Sex Differences in Three-Dimensional Intra-Cycle Velocity Fluctuation and Performance During Freestyle Swimming Among High-Level Swimmers

Sex Differences in Three-Dimensional Intra-Cycle Velocity Fluctuation and Performance During Freestyle Swimming Among High-Level Swimmers | 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 Sex Differences in Three-Dimensional Intra-Cycle Velocity Fluctuation and Performance During Freestyle Swimming Among High-Level Swimmers Zhenyu Jin, Yulin Zhou, Yuhang Zhou, Qian Yu, Dapeng Wang, Sijia Shen, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9387014/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study examined sex differences in three-dimensional intra-cycle velocity fluctuations (IVFs) of the body’s center of mass and the relationship between IVFs and swimming velocity (Vswim) in high-level swimmers during freestyle. Maximal-effort freestyle sprints performed by 13 high-level athletes (7 males and 6 females) were captured using a Qualisys three-dimensional motion capture system. Given the limited sample size, robust statistical approaches, including Welch’s t -tests, Bayesian analyses, and permutation tests, were applied. Male swimmers exhibited significantly higher Vswim ( p < 0.001, ES = 2.94), forward IVF ( p < 0.001, ES = 2.47), and vertical IVF ( p = 0.022, ES = 1.57) compared with female swimmers. Bayesian analysis of interaction terms revealed no statistically significant moderating effect of sex on the relationship between IVF and Vswim. These findings indicate that although clear sex differences are evident in specific IVF components and swimming speed among high-level swimmers, the functional relationship between IVF and performance remains statistically consistent across sexes. From a practical perspective, IVF-based interventions should integrate sex-related physiological characteristics with individualized technical profiling to avoid overgeneralization. This study also establishes a high-fidelity methodological reference for three-dimensional kinematic analysis, providing a valuable dataset for future research and technological validation. High-level swimmers Freestyle Intra-Cycle Velocity Fluctuation Sex Differences 3D motion capture Figures Figure 1 Figure 2 1. Introduction Swimming performance is commonly quantified by time or speed, both influenced by technical execution and physical conditioning 1 , 2 . Higher-level swimmers exhibit greater ability to control velocity stability beyond achieving higher speeds 3 – 5 . Speed regulation involves macro-level coordination of stroke rate and length 2 , 6 – 8 and micro-level control of intra-cycle velocity fluctuation (IVF)—a mechanically meaningful dimension of propulsive stability 9 . As a key parameter linking speed with stroke technique and energy expenditure 10 , 11 , IVF is sensitive to performance level and indicates technical proficiency 12 , 13 . The precise relationship between IVF and performance remains debated 11 , 14 , 15 . Interpreting such complex biomechanical relationships requires rigorous statistical frameworks to distinguish signal from noise 16 . Some studies associate lower IVF with superior performance 13 , 17 – 20 , while others report no significant association 21 , 22 or even higher IVF among better-performing swimmers 23 . These discrepancies stem from variations in data acquisition systems, velocity measurement locations (e.g., hip vs. center of mass [CoM]), analytical techniques, pacing strategies, and fatigue states 18 , 24 – 26 . The sensitivity of IVF to measurement precision is reflected in reported values ranging from over 25% to below 10% 17,27 . Notably, most existing research has focused on male swimmers, with a scarcity of sex-comparative studies 11 . A major methodological challenge is accurately capturing three-dimensional whole-body kinematics in water. Although some studies have used marker-based methods, they relied on hip velocity data 19 , which may not reflect CoM motion. High-precision 3D motion capture is the gold standard in terrestrial biomechanics but remains underutilized in swimming due to technical constraints 28 . Moreover, research has largely focused on forward IVF, overlooking its three-dimensional nature and the distinct influences of different motion planes on performance 11 . Sex may systematically affect both the magnitude of IVF and its functional association with performance due to physiological differences in muscle composition, body morphology, and metabolic profiles 10 , 11 , 29 . However, empirical evidence on sex-specific IVF patterns remains limited. To address this, we employed high-precision 3D motion capture to develop a full‑body kinematic model and derive CoM velocity during freestyle. The aims are to (1) establish a high‑fidelity CoM kinematics dataset; (2) examine sex differences in IVF and performance; and (3) test whether sex moderates the IVF‑performance relationship. This work also proposes a standardized framework for capturing whole‑body CoM kinematics, providing a validated reference for future studies. We hypothesized that (1) significant sex differences exist in performance and three-dimensional IVF, and (2) sex moderates the IVF‑performance relationship. This study aims to clarify the debated role of IVF in elite swimming and provide a biomechanically robust foundation for sex‑inclusive technical training. 2. Methods 2.1 Participants Thirteen high-level swimmers (7 males, 6 females) with a mean age of 22.4 ± 2.8 years participated in the study. Anthropometric and performance characteristics are summarized as follows: male participants had an average height of 1.83 ± 0.03 m and a weight of 77.84 ± 5.31 kg, while female participants averaged 1.73 ± 0.05 m in height and 64.43 ± 4.65 kg in weight. Regarding competitive level, male swimmers’ World Aquatics points for their primary event averaged 746.08 ± 58.33, with personal bests in the 50-m freestyle (long course) corresponding to 87.42 ± 2.56% of the world record. Female swimmers had an average World Aquatics points score of 770.12 ± 46.89 for their primary event, with their best 50-m freestyle performances equating to 87.12 ± 2.35% of the world record. All participants had extensive experience in systematic swimming training. During the testing period, they were not undergoing high-intensity training cycles but maintained a weekly minimum of five weekly sessions, totaling at least 20,000 meters per week. Before testing, all participants were confirmed to be free of injuries and illnesses. Written informed consent was obtained from each participant. The study protocol was approved by the Ethics Committee for Sports Science at Beijing Sport University (Approval No. 2023174H) and conducted in accordance with the Declaration of Helsinki and relevant ethical guidelines. 2.2 Testing Procedure Testing was conducted in a standard 50-m indoor pool. To optimize data acquisition, lane lines were removed from the designated testing area. Before formal data collection, each participant completed an individualized warm-up routine, comprising both onshore and in-water components designed to simulate competition preparation. The warm-up was supervised by researchers to ensure participants achieved sufficient physiological and technical readiness. Following the warm-up, participants’ skin was dried, and reflective markers were attached according to a full-body marker set. Brief onshore movements were performed to allow participants to adapt to the markers. Additional markers were strategically placed to improve modeling accuracy during dynamic swimming. For formal testing, participants first assumed a static underwater posture to capture a reference skeletal model. They then swam slowly to a position approximately 35 m from the starting end of the pool. From this position, participants performed a maximal-effort freestyle sprint toward the starting end, with motion data collected within the calibrated capture volume 5–15 m from the start. 2.3 Data Acquisition Motion data were captured using a Qualisys motion capture system (Qualisys AB, Gothenburg, Sweden), consisting of 10 underwater cameras (Oqus 700+, 12 mm lens) and 13 surface cameras (Aqus 12, 8 mm lens), sampling at 100 Hz, which meets standard criteria for kinematic data acquisition 30 , 31 . Owing to the multi-day testing schedule, the system was spatially recalibrated at the start of each testing session, with calibration errors consistently maintained below 3 mm, which aligns with recommended protocols for minimizing measurement error in kinematic systems 32 . The reliability of the equipment and procedures has been validated in previous studies 19 , 33 . The coordinate system was defined as follows: the x-axis aligned with the swimming direction (toward the starting end), the y-axis represented the lateral direction, and the z-axis indicated the vertical direction Fig. 1 (a). Full-body reflective marker placement is illustrated in Fig. 1 (b), based on the Qualisys full-body marker set guidelines (Supplementary Material), with additional markers on the upper arms to optimize tracking during swimming 33 . The calibrated capture volume, verified using Qualisys Track Manager software, extended from 5 to 15 m from the starting end. To ensure high precision in kinematic analysis, only data within this calibrated volume were used for subsequent calculations. This segment was selected because it corresponded to the phase after participants had completed their initial acceleration and reached a stable maximal swimming velocity. 2.4 Data Processing Reflective marker trajectories from both static calibration and dynamic swimming trials were processed using Qualisys Track Manager software. Aquatic motion capture presents inherent challenges, including frequent marker occlusion, water-surface reflections, and the dynamic nature of swimming, resulting in substantial gaps and labeling errors in the initial automatic tracking output. To maximize accuracy, all marker trajectories were manually identified, inspected, and corrected on a frame-by-frame basis. After trajectory refinement, a full-body skeletal model was constructed in Visual3D (version 2023.01.0, C-Motion, Inc., Germantown, MD, USA), which has been validated for aquatic applications 19 , 33 . Raw marker trajectories were filtered using a fourth-order Butterworth low-pass filter with a cutoff frequency of 6 Hz 34 . The complete workflow for marker tracking, model construction, and data interpolation is summarized in Fig. 1 . Due to marker occlusion from limb-to-body contact, full-body model reconstruction across consecutive cycles was not feasible; thus intra-session reliability was not assessed. 2.5 Data Calculation The CoM position was estimated using Zatsiorsky-Seluyanov human body inertia parameters. Mean swimming velocity (Vswim) and IVF were then calculated from the CoM kinematics. A complete freestyle stroke cycle was defined as the interval between two consecutive entries of the same-side hand. Instantaneous velocity data within this cycle were extracted for analysis, with none of the selected cycles including breathing. This approach is widely used and considered representative in the field 19 , 35 , 36 . This study mainly used traditional dispersion measures to assess IVF. Dispersion metrics are widely employed in kinematic research due to their simplicity and interpretability. Given growing concerns about the use of the coefficient of variation for assessing IVF 14 , 15 , the standard deviation of instantaneous velocities within the stroke cycle 19 was selected as the IVF metric for each directional component (x, y, z), minimizing the potential influence of mean velocity variations. This approach aligns with recent methodological developments in swimming biomechanics, where accelerometry has been employed to detect fatigue-induced variations in technique among high-performance athletes 37 . By integrating this reference, we acknowledge the value of complementary measurement techniques while retaining a focus on traditional kinematic descriptors relevant to the present research questions. Additionally, to align with the growing use of statistical parametric mapping (SPM) in movement analysis, a supplementary SPM analysis was conducted—limited to forward-direction (x-axis) IVF time-series data—and is presented in the methodological figures for comparative illustration (Fig. 1 d) 38 , 39 . 