Musculoskeletal Modelling Coupled with Stress Simulation Reveal Asymmetrical Knee Load and Ligament Stress in Long-Distance Running

Musculoskeletal Modelling Coupled with Stress Simulation Reveal Asymmetrical Knee Load and Ligament Stress in Long-Distance Running | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Musculoskeletal Modelling Coupled with Stress Simulation Reveal Asymmetrical Knee Load and Ligament Stress in Long-Distance Running Zixiang Gao, Liangliang Xiang, Hanhui Jiang, Qichang Mei, Gusztáv Fekete, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6641048/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 Nov, 2025 Read the published version in BMC Sports Science, Medicine and Rehabilitation → Version 1 posted 10 You are reading this latest preprint version Abstract Background Understanding the internal load characteristics of the knee joint is essential for investigating unilateral knee injuries associated with running. This study examined the differences in the location and magnitude of von Mises stress in the internal structures of bilateral knee joints during the stance phase of gait following 10 kilometers running at submaximal speeds. Methods A healthy male recreational runner participated in this study. We employed a synergistic approach, integrating subject-specific knee joint angles, reaction forces, and moments derived from musculoskeletal modeling to inform and drive the finite element modeling of running. This methodology ensured a detailed and accurate representation of knee joint mechanics. The peak stresses of the bilateral knee menisci, tibial cartilage, and five main ligaments were quantified using a finite element model during the stance phase. Results The meniscus, tibial cartilage, anterior (ACL), posterior cruciate ligament (PCL), medial (MCL), and lateral collateral ligament (LCL) experienced larger loads in the non-dominant limb. Additionally, fatigue elevated the peak loading on the non-dominant limb's ACL, PCL, and LCL during the gait stance phase but diminished the load on these ligaments in the dominant knee joint. Conclusions This study substantially enhances our understanding of the impact of running-induced fatigue on bilateral knee joint loading. It provides a detailed analysis of factors leading to unilateral knee overload during extended running. These insights are essential in formulating targeted strategies to reduce injury risks. Knee Running Finite element modeling Overloading injuries Limb dominance Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Background The knee joint, encompassing the tibiofemoral (TF) and patellofemoral (PF) joints, is one of the most complex and vulnerable joints in the human body. It includes intricate internal structures such as bones, menisci, cartilage, ligaments, and other soft tissues, all crucial for functionality and stability during physical activities. Globally, 54% of athletes experience varying degrees of knee pain annually[ 1 ]. Despite exceptional cardiovascular fitness, runners may not possess equivalent muscular strength or neuromuscular coordination. Mechanical loading within the knee joint involves a dynamic interaction between motion and contact mechanics[ 2 ]. While the knee joint's capacity to endure high mechanical loads is remarkable, knee injuries are increasingly prevalent among runners. Annually, 37–56% of runners experience at least one running-related injury[ 3 ], with the incidence of knee injuries ranging from 19.4–79.3% [ 4 ]. Numerous studies in gait biomechanics presuppose completely symmetrical gait patterns and examine only unilateral variables, both in the experimental analysis and numerical simulation [ 5 , 6 ]. However, Sadeghi and colleagues[ 7 ] observed that asymmetry in lower limb gait is present even in healthy individuals. The stronger limb typically compensates for its counterpart to address biomechanical shortcomings in the gait during long-distance running[ 8 ]. Nevertheless, running-related injuries commonly occur in the unilateral limb[ 9 ]. Approximately half of recreational runners sustain an injury annually, many of which are recurrent and side-specific[ 10 ]. Despite extensive studies into factors contributing to these injuries, the mechanisms underlying side-specific injuries are poorly understood. One major factor is the asymmetry of gait-induced inequality in the contribution of the bilateral limbs to load absorption[ 7 ]. Additionally, external factors such as fatigue may shift the main load to the part of the lower limb that has a weaker tolerance to fatigue[ 11 ]. Notably, prolonged repetitive mechanical loading can damage the knee joint, leading to cartilage degeneration and increased chondrocyte apoptosis[ 12 ]. Patellofemoral pain syndrome, meniscal injuries, and ligament injuries[ 13 ] are significant contributors to these pathologies. Approximately 5% of runners sustain meniscal injuries[ 14 ]. Meniscal tears commonly disrupt circumferential fibers, leading to extrusion, displacement, and intra-articular constriction under axial stress[ 15 ]. Previous studies have reported that running fatigue increases tibial stress [ 16 ]. Additionally, the ligaments of the knee joint are vital for the dynamic stability of gait, as they restrict excessive knee extension or rotation, aided by muscular strength. Prolonged running can lead to diminished muscle strength, resulting in an increased load on the ligaments[ 17 ]. However, studies on internal tissue stress within the knee remain limited. Tibiofemoral joint contact forces (JCF) arise from the combined action of muscles and ligaments[ 18 ]. Direct JCF quantification is invasive and ethically complex[ 6 ]. Therefore, musculoskeletal (MS) and finite element (FE) modeling techniques are widely used as non-invasive alternatives to simulate dynamic loads[ 19 ]. MS models typically estimate muscle and joint forces based on inverse kinematics and kinetics but cannot fully evaluate tissue loading response during JCF increase progression or factors influencing cartilage degeneration[ 20 ]. FE modeling provides intuitive graphical results to elucidate localized load distribution and magnitude induced by biomechanical changes in the knee joint[ 21 ]. Running-related knee injuries are caused by the complex interplay of tissues such as the meniscus, cartilage, ligaments, and muscles, and may be due to fatigue or asymmetric gait[ 17 ]. Nonetheless, previous studies on fatigue and differences in load between limbs have not precisely addressed the distribution and extent of the load on the knee joint's internal tissues, potentially missing key insights into the causes of unilateral limb injuries[ 11 ]. Therefore, the aim of this study was to employ coupled person-specific musculoskeletal and finite element models to explore inter-limb variations in internal knee joint loading and assess the effects of a long-distance running event on these variables. We hypothesize that: (1) differences in the loading distribution of the menisci, tibial cartilage, and ligaments on both sides will be observed at the peak value phase, in both pre- and post-fatigue states; (2) disparities in loading magnitude of these structures will be observed throughout gait support phase in both states; and (3) knee loading will increase with fatigue, with a greater increase on the non-dominant side due to different fatigue tolerance during the gait support phase. Methods Participants A 20-year-old healthy male amateur runner was enlisted for this study, with a body mass of 72 kg and a height of 178 cm. The participant needed to meet the following criteria: 1) The right limb was identified as the dominant limb; 2) The striking pattern of running gait was rearfoot striking; 3) an absence of pelvic or lower limb injuries in the preceding six months; and 4) the ability to run 10 kilometers in 45–50 minutes[ 22 ]. Ethical approval for the study protocols was conferred by the Institutional Ethics Committee, ensuring that all methods adhered to the Declaration of Helsinki. Furthermore, the Ethics Committee at University sanctioned all procedures. 2.2 Data acquisition Data collection was divided into four parts: (1) MRI scans, (2) ground running test before and (3) after a 10km treadmill run, and (4) treadmill running at submaximal speed for 10km. The ground running tests before and after the treadmill run employed the same testing procedure (Fig. 1 (A)). Medical image acquisition A 3.0 T clinical MRI scanner (General Electric Healthcare, Milwaukee, WI, USA), equipped with a 12-channel knee joint transmit-receive RF coil, was used for the acquisition of magnetic resonance data. The participant was oriented in a supine, non-weight-bearing posture, with the right knee centrally aligned within the coil. The MRI data was collected in the morning to avoid the day-long load bearing on the knee joint[ 23 ]. Experimental data collection For the 10 km treadmill running (Quasar, h/p Cosmos®, GmbH, Germany), the participant wore standardized lab-provided running footwear and maintained a submaximal speed of approximately 11.5 km/h, representing 80% of their personal best to simulate a casual running pace [ 24 ]. Data were collected during ground running tests before and after the 10km treadmill run. The participant acclimated by running on the track in the data collection area to mitigate the influence of conscious gait adjustments. A total of 38 retroreflective markers were affixed according to a pre-established protocol. Marker trajectory and ground reaction forces (GRFs) were synchronously collected using an eight-camera Vicon 3D motion capture system (Vicon Metrics Ltd.,200Hz, Oxford, United Kingdom) and an AMTI force platform (AMTI, 1000Hz, Watertown, Massachusetts, USA), respectively. The velocity for the ground running tests was consistently monitored at 3.33 m/s using photocells. Five successful trials, meeting the criteria for proximity to the target speed and step location within the force plate area were selected for subsequent MS and FE analysis. In addition, muscle activity from the rectus femoris, biceps femoris, tibialis anterior, medial gastrocnemius, and lateral gastrocnemius of the dominant limb was synchronously captured using a 16-channel surface electromyography system (Delsys, 1000 Hz, Boston, Massachusetts, US). Prior to the testing procedures, maximum voluntary contraction (MVC) levels for these muscles were recorded to establish a baseline for activity assessment. Personalized model development Musculoskeletal model Model development The OpenSim (National Center for Simulation in Rehabilitation Research, Stanford, USA) gait 2392 generic musculoskeletal model was chosen and scaled to establish a personalized model that aligns with individual characteristics (Fig. 1 (A)). An inverse kinematic analysis was then conducted to align the experimental biomechanics with the acquired motion data. The residual reduction algorithm (RRA) was employed to minimize errors in modeling and marker data processing. This application ensured that any computational inaccuracies in inverse dynamics remained within acceptable limits, allowing for dynamic alignment with GRF data, culminating in static optimization. Finally, joint reactions analysis (JRA) was used to calculate the knee reaction forces for the muscle activation scenario and the joint reaction moments relative to the ground. Model validation The root mean square (RMS) values were obtained after preprocessing the electromyographic data. The muscle activation levels were normalized by dividing the maximal values obtained during MVC. To validate the model, we compared the muscle activation levels measured in the laboratory with those calculated using a static optimization algorithm. Finite element modeling Knee Joint Reconstruction Figure 1 (B) presents the structured framework outlining the sequential phases for reconstructing FE models. The three-dimensional reconstruction was carried out using MIMICS 21.0 (Materialise, Leuven, Belgium). Segmentation of magnetic resonance imaging (MRI) data facilitated the delineation of the anatomical boundaries of the articular cartilages (femoral, tibial, and patellar), menisci (medial and lateral), and ligaments (ACL, PCL, MCL, LCL, and PTL). To assure the accuracy of the FE model, manual segmentation of non-osseous elements was meticulously performed under the guidance of experienced orthopedic and radiological experts, achieving a precision of 0.1 mm. The tissues reconstructed in great detail were exported as STL files and further refined for model representation in Geomagic Studio 2021 (Geomagic, Inc., Research Triangle Park, NC, United States), where any problematic surfaces were identified and rectified. The final geometries were then assembled using SolidWorks 17 (SolidWorks Corporation, MA, United States), completing the model construction. Model Assembly and Material Allocation Material properties were allocated to each specific tissue to authentically model the biomechanical variations within the knee joint. The stance phase of running gait, characterized by a comparatively brief load application, permits the characterization of all cartilage tissues under quasi-static conditions using an instantaneous elastic model [ 25 ]. For the sake of computational efficiency without compromising accuracy, ligaments were modeled as transversely isotropic, nearly incompressible materials using the Neo-Hookean approach[ 25 ]. Table 1 enumerates the attributes and values of material constants for each geometric entity[ 26 – 28 ]. In accordance with the knee joint's anatomy and the specifics of the stance phase in running, modeling, meshing, and setting boundary conditions for this finite element knee model were established in Workbench 2021 R1 (ANSYS Inc., Canonsburg, Pennsylvania, USA). The distal portions of the tibia and fibula were fully constrained, immobilizing all translations and rotations. Table 1 Material properties and element types used in the knee joint FE models. Part name References Element number Model assumptions Element Type Material assignment Young’s modulus (MPa) Poisson’s ratio C1 D1 Bone Femur Song et al., 2004 28 51809 Linearly elastic Tetrahedral solid 11000 0.3 \ \ Tibia 43673 Fibula 5935 Patella 8062 Meniscus Medial Li et al., 2001 26 24313 Linearly elastic 59 0.49 Lateral 22276 Cartilage Femoral LeRoux et al., 2002 27 133537 Linearly elastic 55 0.46 Medial tibial 4780 Lateral tibial 5373 Patellar 11524 Tibiofibular 3521 Ligament ACL Li et al., 2001 26 1602 Neo-Hookean Tension-only Tetrahedral solid \ \ 1.95 0.00683 PCL 1902 3.25 0.0041 MCL 1441 1.44 0.00126 LCL 1959 1.44 0.00126 PTL 18163 3.25 0.0041 Note : ACL: anterior cruciate ligament, PCL: posterior cruciate ligament, MCL: medial collateral ligament, LCL: lateral collateral ligament, PL: Patellar ligament Model validation By setting boundary conditions for the model, the rotation center (The midpoint of the trans-epicondylar line) of the femur is used to determine the translational displacement values for the knee joint. The rotational values are based on how the tibial moves, specifically the average rotation angles of the MCL and LCL attachment points on the tibia and fibula in relation to the tibial plateau reference point. We compared the displacements in the antero-posterior, proximal-distal, and medial-lateral directions of the knee model in the present study (the 134N afterload was applied to the center of rotation of the femur under conditions of 0°, 15°, and 30° knee flexion (remote displacement)) with the finite element simulation results of Song et al.