Biomechanical pathways linking push-off enhancement to toe clearance: Insights from a wearable auditory feedback system

Biomechanical pathways linking push-off enhancement to toe clearance: Insights from a wearable auditory feedback system | 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 Biomechanical pathways linking push-off enhancement to toe clearance: Insights from a wearable auditory feedback system Satoshi Ogasawara, Hikaru Yokoyama, Hideyuki Tanaka This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8746981/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 Background Reduced push-off during walking, particularly among older adults, compromises dynamic stability and increases tripping risk. Although push-off enhancement has been proposed as a target for fall prevention, the mechanisms linking increased push-off to minimum toe clearance (MinTC)—a key determinant of tripping risk—remain unclear, and practical interventions are limited. The objectives of this study were (1) elucidate the biomechanical pathways through which push-off enhancement is associated with changes in MinTC and (2) evaluate an inertial measurement unit (IMU)-based auditory feedback (AFB) approach for modulating push-off during walking. Methods An AFB system targeting push-off intensity by peak foot pitch angular velocity (PitchV) was developed using a single shoe-mounted IMU. Twenty-four young adults walked on a treadmill under normal walking, maximal push-off, and PitchV-based AFB conditions. Lower limb kinematics, electromyography, and MinTC were measured. Structural equation modeling (SEM) was used to examine phase-coupled causal pathways linking push-off–related kinematic changes to MinTC, including the influence of stride length. Results PitchV-based AFB increased push-off intensity relative to normal walking. SEM revealed two opposing effects of push-off on toe trajectory: a dominant positive indirect effect mediated by facilitated ankle dorsiflexion during early swing outweighing a smaller negative direct effect of late-stance ankle plantarflexion. This indirect pathway, consistent with a toe-lift mechanism, dominated the net association with MinTC. Importantly, the path coefficient linking PitchV to MinTC remained stable when stride length was included in the model. Conclusion Push-off enhancement is associated with improved toe clearance through coordinated cross-phase ankle plantarflexion–dorsiflexion dynamics, providing mechanistic support for the push-off hypothesis . The proposed IMU-based AFB offers a biomechanically targeted approach to gait modulation with potential relevance to reduce the risk of falls. Biomedical Engineering Physical Medicine & Rehab gait analysis wearable sensors biomechanics fall prevention structural equation modeling Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Highlights Shoe-mounted IMU-based auditory feedback immediately enhances push-off capacity. Enhanced push-off engages a mechanically driven toe-lift mechanism. Causal modeling links push-off–related kinematics to increased minimum toe clearance. 1. Introduction In aging societies, preventing falls among older adults is a major public health challenge [ 1 ]. Walking-related falls often result in serious injuries [ 2 ], highlighting the need for effective, biomechanically based interventions to reduce fall risk. This study focuses on push-off capacity, a critical component of gait that directly contributes to forward progression and stability. Push-off occurs during late stance, when contraction of the triceps surae generates ankle plantarflexion and forward propulsion [ 3 ]. The plantarflexion and propulsive forces contribute substantially to gait stability [ 4 ]. However, push-off capacity declines with age [ 5 ], and older adults with a history of falls exhibit notably reduced ankle plantarflexion during push-off [ 6 ]. Consequently, impaired push-off capacity is widely considered a key biomechanical factor underlying fall risk in older adults. Many gait-related falls in older adults are due to tripping [ 7 ]. Tripping occurs when insufficient foot clearance during the swing phase causes the toes to contact the ground or an obstacle [ 8 ]. Because age-related declines in muscle strength, balance, and agility impair postural recovery, such trips are more likely to result in falls [ 9 ]. Thus, minimum toe clearance (MinTC)—defined as the minimum height between the toes and the ground during mid-swing—is widely used as a biomechanical indicator of trip-related fall risk [ 10 , 11 ]. Traditionally, reductions in push-off capacity and MinTC have been treated as independent biomechanical risk factors for falls in older adults. Although push-off capacity has been suggested to influence the swing leg trajectory [ 12 ], direct evidence demonstrating that enhancing push-off increases MinTC remains limited. Elucidating the causal structure linking push-off mechanics to MinTC is therefore essential for establishing a mechanistic basis for gait interventions aimed at fall prevention. We hypothesize a causal structure in which enhanced push-off capacity increases MinTC by two distinct biomechanical pathways. The first pathway proposes that greater push-off force increases forward propulsion, facilitating leg swing [ 3 , 13 ] and elevating the foot trajectory, thereby increasing MinTC during the swing phase. The second pathway involves ankle dorsiflexion immediately after toe-off, which is critical for securing sufficient MinTC [ 14 ]. This post–toe-off dorsiflexion may result from passive elastic recoil of the tibialis anterior muscle–tendon unit stretched during late-stance ankle plantarflexion [ 15 , 16 ]. Thus, greater plantarflexion during push-off may enable subsequent dorsiflexion and increase MinTC. Collectively, the fall-risk–reduction mechanism mediated by these pathways is called the push-off hypothesis . Visual feedback (VFB) has been the primary approach for enhancing push-off force. VFB targeting ground reaction forces, such as the anterior–posterior component, can immediately increase push-off force in older adults [ 17 ]. Thus, older adults retain latent push-off capacity that can be readily elicited through external feedback. However, VFB-based interventions have two major practical limitations. First, target variables often depend on large-scale laboratory equipment, such as force plates, limiting applicability in daily-life environments. Second, reliance on visual information may compromise walking safety. Because older adults have reduced attentional resources compared with younger adults, VFB may impose excessive cognitive load, potentially increasing the risk of tripping or falling [ 18 , 19 ]. To overcome these limitations, we propose an intervention combining auditory feedback (AFB) with an inertial measurement unit (IMU). AFB does not require visual attention during walking and is therefore expected to be safer than VFB. IMUs are small, lightweight, wearable devices widely used for gait event detection [ 20 ]. Peak foot pitch angular velocity during late stance (PitchV), obtained from a shoe-mounted IMU, is strongly correlated with ankle plantarflexion power [ 21 ]. Notably, AFB targeting PitchV immediately increased ankle plantarflexion work in older adults [ 22 ]. Based on this background, the first objective of this study was to determine whether PitchV-based AFB induces immediate changes in lower limb kinematics and muscle activities during push-off. The second objective was to elucidate the causal structure by which push-off–related kinematic changes increase MinTC through subsequent changes in swing phase kinematics. Addressing this question requires analytical approaches capable of modeling phase-coupled causal relationships across gait phases. Thus, structural equation modeling (SEM) was applied to lower limb kinematic and electromyographic variables during walking to evaluate the effects of PitchV on MinTC. SEM enables the simultaneous evaluation of complex causal structures involving multiple interrelated variables. Because the hypothesized pathways linking PitchV to MinTC cannot be fully captured by observed variables alone, SEM was used to explicitly model latent biomechanical relationships. Finally, age-related declines in muscle strength [ 23 ] and joint flexibility [ 24 ] may confound the hypothesized causal structure. To minimize these effects, this study was conducted in healthy young adults. Nevertheless, the proposed intervention combining AFB and IMUs can be readily applicable to older adults as well. As will be shown, AFB targeting PitchV enhanced push-off mechanics, and analyses revealed a structured relationship between push-off–related kinematic changes, coordinated ankle plantarflexion–dorsiflexion dynamics, and MinTC. 2. Materials and Methods 2.1. Participants Twenty-four healthy young adults (16 males, 8 females; age 22.3 ± 3.1 years) participated after providing written informed consent. The study was approved by the Ethics Committee of Authors’ Institution (Approval No. XXXXX; December 1st, 2025) and conducted in accordance with the Declaration of Helsinki. 