The study involved 26 athletes from the National Women’s Water Polo Team training between February and July 2021, before and after the implementation of the MAFT mode. Among them, 12 were international-level athletes and 14 were national-level athletes. Their ages ranged from 21 to 32 years, with an average age of 24.9 years. The athletes had been participating in professional sports for 8 to 16 years, averaging 10.9 years, and had been involved in water polo for 8 to 15 years, averaging 9.8 years. They had participated in national-level training for 1 to 14 years, averaging 5.6 years. Twelve athletes had participated in preparation for two Olympic Games. The team positions were distributed as 3 centers, 3 defensive centers, 15 perimeter players, and 5 goalkeepers.

In this study, we employed a combination of surveys and clinical diagnoses to analyze and compare the evolution of injury characteristics before and after the implementation of the Male-Assisted Female Training (MAFT) program. The research team spent an extended period residing with the athletes, closely observing the development and progression of injuries. To gather comprehensive data, we used questionnaires to collect basic information, including names, ages, years of athletic experience, injury locations, and causes. Additionally, we recorded pre-analyzed indicators such as training frequency, intensity, duration, recovery time, and physiological metrics like heart rate, blood lactate levels, and VO2 max. The survey also aimed to identify unique injury patterns that emerged following the implementation of the MAFT program. All questionnaires were meticulously collected and processed. During this period, our team was actively involved in diagnosing and treating all athlete injuries, meticulously documenting the occurrence of common injuries and conducting thorough physical examinations. We paid particular attention to any differences in injury processes and severity compared to previous same-gender training scenarios. In summary, through the combination of survey data and clinical records, we captured detailed information on injury locations, types, and severity, providing a comprehensive overview of the impact of the MAFT program on female water polo athletes.

Statistical analysis was conducted using SPSS software version 20.0 (SPSS Inc., USA). The proportions of injuries to the neck, shoulder, elbow-wrist, thoracic spine, lumbar-sacral region, hip, knee, ankle, forearm lateral, and sternoclavicular joint were treated as quantitative data. Injury proportions, presented as counts (percentages), were compared between groups using Fisher’s exact test to assess the significance of changes in injury patterns before and after the MAFT mode, with the level of significance set at a two-tailed p-value of 0.05. There was a noticeable increase in the proportion of injuries to joints involved in confrontational activities after the implementation of the Male-Assisting-Female-Training mode. The most common injury site was the shoulder, accounting for 34.6% of injuries, which further increased to 42.3% post-implementation. This was followed by injuries to the lumbar-sacral-hip region, with an increase from 26.9% to 34.6%. Injuries to the elbow-wrist area showed a significant upward trend, rising from 7.7% to 26.9%. Conversely, injuries to the knee and ankle joints, primarily involved in non-confrontational sliding motions, showed a decreasing trend. Notably, two goalkeepers sustained injuries, including bilateral forearm ulnar side hitting injuries and a dominant hand side sternoclavicular joint injury. The details of the sports-related injuries, including the number of cases and the proportion of each injury, are summarized in Table 1. In water polo, the increase in proportional injuries to confrontational joints is particularly notable. Shoulder injuries occur at a rate of 24% to 51%, primarily due to the frequent use of the dominant hand in passing and shooting, as well as the non-dominant hand in defensive actions, leading to bilateral shoulder injuries (14, 15). In confrontational training with male athletes, female athletes need to pass the ball more frequently and attack from various angles, increasing the burden on the dominant hand and raising the injury probability to about 57 Elbow and wrist injuries are also common, with wrist injuries occurring at a rate of 13.6% to 23.1% and elbow injuries at a rate of 6% to 18.2% (16–19). In confrontations with male athletes, female athletes need to find more flexible passing and offensive paths, increasing the burden on the wrist and elbow joints and leading to an increased risk of injury (20, 21). Conversely, the proportion of injuries to stability joints has decreased. The incidence rate of knee and ankle injuries is 4.5% to 10.8% and 6% to 18.2%, respectively (16). Confrontations with male athletes reduce the time spent “treading water,” lowering the tension on the knee joint and thus reducing the injury rate. Among goalkeepers, sternal-clavicular joint injuries are a new type of injury. These injuries are usually caused by direct high-impact trauma, while indirect force-related collateral injuries can be alleviated with rest (22, 23). The inability of athletes to get adequate rest during the preparation period is the main reason for persistent pain.