[ 28 ] (0°) and cadaveric experiments of Gabriel et al.[ 29 ] ( 0°, 15° and 30°). Running Gait Simulation The stance phase was divided into five stages (initial contact, first peak, mid-stance, second peak, and toe-off) based on the vertical GRF data. The knee rotation center was used to apply the knee flexion angle (translational displacement), joint reaction force, and joint reaction moment calculated by the MS model to the corresponding five gait moments (Figures C1 & C2). Constraints on femoral rotations were imposed only when specific flexion angle-related loads were applied, leaving other directional movements unconstrained. Through binding commands, cartilage and ligament tissues were rigidly attached to their corresponding skeletal points of origin. The meniscus and tibial cartilage were also bound together in the same way. Five discrete contact pairs were featured within the knee joint model, each facilitating surface-to-surface interactions: between the femoral cartilage and the medial meniscus, the lateral tibial cartilage, the lateral tibial cartilage, and the patellar cartilage. A frictionless, finite sliding approach was employed to address the minimal friction between joint cartilage surfaces[ 13 ], as shown in Fig. 1 (D). ***Insert Figure. 1 here*** ***Insert Table. 1 here*** Results Model validation ***Insert Figure. 2 here*** The muscle activation levels of the rectus femoris, biceps femoris, tibialis anterior, medial gastrocnemius, and lateral gastrocnemius calculated in pre- and post-fatigue states were similar to the surface EMG signals recorded in the experiment, as shown in Fig. 2 (A). Additionally, under the condition of 0° knee flexion and a posterior load of 134N on the rotation center of the femur, the displacement in the anterior-posterior, proximal-distal, and medial-lateral directions in this study's knee joint model was similar to the cadaver experiments by Gabriel et al.[ 29 ] and the finite element simulations by Song et al.[ 28 ]. By applying remote displacement to the center of femoral rotation under identical boundary and loading conditions, the knee joint's displacement outcomes at 15° and 30° of flexion were congruent with the cadaveric study findings of Gabriel et al.[ 29 ], as shown in Fig. 2 (B). Kinematics and Kinetics In the pre-fatigue states, a greater internal rotation angle was observed in the left knee compared to the right side, with this difference was more pronounced in the post-fatigue states during mid-stance. Additionally, a greater anterior joint reaction force was observed in the right knee. Similarly, a greater abduction joint reaction moment was noted in the left knee joint. In the post-fatigue states, the left knee exhibited a greater extension angle, and there was more pronounced adduction in the right knee. Furthermore, an increase in right knee flexion reaction moments was observed after fatigue. To test the statistical significance of these differences, we conducted a time-series one-dimensional statistical parametric mapping (SPM1d) analysis in Python 3.8 of five trials on both lower extremities before and after fatigue. A two-way repeated-measures ANOVA (limb × fatigue) with post-hoc paired t-tests was performed for individual condition comparisons. Detailed results of this analysis are presented in Supplementary Material 1 (Figures A1 – A3). Finite element analysis Maximum load simulation of meniscus and tibial cartilage In Fig. 3 , similar stress distributions were observed on both the dominant and non-dominant limb menisci in both states. Maximum stress was predominantly located at the central and anterior horn of the medial meniscus. Notably, the left knee surpassed the right knee by 9.5 MPa, and then decreased by 9.12 MPa after fatigue. The peak stress of the right medial meniscus also decreased by 12.7 MPa after fatigue. Additionally, the anterior segment of the middle region of the lateral meniscus sustained the maximum stress, with the left side experiencing 3.39 MPa more than the right side, which then decreased by 5.47 MPa after fatigue. ***Insert Figure. 3 here*** The tibial cartilage exhibited a consistent stress distribution, with the anteromedial part of the medial tibial cartilage bearing the main load. The stress of the left tibial cartilage was higher than that of the right side by 2.86 MPa but decreased by 1.82 MPa after fatigue. For the lateral tibial cartilage, the left side experienced 4.81 MPa more than the right in pre-fatigue states. The peak stress of the right lateral tibial cartilage then decreased by 12.7 MPa after fatigue. Maximum load simulation of ligaments Similar stress distributions were observed on the ligaments in both states (Fig. 4 ). Maximum stresses for the ACL and PCL were primarily located at the femoral contact points. The left ACL was 17.07 MPa higher than the right side and increased by 3.15 MPa after fatigue. In the post-fatigue states, it surpassed the right side by 11.28 MPa. The left PCL stress was 16.59 MPa higher than the right side and decreased by 8.56 MPa after fatigue. In the post-fatigue states, it was 9.24 MPa higher than the right side. The maximum stress for the MCL was mainly on the anterosuperior side. The left MCL stress was 7.86 MPa higher than the right side and decreased by 2.90 MPa after fatigue. Additionally, the stress on the left LCL was 6.56 MPa higher than the right side and increased by 14.54 MPa after fatigue. In the post-fatigue states, it surpassed the right side by 23.00 MPa. The maximum stress for the PL was mainly in the middle region. Interestingly, the stress on the left side was lower than on the right side by 1.10 MPa but decreased by 1.38 MPa after fatigue. In the post-fatigue states, it was 0.46 MPa higher than the right side. ***Insert Figure. 4 here*** Load simulation of gait stance phase ***Insert Figure. 5 here*** Figure 5 illustrates the variations in stress values for the meniscus, tibial cartilage, and ligaments of the bilateral knee during the gait stance phase in both states. Except for the PCL, the peak stress of the tissues was consistently lowest during the IC phase, gradually increased during the SP phase, reached its maximum, and decreased during the OT phase at both states. Interestingly, the maximum stress for the PCLs occurred at the TO phase, while the stress was lowest at the FP phase, except on the left side in pre-fatigue and post-fatigue states, respectively. The medial and lateral menisci trend graphs reveal that peak stress in pre-fatigue states was consistently higher than in post-fatigue states, with the left side consistently exhibiting greater stress than the right. The ACLs and MCLs showed higher stress on the left side than the right of all states. The stress on the left LCL increased, while it decreased on the right side after fatigue. The peak stress for the left PL was highest at the IC phase, while the right PL was highest for all other phases in pre-fatigue states. Detailed results of this analysis are presented in Appendix 1 (Table A1). Discussion To determine the changes in the dominant and non-dominant knee joints during different running phases and how a 10 km submaximal intensity run affects these variables, this study coupled variables from musculoskeletal models (GRF, knee joint angles, reaction forces, and moments) to drive finite element simulations (menisci, tibial cartilage, ACL, PCL, MCL, LCL, and PL). Specifically, the distribution of loads on the tissues was similar in both knees and in all states. Moreover, the load on the meniscus and tibial cartilage was greater on the non-dominant side and greater in the pre-fatigue state. The load on the ACL, PCL, and LCL of the non-dominant limb increased after fatigue, while it decreased on the dominant side. Interestingly, the load on the PL of the dominant side was greater in the pre- fatigue state. Therefore, the findings of this study are consistent with hypotheses (2) but present some contradictory findings with hypotheses (1) and (3). The knee joint exhibits complex mechanical behaviors due to its intricate structures including bones, cartilage, and ligaments, making the development of efficient and accurate models essential [ 30 ]. In addition to the findings of this study, similar investigations have highlighted the significance of detailed finite element modeling and multiscale approaches in understanding knee joint mechanics and injury mechanisms. Adouni et al. [ 30 ] demonstrated that cartilage fibril stiffness and cross-link density are critical in determining the mechanical response and damage initiation under loading conditions. Furthermore, a similar study utilized a hybrid modeling approach to elucidate the impact of detailed tissue mechanics on joint function and injury risk [ 31 ]. These studies collectively support the need for advanced modeling techniques to improve the predictive accuracy and understanding of knee joint behavior under various loading scenarios. We demonstrate the validity of our knee joint model by conducting a comparative validation with identical boundary conditions against past finite element simulations and cadaveric experimental studies[ 28 , 29 ]. In this study, the stance phase of gait was divided into five distinct postural stages based on the pattern of vertical GRFs. The goal was to explore the disparities in internal loading of the bilateral knee joints across different ground contact stages and the influence of fatigue. Previous research has reported no differences in knee joint angles at the pre-fatigue states[ 11 ]. A greater internal rotation angle in the non-dominant knee joint during the mid-stance period could explain the excessive load on its ACL and LCL. Additionally, the study found a greater anterior joint reaction force peak in the dominant knee, potentially indicating a higher load on the patellofemoral joint of the dominant knee. This is corroborated by the noted excess load on the PL of the dominant knee. Hence, patellofemoral joint pain in the dominant limb should be a consideration for amateur runners [ 32 ]. Furthermore, the fatigue resistance of the hip adductor muscles of the non-dominant limb should be emphasized in the functional training of long-distance runners. The findings of this study show that fatigue heightened the flexion reaction moment in the dominant knee, hinting at diminished quadricep control, which might lead to an increased load on the PCL of the dominant knee post-fatigue[ 33 ]. Therefore, runners and coaches should focus on specific training for quadriceps control in the dominant limb. The larger loading of the dominant knee’s PCL during the mid-stance period after fatigue observed in the current FEM simulations also support this conclusion. Additionally, a greater abduction joint reaction moment of the non-dominant knee joint in the pre-fatigue states occurred during the mid-stance phase, indicating a greater load on the medial tibial plateau[ 24 ]. This finding is consistent with the observation of a greater load on the medial meniscus and tibial cartilage of the non-dominant knee joint. The meniscus functions to transmit and evenly distribute forces from the femur to the tibial plateau. However, this load-transferring mechanism can become compromised due to recurrent overloading, resulting in localized stress peaks and subsequent damage to the knee joint. This study observed that the load on the medial meniscus was primarily concentrated at the anterior horn, and the load on the lateral meniscus was concentrated on the posteromedial side, consistent with previous studies[ 34 ]. Greater loads may cause tears at the anterior horn of the medial meniscus and the middle of the lateral meniscus. Notably, we found a similar load distribution in both the non-dominant and dominant knee joints before and after fatigue. It can be hypothesized that fatigue and limb preference do not affect the location of the meniscus, tibial cartilage, and ligaments where injuries can develop during the running event, and that injuries are generally only related to the magnitude of the load. In addition, the load on the ACL and PCL was primarily concentrated at the contact points with the femur, which is consistent with the findings of a previous study [ 35 ]. By observing the load distribution of the