2.2. Experimental equipment and signal preprocessing Participants walked on a treadmill. Push-off performance was assessed using angular velocity acquired from a single IMU (37 × 46 × 12 mm, 22 g; AMWS020, ATR-Promotions, Japan). The IMU was mounted on the dorsal surface of the right shoe, with the distal edge positioned ~ 1 cm proximal to the metatarsophalangeal joint and the sensor center aligned with the third metatarsal (Fig. 1A). Triaxial angular velocity and quaternion data were sampled at 100 Hz and transmitted wirelessly to a control computer. AFB consisted of a 3.2 kHz sinusoidal beep (50-ms duration) delivered by the computer’s built-in speaker. For kinematic analysis, spherical reflective markers were placed at six points of the right leg: the greater trochanter, lateral femoral epicondyle, lateral malleolus, shoe heel, lateral shoe surface near the distal fifth metatarsal, and the center of the IMU upper surface. Marker trajectories were captured at 100 Hz using nine infrared cameras (OptiTrack Prime13, NaturalPoint Inc., USA). Three-dimensional coordinates were reconstructed with commercial software (MOTIVE, NaturalPoint Inc., USA), with a reconstruction error < 0.5 mm. Lower leg muscle activity was recorded using surface electromyography (EMG) from the gastrocnemius medialis (GM), soleus (SOL), and tibialis anterior (TA). A wireless active electrodes system (TS-MYO, Trunk Solution Inc., Japan) was used to sample EMG signals at 1 kHz. After data collection, marker trajectories were low-pass filtered using a fourth-order Butterworth filter with a 10 Hz cutoff. EMG signals were notch-filtered at 50 Hz using a second-order infinite impulse response filter to remove power-line noise, then band-pass filtered (20–450 Hz) with a zero-phase fourth-order Butterworth filter. Filtered EMG signals were rectified and smoothed using a root mean square method with an 80-ms moving window to obtain EMG envelopes. IMU angular velocity signals were not filtered or smoothed in either online or offline analyses. All data processing and analyses were performed using custom-written code in MATLAB R2025a (MathWorks, Natick, MA, USA). 2.3. Online AFB algorithm Figure 1 illustrates the temporal relationship between gait events—toe-off (TO) and heel strike (HS)—and AFB presentation. TO and HS were detected in real time using an IMU-based algorithm based on the pitch angle ( θ pitch_IMU ) [ 20 ]. Quaternion data were converted to pitch angle, with calibration performed by referencing the mean IMU orientation measured during quiet standing. The pitch angle represents rotation about the Y-axis, orthogonal to the sagittal plane defined by the walking (X) and vertical (Z) axes. Consistent with previous work, real-time detection accuracy for TO and HS was 100% [ 20 ]. AFB was implemented using a binary decision algorithm indicating whether the push-off target was achieved. Push-off intensity was quantified using the pitch angular velocity signal ( ω pitch_IMU ), defined as angular velocity about the IMU Y-axis, with plantarflexion represented by negative values (Fig. 1A). When the negative peak of ω pitch_IMU (PitchV) within a gait cycle—from heel strike i (HS i ) to heel strike i + 1 (HS i+1 )—failed to exceed a predefined threshold (Thr.peak), indicating insufficient push-off, a warning beep was sounded (Fig. 1B, C). The warning was delivered simultaneously with detection of HS i+1 . The latency between feedback presentation and the subsequent push-off (≈ 400–600 ms) was sufficient for participants to consciously adjust push-off intensity. 2.4. Experimental procedure After sensor placement, participants were familiarized with treadmill walking and speed control. They then stood quietly on the treadmill for 10 s, during which baseline IMU orientation and marker coordinates were recorded. The experiment comprised three walking conditions: normal walking (Normal), maximal push-off walking (Max), and walking with AFB, performed in a fixed order (Normal, Max, AFB) to ensure that AFB thresholds were individualized based on prior Normal and Max performance. To minimize fatigue, a 5-min rest was provided between condition blocks. In the Normal condition, participants were instructed to walk at their preferred speed, rhythm, and step length. During practice, treadmill speed was adjusted until a comfortable walking speed was reached (typically within 2 min). After speed stabilization, three tests were performed, each comprising 15 s of data collection with 1-min rest between tests. In the Max condition, participants were instructed to walk while pushing the ground backward as strongly as possible without excessive vertical upper body movement. During practice, treadmill speed was adjusted to a level at which strong push-off could be sustained. Three tests identical in duration and structure to the Normal condition were conducted. After completion of the Normal and Max conditions, PitchV values were averaged separately for each condition and participant. The threshold for AFB presentation (Thr.peak) was set at the midpoint between these two averages. Participants were not informed of this thresholding procedure. In the AFB condition, participants were informed that a beep would sound when push-off intensity fell below a predefined level and were instructed to walk at the same speed as in the Normal condition while aiming to maintain push-off near the feedback threshold. Minor speed adjustments were permitted if participants felt that their natural walking rhythm was disrupted. Three tests identical to those in the Normal condition were performed. 2.5. Measurements To assess the effect of PitchV enhancement on MinTC, kinematic and EMG variables were defined for the push-off interval and the subsequent counter push-off interval. Figure 2 illustrates the segmentation of the push-off and counter push-off intervals. The push-off interval was defined as the period of sustained ankle plantarflexion during stance, and the counter push-off interval as the period of sustained ankle dorsiflexion during early swing. Phase boundaries were determined from sagittal-plane ankle angular velocity ( ω ankle_mocap ) computed from marker trajectories (Fig. 2B). The push-off interval began and ended when ω ankle_mocap exceeded and subsequently fell below 5% of the maximum plantar flexion velocity (PF_Vel), respectively. The counter push-off interval ended when was | ω ankle_mocap | fell below 12.5% of the maximum dorsiflexion velocity (|DF_Vel|). Push-off intensity, the independent variable, was quantified using PitchV (Fig. 2A). Tripping risk was assessed using MinTC, the primary dependent variable, defined as the minimum vertical position of the IMU marker during the swing phase (Fig. 2C); larger MinTC values indicate lower tripping risk. Stride length (StrideL), a secondary dependent variable, was calculated from the sagittal displacement of the heel marker and treadmill speed. Four mediating factors were selected for SEM analysis: muscle activity and joint kinematics during the push-off and counter push-off phases of walking. These factors were selected based on their biomechanical relevance according to prior studies [ 3 , 13 , 14 , 25 – 28 ]. The muscle activity factor during the push-off interval (PO_Mus) was derived from EMG envelopes of the primary ankle plantar flexors, SOL and GM. For each muscle, peak (Pk) and mean (Mn) values within the push-off interval were calculated: SOL_Pk, SOL_Mn, GM_Pk, and GM_Mn (mV). The joint kinematics factor during the push-off interval (PO_Kin) comprised the maximum plantarflexion angle, (PF_Ang, deg), maximum plantarflexion angular velocity (PF_Vel, deg/s), and maximum plantarflexion angular acceleration (PF_Acc, deg/s 2 ). The muscle activity factor during the counter push-off interval (CPO_Mus) was derived from EMG envelopes of the primary ankle dorsiflexor, TA, using peak (TA_Pk) and mean (TA_Mn) values (mV). The joint kinematics factor during the counter push-off interval (CPO_Kin) comprised the maximum dorsiflexion angular velocity (DF_Vel, deg/s), maximum dorsiflexion angular acceleration (DF_Acc, deg/s²), maximum knee flexion angle (KneeA, deg), and maximum heel height (HeelH, mm). Direction-specific magnitudes of ankle motion were expressed as absolute values for dorsiflexion and plantarflexion. 2.6. Statistical analysis For each trial set, ten right-leg strides within the 15-s recording period were analyzed. A total of 2,160 strides (10 strides × 3 trial sets × 3 conditions × 24 participants) were initially included. Strides with missing data due to device malfunction and those exceeding ± 3 standard deviation from the participant-specific mean were excluded. The final analysis included 1,884 strides. 2.6.1 Effects of AFB To evaluate the effects of AFB on push-off modulation, PitchV was compared across the walking conditions. For each participant, PitchV was normalized as (i) a ratio to the mean across all Max-condition tests (%PitchV_max) and (ii) a ratio to the mean of the five largest values in the Max condition (%PitchV_five). Anderson–Darling tests showed that participant-averaged values for both measures did not deviate from normality ( p > 0.01). Condition effects were assessed using one-way repeated-measures ANOVA, with post hoc paired t -tests and Bonferroni correction. 2.6.2 Hypothesis-driven path models Based on the principles of muscle physiology and joint kinematics, four hypothetical regression path models were constructed (Fig. 3). In all models, paths from PitchV were restricted to push-off factors, reflecting the assumption that PitchV directly affects mechanical processes during push-off. Within each stride, muscle activation was assumed to determine kinematic characteristics; therefore, paths from muscle-related latent factors (Mus) to kinematic factors (Kin) within the same phase were permitted. Reverse paths from Kin to Mus (i.e., PO_Kin → PO_Mus and CPO_Kin → CPO_Mus) were not allowed. Briefly, Model 1 allowed direct paths from all four latent factors to MinTC, whereas Model 2 permitted all feedforward paths from push-off to counter push-off factors. Model 3 restricted push-off–counter push-off coupling to homologous muscle and kinematic domains and assumed that only counter push-off factors influenced MinTC. Model 4 further constrained the model by allowing MinTC to be influenced only by the two kinematic factors, PO_Kin and CPO_Kin. 2.6.3 SEM All observed variables were standardized to within-participant z-scores. Confirmatory factor analysis (CFA) was first conducted to identify an appropriate indicator for the four mediating latent factors. Multivariate normality was rejected by the Henze–Zirkler test ( HZ = 1.237, p < 0.001); therefore, CFA used robust maximum likelihood estimation with Huber–White (sandwich) standard errors and a mean-adjusted test statistic (Satorra–Bentler scaled chi-square). Variable selection followed a stepwise elimination procedure, with indicators showing standardized factor loadings < 0.30 considered for removal. Model re-estimation ceased when the robust comparative fit index (CFI) exceeded 0.95 and further improvements in the Akaike (AIC) and Bayesian (BIC) information criteria plateaued. To avoid overfitting, correlated error terms were not estimated. Factor scores were computed from the final CFA model and used in subsequent SEM analyses. Bayesian structural equation modeling (BSEM) was applied to the factor scores to evaluate regression path models linking PitchV to MinTC. To account for between-participant variability, models with random intercepts and fixed slopes were first estimated, and predictive performance was compared across the four hypothetical models. Because multivariate normality was rejected in preliminary analyses ( HZ = 1.237, p < 0.001), BSEM posterior distributions were estimated assuming Student’s t distributions. No residual correlations were specified. Model comparison and selection were performed using Pareto-smoothed importance sampling leave-one-out cross-validation. Model convergence and adequacy were assessed using standard diagnostics: the Gelman–Rubin statistic (R-hat) < 1.01 and effective sample sizes (ESS) ≥ 400 for both bulk and tail estimates. 