A hypergraph is a structure capable of representing complex relationships and multidimensional features, making it suitable for capturing interactions and relationships among athletes. In constructing the hypergraph, we first define nodes and hyperedges.

To capture the complex relationships within the team, we designed a Hypergraph Neural Network (HGNN) model to learn the embeddings of nodes and hyperedges. The architecture of the HGNN model is designed to capture and represent complex higher-order relationships through a multi-layer structure.

We preprocess the data to obtain a feature vector of total dimension RD(D=320), representing the records of all injury-related indicators for the corresponding individual. Then, we use KNN to establish the initial hypergraph structure and utilize the features learned by HGNN for injury type prediction. To better learn the hypergraph structure, we analyzed the characteristics of the dataset and found that introducing a graph regularization mechanism preserves the local geometric structure of the hypergraph data more effectively, preventing overfitting and enhancing the model’s generalization capability. This leads to better classification accuracy, which is beneficial for accurately extracting key influencing factors of injuries before and after the introduction of the MAFT model. Specifically, given an initialized hypergraph structure H(V,E,W), where the symbols denote a set of vertices V, a set of hyperedges E, and a weight matrix W, which is a diagonal matrix representing the weights of the hyperedges. This hypergraph can be succinctly represented by an incidence matrix H∈R|V|×|E|, where each entry h(v,e) is defined as Equation 7:(7)h(v,e)={1,if v∈e0,if v∉e,Graph regularization in HGNNs aims to preserve the local geometric structure of hypergraph data and improve the model’s generalization capability. This is achieved by adding a regularization term to the loss function that measures the smoothness of node embeddings. Given the H=(V,E,W), the incidence matrix H, the vertex degree matrix by Dv, and the hyperedge degree matrix by De. The Laplacian matrix L for a hypergraph can be defined as:L=De−HTWHwhere De is the degree matrix of hyperedges, H is the incidence matrix, and W is the weight matrix. During training, we wish for the low-dimensional representations X of the vertices to preserve the local structure of the hypergraph. The regularized objective function for HGNNs can be written as Equation 8:(8)JrHGNN=12XTLX+λΩ(X)Here, JrHGNN is the regularized loss function, rHGNN represents the regularized form of HGNN in our proposed model, Ω(X) represents other possible regularization terms (such as weight decay), and λ is the regularization parameter that controls the strength of the regularization term. The optimization process involves minimizing JHGNN through gradient descent or other optimization algorithms, thereby learning the low-dimensional representations X of the vertices while maintaining the local structure of the hypergraph. This regularization method helps improve the performance of HGNNs on various downstream tasks such as node classification and clustering.

Notably, The regularization term Ω is constructed to ensure that the node embeddings preserve the local structure of the hypergraph. Specifically, Ω(X) includes both a weight decay term that discourages overly complex models and a graph Laplacian smoothness term that encourages nearby nodes in the hypergraph to have similar embeddings. Mathematically, Ω(X) is defined as Equation 9:(9)Ω(X)=α⋅(∑i,jWij‖Xi−Xj‖2)+β⋅(∑i‖Xi‖2)where Wij represents the elements of the graph Laplacian L, Xi and Xj are the embeddings of nodes i and j, respectively. The first term encourages smooth embeddings across the hypergraph, while the second term, weight decay, penalizes large embedding values. α and β are hyperparameters that control the relative importance of the smoothness and weight decay terms, respectively.