LCL, we found that most of the load was concentrated near the ligament attachment points to the bones, which could be the most vulnerable area to strains. Additionally, larger loads were found in the non-dominant LCL after fatigue, likely induced by foot pronation[ 36 ]. Therefore, footwear with proper arch support is necessary for long distance running. The correlation between CLC loading and the degree of foot pronation should be further addressed in future studies. However, most of the MCL's load was concentrated in the anterosuperior direction and was more pronounced on the non-dominant side. This is a key area where too much MCL load is caused by the femur rotating during knee flexion[ 37 ]. Furthermore, the reduced PL load after fatigue suggests that running fatigue is not the leading cause of patellar pain, which has had mixed results in previous studies[ 38 , 39 ]. The findings of this study demonstrated that the load on the bilateral menisci, tibial cartilage, and ligaments during the gait support phase shows a consistent trend of change both pre- and post-fatigue, being almost at its lowest during the IC phase, then gradually increasing, peaking during the SP phase, and subsequently decreasing during the TO phase. This presents a divergent trend from the findings of a previous study, where the greatest load occurred during the FP phase[ 40 ]. The cause of this discrepancy may be attributed to the different postures associated with walking and running gaits. Previous studies have indicated an increased injury risk in the non-dominant limb within the running gait[ 11 ]. This study indicates that the non-dominant limb typically bears a greater load, particularly in the meniscus, tibial cartilage, ACL, MCL, and LCL, which could potentially account for the overload in a single knee joint. Furthermore, the study observed that the effect of fatigue on the ACL, PCL, and LCL of the non-dominant limb during the gait support phase is often negative, while it has the opposite effect on the dominant limb. The increased load on the knee joint tissues of the non-dominant limb due to fatigue should be given attention by runners and coaches. This may be due to the dominant limb's weaker fatigue tolerance[ 11 ]. When interpreting the significant findings of this study, certain limitations should be considered. Firstly, this study is limited by the inclusion of only one male participant, which may affect the generalizability of the results, particularly with respect to potential differences between male and female physiological structures. However, as males and females may present varying knee biomechanical characteristics and injury mechanisms, this exclusive pilot study limited the sex factor to investigate the present research topic. Future research should aim to include a more diverse participant pool, including female runners, to enable a more robust statistical analysis of the observed differences and to verify the generalizability of the finite element results of the current study. Secondly, the study did not incorporate bilateral knee MRI data for the finite element model. Instead, it applied boundary conditions collected from both knees during the experiment to a single model, which did not account for morphological variances between the two knees. Additionally, Von Mises stress was chosen as the primary metric in this study due to its ability to represent the combined effects of multi-axial stresses within the knee joint tissues. However, we recognize that von Mises stress may not fully account for the complex deformation behaviors of soft tissues. Future research should consider incorporating strain variations and other mechanical metrics to provide a more comprehensive assessment. Lastly, the use of linear elastic material properties for the cartilage and meniscus in this study represents a simplification that may not fully capture the complex mechanical behavior of these tissues. While this approach was chosen for computational efficiency, future studies should consider using more advanced material models, such as fiber-reinforced hyperelastic models, to enhance the accuracy of the simulations. Conclusions This study examines the differences in load distribution and magnitude within the bilateral knee joint's internal tissues and the effects of running-induced fatigue on these aspects. Although the load distribution areas of the menisci, cartilage, and ligaments in both knee joints are similar, the differences in their magnitude should be considered as potential causes of excessive loading. This study found that the internal tissue load in the non-dominant limb during the stance phase of gait is greater than that in the dominant limb, and fatigue has a negative effect on the internal tissue load of the non-dominant limb, whereas the effect is the opposite in the dominant limb. Runners and coaches should consider limb dominance and fatigue effects when designing training programs. Specific exercises to strengthen the non-dominant limb and improve fatigue resistance could help mitigate the risk of knee injuries. Sports medicine professionals should also focus on targeted interventions for runners based on their biomechanical assessments. Abbreviations ACL Anterior Cruciate Ligament EMG Electromyography FE Finite Element FP First Peak GRF Ground Reaction Force IC Initial Contact JCF Joint Contact Force JRA Joint Reaction Analysis LCL Lateral Collateral Ligament MCL Medial Collateral Ligament MRI Magnetic Resonance Imaging MS Mid-Stance MVC Maximum Voluntary Contraction Declarations Acknowledgements None. Authors’ contributions Z.G. and L.X. conceived and designed the study; Z.G., L X., H J., Q.M., G.F. and Y.G. developed the methodology; Z.G. and H.J. performed the software development; Z.G. and L.X. performed data validation, formal analysis and data curation; H.J. contributed to data curation and investigation; Z.G. prepared the original draft and visualizations; L.X., Q.M., J.B. and Y.G. reviewed and edited the manuscript; L.X. and Q.M. handled project administration; G.F., J.B. and Y.G. supervised the study; G.F., Q.M., J.B. and Y.G. secured funding and provided resources. All authors have read and agreed to the published version of the manuscript. Funding This work was supported by the Key R&D Program of Zhejiang Province, (grant number: 2021C03130); The Zhejiang Province Science Fund for Distinguished Young Scholars (grant number: R22A021199), and K. C. Wong Magna Fund in Ningbo University. Data availability The datasets used and analyzed during the current study are available from the corresponding author, on reasonable request. Ethics approval and consent to participate The Ethics Committee of Ningbo University approved this study (code: RAGH20230315). All participants signed the informed consent form. Consent for publication Not applicable. Competing interests The authors declare no competing interests. Author details 1 Faculty of Sports Science, Ningbo University, Ningbo, China 2 Human Performance Laboratory, Faculty of Kinesiology, University of Calgary, Calgary, Canada 3 Faculty of Engineering, University of Pannonia, Veszprém, Hungary 4 KTH MoveAbility Lab, Department of Engineering Mechanics, KTH Royal Institute of Technology,SE-100 44 Stockholm, Sweden. 5 Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand 6 Vehicle Industry Research Center, Széchenyi István University, Győr, Hungary 7 Department of Sport, Physical Education and Health, Hong Kong Baptist University, Hong Kong, China References Calmbach WL, Hutchens M. Evaluation of patients presenting with knee pain: Part I. History, physical examination, radiographs, and laboratory tests. Am Family Phys. 2003;68(5):907–12. Hasler E, Herzog W, Leonard T, Stano A, Nguyen H. In vivo knee joint loading and kinematics before and after ACL transection in an animal model. J Biomech. 1997;31(3):253–62. Van Mechelen W. Running injuries: a review of the epidemiological literature. Sports Med. 1992;14:320–35. Fredericson M, Misra AK. Epidemiology and aetiology of marathon running injuries. Sports Med. 2007;37:437–9. Cho J-R, Park S-B, Ryu S-H, Kim S-H, Lee S-B. Landing impact analysis of sports shoes using 3-D coupled foot-shoe finite element model. J Mech Sci Technol. 2009;23:2583–91. Gilbert S, Chen T, Hutchinson ID, Choi D, Voigt C, Warren RF, Maher SA. Dynamic contact mechanics on the tibial plateau of the human knee during activities of daily living. J Biomech. 2014;47(9):2006–12. Sadeghi H, Allard P, Prince F, Labelle H. Symmetry and limb dominance in able-bodied gait: a review. Gait Posture. 2000;12(1):34–45. Hanley B, Tucker CB. Gait variability and symmetry remain consistent during high-intensity 10,000 m treadmill running. J Biomech. 2018;79:129–34. Zifchock RA, Davis I, Higginson J, McCaw S, Royer T. Side-to-side differences in overuse running injury susceptibility: a retrospective study. Hum Mov Sci. 2008;27(6):888–902. Walter SD, Hart L, McIntosh JM, Sutton JR. The Ontario cohort study of running-related injuries. Arch Intern Med. 1989;149(11):2561–4. Gao Z, Fekete G, Baker JS, Liang M, Xuan R, Gu Y. Effects of running fatigue on lower extremity symmetry among amateur runners: From a biomechanical perspective. Front Physiol. 2022;13:899818. Horisberger M, Fortuna R, Valderrabano V, Herzog W. Long-term repetitive mechanical loading of the knee joint by in vivo muscle stimulation accelerates cartilage degeneration and increases chondrocyte death in a rabbit model. Clin Biomech Elsevier Ltd. 2013;28(5):536–43. Pena E, Calvo B, Martinez M, Doblare M. A three-dimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint. J Biomech. 2006;39(9):1686–701. Taunton JE, Ryan MB, Clement D, McKenzie DC, Lloyd-Smith D, Zumbo B. A retrospective case-control analysis of 2002 running injuries. Br J Sports Med. 2002;36(2):95–101. Adams J, McAlindon T, Dimasi M, Carey J, Eustace S. Contribution of meniscal extrusion and cartilage loss to joint space narrowing in osteoarthritis. Clin Radiol. 1999;54(8):502–6. Khassetarash A, Haider I, Baggaley M, Edwards WB. Tibial Strains During Prolonged Downhill Running: A Finite Element Analysis. J Biomech Eng. 2023;145(4):041007. Van Gent R, Siem D, van Middelkoop M, Van Os A, Bierma-Zeinstra S, Koes B. Incidence and determinants of lower extremity running injuries in long distance runners: a systematic review. Br J Sports Med. 2007;41(8):469–80. DeMers MS, Pal S, Delp SL. Changes in tibiofemoral forces due to variations in muscle activity during walking. J Orthop Res. 2014;32(6):769–76. Xiang L, Gao Z, Wang A, Shim V, Fekete G, Gu Y, Fernandez J. Rethinking running biomechanics: a critical review of ground reaction forces, tibial bone loading, and the role of wearable sensors. Front Bioeng Biotechnol. 2024;12:1377383. Amoako AO, Pujalte GGA. Osteoarthritis in young, active, and athletic individuals. Clin Med Insights: Arthritis Musculoskelet Disorders. 2014;7:CMAMD. S14386. Liukkonen MK, Mononen ME, Vartiainen P, Kaukinen P, Bragge T, Suomalainen J-S, Malo MK, Venesmaa S, Käkelä P, Pihlajamäki J. Evaluation of the effect of bariatric surgery-induced weight loss on knee gait and cartilage degeneration. J Biomech Eng. 2018;140(4):041008. García-Pinillos F, Latorre-Román PÁ, Ramírez-Campillo R, Párraga-Montilla JA, Roche-Seruendo LE. How does the slope gradient affect spatiotemporal parameters during running? Influence of athletic level and vertical and leg stiffness. Gait Posture. 2019;68:72–7. Homyk A, Orsi A, Wibby S, Yang N, Nayeb-Hashemi H, Canavan PK. Failure locus of the anterior cruciate ligament: 3D finite element analysis. Comput Methods Biomech BioMed Eng. 2012;15(8):865–74. Mei Q, Fernandez J, Xiang L, Gao Z, Yu P, Baker JS, Gu Y. Dataset of lower extremity joint angles, moments and forces in distance running. Heliyon 2022, 8(11). Li L, Yang L, Zhang K, Zhu L, Wang X, Jiang Q. Three-dimensional finite-element analysis of aggravating medial meniscus tears on knee osteoarthritis. J Orthop translation. 2020;20:47–55. Li G, Lopez O, Rubash H. Variability of a three-dimensional finite element model constructed using magnetic resonance images of a knee for joint contact stress analysis. J Biomech Eng. 2001;123(4):341–6. LeRoux MA, Setton LA. Experimental and biphasic FEM determinations of the material properties and hydraulic permeability of the meniscus in tension. J Biomech Eng. 2002;124(3):315–21. Song Y, Debski RE, Musahl V, Thomas M, Woo SL-Y. A three-dimensional finite element model of the human anterior cruciate ligament: a computational analysis with experimental validation. J Biomech. 2004;37(3):383–90. Gabriel MT, Wong EK, Woo SLY, Yagi M, Debski RE. Distribution of in situ forces in the anterior cruciate ligament in response to rotatory loads. J Orthop Res. 2004;22(1):85–9. Adouni M, Faisal TR, Gaith M, Dhaher YY. A multiscale synthesis: characterizing acute cartilage failure under an aggregate tibiofemoral joint loading. Biomech Model Mechanobiol. 2019;18:1563–75. Adouni M, Alkhatib F, Gouissem A, Faisal TR. Knee joint biomechanics and cartilage damage prediction during landing: A hybrid MD-FE-musculoskeletal modeling. PLoS ONE. 2023;18(8):e0287479. Gao Z, Mei Q, Fekete G, Baker JS, Gu Y. The effect of prolonged running on the symmetry of biomechanical variables of the lower limb joints. Symmetry. 2020;12(5):720. Brown AM, Zifchock RA, Hillstrom HJ. The effects of limb dominance and fatigue on running biomechanics. Gait Posture. 2014;39(3):915–9. Guess TM, Razu S, Jahandar H, Stylianou A. Predicted loading on the menisci during gait: The effect of horn laxity. J Biomech. 