC, demonstrating satisfactory performance.12,13 In contrast, deep learning (DL) models can learn abstract features and model complex data through multilayer nonlinear transformations, thereby improving the identification and classification accuracy via end-to-end learning with large, labeled datasets. DL has also been applied to evaluate LVI in patients with IBC based on MR images, yielding promising results.14,15 However, DL has inherent limitations. 16 The opaque nature of DL models complicates the explanation of their internal decision-making processes, and they are vulnerable to adversarial attacks, which can lead to misclassification even with minor perturbations. Achieving optimal performance requires extensive parameter tuning, expertise, and time for adjustments, including the selection of appropriate network architectures, loss functions, learning rates, and other hyperparameters.
Herein, we propose a novel prior-radiomics-guided multi-scale feature extraction network (PRM-Net), which integrates DL and radiomics by the fusion of multiscale deep features and engineered radiomic features. This approach aims to improve model accuracy and stability for LVI prediction in IBC, further supporting the development of more precise treatment plans, aiding in surgical decision-making, and enabling personalized treatment strategies for patients with IBC.
Methods
Study Design and Ethical Approval
This retrospective study was conducted in accordance with the relevant institutional ethical guidelines and received approval from the Xiangtan Central Hospital Review Board (Approval No: 2024-01-002; Date of Review: January 29, 2024; Location: Xiangtan City). A waiver of informed consent was granted due to the study's retrospective nature and use of anonymized patient data.
Female patients diagnosed with IBC who underwent preoperative breast MRI followed by surgical resection at Xiangtan Central Hospital between January 2019 and December 2023 were consecutively included in the study. All patient details were de-identified prior to analysis: unique identifiers, such as names and medical record numbers, were removed, and the data were anonymized to prevent re-identification. The reporting of this study conforms to the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) guidelines for cohort studies. 17
The inclusion criteria were as follows: 1) MRI-visible primary breast lesions with radiologically assessable tumor characteristics; 2) histopathologically confirmed IBC following surgical resection; and 3) surgery performed within 14 days of MRI to minimize discrepancies between imaging and pathological findings. Exclusion criteria comprised: 1) bilateral or secondary breast malignancies to avoid confounding effects from multifocal disease; 2) indeterminate pathological or histological diagnoses that could confound the relationship with imaging findings; and 3) suboptimal MRI quality (eg, motion artifacts, incomplete sequences) that could compromise the diagnostic assessment. A detailed flowchart summarizing the patient enrollment is provided in Figure 1.
Enrollment Criteria for Patient Selection.
MRI Protocol
All examinations were performed using a 1.5-Tesla MAGNETOM Aera MRI system (Siemens Healthineers, Erlangen, Germany) equipped with an 18-channel dedicated breast surface coil, with patients in the prone position to optimize breast immobilization and signal reception. The standardized imaging protocol comprised four sequences: 1) axial T2-weighted imaging (T2WI) with spectral fat suppression [echo time (TE) = 48 ms, repetition time (TR) = 4830 ms, field of view (FOV) = 340 × 340 mm2, matrix = 336 × 448, flip angle = 170°, slice thickness = 4 mm]; 2) axial T1-weighted imaging (T1WI) without fat suppression (TE = 4.77 ms, TR = 8.08 ms, FOV = 320 × 320 mm2, matrix = 336 × 448, flip angle = 20°, slice thickness = 1.1 mm); 3) Diffusion-weighted image with b-values of 0 and 1000 s/mm2 (TR = 7460 ms, TE = 66 ms, FOV = 153 × 340 mm2, matrix = 72 × 160, slice thickness = 5 mm); and 4) DCE-MRI (TE = 2.39 ms, TR = 5.03 ms, FOV = 360 × 360 mm2, matrix = 218 × 256, flip angle = 10°, slice thickness = 1.6 mm). Gadoteric acid meglumine (Dotarem®, Guerbet, France) was administered intravenously as a bolus at 2 mL/s (dose: 0.2 mL/kg), followed by a 20-mL saline flush. Six consecutive dynamic acquisitions (A1–A6; temporal resolution = 90 s each) were obtained after contrast administration to assess the enhancement kinetics, and the A1 phase image was used for image analysis.
Image Preprocessing
All image segmentation and registration procedures were performed using 3D Slicer (version 4.6; https://www.slicer.org), an open-source platform for medical image computing and visualization. The tumor volume of interest (VOI) was manually delineated by a fellowship-trained breast radiologist with 10 years of experience using the first-phase DCE images (A1 phase) as the primary reference. To ensure segmentation accuracy, all contours were independently reviewed and refined by a senior breast radiologist with 15 years of experience.