2.6.4 Individual differences and stride length effect For the model with the highest predictive accuracy, additional BSEM models including participant-specific random slopes were fitted to evaluate inter-individual variability (IIV) in standardized path coefficients ( β ). Three random slope models were tested: Model I , allowing IIV in input paths from PitchV to PO_Mus and PO_Kin; Model O , allowing IIV in output paths from selected latent factors to MinTC; and Model IO , allowing IIV in both input and output paths. IIV in pathway sensitivity was assessed using the 95% confidence intervals (CIs) of between-participant standard deviations for the random slopes. Finally, the effect of stride length (StrideL) was examined in the optimal random slope model. Because StrideL lies downstream of the causal pathway, including StrideL as a fixed covariate for MinTC could induce collider bias. Instead, an alternative model was specified in which StrideL variability was assumed to reflect push-off–related mechanisms and to influence MinTC as part of the push-off causal pathway. Thus, paths from push-off–related factors to StrideL were added, treating StrideL as an auxiliary outcome. Predictive accuracy was then compared between models with and without StrideL. Statistical analyses were performed in R (v.4.3.1; R Foundation, Vienna, Austria). CFA and BSEM were performed using the “cfa” and “brms” packages, respectively. 3. Results 3.1. Manipulation check Figure 4 compares %PitchV_max and %PitchV_five across walking conditions. Significant condition effects were found for both %PitchV_max ( F (2,46) = 257.49, p < 0.001, η p ² = 0.918) and %PitchV_five ( F (2,46) = 269.93, p < 0.001, η p ² = 0.921). Post hoc comparisons revealed significant differences across all condition pairs ( p < 0.05/3). 3.2. Factor validity of observed variables Stepwise CFA eliminated five observed variables (GM_Mn, GM_Pk, PF_Vel, PF_Acc, and KneeA) from the factor structure. AIC and BIC decreased with each step and plateaued at the sixth step. The resulting factor structure met model-fit criteria (robust CFI = 0.971). All remaining observed variables exhibited factor loadings > 0.80, which were all statistically significant ( p < 0.01). PO_Kin, defined by a single observed variable (PF_Ang), had its factor loading fixed at 1.0. The other three latent factors demonstrated high internal consistency and convergent validity: Cronbach’s α and McDonald’s ω were 0.944 and 0.945 for PO_Mus, 0.947 and 0.949 for CPO_Mus, and 0.915 and 0.916 for CPO_Kin. The means and standard errors of factor loadings are summarized within the optimal SEM model (Fig. 6). 3.3. Path structural modeling All four path-structure models with random intercepts and fixed slopes converged well, meeting the criteria of R-hat < 1.01 and Bulk ESS/Tail ESS ≥ 400. Figure 5A compared models using the widely applicable information criterion (WAIC). Model 4 showed the highest predictive accuracy, followed by Model 3, 1, and 2, suggesting it as the provisional optimal model. 3.4 Individual differences For Model 4, three random slope models (Model 4_I, 4_O, and 4_IO) were fitted, all converging well (R-hat < 1.01; Bulk ESS/Tail ESS ≥ 400). Compared with the fixed slope Model 4, all random slope models improved predictive accuracy (Fig. 5B), with Model 4_IO performing best. Figure 6 presents the means and 95% CIs of standardized path coefficients ( β ) for the best-performing Model 4_IO. The mean β values in the fixed slope Model 4 were 0.724 (PitchV → PO_Mus), 0.575 (PitchV → PO_Kin), 0.273 (PO_Mus → PO_Kin), 0.620 (PO_Mus → CPO_Mus), 0.856 (PO_Kin → CPO_Kin), 0.169 (CPO_Mus → CPO_Kin), 1.326 (CPO_Kin → MinTC), and − 0.794 (PO_Kin → MinTC). Corresponding values in Model 4_IO were similar, indicating minimal changes in average path strength. The 95% CIs of between-participant standard deviations for random slopes in Model 4_IO were 0.147–0.300 (PitchV → PO_Mus), 0.075–0.180 (PitchV → PO_Kin), 0.202–0.422 (PO_Kin → MinTC), and 0.151–0.326 (CPO_Kin → MinTC). All lower bounds exceeded zero, indicating that these path strengths were influenced by IIV. 3.5. Effect of stride length Figure 7 presents the means and 95% CIs of standardized path coefficients ( β ) for the model including StrideL. Compared with Model 4_IO, predictive accuracy decreased markedly with StrideL (ΔELPD = − 1337.3 ± 34.7). Mean β values remained comparable to those in Model 4_IO (Fig. 6). The minimal changes in path coefficients, despite the pronounced reduction in predictive accuracy, indicate that Model 4_IO without StrideL is robust and that StrideL adds little explanatory value beyond the push-off–related latent factors. 4. Discussion This study examined whether AFB based on peak foot pitch angular velocity (PitchV), derived from a single shoe-mounted IMU, can modulate push-off during walking and how push-off–related kinematic changes are associated with MinTC. The results showed that PitchV-based AFB increased push-off output relative to normal walking and revealed a structured pattern of inter-phase associations linking late-stance kinematics to early-swing mechanisms related to MinTC. 4.1. Immediate enhancement of push-off performance By incorporating three walking conditions (Normal, Max, and AFB), the present design distinguished AFB-induced modulation of push-off from both baseline gait and voluntary maximal execution, clarifying that AFB enhances push-off within a submaximal, yet functionally relevant, operating range. PitchV-based AFB immediately enhanced push-off–related mechanical output by increasing ankle plantarflexor activity during late stance, particularly in the soleus. Because PitchV is closely associated with ankle plantarflexor power generation [ 21 ], these coordinated increases indicate a mechanically meaningful enhancement of push-off rather than a superficial alteration of gait pattern. During normal walking, PitchV reached only 50%–60% of the maximal value observed during maximal push-off walking, indicating substantial underutilization of available push-off capacity even in healthy young adults [ 29 ]. Such underutilization is considered an adaptive energy-saving strategy rather than a limitation of mechanical capacity [ 30 ]. The present results extend this concept by showing that AFB can rapidly access this reserve, producing a 20%–25% increase in push-off intensity. These observations are consistent with previous studies showing that VFB based on the ground reaction forces can immediately enhance push-off performance [ 17 , 26 ]. Importantly, the present approach achieves a comparable effect using a shoe-mounted IMU and AFB, eliminating the need for force plates or visual attention. From a clinical perspective, chronic underuse of push-off capacity may contribute to reduced lower limb muscle activation and increased fall risk with aging [ 4 ]. Although only immediate effects were examined, the ability to promote active use of push-off reserve capacity suggests potential value for early, preventive interventions aimed at preserving ankle function. 4.2. Integrated interpretation of direct and indirect pathways SEM clarified how push-off enhancement influenced MinTC through the interaction of direct and indirect pathways. Enhancement of push-off kinematics exerted a negative direct effect on MinTC, reflecting a transient lowering of the toe associated with increased plantarflexion during late stance. However, this effect was outweighed by a larger positive indirect effect mediated through early-swing kinematics, resulting in a net increase in toe clearance. From a biomechanical perspective, push-off enhancement induces two sequential effects. First, increased ankle plantarflexion during late stance serves as the mechanical initiator of subsequent swing phase dynamics. This is followed by facilitated dorsiflexion during early swing, which elevates the foot trajectory. The dominance of the latter mechanism explains why overall MinTC increased despite the negative direct pathway. These findings demonstrate that the influence of push-off on toe clearance cannot be understood from late-stance mechanics alone, but must be interpreted within a phase-coupled framework spanning push-off and early swing. 4.3. Biomechanical pathways supporting the push-off hypothesis Building on this phase-coupled interpretation, the present results provide biomechanical support for the push-off hypothesis by identifying two pathways linking enhanced push-off to MinTC. The first pathway involves increased forward propulsion during late stance, which facilitates swing initiation and contributes to elevation of the foot trajectory. This mechanism is consistent with previous research linking push-off intensity to swing leg dynamics and gait stability [ 3 , 13 ]. The second pathway, which emerged as the dominant mediator, involves a passive toe-lift mechanism initiated during late stance. Enhanced ankle plantarflexion stretches the antagonist tibialis anterior muscle–tendon unit, storing elastic energy that is released during early swing [ 15 , 16 ]. This elastic recoil enables rapid dorsiflexion immediately after toe-off, promoting toe lift and increasing MinTC [ 14 ]. SEM strongly supported this mediating pathway, whereas the direct pathway from push-off kinematics to MinTC was negative. Although stretch reflexes may contribute to early-swing dorsiflexion, prior work indicates that within the normal walking speed range (1.0–1.3 m/s), elastic energy storage and recoil in the muscle–tendon unit outweigh reflex-mediated contributions to ankle dorsiflexion [ 31 ]. Therefore, the present findings emphasize a predominantly mechanical interpretation, in which elastic energy storage and release play a central role. By demonstrating that enhanced push-off simultaneously induces opposing effects on toe trajectory, with early-swing dorsiflexion predominating, this study provides quantitative validation of the push-off hypothesis. 