2015;48(8):1490–8. Wan C, Hao Z, Wen S. The effect of the variation in ACL constitutive model on joint kinematics and biomechanics under different loads: a finite element study. J Biomech Eng. 2013;135(4):041002. Xiang L, Gu Y, Wang A, Shim V, Gao Z, Fernandez J. Foot Pronation Prediction with Inertial Sensors during Running: A Preliminary Application of Data-Driven Approaches. J Hum Kinetics 2023, 88. Weiss ND. Knee Ligaments: Structure, Function, Injury, and Repair. Yale J Biol Med. 1991;64(2):194. Powers CM, Witvrouw E, Davis IS, Crossley KM. Evidence-based framework for a pathomechanical model of patellofemoral pain: 2017 patellofemoral pain consensus statement from the 4th International Patellofemoral Pain Research Retreat, Manchester, UK: part 3. Br J Sports Med. 2017;51(24):1713–23. Briani RV, Pazzinatto MF, Silva DDO, Azevedo FM. Different pain responses to distinct levels of physical activity in women with patellofemoral pain. Braz J Phys Ther. 2017;21(2):138–43. Park S, Lee S, Yoon J, Chae S-W. Finite element analysis of knee and ankle joint during gait based on motion analysis. Med Eng Phys. 2019;63:33–41. Additional Declarations No competing interests reported. Supplementary Files SupplementaryMaterial1.docx Cite Share Download PDF Status: Published Journal Publication published 17 Nov, 2025 Read the published version in BMC Sports Science, Medicine and Rehabilitation → Version 1 posted Editorial decision: Revision requested 16 Jun, 2025 Reviews received at journal 14 Jun, 2025 Reviews received at journal 11 Jun, 2025 Reviewers agreed at journal 06 Jun, 2025 Reviewers agreed at journal 05 Jun, 2025 Reviewers invited by journal 05 Jun, 2025 Editor invited by journal 15 May, 2025 Editor assigned by journal 13 May, 2025 Submission checks completed at journal 13 May, 2025 First submitted to journal 11 May, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6641048","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":467350059,"identity":"037f669b-ad17-4bed-b56b-d4f3c713db30","order_by":0,"name":"Zixiang Gao","email":"","orcid":"","institution":"Ningbo No. 2 Hospital","correspondingAuthor":false,"prefix":"","firstName":"Zixiang","middleName":"","lastName":"Gao","suffix":""},{"id":467350060,"identity":"1e9c997c-e969-4b31-840b-569f18af9bb7","order_by":1,"name":"Liangliang Xiang","email":"","orcid":"","institution":"KTH Royal Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Liangliang","middleName":"","lastName":"Xiang","suffix":""},{"id":467350064,"identity":"24853dc5-f6ef-4800-bbd2-5b8d7e2cb319","order_by":2,"name":"Hanhui Jiang","email":"","orcid":"","institution":"Ningbo University","correspondingAuthor":false,"prefix":"","firstName":"Hanhui","middleName":"","lastName":"Jiang","suffix":""},{"id":467350065,"identity":"313a1a6c-9f79-48cc-a95e-5e8ca78b8317","order_by":3,"name":"Qichang Mei","email":"","orcid":"","institution":"Ningbo University","correspondingAuthor":false,"prefix":"","firstName":"Qichang","middleName":"","lastName":"Mei","suffix":""},{"id":467350067,"identity":"70dc26f4-dcd7-4c0d-92df-f33a484466d3","order_by":4,"name":"Gusztáv Fekete","email":"","orcid":"","institution":"Széchenyi István University","correspondingAuthor":false,"prefix":"","firstName":"Gusztáv","middleName":"","lastName":"Fekete","suffix":""},{"id":467350071,"identity":"181cfe27-c03b-4a7e-9504-8e30f4628d48","order_by":5,"name":"Julien S. Baker","email":"","orcid":"","institution":"Hong Kong Baptist University","correspondingAuthor":false,"prefix":"","firstName":"Julien","middleName":"S.","lastName":"Baker","suffix":""},{"id":467350073,"identity":"52f062b7-15b9-4590-8084-0d2c36f58295","order_by":6,"name":"Yaodong Gu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIiWNgGAWjYNACNiBm7wEzefiI18JzhoHhAJBiI16LRA5YCwNBLfIROYYfPpTZ5MlHvj34+GOOnQwbA/PDRzfwaDG8kWMsOeNcWrHh7bxkg4PbkoEOYzM2zsGnZUaOgTRv2+HEjbNzzCQObmMGauFhkyagxfg3WMvMMyAt9YS1yEvkmIFtmS/BA9JymLAWA55nZZZAvyRu4MkxNji77TgPGzMBv8i3J2++AQyxxPntZwwfVG6rtudnb374GK8tBzgMoAyYEDMe5WBbGtgfQBkEVI6CUTAKRsHIBQBMD0hrGPJ4ywAAAABJRU5ErkJggg==","orcid":"","institution":"Ningbo University","correspondingAuthor":true,"prefix":"","firstName":"Yaodong","middleName":"","lastName":"Gu","suffix":""}],"badges":[],"createdAt":"2025-05-11 18:08:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6641048/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6641048/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s13102-025-01372-3","type":"published","date":"2025-11-17T15:57:39+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":84185755,"identity":"8cfe33b0-cd6f-4bd8-8621-bba6246191a5","added_by":"auto","created_at":"2025-06-09 05:29:43","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":596455,"visible":true,"origin":"","legend":"\u003cp\u003eMusculoskeletal Modeling and Finite Element Modeling and Analysis. (A) Typical flow of motion simulation of OpenSim. (B) Optimized three-dimensional model of the knee joint. (C1) Ground reaction forces, joint rection forces, and joint reaction moments correspond to the five phases of the stance phase; (C2) the center of rotation of the knee joint and knee flexion angles correspond to the five moments of the stance phase. (D) Knee joint model after meshing and solutions. Note: Pre left: Non-dominant leg before 10km running. Pre right: Dominant leg before 10km running. Post left: Non-dominant leg after 10km running, Post right: Dominant leg after 10km running. ACL: anterior cruciate ligament, PCL: posterior cruciate ligament, MCL: medial collateral ligament, LCL: lateral collateral ligament, PTL: Patellar tibial ligaments. IC: initial contact; FP: first peak; MS: mid-stance; SP: second peak; TO: Toe off.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-6641048/v1/1595754039afa00602c2553f.png"},{"id":84183937,"identity":"68b30803-6573-48a4-8c96-b3fb6a76991b","added_by":"auto","created_at":"2025-06-09 05:05:43","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":474985,"visible":true,"origin":"","legend":"\u003cp\u003eValidation of the musculoskeletal model and finite element model.(A) Comparison of muscle activity levels from simulation versus experimentally recorded EMG data; (B) Attachment positions of EMG sensors on the participant; (C) Comparison of the results obtained from the finite element model in this study under the same boundary conditions with the cadaver experiments and finite element simulation results of previous studies; (D) Schematic diagram of finite element model validation.\u003c/p\u003e","description":"","filename":"image2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6641048/v1/fbf7028cf93ca05dd5af5744.jpeg"},{"id":84183935,"identity":"a60e643f-56a8-4c0b-9dcf-16a66e8c8a7d","added_by":"auto","created_at":"2025-06-09 05:05:43","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":420450,"visible":true,"origin":"","legend":"\u003cp\u003eVon Mises stresses in the bilateral knee joint in the meniscus and tibial cartilage before and after 10km of running at the moment of maximum GRF of the stance phase. The color scale indicates the magnitude of stress, with red representing high stress and blue representing low stress. Note: Pre left: Non-dominant leg before 10km running. Pre right: Dominant leg before 10km running. Post left: Non-dominant leg after 10km running, Post right: Dominant leg after 10km running.\u003c/p\u003e","description":"","filename":"image3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6641048/v1/8abc93ef8df18eead186e75f.jpeg"},{"id":84183943,"identity":"368f7cc7-6e3f-4932-a0a9-64a202a3b8f0","added_by":"auto","created_at":"2025-06-09 05:05:43","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":441623,"visible":true,"origin":"","legend":"\u003cp\u003eVon Mises stresses in the bilateral knee joint in the ACL, PCL, MCL, LCL, and PTL before and after 10km running at the moment of maximum GRF of the stance phase. The color scale indicates the magnitude of stress, with red representing high stress and blue representing low stress. Note: Pre left: Non-dominant leg before 10km running. Pre right: Dominant leg before 10km running. Post left: Non-dominant leg after 10km running, Post right: Dominant leg after 10km running. ACL: anterior cruciate ligament, PCL: posterior cruciate ligament, MCL: medial collateral ligament, LCL: lateral collateral ligament, PL: Patellar ligaments.\u003c/p\u003e","description":"","filename":"image4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6641048/v1/c043d8527d160af79b1a56f4.jpeg"},{"id":84185756,"identity":"66cf126b-75b9-4fc9-a48c-8c0990a48cca","added_by":"auto","created_at":"2025-06-09 05:29:43","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":338140,"visible":true,"origin":"","legend":"\u003cp\u003ePeak von Mises stresses changes in the meniscus, cartilage, and ligaments of the bilateral knee joint across 5 phases of the stance phase before and after 10km running. Note: Pre left: Left leg before 10km running. Pre right: Right leg before 10km running. Post left: Left leg after 10km running. ACL: anterior cruciate ligament, PCL: posterior cruciate ligament, MCL: medial collateral ligament, LCL: lateral collateral ligament, PL: Patellar ligaments. IC: Initial contact, FP: First Peak, MS: Mid-stance, SP: Second Peak, TO: Toe off.\u003c/p\u003e","description":"","filename":"image5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6641048/v1/b6c1286f45bb901cf5fe8140.jpeg"},{"id":96650108,"identity":"1f655d6e-c571-41b5-82b2-aa51536a776f","added_by":"auto","created_at":"2025-11-24 16:07:53","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3121701,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6641048/v1/7f923517-90c6-45ef-8ea9-7b87a9d03e90.pdf"},{"id":84183939,"identity":"9bba7a43-a0d6-433c-9d00-8db67fc9055b","added_by":"auto","created_at":"2025-06-09 05:05:43","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1043216,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryMaterial1.docx","url":"https://assets-eu.researchsquare.com/files/rs-6641048/v1/79d85448c99827488f7e4bda.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Musculoskeletal Modelling Coupled with Stress Simulation Reveal Asymmetrical Knee Load and Ligament Stress in Long-Distance Running","fulltext":[{"header":"Background","content":"\u003cp\u003eThe knee joint, encompassing the tibiofemoral (TF) and patellofemoral (PF) joints, is one of the most complex and vulnerable joints in the human body. It includes intricate internal structures such as bones, menisci, cartilage, ligaments, and other soft tissues, all crucial for functionality and stability during physical activities. Globally, 54% of athletes experience varying degrees of knee pain annually[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Despite exceptional cardiovascular fitness, runners may not possess equivalent muscular strength or neuromuscular coordination. Mechanical loading within the knee joint involves a dynamic interaction between motion and contact mechanics[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. While the knee joint's capacity to endure high mechanical loads is remarkable, knee injuries are increasingly prevalent among runners. Annually, 37\u0026ndash;56% of runners experience at least one running-related injury[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], with the incidence of knee injuries ranging from 19.4\u0026ndash;79.3% [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eNumerous studies in gait biomechanics presuppose completely symmetrical gait patterns and examine only unilateral variables, both in the experimental analysis and numerical simulation [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. However, Sadeghi and colleagues[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] observed that asymmetry in lower limb gait is present even in healthy individuals. The stronger limb typically compensates for its counterpart to address biomechanical shortcomings in the gait during long-distance running[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Nevertheless, running-related injuries commonly occur in the unilateral limb[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Approximately half of recreational runners sustain an injury annually, many of which are recurrent and side-specific[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Despite extensive studies into factors contributing to these injuries, the mechanisms underlying side-specific injuries are poorly understood. One major factor is the asymmetry of gait-induced inequality in the contribution of the bilateral limbs to load absorption[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Additionally, external factors such as fatigue may shift the main load to the part of the lower limb that has a weaker tolerance to fatigue[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eNotably, prolonged repetitive mechanical loading can damage the knee joint, leading to cartilage degeneration and increased chondrocyte apoptosis[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Patellofemoral pain syndrome, meniscal injuries, and ligament injuries[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] are significant contributors to these pathologies. Approximately 5% of runners sustain meniscal injuries[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Meniscal tears commonly disrupt circumferential fibers, leading to extrusion, displacement, and intra-articular constriction under axial stress[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Previous studies have reported that running fatigue increases tibial stress [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Additionally, the ligaments of the knee joint are vital for the dynamic stability of gait, as they restrict excessive knee extension or rotation, aided by muscular strength. Prolonged running can lead to diminished muscle strength, resulting in an increased load on the ligaments[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. However, studies on internal tissue stress within the knee remain limited.