2.6 Statistical Analysis Statistical analyses were conducted in R (version 4.2.2) and RStudio (2023.03.0 + 386) using robust methods suitable for the small sample size (N = 13; 7 males, 6 females) without assuming normality or homoscedasticity. Analyses were performed in three phases. Phase 1: Sex Differences. Welch’s independent samples t -tests were used to compare males and females on mean swimming velocity (Vswim) and directional IVFs (x, y, z). Effect sizes were calculated using Cohen’s d . Complementary Bayesian independent samples t -tests provided Bayes factors (BF 10 ) to quantify evidence for or against the null hypothesis of no difference. Phase 2: IVF-Performance Relationship Visualization and Slope Comparison. Associations between each directional IVF component and Vswim were visualized using sex-stratified scatter plots. Sex-specific linear regression slopes were estimated via bootstrap resampling (5,000 replicates) with 95% percentile confidence intervals. Differences between male and female slopes for each IVF direction were assessed using a permutation test (10,000 iterations) under the null hypothesis of equal slopes. Phase 3: Testing Sex as a Moderator. Bayesian robust linear regression (using the brms package) was employed to assess whether sex moderated the relationship between each IVF component and Vswim. Models included a sex × IVF interaction term and used Student- t error distributions to account for potential outliers. Weakly informative priors were specified: Normal(0, 1) for regression coefficients (including the interaction β ) and Exponential(1) for the scale ( σ ) and degrees-of-freedom ( ν ) parameters. These priors were selected to constrain parameter estimates to plausible ranges without overly influencing the posterior distributions, which is appropriate given the exploratory nature of the study and the small sample size 40 . Four Markov chains were run (4,000 iterations each, with 1,000 warm-up iterations), and convergence was confirmed (R̂ < 1.01). Sensitivity analyses were conducted to evaluate robustness to alternative priors (e.g., Normal(0, 2), Student- t (3, 0, 1)). Evidence for moderation was assessed using two criteria: (1) Bayes factors (BF 10 ) comparing models with and without the interaction term, and (2) whether the 95% highest density credible interval (HDI) for β interaction excluded zero. 2.7 Statistical Size Considerations for Future Research Given the exploratory nature of this study and the lack of established effect size estimates in the literature, a prospective sample size calculation was not performed. To provide guidance for future research, the sample size required per group to achieve 80% power for each observed effect size was calculated based on the observed effect sizes and sample sizes. Analyses were conducted using G*Power 3.1.9.7 (“difference between two independent means,” allocation ratio = 6/7). Results are reported alongside the primary findings in Section 3.1 . 3. Results 3.1 Sex Differences in IVF and Performance Descriptive statistics for swimming velocity (Vswim) and three-directional IVFs (IVFx, IVFy, IVFz) in male (n = 7) and female (n = 6) high-level swimmers are presented in Table 1 . Male swimmers showed higher mean values than females for Vswim (1.75 ± 0.04 m/s vs. 1.58 ± 0.06 m/s), IVFx (0.12 ± 0.02 m/s vs. 0.08 ± 0.01 m/s), and IVFz (0.10 ± 0.02 m/s vs. 0.07 ± 0.02 m/s). In contrast, mean IVFy was similar between groups (0.07 ± 0.02 m/s for both). Welch’s t -tests indicated significant sex differences for Vswim ( t = 5.10, p < 0.001), IVFx ( t = 4.67, p < 0.001), and IVFz ( t = 2.76, p = 0.022), but not for IVFy ( t = -0.21, p = 0.835). Corresponding effect sizes were large for Vswim (Cohen’s d = 2.94), IVFx ( d = 2.47), and IVFz ( d = 1.57), and negligible for IVFy ( d = -0.12). These findings are summarized visually in Table 1 . Table 1 Descriptive Statistics of Swimming Velocity (Vswim) and Intra-cycle Velocity Fluctuations (IVF) in Male and Female High-Level Swimmers. Variable Group(n) Mean ± SD Min Max Welch’s t p Cohen’s d Vswim Male(7) 1.75 ± 0.04 1.69 1.80 5.10 < 0.001 2.94 [1.97, 6.15] Female(6) 1.58 ± 0.06 1.49 1.68 IVFx Male(7) 0.12 ± 0.02 0.10 0.15 4.67 < 0.001 2.47 [1.91, 4.41] Female(6) 0.08 ± 0.01 0.07 0.09 IVFy Male(7) 0.07 ± 0.02 0.04 0.11 −0.21 0.835 −0.12 [−1.57, 1.01] Female(6) 0.07 ± 0.02 0.03 0.10 IVFz Male(7) 0.10 ± 0.02 0.07 0.12 2.76 0.022 1.57 [0.40, 5.77] Female(6) 0.07 ± 0.02 0.05 0.11 Note: SD = standard deviation; IVFx, y, z = intra-cycle velocity fluctuation in the forward, lateral, and vertical directions, respectively. Bayesian t -tests provided strong corroborative evidence: extremely strong support for sex differences in Vswim (BF 10 = 82.41) and IVFx (BF 10 = 28.48), substantial evidence for IVFz (BF 10 = 3.71), and support for the null hypothesis of no difference in IVFy (BF 10 = 0.46). To inform future study planning, the sample sizes required to achieve 80% power for detecting the observed effect sizes are presented in Table 2 . For the large effect sizes observed in Vswim and IVFx, approximately 12 participants per group would be sufficient, whereas the effect size observed for IVFz (d = 1.57) would require approximately 24 participants per group under similar experimental conditions. As expected, the negligible effect observed for IVFy would require an impractically large sample (approximately 3,634 per group), indicating that meaningful sex differences in lateral IVF are unlikely to exist in this population. Table 2 Sample Size Requirements per Group to Achieve 80% Power for Detecting Observed Sex Differences. Variable Observed Cohen’s d Post-hoc Power (1- β ) Required N per group for 80% Power* Vswim 2.94 0.98 12 IVFx 2.47 0.97 12 IVFy -0.12 0.06 3634 IVFz 1.57 0.95 24 Note: * Calculations based on two-tailed independent samples t -tests (Welch’s procedure) with α = 0.05, power = 0.80, observed effect sizes, and an allocation ratio of N 2 /N 1 = 6/7. Post-hoc power values are reported for completeness but should be interpreted with caution due to their inherent circularity (they are directly derived from the observed p -values). The required sample size per group is the primary guidance for designing future studies. 3.2 Influence of Sex on the IVF-Performance Relationship To evaluate whether sex moderates the relationship between IVF and swimming performance (Vswim), we first visualized these associations using scatter plots with sex-specific regression lines (Fig. 2 ). The plots suggested possible differences in slope magnitude between males and females, particularly for IVFx and IVFz. Permutation analysis revealed no statistically significant sex differences in regression slopes for any direction: IVFx (Δ β = 1.86, p = 0.246), IVFy (Δ β = − 0.84, p = 0.624), and IVFz (Δ β = 0.55, p = 0.409). These findings indicate that, despite observed sex differences in absolute IVF values (Section 3.1 ), the functional relationships between IVF and performance are consistent across sexes. Notably, although visual inspection of Fig. 2 suggested that male and female swimmers exhibited opposite slope directions for the IVFx-Vswim and IVFz-Vswim relationships, formal analyses did not detect statistically significant moderation by sex. This discrepancy between graphical patterns and inferential results highlights the need for further investigation with larger samples to determine whether subtle, sex-specific associations exist in these directional components of IVF. Bayesian robust regression provided additional evidence against a moderating effect of sex. The 95% HDIs for interaction terms included zero: IVFx [–2.08, 1.75], IVFy [–0.98, 1.91], and IVFz [–1.74, 1.49]. Corresponding Bayes factors offered anecdotal support for the null model (no interaction): IVFx (BF 10 = 0.96), IVFy (BF 10 = 0.94), and IVFz (BF 10 = 0.849). Together, these results indicate a lack of reliable evidence for sex moderation of the IVF-performance relationship in high-level freestyle swimmers. Sensitivity analyses confirmed that these findings were robust across alternative prior specifications, with all interaction term 95% HDIs remaining inclusive of zero. 4. Discussion 4.1 Sex Differences in Three-Dimensional Intra-Cycle Velocity Fluctuations This study revealed significant sex differences in freestyle swimming performance and specific components of IVF among high-level swimmers. Male swimmers demonstrated faster mean swimming velocity (Vswim) and greater forward (IVFx) and vertical (IVFz) velocity fluctuations compared with females, whereas lateral fluctuation (IVFy) showed no significant difference. These findings suggest that, within this elite cohort, higher performance in short-distance freestyle is associated with a more pronounced intra-cycle velocity pattern, particularly in the forward and vertical directions. The higher IVFx in males aligns with some reports on sprint performance 23 , but direct evidence linking forward IVF to superior performance remains inconsistent: some studies report negative associations 20 , while others find no relationship 21 , 23 . These discrepancies likely reflect methodological differences in measurement points (hip vs. CoM) and analytical protocols 18 , 24 . The present study addresses these by using full-body CoM kinematics from high-precision 3D motion capture, providing a more accurate representation, as hip-based estimates overestimate vertical displacement compared to CoM 41 . The greater IVFz observed in males may be biomechanically attributed to sex-related differences in lower-limb power and kick amplitude 42 , as well as the magnitude of body roll, which influences vertical trunk displacement. Although direct evidence linking these specific factors to IVFz magnitude is limited, the observed absence of sex moderation in the IVFz-performance relationship suggests that minimizing non-propulsive vertical oscillations remains a universal technical objective for maximizing speed, a notion supported by the negative correlation between IVFz and swimming velocity 43 . Physiologically, these sex differences in IVF likely reflect variations in force production capacity, body composition, and metabolic profiles. Greater muscle mass and a higher proportion of type II fibers in males 44 may enable more powerful propulsive phases 45 , increasing IVFx and IVFz. Females’ generally higher body fat percentage and distinct morphology may influence swimming performance through multiple pathways. These characteristics not only potentially enhance buoyancy and passive hydrodynamic efficiency but also interact with factors that are known to directly affect the IVF-performance relationship, such as energy cost and propelling efficiency 10 , 46 – 48 . Methodologically, this study builds on previous work by quantifying three-dimensional CoM kinematics rather than relying on hip-point tracking. While hip kinematics have been validated for overall stroke analysis 35 , they may overestimate vertical displacement 41 , necessitating whole-body CoM assessment for accurate IVFz quantification. The resulting high-fidelity dataset provides a validated reference for future studies employing more accessible measurement tools. In summary, although sex differences in IVF magnitude are evident among elite freestyle swimmers, they likely reflect underlying physiological and technical adaptations rather than fundamentally distinct biomechanical principles. The strong association between IVFx and performance in males—and its sensitivity to methodological choices–highlights the importance of standardized, CoM-based assessments in future sex-comparative research. 4.2 Absence of Sex Moderation in the IVF-Performance Relationship A key finding of this study is the absence of a moderating effect of sex on the relationship between IVF and swimming performance (Vswim). Although significant sex differences were observed in the absolute magnitudes of Vswim, IVFx, and IVFz (Section 4.1 ), both frequentist (permutation tests) and Bayesian robust regression analyses showed that the slopes linking each directional IVF component to Vswim did not differ significantly between males and females. In the Bayesian analyses, the 95% HDIs for all sex × IVF interaction terms included zero, and Bayes factors provided support for the null models (no interaction). This suggests that the fundamental biomechanical relationship between velocity fluctuation and mean swimming speed is preserved across sexes. The contrast between group differences in absolute values and the consistency of functional relationships indicates that male and female swimmers share a common performance continuum, where IVF acts as a technical descriptor whose association with speed is not inherently sex‑specific. The absence of observed moderation can be understood from several complementary perspectives. First, it reflects the high degree of technical individualization characteristic of elite swimmers. Elite performance is shaped by highly individualized movement patterns 49 , supporting the need for personalized analysis. IVF arises from each swimmer's unique balance of propulsion, drag, and coordination 11 , 39 . Even within elite cohorts, considerable inter-individual variability exists, making a universal “optimal” IVF unlikely. Performance can be optimized either by minimizing fluctuations for mechanical efficiency or by strategically exploiting larger fluctuations for propulsive impulse, depending on the swimmer's force production and coordination 20 , 50 . This principle of individualized optimization appears to operate similarly in both sexes. Second, the high methodological precision afforded by full-body CoM kinematics used in this study may