4.4. Implications for gait intervention strategies The identified causal structure was robust to IIV and independent of stride length, supporting its relevance for intervention design. Conventional gait interventions often emphasize increasing walking speed or step length [ 32 ]; however, when push-off capacity is reduced, such strategies may promote proximal compensations that are metabolically inefficient and potentially destabilizing [ 33 , 34 ]. In contrast, PitchV-based AFB selectively enhanced ankle push-off while walking speed was controlled, strengthening the mechanical basis of gait without causing speed-dependent trade-offs. By directly targeting push-off capacity, this approach may reduce reliance on proximal compensations, a possibility that should be examined directly in future studies. It may also limit unnecessary increases in metabolic cost and avoid increases in fall risk associated with faster walking [ 35 ]. Thus, push-off–focused feedback interventions represent a biomechanically efficient alternative to speed- or step-length–based strategies. Finally, the magnitude of the effects linking PitchV to late-stance plantarflexion and early-swing dorsiflexion to MinTC varied across individuals. This variability indicates that push-off–focused feedback may benefit from individual tuning of feedback targets, rather than limiting its potential as a scalable intervention. 4.5. Limitations and future directions Several limitations should be acknowledged. First, the study was conducted in healthy young adults to minimize age-related confounding effects. Age-related declines in muscle strength and joint flexibility may attenuate the identified mechanisms in older adults, and push-off reserve capacity itself may be reduced. Second, walking was performed on a treadmill with controlled speed; effects during overground walking in unconstrained environments require further investigation. Third, although the toe-lift mechanism was interpreted primarily as mechanical, more detailed neuromuscular analyses and musculoskeletal modeling are needed to dissociate passive elastic contributions from active control. Fourth, MinTC was used as a surrogate marker of fall risk, and prospective studies incorporating fall-related outcomes are required to establish real-world relevance. Finally, only immediate effects of AFB were examined; whether repeated exposure induces motor learning or long-term adaptations remains unknown. Longitudinal intervention studies are therefore required. 5. Conclusions This study demonstrated that AFB based on peak foot pitch angular velocity (PitchV), derived from a single shoe-mounted IMU, can immediately enhance push-off during walking. SEM revealed that push-off–related kinematic changes are organized across gait phases, with early-swing ankle dorsiflexion emerging as a key mediator associated with MinTC. These findings provide biomechanical support for the push-off hypothesis and suggest that modulation of push-off mechanics influences tripping-related gait characteristics without increasing walking speed or stride length. By requiring only a wearable IMU and simple AFB, the proposed approach shows promise as a practical and scalable strategy for future gait interventions, particularly in older adults. Abbreviations IMU, inertial measurement unit MinTC, minimum toe clearance AFB, auditory feedback EMG, electromyogram Declarations Ethical approval statement The study was approved by the Ethics Committee of Tokyo University of Agriculture and Technology (Approval No. 251106-0417, December 1st, 2025). Declaration of interest The authors have no competing interests to declare that are relevant to the content of this article. Data availability statement The datasets used and/or analyzed in the present study are available from the corresponding author on reasonable request. References World Health Organization, ed (2008) WHO global report on falls prevention in older age. 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Arch Phys Med Rehabil 79:317–322. https://doi.org/10.1016/S0003-9993(98)90013-2 Kerrigan DC, Lee LW, Nieto TJ, Markman JD, Collins JJ, Riley PO (2000) Kinetic alterations independent of walking speed in elderly fallers. Arch Phys Med Rehabil 81:730–735. https://doi.org/10.1053/apmr.2000.5581 Tinetti ME, Williams CS (1997) Falls, injuries due to falls, and the risk of admission to a nursing home. N Engl J Med 337:1279–1284. https://doi.org/10.1056/NEJM199710303371806 Winter DA (1992) Foot trajectory in human gait: A precise and multifactorial motor control task. Phys Ther 72:45–53. https://doi.org/10.1093/ptj/72.1.45 Van Dieën JH, Pijnappels M, Bobbert MF (2005) Age-related intrinsic limitations in preventing a trip and regaining balance after a trip. Saf Sci 43:437–453. https://doi.org/10.1016/j.ssci.2005.08.008 Barrett RS, Mills PM, Begg RK (2010) A systematic review of the effect of ageing and falls history on minimum foot clearance characteristics during level walking. Gait Posture 32:429–435. https://doi.org/10.1016/j.gaitpost.2010.07.010 Killeen T, Easthope CS, Demkó L, Filli L, Lőrincz L, Linnebank M, Curt A, Zörner B, Bolliger M (2017) Minimum toe clearance: Probing the neural control of locomotion, Sci. Rep. 7 1922. https://doi.org/10.1038/s41598-017-02189-y Nagano H, Begg RK, Sparrow WA, Taylor S (2011) Ageing and limb dominance effects on foot-ground clearance during treadmill and overground walking. Clin Biomech 26:962–968. https://doi.org/10.1016/j.clinbiomech.2011.05.013 Neptune RR, Kautz SA, Zajac FE (2001) Contributions of the individual ankle plantar flexors to support, forward progression and swing initiation during walking. J Biomech 34:1387–1398. https://doi.org/10.1016/S0021-9290(01)00105-1 Bajelan S, Sparrow WA, Begg R (2024) The ankle dorsiflexion kinetics demand to increase swing phase foot-ground clearance: Implications for assistive device design and energy demands. J Neuroeng Rehabil 21:105. https://doi.org/10.1186/s12984-024-01394-x Chleboun GS, Busic AB, Graham KK, Stuckey HA (2007) Fascicle length change of the human tibialis anterior and vastus lateralis during walking. J Orthop Sports Phys Ther 37:372–379. https://doi.org/10.2519/jospt.2007.2440 Maharaj JN, Cresswell AG, Lichtwark GA (2019) Tibialis anterior tendinous tissue plays a key role in energy absorption during human walking. J Exp Biol jeb191247. https://doi.org/10.1242/jeb.191247 Franz JR, Maletis M, Kram R (2014) Real-time feedback enhances forward propulsion during walking in old adults. Clin Biomech 29:68–74. https://doi.org/10.1016/j.clinbiomech.2013.10.018 Ebaid D, Crewther SG (2019) Visual information processing in young and older adults. Front Aging Neurosci 11:116. https://doi.org/10.3389/fnagi.2019.00116 Madden DJ (2007) Aging and visual attention. Curr Dir Psychol Sci 16:70–74. https://doi.org/10.1111/j.1467-8721.2007.00478.x Nazarahari M, Khandan A, Khan A, Rouhani H (2022) Foot angular kinematics measured with inertial measurement units: A reliable criterion for real-time gait event detection. J Biomech 130:110880. https://doi.org/10.1016/j.jbiomech.2021.110880 Hafer JF, Zernicke RF (2020) Propulsive joint powers track with sensor-derived angular velocity: A potential tool for lab-less gait retraining. J Biomech 106:109821. https://doi.org/10.1016/j.jbiomech.2020.109821 Lyons SM, Vickery TM, Powell DW, Paquette MR (2025) Influence of auditory biofeedback of foot angular velocity on propulsive function and gait performance in old healthy adults. Gait Posture 120:34–39. https://doi.org/10.1016/j.gaitpost.2025.03.030 Vandervoort AA, McComas AJ (1986) Contractile changes in opposing muscles of the human ankle joint with aging. J Appl Physiol 61:361–367. https://doi.org/10.1152/jappl.1986.61.1.361 Grimston SK, Nigg BM, Hanley DA, Engsberg JR (1993) Differences in ankle joint complex range of motion as a function of age. Foot Ankle 14:215–222. https://doi.org/10.1177/107110079301400407 Brockett CL, Chapman GJ (2016) Biomechanics of the ankle. Orthop Trauma 30:232–238. https://doi.org/10.1016/j.mporth.2016.04.015 Browne MG, Franz JR (2019) Ankle power biofeedback attenuates the distal-to-proximal redistribution in older adults. Gait Posture 71:44–49. https://doi.org/10.1016/j.gaitpost.2019.04.011 Levinger P, Lai DTH, Menz HB, Morrow AD, Feller JA, Bartlett JR, Bergman NR, Begg R (2012) Swing limb mechanics and minimum toe clearance in people with knee osteoarthritis. Gait Posture 35:277–281. https://doi.org/10.1016/j.gaitpost.2011.09.020 Moosabhoy MA, Gard SA (2006) Methodology for determining the sensitivity of swing leg toe clearance and leg length to swing leg joint angles during gait. Gait Posture 24:493–501. https://doi.org/10.1016/j.gaitpost.2005.12.004 Conway KA, Bissette RG, Franz JR (2018) The functional utilization of propulsive capacity during human walking. J Appl Biomech 34:474–482. https://doi.org/10.1123/jab.2017-0389 McDonald KA, Cusumano JP, Hieronymi A, Rubenson J (2022) Humans trade off whole-body energy cost to avoid overburdening muscles while walking, Proc. R. Soc. B Biol. Sci. 289 20221189. https://doi.org/10.1098/rspb.2022.1189 Christensen LOD, Andersen JB, Sinkjær T, Nielsen J (2001) Transcranial magnetic stimulation and stretch reflexes in the tibialis anterior muscle during human walking. J Physiol 531:545–557. https://doi.org/10.1111/j.1469-7793.2001.0545i.x Rodríguez-Molinero A, Herrero-Larrea A, Miñarro A, Narvaiza L, Gálvez-Barrón C, Gonzalo N, León E, Valldosera E, De Mingo O, Macho D, Aivar E, Pinzón A, Alba J, Passarelli N, Stasi RA, Valverde L, Kruse E, Felipe I, Collado JB, Sabater (2019) The spatial parameters of gait and their association with falls, functional decline and death in older adults: a prospective study. Sci Rep 9:8813. https://doi.org/10.1038/s41598-019-45113-2 Delabastita T, Hollville E, Catteau A, Cortvriendt P, De Groote F, Vanwanseele B (2021) Distal-to‐proximal joint mechanics redistribution is a main contributor to reduced walking economy in older adults. Scand J Med Sci Sports 31:1036–1047. https://doi.org/10.1111/sms.13929 DeVita P, Hortobagyi T (2000) Age causes a redistribution of joint torques and powers during gait. J Appl Physiol 88:1804–1811. https://doi.org/10.1152/jappl.2000.88.5.1804 Quach L, Galica AM, Jones RN, Procter-Gray E, Manor B, Hannan MT, Lipsitz LA (2011) The nonlinear relationship between gait speed and falls: The maintenance of balance, independent living, intellect, and zest in the elderly of boston Study. J Am Geriatr Soc 59:1069–1073. https://doi.org/10.1111/j.1532-5415.2011.03408.x Additional Declarations The authors declare no competing interests. 