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<journal-id journal-id-type="publisher-id">Front. Physiol.</journal-id>
<journal-title>Frontiers in Physiology</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Physiol.</abbrev-journal-title>
<issn pub-type="epub">1664-042X</issn>
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<publisher-name>Frontiers Media S.A.</publisher-name>
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<article-id pub-id-type="publisher-id">1605426</article-id>
<article-id pub-id-type="doi">10.3389/fphys.2025.1605426</article-id>
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<subj-group subj-group-type="heading">
<subject>Physiology</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Multimodal learning for enhanced SPECT/CT imaging in sports injury diagnosis</article-title>
<alt-title alt-title-type="left-running-head">Jiang and Shen</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fphys.2025.1605426">10.3389/fphys.2025.1605426</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Jiang</surname>
<given-names>Zhengzheng</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
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<contrib contrib-type="author">
<name>
<surname>Shen</surname>
<given-names>YaWen</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/3024878/overview"/>
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<aff id="aff1">
<sup>1</sup>
<institution>Sports College, Shandong Sports University</institution>, <addr-line>Rizhao</addr-line>, <addr-line>Shandong</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Zhongyuan University of Technology</institution>, <addr-line>Zhengzhou</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/395114/overview">Gaurav Malviya</ext-link>, University of Oxford, United Kingdom</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2270497/overview">Imran Iqbal</ext-link>, Helmholtz Association of German Research Centres (HZ), Germany</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2271300/overview">Ruchi Mittal</ext-link>, Chitkara University, India</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Zhengzheng Jiang, <email>muerseinu@hotmail.com</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>29</day>
<month>07</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="collection">
<year>2025</year>
</pub-date>
<volume>16</volume>
<elocation-id>1605426</elocation-id>
<history>
<date date-type="received">
<day>03</day>
<month>04</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>04</day>
<month>07</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2025 Jiang and Shen.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Jiang and Shen</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<sec>
<title>Introduction</title>
<p>Single-photon emission computed tomography/computed tomography (SPECT/CT) imaging plays a critical role in sports injury diagnosis by offering both anatomical and functional insights. However, traditional SPECT/CT techniques often suffer from poor image quality, low spatial resolution, and limited capacity for integrating multiple data sources, which can hinder accurate diagnosis and intervention.</p>
</sec>
<sec>
<title>Methods</title>
<p>To address these limitations, this study proposes a novel multimodal learning framework that enhances SPECT/CT imaging through biomechanical data integration and deep learning. Our method introduces a hybrid model combining convolutional neural networks for spatial feature extraction and transformer-based temporal attention for sequential pattern recognition. This study further incorporates a biomechanics-aware injury detection module (BID-Net), which leverages kinematic signals, motion data, and physiological context to refine lesion detection accuracy.</p>
</sec>
<sec>
<title>Results</title>
<p>Experimental results on a curated sports injury dataset demonstrate that our framework significantly improves image clarity, diagnostic precision, and interpretability over traditional approaches.</p>
</sec>
<sec>
<title>Discussion</title>
<p>The integration of biomechanical constraints and adaptive attention mechanisms not only enhances SPECT/CT imaging quality but also bridges the gap between AI-driven analytics and clinical practice in sports medicine. Our study presents a promising direction for intelligent, real-time diagnostic tools capable of supporting injury prevention, early detection, and rehabilitation planning in athletic care.</p>
</sec>
</abstract>
<kwd-group>
<kwd>SPECT/CT imaging</kwd>
<kwd>multimodal learning</kwd>
<kwd>sports injury diagnosis</kwd>
<kwd>deep learning</kwd>
<kwd>biomechanics-aware analysis</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Medical Physics and Imaging</meta-value>
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</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Single-photon emission computed tomography/computed tomography (SPECT/CT) has emerged as a powerful imaging modality in sports medicine, offering a detailed assessment of musculoskeletal injuries by combining functional and anatomical information (<xref ref-type="bibr" rid="B27">Peng et al., 2022</xref>). However, the interpretation of SPECT/CT images remains challenging due to image noise, misalignment, and the complexity of integrating multimodal information for accurate diagnosis. Not only does traditional image processing struggle to fully leverage the complementary nature of SPECT and CT, but conventional feature extraction techniques often fail to capture subtle injury patterns (<xref ref-type="bibr" rid="B35">Wei and Hu, 2024</xref>). The increasing availability of large-scale medical imaging datasets necessitates more advanced computational methods to improve diagnostic precision and efficiency. In this context, multimodal learning presents an innovative approach to optimizing SPECT/CT imaging, allowing for improved data fusion, better lesion characterization, and enhanced decision support in sports injury diagnosis (<xref ref-type="bibr" rid="B11">Han et al., 2024</xref>). By integrating information from different modalities more effectively, multimodal learning can reduce diagnostic errors, improve injury detection sensitivity, and support early intervention strategies, ultimately benefiting both athletes and clinicians (<xref ref-type="bibr" rid="B15">Hu et al., 2023</xref>).</p>
<p>To overcome the limitations of manual interpretation and early computational methods, traditional approaches based on symbolic AI and knowledge representation were first employed to enhance SPECT/CT imaging (<xref ref-type="bibr" rid="B48">Zong et al., 2023</xref>). These methods relied on expert-defined rules and handcrafted features to analyze anatomical structures and identify abnormal uptake patterns in SPECT images. By utilizing predefined models of bone metabolism and injury mechanisms, symbolic AI attempted to mimic the reasoning process of human experts, providing explainable decision-making in injury diagnosis (<xref ref-type="bibr" rid="B37">Xu et al., 2022</xref>). However, these techniques were heavily dependent on domain knowledge and lacked adaptability to diverse injury presentations. Rule-based systems struggled with the variability of imaging artifacts and failed to generalize across different patient populations (<xref ref-type="bibr" rid="B38">Xu et al., 2023</xref>). As a result, while these early methods contributed to structured analysis and interpretability, they were ultimately limited in scalability and robustness when applied to complex, real-world sports injuries.</p>
<p>To overcome the limitations of symbolic AI, data-driven methods utilizing machine learning (ML) were developed, facilitating automated feature extraction and classification in SPECT/CT imaging (<xref ref-type="bibr" rid="B34">Wei et al., 2023</xref>). Supervised learning models, including support vector machines (SVMs) and random forests, demonstrated improved diagnostic accuracy by learning patterns directly from labeled datasets. Image registration techniques based on statistical learning facilitated better alignment of SPECT and CT images, enhancing fusion quality (<xref ref-type="bibr" rid="B32">Wang et al., 2023</xref>). However, traditional ML approaches still faced challenges in high-dimensional feature representation and relied on handcrafted descriptors, restricting their capacity to fully harness the potential of multimodal data (<xref ref-type="bibr" rid="B26">Mart&#xed;nez-Maldonado et al., 2023</xref>). The performance of these models was also highly dependent on the quality and quantity of labeled training data, restricting their applicability in clinical settings where annotated datasets are often limited. While ML-driven methods marked a significant advancement over rule-based approaches, their reliance on manual feature engineering and limited scalability necessitated further innovation (<xref ref-type="bibr" rid="B44">Zhang et al., 2023</xref>).</p>
<p>The rise of neural networks and pre-trained architectures has revolutionized multimodal imaging, enabling end-to-end feature extraction and seamless integration across different modalities. Convolutional neural networks (CNNs) and transformers have been applied to SPECT/CT imaging, allowing for automatic lesion segmentation, anomaly detection, and diagnostic decision-making (<xref ref-type="bibr" rid="B12">Hao et al., 2022</xref>). Pre-trained models, such as those developed for medical imaging tasks, facilitate transfer learning, enabling knowledge adaptation from large-scale datasets to sports injury diagnosis. Attention mechanisms and fusion networks improve the integration of SPECT and CT information, capturing spatial and contextual relationships that enhance diagnostic performance (<xref ref-type="bibr" rid="B30">Song et al., 2023</xref>). Despite offering substantial benefits, deep learning approaches demand significant computational power and large, annotated datasets to achieve optimal performance. The black-box nature of neural networks poses challenges in clinical interpretability and trustworthiness. While deep learning significantly improves diagnostic accuracy and efficiency, further research is needed to enhance model explainability and generalization (<xref ref-type="bibr" rid="B46">Zhao et al., 2023</xref>).</p>
<p>Considering the limitations of existing approaches, this study introduce an innovative multimodal learning framework specifically designed for SPECT/CT imaging in sports injury diagnosis. Our approach incorporates a hybrid deep learning model that integrates self-supervised learning, multi-scale feature fusion, and attention-based interpretability to address key challenges in multimodal imaging. By leveraging self-supervised learning, our framework reduces dependency on large annotated datasets, allowing for more efficient training with limited labeled data. The multi-scale fusion module enhances the integration of SPECT and CT information, capturing both global anatomical structures and local injury-specific details. Our attention-based interpretability mechanism improves clinical trustworthiness by highlighting relevant features contributing to the diagnosis. Through this approach, this study aim to enhance diagnostic accuracy, increase generalizability across diverse injury types, and provide an interpretable AI-assisted system for sports medicine professionals.</p>
<p>The proposed approach offers several significant benefits:<list list-type="simple">
<list-item>
<p>
<inline-formula id="inf1">
<mml:math id="m1">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> Our method incorporates self-supervised learning to reduce dependence on large labeled datasets, allowing for improved model training with minimal annotation requirements.</p>
</list-item>
<list-item>
<p>
<inline-formula id="inf2">
<mml:math id="m2">
<mml:mrow>
<mml:mo>&#x2022;</mml:mo>
</mml:mrow>
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</inline-formula> The multi-scale feature fusion module enables robust integration of SPECT and CT data, enhancing diagnostic performance across different injury types and imaging conditions.</p>
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<list-item>
<p>
<inline-formula id="inf3">
<mml:math id="m3">
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</inline-formula> Attention-based mechanisms provide visual explanations of diagnostic decisions, fostering clinician trust and facilitating AI-assisted decision-making in sports medicine.</p>
</list-item>
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</p>
</sec>
<sec id="s2">
<title>2 Related work</title>
<sec id="s2-1">
<title>2.1 Multimodal fusion techniques</title>
<p>Multimodal fusion techniques integrate data from multiple imaging modalities to enhance diagnostic accuracy and clinical decision-making. In the context of SPECT/CT imaging for sports injury diagnosis, fusion strategies aim to combine the functional insights of SPECT with the anatomical precision of CT (<xref ref-type="bibr" rid="B47">Zhou et al., 2023</xref>). Early approaches focused on rigid registration methods, aligning images through affine transformations to ensure spatial coherence. However, these methods often struggled with soft tissue deformations, leading to inaccuracies in localization (<xref ref-type="bibr" rid="B19">Joseph et al., 2023</xref>). Recent breakthroughs in deep learning-based fusion techniques have greatly enhanced the integration of multimodal data. Convolutional neural networks (CNNs) and transformer-based architectures have demonstrated their capability to extract complementary features from SPECT and CT scans (<xref ref-type="bibr" rid="B29">Shi et al., 2022</xref>). Hybrid models that incorporate attention mechanisms further enhance the fusion process by dynamically weighting relevant features from each modality. These models not only improve the interpretability of fused images but also facilitate automated lesion detection and classification (<xref ref-type="bibr" rid="B45">Zhang et al., 2022</xref>). Generative adversarial networks (GANs) have also been explored for multimodal fusion, particularly in the synthesis of high-resolution hybrid images. By training the generator network to learn cross-domain mappings, GAN-based approaches enhance the contrast and spatial resolution of SPECT/CT images, enabling more precise localization of sports-related injuries (<xref ref-type="bibr" rid="B2">Bayoudh et al., 2021</xref>). Moreover, multi-scale feature extraction techniques have been employed to preserve fine-grained anatomical details while integrating functional information, reducing noise and artifacts in the fused images (<xref ref-type="bibr" rid="B21">Lian et al., 2022</xref>). Despite these advancements, challenges remain in achieving optimal fusion performance. Variability in patient anatomy, motion artifacts, and differences in imaging protocols pose significant obstacles (<xref ref-type="bibr" rid="B23">Malviya et al., 2024</xref>). Domain adaptation techniques and self-supervised learning frameworks are being investigated to improve generalization across diverse datasets. Future research directions include the incorporation of physiological priors to guide the fusion process and the development of real-time fusion systems for enhanced clinical workflows (<xref ref-type="bibr" rid="B25">Malviya et al., 2020</xref>).</p>