provide a more reliable foundation for identifying common biomechanical principles. Previous inconsistencies in the IVF-performance relationship may partly reflect methodological noise, such as relying on hip-point proxies that poorly approximate CoM motion, particularly in the vertical axis 35 . By establishing a high-fidelity kinematic reference, the present study reduces such noise, potentially uncovering the underlying consistency across sexes. Statistical equivalence in the IVF-performance slope does not mean that physiological sex differences are irrelevant for training. On the contrary, well-established distinctions in muscle composition, strength, body morphology, and metabolic profiles 29 should guide individualized training. For example, male swimmers may benefit from interventions that enhance power during propulsive phases, whereas female swimmers may gain more from technical refinements that improve efficiency and stability. The key takeaway is that coaches should tailor training by integrating each athlete’s physiological profile with their individual IVF characteristics, rather than relying on broad sex-based generalizations, a strategy consistent with recent performance monitoring frameworks in competitive swimming 51 . Therefore, the absence of a statistically significant moderating effect should not be interpreted as justification for sex-generalized training prescriptions. This null finding may reflect the limited sample size, high inter-individual variability among high-level swimmers, and reduced statistical power to detect interaction effects. As a result, training should remain athlete-centered, incorporating individualized 3D IVF profiles alongside each swimmer’s specific physiological and technical characteristics, rather than relying on broad sex-based strategies. Future research with larger cohorts is needed to investigate potential subtle moderating effects and to establish optimal IVF ranges within a sex-sensitive framework. 4.3 Methodological Contribution and Reference Role This study has inherent limitations that also inform future research. The small elite sample restricts generalizability and reduce the ability to detect subtle effects, underscoring the need for replication in larger cohorts. Although this study provides detailed CoM kinematics, the absence of concurrent physiological or force measurements limits mechanistic interpretation. Future research should combine high-fidelity kinematics with kinetic and physiological data to achieve a more comprehensive understanding. Although the analysis was three-dimensional, it relied on discrete IVF metrics. Continuous approaches, such as SPM, could provide deeper insights into coordination dynamics throughout the stroke cycle. Logistical constraints prevented assessment of test-retest reliability; future studies should include this where feasible. Overall, future research should prioritize larger sample sizes, integration of multimodal data, application of this study’s reference model for more detailed analysis, and the translation of laboratory findings into practical training tools. 4.4 Limitations and Future Directions First, the small sample size limits the precision of estimates and generalizability, a common challenge in research involving elite athletes. To address this, robust statistical methods (e.g., Welch’s t -tests, Bayesian analysis, and permutation tests) were employed, specifically chosen for small-sample inference, thereby strengthening the internal validity of the comparisons. Although statistical power was high for the observed large effects, replication in larger cohorts is needed to confirm and extend these findings. Second, while detailed CoM kinematics were captured, the absence of concurrent measurements of physical capacities or propulsive forces restricts a fully mechanistic interpretation of the observed sex differences. Nonetheless, the high-fidelity, full-body 3D kinematic dataset established in this study provides a critical foundation for future research integrating physiological and kinetic measures. Third, although the analysis captured three-dimensional velocity fluctuations, it relied on discrete IVF metrics. Extending these analyses to continuous profiles across the entire stroke cycle, using approaches such as SPM, could provide deeper insights into inter-segment coordination 14 , 38 , 39 . Finally, test-retest reliability was not assessed due to the extensive time required for manual trajectory reconstruction and frequent marker occlusion from limb-to-body contact. Methodological frameworks for such reliability are available 32 , 52 , but intra-session ICC could not be implemented here. Future studies should address this. Future research should prioritize larger cohorts to identify optimal IVF ranges and integrate time-frequency analyses with biomechanical modeling, supporting personalized, data-driven training frameworks. 5. Conclusion Using 3D motion capture, this study investigated sex differences in three-dimensional IVF and swimming performance in high-level freestyle swimmers. Males exhibited higher swimming velocity, forward IVF, and vertical IVF than females, whereas lateral IVF showed no difference. Sex did not moderate the IVF–performance relationship, indicating a similar biomechanical link across sexes, though this does not justify sex‑based training generalizations. Integrating individualized IVF profiles with performance monitoring frameworks supports athlete‑centered technical development. This study also provides a standardized, high‑fidelity kinematic dataset as a methodological reference for future research. Declarations Acknowledgment We extend our sincere gratitude to all participants in the experiments and to the staff who assisted in completing this study. Author Contributions Jin Zhenyu: Conceptualization, Data curation, Formal analysis, Methodology, Visualization, Writing – original draft. Zhou Yulin, Zhou Yuhang: Data curation, Methodology, Resources, Software, Writing – review and editing. Yu Qian, Wang Dapeng and Shen Sijia: Methodology, Resources. Wen Yuhong: Funding acquisition, Methodology, Project administration, Supervision, Validation. Funding This work was supported by the Central Universities Basic Research Program, Grant No. 2024YDXL003. Declaration of generative AI in scientific writing The authors confirm that no generative AI or AI-assisted technologies were used in the writing of this manuscript. Data availability statement The data can be obtained by contacting the first author or the corresponding author of the article. Conflict of Interest Statement The authors report there are no competing interests to declare. References D.J. Smith, S.R. Norris & J.M. Hogg. Performance evaluation of swimmers: scientific tools. Sports Med . 32 , 539--554 (2002). T.M. Barbosa et al. The role of the biomechanics analyst in swimming training and competition analysis. Sports Biomech . 22, 1734--1751 (2023). L. Seifert et al. Coordination pattern variability provides functional adaptations to constraints in swimming performance. Sports Med . 44, 1333--1345 (2014). K.E. McGibbon, D.B. Pyne, M.E. Shephard & K.G. Thompson. Pacing in swimming: A systematic review. Sports Med . 48, 1621--1633 (2018). M.A. Maloney & A.D. Gorman. Skilled swimmers maintain performance stability under changing attentional focus constraints. Hum. Mov. Sci. 77, 102789 (2021). A.B. Craig & D.R. Pendeegast. Relationships of stroke rate, distance per stroke, and velocity in competitive swimming. Med. Sci. Sports. 11, 278 (1979). T.M. Barbosa, R.J. Fernandes, K.L. Keskinen & J.P. Vilas-Boas. The influence of stroke mechanics into energy cost of elite swimmers. Eur. J. Appl. Physiol. 103, 139--149 (2008). H. Takagi et al. How do swimmers control their front crawl swimming velocity? Current knowledge and gaps from hydrodynamic perspectives. Sports Biomech. 22, 1552--1571 (2023). Barbosa, T. M., Lima, F., Portela, A., Novais, D., Machado, L., Colaco, P., Goncalves, P., Fernandes, R., Keskinen, K. L. & Vilas-Boas, J. P. Relationships between energy cost, swimming velocity and speed fluctuation in competitive swimming strokes. Rev. Port. Cien. Desp . 6 , 192--194 (2006). P. Zamparo, M. Cortesi & G. Gatta. The energy cost of swimming and its determinants. Eur. J. Appl. Physiol. 120, 41--66 (2020). A. Fernandes, J. Afonso, F. Noronha et al. Intracycle Velocity Variation in Swimming: A Systematic Scoping Review. Bioengineering 10, 308 (2023). T.M. Barbosa et al. Energetics and biomechanics as determining factors of swimming performance: updating the state of the art. J. Sci. Med. Sport. 13, 262--269 (2010). Y. Matsuda, Y. Yamada, Y. Ikuta, T. Nomura & S. Oda. Intracyclic velocity variation and arm coordination for different skilled swimmers in the front crawl. J. Hum. Kinet . 44, 67--74 (2014). M.P. Pinto, D.A. Marinho, H.P Neiva, T.M. Barbosa & J.E. Morais. Insights on the Selection of the Coefficient of Variation to Assess Speed Fluctuation in Swimming. J. Funct. Morphol. Kinesiol . 9, 129 (2024). T. Gonjo, R.J. Fernandes, J.P. Vilas-Boas & R. Sanders. Is the use of the coefficient of variation a valid way to assess the swimming intra-cycle velocity fluctuation? J. Sci. Med. Sport. 26, 328--334 (2023). J. Padulo, N. Maffulli & L.P. Ardigò. Signal or noise, a statistical perspective. Proc. Natl. Acad. Sci. U.S.A. 111, E1160-E1160 (2014). Schnitzler, C., Seifert, L., Alberty, M. & Chollet, D. Hip velocity and arm coordination in front crawl swimming. Int. J. Sports Med . 31 , 875--881 (2010). P. Figueiredo, A. Silva, A. Sampaio et al. Front crawl sprint performance: A cluster analysis of biomechanics, energetics, coordinative, and anthropometric determinants in young swimmers. Motor Control. 20, 209--221 (2016). A.F. Silva et al. Integrated analysis of young swimmers’ sprint performance. Motor Control 23, 354--364 (2019). P.G. Morouço, T.M. Barbosa, R. Arellano & J.P. Vilas-Boas. Intracyclic variation of force and swimming performance. Int. J. Sports Physiol. Perform . 13, 897--902 (2018). S.G. Psycharakis, R. Naemi, C. Connaboy, C. McCabe & R.H. Sanders. Three‐dimensional analysis of intracycle velocity fluctuations in frontcrawl swimming. Scand. J. Med. Sci. Sports 20, 128--135 (2010). M.P. Pinto, D.A. Marinho, H.P. Neiva & J.E. Morais. Relationship between swimming speed, intra-cycle variation of horizontal speed, and Froude efficiency during consecutive stroke cycles in adolescent swimmers. PeerJ 11, e16019 (2023). A.C. Barbosa et al. 50 m freestyle in 21, 22 and 23 s: What differentiates the speed curve of world-class and elite male swimmers? Int. J. Perform. Anal. Sport . 21, 1055--1065 (2021). T.M. Barbosa et al. The interaction between intra-cyclic variation of the velocity and mean swimming velocity in young competitive swimmers. Int. J. Sports Med . 34 , 123--130 (2012). M. Alberty, M. Sidney, F. Huot-Marchand, J.M. Hespel & P. Pelayo. Intracyclic velocity variations and arm coordination during exhaustive exercise in front crawl stroke. Int. J. Sports Med . 25 , 471--475 (2004). M. Alberty, M. Sidney, P. Pelayo & H.M. Toussaint. Stroking characteristics during time to exhaustion tests. Med. Sci. Sports Exerc . 41, 637--644 (2009). T. Gonjo et al. Differences in kinematics and energy cost between front crawl and backstroke below the anaerobic threshold. Eur. J. Appl. Physiol . 118, 1107--1118 (2018). A. Stamm, D.A. James & D.V. Thiel. Velocity profiling using inertial sensors for freestyle swimming. Sports Eng . 16, 1--11 (2013). S.K. Hunter & J.W. Senefeld. Sex differences in human performance. J. Physiol . 602, 4129--4156 (2024). Padulo, J., Chamari, K. & Ardigò, L. P. Walking and running on treadmill: the standard criteria for kinematics studies. Muscles Ligaments Tendons J . 4 , 159--162 (2014). Samozino, P., Morin, J. B., Hintzy, F. & Belli, A. A simple method for measuring force, velocity and power output during squat jump. J. Biomech . 41 , 2940--2945 (2008). Attia, A., Dhahbi, W., Chaouachi, A., Padulo, J., Wong, D. P. & Chamari, K. Measurement errors when estimating the vertical jump height with flight time using photocell devices: the example of Optojump. Biol. Sport 34 , 63--70 (2017). Hong, Q., Li, N., Zhang, X., Zhou, Y. & Guo, J. Analysis method of breaststroke movements based on biomechanical multi-body dynamics. Chin. J. Appl. Mech . (2025). https://link.cnki.net/urlid/61.1112.O3.20251222.0956.002 B. Yu, D. Gabriel, L. Noble & K. An. Estimate of the optimum cutoff frequency for the Butterworth low-pass digital filter. J. Appl. Biomech . 15, 318--329 (1999). P. Figueiredo, J.P.V. Boas, J. Maia, P. Gonçalves & R.J. Fernandes. Does the hip reflect the centre of mass swimming kinematics? Int. J. Sports Med . 30, 779--781 (2009). A. Bouvet, R. Pla, E. Delhaye, G. Nicolas & N. Bideau. Profiling biomechanical abilities during sprint front-crawl swimming using IMU and functional clustering of variabilities. Sports Biomech . 23 , 1--21 (2024). M. Skorulski, M. Stachowicz, S. Kuliś & J. Gajewski. Accelerometric assessment of fatigue-induced changes in swimming technique in high performance adolescent athletes. Sci. Rep . 