For multimodal image alignment, we employed a deformable registration approach using the Elastix module within 3D Slicer. The registration protocol specifically utilized the “3D DCE-MRI (breast)” algorithm, optimized for breast imaging applications. This method accounted for potential anatomical deformations between sequences while preserving the tumor morphology and spatial relationships with the surrounding tissues. The registered datasets maintained submillimeter spatial accuracy, ensuring the close correlation of tumor characteristics across different MRI sequences.
The MR images underwent the following pre-processing steps: For radiomics feature extraction, a z-score normalization technique was applied to standardize the gray-level intensity ranges across different images. This involved calculating the z-score for each pixel intensity value using the formula z = (x-μ)/σ, where×represents the pixel intensity, μ is the mean, and σ is the standard deviation. This process ensured consistency in the intensity values across the dataset. Subsequently, all images were resampled to achieve a voxel size of 1 × 1 × 1 mm³ using the PyRadiomics package in a Python environment. The resampling algorithm used a basis spline curve, with the interpolator set to sitkBSpline (= 3). The bin width was adjusted to divide the pixel intensity range of 0–255 into five intervals to ensure consistency across all images. To effectively extract the DL features, pixel values < 0 were filtered out in various images, and the grayscale intensity range of these images was calibrated to fit within 0–1.
Diagnostic Imaging Hallmarks
Two experienced physicians independently reviewed the MR images using a double-blinded approach and held discussions whenever disagreements arose. This study recorded several diagnostic imaging features, as previously described.8–11 Peritumoral edema, defined as a hyperintense signal surrounding the tumor mass relative to the adjacent breast parenchyma, was qualitatively assessed on fat-suppressed T2WI. 8 Intratumoral signal characteristics were evaluated using the following criteria: 1) High intratumoral signal intensity: the signal intensity within the tumor exceeding that of the surrounding breast tissue on fat-suppressed T2 W sequences10,11; 2) Adjacent vessel sign: enhancement of vascular structures directly entering or contacting the tumor margin on contrast-enhanced images10,11; 3) Increased ipsilateral vascularity: quantitative asymmetry in vascularity, defined as ≥1 additional visible vessels in the tumor-bearing breast compared to the contralateral side.10,11
All assessments were performed by two board-certified breast radiologists in consensus, with discrepancies resolved through joint re-evaluation and reference to established diagnostic criteria.
Radiomics Classifier
To address feature redundancy and optimize model performance, a rigorous multi-stage feature selection pipeline was implemented. Initially, all radiomic features underwent z-score normalization (z = [x-μ]/σ) to standardize the values across the patient cohort. A three-tiered dimensionality reduction approach was then applied: 1) univariate analysis using independent-sample t-tests to exclude non-discriminative features (p ≥ 0.05); 2) Pearson's correlation analysis (threshold r > 0.9) to eliminate highly correlated redundant features; and 3) Least absolute shrinkage and selection operator (LASSO) regression with 10-fold cross-validation to automatically select the most predictive features while penalizing less informative ones through L1 regularization. The optimal lambda value was determined through cross-validation (Figure 2). Finally, we constructed a robust radiomics classifier by integrating features with non-zero LASSO coefficients into a logistic regression model, ensuring both clinical interpretability and predictive performance.
Radiomics Analysis Demonstrates the Process of Dimensionality Reduction LASSO Regression and 10-Fold Cross-Validation Were Applied. LASSO, Least Absolute Shrinkage and Selection Operator.
Development of the multi-Scale Feature Extraction Network (M-Net)
Given the limited availability of medical data, a compact convolutional neural network (CNN) with fewer parameters was developed to simplify the training process. DL features were extracted using multiscale, dilated convolutions to obtain semantic representations from different images.
The proposed network used three cubic blocks derived from DCE-MRI, T1WI, and T2WI as inputs. All pixel values < 0 in the images were set to 0, and values > 0 were scaled to a range of 0–1. These images, centered on the VOIs, were cropped into three 32 × 32 × 32 cubic blocks. The backbone architecture included five multilevel blocks, incorporating max pooling and residual connections.18,19 These multilevel blocks generated multilevel features related to LVI status.