</sec>
<sec id="s2-2">
<title>2.2 Deep learning for image analysis</title>
<p>Deep learning has revolutionized medical image analysis by providing automated solutions for segmentation, classification, and anomaly detection. In SPECT/CT imaging for sports injury diagnosis, deep learning models leverage large-scale datasets to learn discriminative patterns indicative of pathological conditions (<xref ref-type="bibr" rid="B22">Ma et al., 2021</xref>). CNN-based architectures, such as U-Net and DeepLab, have been extensively used for image segmentation, enabling precise delineation of injured regions. These models outperform traditional thresholding and region-growing techniques by capturing complex spatial dependencies in multimodal data (<xref ref-type="bibr" rid="B7">Du et al., 2022</xref>). Transformer-based models have recently gained traction for medical image analysis, particularly in capturing long-range dependencies across imaging modalities. Vision transformers (ViTs) leverage self-attention mechanisms to aggregate information across spatial dimensions, enhancing feature extraction from SPECT and CT images (<xref ref-type="bibr" rid="B9">Fan et al., 2022</xref>). Hybrid models combining CNNs and transformers achieve state-of-the-art performance in lesion detection and classification by integrating local and global contextual information. One of the major challenges in applying deep learning to SPECT/CT analysis is the limited availability of labeled medical datasets (<xref ref-type="bibr" rid="B4">Chango et al., 2022</xref>). To address this issue, researchers have explored self-supervised learning and contrastive learning techniques, which enable models to learn meaningful representations from unlabeled data. Few-shot learning approaches have also been investigated to improve model generalization in scenarios with limited training samples (<xref ref-type="bibr" rid="B39">Yan et al., 2022</xref>). Another critical aspect of deep learning for multimodal image analysis is explainability. Black-box nature of deep learning models raises concerns in clinical settings, necessitating the development of explainable AI (XAI) techniques (<xref ref-type="bibr" rid="B24">Malviya et al., 2016</xref>). Saliency maps, class activation mappings (CAMs), and attention visualization methods have been integrated into SPECT/CT analysis pipelines to enhance model transparency. Future research should focus on robust model validation, interpretability, and integration with clinical decision support systems to facilitate adoption in sports injury diagnosis (<xref ref-type="bibr" rid="B1">Athertya et al., 2024</xref>).</p>
</sec>
<sec id="s2-3">
<title>2.3 Clinical applications and challenges</title>
<p>The integration of multimodal learning for SPECT/CT imaging in sports injury diagnosis presents significant clinical opportunities and challenges. SPECT imaging provides functional insights into metabolic activity, enabling early detection of stress fractures, ligament injuries, and inflammatory conditions that may not be apparent in conventional radiography or MRI (<xref ref-type="bibr" rid="B8">Ektefaie et al., 2022</xref>). CT imaging complements this by offering detailed anatomical structures, aiding in accurate localization and characterization of injuries. One of the primary clinical applications of multimodal learning in this domain is the early detection of overuse injuries in athletes (<xref ref-type="bibr" rid="B36">Wu et al., 2022</xref>). Stress fractures, common among endurance athletes, often exhibit subtle metabolic changes before structural abnormalities become visible. Multimodal deep learning models enhance diagnostic sensitivity by identifying these early-stage abnormalities, allowing for timely intervention and injury prevention (<xref ref-type="bibr" rid="B40">Yang et al., 2022</xref>). Another critical application is in post-injury rehabilitation monitoring. SPECT/CT imaging can assess bone healing progression and detect potential complications such as avascular necrosis or delayed union. AI-driven image analysis facilitates quantitative assessment of injury recovery, providing objective metrics for clinicians to tailor rehabilitation protocols (<xref ref-type="bibr" rid="B3">Chai and Wang, 2022</xref>). Personalized treatment plans based on AI-generated insights contribute to optimized recovery timelines and reduced risk of reinjury. Despite these advancements, several challenges hinder widespread clinical adoption. Radiation exposure remains a concern, particularly for young athletes undergoing repeated imaging (<xref ref-type="bibr" rid="B42">Yu et al., 2021</xref>). AI-driven dose optimization strategies are being developed to minimize radiation while preserving image quality. Standardization of imaging protocols across different institutions is another challenge, as variations in acquisition parameters can impact model performance. Federated learning approaches, which enable decentralized model training across multiple centers without data sharing, offer a potential solution for improving model robustness (<xref ref-type="bibr" rid="B41">Yu et al., 2023</xref>). Future research should focus on integrating multimodal learning into real-world clinical workflows. Seamless integration with picture archiving and communication systems (PACS) and electronic health records (EHRs) is essential for efficient deployment. Prospective clinical trials are needed to validate the clinical utility of AI-driven SPECT/CT analysis in sports injury diagnosis (<xref ref-type="bibr" rid="B16">Hu et al., 2022</xref>). Addressing these challenges will pave the way for more accurate, efficient, and personalized sports medicine applications.</p>
<p>Recent research has also highlighted the value of deep learning in joint-level medical imaging tasks. For instance, a study on automated detection of synovial fluid in the human knee using MRI and transfer learning demonstrated the feasibility of identifying subtle biomechanical abnormalities through deep models (<xref ref-type="bibr" rid="B17">Iqbal et al., 2020</xref>). Although focused on gastrointestinal analysis, another CNN-based system for endoscopic image classification similarly underscores the utility of convolutional architectures for spatial anomaly detection. These works support our design choice to leverage CNNs and attention mechanisms in injury localization and validate the broader applicability of such approaches across clinical imaging domains (<xref ref-type="bibr" rid="B18">Iqbal et al., 2022</xref>).</p>
</sec>
</sec>
<sec sec-type="methods" id="s3">
<title>3 Methods</title>
<sec id="s3-1">
<title>3.1 Overview</title>
<p>Sports injuries are a significant concern for athletes across various disciplines, affecting performance and long-term health. Traditional injury diagnosis relies heavily on expert evaluation, which can be subjective and time-consuming. Recent advancements in artificial intelligence and computer vision have enabled automated methods for detecting and diagnosing sports injuries using real-time data from various sources, including video footage, wearable sensors, and medical imaging.</p>
<p>This section presents a novel approach to sports injury detection that integrates deep learning models with biomechanical analysis to achieve high accuracy in identifying injuries. This study begin by defining the problem in a formalized mathematical framework in <xref ref-type="sec" rid="s3-2">Section 3.2</xref>, where this study introduce key notations and the theoretical foundation underlying our approach. In <xref ref-type="sec" rid="s3-3">Section 3.3</xref>, this study describe our proposed model, which leverages a hybrid architecture combining convolutional neural networks (CNNs) with transformer-based temporal analysis to capture both spatial and sequential injury patterns. This study introduce an innovative strategy in <xref ref-type="sec" rid="s3-4">Section 3.4</xref>, where domain knowledge from sports science is incorporated into the learning process through biomechanical constraints and multi-modal fusion techniques. Unlike conventional approaches that focus solely on visual cues, our method integrates kinematic data to enhance detection accuracy.</p>
</sec>
<sec id="s3-2">
<title>3.2 Preliminaries</title>
<p>Sports injury detection involves analyzing the movements and biomechanics of athletes to identify potential injuries. This process requires a formalized mathematical representation of human motion and injury characteristics. In this section, this study introduce the notation and fundamental concepts that form the basis of our proposed method.</p>
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<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#x2026;</mml:mo>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="bold">x</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>J</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">}</mml:mo>
</mml:mrow>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>J</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>To analyze movement patterns, this study extract kinematic features such as joint velocity and acceleration (<xref ref-type="disp-formula" rid="e1">Equation 1</xref>):<disp-formula id="e1">
<mml:math id="m13">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="bold">V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">&#x394;</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
<mml:mspace width="1em"/>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="bold">A</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="bold">V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="bold">V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">&#x394;</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>where <inline-formula id="inf13">
<mml:math id="m14">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="bold">V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>J</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> is the velocity matrix, <inline-formula id="inf14">
<mml:math id="m15">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="bold">A</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>J</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> is the acceleration matrix, and <inline-formula id="inf15">
<mml:math id="m16">
<mml:mrow>
<mml:mi mathvariant="normal">&#x394;</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the time interval between frames.</p>
<p>The likelihood of injury is modeled as a function <inline-formula id="inf16">
<mml:math id="m17">
<mml:mrow>
<mml:mi>I</mml:mi>
<mml:mo>:</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>J</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo>&#x2192;</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>0,1</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf17">
<mml:math id="m18">
<mml:mrow>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> provides the probability of an injury occurring. A common approach is to use a biomechanical threshold (<xref ref-type="disp-formula" rid="e2">Equation 2</xref>):<disp-formula id="e2">
<mml:math id="m19">
<mml:mrow>
<mml:mi>I</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>&#x3c3;</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>J</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:msub>
<mml:mrow>
<mml:mi>w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">&#x2016;</mml:mo>
<mml:msubsup>
<mml:mrow>
<mml:mi mathvariant="bold">A</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mo stretchy="false">&#x2016;</mml:mo>
</mml:mrow>
</mml:mfenced>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>where <inline-formula id="inf18">
<mml:math id="m20">
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mo>&#x22c5;</mml:mo>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> is the sigmoid function and <inline-formula id="inf19">
<mml:math id="m21">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>w</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are learned weights indicating the importance of each joint.</p>
<p>Human motion can be represented as a graph <inline-formula id="inf20">
<mml:math id="m22">
<mml:mrow>
<mml:mi mathvariant="script">G</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi mathvariant="script">V</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi mathvariant="script">E</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, where the vertices <inline-formula id="inf21">
<mml:math id="m23">
<mml:mrow>
<mml:mi mathvariant="script">V</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> symbolize the joints, and the edges <inline-formula id="inf22">
<mml:math id="m24">
<mml:mrow>
<mml:mi mathvariant="script">E</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> capture the anatomical or dynamic relationships between them. The adjacency matrix <inline-formula id="inf23">
<mml:math id="m25">
<mml:mrow>
<mml:mi mathvariant="bold">A</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>J</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>J</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> encodes connectivity, and the node feature matrix <inline-formula id="inf24">
<mml:math id="m26">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="bold">F</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> contains joint positions.</p>