15, 2409 (2025). S. Wang, Y. Zhao, X. Chen, Y. Shen. Effect of Increasing the Foot Area on the Load-Velocity Relationship of the Underwater Dolphin Kick. J. Hum. Kinet . 95, 17 (2024). J.E. Morais, T.M. Barbosa, T. Lopes, S. Moriyama & D.A. Marinho. Comparison of swimming velocity between age-group swimmers through discrete variables and continuous variables by Statistical Parametric Mapping. Sports Biomech . 23, 3394--3405 (2024). R.E. Kass & A.E. Raftery. Bayes factors. J. Am. Stat. Assoc . 90, 773--795 (1995). R.J. Fernandes, J. Ribeiro, P. Figueiredo, L. Seifert & J.P. Vilas-Boas. Kinematics of the hip and body center of mass in front crawl. J. Hum. Kinet . 33, 15 (2012). Laffaye, G., Choukou, M. A., Benguigui, N. & Padulo, J. Age- and gender-related development of stretch shortening cycle during a sub-maximal hopping task. Biol. Sport 33 , 29--35 (2016). P. Figueiredo, P.L. Kjendlie, J.P. Vilas-Boas, R.J. Fernandes. Intracycle velocity variation of the body centre of mass in front crawl. Int. J. Sports Med . 33, 285--290 (2012). D.J. Handelsman, A.L. Hirschberg & S. Bermon. Circulating testosterone as the hormonal basis of sex differences in athletic performance. Endocr. Rev . 39, 803--829 (2018). Gatta, G. et al. The development of swimming power. Muscles Ligaments Tendons J . 4 , 438--445 (2014). Pinna, M. et al. Effect of beetroot juice supplementation on aerobic response during swimming. Nutrients 6 , 605--615 (2014). S.P. McLean & R.N. Hinrichs. Buoyancy, gender, and swimming performance. J. Appl. Biomech . 16, 248--263 (2000). L. Seifert, T.M. Barbosa & P.L. Kjendlie. Biophysical approach to swimming: Gender effect. Gender gap: Causes, experiences and effects 1, 59--80 (2010). S. Kuliś et al. Kinematic criteria determining swing movement of world class dancesport athletes. Hum. Mov . 25, 60--67 (2024). S.P.M. Ganzevles, P.J. Beek, H.A.M. Daanen, B.M.A. Coolen & M.J. Truijens. Differences in swimming smoothness between elite and non-elite swimmers. Sports Biomech . 22, 675--688 (2023). Kuliś, S. et al. Application of the performance index for monitoring anaerobic endurance of competitive swimmers. J. Hum. Kinet . https://doi.org/10.5114/jhk/196823 (2025). Dos Santos, T. T. S. et al. Intra and inter-device reliabilities of the instrumented timed-up and go test using smartphones in young adult population. Sensors 24 , 2918 (2024). Additional Declarations The authors declare no competing interests. Supplementary Files SupplementaryMaterial.pdf Cite Share Download PDF Status: Posted Version 1 posted 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. 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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-9387014","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":621385101,"identity":"e546fd64-f91a-465f-8fc9-5723e42a2f7b","order_by":0,"name":"Zhenyu Jin","email":"","orcid":"","institution":"Beijing Sport University","correspondingAuthor":false,"prefix":"","firstName":"Zhenyu","middleName":"","lastName":"Jin","suffix":""},{"id":621385102,"identity":"29268a08-f7d8-4dc8-863b-b603b7722342","order_by":1,"name":"Yulin Zhou","email":"","orcid":"","institution":"Beijing Sport University","correspondingAuthor":false,"prefix":"","firstName":"Yulin","middleName":"","lastName":"Zhou","suffix":""},{"id":621385103,"identity":"7784d7b1-6324-4bf8-aa86-d2cc5932483e","order_by":2,"name":"Yuhang Zhou","email":"","orcid":"","institution":"Beijing Sport University","correspondingAuthor":false,"prefix":"","firstName":"Yuhang","middleName":"","lastName":"Zhou","suffix":""},{"id":621385104,"identity":"cdffa931-6872-4853-a5a9-4eb0d046c2d1","order_by":3,"name":"Qian Yu","email":"","orcid":"","institution":"Peking University","correspondingAuthor":false,"prefix":"","firstName":"Qian","middleName":"","lastName":"Yu","suffix":""},{"id":621385105,"identity":"ce5253a4-722c-4e80-843f-b9bb0c561205","order_by":4,"name":"Dapeng Wang","email":"","orcid":"","institution":"Beijing Sport University","correspondingAuthor":false,"prefix":"","firstName":"Dapeng","middleName":"","lastName":"Wang","suffix":""},{"id":621385106,"identity":"bd1ca504-a495-44c4-97c0-cc62823693dc","order_by":5,"name":"Sijia Shen","email":"","orcid":"","institution":"Beijing Sport University","correspondingAuthor":false,"prefix":"","firstName":"Sijia","middleName":"","lastName":"Shen","suffix":""},{"id":621385107,"identity":"7ce6ee5d-fb2b-4ef1-8b7e-526c170bde63","order_by":6,"name":"Yuhong Wen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsklEQVRIiWNgGAWjYFACHiA2YJBjY28+QJoWYz6eYwmkaGFgSJwnkaNAnAaDG7mHP/MUbEtvY8hhYPhRsY0YLXlp0jwGt3PbGM4eYOw5c5uwFrMbOWbMOSAtjH0JzIxtxGkx/gzUks7GzGNAtBYDaaCWBDY2YrXYn3ljJv3H4LZhGw9bwkGi/CLZnmP8ccaf2/Ly8x8ffPCjgggtDAIJCPYBItQDAT+R6kbBKBgFo2AEAwBgPDs/eJ0+6wAAAABJRU5ErkJggg==","orcid":"","institution":"Beijing Sport University","correspondingAuthor":true,"prefix":"","firstName":"Yuhong","middleName":"","lastName":"Wen","suffix":""}],"badges":[],"createdAt":"2026-04-11 10:27:46","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9387014/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9387014/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106960720,"identity":"5d55cf92-55eb-4a21-b3b5-8a916975da72","added_by":"auto","created_at":"2026-04-15 09:22:50","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":509408,"visible":true,"origin":"","legend":"\u003cp\u003eResearch data processing workflow.\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-9387014/v1/a04d521a997193a49d0a6562.png"},{"id":106867255,"identity":"75b1f894-2467-42e5-ad22-2652147539d9","added_by":"auto","created_at":"2026-04-14 09:21:50","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":263639,"visible":true,"origin":"","legend":"\u003cp\u003eScatter plots showing the relationship between directional IVF (x, y, z) and swimming velocity (Vswim) in male and female swimmers.\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-9387014/v1/f660811c8a5e5cca764ddde7.png"},{"id":106963096,"identity":"a46810a1-7758-4bdd-9b7f-6abfeea44cf8","added_by":"auto","created_at":"2026-04-15 09:42:06","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1774522,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9387014/v1/7a59434e-d432-4cd1-bcdc-2ff37c7f5b46.pdf"},{"id":106867253,"identity":"4c5d04b6-0c38-45b3-a2d0-b97f7b0895b2","added_by":"auto","created_at":"2026-04-14 09:21:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":586907,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryMaterial.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9387014/v1/90aa615da5f3c5eb0c6c9dd7.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eSex Differences in Three-Dimensional Intra-Cycle Velocity Fluctuation and Performance During Freestyle Swimming Among High-Level Swimmers\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eSwimming performance is commonly quantified by time or speed, both influenced by technical execution and physical conditioning\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Higher-level swimmers exhibit greater ability to control velocity stability beyond achieving higher speeds\u003csup\u003e\u003cspan additionalcitationids=\"CR4\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. Speed regulation involves macro-level coordination of stroke rate and length\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan additionalcitationids=\"CR7\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e and micro-level control of intra-cycle velocity fluctuation (IVF)\u0026mdash;a mechanically meaningful dimension of propulsive stability\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. As a key parameter linking speed with stroke technique and energy expenditure\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e, IVF is sensitive to performance level and indicates technical proficiency\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe precise relationship between IVF and performance remains debated\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. Interpreting such complex biomechanical relationships requires rigorous statistical frameworks to distinguish signal from noise\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Some studies associate lower IVF with superior performance\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan additionalcitationids=\"CR18 CR19\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, while others report no significant association\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e or even higher IVF among better-performing swimmers\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. These discrepancies stem from variations in data acquisition systems, velocity measurement locations (e.g., hip vs. center of mass [CoM]), analytical techniques, pacing strategies, and fatigue states \u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan additionalcitationids=\"CR25\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. The sensitivity of IVF to measurement precision is reflected in reported values ranging from over 25% to below 10%\u003csup\u003e17,27\u003c/sup\u003e. Notably, most existing research has focused on male swimmers, with a scarcity of sex-comparative studies\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eA major methodological challenge is accurately capturing three-dimensional whole-body kinematics in water. Although some studies have used marker-based methods, they relied on hip velocity data\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e, which may not reflect CoM motion. High-precision 3D motion capture is the gold standard in terrestrial biomechanics but remains underutilized in swimming due to technical constraints\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. Moreover, research has largely focused on forward IVF, overlooking its three-dimensional nature and the distinct influences of different motion planes on performance\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eSex may systematically affect both the magnitude of IVF and its functional association with performance due to physiological differences in muscle composition, body morphology, and metabolic profiles\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. However, empirical evidence on sex-specific IVF patterns remains limited. To address this, we employed high-precision 3D motion capture to develop a full‑body kinematic model and derive CoM velocity during freestyle. The aims are to (1) establish a high‑fidelity CoM kinematics dataset; (2) examine sex differences in IVF and performance; and (3) test whether sex moderates the IVF‑performance relationship. This work also proposes a standardized framework for capturing whole‑body CoM kinematics, providing a validated reference for future studies.\u003c/p\u003e \u003cp\u003eWe hypothesized that (1) significant sex differences exist in performance and three-dimensional IVF, and (2) sex moderates the IVF‑performance relationship. This study aims to clarify the debated role of IVF in elite swimming and provide a biomechanically robust foundation for sex‑inclusive technical training.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Participants\u003c/h2\u003e \u003cp\u003eThirteen high-level swimmers (7 males, 6 females) with a mean age of 22.4\u0026thinsp;\u0026plusmn;\u0026thinsp;2.8 years participated in the study. Anthropometric and performance characteristics are summarized as follows: male participants had an average height of 1.83\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03 m and a weight of 77.84\u0026thinsp;\u0026plusmn;\u0026thinsp;5.31 kg, while female participants averaged 1.73\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05 m in height and 64.43\u0026thinsp;\u0026plusmn;\u0026thinsp;4.65 kg in weight. Regarding competitive level, male swimmers\u0026rsquo; World Aquatics points for their primary event averaged 746.08\u0026thinsp;\u0026plusmn;\u0026thinsp;58.33, with personal bests in the 50-m freestyle (long course) corresponding to 87.42\u0026thinsp;\u0026plusmn;\u0026thinsp;2.56% of the world record. Female swimmers had an average World Aquatics points score of 770.12\u0026thinsp;\u0026plusmn;\u0026thinsp;46.89 for their primary event, with their best 50-m freestyle performances equating to 87.12\u0026thinsp;\u0026plusmn;\u0026thinsp;2.35% of the world record.\u003c/p\u003e \u003cp\u003eAll participants had extensive experience in systematic swimming training. During the testing period, they were not undergoing high-intensity training cycles but maintained a weekly minimum of five weekly sessions, totaling at least 20,000 meters per week. Before testing, all participants were confirmed to be free of injuries and illnesses. Written informed consent was obtained from each participant. The study protocol was approved by the Ethics Committee for Sports Science at Beijing Sport University (Approval No. 2023174H) and conducted in accordance with the Declaration of Helsinki and relevant ethical guidelines.