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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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-8746981","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":583399885,"identity":"a0185ae5-5e54-4d78-a89a-684c05c2d2dc","order_by":0,"name":"Satoshi Ogasawara","email":"","orcid":"","institution":"Cooperative Major in Advanced Health Science, Graduate School of Bio-Applications and Systems Engineering, Tokyo University of Agriculture and Technology, Tokyo, Japan","correspondingAuthor":false,"prefix":"","firstName":"Satoshi","middleName":"","lastName":"Ogasawara","suffix":""},{"id":583399886,"identity":"3442242b-e40d-4136-bfcc-a9ece132c0c7","order_by":1,"name":"Hikaru Yokoyama","email":"","orcid":"","institution":"Institute of Engineering, Tokyo University of Agriculture and Technology, Tokyo, Japan","correspondingAuthor":false,"prefix":"","firstName":"Hikaru","middleName":"","lastName":"Yokoyama","suffix":""},{"id":583399887,"identity":"2ef8fe81-ad12-4414-8028-0e682d0e6706","order_by":2,"name":"Hideyuki Tanaka","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7klEQVRIiWNgGAWjYJACZgYDZgZ+FCEJPMp5YFokG4CsAzDFhLWAdB1A1oIP2LOfPfi5oMBazvj44QfMH9vs6hjYDz9gsNyBxxaevGTpGQbpxmZn0gwYDrYlSzDwABmSZ/A5LMdAmsfgcOK2G0A3HmxjBjosh4FBsg2PFv43xr+BWuo3zwBrqZdg4H9DQItEjhnIlgQDCbCWwxIMEoRsufHGzJrHIN1wBtAvB86cOy7ZJvHM4AA+v7D35xjf5vljLc/ffvjhg4qyan5+/uSHjyXxhBgKOAAi2ID4MDhiSQKMH0nWMgpGwSgYBcMYAADMtkWNaf0BUQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-5988-8807","institution":"Human Movement Science, Institute of Engineering, Tokyo University of Agriculture and Technology, Tokyo, Japan","correspondingAuthor":true,"prefix":"","firstName":"Hideyuki","middleName":"","lastName":"Tanaka","suffix":""}],"badges":[],"createdAt":"2026-01-31 06:17:31","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-8746981/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8746981/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101765387,"identity":"2b226f79-05c3-4317-b03d-bc8a864ff533","added_by":"auto","created_at":"2026-02-03 11:58:58","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":548153,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 1. Detection of gait events and presentation of auditory feedback (AFB).\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e(A) Sensor placement on the shoe and definition of the coordinate system. \u003cem\u003eω\u003c/em\u003e\u003csub\u003epitch_IMU\u003c/sub\u003e indicates pitch angular velocity about the Y-axis. (B) Representative time series of \u003cem\u003eω\u003c/em\u003e\u003csub\u003epitch_IMU\u003c/sub\u003e. The system detects the peak plantarflexion velocity (PitchV, orange dots) during push-off. An auditory beep is triggered if PitchV does not exceed a predefined threshold (Thr.peak, black dashed line). (C) Corresponding foot pitch angle showing gait events. The AFB signal derived in (B) is presented at the subsequent heel strike. DF, dorsiflexion; PF, plantarflexion; HS, heel strike; TO, toe-off.\u003c/p\u003e","description":"","filename":"figure1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8746981/v1/1dcbf70ecf417e1942ac1686.jpg"},{"id":101765332,"identity":"0e561cac-057e-4c06-9ca9-8243595c9f89","added_by":"auto","created_at":"2026-02-03 11:58:49","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":492007,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 2. Gait phase definitions and minimum toe clearance (MinTC) measurement.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e(A) Foot pitch angular velocity (\u003cem\u003eω\u003c/em\u003e\u003csub\u003epitch_IMU\u003c/sub\u003e) obtained from the inertial measurement unit (IMU). (B) Ankle angular velocity (\u003cem\u003eω\u003c/em\u003e\u003csub\u003eankle_mocap\u003c/sub\u003e) and (C) toe clearance (i.e., height between the toes and the ground) obtained from the motion capture system. The horizontal axis represents the gait cycle (%) normalized from heel-off (HO) to toe contact (TC). PF_Vel and DF_Vel denote the maximum plantarflexion and dorsiflexion velocities, respectively. MinTC is the minimum height between the toes and the ground during the swing phase (toe-off [TO] to heel strike [HS]). Asterisks (*) indicate phase boundaries. PO, push-off interval; CPO, counter push-off interval.\u003c/p\u003e","description":"","filename":"figure2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8746981/v1/51da05e7d2bf8e247d4fbbd1.jpg"},{"id":101765330,"identity":"c2629e27-a3a5-4ab6-a2fa-9f3234033807","added_by":"auto","created_at":"2026-02-03 11:58:47","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1280012,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 3. Hypothetical regression path models.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePO and CPO denote push-off and counter-push-off phases, respectively. Suffixes _Mus and _Kin represent muscle contraction and kinematic characteristics within each phase. The models test causal pathways from push-off intensity (PitchV) to minimum toe clearance (MinTC).\u003c/p\u003e","description":"","filename":"figure3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8746981/v1/dcba2f70b5a42e2d79932c3a.jpg"},{"id":101765424,"identity":"1bc33bdb-68fa-4631-9797-b4d46946c68c","added_by":"auto","created_at":"2026-02-03 11:59:02","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":248907,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 4. Comparison of inertial measurement unit (IMU)-derived peak foot pitch angular velocity (PitchV) across walking conditions.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e(A) Values normalized to the mean of all maximal tests. (B) Values normalized to the mean of the five highest maximal tests. Normal, AFB, and Max correspond to normal, auditory feedback, and maximal walking. Boxes show medians, interquartile ranges (IQRs), and means (filled circle); whiskers represent 1.5 × IQR with outliers as open circles. Values are means ± standard deviation. * \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.05 (Bonferroni-corrected).\u003c/p\u003e","description":"","filename":"figure4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8746981/v1/1375e66e613e8903c1f8e922.jpg"},{"id":101765397,"identity":"278205e9-d710-4afb-b54f-34b2fc90f0e4","added_by":"auto","created_at":"2026-02-03 11:59:01","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":385565,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 5. Comparison of model predictive performance.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eMean differences in expected log predictive density (ELPD) for (A) hypothetical path models 1–4 and (B) random-slope variants of Model 4. Points and error bars represent means and standard errors, respectively. The dashed line indicates the reference model with the highest predictive accuracy in each comparison.\u003c/p\u003e","description":"","filename":"figure5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8746981/v1/5b146ed39f8c22406cbdf1da.jpg"},{"id":101765362,"identity":"dbf02bb5-9795-4f81-8a30-b1362b9a728f","added_by":"auto","created_at":"2026-02-03 11:58:56","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1063765,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 6. Path coefficients of the optimal regression model (Model 4_IO).\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eEllipses and rectangles represent latent and observed variables, respectively. Values for observed variables indicate means ± standard errors of factor loadings from confirmatory factor analysis. Values on path arrows denote standardized partial regression coefficients (\u003cem\u003eβ\u003c/em\u003e) derived from Bayesian posterior distributions, with 95% confidence intervals in brackets. Blue and red arrows indicate positive and negative effects, respectively.\u003c/p\u003e","description":"","filename":"figure6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8746981/v1/7b58e5d9392f2b5dfd0b0454.jpg"},{"id":101765304,"identity":"52615b0e-2f3a-4750-9003-9c196a70c0b6","added_by":"auto","created_at":"2026-02-03 11:58:36","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":795759,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFigure 7. Regression path model including stride length (StrideL) as an auxiliary outcome.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eValues on path arrows denote standardized partial regression coefficients (\u003cem\u003eβ\u003c/em\u003e) derived from Bayesian posterior distributions, with 95% confidence intervals in brackets. Dashed lines indicate pathways to the auxiliary outcome, confirming that the primary effects on MinTC are independent of stride length. Blue and red arrows represent positive and negative effects, respectively.\u003c/p\u003e","description":"","filename":"figure7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8746981/v1/29b32cfdf7e4e6b784deaaa1.jpg"},{"id":101765438,"identity":"7848820b-f56e-4245-b22e-18636e82002c","added_by":"auto","created_at":"2026-02-03 11:59:13","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5863980,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8746981/v1/8a5facb0-084f-4e18-8c88-ca005bbc23c5.