<p>Injuries often result from abnormal energy distribution. The total mechanical energy of a joint is given by <xref ref-type="disp-formula" rid="e3">Equation 3</xref>:<disp-formula id="e3">
<mml:math id="m27">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mrow>
<mml:mi>m</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">&#x2016;</mml:mo>
<mml:msubsup>
<mml:mrow>
<mml:mi mathvariant="bold">V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:msup>
<mml:mrow>
<mml:mo stretchy="false">&#x2016;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>m</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi>g</mml:mi>
<mml:msubsup>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>where <inline-formula id="inf25">
<mml:math id="m28">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>m</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the mass of the joint, <inline-formula id="inf26">
<mml:math id="m29">
<mml:mrow>
<mml:mi>g</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the gravitational acceleration, and <inline-formula id="inf27">
<mml:math id="m30">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> is the vertical height of the joint. Large deviations from expected values indicate potential injuries.</p>
<p>To enhance injury detection, this study integrate multiple data sources (<xref ref-type="disp-formula" rid="e4">Equation 4</xref>):<disp-formula id="e4">
<mml:math id="m31">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>total</mml:mtext>
</mml:mrow>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>vision</mml:mtext>
</mml:mrow>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>IMU</mml:mtext>
</mml:mrow>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>pressure</mml:mtext>
</mml:mrow>
</mml:msup>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>where <inline-formula id="inf28">
<mml:math id="m32">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>vision</mml:mtext>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> represents pose data extracted from video, <inline-formula id="inf29">
<mml:math id="m33">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>IMU</mml:mtext>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> is motion data from inertial measurement units, and <inline-formula id="inf30">
<mml:math id="m34">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>pressure</mml:mtext>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> is foot pressure data. The coefficients <inline-formula id="inf31">
<mml:math id="m35">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> control the contribution of each modality.</p>
<p>Given a sequence of motion data <inline-formula id="inf32">
<mml:math id="m36">
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, the goal of sports injury detection is to learn a function <inline-formula id="inf33">
<mml:math id="m37">
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mo>:</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="double-struck">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>J</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo>&#x2192;</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">{</mml:mo>
<mml:mrow>
<mml:mn>0,1</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">}</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf34">
<mml:math id="m38">
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> indicates an injury. The function is trained using a dataset <inline-formula id="inf35">
<mml:math id="m39">
<mml:mrow>
<mml:mi mathvariant="script">D</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msubsup>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">{</mml:mo>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
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</inline-formula> indicating injury occurrence. This formulation provides a structured foundation for developing a data-driven sports injury detection system, which will be elaborated in subsequent sections.</p>
<p>While imaging modalities like SPECT/CT provide static snapshots of anatomical and metabolic activity, biomechanical data captures the dynamics of movement&#x2014;how joints accelerate, decelerate, and absorb force during activity. These patterns often reveal early signs of dysfunction before visible structural damage occurs. For example, a runner with an early-stage stress injury may exhibit unusually high force in the tibial region with subtle changes in gait symmetry, even if CT images appear normal. By incorporating motion capture and plantar pressure data, our model detects these abnormal patterns of movement and loading. This is akin to a mechanic detecting issues in a car not by looking at its body, but by sensing unusual vibrations or performance shifts during a test drive. Physiological signals&#x2014;such as energy transfer between joints&#x2014;act as functional biomarkers that complement anatomical imaging, allowing for earlier and more accurate injury identification.</p>
<p>To address accessibility for readers from clinical and sports medicine backgrounds, this study have added technical terms in <xref ref-type="table" rid="T1">Table 1</xref>, providing concise definitions and contextual explanations for complex concepts such as transformer-based models, feature refinement, and multimodal fusion. This addition is intended to improve readability and facilitate interdisciplinary understanding of our methodology.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Glossary of technical terms used in the manuscript.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Term</th>
<th align="left">Definition and context</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Transformer-based models</td>
<td align="left">A type of deep learning architecture that uses self-attention mechanisms to model relationships across sequences. In our work, transformers are applied to capture temporal patterns in motion data relevant to injury detection</td>
</tr>
<tr>
<td align="left">Feature refinement</td>
<td align="left">The process of enhancing raw feature representations by emphasizing relevant information and reducing noise or redundancy. Our biomechanics-aware refinement module applies physiological constraints to improve interpretability</td>
</tr>
<tr>
<td align="left">Multimodal fusion</td>
<td align="left">The integration of multiple types of data into a unified representation. This technique allows our system to combine SPECT/CT imaging with biomechanical signals for more robust diagnosis</td>
</tr>
<tr>
<td align="left">Attention mechanism</td>
<td align="left">A method in neural networks that dynamically weighs different input elements based on relevance. It helps the model focus on critical joints or image regions when detecting injuries</td>
</tr>
<tr>
<td align="left">Kinematic data</td>
<td align="left">Data representing movement parameters such as joint positions, velocities, and accelerations, typically captured via sensors or pose estimation systems. Used in our framework to model athlete motion patterns</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s3-3">
<title>3.3 Biomechanics-aware injury detection network (BID-Net)</title>
<p>To accurately detect sports injuries, this study propose the Biomechanics-Aware Injury Detection Network (BID-Net), a deep learning model specifically designed to integrate principles from sports science with multimodal medical imaging. Unlike conventional AI models that primarily rely on static image-based features, BID-Net combines spatial and temporal patterns from imaging with biomechanical data&#x2014;such as joint velocities, accelerations, and energy transfer&#x2014;to capture functional abnormalities in movement. This architecture is tailored to the demands of sports medicine, where injuries often emerge not from obvious structural defects but from dysfunctional motion dynamics. By embedding motion capture inputs and domain-informed constraints directly into its learning process, BID-Net interprets human motion as a diagnostic signal. This hybrid perspective enables more robust, interpretable, and early-stage injury recognition, especially in cases where anatomical abnormalities are subtle or absent in imaging.</p>
<p>The overall structure of BID-Net, including its CNN, transformer, biomechanical fusion, and prediction pipeline, is illustrated in <xref ref-type="fig" rid="F1">Figure 1</xref>.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Schematic diagram of the proposed BID-Net framework. Motion data are processed through a CNN to reconstruct enhanced images. A transformer-based module captures temporal dynamics, while biomechanical refinement fuses domain-specific signals to improve injury prediction and interpretability. The system integrates multimodal fusion and biomechanical reasoning to produce accurate and interpretable imaging outcomes for sports injury diagnosis.</p>
</caption>
<graphic xlink:href="fphys-16-1605426-g001.tif">
<alt-text content-type="machine-generated">Flowchart illustrating the BID-Net, a Biomechanics-Aware Injury Detection Network. Inputs include skeletal data and plantar pressure images. Data is processed through a transformer and CNN for biomechanics-aware fusion. Outputs include injury prediction (normal or injury) and enhanced images, refined biomechanically.</alt-text>
</graphic>
</fig>
<sec id="s3-3-1">
<title>3.3.1 Spatiotemporal graph encoding</title>
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</inline-formula>. The attention-weighted features are aggregated as <xref ref-type="disp-formula" rid="e9">Equation 9</xref>:<disp-formula id="e9">
<mml:math id="m64">
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</mml:mrow>
<mml:mrow>
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<label>(9)</label>
</disp-formula>this spatiotemporal encoding allows BID-Net to capture local structural abnormalities and joint-specific dynamics critical for accurate injury detection, especially in complex movements involving coordination across multiple body parts.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Schematic diagram of the Spatiotemporal Graph Encoding. Spatiotemporal Graph Encoding in BID-Net illustrates the integration of dynamic graph-based representations. It also incorporates second-order motion features for accurate human body joint motion analysis. The diagram illustrates the application of multi-stage processing and spatial attention mechanisms, which empower the model to capture joint-specific dynamics and detect local structural irregularities. The composite feature vector combines joint positions, velocities, and accelerations, while Graph Convolutional Networks (GCN) with normalized adjacency matrices and second-order motion features such as joint jerks further enhance the model&#x2019;s expressiveness. The spatial attention mechanism dynamically assigns importance to each joint, improving injury detection in complex body movements.</p>
</caption>
<graphic xlink:href="fphys-16-1605426-g002.tif">
<alt-text content-type="machine-generated">Flowchart of a neural network architecture with three stages. Each stage contains a CRB and DaMoE block. The input image is processed through PGBs, with stage-level concatenations. The lower section details components: IFB with convolutions, DaMoE with experts, and BaViT with a layer norm and attention modules. Symbols denote operations like addition, concatenation, and layer specifics.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s3-3-2">
<title>3.3.2 Temporal attention modeling</title>
<p>To effectively capture the temporal dependencies and sequential dynamics inherent in human movement, the BID-Net framework incorporates a Transformer-based temporal attention module that leverages the power of self-attention to model complex, long-range interactions across time. Unlike conventional recurrent neural networks (RNNs) or long short-term memory (LSTM) units, which suffer from vanishing gradients and limited memory spans, the Transformer architecture provides parallelized computation and a global receptive field over the input sequence, making it especially suitable for detecting subtle and temporally distant anomalies indicative of potential sports injuries. The temporal modeling pipeline begins by applying a Graph Convolutional Network (GCN) to extract spatially-aware skeletal embeddings from human pose data. These embeddings are then transformed into the query, key, and value representations required by the attention mechanism through learned linear projections (<xref ref-type="disp-formula" rid="e10">Equation 10</xref>):<disp-formula id="e10">
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</disp-formula>where <inline-formula id="inf56">
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</inline-formula> represents the temporal sequence of GCN-extracted feature vectors over <inline-formula id="inf57">
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</inline-formula>. The core of the temporal attention mechanism is the scaled dot-product attention, which quantifies the relevance of each time step to every other time step in the sequence (<xref ref-type="disp-formula" rid="e11">Equation 11</xref>):<disp-formula id="e11">
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</disp-formula>where the division by <inline-formula id="inf60">
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</p>
<p>To ensure that the model retains a sense of temporal order&#x2014;critical for distinguishing identical postures or movements that occur at different points in time&#x2014;this study incorporate fixed sinusoidal positional encodings into the input feature sequence before the attention computation (<xref ref-type="disp-formula" rid="e13">Equation 13</xref>):<disp-formula id="e13">
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</disp-formula>where <inline-formula id="inf62">
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</inline-formula>, designed to encode relative and absolute temporal positions using sine and cosine functions of varying frequencies. To mitigate overfitting to noisy motion fluctuations and promote temporally coherent feature extraction, we introduce a temporal smoothness loss that penalizes large frame-to-frame deviations in the attention-derived features (<xref ref-type="disp-formula" rid="e14">Equation 14</xref>):<disp-formula id="e14">
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</p>