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Testing Procedure\u003c/h2\u003e \u003cp\u003eTesting was conducted in a standard 50-m indoor pool. To optimize data acquisition, lane lines were removed from the designated testing area. Before formal data collection, each participant completed an individualized warm-up routine, comprising both onshore and in-water components designed to simulate competition preparation. The warm-up was supervised by researchers to ensure participants achieved sufficient physiological and technical readiness.\u003c/p\u003e \u003cp\u003eFollowing the warm-up, participants\u0026rsquo; skin was dried, and reflective markers were attached according to a full-body marker set. Brief onshore movements were performed to allow participants to adapt to the markers. Additional markers were strategically placed to improve modeling accuracy during dynamic swimming.\u003c/p\u003e \u003cp\u003eFor formal testing, participants first assumed a static underwater posture to capture a reference skeletal model. They then swam slowly to a position approximately 35 m from the starting end of the pool. From this position, participants performed a maximal-effort freestyle sprint toward the starting end, with motion data collected within the calibrated capture volume 5\u0026ndash;15 m from the start.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Data Acquisition\u003c/h2\u003e \u003cp\u003eMotion data were captured using a Qualisys motion capture system (Qualisys AB, Gothenburg, Sweden), consisting of 10 underwater cameras (Oqus 700+, 12 mm lens) and 13 surface cameras (Aqus 12, 8 mm lens), sampling at 100 Hz, which meets standard criteria for kinematic data acquisition\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e,\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. Owing to the multi-day testing schedule, the system was spatially recalibrated at the start of each testing session, with calibration errors consistently maintained below 3 mm, which aligns with recommended protocols for minimizing measurement error in kinematic systems\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. The reliability of the equipment and procedures has been validated in previous studies \u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e,\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe coordinate system was defined as follows: the x-axis aligned with the swimming direction (toward the starting end), the y-axis represented the lateral direction, and the z-axis indicated the vertical direction Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a). Full-body reflective marker placement is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b), based on the Qualisys full-body marker set guidelines (Supplementary Material), with additional markers on the upper arms to optimize tracking during swimming\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe calibrated capture volume, verified using Qualisys Track Manager software, extended from 5 to 15 m from the starting end. To ensure high precision in kinematic analysis, only data within this calibrated volume were used for subsequent calculations. This segment was selected because it corresponded to the phase after participants had completed their initial acceleration and reached a stable maximal swimming velocity.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Data Processing\u003c/h2\u003e \u003cp\u003eReflective marker trajectories from both static calibration and dynamic swimming trials were processed using Qualisys Track Manager software. Aquatic motion capture presents inherent challenges, including frequent marker occlusion, water-surface reflections, and the dynamic nature of swimming, resulting in substantial gaps and labeling errors in the initial automatic tracking output. To maximize accuracy, all marker trajectories were manually identified, inspected, and corrected on a frame-by-frame basis. After trajectory refinement, a full-body skeletal model was constructed in Visual3D (version 2023.01.0, C-Motion, Inc., Germantown, MD, USA), which has been validated for aquatic applications\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e,\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. Raw marker trajectories were filtered using a fourth-order Butterworth low-pass filter with a cutoff frequency of 6 Hz\u003csup\u003e34\u003c/sup\u003e. The complete workflow for marker tracking, model construction, and data interpolation is summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eDue to marker occlusion from limb-to-body contact, full-body model reconstruction across consecutive cycles was not feasible; thus intra-session reliability was not assessed.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Data Calculation\u003c/h2\u003e \u003cp\u003eThe CoM position was estimated using Zatsiorsky-Seluyanov human body inertia parameters. Mean swimming velocity (Vswim) and IVF were then calculated from the CoM kinematics. A complete freestyle stroke cycle was defined as the interval between two consecutive entries of the same-side hand. Instantaneous velocity data within this cycle were extracted for analysis, with none of the selected cycles including breathing. This approach is widely used and considered representative in the field\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e,\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e,\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThis study mainly used traditional dispersion measures to assess IVF. Dispersion metrics are widely employed in kinematic research due to their simplicity and interpretability. Given growing concerns about the use of the coefficient of variation for assessing IVF\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e, the standard deviation of instantaneous velocities within the stroke cycle\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e was selected as the IVF metric for each directional component (x, y, z), minimizing the potential influence of mean velocity variations. This approach aligns with recent methodological developments in swimming biomechanics, where accelerometry has been employed to detect fatigue-induced variations in technique among high-performance athletes\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. By integrating this reference, we acknowledge the value of complementary measurement techniques while retaining a focus on traditional kinematic descriptors relevant to the present research questions. Additionally, to align with the growing use of statistical parametric mapping (SPM) in movement analysis, a supplementary SPM analysis was conducted\u0026mdash;limited to forward-direction (x-axis) IVF time-series data\u0026mdash;and is presented in the methodological figures for comparative illustration (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed)\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.6 Statistical Analysis\u003c/h2\u003e \u003cp\u003eStatistical analyses were conducted in R (version 4.2.2) and RStudio (2023.03.0\u0026thinsp;+\u0026thinsp;386) using robust methods suitable for the small sample size (N\u0026thinsp;=\u0026thinsp;13; 7 males, 6 females) without assuming normality or homoscedasticity. Analyses were performed in three phases.\u003c/p\u003e \u003cp\u003ePhase 1: Sex Differences. Welch\u0026rsquo;s independent samples \u003cem\u003et\u003c/em\u003e-tests were used to compare males and females on mean swimming velocity (Vswim) and directional IVFs (x, y, z). Effect sizes were calculated using Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e. Complementary Bayesian independent samples \u003cem\u003et\u003c/em\u003e-tests provided Bayes factors (BF\u003csub\u003e10\u003c/sub\u003e) to quantify evidence for or against the null hypothesis of no difference.\u003c/p\u003e \u003cp\u003ePhase 2: IVF-Performance Relationship Visualization and Slope Comparison. Associations between each directional IVF component and Vswim were visualized using sex-stratified scatter plots. Sex-specific linear regression slopes were estimated via bootstrap resampling (5,000 replicates) with 95% percentile confidence intervals. Differences between male and female slopes for each IVF direction were assessed using a permutation test (10,000 iterations) under the null hypothesis of equal slopes.\u003c/p\u003e \u003cp\u003ePhase 3: Testing Sex as a Moderator. Bayesian robust linear regression (using the brms package) was employed to assess whether sex moderated the relationship between each IVF component and Vswim. Models included a sex \u0026times; IVF interaction term and used Student-\u003cem\u003et\u003c/em\u003e error distributions to account for potential outliers. Weakly informative priors were specified: Normal(0, 1) for regression coefficients (including the interaction \u003cem\u003eβ\u003c/em\u003e) and Exponential(1) for the scale (\u003cem\u003eσ\u003c/em\u003e) and degrees-of-freedom (\u003cem\u003eν\u003c/em\u003e) parameters. These priors were selected to constrain parameter estimates to plausible ranges without overly influencing the posterior distributions, which is appropriate given the exploratory nature of the study and the small sample size\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. Four Markov chains were run (4,000 iterations each, with 1,000 warm-up iterations), and convergence was confirmed (R̂ \u0026lt; 1.01). Sensitivity analyses were conducted to evaluate robustness to alternative priors (e.g., Normal(0, 2), Student-\u003cem\u003et\u003c/em\u003e(3, 0, 1)). Evidence for moderation was assessed using two criteria: (1) Bayes factors (BF\u003csub\u003e10\u003c/sub\u003e) comparing models with and without the interaction term, and (2) whether the 95% highest density credible interval (HDI) for \u003cem\u003eβ\u003c/em\u003e\u003csub\u003einteraction\u003c/sub\u003e excluded zero.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e2.7 Statistical Size Considerations for Future Research\u003c/h2\u003e \u003cp\u003eGiven the exploratory nature of this study and the lack of established effect size estimates in the literature, a prospective sample size calculation was not performed. To provide guidance for future research, the sample size required per group to achieve 80% power for each observed effect size was calculated based on the observed effect sizes and sample sizes. Analyses were conducted using G*Power 3.1.9.7 (\u0026ldquo;difference between two independent means,\u0026rdquo; allocation ratio\u0026thinsp;=\u0026thinsp;6/7). Results are reported alongside the primary findings in Section \u003cspan refid=\"Sec11\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Sex Differences in IVF and Performance\u003c/h2\u003e \u003cp\u003eDescriptive statistics for swimming velocity (Vswim) and three-directional IVFs (IVFx, IVFy, IVFz) in male (n\u0026thinsp;=\u0026thinsp;7) and female (n\u0026thinsp;=\u0026thinsp;6) high-level swimmers are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Male swimmers showed higher mean values than females for Vswim (1.75\u0026thinsp;\u0026plusmn;\u0026thinsp;0.04 m/s vs. 1.58\u0026thinsp;\u0026plusmn;\u0026thinsp;0.06 m/s), IVFx (0.12\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02 m/s vs. 0.08\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01 m/s), and IVFz (0.10\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02 m/s vs. 0.07\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02 m/s). In contrast, mean IVFy was similar between groups (0.07\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02 m/s for both).\u003c/p\u003e \u003cp\u003eWelch\u0026rsquo;s \u003cem\u003et\u003c/em\u003e-tests indicated significant sex differences for Vswim (\u003cem\u003et\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.10, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001), IVFx (\u003cem\u003et\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4.67, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001), and IVFz (\u003cem\u003et\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.76, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.022), but not for IVFy (\u003cem\u003et\u003c/em\u003e = -0.21, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.835). Corresponding effect sizes were large for Vswim (Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.94), IVFx (\u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.47), and IVFz (\u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.57), and negligible for IVFy (\u003cem\u003ed\u003c/em\u003e = -0.12). These findings are summarized visually in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\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\u003eDescriptive Statistics of Swimming Velocity (Vswim) and Intra-cycle Velocity Fluctuations (IVF) in Male and Female High-Level Swimmers.