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eBiomechanical pathways linking push-off enhancement to toe clearance: Insights from a wearable auditory feedback system\u003c/p\u003e","fulltext":[{"header":"Highlights","content":"\u003cp\u003eShoe-mounted IMU-based auditory feedback immediately enhances push-off capacity.\u003c/p\u003e\u003cp\u003eEnhanced push-off engages a mechanically driven toe-lift mechanism.\u003c/p\u003e\u003cp\u003eCausal modeling links push-off\u0026ndash;related kinematics to increased minimum toe clearance.\u003c/p\u003e"},{"header":"1. Introduction","content":"\u003cp\u003eIn aging societies, preventing falls among older adults is a major public health challenge [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Walking-related falls often result in serious injuries [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], highlighting the need for effective, biomechanically based interventions to reduce fall risk. This study focuses on push-off capacity, a critical component of gait that directly contributes to forward progression and stability.\u003c/p\u003e \u003cp\u003ePush-off occurs during late stance, when contraction of the triceps surae generates ankle plantarflexion and forward propulsion [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. The plantarflexion and propulsive forces contribute substantially to gait stability [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. However, push-off capacity declines with age [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], and older adults with a history of falls exhibit notably reduced ankle plantarflexion during push-off [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Consequently, impaired push-off capacity is widely considered a key biomechanical factor underlying fall risk in older adults.\u003c/p\u003e \u003cp\u003eMany gait-related falls in older adults are due to tripping [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Tripping occurs when insufficient foot clearance during the swing phase causes the toes to contact the ground or an obstacle [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Because age-related declines in muscle strength, balance, and agility impair postural recovery, such trips are more likely to result in falls [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Thus, minimum toe clearance (MinTC)\u0026mdash;defined as the minimum height between the toes and the ground during mid-swing\u0026mdash;is widely used as a biomechanical indicator of trip-related fall risk [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTraditionally, reductions in push-off capacity and MinTC have been treated as independent biomechanical risk factors for falls in older adults. Although push-off capacity has been suggested to influence the swing leg trajectory [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], direct evidence demonstrating that enhancing push-off increases MinTC remains limited. Elucidating the causal structure linking push-off mechanics to MinTC is therefore essential for establishing a mechanistic basis for gait interventions aimed at fall prevention.\u003c/p\u003e \u003cp\u003eWe hypothesize a causal structure in which enhanced push-off capacity increases MinTC by two distinct biomechanical pathways. The first pathway proposes that greater push-off force increases forward propulsion, facilitating leg swing [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] and elevating the foot trajectory, thereby increasing MinTC during the swing phase. The second pathway involves ankle dorsiflexion immediately after toe-off, which is critical for securing sufficient MinTC [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. This post\u0026ndash;toe-off dorsiflexion may result from passive elastic recoil of the tibialis anterior muscle\u0026ndash;tendon unit stretched during late-stance ankle plantarflexion [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Thus, greater plantarflexion during push-off may enable subsequent dorsiflexion and increase MinTC. Collectively, the fall-risk\u0026ndash;reduction mechanism mediated by these pathways is called the \u003cem\u003epush-off hypothesis\u003c/em\u003e.\u003c/p\u003e \u003cp\u003eVisual feedback (VFB) has been the primary approach for enhancing push-off force. VFB targeting ground reaction forces, such as the anterior\u0026ndash;posterior component, can immediately increase push-off force in older adults [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Thus, older adults retain latent push-off capacity that can be readily elicited through external feedback.\u003c/p\u003e \u003cp\u003eHowever, VFB-based interventions have two major practical limitations. First, target variables often depend on large-scale laboratory equipment, such as force plates, limiting applicability in daily-life environments. Second, reliance on visual information may compromise walking safety. Because older adults have reduced attentional resources compared with younger adults, VFB may impose excessive cognitive load, potentially increasing the risk of tripping or falling [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo overcome these limitations, we propose an intervention combining auditory feedback (AFB) with an inertial measurement unit (IMU). AFB does not require visual attention during walking and is therefore expected to be safer than VFB. IMUs are small, lightweight, wearable devices widely used for gait event detection [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Peak foot pitch angular velocity during late stance (PitchV), obtained from a shoe-mounted IMU, is strongly correlated with ankle plantarflexion power [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Notably, AFB targeting PitchV immediately increased ankle plantarflexion work in older adults [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eBased on this background, the first objective of this study was to determine whether PitchV-based AFB induces immediate changes in lower limb kinematics and muscle activities during push-off. The second objective was to elucidate the causal structure by which push-off\u0026ndash;related kinematic changes increase MinTC through subsequent changes in swing phase kinematics.\u003c/p\u003e \u003cp\u003eAddressing this question requires analytical approaches capable of modeling phase-coupled causal relationships across gait phases. Thus, structural equation modeling (SEM) was applied to lower limb kinematic and electromyographic variables during walking to evaluate the effects of PitchV on MinTC. SEM enables the simultaneous evaluation of complex causal structures involving multiple interrelated variables. Because the hypothesized pathways linking PitchV to MinTC cannot be fully captured by observed variables alone, SEM was used to explicitly model latent biomechanical relationships.\u003c/p\u003e \u003cp\u003eFinally, age-related declines in muscle strength [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] and joint flexibility [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] may confound the hypothesized causal structure. To minimize these effects, this study was conducted in healthy young adults. Nevertheless, the proposed intervention combining AFB and IMUs can be readily applicable to older adults as well.\u003c/p\u003e \u003cp\u003eAs will be shown, AFB targeting PitchV enhanced push-off mechanics, and analyses revealed a structured relationship between push-off\u0026ndash;related kinematic changes, coordinated ankle plantarflexion\u0026ndash;dorsiflexion dynamics, and MinTC.\u003c/p\u003e"},{"header":"2. Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Participants\u003c/h2\u003e \u003cp\u003e Twenty-four healthy young adults (16 males, 8 females; age 22.3\u0026thinsp;\u0026plusmn;\u0026thinsp;3.1 years) participated after providing written informed consent. The study was approved by the Ethics Committee of Authors\u0026rsquo; Institution (Approval No. XXXXX; December 1st, 2025) and conducted in accordance with the Declaration of Helsinki.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Experimental equipment and signal preprocessing\u003c/h2\u003e \u003cp\u003eParticipants walked on a treadmill. Push-off performance was assessed using angular velocity acquired from a single IMU (37 \u0026times; 46 \u0026times; 12 mm, 22 g; AMWS020, ATR-Promotions, Japan). The IMU was mounted on the dorsal surface of the right shoe, with the distal edge positioned\u0026thinsp;~\u0026thinsp;1 cm proximal to the metatarsophalangeal joint and the sensor center aligned with the third metatarsal (Fig.\u0026nbsp;1A). Triaxial angular velocity and quaternion data were sampled at 100 Hz and transmitted wirelessly to a control computer. AFB consisted of a 3.2 kHz sinusoidal beep (50-ms duration) delivered by the computer\u0026rsquo;s built-in speaker.\u003c/p\u003e \u003cp\u003eFor kinematic analysis, spherical reflective markers were placed at six points of the right leg: the greater trochanter, lateral femoral epicondyle, lateral malleolus, shoe heel, lateral shoe surface near the distal fifth metatarsal, and the center of the IMU upper surface. Marker trajectories were captured at 100 Hz using nine infrared cameras (OptiTrack Prime13, NaturalPoint Inc., USA). Three-dimensional coordinates were reconstructed with commercial software (MOTIVE, NaturalPoint Inc., USA), with a reconstruction error\u0026thinsp;\u0026lt;\u0026thinsp;0.5 mm.\u003c/p\u003e \u003cp\u003eLower leg muscle activity was recorded using surface electromyography (EMG) from the gastrocnemius medialis (GM), soleus (SOL), and tibialis anterior (TA). A wireless active electrodes system (TS-MYO, Trunk Solution Inc., Japan) was used to sample EMG signals at 1 kHz.