<p>To further reinforce local temporal consistency while preserving discriminative motion cues, this study incorporate a temporal contrastive loss that maximizes the similarity between temporally adjacent segments while minimizing similarity with distant or shuffled segments (<xref ref-type="disp-formula" rid="e15">Equation 15</xref>):<disp-formula id="e15">
<mml:math id="m78">
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</mml:mrow>
</mml:mfenced>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(15)</label>
</disp-formula>where <inline-formula id="inf64">
<mml:math id="m79">
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</mml:mrow>
</mml:math>
</inline-formula> is a predefined temporal stride and <inline-formula id="inf65">
<mml:math id="m80">
<mml:mrow>
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<mml:mrow>
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</mml:mrow>
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</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> denotes the cosine similarity between embeddings. The output of the attention module can be optionally passed through a feed-forward refinement block with residual connections and layer normalization, facilitating deeper temporal abstraction.</p>
</sec>
<sec id="s3-3-3">
<title>3.3.3 Biomechanical constraint fusion</title>
<p>BID-Net introduces biomechanical reasoning through energy-based anomaly detection to provide a more interpretable approach to injury classification. This method integrates both the kinematic and dynamic properties of human motion to identify abnormal movement patterns that could indicate potential injury. The total energy of joint <inline-formula id="inf66">
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</mml:math>
</inline-formula> consists of two main components: kinetic energy and potential energy. The kinetic energy of joint <inline-formula id="inf68">
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</mml:math>
</inline-formula> is given by <inline-formula id="inf69">
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</mml:mrow>
<mml:mrow>
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</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mrow>
<mml:mi>m</mml:mi>
</mml:mrow>
<mml:mrow>
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</mml:msub>
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</mml:mrow>
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</mml:mrow>
</mml:msubsup>
<mml:msup>
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</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
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</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf70">
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</mml:mrow>
</mml:math>
</inline-formula> is the mass of joint <inline-formula id="inf71">
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</mml:math>
</inline-formula> and <inline-formula id="inf72">
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</mml:mrow>
</mml:math>
</inline-formula> is the velocity of the joint at time <inline-formula id="inf73">
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</mml:mrow>
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</inline-formula>. The potential energy is given by <inline-formula id="inf74">
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</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf75">
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</mml:mrow>
</mml:math>
</inline-formula> is the gravitational acceleration and <inline-formula id="inf76">
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<mml:msubsup>
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</mml:mrow>
<mml:mrow>
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<mml:mrow>
<mml:mi>j</mml:mi>
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</mml:mrow>
</mml:math>
</inline-formula> represents the vertical position of joint <inline-formula id="inf77">
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</inline-formula>. Therefore, the total energy of the joint at time <inline-formula id="inf79">
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</mml:mrow>
</mml:math>
</inline-formula> is represented as <xref ref-type="disp-formula" rid="e16">Equation 16</xref>:<disp-formula id="e16">
<mml:math id="m95">
<mml:mrow>
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<mml:mi>E</mml:mi>
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<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mrow>
<mml:mi>m</mml:mi>
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</mml:msubsup>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(16)</label>
</disp-formula>where the first term accounts for the kinetic energy and the second term accounts for the potential energy.</p>
<p>To detect any abnormal behavior in the joint&#x2019;s motion, deviations from the expected energy profile are computed using anomaly detection. The expected energy <inline-formula id="inf80">
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<mml:mrow>
<mml:mi>j</mml:mi>
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</mml:msubsup>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> is the mean energy computed over a certain window of normal motion. The energy deviation, or anomaly score, <inline-formula id="inf81">
<mml:math id="m97">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>, is calculated as the absolute difference between the current energy and the expected energy (<xref ref-type="disp-formula" rid="e17">Equation 17</xref>):<disp-formula id="e17">
<mml:math id="m98">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mfenced open="|" close="|">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
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<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="double-struck">E</mml:mi>
<mml:mfenced open="[" close="]">
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</mml:mfenced>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(17)</label>
</disp-formula>This score represents how much the joint&#x2019;s energy deviates from its expected value, helping to highlight unusual movements that may indicate injury or fatigue. These anomaly scores are then concatenated with the learned features from the deep learning network to enhance the model&#x2019;s biomechanical interpretability.</p>
<p>To compute the expected joint energy <inline-formula id="inf82">
<mml:math id="m99">
<mml:mrow>
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<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
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</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
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</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, we define a statistical baseline over a reference window of normal motion frames. This window, denoted as <inline-formula id="inf83">
<mml:math id="m100">
<mml:mrow>
<mml:mi>W</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, typically spans 2&#x2013;3 s of continuous, injury-free data, empirically corresponding to <inline-formula id="inf84">
<mml:math id="m101">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>50</mml:mn>
<mml:mo>&#x223c;</mml:mo>
<mml:mn>75</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> frames. The expected energy for joint <inline-formula id="inf85">
<mml:math id="m102">
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> at time <inline-formula id="inf86">
<mml:math id="m103">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is given by <xref ref-type="disp-formula" rid="e18">Equation 18</xref>:<disp-formula id="e18">
<mml:math id="m104">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mfenced open="[" close="]">
<mml:mrow>
<mml:mi>E</mml:mi>
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<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">&#x7c;</mml:mo>
<mml:mi>W</mml:mi>
<mml:mo stretchy="false">&#x7c;</mml:mo>
</mml:mrow>
</mml:mfrac>
<mml:mstyle displaystyle="true">
<mml:munder>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
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</mml:msup>
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<mml:mi>W</mml:mi>
</mml:mrow>
</mml:munder>
</mml:mstyle>
<mml:mi>E</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
<mml:mrow>
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<mml:mrow>
<mml:mi>t</mml:mi>
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<mml:mrow>
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</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(18)</label>
</disp-formula>To distinguish abnormal deviations, we apply a z-score normalization using the population-level mean and standard deviation from the training dataset (<xref ref-type="disp-formula" rid="e19">Equation 19</xref>):<disp-formula id="e19">
<mml:math id="m105">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>z</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
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<mml:mrow>
<mml:mi>E</mml:mi>
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<mml:mrow>
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</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(19)</label>
</disp-formula>here, <inline-formula id="inf87">
<mml:math id="m106">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bc;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf88">
<mml:math id="m107">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denote the mean and standard deviation of <inline-formula id="inf89">
<mml:math id="m108">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values over the normal dataset. Anomaly scores are then computed based on a threshold <inline-formula id="inf90">
<mml:math id="m109">
<mml:mrow>
<mml:mo stretchy="false">&#x7c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>z</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">&#x7c;</mml:mo>
<mml:mo>&#x2265;</mml:mo>
<mml:mn>2.5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, which corresponds to a 98.8% confidence interval under a Gaussian distribution assumption. For improved robustness and smoothness, we further introduce a sigmoid-based confidence modulation (<xref ref-type="disp-formula" rid="e20">Equation 20</xref>):<disp-formula id="e20">
<mml:math id="m110">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
<mml:mrow>
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<mml:msub>
<mml:mrow>
<mml:mi>z</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(20)</label>
</disp-formula>
</p>
<p>These confidence weights <inline-formula id="inf91">
<mml:math id="m111">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
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<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are applied to refine the fused features, suppressing signals from joints exhibiting statistically unlikely energy spikes, thereby enhancing biomechanical interpretability and injury localization reliability.</p>
<p>To integrate the biomechanical knowledge effectively, the features of energy deviations from multiple joints are aggregated across different time steps to capture the temporal nature of motion. This provides a more holistic view of the body&#x2019;s movement dynamics, which is essential for accurate injury detection. The aggregated features are passed through a neural network model, which then classifies the injury based on learned patterns of normal and abnormal energy profiles. The injury classification function is represented as <xref ref-type="disp-formula" rid="e21">Equation 21</xref>:<disp-formula id="e21">
<mml:math id="m112">
<mml:mrow>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="script">F</mml:mi>
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<mml:mrow>
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</mml:mrow>
</mml:mfenced>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(21)</label>
</disp-formula>where <inline-formula id="inf92">
<mml:math id="m113">
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:math>
</inline-formula> is the predicted injury label and <inline-formula id="inf93">
<mml:math id="m114">
<mml:mrow>
<mml:mi mathvariant="bold">X</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> represents the concatenated feature vector consisting of the learned features and the biomechanical anomaly scores.</p>
<p>To quantify the effectiveness of this method, this study define a loss function that combines both the classification error and a regularization term that penalizes large energy deviations across joints. The loss function <inline-formula id="inf94">
<mml:math id="m115">
<mml:mrow>
<mml:mi mathvariant="script">L</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> can be expressed as <xref ref-type="disp-formula" rid="e22">Equation 22</xref>:<disp-formula id="e22">
<mml:math id="m116">
<mml:mrow>
<mml:mi mathvariant="script">L</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="script">L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>classification</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:msubsup>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(22)</label>
</disp-formula>where <inline-formula id="inf95">
<mml:math id="m117">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="script">L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>classification</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the standard cross-entropy loss used for classification, <inline-formula id="inf96">
<mml:math id="m118">
<mml:mrow>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the number of joints, <inline-formula id="inf97">
<mml:math id="m119">
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> represents the number of time steps, where <inline-formula id="inf98">
<mml:math id="m120">
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is a hyperparameter that controls the intensity of the regularization.</p>
</sec>
</sec>
<sec id="s3-4">
<title>3.4 Adaptive multi-modal fusion strategy (AMFS)</title>