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\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=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGroup(n)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMin\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMax\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eWelch\u0026rsquo;s \u003cem\u003et\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eCohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eVswim\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale(7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e1.75\u0026thinsp;\u0026plusmn;\u0026thinsp;0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e5.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e2.94 [1.97, 6.15]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale(6)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e1.58\u0026thinsp;\u0026plusmn;\u0026thinsp;0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eIVFx\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale(7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.12\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e4.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e2.47 [1.91, 4.41]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale(6)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.08\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eIVFy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale(7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.07\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u0026minus;0.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.835\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u0026minus;0.12 [\u0026minus;1.57, 1.01]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale(6)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.07\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eIVFz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale(7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.10\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e2.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e1.57 [0.40, 5.77]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale(6)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.07\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"8\"\u003eNote: SD\u0026thinsp;=\u0026thinsp;standard deviation; IVFx, y, z\u0026thinsp;=\u0026thinsp;intra-cycle velocity fluctuation in the forward, lateral, and vertical directions, respectively.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eBayesian \u003cem\u003et\u003c/em\u003e-tests provided strong corroborative evidence: extremely strong support for sex differences in Vswim (BF\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;82.41) and IVFx (BF\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;28.48), substantial evidence for IVFz (BF\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;3.71), and support for the null hypothesis of no difference in IVFy (BF\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.46).\u003c/p\u003e \u003cp\u003eTo inform future study planning, the sample sizes required to achieve 80% power for detecting the observed effect sizes are presented in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. For the large effect sizes observed in Vswim and IVFx, approximately 12 participants per group would be sufficient, whereas the effect size observed for IVFz (d\u0026thinsp;=\u0026thinsp;1.57) would require approximately 24 participants per group under similar experimental conditions. As expected, the negligible effect observed for IVFy would require an impractically large sample (approximately 3,634 per group), indicating that meaningful sex differences in lateral IVF are unlikely to exist in this population.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSample Size Requirements per Group to Achieve 80% Power for Detecting Observed Sex Differences.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eObserved Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePost-hoc Power (1-\u003cem\u003eβ\u003c/em\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRequired N per group for 80% Power*\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVswim\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIVFx\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIVFy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3634\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIVFz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003eNote: * Calculations based on two-tailed independent samples \u003cem\u003et\u003c/em\u003e-tests (Welch\u0026rsquo;s procedure) with \u003cem\u003eα\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.05, power\u0026thinsp;=\u0026thinsp;0.80, observed effect sizes, and an allocation ratio of N\u003csub\u003e2\u003c/sub\u003e/N\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;6/7. Post-hoc power values are reported for completeness but should be interpreted with caution due to their inherent circularity (they are directly derived from the observed \u003cem\u003ep\u003c/em\u003e-values). The required sample size per group is the primary guidance for designing future studies.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Influence of Sex on the IVF-Performance Relationship\u003c/h2\u003e \u003cp\u003eTo evaluate whether sex moderates the relationship between IVF and swimming performance (Vswim), we first visualized these associations using scatter plots with sex-specific regression lines (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The plots suggested possible differences in slope magnitude between males and females, particularly for IVFx and IVFz.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003ePermutation analysis revealed no statistically significant sex differences in regression slopes for any direction: IVFx (Δ\u003cem\u003eβ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.86, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.246), IVFy (Δ\u003cem\u003eβ\u003c/em\u003e = \u0026minus;\u0026thinsp;0.84, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.624), and IVFz (Δ\u003cem\u003eβ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.55, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.409). These findings indicate that, despite observed sex differences in absolute IVF values (Section \u003cspan refid=\"Sec11\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e), the functional relationships between IVF and performance are consistent across sexes. Notably, although visual inspection of Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e suggested that male and female swimmers exhibited opposite slope directions for the IVFx-Vswim and IVFz-Vswim relationships, formal analyses did not detect statistically significant moderation by sex. This discrepancy between graphical patterns and inferential results highlights the need for further investigation with larger samples to determine whether subtle, sex-specific associations exist in these directional components of IVF.\u003c/p\u003e \u003cp\u003eBayesian robust regression provided additional evidence against a moderating effect of sex. The 95% HDIs for interaction terms included zero: IVFx [\u0026ndash;2.08, 1.75], IVFy [\u0026ndash;0.98, 1.91], and IVFz [\u0026ndash;1.74, 1.49]. Corresponding Bayes factors offered anecdotal support for the null model (no interaction): IVFx (BF\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.96), IVFy (BF\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.94), and IVFz (BF\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.849). Together, these results indicate a lack of reliable evidence for sex moderation of the IVF-performance relationship in high-level freestyle swimmers. Sensitivity analyses confirmed that these findings were robust across alternative prior specifications, with all interaction term 95% HDIs remaining inclusive of zero.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Sex Differences in Three-Dimensional Intra-Cycle Velocity Fluctuations\u003c/h2\u003e \u003cp\u003eThis study revealed significant sex differences in freestyle swimming performance and specific components of IVF among high-level swimmers. Male swimmers demonstrated faster mean swimming velocity (Vswim) and greater forward (IVFx) and vertical (IVFz) velocity fluctuations compared with females, whereas lateral fluctuation (IVFy) showed no significant difference. These findings suggest that, within this elite cohort, higher performance in short-distance freestyle is associated with a more pronounced intra-cycle velocity pattern, particularly in the forward and vertical directions.\u003c/p\u003e \u003cp\u003eThe higher IVFx in males aligns with some reports on sprint performance\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e, but direct evidence linking forward IVF to superior performance remains inconsistent: some studies report negative associations\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, while others find no relationship\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. These discrepancies likely reflect methodological differences in measurement points (hip vs. CoM) and analytical protocols\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. The present study addresses these by using full-body CoM kinematics from high-precision 3D motion capture, providing a more accurate representation, as hip-based estimates overestimate vertical displacement compared to CoM\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe greater IVFz observed in males may be biomechanically attributed to sex-related differences in lower-limb power and kick amplitude\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e, as well as the magnitude of body roll, which influences vertical trunk displacement. Although direct evidence linking these specific factors to IVFz magnitude is limited, the observed absence of sex moderation in the IVFz-performance relationship suggests that minimizing non-propulsive vertical oscillations remains a universal technical objective for maximizing speed, a notion supported by the negative correlation between IVFz and swimming velocity\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003ePhysiologically, these sex differences in IVF likely reflect variations in force production capacity, body composition, and metabolic profiles. Greater muscle mass and a higher proportion of type II fibers in males\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e may enable more powerful propulsive phases\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e, increasing IVFx and IVFz. Females\u0026rsquo; generally higher body fat percentage and distinct morphology may influence swimming performance through multiple pathways. These characteristics not only potentially enhance buoyancy and passive hydrodynamic efficiency but also interact with factors that are known to directly affect the IVF-performance relationship, such as energy cost and propelling efficiency\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan additionalcitationids=\"CR47\" citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eMethodologically, this study builds on previous work by quantifying three-dimensional CoM kinematics rather than relying on hip-point tracking. While hip kinematics have been validated for overall stroke analysis\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e, they may overestimate vertical displacement\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e, necessitating whole-body CoM assessment for accurate IVFz quantification. The resulting high-fidelity dataset provides a validated reference for future studies employing more accessible measurement tools.\u003c/p\u003e \u003cp\u003eIn summary, although sex differences in IVF magnitude are evident among elite freestyle swimmers, they likely reflect underlying physiological and technical adaptations rather than fundamentally distinct biomechanical principles. The strong association between IVFx and performance in males\u0026mdash;and its sensitivity to methodological choices\u0026ndash;highlights the importance of standardized, CoM-based assessments in future sex-comparative research.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Absence of Sex Moderation in the IVF-Performance Relationship\u003c/h2\u003e \u003cp\u003eA key finding of this study is the absence of a moderating effect of sex on the relationship between IVF and swimming performance (Vswim). Although significant sex differences were observed in the absolute magnitudes of Vswim, IVFx, and IVFz (Section \u003cspan refid=\"Sec14\" class=\"InternalRef\"\u003e4.1\u003c/span\u003e), both frequentist (permutation tests) and Bayesian robust regression analyses showed that the slopes linking each directional IVF component to Vswim did not differ significantly between males and females. In the Bayesian analyses, the 95% HDIs for all sex \u0026times; IVF interaction terms included zero, and Bayes factors provided support for the null models (no interaction).