\u003c/p\u003e \u003cp\u003eAfter data collection, marker trajectories were low-pass filtered using a fourth-order Butterworth filter with a 10 Hz cutoff. EMG signals were notch-filtered at 50 Hz using a second-order infinite impulse response filter to remove power-line noise, then band-pass filtered (20\u0026ndash;450 Hz) with a zero-phase fourth-order Butterworth filter. Filtered EMG signals were rectified and smoothed using a root mean square method with an 80-ms moving window to obtain EMG envelopes. IMU angular velocity signals were not filtered or smoothed in either online or offline analyses.\u003c/p\u003e \u003cp\u003e All data processing and analyses were performed using custom-written code in MATLAB R2025a (MathWorks, Natick, MA, USA).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Online AFB algorithm\u003c/h2\u003e \u003cp\u003eFigure 1 illustrates the temporal relationship between gait events\u0026mdash;toe-off (TO) and heel strike (HS)\u0026mdash;and AFB presentation. TO and HS were detected in real time using an IMU-based algorithm based on the pitch angle (\u003cem\u003eθ\u003c/em\u003e\u003csub\u003epitch_IMU\u003c/sub\u003e) [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Quaternion data were converted to pitch angle, with calibration performed by referencing the mean IMU orientation measured during quiet standing. The pitch angle represents rotation about the Y-axis, orthogonal to the sagittal plane defined by the walking (X) and vertical (Z) axes. Consistent with previous work, real-time detection accuracy for TO and HS was 100% [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAFB was implemented using a binary decision algorithm indicating whether the push-off target was achieved. Push-off intensity was quantified using the pitch angular velocity signal (\u003cem\u003eω\u003c/em\u003e\u003csub\u003epitch_IMU\u003c/sub\u003e), defined as angular velocity about the IMU Y-axis, with plantarflexion represented by \u003cem\u003enegative\u003c/em\u003e values (Fig.\u0026nbsp;1A). When the negative peak of \u003cem\u003eω\u003c/em\u003e\u003csub\u003epitch_IMU\u003c/sub\u003e (PitchV) within a gait cycle\u0026mdash;from heel strike \u003cem\u003ei\u003c/em\u003e (HS\u003csub\u003ei\u003c/sub\u003e) to heel strike \u003cem\u003ei\u003c/em\u003e\u0026thinsp;+\u0026thinsp;1 (HS\u003csub\u003ei+1\u003c/sub\u003e)\u0026mdash;failed to exceed a predefined threshold (Thr.peak), indicating \u003cem\u003einsufficient\u003c/em\u003e push-off, a warning beep was sounded (Fig.\u0026nbsp;1B, C). The warning was delivered simultaneously with detection of HS\u003csub\u003ei+1\u003c/sub\u003e. The latency between feedback presentation and the subsequent push-off (\u0026asymp;\u0026thinsp;400\u0026ndash;600 ms) was sufficient for participants to consciously adjust push-off intensity.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Experimental procedure\u003c/h2\u003e \u003cp\u003eAfter sensor placement, participants were familiarized with treadmill walking and speed control. They then stood quietly on the treadmill for 10 s, during which baseline IMU orientation and marker coordinates were recorded.\u003c/p\u003e \u003cp\u003eThe experiment comprised three walking conditions: normal walking (Normal), maximal push-off walking (Max), and walking with AFB, performed in a fixed order (Normal, Max, AFB) to ensure that AFB thresholds were individualized based on prior Normal and Max performance. To minimize fatigue, a 5-min rest was provided between condition blocks.\u003c/p\u003e \u003cp\u003eIn the Normal condition, participants were instructed to walk at their preferred speed, rhythm, and step length. During practice, treadmill speed was adjusted until a comfortable walking speed was reached (typically within 2 min). After speed stabilization, three tests were performed, each comprising 15 s of data collection with 1-min rest between tests.\u003c/p\u003e \u003cp\u003eIn the Max condition, participants were instructed to walk while pushing the ground backward as strongly as possible without excessive vertical upper body movement. During practice, treadmill speed was adjusted to a level at which strong push-off could be sustained. Three tests identical in duration and structure to the Normal condition were conducted.\u003c/p\u003e \u003cp\u003eAfter completion of the Normal and Max conditions, PitchV values were averaged separately for each condition and participant. The threshold for AFB presentation (Thr.peak) was set at the midpoint between these two averages. Participants were not informed of this thresholding procedure.\u003c/p\u003e \u003cp\u003eIn the AFB condition, participants were informed that a beep would sound when push-off intensity fell below a predefined level and were instructed to walk at the same speed as in the Normal condition while aiming to maintain push-off near the feedback threshold. Minor speed adjustments were permitted if participants felt that their natural walking rhythm was disrupted. Three tests identical to those in the Normal condition were performed.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5. Measurements\u003c/h2\u003e \u003cp\u003eTo assess the effect of PitchV enhancement on MinTC, kinematic and EMG variables were defined for the push-off interval and the subsequent counter push-off interval. Figure\u0026nbsp;2 illustrates the segmentation of the push-off and counter push-off intervals.\u003c/p\u003e \u003cp\u003eThe push-off interval was defined as the period of sustained ankle plantarflexion during stance, and the counter push-off interval as the period of sustained ankle dorsiflexion during early swing. Phase boundaries were determined from sagittal-plane ankle angular velocity (\u003cem\u003eω\u003c/em\u003e\u003csub\u003eankle_mocap\u003c/sub\u003e) computed from marker trajectories (Fig.\u0026nbsp;2B). The push-off interval began and ended when \u003cem\u003eω\u003c/em\u003e\u003csub\u003eankle_mocap\u003c/sub\u003e exceeded and subsequently fell below 5% of the maximum plantar flexion velocity (PF_Vel), respectively. The counter push-off interval ended when was |\u003cem\u003eω\u003c/em\u003e\u003csub\u003eankle_mocap\u003c/sub\u003e| fell below 12.5% of the maximum dorsiflexion velocity (|DF_Vel|).\u003c/p\u003e \u003cp\u003ePush-off intensity, the independent variable, was quantified using PitchV (Fig.\u0026nbsp;2A). Tripping risk was assessed using MinTC, the primary dependent variable, defined as the minimum vertical position of the IMU marker during the swing phase (Fig.\u0026nbsp;2C); larger MinTC values indicate lower tripping risk. Stride length (StrideL), a secondary dependent variable, was calculated from the sagittal displacement of the heel marker and treadmill speed.\u003c/p\u003e \u003cp\u003eFour mediating factors were selected for SEM analysis: muscle activity and joint kinematics during the push-off and counter push-off phases of walking. These factors were selected based on their biomechanical relevance according to prior studies [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan additionalcitationids=\"CR26 CR27\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe muscle activity factor during the push-off interval (PO_Mus) was derived from EMG envelopes of the primary ankle plantar flexors, SOL and GM. For each muscle, peak (Pk) and mean (Mn) values within the push-off interval were calculated: SOL_Pk, SOL_Mn, GM_Pk, and GM_Mn (mV).\u003c/p\u003e \u003cp\u003eThe joint kinematics factor during the push-off interval (PO_Kin) comprised the maximum plantarflexion angle, (PF_Ang, deg), maximum plantarflexion angular velocity (PF_Vel, deg/s), and maximum plantarflexion angular acceleration (PF_Acc, deg/s\u003csup\u003e2\u003c/sup\u003e).\u003c/p\u003e \u003cp\u003eThe muscle activity factor during the counter push-off interval (CPO_Mus) was derived from EMG envelopes of the primary ankle dorsiflexor, TA, using peak (TA_Pk) and mean (TA_Mn) values (mV).\u003c/p\u003e \u003cp\u003eThe joint kinematics factor during the counter push-off interval (CPO_Kin) comprised the maximum dorsiflexion angular velocity (DF_Vel, deg/s), maximum dorsiflexion angular acceleration (DF_Acc, deg/s\u0026sup2;), maximum knee flexion angle (KneeA, deg), and maximum heel height (HeelH, mm).\u003c/p\u003e \u003cp\u003eDirection-specific magnitudes of ankle motion were expressed as absolute values for dorsiflexion and plantarflexion.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.6. Statistical analysis\u003c/h2\u003e \u003cp\u003eFor each trial set, ten right-leg strides within the 15-s recording period were analyzed. A total of 2,160 strides (10 strides \u0026times; 3 trial sets \u0026times; 3 conditions \u0026times; 24 participants) were initially included. Strides with missing data due to device malfunction and those exceeding\u0026thinsp;\u0026plusmn;\u0026thinsp;3 standard deviation from the participant-specific mean were excluded. The final analysis included 1,884 strides.\u003c/p\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e2.6.1 Effects of AFB\u003c/h2\u003e \u003cp\u003eTo evaluate the effects of AFB on push-off modulation, PitchV was compared across the walking conditions. For each participant, PitchV was normalized as (i) a ratio to the mean across all Max-condition tests (%PitchV_max) and (ii) a ratio to the mean of the five largest values in the Max condition (%PitchV_five). Anderson\u0026ndash;Darling tests showed that participant-averaged values for both measures did not deviate from normality (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.01). Condition effects were assessed using one-way repeated-measures ANOVA, with post hoc paired \u003cem\u003et\u003c/em\u003e-tests and Bonferroni correction.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e2.6.2 Hypothesis-driven path models\u003c/h2\u003e \u003cp\u003eBased on the principles of muscle physiology and joint kinematics, four hypothetical regression path models were constructed (Fig.\u0026nbsp;3). In all models, paths from PitchV were restricted to push-off factors, reflecting the assumption that PitchV directly affects mechanical processes during push-off. Within each stride, muscle activation was assumed to determine kinematic characteristics; therefore, paths from muscle-related latent factors (Mus) to kinematic factors (Kin) within the same phase were permitted. Reverse paths from Kin to Mus (i.e., PO_Kin \u0026rarr; PO_Mus and CPO_Kin \u0026rarr; CPO_Mus) were not allowed.