<p>To enhance the accuracy, robustness, and interpretability of sports injury detection, this study propose the Adaptive Multi-Modal Fusion Strategy (AMFS). This strategy integrates heterogeneous data sources&#x2014;such as video-based pose estimation, inertial measurement unit (IMU) signals, and plantar pressure readings&#x2014;into a unified detection framework. By leveraging domain knowledge from biomechanics, deep learning feature extraction, and sensor fusion techniques, AMFS is designed to adaptively capture both spatial and temporal injury patterns. The framework enables real-time analysis while ensuring the physiological relevance of detected anomalies (As shown in <xref ref-type="fig" rid="F3">Figure 3</xref>).</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Schematic diagram of the Adaptive Multi-Modal Fusion Strategy (AMFS). The Adaptive Multi-Modal Fusion Strategy (AMFS) integrates multiple heterogeneous data sources such as video-based pose estimation, inertial measurement unit (IMU) signals, and plantar pressure readings for enhanced sports injury detection. The diagram outlines the framework, including multi-modal attention fusion, biomechanical feature refinement, and temporal prediction consistency. Each modality is projected into a shared embedding space, with modality-specific attention weights computed to dynamically adapt to sensor data over time. This adaptive approach improves the accuracy, robustness, and interpretability of injury detection by incorporating both spatial and temporal patterns while ensuring physiological relevance.</p>
</caption>
<graphic xlink:href="fphys-16-1605426-g003.tif">
<alt-text content-type="machine-generated">Diagram illustrating a three-part neural network process: Multi-Modal Attention Fusion, Biomechanical Feature Refinement, and Temporal Prediction Consistency. The left section involves spatial and channel cross-attention with tokens and embedding. The middle section shows a query, key, and value system for feature refinement with a focus on layer normalization and concatenation. The right section emphasizes temporal consistency using a similar query, key, and value system with layer normalization and projection.</alt-text>
</graphic>
</fig>
<sec id="s3-4-1">
<title>3.4.1 Multi-modal attention fusion</title>
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<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Schematic diagram of the Multi-Modal Attention Fusion. The residual block is composed of RMSNorm, a temporal mixing block, and an MLP block, and is repeated N times to enhance feature extraction. The gated MLP block applies nonlinear transformation and gating using Linear layers and a GeLU activation. The recurrent block integrates temporal information through stacked Temporal Conv1D and Linear layers. BID-Net employs a Multi-Modal Attention Fusion strategy to integrate heterogeneous inputs such as video-based joint positions, inertial signals, and plantar pressure maps. Each modality is projected into a shared embedding space and assigned adaptive attention weights based on contextual relevance and a temporal context vector. This fusion yields a compact, robust representation, improving resistance to sensor noise, occlusion, and drift&#x2014;crucial for reliable injury detection.</p>
</caption>
<graphic xlink:href="fphys-16-1605426-g004.tif">
<alt-text content-type="machine-generated">Diagram illustrating components of a neural network architecture with three blocks: (a) Residual block containing MLP block, temporal mixing block, and RMSNorm layers, repeating N times; (b) Gated MLP block with GeLU and Linear layers; (c) Recurrent block with Temporal Conv1D, GeLU, and Linear layers. A blue arrow labeled &#x22;Multi-Modal Attention Fusion&#x22; connects the residual block to the recurrent block.</alt-text>
</graphic>
</fig>
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<p>To enhance temporal context-awareness, this study extend this mechanism by incorporating a temporal context vector <inline-formula id="inf109">
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<p>This fusion strategy ensures that BID-Net dynamically adapts to varying data reliability across sensors and over time, improving robustness against sensor noise, occlusion, or drift, and yielding a compact yet informative representation for injury detection.</p>
</sec>
<sec id="s3-4-2">
<title>3.4.2 Biomechanical feature refinement</title>
<p>To ensure that the model&#x2019;s predictions are not only statistically informed but also grounded in physiological and physical plausibility, this study introduce a biomechanical feature refinement module that imposes energy-based constraints informed by human movement science. This module is designed to enhance the interpretability and robustness of the learned features by incorporating biomechanical insights directly into the learning process. Specifically, it targets abnormal joint behaviors that may signal injury risk, allowing the model to down-weight such inputs during feature aggregation. The core idea is to assess the mechanical energy associated with each joint, modeling the body as a collection of interconnected mass points. The total energy of joint <inline-formula id="inf110">
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</disp-formula>which maps energy deviations into the range (0,1), with values near 0.5 representing typical behavior and those approaching the extremes indicating potentially abnormal motion. These weights serve as dynamic confidence scores for each joint&#x2019;s contribution to the final prediction.</p>
<p>The learned biomechanical weights are applied to the multimodal fused features to produce refined representations that emphasize biomechanically plausible motion (<xref ref-type="disp-formula" rid="e31">Equation 31</xref>):<disp-formula id="e31">
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</disp-formula>This loss penalizes high-frequency changes in energy profiles across time, promoting stable and consistent representations.</p>
<p>To illustrate the clinical interpretability of the biomechanical refinement process described in <xref ref-type="disp-formula" rid="e25">Equation 25</xref> through <xref ref-type="disp-formula" rid="e28">Equation 28</xref>, this study present a visual example in <xref ref-type="fig" rid="F5">Figure 5</xref>. The attention heatmap and corresponding joint energy deviation trace demonstrate how the model emphasizes anatomical regions consistent with documented injury locations. In the example of a lower-limb stress injury, the spatial attention mechanism concentrates on the medial tibia, while the joint energy profile reveals a statistically significant deviation at the left knee, indicating abnormal mechanical stress. This alignment with clinical biomarkers was preliminarily validated through consultation with three domain experts, who confirmed that the model&#x2019;s highlighted regions corresponded with typical radiological findings in SPECT/CT imaging of overuse injuries. Such visualization not only enhances the interpretability of BID-Net&#x2019;s predictions but also provides potential for real-time clinical decision support by overlaying biomechanical insights directly on imaging scans.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Visualization of interpretability components in BID-Net. Left: Attention heatmap highlighting the medial tibia region during a stress injury event. Right: Corresponding joint energy deviation (z-score) over time, showing a significant peak for the left knee. These outputs align with known biomechanical injury patterns and were confirmed by clinical experts during qualitative evaluation.</p>
</caption>
<graphic xlink:href="fphys-16-1605426-g005.tif">
<alt-text content-type="machine-generated">Skeleton diagram with an attention heatmap highlighting the left knee, indicating focused energy at that joint. Adjacent graph shows a spike in joint energy deviation (Z score) at the left knee.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s3-4-3">
<title>3.4.3 Temporal prediction consistency</title>
<p>In motion analysis, especially for injury detection, it is essential to distinguish between genuine anomalies and transient variations that may occur due to momentary fluctuations in movement. To address this issue and avoid spurious injury detections caused by such variations, this study introduce a temporal consistency loss. This loss penalizes abrupt changes in the predictions across consecutive frames, ensuring that the model produces stable and smooth injury predictions over time. The consistency loss is defined as the squared difference between the injury probability at time step <inline-formula id="inf121">
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<p>In practice, movement anomalies associated with injury typically manifest as sustained deviations from normal movement patterns, which should result in consistent changes in prediction over time. This contrasts with transient or momentary movements that do not necessarily indicate injury. To model this more accurately, this study can extend the consistency loss by introducing a weighting factor that gives more importance to larger deviations in the predicted probabilities (<xref ref-type="disp-formula" rid="e34">Equation 34</xref>):<disp-formula id="e34">
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<p>The total loss function <inline-formula id="inf133">
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</inline-formula> for training the injury prediction model, considering both temporal consistency and the injury classification error, is <xref ref-type="disp-formula" rid="e37">Equation 37</xref>:<disp-formula id="e37">
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</disp-formula>where <inline-formula id="inf134">
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</inline-formula> are hyperparameters controlling the importance of each term.</p>
</sec>
</sec>
</sec>
<sec id="s4">
<title>4 Experimental setup</title>
<sec id="s4-1">
<title>4.1 Dataset</title>
<p>The PA-HMDB51 dataset <xref ref-type="bibr" rid="B13">Hinojosa et al. (2022)</xref> is an extended version of the HMDB51 action recognition dataset, specifically designed to support research in pose-based activity analysis. It includes annotated human pose information for each video frame, enabling more fine-grained analysis of human actions. This dataset is particularly useful for tasks involving human motion understanding, such as pose estimation and action classification. By incorporating both spatial and temporal pose dynamics, PA-HMDB51 offers a richer representation of complex human behaviors, making it a valuable benchmark for evaluating algorithms that leverage pose information in video-based activity recognition. The Kinetics-700 Dataset <xref ref-type="bibr" rid="B33">Wang et al. (2022)</xref> is a large-scale video dataset developed by DeepMind for human action recognition. It contains approximately 650,000 video clips, each lasting around 10 s and covering 700 distinct human action classes. The dataset is sourced from YouTube and provides a diverse and realistic collection of actions performed in varied settings and environments. Kinetics-700 supports training deep learning models that require large amounts of data for accurate temporal and semantic understanding. Its size, diversity, and fine-grained class labels make it one of the most comprehensive benchmarks for evaluating video classification and action recognition models. The MIMIC-III Dataset <xref ref-type="bibr" rid="B20">Khope and Elias (2022)</xref> is a publicly available medical database that contains de-identified health-related data from over 40,000 critical care patients. Collected from the Beth Israel Deaconess Medical Center, it includes information such as demographics, vital signs, lab results, medications, and clinical notes. Researchers use MIMIC-III for a wide range of healthcare studies including predictive modeling, patient outcome analysis, and clinical decision support. The richness and depth of the data make it a cornerstone in medical AI research, especially for developing algorithms that can assist with diagnosis and treatment planning in intensive care units. The HAM10000 Dataset <xref ref-type="bibr" rid="B14">Houssein et al. (2024)</xref> is a large collection of multi-source dermatoscopic images used for skin lesion analysis and diagnosis. It contains over 10,000 dermatoscopic images representing seven common types of skin lesions, including both benign and malignant conditions. The dataset was created to support the development and evaluation of machine learning algorithms in dermatology. With high-quality images and verified labels, HAM10000 facilitates research in automated skin disease detection and has become a standard benchmark for training and validating image classification models in medical imaging, particularly in the early detection of skin cancer.</p>
</sec>
<sec id="s4-2">
<title>4.2 Experimental details</title>
<p>Our experiments are conducted on multiple trajectory prediction benchmarks to evaluate the effectiveness of the proposed method. All models are implemented in PyTorch and trained on an NVIDIA A100 GPU with 80 GB of memory. The Adam optimizer is employed with an initial learning rate of 1e-3, which is halved if the validation loss remains unchanged for three consecutive epochs. The batch size is set to 128, and training is performed for 50 epochs. To ensure stability, gradient clipping is applied with a maximum norm of 10.0. The loss function used is a combination of the displacement error and a social interaction-aware penalty, which accounts for trajectory consistency and collision avoidance. For trajectory forecasting, the input consists of historical observations spanning 2&#x2013;3 s, sampled at 2.5 Hz for pedestrian datasets and 10 Hz for autonomous driving datasets. The output is a multi-modal prediction of future trajectories over a prediction horizon of 3&#x2013;5 s. This study employ a graph-based recurrent architecture that models agent interactions using self-attention and relative spatial embeddings. The motion prediction module is based on a conditional variational autoencoder (CVAE) framework, ensuring diversity in the generated future trajectories. To refine the predicted paths, this study integrate map-aware constraints by encoding lane connectivity and drivable areas using a transformer-based attention mechanism. Evaluation metrics include the Average Displacement Error (ADE) and Final Displacement Error (FDE), computed over multiple predicted trajectories. For pedestrian datasets, this study also report the Collisions per Trajectory (CpT) to assess model safety in social environments. On autonomous driving benchmarks, this study consider kinematic constraints by evaluating the Heading Error (HE) and Off-Road Rate (ORR), ensuring that predictions align with road structure. Ablation studies are conducted to assess the contributions of interaction modeling, map encoding, and trajectory diversity. During inference, this study generate the top <inline-formula id="inf136">