\u003c/p\u003e \u003cp\u003eThis suggests that the fundamental biomechanical relationship between velocity fluctuation and mean swimming speed is preserved across sexes. The contrast between group differences in absolute values and the consistency of functional relationships indicates that male and female swimmers share a common performance continuum, where IVF acts as a technical descriptor whose association with speed is not inherently sex‑specific.\u003c/p\u003e \u003cp\u003eThe absence of observed moderation can be understood from several complementary perspectives. First, it reflects the high degree of technical individualization characteristic of elite swimmers. Elite performance is shaped by highly individualized movement patterns\u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e, supporting the need for personalized analysis. IVF arises from each swimmer's unique balance of propulsion, drag, and coordination\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. Even within elite cohorts, considerable inter-individual variability exists, making a universal \u0026ldquo;optimal\u0026rdquo; IVF unlikely. Performance can be optimized either by minimizing fluctuations for mechanical efficiency or by strategically exploiting larger fluctuations for propulsive impulse, depending on the swimmer's force production and coordination\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e. This principle of individualized optimization appears to operate similarly in both sexes.\u003c/p\u003e \u003cp\u003eSecond, the high methodological precision afforded by full-body CoM kinematics used in this study may provide a more reliable foundation for identifying common biomechanical principles. Previous inconsistencies in the IVF-performance relationship may partly reflect methodological noise, such as relying on hip-point proxies that poorly approximate CoM motion, particularly in the vertical axis\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. By establishing a high-fidelity kinematic reference, the present study reduces such noise, potentially uncovering the underlying consistency across sexes.\u003c/p\u003e \u003cp\u003eStatistical equivalence in the IVF-performance slope does not mean that physiological sex differences are irrelevant for training. On the contrary, well-established distinctions in muscle composition, strength, body morphology, and metabolic profiles\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e should guide individualized training. For example, male swimmers may benefit from interventions that enhance power during propulsive phases, whereas female swimmers may gain more from technical refinements that improve efficiency and stability. The key takeaway is that coaches should tailor training by integrating each athlete\u0026rsquo;s physiological profile with their individual IVF characteristics, rather than relying on broad sex-based generalizations, a strategy consistent with recent performance monitoring frameworks in competitive swimming\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eTherefore, the absence of a statistically significant moderating effect should not be interpreted as justification for sex-generalized training prescriptions. This null finding may reflect the limited sample size, high inter-individual variability among high-level swimmers, and reduced statistical power to detect interaction effects. As a result, training should remain athlete-centered, incorporating individualized 3D IVF profiles alongside each swimmer\u0026rsquo;s specific physiological and technical characteristics, rather than relying on broad sex-based strategies. Future research with larger cohorts is needed to investigate potential subtle moderating effects and to establish optimal IVF ranges within a sex-sensitive framework.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Methodological Contribution and Reference Role\u003c/h2\u003e \u003cp\u003eThis study has inherent limitations that also inform future research. The small elite sample restricts generalizability and reduce the ability to detect subtle effects, underscoring the need for replication in larger cohorts.\u003c/p\u003e \u003cp\u003eAlthough this study provides detailed CoM kinematics, the absence of concurrent physiological or force measurements limits mechanistic interpretation. Future research should combine high-fidelity kinematics with kinetic and physiological data to achieve a more comprehensive understanding.\u003c/p\u003e \u003cp\u003eAlthough the analysis was three-dimensional, it relied on discrete IVF metrics. Continuous approaches, such as SPM, could provide deeper insights into coordination dynamics throughout the stroke cycle.\u003c/p\u003e \u003cp\u003eLogistical constraints prevented assessment of test-retest reliability; future studies should include this where feasible.\u003c/p\u003e \u003cp\u003eOverall, future research should prioritize larger sample sizes, integration of multimodal data, application of this study\u0026rsquo;s reference model for more detailed analysis, and the translation of laboratory findings into practical training tools.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Limitations and Future Directions\u003c/h2\u003e \u003cp\u003eFirst, the small sample size limits the precision of estimates and generalizability, a common challenge in research involving elite athletes. To address this, robust statistical methods (e.g., Welch\u0026rsquo;s \u003cem\u003et\u003c/em\u003e-tests, Bayesian analysis, and permutation tests) were employed, specifically chosen for small-sample inference, thereby strengthening the internal validity of the comparisons. Although statistical power was high for the observed large effects, replication in larger cohorts is needed to confirm and extend these findings.\u003c/p\u003e \u003cp\u003eSecond, while detailed CoM kinematics were captured, the absence of concurrent measurements of physical capacities or propulsive forces restricts a fully mechanistic interpretation of the observed sex differences. Nonetheless, the high-fidelity, full-body 3D kinematic dataset established in this study provides a critical foundation for future research integrating physiological and kinetic measures.\u003c/p\u003e \u003cp\u003eThird, although the analysis captured three-dimensional velocity fluctuations, it relied on discrete IVF metrics. Extending these analyses to continuous profiles across the entire stroke cycle, using approaches such as SPM, could provide deeper insights into inter-segment coordination\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFinally, test-retest reliability was not assessed due to the extensive time required for manual trajectory reconstruction and frequent marker occlusion from limb-to-body contact. Methodological frameworks for such reliability are available\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e, but intra-session ICC could not be implemented here. Future studies should address this.\u003c/p\u003e \u003cp\u003eFuture research should prioritize larger cohorts to identify optimal IVF ranges and integrate time-frequency analyses with biomechanical modeling, supporting personalized, data-driven training frameworks.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eUsing 3D motion capture, this study investigated sex differences in three-dimensional IVF and swimming performance in high-level freestyle swimmers. Males exhibited higher swimming velocity, forward IVF, and vertical IVF than females, whereas lateral IVF showed no difference. Sex did not moderate the IVF\u0026ndash;performance relationship, indicating a similar biomechanical link across sexes, though this does not justify sex‑based training generalizations. Integrating individualized IVF profiles with performance monitoring frameworks supports athlete‑centered technical development. This study also provides a standardized, high‑fidelity kinematic dataset as a methodological reference for future research.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgment\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe extend our sincere gratitude to all participants in the experiments and to the staff who assisted in completing this study.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eJin Zhenyu: Conceptualization, Data curation, Formal analysis, Methodology, Visualization, Writing \u0026ndash; original draft. Zhou Yulin, Zhou Yuhang: Data curation, Methodology, Resources, Software, Writing \u0026ndash; review and editing. Yu Qian, Wang Dapeng and Shen Sijia: Methodology, Resources. Wen Yuhong: Funding acquisition, Methodology, Project administration, Supervision, Validation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Central Universities Basic Research Program, Grant No. 2024YDXL003.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of generative AI in scientific writing\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors confirm that no generative AI or AI-assisted technologies were used in the writing of this manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data can be obtained by contacting the first author or the corresponding author of the article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of Interest Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors report there are no competing interests to declare.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eD.J. Smith, S.R. Norris \u0026amp; J.M. Hogg. Performance evaluation of swimmers: scientific tools. \u003cem\u003eSports Med\u003c/em\u003e. \u003cstrong\u003e32\u003c/strong\u003e\u003cstrong\u003e,\u003c/strong\u003e 539--554 (2002).\u003c/li\u003e\n\u003cli\u003eT.M. Barbosa et al. The role of the biomechanics analyst in swimming training and competition analysis. \u003cem\u003eSports Biomech\u003c/em\u003e. \u003cstrong\u003e22,\u003c/strong\u003e 1734--1751 (2023).\u003c/li\u003e\n\u003cli\u003eL. Seifert et al. Coordination pattern variability provides functional adaptations to constraints in swimming performance. \u003cem\u003eSports Med\u003c/em\u003e. \u003cstrong\u003e44,\u003c/strong\u003e 1333--1345 (2014).\u003c/li\u003e\n\u003cli\u003eK.E. McGibbon, D.B. Pyne, M.E. Shephard \u0026amp; K.G. Thompson. Pacing in swimming: A systematic review. \u003cem\u003eSports Med\u003c/em\u003e. \u003cstrong\u003e48,\u003c/strong\u003e 1621--1633 (2018).\u003c/li\u003e\n\u003cli\u003eM.A. Maloney \u0026amp; A.D. Gorman. Skilled swimmers maintain performance stability under changing attentional focus constraints. \u003cem\u003eHum. Mov. Sci.\u003c/em\u003e \u003cstrong\u003e77,\u003c/strong\u003e 102789 (2021).\u003c/li\u003e\n\u003cli\u003eA.B. Craig \u0026amp; D.R. Pendeegast. Relationships of stroke rate, distance per stroke, and velocity in competitive swimming. \u003cem\u003eMed. Sci. Sports.\u003c/em\u003e \u003cstrong\u003e11,\u003c/strong\u003e 278 (1979).\u003c/li\u003e\n\u003cli\u003eT.M. Barbosa, R.J. Fernandes, K.L. Keskinen \u0026amp; J.P. Vilas-Boas. The influence of stroke mechanics into energy cost of elite swimmers. \u003cem\u003eEur. J. Appl. Physiol.\u003c/em\u003e \u003cstrong\u003e103,\u003c/strong\u003e 139--149 (2008).\u003c/li\u003e\n\u003cli\u003eH. Takagi et al. How do swimmers control their front crawl swimming velocity? Current knowledge and gaps from hydrodynamic perspectives. \u003cem\u003eSports Biomech.\u003c/em\u003e \u003cstrong\u003e22,\u003c/strong\u003e 1552--1571 (2023).\u003c/li\u003e\n\u003cli\u003eBarbosa, T. M., Lima, F., Portela, A., Novais, D., Machado, L., Colaco, P., Goncalves, P., Fernandes, R., Keskinen, K. L. \u0026amp; Vilas-Boas, J. P. Relationships between energy cost, swimming velocity and speed fluctuation in competitive swimming strokes. \u003cem\u003eRev. Port. Cien. Desp\u003c/em\u003e. \u003cstrong\u003e6\u003c/strong\u003e, 192--194 (2006).\u003c/li\u003e\n\u003cli\u003eP. Zamparo, M. Cortesi \u0026amp; G. Gatta. The energy cost of swimming and its determinants. \u003cem\u003eEur. J. Appl. Physiol.\u003c/em\u003e \u003cstrong\u003e120,\u003c/strong\u003e 41--66 (2020).\u003c/li\u003e\n\u003cli\u003eA. Fernandes, J. Afonso, F. Noronha et al. Intracycle Velocity Variation in Swimming: A Systematic Scoping Review. \u003cem\u003eBioengineering\u003c/em\u003e \u003cstrong\u003e10,\u003c/strong\u003e 308 (2023).\u003c/li\u003e\n\u003cli\u003eT.M. Barbosa et al. Energetics and biomechanics as determining factors of swimming performance: updating the state of the art. \u003cem\u003eJ. Sci. Med. Sport.\u003c/em\u003e \u003cstrong\u003e13,\u003c/strong\u003e 262--269 (2010).\u003c/li\u003e\n\u003cli\u003eY. Matsuda, Y. Yamada, Y. Ikuta, T. Nomura \u0026amp; S. Oda. Intracyclic velocity variation and arm coordination for different skilled swimmers in the front crawl. \u003cem\u003eJ. Hum. Kinet\u003c/em\u003e. \u003cstrong\u003e44,\u003c/strong\u003e 67--74 (2014).\u003c/li\u003e\n\u003cli\u003eM.P. Pinto, D.A. Marinho, H.P Neiva, T.M. Barbosa \u0026amp; J.E. Morais. Insights on the Selection of the Coefficient of Variation to Assess Speed Fluctuation in Swimming. \u003cem\u003eJ. Funct. Morphol. Kinesiol\u003c/em\u003e. \u003cstrong\u003e9,\u003c/strong\u003e 129 (2024).