\u003c/p\u003e \u003cp\u003eTibiofemoral joint contact forces (JCF) arise from the combined action of muscles and ligaments[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Direct JCF quantification is invasive and ethically complex[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Therefore, musculoskeletal (MS) and finite element (FE) modeling techniques are widely used as non-invasive alternatives to simulate dynamic loads[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. MS models typically estimate muscle and joint forces based on inverse kinematics and kinetics but cannot fully evaluate tissue loading response during JCF increase progression or factors influencing cartilage degeneration[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. FE modeling provides intuitive graphical results to elucidate localized load distribution and magnitude induced by biomechanical changes in the knee joint[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Running-related knee injuries are caused by the complex interplay of tissues such as the meniscus, cartilage, ligaments, and muscles, and may be due to fatigue or asymmetric gait[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Nonetheless, previous studies on fatigue and differences in load between limbs have not precisely addressed the distribution and extent of the load on the knee joint's internal tissues, potentially missing key insights into the causes of unilateral limb injuries[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTherefore, the aim of this study was to employ coupled person-specific musculoskeletal and finite element models to explore inter-limb variations in internal knee joint loading and assess the effects of a long-distance running event on these variables. We hypothesize that: (1) differences in the loading distribution of the menisci, tibial cartilage, and ligaments on both sides will be observed at the peak value phase, in both pre- and post-fatigue states; (2) disparities in loading magnitude of these structures will be observed throughout gait support phase in both states; and (3) knee loading will increase with fatigue, with a greater increase on the non-dominant side due to different fatigue tolerance during the gait support phase.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eParticipants\u003c/h2\u003e \u003cp\u003eA 20-year-old healthy male amateur runner was enlisted for this study, with a body mass of 72 kg and a height of 178 cm. The participant needed to meet the following criteria: 1) The right limb was identified as the dominant limb; 2) The striking pattern of running gait was rearfoot striking; 3) an absence of pelvic or lower limb injuries in the preceding six months; and 4) the ability to run 10 kilometers in 45\u0026ndash;50 minutes[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Ethical approval for the study protocols was conferred by the Institutional Ethics Committee, ensuring that all methods adhered to the Declaration of Helsinki. Furthermore, the Ethics Committee at University sanctioned all procedures.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003e2.2 Data acquisition\u003c/h3\u003e\n\u003cp\u003eData collection was divided into four parts: (1) MRI scans, (2) ground running test before and (3) after a 10km treadmill run, and (4) treadmill running at submaximal speed for 10km. The ground running tests before and after the treadmill run employed the same testing procedure (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(A)).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eMedical image acquisition\u003c/h3\u003e\n\u003cp\u003eA 3.0 T clinical MRI scanner (General Electric Healthcare, Milwaukee, WI, USA), equipped with a 12-channel knee joint transmit-receive RF coil, was used for the acquisition of magnetic resonance data. The participant was oriented in a supine, non-weight-bearing posture, with the right knee centrally aligned within the coil. The MRI data was collected in the morning to avoid the day-long load bearing on the knee joint[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e\n\u003ch3\u003eExperimental data collection\u003c/h3\u003e\n\u003cp\u003eFor the 10 km treadmill running (Quasar, h/p Cosmos\u0026reg;, GmbH, Germany), the participant wore standardized lab-provided running footwear and maintained a submaximal speed of approximately 11.5 km/h, representing 80% of their personal best to simulate a casual running pace [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Data were collected during ground running tests before and after the 10km treadmill run. The participant acclimated by running on the track in the data collection area to mitigate the influence of conscious gait adjustments.\u003c/p\u003e \u003cp\u003eA total of 38 retroreflective markers were affixed according to a pre-established protocol. Marker trajectory and ground reaction forces (GRFs) were synchronously collected using an eight-camera Vicon 3D motion capture system (Vicon Metrics Ltd.,200Hz, Oxford, United Kingdom) and an AMTI force platform (AMTI, 1000Hz, Watertown, Massachusetts, USA), respectively. The velocity for the ground running tests was consistently monitored at 3.33 m/s using photocells. Five successful trials, meeting the criteria for proximity to the target speed and step location within the force plate area were selected for subsequent MS and FE analysis.\u003c/p\u003e \u003cp\u003eIn addition, muscle activity from the rectus femoris, biceps femoris, tibialis anterior, medial gastrocnemius, and lateral gastrocnemius of the dominant limb was synchronously captured using a 16-channel surface electromyography system (Delsys, 1000 Hz, Boston, Massachusetts, US). Prior to the testing procedures, maximum voluntary contraction (MVC) levels for these muscles were recorded to establish a baseline for activity assessment.\u003c/p\u003e\n\u003ch3\u003ePersonalized model development\u003c/h3\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eMusculoskeletal model\u003c/h2\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003eModel development\u003c/h2\u003e \u003cp\u003eThe OpenSim (National Center for Simulation in Rehabilitation Research, Stanford, USA) gait 2392 generic musculoskeletal model was chosen and scaled to establish a personalized model that aligns with individual characteristics (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(A)). An inverse kinematic analysis was then conducted to align the experimental biomechanics with the acquired motion data. The residual reduction algorithm (RRA) was employed to minimize errors in modeling and marker data processing. This application ensured that any computational inaccuracies in inverse dynamics remained within acceptable limits, allowing for dynamic alignment with GRF data, culminating in static optimization. Finally, joint reactions analysis (JRA) was used to calculate the knee reaction forces for the muscle activation scenario and the joint reaction moments relative to the ground.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e\n\u003ch3\u003eModel validation\u003c/h3\u003e\n\u003cp\u003eThe root mean square (RMS) values were obtained after preprocessing the electromyographic data. The muscle activation levels were normalized by dividing the maximal values obtained during MVC. To validate the model, we compared the muscle activation levels measured in the laboratory with those calculated using a static optimization algorithm.\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eFinite element modeling\u003c/h2\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003eKnee Joint Reconstruction\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(B) presents the structured framework outlining the sequential phases for reconstructing FE models. The three-dimensional reconstruction was carried out using MIMICS 21.0 (Materialise, Leuven, Belgium). Segmentation of magnetic resonance imaging (MRI) data facilitated the delineation of the anatomical boundaries of the articular cartilages (femoral, tibial, and patellar), menisci (medial and lateral), and ligaments (ACL, PCL, MCL, LCL, and PTL).\u003c/p\u003e \u003cp\u003eTo assure the accuracy of the FE model, manual segmentation of non-osseous elements was meticulously performed under the guidance of experienced orthopedic and radiological experts, achieving a precision of 0.1 mm. The tissues reconstructed in great detail were exported as STL files and further refined for model representation in Geomagic Studio 2021 (Geomagic, Inc., Research Triangle Park, NC, United States), where any problematic surfaces were identified and rectified. The final geometries were then assembled using SolidWorks 17 (SolidWorks Corporation, MA, United States), completing the model construction.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eModel Assembly and Material Allocation\u003c/h2\u003e \u003cp\u003eMaterial properties were allocated to each specific tissue to authentically model the biomechanical variations within the knee joint. The stance phase of running gait, characterized by a comparatively brief load application, permits the characterization of all cartilage tissues under quasi-static conditions using an instantaneous elastic model [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. For the sake of computational efficiency without compromising accuracy, ligaments were modeled as transversely isotropic, nearly incompressible materials using the Neo-Hookean approach[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e enumerates the attributes and values of material constants for each geometric entity[\u003cspan additionalcitationids=\"CR27\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. In accordance with the knee joint's anatomy and the specifics of the stance phase in running, modeling, meshing, and setting boundary conditions for this finite element knee model were established in Workbench 2021 R1 (ANSYS Inc., Canonsburg, Pennsylvania, USA). The distal portions of the tibia and fibula were fully constrained, immobilizing all translations and rotations.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMaterial properties and element types used in the knee joint FE models.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e \u003cp\u003ePart name\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eReferences\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eElement number\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eModel assumptions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eElement Type\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c10\" namest=\"c7\"\u003e \u003cp\u003eMaterial assignment\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eYoung\u0026rsquo;s modulus\u003c/p\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003ePoisson\u0026rsquo;s\u003c/p\u003e \u003cp\u003eratio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eD1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eBone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemur\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eSong et al., 2004\u003csup\u003e28\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e51809\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eLinearly elastic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"10\" rowspan=\"11\"\u003e \u003cp\u003eTetrahedral solid\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e11000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\" morerows=\"10\" rowspan=\"11\"\u003e \u003cp\u003e\\\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\" morerows=\"10\" rowspan=\"11\"\u003e \u003cp\u003e\\\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTibia\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e43673\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFibula\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5935\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePatella\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8062\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eMeniscus\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMedial\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eLi et al., 2001\u003csup\u003e26\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e24313\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eLinearly elastic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.49\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLateral\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e22276\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003eCartilage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemoral\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003eLeRoux et al., 2002\u003csup\u003e27\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e133537\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003eLinearly elastic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMedial tibial\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4780\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLateral tibial\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5373\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePatellar\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e11524\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTibiofibular\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3521\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003eLigament\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eACL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003eLi et al., 2001\u003csup\u003e26\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1602\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003eNeo-Hookean\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003eTension-only\u003c/p\u003e \u003cp\u003eTetrahedral solid\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e\\\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\" morerows=\"4\" rowspan=\"5\"\u003e \u003cp\u003e\\\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.00683\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePCL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1902\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.0041\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMCL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1441\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.00126\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLCL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1959\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.00126\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePTL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e18163\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.0041\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"10\"\u003e\u003cem\u003eNote\u003c/em\u003e: ACL: anterior cruciate ligament, PCL: posterior cruciate ligament, MCL: medial collateral ligament, LCL: lateral collateral ligament, PL: Patellar ligament\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eModel validation\u003c/h2\u003e \u003cp\u003eBy setting boundary conditions for the model, the rotation center (The midpoint of the trans-epicondylar line) of the femur is used to determine the translational displacement values for the knee joint. The rotational values are based on how the tibial moves, specifically the average rotation angles of the MCL and LCL attachment points on the tibia and fibula in relation to the tibial plateau reference point. We compared the displacements in the antero-posterior, proximal-distal, and medial-lateral directions of the knee model in the present study (the 134N afterload was applied to the center of rotation of the femur under conditions of 0\u0026deg;, 15\u0026deg;, and 30\u0026deg; knee flexion (remote displacement)) with the finite element simulation results of Song et al.