In each multiscale block, features were initially extracted using a multilevel convolution layer consisting of dilated convolutions with four different dilation rates (1, 2, 3, and 4).20,21,22 These features were then merged across channels and, following batch normalization 23 and rectified linear unit activation, passed through convolution and residual blocks to further refine the multiscale features. Convolutions with larger dilation rates significantly expanded the receptive field compared to that of standard convolutions, capturing a broader range of semantic information. The different semantic features extracted by the dilated convolutions with varying dilation rates complemented each other effectively, contributing to improved diagnostic predictions. All convolution and max-pooling operations used kernel sizes of 3 × 3 with a padding of 1. The number of convolution channels was set to 32, and the stride for max pooling was 2. Finally, all extracted DL features were input into a fully connected classifier with two hidden layers, each containing 50 neurons, for training.
The proposed multilevel feature extraction network was trained from scratch and evaluated using the same training and testing datasets as those used for the radiomics model. Random flipping along three volume axes was applied to the training data. The training utilized a cross-entropy loss function. LVI (−) and LVI (+) were absent from the data; thus, loss coefficients of 1 and 3 were set for LVI (−) and LVI (+), respectively, to assign higher weights to LVI (+) during training, thereby enhancing the model's ability to handle data distribution imbalances. The Adam optimizer was used with a learning rate of 0.00005 and batch size of 16. This network underwent 50 epochs of training to ensure convergence. 24 Implementation of the proposed network utilized PyTorch 1.7.1 and Python 3.7.0. Both training and testing were conducted on a workstation equipped with an Intel Xeon CPU E5-2630 (Intel, Santa Clara, CA, USA) and an Nvidia Tesla V100 Ti (NVIDIA, Santa Clara, CA, USA).
PRM-Net Implementation
The data flowchart of this study involved two parts: feature extraction and diagnostic prediction (Figure 3). The first part included the extraction and dimensionality reduction of radiomics features, as well as the extraction of DL features using a specially designed multilevel feature extraction network. The second part involved classifying the extracted multisource features and providing diagnostic predictions.
Schematic Representation of the PRM-Net Framework. PRM-Net, Prior-Radiomics-Guided Multiscale Feature Extraction Network.
Owing to the limited availability of medical data and the challenge of tuning parameters for 3D CNNs, model overfitting was a potential issue, which can restrict the diagnostic performance. To mitigate this, our approach combined various data sources to overcome the limitations of solely network-based methods and to enhance diagnostic performance. First, a multilevel feature extraction network was trained for DL feature extraction. Subsequently, the feature extraction component of PRM-Net was frozen, and selected radiomics features were integrated to retrain a multi-layer perceptron (MLP) classifier. The MLP classifier comprised two hidden layers, each with 50 neurons. This strategy simplifies training while enhancing overall diagnostic performance.
Pathological Evaluation
An expert histopathologist (non-author with >10 years of experience) conducted the pathological evaluations of the surgical specimens. Following the detailed histological criteria proposed and recommended for diagnosing LVI in breast pathology, 25 routine assessments were conducted on hematoxylin and eosin-stained preparations (Figure 4).
Histological Assessment for the Diagnosis of LVI in Breast Cancer Pathology Based on Detailed Criteria. LVI, Lymphovascular Invasion.
Statistical Analysis
The analytical workflow is summarized in Figure 5. Continuous variables were first evaluated for normality using the Kolmogorov–Smirnov test. Normally distributed variables were analyzed with independent samples t-tests, while non-parametric data are expressed as medians with interquartile ranges (IQRs) and were compared using the Mann–Whitney U test. Categorical variables were assessed with the χ² test. A statistical significance threshold of p < 0.05 was set for all analyses.
Schematic Depiction of the Study Design Framework.
We assessed the predictive performance of all classifiers using the receiver operating characteristic (ROC) and corresponding area under the curve (AUC). The trained models were tested on an independent validation cohort, and their classification performance was evaluated based on the AUC. The final model was determined by the highest AUC value obtained from the validation cohort. 26 To further assess the selected model, metrics derived from the confusion matrix, including accuracy, sensitivity, and specificity, were used along with their corresponding 95% confidence intervals (CIs).
Results
Baseline Information Comparison
The study enrolled 303 female patients with IBC, with a median age of 51 (IQR, 45-58) years. Among them, 71 (23.4%) received a postoperative pathological diagnosis of LVI (+). To achieve a balanced distribution of LVI (+) patients between the training and validation cohorts, a 7:3 ratio was used, allocating 210 patients for training and 93 for validation. The baseline information of each cohort is detailed in Table 1, with no statistically significant differences found (p ≥ 0.05).