\u003c/li\u003e\n\u003cli\u003eT. Gonjo, R.J. Fernandes, J.P. Vilas-Boas \u0026amp; R. Sanders. Is the use of the coefficient of variation a valid way to assess the swimming intra-cycle velocity fluctuation? \u003cem\u003eJ. Sci. Med. Sport.\u003c/em\u003e \u003cstrong\u003e26,\u003c/strong\u003e 328--334 (2023).\u003c/li\u003e\n\u003cli\u003eJ. Padulo, N. Maffulli \u0026amp; L.P. Ardig\u0026ograve;. Signal or noise, a statistical perspective. \u003cem\u003eProc. Natl. Acad. Sci. U.S.A.\u003c/em\u003e \u003cstrong\u003e111,\u003c/strong\u003e E1160-E1160 (2014).\u003c/li\u003e\n\u003cli\u003eSchnitzler, C., Seifert, L., Alberty, M. \u0026amp; Chollet, D. Hip velocity and arm coordination in front crawl swimming. \u003cem\u003eInt. J. Sports Med\u003c/em\u003e. \u003cstrong\u003e31\u003c/strong\u003e, 875--881 (2010).\u003c/li\u003e\n\u003cli\u003eP. Figueiredo, A. Silva, A. Sampaio et al. Front crawl sprint performance: A cluster analysis of biomechanics, energetics, coordinative, and anthropometric determinants in young swimmers. \u003cem\u003eMotor Control.\u003c/em\u003e \u003cstrong\u003e20,\u003c/strong\u003e 209--221 (2016).\u003c/li\u003e\n\u003cli\u003eA.F. Silva et al. Integrated analysis of young swimmers\u0026rsquo; sprint performance. \u003cem\u003eMotor Control\u003c/em\u003e \u003cstrong\u003e23,\u003c/strong\u003e 354--364 (2019).\u003c/li\u003e\n\u003cli\u003eP.G. Morou\u0026ccedil;o, T.M. Barbosa, R. Arellano \u0026amp; J.P. Vilas-Boas. Intracyclic variation of force and swimming performance. \u003cem\u003eInt. J. Sports Physiol. Perform\u003c/em\u003e. \u003cstrong\u003e13,\u003c/strong\u003e 897--902 (2018).\u003c/li\u003e\n\u003cli\u003eS.G. Psycharakis, R. Naemi, C. Connaboy, C. McCabe \u0026amp; R.H. Sanders. Three‐dimensional analysis of intracycle velocity fluctuations in frontcrawl swimming. \u003cem\u003eScand. J. Med. Sci. Sports\u003c/em\u003e \u003cstrong\u003e20,\u003c/strong\u003e 128--135 (2010).\u003c/li\u003e\n\u003cli\u003eM.P. Pinto, D.A. Marinho, H.P. Neiva \u0026amp; J.E. Morais. Relationship between swimming speed, intra-cycle variation of horizontal speed, and Froude efficiency during consecutive stroke cycles in adolescent swimmers. \u003cem\u003ePeerJ\u003c/em\u003e \u003cstrong\u003e11, \u003c/strong\u003ee16019 (2023).\u003c/li\u003e\n\u003cli\u003eA.C. Barbosa et al. 50 m freestyle in 21, 22 and 23 s: What differentiates the speed curve of world-class and elite male swimmers? \u003cem\u003eInt. J. Perform. Anal. Sport\u003c/em\u003e. \u003cstrong\u003e21,\u003c/strong\u003e 1055--1065 (2021).\u003c/li\u003e\n\u003cli\u003eT.M. Barbosa et al. The interaction between intra-cyclic variation of the velocity and mean swimming velocity in young competitive swimmers. \u003cem\u003eInt. J. Sports Med\u003c/em\u003e. \u003cstrong\u003e34\u003c/strong\u003e, 123--130 (2012).\u003c/li\u003e\n\u003cli\u003eM. Alberty, M. Sidney, F. Huot-Marchand, J.M. Hespel \u0026amp; P. Pelayo. Intracyclic velocity variations and arm coordination during exhaustive exercise in front crawl stroke. \u003cem\u003eInt. J. Sports Med\u003c/em\u003e. \u003cstrong\u003e25\u003c/strong\u003e, 471--475 (2004).\u003c/li\u003e\n\u003cli\u003eM. Alberty, M. Sidney, P. Pelayo \u0026amp; H.M. Toussaint. Stroking characteristics during time to exhaustion tests. \u003cem\u003eMed. Sci. Sports Exerc\u003c/em\u003e. \u003cstrong\u003e41,\u003c/strong\u003e 637--644 (2009).\u003c/li\u003e\n\u003cli\u003eT. Gonjo et al. Differences in kinematics and energy cost between front crawl and backstroke below the anaerobic threshold. \u003cem\u003eEur. J. Appl. Physiol\u003c/em\u003e. \u003cstrong\u003e118,\u003c/strong\u003e 1107--1118 (2018).\u003c/li\u003e\n\u003cli\u003eA. Stamm, D.A. James \u0026amp; D.V. Thiel. Velocity profiling using inertial sensors for freestyle swimming. \u003cem\u003eSports Eng\u003c/em\u003e. \u003cstrong\u003e16,\u003c/strong\u003e 1--11 (2013).\u003c/li\u003e\n\u003cli\u003eS.K. Hunter \u0026amp; J.W. Senefeld. Sex differences in human performance. \u003cem\u003eJ. Physiol\u003c/em\u003e. \u003cstrong\u003e602,\u003c/strong\u003e 4129--4156 (2024).\u003c/li\u003e\n\u003cli\u003ePadulo, J., Chamari, K. \u0026amp; Ardig\u0026ograve;, L. P. Walking and running on treadmill: the standard criteria for kinematics studies. \u003cem\u003eMuscles Ligaments Tendons J\u003c/em\u003e. \u003cstrong\u003e4\u003c/strong\u003e, 159--162 (2014).\u003c/li\u003e\n\u003cli\u003eSamozino, P., Morin, J. B., Hintzy, F. \u0026amp; Belli, A. A simple method for measuring force, velocity and power output during squat jump. \u003cem\u003eJ. Biomech\u003c/em\u003e. \u003cstrong\u003e41\u003c/strong\u003e, 2940--2945 (2008).\u003c/li\u003e\n\u003cli\u003eAttia, A., Dhahbi, W., Chaouachi, A., Padulo, J., Wong, D. P. \u0026amp; Chamari, K. Measurement errors when estimating the vertical jump height with flight time using photocell devices: the example of Optojump. \u003cem\u003eBiol. Sport\u003c/em\u003e \u003cstrong\u003e34\u003c/strong\u003e, 63--70 (2017).\u003c/li\u003e\n\u003cli\u003eHong, Q., Li, N., Zhang, X., Zhou, Y. \u0026amp; Guo, J. Analysis method of breaststroke movements based on biomechanical multi-body dynamics. \u003cem\u003eChin. J. Appl. Mech\u003c/em\u003e. (2025). https://link.cnki.net/urlid/61.1112.O3.20251222.0956.002\u003c/li\u003e\n\u003cli\u003eB. Yu, D. Gabriel, L. Noble \u0026amp; K. An. Estimate of the optimum cutoff frequency for the Butterworth low-pass digital filter. \u003cem\u003eJ. Appl. Biomech\u003c/em\u003e. \u003cstrong\u003e15,\u003c/strong\u003e 318--329 (1999).\u003c/li\u003e\n\u003cli\u003eP. Figueiredo, J.P.V. Boas, J. Maia, P. Gon\u0026ccedil;alves \u0026amp; R.J. Fernandes. Does the hip reflect the centre of mass swimming kinematics? \u003cem\u003eInt. J. Sports Med\u003c/em\u003e. \u003cstrong\u003e30,\u003c/strong\u003e 779--781 (2009).\u003c/li\u003e\n\u003cli\u003eA. Bouvet, R. Pla, E. Delhaye, G. Nicolas \u0026amp; N. Bideau. Profiling biomechanical abilities during sprint front-crawl swimming using IMU and functional clustering of variabilities. \u003cem\u003eSports Biomech\u003c/em\u003e. \u003cstrong\u003e23\u003c/strong\u003e, 1--21 (2024).\u003c/li\u003e\n\u003cli\u003eM. Skorulski, M. Stachowicz, S. Kuliś \u0026amp; J. Gajewski. Accelerometric assessment of fatigue-induced changes in swimming technique in high performance adolescent athletes. \u003cem\u003eSci. Rep\u003c/em\u003e. \u003cstrong\u003e15,\u003c/strong\u003e 2409 (2025).\u003c/li\u003e\n\u003cli\u003eS. Wang, Y. Zhao, X. Chen, Y. Shen. Effect of Increasing the Foot Area on the Load-Velocity Relationship of the Underwater Dolphin Kick. \u003cem\u003eJ. Hum. Kinet\u003c/em\u003e. \u003cstrong\u003e95,\u003c/strong\u003e 17 (2024).\u003c/li\u003e\n\u003cli\u003eJ.E. Morais, T.M. Barbosa, T. Lopes, S. Moriyama \u0026amp; D.A. Marinho. Comparison of swimming velocity between age-group swimmers through discrete variables and continuous variables by Statistical Parametric Mapping. \u003cem\u003eSports Biomech\u003c/em\u003e. \u003cstrong\u003e23,\u003c/strong\u003e 3394--3405 (2024).\u003c/li\u003e\n\u003cli\u003eR.E. Kass \u0026amp; A.E. Raftery. Bayes factors. \u003cem\u003eJ. Am. Stat. Assoc\u003c/em\u003e. \u003cstrong\u003e90,\u003c/strong\u003e 773--795 (1995).\u003c/li\u003e\n\u003cli\u003eR.J. Fernandes, J. Ribeiro, P. Figueiredo, L. Seifert \u0026amp; J.P. Vilas-Boas. Kinematics of the hip and body center of mass in front crawl. \u003cem\u003eJ. Hum. Kinet\u003c/em\u003e. \u003cstrong\u003e33,\u003c/strong\u003e 15 (2012).\u003c/li\u003e\n\u003cli\u003eLaffaye, G., Choukou, M. A., Benguigui, N. \u0026amp; Padulo, J. Age- and gender-related development of stretch shortening cycle during a sub-maximal hopping task. \u003cem\u003eBiol. Sport\u003c/em\u003e \u003cstrong\u003e33\u003c/strong\u003e, 29--35 (2016).\u003c/li\u003e\n\u003cli\u003eP. Figueiredo, P.L. Kjendlie, J.P. Vilas-Boas, R.J. Fernandes. Intracycle velocity variation of the body centre of mass in front crawl. \u003cem\u003eInt. J. Sports Med\u003c/em\u003e. \u003cstrong\u003e33,\u003c/strong\u003e 285--290 (2012).\u003c/li\u003e\n\u003cli\u003eD.J. Handelsman, A.L. Hirschberg \u0026amp; S. Bermon. Circulating testosterone as the hormonal basis of sex differences in athletic performance. \u003cem\u003eEndocr. Rev\u003c/em\u003e. \u003cstrong\u003e39,\u003c/strong\u003e 803--829 (2018).\u003c/li\u003e\n\u003cli\u003eGatta, G. et al. The development of swimming power. \u003cem\u003eMuscles Ligaments Tendons J\u003c/em\u003e. \u003cstrong\u003e4\u003c/strong\u003e, 438--445 (2014).\u003c/li\u003e\n\u003cli\u003ePinna, M. et al. Effect of beetroot juice supplementation on aerobic response during swimming. \u003cem\u003eNutrients\u003c/em\u003e \u003cstrong\u003e6\u003c/strong\u003e, 605--615 (2014).\u003c/li\u003e\n\u003cli\u003eS.P. McLean \u0026amp; R.N. Hinrichs. Buoyancy, gender, and swimming performance. \u003cem\u003eJ. Appl. Biomech\u003c/em\u003e. \u003cstrong\u003e16,\u003c/strong\u003e 248--263 (2000).\u003c/li\u003e\n\u003cli\u003eL. Seifert, T.M. Barbosa \u0026amp; P.L. Kjendlie. Biophysical approach to swimming: Gender effect. \u003cem\u003eGender gap: Causes, experiences and effects\u003c/em\u003e \u003cstrong\u003e1,\u003c/strong\u003e 59--80 (2010).\u003c/li\u003e\n\u003cli\u003eS. Kuliś et al. Kinematic criteria determining swing movement of world class dancesport athletes. \u003cem\u003eHum. Mov\u003c/em\u003e. \u003cstrong\u003e25,\u003c/strong\u003e 60--67 (2024).\u003c/li\u003e\n\u003cli\u003eS.P.M. Ganzevles, P.J. Beek, H.A.M. Daanen, B.M.A. Coolen \u0026amp; M.J. Truijens. Differences in swimming smoothness between elite and non-elite swimmers. \u003cem\u003eSports Biomech\u003c/em\u003e. \u003cstrong\u003e22,\u003c/strong\u003e 675--688 (2023).\u003c/li\u003e\n\u003cli\u003eKuliś, S. et al. Application of the performance index for monitoring anaerobic endurance of competitive swimmers. \u003cem\u003eJ. Hum. Kinet\u003c/em\u003e. https://doi.org/10.5114/jhk/196823 (2025).\u003c/li\u003e\n\u003cli\u003eDos Santos, T. T. S. et al. Intra and inter-device reliabilities of the instrumented timed-up and go test using smartphones in young adult population. \u003cem\u003eSensors\u003c/em\u003e \u003cstrong\u003e24\u003c/strong\u003e, 2918 (2024).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Beijing Sport University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"High-level swimmers, Freestyle, Intra-Cycle Velocity Fluctuation, Sex Differences, 3D motion capture","lastPublishedDoi":"10.21203/rs.3.rs-9387014/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9387014/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study examined sex differences in three-dimensional intra-cycle velocity fluctuations (IVFs) of the body\u0026rsquo;s center of mass and the relationship between IVFs and swimming velocity (Vswim) in high-level swimmers during freestyle. Maximal-effort freestyle sprints performed by 13 high-level athletes (7 males and 6 females) were captured using a Qualisys three-dimensional motion capture system. Given the limited sample size, robust statistical approaches, including Welch\u0026rsquo;s \u003cem\u003et\u003c/em\u003e-tests, Bayesian analyses, and permutation tests, were applied. Male swimmers exhibited significantly higher Vswim (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001, ES\u0026thinsp;=\u0026thinsp;2.94), forward IVF (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001, ES\u0026thinsp;=\u0026thinsp;2.47), and vertical IVF (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.022, ES\u0026thinsp;=\u0026thinsp;1.57) compared with female swimmers. Bayesian analysis of interaction terms revealed no statistically significant moderating effect of sex on the relationship between IVF and Vswim. These findings indicate that although clear sex differences are evident in specific IVF components and swimming speed among high-level swimmers, the functional relationship between IVF and performance remains statistically consistent across sexes. From a practical perspective, IVF-based interventions should integrate sex-related physiological characteristics with individualized technical profiling to avoid overgeneralization. This study also establishes a high-fidelity methodological reference for three-dimensional kinematic analysis, providing a valuable dataset for future research and technological validation.\u003c/p\u003e","manuscriptTitle":"Sex Differences in Three-Dimensional Intra-Cycle Velocity Fluctuation and Performance During Freestyle Swimming Among High-Level Swimmers","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-14 09:21:40","doi":"10.21203/rs.3.rs-9387014/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"bb1506cf-e33a-42f9-a02a-7125c0c4ab4c","owner":[],"postedDate":"April 14th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-14T09:21:40+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-14 09:21:40","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9387014","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9387014","identity":"rs-9387014","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}