[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] (0\u0026deg;) and cadaveric experiments of Gabriel et al.[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] ( 0\u0026deg;, 15\u0026deg; and 30\u0026deg;).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eRunning Gait Simulation\u003c/h2\u003e \u003cp\u003eThe stance phase was divided into five stages (initial contact, first peak, mid-stance, second peak, and toe-off) based on the vertical GRF data. The knee rotation center was used to apply the knee flexion angle (translational displacement), joint reaction force, and joint reaction moment calculated by the MS model to the corresponding five gait moments (Figures C1 \u0026amp; C2). Constraints on femoral rotations were imposed only when specific flexion angle-related loads were applied, leaving other directional movements unconstrained.\u003c/p\u003e \u003cp\u003eThrough binding commands, cartilage and ligament tissues were rigidly attached to their corresponding skeletal points of origin. The meniscus and tibial cartilage were also bound together in the same way. Five discrete contact pairs were featured within the knee joint model, each facilitating surface-to-surface interactions: between the femoral cartilage and the medial meniscus, the lateral tibial cartilage, the lateral tibial cartilage, and the patellar cartilage. A frictionless, finite sliding approach was employed to address the minimal friction between joint cartilage surfaces[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(D).\u003c/p\u003e \u003cp\u003e \u003cem\u003e***Insert\u003c/em\u003e \u003cb\u003eFigure. 1\u003c/b\u003e \u003cem\u003ehere***\u003c/em\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003e***Insert\u003c/em\u003e \u003cb\u003eTable. 1\u003c/b\u003e \u003cem\u003ehere***\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eModel validation\u003c/h2\u003e \u003cp\u003e \u003cem\u003e***Insert\u003c/em\u003e \u003cb\u003eFigure. 2\u003c/b\u003e \u003cem\u003ehere***\u003c/em\u003e\u003c/p\u003e \u003cp\u003eThe muscle activation levels of the rectus femoris, biceps femoris, tibialis anterior, medial gastrocnemius, and lateral gastrocnemius calculated in pre- and post-fatigue states were similar to the surface EMG signals recorded in the experiment, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(A). Additionally, under the condition of 0\u0026deg; knee flexion and a posterior load of 134N on the rotation center of the femur, the displacement in the anterior-posterior, proximal-distal, and medial-lateral directions in this study's knee joint model was similar to the cadaver experiments by Gabriel et al.[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] and the finite element simulations by Song et al.[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. By applying remote displacement to the center of femoral rotation under identical boundary and loading conditions, the knee joint's displacement outcomes at 15\u0026deg; and 30\u0026deg; of flexion were congruent with the cadaveric study findings of Gabriel et al.[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(B).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003eKinematics and Kinetics\u003c/h2\u003e \u003cp\u003eIn the pre-fatigue states, a greater internal rotation angle was observed in the left knee compared to the right side, with this difference was more pronounced in the post-fatigue states during mid-stance. Additionally, a greater anterior joint reaction force was observed in the right knee. Similarly, a greater abduction joint reaction moment was noted in the left knee joint. In the post-fatigue states, the left knee exhibited a greater extension angle, and there was more pronounced adduction in the right knee. Furthermore, an increase in right knee flexion reaction moments was observed after fatigue. To test the statistical significance of these differences, we conducted a time-series one-dimensional statistical parametric mapping (SPM1d) analysis in Python 3.8 of five trials on both lower extremities before and after fatigue. A two-way repeated-measures ANOVA (limb \u0026times; fatigue) with post-hoc paired t-tests was performed for individual condition comparisons. Detailed results of this analysis are presented in Supplementary Material 1 (Figures A1 \u0026ndash; A3).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003eFinite element analysis\u003c/h2\u003e \u003cdiv id=\"Sec20\" class=\"Section3\"\u003e \u003ch2\u003eMaximum load simulation of meniscus and tibial cartilage\u003c/h2\u003e \u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, similar stress distributions were observed on both the dominant and non-dominant limb menisci in both states. Maximum stress was predominantly located at the central and anterior horn of the medial meniscus. Notably, the left knee surpassed the right knee by 9.5 MPa, and then decreased by 9.12 MPa after fatigue. The peak stress of the right medial meniscus also decreased by 12.7 MPa after fatigue. Additionally, the anterior segment of the middle region of the lateral meniscus sustained the maximum stress, with the left side experiencing 3.39 MPa more than the right side, which then decreased by 5.47 MPa after fatigue.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003e***Insert\u003c/em\u003e \u003cb\u003eFigure. 3\u003c/b\u003e \u003cem\u003ehere***\u003c/em\u003e\u003c/p\u003e \u003cp\u003eThe tibial cartilage exhibited a consistent stress distribution, with the anteromedial part of the medial tibial cartilage bearing the main load. The stress of the left tibial cartilage was higher than that of the right side by 2.86 MPa but decreased by 1.82 MPa after fatigue. For the lateral tibial cartilage, the left side experienced 4.81 MPa more than the right in pre-fatigue states. The peak stress of the right lateral tibial cartilage then decreased by 12.7 MPa after fatigue.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003eMaximum load simulation of ligaments\u003c/h2\u003e \u003cp\u003eSimilar stress distributions were observed on the ligaments in both states (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Maximum stresses for the ACL and PCL were primarily located at the femoral contact points. The left ACL was 17.07 MPa higher than the right side and increased by 3.15 MPa after fatigue. In the post-fatigue states, it surpassed the right side by 11.28 MPa. The left PCL stress was 16.59 MPa higher than the right side and decreased by 8.56 MPa after fatigue. In the post-fatigue states, it was 9.24 MPa higher than the right side.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe maximum stress for the MCL was mainly on the anterosuperior side. The left MCL stress was 7.86 MPa higher than the right side and decreased by 2.90 MPa after fatigue. Additionally, the stress on the left LCL was 6.56 MPa higher than the right side and increased by 14.54 MPa after fatigue. In the post-fatigue states, it surpassed the right side by 23.00 MPa. The maximum stress for the PL was mainly in the middle region. Interestingly, the stress on the left side was lower than on the right side by 1.10 MPa but decreased by 1.38 MPa after fatigue. In the post-fatigue states, it was 0.46 MPa higher than the right side.\u003c/p\u003e \u003cp\u003e \u003cem\u003e***Insert\u003c/em\u003e \u003cb\u003eFigure. 4\u003c/b\u003e \u003cem\u003ehere***\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003eLoad simulation of gait stance phase\u003c/h2\u003e \u003cp\u003e \u003cem\u003e***Insert\u003c/em\u003e \u003cb\u003eFigure. 5\u003c/b\u003e \u003cem\u003ehere***\u003c/em\u003e\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates the variations in stress values for the meniscus, tibial cartilage, and ligaments of the bilateral knee during the gait stance phase in both states. Except for the PCL, the peak stress of the tissues was consistently lowest during the IC phase, gradually increased during the SP phase, reached its maximum, and decreased during the OT phase at both states. Interestingly, the maximum stress for the PCLs occurred at the TO phase, while the stress was lowest at the FP phase, except on the left side in pre-fatigue and post-fatigue states, respectively. The medial and lateral menisci trend graphs reveal that peak stress in pre-fatigue states was consistently higher than in post-fatigue states, with the left side consistently exhibiting greater stress than the right. The ACLs and MCLs showed higher stress on the left side than the right of all states. The stress on the left LCL increased, while it decreased on the right side after fatigue. The peak stress for the left PL was highest at the IC phase, while the right PL was highest for all other phases in pre-fatigue states. Detailed results of this analysis are presented in Appendix 1 (Table A1).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eTo determine the changes in the dominant and non-dominant knee joints during different running phases and how a 10 km submaximal intensity run affects these variables, this study coupled variables from musculoskeletal models (GRF, knee joint angles, reaction forces, and moments) to drive finite element simulations (menisci, tibial cartilage, ACL, PCL, MCL, LCL, and PL). Specifically, the distribution of loads on the tissues was similar in both knees and in all states. Moreover, the load on the meniscus and tibial cartilage was greater on the non-dominant side and greater in the pre-fatigue state. The load on the ACL, PCL, and LCL of the non-dominant limb increased after fatigue, while it decreased on the dominant side. Interestingly, the load on the PL of the dominant side was greater in the pre- fatigue state. Therefore, the findings of this study are consistent with hypotheses (2) but present some contradictory findings with hypotheses (1) and (3).\u003c/p\u003e \u003cp\u003eThe knee joint exhibits complex mechanical behaviors due to its intricate structures including bones, cartilage, and ligaments, making the development of efficient and accurate models essential [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. In addition to the findings of this study, similar investigations have highlighted the significance of detailed finite element modeling and multiscale approaches in understanding knee joint mechanics and injury mechanisms. Adouni et al. [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] demonstrated that cartilage fibril stiffness and cross-link density are critical in determining the mechanical response and damage initiation under loading conditions. Furthermore, a similar study utilized a hybrid modeling approach to elucidate the impact of detailed tissue mechanics on joint function and injury risk [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. These studies collectively support the need for advanced modeling techniques to improve the predictive accuracy and understanding of knee joint behavior under various loading scenarios.\u003c/p\u003e \u003cp\u003eWe demonstrate the validity of our knee joint model by conducting a comparative validation with identical boundary conditions against past finite element simulations and cadaveric experimental studies[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. In this study, the stance phase of gait was divided into five distinct postural stages based on the pattern of vertical GRFs. The goal was to explore the disparities in internal loading of the bilateral knee joints across different ground contact stages and the influence of fatigue. Previous research has reported no differences in knee joint angles at the pre-fatigue states[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. A greater internal rotation angle in the non-dominant knee joint during the mid-stance period could explain the excessive load on its ACL and LCL. Additionally, the study found a greater anterior joint reaction force peak in the dominant knee, potentially indicating a higher load on the patellofemoral joint of the dominant knee. This is corroborated by the noted excess load on the PL of the dominant knee. Hence, patellofemoral joint pain in the dominant limb should be a consideration for amateur runners [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. Furthermore, the fatigue resistance of the hip adductor muscles of the non-dominant limb should be emphasized in the functional training of long-distance runners.