For pattern analysis, we focus primarily on visualization differences. This involves visualizing the structure and features of the hypergraph after optimizing reconstruction loss. We visualize differences in the global hypergraph and the MAFT-induced changes under single-factor influences. Specifically, when visualizing the hypergraph structure, we highlight the clustering of nodes. For visualizing hypergraph features, we employ dimensionality reduction techniques to create 2D visualizations.

For classification analysis, to assess the model’s performance, we utilize several key metrics. Firstly, Accuracy (ACC) is calculated as TP+TNTP+TN+FP+FN, reflecting the model’s overall ability to correctly classify instances across all categories. Sensitivity (SEN), given by TPTP+FN, measures how effectively the model identifies true positive cases. Specificity (SPEC), defined as TNTN+FP, evaluates the model’s capability to accurately recognize true negative cases without misclassifying them as positive. The Positive Predictive Value (PPV), calculated as TPTP+FP, represents the fraction of correctly identified positive cases among all cases predicted as positive. Lastly, the Negative Predictive Value (NPV), given by TNTN+FN, indicates the proportion of true negatives among the cases predicted as negative. These metrics collectively provide a comprehensive evaluation of the model’s classification performance.

For pattern analysis, the MLP consists of two hidden layers with 64 and 32 neurons respectively, followed by a ReLU activation function. The output layer uses a sigmoid activation function to produce the final pattern recognition output. The HGNN and MLP models are trained simultaneously using the Adam optimizer with a learning rate of 0.001. The training process includes early stopping with a patience parameter set to 10 epochs to prevent overfitting. The models are trained for a total of 100 epochs or until the validation loss stops improving.

For classification analysis, the rHGNN model is trained by minimizing the Equation 8. We employ stochastic gradient descent (SGD) as our optimization algorithm, with a learning rate of 0.01 and a decay schedule to adjust the learning rate over time. The training process is carefully monitored to ensure convergence towards a minimum of the loss function. The hyperparameters λ, α and β in the regularization term Ω(X) are crucial for balancing the weight decay and smoothness constraints. The default values are set as λ=0.2, α=0.03, and β=0.005. For more details on the ablation experiments, please refer to the subsequent sections.

We selected several comparative methods for our evaluation, including MLP, SVM, GNN, B-GNN, HGNN, and HGNNP. •

MLP (24): MLP is a class of feedforward artificial neural networks consisting of multiple layers of nodes, each fully connected to the next. It is widely used for classification and regression tasks due to its ability to capture non-linear relationships.

Figure 2 illustrates the distribution of various features in a two-dimensional space, comparing the scenarios with and without the application of MAFT. The figure is divided into four subplots, each representing different types of features: Global Feature, Training Load Factor, Psychological State Factor, and Physiological Indicators Factor. In the case of Global Features, it is observed that without MAFT, the data points are sparsely distributed with no apparent clustering pattern. However, when MAFT is applied, the data points become more densely packed and exhibit a certain degree of structural organization. This indicates that MAFT effectively enhances the correlation among global features. For Training Load Factors, a similar trend is observed. Without MAFT, the data points appear scattered and lack discernible patterns. Upon applying MAFT, the points converge into tighter clusters, suggesting that MAFT can extract more meaningful features from training load data. When examining Psychological State Factors, it is evident that without MAFT, the data points are randomly dispersed with no significant clustering. With MAFT applied, small clusters begin to form among the data points. This transformation implies that psychological state data becomes more consistent and interpretable after undergoing feature transformation through MAFT. Lastly, for Physiological Indicators Factors, the untransformed data exhibits a disordered scatter. However, post-MAFT application, the data points reveal clearer structural patterns. This suggests that physiological indicators processed through MAFT better reflect their intrinsic relationships. In summary, the comparison clearly demonstrates that applying MAFT results in more compact and organized distributions across all types of features.