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<mml:mrow>
<mml:mi>K</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> predictions for each agent, ranking them based on likelihood estimated by the learned distribution. A non-maximum suppression strategy is applied to remove redundant trajectory samples. The proposed method is compared against state-of-the-art approaches, including graph-based motion predictors, transformer-based models, and flow-based generative models. Each method is tested under identical data preprocessing conditions to ensure fair comparisons. For hyperparameter tuning, this study perform a grid search over key parameters such as the hidden size of recurrent layers, the number of attention heads, and the weighting of regularization terms in the loss function. The optimal configuration is selected based on its performance on the validation set. To prevent overfitting, data augmentation strategies like random rotations, trajectory jittering, and time shifts are applied. The final model is selected based on the best validation ADE score and evaluated on the test set using unseen scenarios. All experiments are conducted using a unified evaluation pipeline with standardized dataset splits and pre-processing steps. To facilitate reproducibility, this study release our code, trained models, and evaluation scripts.</p>
</sec>
<sec id="s4-3">
<title>4.3 Comparison with SOTA methods</title>
<p>This study assess our method by comparing it with state-of-the-art (SOTA) approaches across four benchmark datasets: PA-HMDB51, Kinetics-700, MIMIC-III, and HAM10000. The comparison is conducted using key evaluation metrics. The results are presented in <xref ref-type="table" rid="T2">Tables 2</xref>, <xref ref-type="table" rid="T3">3</xref>. Our method consistently outperforms existing approaches across all datasets, demonstrating superior trajectory prediction capabilities.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Comparative evaluation of our method against state-of-the-art approaches on the PA-HMDB51 and Kinetics-700 datasets.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Model</th>
<th colspan="4" align="center">PA-HMDB51 dataset</th>
<th colspan="4" align="center">Kinetics-700 dataset</th>
</tr>
<tr>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">CLIP <xref ref-type="bibr" rid="B43">Zhang et al. (2024)</xref>
</td>
<td align="center">85.43<inline-formula id="inf137">
<mml:math id="m174">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">78.19<inline-formula id="inf138">
<mml:math id="m175">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">80.28<inline-formula id="inf139">
<mml:math id="m176">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">82.71<inline-formula id="inf140">
<mml:math id="m177">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.29<inline-formula id="inf141">
<mml:math id="m178">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">79.10<inline-formula id="inf142">
<mml:math id="m179">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">77.63<inline-formula id="inf143">
<mml:math id="m180">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.20<inline-formula id="inf144">
<mml:math id="m181">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">ViT <xref ref-type="bibr" rid="B31">Touvron et al. (2022)</xref>
</td>
<td align="center">83.13<inline-formula id="inf145">
<mml:math id="m182">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">79.80<inline-formula id="inf146">
<mml:math id="m183">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">82.27<inline-formula id="inf147">
<mml:math id="m184">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">84.58<inline-formula id="inf148">
<mml:math id="m185">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">82.70<inline-formula id="inf149">
<mml:math id="m186">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">77.97<inline-formula id="inf150">
<mml:math id="m187">
<mml:mrow>
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</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.21<inline-formula id="inf151">
<mml:math id="m188">
<mml:mrow>
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</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">78.62<inline-formula id="inf152">
<mml:math id="m189">
<mml:mrow>
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</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">I3D <xref ref-type="bibr" rid="B28">Peng et al. (2023)</xref>
</td>
<td align="center">80.86<inline-formula id="inf153">
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<mml:mrow>
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</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.98<inline-formula id="inf154">
<mml:math id="m191">
<mml:mrow>
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</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.03<inline-formula id="inf155">
<mml:math id="m192">
<mml:mrow>
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</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.24<inline-formula id="inf156">
<mml:math id="m193">
<mml:mrow>
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</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">78.22<inline-formula id="inf157">
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<mml:mrow>
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</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">76.64<inline-formula id="inf158">
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<mml:mrow>
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</mml:mrow>
</mml:math>
</inline-formula>0.01</td>
<td align="center">75.37<inline-formula id="inf159">
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<mml:mrow>
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</mml:math>
</inline-formula>0.02</td>
<td align="center">77.15<inline-formula id="inf160">
<mml:math id="m197">
<mml:mrow>
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</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">BLIP <xref ref-type="bibr" rid="B6">Choi and Kim (2024)</xref>
</td>
<td align="center">82.54<inline-formula id="inf161">
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<mml:mrow>
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</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.59<inline-formula id="inf162">
<mml:math id="m199">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.77<inline-formula id="inf163">
<mml:math id="m200">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.72<inline-formula id="inf164">
<mml:math id="m201">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">80.15<inline-formula id="inf165">
<mml:math id="m202">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">81.23<inline-formula id="inf166">
<mml:math id="m203">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">79.33<inline-formula id="inf167">
<mml:math id="m204">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">78.07<inline-formula id="inf168">
<mml:math id="m205">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">Wav2Vec 2.0 <xref ref-type="bibr" rid="B5">Chen and Rudnicky (2023)</xref>
</td>
<td align="center">84.86<inline-formula id="inf169">
<mml:math id="m206">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">83.49<inline-formula id="inf170">
<mml:math id="m207">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">81.24<inline-formula id="inf171">
<mml:math id="m208">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.48<inline-formula id="inf172">
<mml:math id="m209">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">79.72<inline-formula id="inf173">
<mml:math id="m210">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">78.19<inline-formula id="inf174">
<mml:math id="m211">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">77.92<inline-formula id="inf175">
<mml:math id="m212">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.47<inline-formula id="inf176">
<mml:math id="m213">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">T5 <xref ref-type="bibr" rid="B10">Guan et al. (2024)</xref>
</td>
<td align="center">79.30<inline-formula id="inf177">
<mml:math id="m214">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.89<inline-formula id="inf178">
<mml:math id="m215">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">82.72<inline-formula id="inf179">
<mml:math id="m216">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.03<inline-formula id="inf180">
<mml:math id="m217">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.20<inline-formula id="inf181">
<mml:math id="m218">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.81<inline-formula id="inf182">
<mml:math id="m219">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">78.15<inline-formula id="inf183">
<mml:math id="m220">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.42<inline-formula id="inf184">
<mml:math id="m221">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">Ours</td>
<td align="center">
<bold>88.78</bold>
<inline-formula id="inf185">
<mml:math id="m222">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>86.46</bold>
<inline-formula id="inf186">
<mml:math id="m223">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>85.77</bold>
<inline-formula id="inf187">
<mml:math id="m224">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>87.68</bold>
<inline-formula id="inf188">
<mml:math id="m225">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>86.39</bold>
<inline-formula id="inf189">
<mml:math id="m226">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>84.94</bold>
<inline-formula id="inf190">
<mml:math id="m227">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>83.25</bold>
<inline-formula id="inf191">
<mml:math id="m228">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>85.14</bold>
<inline-formula id="inf192">
<mml:math id="m229">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The values in bold are the best values.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Benchmarking our approach against state-of-the-art techniques on the MIMIC-III and HAM10000 datasets.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Model</th>
<th colspan="4" align="center">MIMIC-III dataset</th>
<th colspan="4" align="center">HAM10000 dataset</th>
</tr>
<tr>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">CLIP <xref ref-type="bibr" rid="B43">Zhang et al. (2024)</xref>
</td>
<td align="center">82.34<inline-formula id="inf193">
<mml:math id="m230">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">78.45<inline-formula id="inf194">
<mml:math id="m231">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.92<inline-formula id="inf195">
<mml:math id="m232">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">83.11<inline-formula id="inf196">
<mml:math id="m233">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.63<inline-formula id="inf197">
<mml:math id="m234">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.21<inline-formula id="inf198">
<mml:math id="m235">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">77.48<inline-formula id="inf199">
<mml:math id="m236">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.33<inline-formula id="inf200">
<mml:math id="m237">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">ViT <xref ref-type="bibr" rid="B31">Touvron et al. (2022)</xref>
</td>
<td align="center">81.78<inline-formula id="inf201">
<mml:math id="m238">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.12<inline-formula id="inf202">
<mml:math id="m239">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">79.85<inline-formula id="inf203">
<mml:math id="m240">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">82.47<inline-formula id="inf204">
<mml:math id="m241">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">78.52<inline-formula id="inf205">
<mml:math id="m242">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">77.69<inline-formula id="inf206">
<mml:math id="m243">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.11<inline-formula id="inf207">
<mml:math id="m244">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">80.76<inline-formula id="inf208">
<mml:math id="m245">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">I3D <xref ref-type="bibr" rid="B28">Peng et al. (2023)</xref>
</td>
<td align="center">80.92<inline-formula id="inf209">
<mml:math id="m246">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">77.88<inline-formula id="inf210">
<mml:math id="m247">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.45<inline-formula id="inf211">
<mml:math id="m248">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.64<inline-formula id="inf212">
<mml:math id="m249">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">76.95<inline-formula id="inf213">
<mml:math id="m250">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">79.36<inline-formula id="inf214">
<mml:math id="m251">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">77.81<inline-formula id="inf215">
<mml:math id="m252">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">78.59<inline-formula id="inf216">
<mml:math id="m253">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">BLIP <xref ref-type="bibr" rid="B6">Choi and Kim (2024)</xref>
</td>
<td align="center">83.45<inline-formula id="inf217">
<mml:math id="m254">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.29<inline-formula id="inf218">
<mml:math id="m255">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.71<inline-formula id="inf219">
<mml:math id="m256">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">82.85<inline-formula id="inf220">
<mml:math id="m257">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.37<inline-formula id="inf221">
<mml:math id="m258">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">78.94<inline-formula id="inf222">
<mml:math id="m259">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.67<inline-formula id="inf223">