\u003c/p\u003e \u003cp\u003eThe findings of this study show that fatigue heightened the flexion reaction moment in the dominant knee, hinting at diminished quadricep control, which might lead to an increased load on the PCL of the dominant knee post-fatigue[\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. Therefore, runners and coaches should focus on specific training for quadriceps control in the dominant limb. The larger loading of the dominant knee\u0026rsquo;s PCL during the mid-stance period after fatigue observed in the current FEM simulations also support this conclusion. Additionally, a greater abduction joint reaction moment of the non-dominant knee joint in the pre-fatigue states occurred during the mid-stance phase, indicating a greater load on the medial tibial plateau[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. This finding is consistent with the observation of a greater load on the medial meniscus and tibial cartilage of the non-dominant knee joint.\u003c/p\u003e \u003cp\u003eThe meniscus functions to transmit and evenly distribute forces from the femur to the tibial plateau. However, this load-transferring mechanism can become compromised due to recurrent overloading, resulting in localized stress peaks and subsequent damage to the knee joint. This study observed that the load on the medial meniscus was primarily concentrated at the anterior horn, and the load on the lateral meniscus was concentrated on the posteromedial side, consistent with previous studies[\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. Greater loads may cause tears at the anterior horn of the medial meniscus and the middle of the lateral meniscus. Notably, we found a similar load distribution in both the non-dominant and dominant knee joints before and after fatigue. It can be hypothesized that fatigue and limb preference do not affect the location of the meniscus, tibial cartilage, and ligaments where injuries can develop during the running event, and that injuries are generally only related to the magnitude of the load. In addition, the load on the ACL and PCL was primarily concentrated at the contact points with the femur, which is consistent with the findings of a previous study [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eBy observing the load distribution of the LCL, we found that most of the load was concentrated near the ligament attachment points to the bones, which could be the most vulnerable area to strains. Additionally, larger loads were found in the non-dominant LCL after fatigue, likely induced by foot pronation[\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Therefore, footwear with proper arch support is necessary for long distance running. The correlation between CLC loading and the degree of foot pronation should be further addressed in future studies. However, most of the MCL's load was concentrated in the anterosuperior direction and was more pronounced on the non-dominant side. This is a key area where too much MCL load is caused by the femur rotating during knee flexion[\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Furthermore, the reduced PL load after fatigue suggests that running fatigue is not the leading cause of patellar pain, which has had mixed results in previous studies[\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe findings of this study demonstrated that the load on the bilateral menisci, tibial cartilage, and ligaments during the gait support phase shows a consistent trend of change both pre- and post-fatigue, being almost at its lowest during the IC phase, then gradually increasing, peaking during the SP phase, and subsequently decreasing during the TO phase. This presents a divergent trend from the findings of a previous study, where the greatest load occurred during the FP phase[\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. The cause of this discrepancy may be attributed to the different postures associated with walking and running gaits. Previous studies have indicated an increased injury risk in the non-dominant limb within the running gait[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. This study indicates that the non-dominant limb typically bears a greater load, particularly in the meniscus, tibial cartilage, ACL, MCL, and LCL, which could potentially account for the overload in a single knee joint. Furthermore, the study observed that the effect of fatigue on the ACL, PCL, and LCL of the non-dominant limb during the gait support phase is often negative, while it has the opposite effect on the dominant limb. The increased load on the knee joint tissues of the non-dominant limb due to fatigue should be given attention by runners and coaches. This may be due to the dominant limb's weaker fatigue tolerance[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eWhen interpreting the significant findings of this study, certain limitations should be considered. Firstly, this study is limited by the inclusion of only one male participant, which may affect the generalizability of the results, particularly with respect to potential differences between male and female physiological structures. However, as males and females may present varying knee biomechanical characteristics and injury mechanisms, this exclusive pilot study limited the sex factor to investigate the present research topic. Future research should aim to include a more diverse participant pool, including female runners, to enable a more robust statistical analysis of the observed differences and to verify the generalizability of the finite element results of the current study.\u003c/p\u003e \u003cp\u003eSecondly, the study did not incorporate bilateral knee MRI data for the finite element model. Instead, it applied boundary conditions collected from both knees during the experiment to a single model, which did not account for morphological variances between the two knees. Additionally, Von Mises stress was chosen as the primary metric in this study due to its ability to represent the combined effects of multi-axial stresses within the knee joint tissues. However, we recognize that von Mises stress may not fully account for the complex deformation behaviors of soft tissues. Future research should consider incorporating strain variations and other mechanical metrics to provide a more comprehensive assessment.\u003c/p\u003e \u003cp\u003eLastly, the use of linear elastic material properties for the cartilage and meniscus in this study represents a simplification that may not fully capture the complex mechanical behavior of these tissues. While this approach was chosen for computational efficiency, future studies should consider using more advanced material models, such as fiber-reinforced hyperelastic models, to enhance the accuracy of the simulations.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThis study examines the differences in load distribution and magnitude within the bilateral knee joint's internal tissues and the effects of running-induced fatigue on these aspects. Although the load distribution areas of the menisci, cartilage, and ligaments in both knee joints are similar, the differences in their magnitude should be considered as potential causes of excessive loading. This study found that the internal tissue load in the non-dominant limb during the stance phase of gait is greater than that in the dominant limb, and fatigue has a negative effect on the internal tissue load of the non-dominant limb, whereas the effect is the opposite in the dominant limb. Runners and coaches should consider limb dominance and fatigue effects when designing training programs. Specific exercises to strengthen the non-dominant limb and improve fatigue resistance could help mitigate the risk of knee injuries. Sports medicine professionals should also focus on targeted interventions for runners based on their biomechanical assessments.\u003c/p\u003e"},{"header":"Abbreviations","content":" \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cdiv class=\"SimplePara\"\u003eACL\u003c/div\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cdiv class=\"SimplePara\"\u003eAnterior Cruciate Ligament\u003c/div\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cdiv class=\"SimplePara\"\u003eEMG\u003c/div\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cdiv class=\"SimplePara\"\u003eElectromyography\u003c/div\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cdiv class=\"SimplePara\"\u003eFE\u003c/div\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cdiv class=\"SimplePara\"\u003eFinite Element\u003c/div\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cdiv class=\"SimplePara\"\u003eFP\u003c/div\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cdiv class=\"SimplePara\"\u003eFirst Peak\u003c/div\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cdiv class=\"SimplePara\"\u003eGRF\u003c/div\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cdiv class=\"SimplePara\"\u003eGround Reaction Force\u003c/div\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cdiv class=\"SimplePara\"\u003eIC\u003c/div\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cdiv class=\"SimplePara\"\u003eInitial Contact\u003c/div\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cdiv class=\"SimplePara\"\u003eJCF\u003c/div\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cdiv class=\"SimplePara\"\u003eJoint Contact Force\u003c/div\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cdiv class=\"SimplePara\"\u003eJRA\u003c/div\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cdiv class=\"SimplePara\"\u003eJoint Reaction Analysis\u003c/div\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cdiv class=\"SimplePara\"\u003eLCL\u003c/div\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cdiv class=\"SimplePara\"\u003eLateral Collateral Ligament\u003c/div\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cdiv class=\"SimplePara\"\u003eMCL\u003c/div\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cdiv class=\"SimplePara\"\u003eMedial Collateral Ligament\u003c/div\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cdiv class=\"SimplePara\"\u003eMRI\u003c/div\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cdiv class=\"SimplePara\"\u003eMagnetic Resonance Imaging\u003c/div\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cdiv class=\"SimplePara\"\u003eMS\u003c/div\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cdiv class=\"SimplePara\"\u003eMid-Stance\u003c/div\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cdiv class=\"SimplePara\"\u003eMVC\u003c/div\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cdiv class=\"SimplePara\"\u003eMaximum Voluntary Contraction\u003c/div\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003cbr/\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNone.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026rsquo; contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eZ.G. and L.X. conceived and designed the study; Z.G., L X., H J., Q.M., G.F. and Y.G. developed the methodology; Z.G. and H.J. performed the software development; Z.G. and L.X. performed data validation, formal analysis and data curation; H.J. contributed to data curation and investigation; Z.G. prepared the original draft and visualizations; L.X., Q.M., J.B. and Y.G. reviewed and edited the manuscript; L.X. and Q.M. handled project administration; G.F., J.B. and Y.G. supervised the study; G.F., Q.M., J.B. and Y.G. secured funding and provided resources. All authors have read and agreed to the published version of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Key R\u0026amp;D Program of Zhejiang Province, (grant number: 2021C03130); The Zhejiang Province Science Fund for Distinguished Young Scholars (grant number: R22A021199), and K. C. Wong Magna Fund in Ningbo University.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets used and analyzed during the current study are available from the corresponding author, on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe Ethics Committee of Ningbo University approved this study (code: RAGH20230315). All participants signed the informed consent form.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor details\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e1\u0026nbsp;\u003c/sup\u003eFaculty of Sports Science, Ningbo University, Ningbo, China\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e2\u0026nbsp;\u003c/sup\u003eHuman Performance Laboratory, Faculty of Kinesiology, University of Calgary, Calgary, Canada\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e3\u0026nbsp;\u003c/sup\u003eFaculty of Engineering, University of Pannonia, Veszpr\u0026eacute;m, Hungary\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e4\u0026nbsp;\u003c/sup\u003eKTH MoveAbility Lab, Department of Engineering Mechanics, KTH Royal Institute of Technology,SE-100 44 Stockholm, Sweden.\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e5\u0026nbsp;\u003c/sup\u003eAuckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e6\u0026nbsp;\u003c/sup\u003eVehicle Industry Research Center, Sz\u0026eacute;chenyi Istv\u0026aacute;n University, Győr, Hungary\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e7\u0026nbsp;\u003c/sup\u003eDepartment of Sport, Physical Education and Health, Hong Kong Baptist University, Hong Kong, China\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eCalmbach WL, Hutchens M. Evaluation of patients presenting with knee pain: Part I. History, physical examination, radiographs, and laboratory tests. Am Family Phys. 2003;68(5):907\u0026ndash;12.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHasler E, Herzog W, Leonard T, Stano A, Nguyen H. In vivo knee joint loading and kinematics before and after ACL transection in an animal model. J Biomech. 1997;31(3):253\u0026ndash;62.