Comparisons of Clinical-Radiological Characteristics in the Training and Validation Cohorts.
Abbreviation: TIC, time-signal intensity; FGT, fibroglandular tissue; BPE, breast parenchymal enhancement; ALN, axillary lymph node; DWI, diffusion weighted imaging; LVI, lymphovascular invasion.
Diagnostic Imaging Hallmarks for LVI Prediction
Table 2 presents the results of both univariate and multivariate logistic analyses assessing the predictive capacity of diagnostic imaging hallmarks for LVI in patients with IBC. The multivariate logistic analysis identified peritumoral edema [odds ratio (OR): 4.78, 95% CI: 2.35–9.74, p < 0.001] and the DWI rim sign (OR: 2.19, 95% CI: 1.05-4.59, p = 0.037) as significant independent predictors of LVI in patients with IBC. The diagnostic imaging hallmarks achieved an AUC of 0.761 (95% CI: 0.655-0.866).
Univariate and Multivariate Logistic Analysis for LVI in Patients with IBC.
Abbreviation: TIC, time-signal intensity; FGT, fibroglandular tissue; BPE, breast parenchymal enhancement; ALN, axillary lymph node; DWI, diffusion weighted imaging; LVI, lymphovascular invasion; IBC, invasive breast cancer.
Radiomics Classifier for LVI Prediction
A total of 2589 radiomics features were initially extracted for T1WI, T2WI, and DCE, resulting in 863 features per sequence. After redundancy assessment using t-tests, 57 features remained. Subsequently, following Pearson's correlation analysis, 52 features were deemed suitable for integration into LASSO regression using 10-fold cross-validation (λ = 0.020). Ultimately, nine important features were identified (Figure 6). The radiomics classifier achieved an AUC of 0.771 (0.648-0.894).
Final Radiomics Features Selected Via LASSA Regression Analysis. LASSO, Least Absolute Shrinkage and Selection Operator.
Comparison of Diagnostic Performance among Different Models
The diagnostic performance of the models is outlined in Table 3, and Figures 7 and 8 provide a visual representation of the ROC curve and associated performance metrics. Notably, the PRM-Net achieved an AUC of 0.854 (95% CI: 0.779-0.929), demonstrating its robust performance. Similarly, M-Net exhibited commendable performance, with an AUC of 0.816 (95% CI: 0.732-0.901). These DL-based classifiers (PRM-Net and M-Net) outperformed both traditional diagnostic imaging hallmarks and radiomics classifiers, highlighting the exceptional performance of PRM-Net.
Comparative Receiver Operating Characteristic Curves Among Various Predictive Models.
Diagnostic Performance of PRM-Net, M-Net, Diagnostic Imaging Hallmarks, and Radiomics Classifier in Predicting LVI in Patients With IBC. PRM-Net, Prior-Radiomics-Guided Multiscale Feature Extraction Network; M-Net, Multiscale Feature Extraction Network; LVI, Lymphovascular Invasion; IBC, Invasive Breast Cancer.
Comparison of Diagnostic Performance Metrics among Different Predictive Models.
Abbreviation: PRM-Net, prior-radiomics-guided multi-scale feature extraction network; M-Net, the multi-scale feature extraction network；AUC, area under the curve.
Discussion
This study introduces PRM-Net, a diagnostic algorithm integrating multiscale DL and engineered radiomic features to predict LVI in patients with IBC. PRM-Net outperformed M-Net, a model trained without radiomics information. Moreover, both PRM-Net and M-Net demonstrated superior performance compared with radiomics classifiers and traditional diagnostic imaging hallmarks, with the latter exhibiting the lowest performance.
While traditional diagnostic imaging hallmarks—reliant on qualitative assessments of tumor morphology and enhancement patterns—provide a baseline reference, they showed limited efficacy for predicting LVI in IBC (AUC = 0.761, 95% CI: 0.655-0.866). Multivariate logistic analysis identified peritumoral edema and the DWI rim sign as independent predictors of LVI in patients with IBC, in line with previous studies.8–13,27–31 However, these conventional approaches, while clinically accessible, struggle to quantify subtle tumor heterogeneities that may reflect the invasive potential.