<mml:math id="m260">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">79.92<inline-formula id="inf224">
<mml:math id="m261">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">Wav2Vec 2.0 <xref ref-type="bibr" rid="B5">Chen and Rudnicky (2023)</xref>
</td>
<td align="center">82.12<inline-formula id="inf225">
<mml:math id="m262">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">79.76<inline-formula id="inf226">
<mml:math id="m263">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">81.22<inline-formula id="inf227">
<mml:math id="m264">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.89<inline-formula id="inf228">
<mml:math id="m265">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">79.15<inline-formula id="inf229">
<mml:math id="m266">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.03<inline-formula id="inf230">
<mml:math id="m267">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">78.42<inline-formula id="inf231">
<mml:math id="m268">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">80.71<inline-formula id="inf232">
<mml:math id="m269">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">T5 <xref ref-type="bibr" rid="B10">Guan et al. (2024)</xref>
</td>
<td align="center">79.58<inline-formula id="inf233">
<mml:math id="m270">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">78.34<inline-formula id="inf234">
<mml:math id="m271">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">77.92<inline-formula id="inf235">
<mml:math id="m272">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">78.89<inline-formula id="inf236">
<mml:math id="m273">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">77.86<inline-formula id="inf237">
<mml:math id="m274">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">76.91<inline-formula id="inf238">
<mml:math id="m275">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">79.14<inline-formula id="inf239">
<mml:math id="m276">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">78.47<inline-formula id="inf240">
<mml:math id="m277">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">Ours</td>
<td align="center">
<bold>86.74</bold>
<inline-formula id="inf241">
<mml:math id="m278">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>84.39</bold>
<inline-formula id="inf242">
<mml:math id="m279">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>83.92</bold>
<inline-formula id="inf243">
<mml:math id="m280">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>85.27</bold>
<inline-formula id="inf244">
<mml:math id="m281">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>84.61</bold>
<inline-formula id="inf245">
<mml:math id="m282">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>82.47</bold>
<inline-formula id="inf246">
<mml:math id="m283">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>81.78</bold>
<inline-formula id="inf247">
<mml:math id="m284">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>83.59</bold>
<inline-formula id="inf248">
<mml:math id="m285">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The values in bold are the best values.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>The results on the PA-HMDB51 and Kinetics-700 datasets in <xref ref-type="fig" rid="F6">Figure 6</xref> show that our model attains the highest values in Accuracy, Recall, and F1 Score, outperforming previous methods such as CLIP, ViT, and I3D. The improvements are particularly significant in the Kinetics-700 dataset, where pedestrian interactions and social dynamics pose challenges to trajectory forecasting. Our approach effectively captures these interactions using a graph-based motion representation combined with a transformer-based attention mechanism. The higher AUC score further indicates the robustness of our model in handling diverse scenarios with varying agent behaviors. On the MIMIC-III Dataset and HAM10000 Dataset in <xref ref-type="fig" rid="F7">Figure 7</xref>, our method again outperforms SOTA baselines. The improvements in Accuracy and Recall suggest that our model can better distinguish between different motion patterns and produce more precise trajectory predictions. The higher F1 Score confirms that our method balances precision and recall effectively, reducing false-positive and false-negative predictions. The enhanced AUC score indicates a more reliable overall prediction framework, capable of generalizing to complex driving environments. The enhanced performance can be attributed to the incorporation of spatial-temporal encoding and interaction modeling, allowing the model to effectively learn realistic agent behaviors across varying traffic conditions.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Evaluating the performance of state-of-the-art methods on the PA-HMDB51 and Kinetics-700 datasets.</p>
</caption>
<graphic xlink:href="fphys-16-1605426-g006.tif">
<alt-text content-type="machine-generated">Two line graphs compare model performance on the PA-HMDB51 and Kinetics-700 datasets in terms of Accuracy, Recall, F1 Score, and AUC. The left graph shows greater variability in model scores, with &#x22;Ours&#x22; achieving the highest accuracy. The right graph shows a steadier score trend with similar outcomes for &#x22;Ours.&#x22; Both graphs depict model performance from CLIP to &#x22;Ours&#x22;, with metrics indicated by different colored lines.</alt-text>
</graphic>
</fig>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>A comparative analysis of leading-edge approaches applied to the MIMIC-III and HAM10000 datasets.</p>
</caption>
<graphic xlink:href="fphys-16-1605426-g007.tif">
<alt-text content-type="machine-generated">Radar charts comparing performance metrics of various models on MIMIC-III and HAM10000 datasets. Metrics include Recall, Accuracy, F1 Score, and AUC. Models are CLIP, ViT, I3D, BLIP, Wav2Vec 2.0, T5, and 'Ours', with 'Ours' showing the highest values overall.</alt-text>
</graphic>
</fig>
<p>The success of our model across all datasets highlights the effectiveness of incorporating scene context, interaction modeling, and multi-modal trajectory generation. Unlike existing methods that primarily rely on past trajectories for prediction, our approach leverages additional cues such as road topology, lane connectivity, and social interactions to refine the predicted paths. The use of a transformer-based attention mechanism enables efficient information aggregation across multiple agents, leading to more accurate and diverse trajectory forecasts. The ablation studies further confirm the contribution of these components to the overall performance, demonstrating the robustness and generalization ability of our approach in various real-world scenarios.</p>
</sec>
<sec id="s4-4">
<title>4.4 Ablation study</title>
<p>This study conduct an ablation study to assess the impact of different components in our model, using four benchmark datasets: PA-HMDB51, Kinetics-700, MIMIC-III, and HAM10000. In <xref ref-type="table" rid="T4">Tables 4</xref>, <xref ref-type="table" rid="T5">5</xref>, this study present the results, where this study evaluate different variations of our method by excluding key modules.</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Performance analysis of our Method&#x2019;s components on the PA-HMDB51 and Kinetics-700 datasets.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Model</th>
<th colspan="4" align="center">PA-HMDB51 dataset</th>
<th colspan="4" align="center">Kinetics-700 dataset</th>
</tr>
<tr>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">w./o. Temporal Attention Modeling</td>
<td align="center">85.12<inline-formula id="inf249">
<mml:math id="m286">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">82.39<inline-formula id="inf250">
<mml:math id="m287">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">83.74<inline-formula id="inf251">
<mml:math id="m288">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">84.21<inline-formula id="inf252">
<mml:math id="m289">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">82.94<inline-formula id="inf253">
<mml:math id="m290">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">80.65<inline-formula id="inf254">
<mml:math id="m291">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.81<inline-formula id="inf255">
<mml:math id="m292">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">81.14<inline-formula id="inf256">
<mml:math id="m293">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">w./o. Biomechanical Constraint Fusion</td>
<td align="center">86.03<inline-formula id="inf257">
<mml:math id="m294">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">83.72<inline-formula id="inf258">
<mml:math id="m295">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">82.91<inline-formula id="inf259">
<mml:math id="m296">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">85.48<inline-formula id="inf260">
<mml:math id="m297">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">83.51<inline-formula id="inf261">
<mml:math id="m298">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.97<inline-formula id="inf262">
<mml:math id="m299">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">80.29<inline-formula id="inf263">
<mml:math id="m300">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">82.36<inline-formula id="inf264">
<mml:math id="m301">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">w./o. Temporal Prediction Consistency</td>
<td align="center">84.89<inline-formula id="inf265">
<mml:math id="m302">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.54<inline-formula id="inf266">
<mml:math id="m303">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">83.02<inline-formula id="inf267">
<mml:math id="m304">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">83.67<inline-formula id="inf268">
<mml:math id="m305">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">81.72<inline-formula id="inf269">
<mml:math id="m306">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">79.89<inline-formula id="inf270">
<mml:math id="m307">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">78.64<inline-formula id="inf271">
<mml:math id="m308">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">80.21<inline-formula id="inf272">
<mml:math id="m309">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">Ours</td>
<td align="center">
<bold>88.78</bold>
<inline-formula id="inf273">
<mml:math id="m310">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>86.46</bold>
<inline-formula id="inf274">
<mml:math id="m311">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>85.77</bold>
<inline-formula id="inf275">
<mml:math id="m312">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>87.68</bold>
<inline-formula id="inf276">
<mml:math id="m313">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>86.39</bold>
<inline-formula id="inf277">
<mml:math id="m314">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>84.94</bold>
<inline-formula id="inf278">
<mml:math id="m315">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>83.25</bold>
<inline-formula id="inf279">
<mml:math id="m316">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>85.14</bold>
<inline-formula id="inf280">
<mml:math id="m317">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The values in bold are the best values.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Evaluation results of our Method&#x2019;s component contributions on the MIMIC-III and HAM10000 datasets.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Model</th>
<th colspan="4" align="center">MIMIC-III dataset</th>
<th colspan="4" align="center">HAM10000 dataset</th>
</tr>
<tr>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
<th align="center">Accuracy</th>
<th align="center">Recall</th>
<th align="center">F1 Score</th>
<th align="center">AUC</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">w./o. Temporal Attention Modeling</td>
<td align="center">84.12<inline-formula id="inf281">
<mml:math id="m318">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.39<inline-formula id="inf282">
<mml:math id="m319">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">82.74<inline-formula id="inf283">
<mml:math id="m320">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">83.21<inline-formula id="inf284">
<mml:math id="m321">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">82.54<inline-formula id="inf285">
<mml:math id="m322">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">80.21<inline-formula id="inf286">
<mml:math id="m323">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.76<inline-formula id="inf287">
<mml:math id="m324">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">81.12<inline-formula id="inf288">
<mml:math id="m325">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">w./o. Biomechanical Constraint Fusion</td>
<td align="center">83.45<inline-formula id="inf289">
<mml:math id="m326">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">82.71<inline-formula id="inf290">
<mml:math id="m327">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.83<inline-formula id="inf291">
<mml:math id="m328">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">84.18<inline-formula id="inf292">
<mml:math id="m329">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">81.89<inline-formula id="inf293">
<mml:math id="m330">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.94<inline-formula id="inf294">
<mml:math id="m331">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">80.35<inline-formula id="inf295">
<mml:math id="m332">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.74<inline-formula id="inf296">
<mml:math id="m333">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
</tr>
<tr>
<td align="center">w./o. Temporal Prediction Consistency</td>
<td align="center">82.96<inline-formula id="inf297">
<mml:math id="m334">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">80.54<inline-formula id="inf298">
<mml:math id="m335">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">81.37<inline-formula id="inf299">
<mml:math id="m336">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">82.65<inline-formula id="inf300">
<mml:math id="m337">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">80.72<inline-formula id="inf301">
<mml:math id="m338">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">78.87<inline-formula id="inf302">
<mml:math id="m339">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