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVan Mechelen W. Running injuries: a review of the epidemiological literature. Sports Med. 1992;14:320\u0026ndash;35.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFredericson M, Misra AK. Epidemiology and aetiology of marathon running injuries. Sports Med. 2007;37:437\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCho J-R, Park S-B, Ryu S-H, Kim S-H, Lee S-B. Landing impact analysis of sports shoes using 3-D coupled foot-shoe finite element model. J Mech Sci Technol. 2009;23:2583\u0026ndash;91.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGilbert S, Chen T, Hutchinson ID, Choi D, Voigt C, Warren RF, Maher SA. Dynamic contact mechanics on the tibial plateau of the human knee during activities of daily living. J Biomech. 2014;47(9):2006\u0026ndash;12.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSadeghi H, Allard P, Prince F, Labelle H. Symmetry and limb dominance in able-bodied gait: a review. Gait Posture. 2000;12(1):34\u0026ndash;45.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHanley B, Tucker CB. Gait variability and symmetry remain consistent during high-intensity 10,000 m treadmill running. J Biomech. 2018;79:129\u0026ndash;34.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZifchock RA, Davis I, Higginson J, McCaw S, Royer T. Side-to-side differences in overuse running injury susceptibility: a retrospective study. Hum Mov Sci. 2008;27(6):888\u0026ndash;902.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWalter SD, Hart L, McIntosh JM, Sutton JR. The Ontario cohort study of running-related injuries. Arch Intern Med. 1989;149(11):2561\u0026ndash;4.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGao Z, Fekete G, Baker JS, Liang M, Xuan R, Gu Y. Effects of running fatigue on lower extremity symmetry among amateur runners: From a biomechanical perspective. Front Physiol. 2022;13:899818.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHorisberger M, Fortuna R, Valderrabano V, Herzog W. Long-term repetitive mechanical loading of the knee joint by in vivo muscle stimulation accelerates cartilage degeneration and increases chondrocyte death in a rabbit model. Clin Biomech Elsevier Ltd. 2013;28(5):536\u0026ndash;43.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePena E, Calvo B, Martinez M, Doblare M. A three-dimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint. J Biomech. 2006;39(9):1686\u0026ndash;701.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTaunton JE, Ryan MB, Clement D, McKenzie DC, Lloyd-Smith D, Zumbo B. A retrospective case-control analysis of 2002 running injuries. Br J Sports Med. 2002;36(2):95\u0026ndash;101.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAdams J, McAlindon T, Dimasi M, Carey J, Eustace S. Contribution of meniscal extrusion and cartilage loss to joint space narrowing in osteoarthritis. Clin Radiol. 1999;54(8):502\u0026ndash;6.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKhassetarash A, Haider I, Baggaley M, Edwards WB. Tibial Strains During Prolonged Downhill Running: A Finite Element Analysis. J Biomech Eng. 2023;145(4):041007.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVan Gent R, Siem D, van Middelkoop M, Van Os A, Bierma-Zeinstra S, Koes B. Incidence and determinants of lower extremity running injuries in long distance runners: a systematic review. Br J Sports Med. 2007;41(8):469\u0026ndash;80.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDeMers MS, Pal S, Delp SL. Changes in tibiofemoral forces due to variations in muscle activity during walking. J Orthop Res. 2014;32(6):769\u0026ndash;76.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXiang L, Gao Z, Wang A, Shim V, Fekete G, Gu Y, Fernandez J. Rethinking running biomechanics: a critical review of ground reaction forces, tibial bone loading, and the role of wearable sensors. Front Bioeng Biotechnol. 2024;12:1377383.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAmoako AO, Pujalte GGA. Osteoarthritis in young, active, and athletic individuals. Clin Med Insights: Arthritis Musculoskelet Disorders. 2014;7:CMAMD. S14386.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiukkonen MK, Mononen ME, Vartiainen P, Kaukinen P, Bragge T, Suomalainen J-S, Malo MK, Venesmaa S, K\u0026auml;kel\u0026auml; P, Pihlajam\u0026auml;ki J. Evaluation of the effect of bariatric surgery-induced weight loss on knee gait and cartilage degeneration. J Biomech Eng. 2018;140(4):041008.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGarc\u0026iacute;a-Pinillos F, Latorre-Rom\u0026aacute;n P\u0026Aacute;, Ram\u0026iacute;rez-Campillo R, P\u0026aacute;rraga-Montilla JA, Roche-Seruendo LE. How does the slope gradient affect spatiotemporal parameters during running? Influence of athletic level and vertical and leg stiffness. Gait Posture. 2019;68:72\u0026ndash;7.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHomyk A, Orsi A, Wibby S, Yang N, Nayeb-Hashemi H, Canavan PK. Failure locus of the anterior cruciate ligament: 3D finite element analysis. Comput Methods Biomech BioMed Eng. 2012;15(8):865\u0026ndash;74.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMei Q, Fernandez J, Xiang L, Gao Z, Yu P, Baker JS, Gu Y. Dataset of lower extremity joint angles, moments and forces in distance running. Heliyon 2022, 8(11).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi L, Yang L, Zhang K, Zhu L, Wang X, Jiang Q. Three-dimensional finite-element analysis of aggravating medial meniscus tears on knee osteoarthritis. J Orthop translation. 2020;20:47\u0026ndash;55.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi G, Lopez O, Rubash H. Variability of a three-dimensional finite element model constructed using magnetic resonance images of a knee for joint contact stress analysis. J Biomech Eng. 2001;123(4):341\u0026ndash;6.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLeRoux MA, Setton LA. Experimental and biphasic FEM determinations of the material properties and hydraulic permeability of the meniscus in tension. J Biomech Eng. 2002;124(3):315\u0026ndash;21.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSong Y, Debski RE, Musahl V, Thomas M, Woo SL-Y. A three-dimensional finite element model of the human anterior cruciate ligament: a computational analysis with experimental validation. J Biomech. 2004;37(3):383\u0026ndash;90.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGabriel MT, Wong EK, Woo SLY, Yagi M, Debski RE. Distribution of in situ forces in the anterior cruciate ligament in response to rotatory loads. J Orthop Res. 2004;22(1):85\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAdouni M, Faisal TR, Gaith M, Dhaher YY. A multiscale synthesis: characterizing acute cartilage failure under an aggregate tibiofemoral joint loading. Biomech Model Mechanobiol. 2019;18:1563\u0026ndash;75.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAdouni M, Alkhatib F, Gouissem A, Faisal TR. Knee joint biomechanics and cartilage damage prediction during landing: A hybrid MD-FE-musculoskeletal modeling. PLoS ONE. 2023;18(8):e0287479.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGao Z, Mei Q, Fekete G, Baker JS, Gu Y. The effect of prolonged running on the symmetry of biomechanical variables of the lower limb joints. Symmetry. 2020;12(5):720.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBrown AM, Zifchock RA, Hillstrom HJ. The effects of limb dominance and fatigue on running biomechanics. Gait Posture. 2014;39(3):915\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGuess TM, Razu S, Jahandar H, Stylianou A. Predicted loading on the menisci during gait: The effect of horn laxity. J Biomech. 2015;48(8):1490\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWan C, Hao Z, Wen S. The effect of the variation in ACL constitutive model on joint kinematics and biomechanics under different loads: a finite element study. J Biomech Eng. 2013;135(4):041002.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXiang L, Gu Y, Wang A, Shim V, Gao Z, Fernandez J. Foot Pronation Prediction with Inertial Sensors during Running: A Preliminary Application of Data-Driven Approaches. J Hum Kinetics 2023, 88.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWeiss ND. Knee Ligaments: Structure, Function, Injury, and Repair. Yale J Biol Med. 1991;64(2):194.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePowers CM, Witvrouw E, Davis IS, Crossley KM. Evidence-based framework for a pathomechanical model of patellofemoral pain: 2017 patellofemoral pain consensus statement from the 4th International Patellofemoral Pain Research Retreat, Manchester, UK: part 3. Br J Sports Med. 2017;51(24):1713\u0026ndash;23.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBriani RV, Pazzinatto MF, Silva DDO, Azevedo FM. Different pain responses to distinct levels of physical activity in women with patellofemoral pain. Braz J Phys Ther. 2017;21(2):138\u0026ndash;43.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePark S, Lee S, Yoon J, Chae S-W. Finite element analysis of knee and ankle joint during gait based on motion analysis. Med Eng Phys. 2019;63:33\u0026ndash;41.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-sports-science-medicine-and-rehabilitation","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ssmr","sideBox":"Learn more about [BMC Sports Science, Medicine and Rehabilitation](http://bmcsportsscimedrehabil.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/ssmr/default.aspx","title":"BMC Sports Science, Medicine and Rehabilitation","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Knee, Running, Finite element modeling, Overloading injuries, Limb dominance","lastPublishedDoi":"10.21203/rs.3.rs-6641048/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6641048/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eUnderstanding the internal load characteristics of the knee joint is essential for investigating unilateral knee injuries associated with running. This study examined the differences in the location and magnitude of von Mises stress in the internal structures of bilateral knee joints during the stance phase of gait following 10 kilometers running at submaximal speeds.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eA healthy male recreational runner participated in this study. We employed a synergistic approach, integrating subject-specific knee joint angles, reaction forces, and moments derived from musculoskeletal modeling to inform and drive the finite element modeling of running. This methodology ensured a detailed and accurate representation of knee joint mechanics. The peak stresses of the bilateral knee menisci, tibial cartilage, and five main ligaments were quantified using a finite element model during the stance phase.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eThe meniscus, tibial cartilage, anterior (ACL), posterior cruciate ligament (PCL), medial (MCL), and lateral collateral ligament (LCL) experienced larger loads in the non-dominant limb. Additionally, fatigue elevated the peak loading on the non-dominant limb's ACL, PCL, and LCL during the gait stance phase but diminished the load on these ligaments in the dominant knee joint.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eThis study substantially enhances our understanding of the impact of running-induced fatigue on bilateral knee joint loading. It provides a detailed analysis of factors leading to unilateral knee overload during extended running. These insights are essential in formulating targeted strategies to reduce injury risks.\u003c/p\u003e","manuscriptTitle":"Musculoskeletal Modelling Coupled with Stress Simulation Reveal Asymmetrical Knee Load and Ligament Stress in Long-Distance Running","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-09 05:05:38","doi":"10.21203/rs.3.rs-6641048/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-06-16T10:00:00+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-14T13:09:13+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-06-11T14:12:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"40095578823158836915956361355015835342","date":"2025-06-06T05:39:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"156734113456105761499697204686735933537","date":"2025-06-05T11:52:55+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-06-05T11:35:37+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-05-15T04:36:38+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-05-14T02:58:37+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-05-14T02:55:35+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Sports Science, Medicine and Rehabilitation","date":"2025-05-11T17:56:02+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-sports-science-medicine-and-rehabilitation","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ssmr","sideBox":"Learn more about [BMC Sports Science, Medicine and Rehabilitation](http://bmcsportsscimedrehabil.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/ssmr/default.aspx","title":"BMC Sports Science, Medicine and Rehabilitation","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ef43932a-9d32-4726-bc64-5e0dc146aa37","owner":[],"postedDate":"June 9th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-11-24T16:01:12+00:00","versionOfRecord":{"articleIdentity":"rs-6641048","link":"https://doi.org/10.1186/s13102-025-01372-3","journal":{"identity":"bmc-sports-science-medicine-and-rehabilitation","isVorOnly":false,"title":"BMC Sports Science, Medicine and Rehabilitation"},"publishedOn":"2025-11-17 15:57:39","publishedOnDateReadable":"November 17th, 2025"},"versionCreatedAt":"2025-06-09 05:05:38","video":"","vorDoi":"10.1186/s13102-025-01372-3","vorDoiUrl":"https://doi.org/10.1186/s13102-025-01372-3","workflowStages":[]},"version":"v1","identity":"rs-6641048","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6641048","identity":"rs-6641048","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}