Figure 3 illustrates the changes in hypergraph structures for specific factor indicators before and after implementing the MAFT program, focusing on Heart Rate Variability (HRV) and Training Frequency. Before MAFT, the HRV hypergraph shows numerous dispersed connections with some isolated nodes, indicating weak correlations. This disorganized structure may hinder effective information capture by models. After applying MAFT, the HRV hypergraph becomes more structured and cohesive, with fewer isolated nodes. Enhanced connectivity suggests improved correlation among nodes, facilitating better data utilization by models. Similarly, the pre-MAFT hypergraph for Training Frequency is characterized by scattered connections and weak node associations. This loose network structure can impede meaningful feature extraction. Post-MAFT application reveals a more organized network with tighter clusters and stronger internal associations. This improved structure enhances data consistency and information flow, aiding models in accurately capturing training frequency impacts.

Table 2 presents a comprehensive evaluation of various models, highlighting the performance of our proposed method, rHGNN. The results demonstrate that rHGNN consistently outperforms other methods across all evaluated metrics, including Accuracy (ACC), Positive Predictive Value (PPV), Negative Predictive Value (NPV), Sensitivity (SEN), and Specificity (SPEC). The ACC for rHGNN is notably high at 0.90635, surpassing traditional models such as MLP and SVM, which achieve ACCs of 0.68637 and 0.65817 respectively. This indicates a significant improvement in overall model accuracy. In terms of PPV and NPV, rHGNN achieves values of 0.92572 and 0.91092 respectively, reflecting its superior ability to correctly predict positive and negative cases compared to other models like GNN and B-GNN. Furthermore, the SEN value for rHGNN is the highest among all methods at 0.93216, demonstrating its exceptional sensitivity in identifying true positive cases. Similarly, SPEC is also maximized at 0.92785, indicating robust specificity in distinguishing true negatives. Overall, these results underscore the efficacy of the rHGNN model in achieving superior performance across multiple dimensions compared to conventional approaches such as HGNN and HGNNP. The consistent excellence across all metrics suggests that our method offers a highly reliable solution for the given task, setting a new benchmark for future research endeavors in this domain.

In Table 3, we provide a detailed and comprehensive analysis of how different regularization hyperparameters affect our accuracy. It is evident that λ is optimal around the 0.1 range, α is best suited for the 0.01 range, and β performs well in the 0.001 range.

When examining the impact of varying the hyperparameter λ, it is observed that smaller values such as λ=0.01 result in a slight decrease in ACC to 0.89049, while PPV and NPV also show minor reductions compared to the full model. As λ increases to 1.0, there is a more pronounced decline in ACC to 0.87687, indicating that larger values may negatively affect overall accuracy. Adjustments to the hyperparameter α reveal similar trends; for instance, at α=0.001, ACC drops to 0.88735 with corresponding decreases in other metrics such as PPV and NPV compared to the baseline model’s performance. For the hyperparameter β, we observe that at β=0.0001, ACC remains relatively high at 0.89944. However, increasing β leads to lower performance metrics, with β=0.01 resulting in an ACC of 0.88584. Overall, the full model (rHGNN) consistently outperforms variations with different hyperparameters. This suggests that optimal tuning plays a crucial role in achieving superior model performance.

The introduction of the MAFT mode has had a significant impact on the injury patterns among female water polo players. HGNN provided valuable insights into the complex interactions within the team and identified specific patterns associated with increased injury risk. These findings suggest that tailored training interventions and injury prevention strategies should be developed, considering the unique demands of the MAFT mode. Future research should focus on validating these findings and exploring additional applications of HGNN in sports injury prevention. We recommend paying attention to the following points when implementing the MAFT training program:

1.

It is essential to adjust the frequency of training sessions to prevent overtraining and potential injuries. Sufficient rest periods should be incorporated into the training plan to allow athletes to fully recover. Excessive training frequency can lead to fatigue, decreased performance, and an increased risk of injury.