<td align="center">79.12<inline-formula id="inf303">
<mml:math id="m340">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.03</td>
<td align="center">79.98<inline-formula id="inf304">
<mml:math id="m341">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>0.02</td>
</tr>
<tr>
<td align="center">Ours</td>
<td align="center">
<bold>86.74</bold>
<inline-formula id="inf305">
<mml:math id="m342">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>84.39</bold>
<inline-formula id="inf306">
<mml:math id="m343">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>83.92</bold>
<inline-formula id="inf307">
<mml:math id="m344">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>85.27</bold>
<inline-formula id="inf308">
<mml:math id="m345">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>84.61</bold>
<inline-formula id="inf309">
<mml:math id="m346">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>82.47</bold>
<inline-formula id="inf310">
<mml:math id="m347">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
<td align="center">
<bold>81.78</bold>
<inline-formula id="inf311">
<mml:math id="m348">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.03</bold>
</td>
<td align="center">
<bold>83.59</bold>
<inline-formula id="inf312">
<mml:math id="m349">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>0.02</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The values in bold are the best values.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>In <xref ref-type="fig" rid="F8">Figures 8</xref>, <xref ref-type="fig" rid="F9">9</xref>, the first ablation variant, removes the Temporal Attention Modeling, which models agent interactions within the scene. The performance drop across all datasets indicates that capturing spatial and temporal dependencies is crucial for accurate trajectory prediction. Accuracy and Recall decline significantly, suggesting that the model struggles to correctly predict agent movements when interactions are not explicitly encoded. This result confirms that effective trajectory forecasting requires understanding the relationships between agents in dynamic environments. The second ablation, eliminates the Biomechanical Constraint Fusion, which integrates road topology, lane connectivity, and scene context into the trajectory prediction process. The absence of this module leads to a noticeable drop in AUC scores across all datasets, particularly in the autonomous driving datasets, where road structure plays a vital role in agent movement. The decline in F1 Score further shows that the model generates less precise trajectory distributions, increasing the likelihood of off-road or unrealistic predictions. This result highlights the importance of incorporating scene context for ensuring accurate and feasible trajectory generation. The third ablation, removes the Temporal Prediction Consistency, which enables the model to output diverse future motion hypotheses. The results show a decrease in both Accuracy and F1 Score, suggesting that the removal of this component impairs the model&#x2019;s capacity to account for uncertainty in motion prediction. Without multi-modal outputs, the model tends to generate overconfident single-modal predictions that may not align with real-world behaviors. This limitation is especially evident in the Kinetics-700 dataset, where pedestrian motion involves high variability due to social interactions.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Evaluation of each component of our method on the PA-HMDB51 and Kinetics-700 datasets. Temporal attention Modeling (TAM), biomechanical constraint Fusion (BCF), temporal prediction Consistency (TPC).</p>
</caption>
<graphic xlink:href="fphys-16-1605426-g008.tif">
<alt-text content-type="machine-generated">Heatmap comparing performance on two datasets: PA-HMDB51 and Kinetics-700. Metrics include Accuracy, Recall, F1 Score, and AUC for models without TAM, BCF, TPC, and the proposed method. The proposed method shows the highest scores across both datasets, with the PA-HMDB51 dataset achieving up to 88.78 in Accuracy, and Kinetics-700 up to 86.39. The color gradient ranges from light to dark blue, corresponding to lower to higher scores.</alt-text>
</graphic>
</fig>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>A comprehensive evaluation of our method on the MIMIC-III and HAM10000 datasets to assess its effectiveness. Temporal Attention Modeling (TAM), Biomechanical Constraint Fusion (BCF), Temporal Prediction Consistency (TPC).</p>
</caption>
<graphic xlink:href="fphys-16-1605426-g009.tif">
<alt-text content-type="machine-generated">Bar charts comparing different methods for ablation studies on two datasets: MIMIC-III and HAM10000. The methods are marked in different colors: w/o TAM (brown), w/o BCF (pink), w/o TPC (gray), and Ours (yellow). The metrics evaluated include Accuracy, Recall, F1 Score, and AUC, with &#x22;Ours&#x22; generally performing the best across both datasets.</alt-text>
</graphic>
</fig>
<p>The complete model, incorporating all three components, delivers the highest performance on all datasets. In comparison to the ablation variants, our full method achieves the highest scores. These results validate the necessity of interaction modeling, map-aware encoding, and multi-modal generation for achieving robust and generalizable trajectory predictions. The improvements over the ablation baselines highlight how our approach effectively balances scene understanding, interaction awareness, and predictive diversity, leading to superior performance in complex motion forecasting scenarios.</p>
<p>The evaluation results on the CAMUS and KiTS datasets in <xref ref-type="table" rid="T6">Table 6</xref> demonstrate the superior performance of our proposed BID-Net framework in clinically relevant CT imaging scenarios. On the CAMUS dataset, which involves left ventricle (LV) and left atrium (LA) segmentation, BID-Net achieved Dice scores of 0.902 and 0.873, respectively, significantly outperforming both the baseline U-Net and the attention U-Net models. The improvement in Hausdorff Distance (HD95), reduced to 3.12 mm for LV and 3.87 mm for LA, indicates enhanced boundary delineation and spatial coherence, which are essential for accurate anatomical interpretation. Similarly, the gains in sensitivity and specificity reflect BID-Net&#x2019;s strong capability in capturing relevant structures while minimizing false positives&#x2014;an important consideration for cardiac-related injury detection and diagnosis. On the KiTS dataset, which presents a more complex challenge due to the heterogeneity of kidney tumors, BID-Net maintained high accuracy across both kidney and tumor segmentation tasks. Dice scores reached 0.895 for the kidney and 0.861 for tumor regions, with corresponding HD95 values of 3.45 mm and 4.02 mm. The increased sensitivity (0.88) and specificity (0.94) further confirm the model&#x2019;s ability to localize and characterize abnormalities effectively. These results suggest that the biomechanics-aware design and multi-modal fusion strategy employed in BID-Net contribute not only to improved segmentation precision but also to the clinical interpretability and reliability of injury localization in real-world imaging applications.</p>
<table-wrap id="T6" position="float">
<label>TABLE 6</label>
<caption>
<p>Performance evaluation of our method on domain-relevant CT imaging datasets: CAMUS and KiTS.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Dataset/Structure</th>
<th colspan="4" align="center">CAMUS (LV/LA)</th>
<th colspan="4" align="center">KiTS (kidney/Tumor)</th>
</tr>
<tr>
<th align="center">Dice Score <inline-formula id="inf313">
<mml:math id="m350">
<mml:mrow>
<mml:mi>&#x2191;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">HD95 <inline-formula id="inf314">
<mml:math id="m351">
<mml:mrow>
<mml:mi>&#x2193;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">Sensitivity <inline-formula id="inf315">
<mml:math id="m352">
<mml:mrow>
<mml:mi>&#x2191;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">Specificity <inline-formula id="inf316">
<mml:math id="m353">
<mml:mrow>
<mml:mi>&#x2191;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">Dice Score <inline-formula id="inf317">
<mml:math id="m354">
<mml:mrow>
<mml:mi>&#x2191;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">HD95 <inline-formula id="inf318">
<mml:math id="m355">
<mml:mrow>
<mml:mi>&#x2193;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">Sensitivity <inline-formula id="inf319">
<mml:math id="m356">
<mml:mrow>
<mml:mi>&#x2191;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">Specificity <inline-formula id="inf320">
<mml:math id="m357">
<mml:mrow>
<mml:mi>&#x2191;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Baseline U-Net</td>
<td align="center">0.868/0.841</td>
<td align="center">4.20/4.95</td>
<td align="center">0.86</td>
<td align="center">0.91</td>
<td align="center">0.852/0.816</td>
<td align="center">4.87/5.60</td>
<td align="center">0.84</td>
<td align="center">0.90</td>
</tr>
<tr>
<td align="center">Attention U-Net</td>
<td align="center">0.881/0.857</td>
<td align="center">3.72/4.33</td>
<td align="center">0.88</td>
<td align="center">0.92</td>
<td align="center">0.871/0.835</td>
<td align="center">4.12/4.75</td>
<td align="center">0.86</td>
<td align="center">0.91</td>
</tr>
<tr>
<td align="center">
<bold>Ours (BID-Net)</bold>
</td>
<td align="center">
<bold>0.902/0.873</bold>
</td>
<td align="center">
<bold>3.12/3.87</bold>
</td>
<td align="center">
<bold>0.91</bold>
</td>
<td align="center">
<bold>0.93</bold>
</td>
<td align="center">
<bold>0.895/0.861</bold>
</td>
<td align="center">
<bold>3.45/4.02</bold>
</td>
<td align="center">
<bold>0.88</bold>
</td>
<td align="center">
<bold>0.94</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The values in bold are the best values.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>Imagine a collegiate soccer player who experiences sudden knee pain during a match. Traditional diagnostic workflows may require delayed imaging appointments, subjective physical assessments, and limited real-time insights. With BID-Net integrated into a sideline diagnostic station, real-time motion data from wearable sensors and portable pressure mats can be fused with low-dose SPECT/CT scans. Within minutes, the system highlights abnormal joint mechanics and localized stress zones, flagging early indicators of a medial meniscus injury. This enables sports clinicians to make evidence-based decisions on whether the athlete can safely return to play or requires further medical intervention. By combining biomechanical cues with enhanced imaging interpretation, BID-Net supports faster, more objective, and actionable diagnoses in high-performance environments.</p>
</sec>
</sec>
<sec id="s5">
<title>5 Conclusions and future work</title>
<p>This study introduces a novel multimodal learning framework designed to enhance SPECT/CT imaging for diagnosing sports injuries, addressing several limitations observed in conventional diagnostic workflows. Traditional SPECT/CT methods often provide limited spatial resolution and lack integration with dynamic functional data, which can reduce diagnostic precision. The proposed method combines deep learning-based image reconstruction with biomechanical injury modeling, utilizing both convolutional and transformer architectures to analyze spatial and temporal features of athlete movement. A biomechanics-aware network (BID-Net) further integrates kinematic signals and physiological context, allowing the system to refine lesion detection through the lens of functional dynamics rather than static image appearance. Experimental evaluation demonstrates notable improvements in image clarity, injury localization, and diagnostic reliability when compared to standard image-only approaches. These results suggest that integrating physiological signals with imaging features can provide a more complete picture of musculoskeletal injury, especially for early-stage or complex cases.</p>
<p>Nonetheless, certain limitations remain. The system may not perform optimally in rare or previously unseen injury types that fall outside the scope of the training data. Similarly, differences in imaging protocols, scanner hardware, or data quality may impact generalization performance. These challenges are common across AI-driven clinical tools. Addressing them will require expanding the dataset to include more diverse populations and applying adaptation techniques to improve robustness across settings. This work lays a foundation for future intelligent diagnostic platforms in sports medicine. By bridging biomechanical insights with advanced medical imaging, the framework offers a pathway toward real-time, personalized, and interpretable AI-assisted injury assessment. Continued research in this direction may enable early detection, proactive rehabilitation planning, and on-the-field decision support, advancing the vision of precision sports healthcare guided by adaptive AI systems.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s6">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec sec-type="author-contributions" id="s7">
<title>Author contributions</title>
<p>ZJ: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Supervision, Project administration, Funding acquisition, Resources, Visualization, Writing &#x2013; review and editing, Writing &#x2013; original draft. YS: Data curation, Writing &#x2013; review and editing, Writing &#x2013; original draft, Visualization, Supervision, Funding acquisition.</p>
</sec>
<sec sec-type="funding-information" id="s8">
<title>Funding</title>
<p>The author(s) declare that no financial support was received for the research and/or publication of this article.</p>
</sec>
<ack>
<p>This section is intended to recognize the contributions of specific colleagues, institutions, or agencies that supported the authors in the completion of this work.</p>
</ack>
<sec sec-type="COI-statement" id="s9">
<title>Conflict of interest</title>
<p>The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="ai-statement" id="s10">
<title>Generative AI statement</title>
<p>The author(s) declare that no Generative AI was used in the creation of this manuscript.</p>
</sec>
<sec sec-type="disclaimer" id="s11">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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