Radiomics classifiers advance the diagnostic paradigm by extracting high-throughput, quantitative features from medical images, thus capturing phenotypic information that extends beyond visual perception.12,13 The radiomics model developed in the present study demonstrated a moderate improvement in performance (AUC = 0.771, 95% CI: 0.648-0.894), underscoring its ability to identify latent heterogeneous factors associated with LVI. Despite these advances, the model's performance remains constrained by its reliance on predefined features and its limited representation of hierarchical tissue architectures. Furthermore, it was outperformed by DL classifier, consistent with the findings of Yang et al 14
DL classifiers, exemplified by M-Net, further improved the diagnostic accuracy through the automatic extraction of multiscale image features. To achieve more effective feature learning, ResNet was adopted, which leverages residual connections to preserve original features and facilitates smoother, more stable training, thereby improving the model accuracy and generalization. ResNet has been widely applied in object detection, image classification, and semantic segmentation. Similarly, dilated convolutions increase the receptive field of CNNs and have been employed to construct lightweight networks. By incorporating multiscale, dilated convolutions, our approach improved the internal structure of CNNs, enabling better feature extraction in limited-data medical imaging tasks. By leveraging neural networks with multiple hidden layers, M-Net enabled multilevel abstraction of imaging patterns and achieved an AUC of 0.816 (95% CI: 0.732-0.901). This superiority underscores the advantage of DL in detecting subtle structural changes; nevertheless, challenges such as extensive parameter tuning and reduced interpretability persist.14–16
To address these limitations, PRM-Net—an end-to-end framework synergizing multiscale DL and engineered radiomic features—was developed in the current study. By integrating refined radiomic signatures—which provide deep phenotypic characterization—with DL's capacity for automatic feature learning, PRM-Net achieved the highest performance, with an AUC of 0.854 (95% CI: 0.779-0.929). This architecture eliminates the need for manual feature optimization and multistep workflows, instead enabling autonomous extraction of LVI-associated features through joint training. The model's end-to-end design not only streamlines the diagnostic pipeline but also enhances interpretability by preserving the contextual relationship between radiomic and DL-derived features.15,16 Collectively, these findings delineate a methodological trajectory from conventional diagnostic imaging hallmarks—characterized by qualitative assessments—to radiomics, providing quantitative feature enhancement; then to DL, enabling automated feature extraction; and finally to PRM-Net—a multimodal fusion framework integrating these representations. This progression underscores the incremental value of combining complementary feature representations to address the complexities of LVI prediction in IBC.
This study has certain limitations. First, as a retrospective analysis, it carries an inherent selection bias that may affect the representativeness of the cohort. To address this issue, we plan to conduct a prospective, multicenter cohort study to validate PRM-Net in real-world clinical workflows, thereby ensuring broader demographic and clinical diversity. Second, the limited sample size prevented subgroup analyses, consequently limiting the generalizability of the findings. Future efforts will focus on expanding the cohort and conducting external validation on independent datasets to assess the robustness of the model. Third, although prognosis was not the primary focus, the short follow-up period prevented long-term outcome analyses. We intend to establish a longitudinal registry to explore the relationships between PRM-Net and survival endpoints. Finally, while PRM-Net effectively utilizes refined MRI radiomics, the integration of multiomic data (eg, genomics, histopathology) could enhance the understanding of underlying mechanisms. In the next phase, we aim to develop a multimodal fusion framework combining genomic biomarkers and histopathological features.
Conclusions
In summary, PRM-Net—integrating refined radiomic features utilizing preoperative MRI—embodies the strengths of DL and radiomics and represents a significant advancement in predicting LVI in patients with IBC. Its practical utility in real-world clinical scenarios has the potential to facilitate the identification of optimal surgical strategies tailored to individual patient needs.
Footnotes
Abbreviations
Acknowledgements
We would like to express our sincere gratitude to Editage for their language editing services, which have greatly improved the quality and readability of this manuscript.
Ethics Approval and Consent to Participate
This retrospective study was conducted in accordance with institutional ethical guidelines and received approval from the Xiangtan Central Hospital Review Board (Approval No: 2024-01-002; Date of Review: January 29, 2024; Location: Xiangtan City).
Consent to Participate
A waiver of informed consent was granted due to the study's retrospective nature and the anonymized data of the participants.
Funding
The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research received financial support from the Hunan Province Undergraduate College Teaching Reform Project (Grant No. 202401001516).
Declaration of Conflicting Interests
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Availability of Data and Materials
The data for this study are available by contacting the corresponding author upon reasonable request.