\u003c/p\u003e \u003cp\u003eBriefly, \u003cb\u003eModel 1\u003c/b\u003e allowed direct paths from all four latent factors to MinTC, whereas \u003cb\u003eModel 2\u003c/b\u003e permitted all feedforward paths from push-off to counter push-off factors. \u003cb\u003eModel 3\u003c/b\u003e restricted push-off\u0026ndash;counter push-off coupling to homologous muscle and kinematic domains and assumed that only counter push-off factors influenced MinTC. \u003cb\u003eModel 4\u003c/b\u003e further constrained the model by allowing MinTC to be influenced only by the two kinematic factors, PO_Kin and CPO_Kin.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e2.6.3 SEM\u003c/h2\u003e \u003cp\u003eAll observed variables were standardized to within-participant z-scores. Confirmatory factor analysis (CFA) was first conducted to identify an appropriate indicator for the four mediating latent factors. Multivariate normality was rejected by the Henze\u0026ndash;Zirkler test (\u003cem\u003eHZ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.237, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001); therefore, CFA used robust maximum likelihood estimation with Huber\u0026ndash;White (sandwich) standard errors and a mean-adjusted test statistic (Satorra\u0026ndash;Bentler scaled chi-square).\u003c/p\u003e \u003cp\u003eVariable selection followed a stepwise elimination procedure, with indicators showing standardized factor loadings\u0026thinsp;\u0026lt;\u0026thinsp;0.30 considered for removal. Model re-estimation ceased when the robust comparative fit index (CFI) exceeded 0.95 and further improvements in the Akaike (AIC) and Bayesian (BIC) information criteria plateaued. To avoid overfitting, correlated error terms were not estimated. Factor scores were computed from the final CFA model and used in subsequent SEM analyses.\u003c/p\u003e \u003cp\u003eBayesian structural equation modeling (BSEM) was applied to the factor scores to evaluate regression path models linking PitchV to MinTC. To account for between-participant variability, models with random intercepts and fixed slopes were first estimated, and predictive performance was compared across the four hypothetical models.\u003c/p\u003e \u003cp\u003eBecause multivariate normality was rejected in preliminary analyses (\u003cem\u003eHZ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.237, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001), BSEM posterior distributions were estimated assuming Student\u0026rsquo;s \u003cem\u003et\u003c/em\u003e distributions. No residual correlations were specified. Model comparison and selection were performed using Pareto-smoothed importance sampling leave-one-out cross-validation. Model convergence and adequacy were assessed using standard diagnostics: the Gelman\u0026ndash;Rubin statistic (R-hat)\u0026thinsp;\u0026lt;\u0026thinsp;1.01 and effective sample sizes (ESS)\u0026thinsp;\u0026ge;\u0026thinsp;400 for both bulk and tail estimates.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e2.6.4 Individual differences and stride length effect\u003c/h2\u003e \u003cp\u003eFor the model with the highest predictive accuracy, additional BSEM models including participant-specific random slopes were fitted to evaluate inter-individual variability (IIV) in standardized path coefficients (\u003cem\u003eβ\u003c/em\u003e). Three random slope models were tested:\u003c/p\u003e \u003cp\u003e \u003cb\u003eModel I\u003c/b\u003e, allowing IIV in input paths from PitchV to PO_Mus and PO_Kin;\u003c/p\u003e \u003cp\u003e \u003cb\u003eModel O\u003c/b\u003e, allowing IIV in output paths from selected latent factors to MinTC; and\u003c/p\u003e \u003cp\u003e \u003cb\u003eModel IO\u003c/b\u003e, allowing IIV in both input and output paths.\u003c/p\u003e \u003cp\u003eIIV in pathway sensitivity was assessed using the 95% confidence intervals (CIs) of between-participant standard deviations for the random slopes.\u003c/p\u003e \u003cp\u003eFinally, the effect of stride length (StrideL) was examined in the optimal random slope model. Because StrideL lies downstream of the causal pathway, including StrideL as a fixed covariate for MinTC could induce collider bias. Instead, an alternative model was specified in which StrideL variability was assumed to reflect push-off\u0026ndash;related mechanisms and to influence MinTC as part of the push-off causal pathway. Thus, paths from push-off\u0026ndash;related factors to StrideL were added, treating StrideL as an auxiliary outcome. Predictive accuracy was then compared between models with and without StrideL.\u003c/p\u003e \u003cp\u003eStatistical analyses were performed in R (v.4.3.1; R Foundation, Vienna, Austria). CFA and BSEM were performed using the \u0026ldquo;cfa\u0026rdquo; and \u0026ldquo;brms\u0026rdquo; packages, respectively.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Manipulation check\u003c/h2\u003e \u003cp\u003eFigure 4 compares %PitchV_max and %PitchV_five across walking conditions. Significant condition effects were found for both %PitchV_max (\u003cem\u003eF\u003c/em\u003e(2,46)\u0026thinsp;=\u0026thinsp;257.49, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e\u0026sup2; = 0.918) and %PitchV_five (\u003cem\u003eF\u003c/em\u003e(2,46)\u0026thinsp;=\u0026thinsp;269.93, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001, \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e\u0026sup2; = 0.921). Post hoc comparisons revealed significant differences across all condition pairs (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05/3).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Factor validity of observed variables\u003c/h2\u003e \u003cp\u003eStepwise CFA eliminated five observed variables (GM_Mn, GM_Pk, PF_Vel, PF_Acc, and KneeA) from the factor structure. AIC and BIC decreased with each step and plateaued at the sixth step. The resulting factor structure met model-fit criteria (robust CFI\u0026thinsp;=\u0026thinsp;0.971).\u003c/p\u003e \u003cp\u003eAll remaining observed variables exhibited factor loadings\u0026thinsp;\u0026gt;\u0026thinsp;0.80, which were all statistically significant (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.01). PO_Kin, defined by a single observed variable (PF_Ang), had its factor loading fixed at 1.0. The other three latent factors demonstrated high internal consistency and convergent validity: Cronbach\u0026rsquo;s \u003cem\u003eα\u003c/em\u003e and McDonald\u0026rsquo;s \u003cem\u003eω\u003c/em\u003e were 0.944 and 0.945 for PO_Mus, 0.947 and 0.949 for CPO_Mus, and 0.915 and 0.916 for CPO_Kin. The means and standard errors of factor loadings are summarized within the optimal SEM model (Fig.\u0026nbsp;6).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Path structural modeling\u003c/h2\u003e \u003cp\u003eAll four path-structure models with random intercepts and fixed slopes converged well, meeting the criteria of R-hat\u0026thinsp;\u0026lt;\u0026thinsp;1.01 and Bulk ESS/Tail ESS\u0026thinsp;\u0026ge;\u0026thinsp;400. Figure\u0026nbsp;5A compared models using the widely applicable information criterion (WAIC). Model 4 showed the highest predictive accuracy, followed by Model 3, 1, and 2, suggesting it as the provisional optimal model.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Individual differences\u003c/h2\u003e \u003cp\u003eFor Model 4, three random slope models (Model 4_I, 4_O, and 4_IO) were fitted, all converging well (R-hat\u0026thinsp;\u0026lt;\u0026thinsp;1.01; Bulk ESS/Tail ESS\u0026thinsp;\u0026ge;\u0026thinsp;400). Compared with the fixed slope Model 4, all random slope models improved predictive accuracy (Fig.\u0026nbsp;5B), with Model 4_IO performing best.\u003c/p\u003e \u003cp\u003eFigure 6 presents the means and 95% CIs of standardized path coefficients (\u003cem\u003eβ\u003c/em\u003e) for the best-performing Model 4_IO. The mean \u003cem\u003eβ\u003c/em\u003e values in the fixed slope Model 4 were 0.724 (PitchV \u0026rarr; PO_Mus), 0.575 (PitchV \u0026rarr; PO_Kin), 0.273 (PO_Mus \u0026rarr; PO_Kin), 0.620 (PO_Mus \u0026rarr; CPO_Mus), 0.856 (PO_Kin \u0026rarr; CPO_Kin), 0.169 (CPO_Mus \u0026rarr; CPO_Kin), 1.326 (CPO_Kin \u0026rarr; MinTC), and \u0026minus;\u0026thinsp;0.794 (PO_Kin \u0026rarr; MinTC). Corresponding values in Model 4_IO were similar, indicating minimal changes in average path strength.\u003c/p\u003e \u003cp\u003eThe 95% CIs of between-participant standard deviations for random slopes in Model 4_IO were 0.147\u0026ndash;0.300 (PitchV \u0026rarr; PO_Mus), 0.075\u0026ndash;0.180 (PitchV \u0026rarr; PO_Kin), 0.202\u0026ndash;0.422 (PO_Kin \u0026rarr; MinTC), and 0.151\u0026ndash;0.326 (CPO_Kin \u0026rarr; MinTC). All lower bounds exceeded zero, indicating that these path strengths were influenced by IIV.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e3.5. Effect of stride length\u003c/h2\u003e \u003cp\u003eFigure 7 presents the means and 95% CIs of standardized path coefficients (\u003cem\u003eβ\u003c/em\u003e) for the model including StrideL. Compared with Model 4_IO, predictive accuracy decreased markedly with StrideL (ΔELPD = \u0026minus;\u0026thinsp;1337.3\u0026thinsp;\u0026plusmn;\u0026thinsp;34.7). Mean \u003cem\u003eβ\u003c/em\u003e values remained comparable to those in Model 4_IO (Fig.\u0026nbsp;6).\u003c/p\u003e \u003cp\u003eThe minimal changes in path coefficients, despite the pronounced reduction in predictive accuracy, indicate that Model 4_IO without StrideL is robust and that StrideL adds little explanatory value beyond the push-off\u0026ndash;related latent factors.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThis study examined whether AFB based on peak foot pitch angular velocity (PitchV), derived from a single shoe-mounted IMU, can modulate push-off during walking and how push-off\u0026ndash;related kinematic changes are associated with MinTC. The results showed that PitchV-based AFB increased push-off output relative to normal walking and revealed a structured pattern of inter-phase associations linking late-stance kinematics to early-swing mechanisms related to MinTC.\u003c/p\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Immediate enhancement of push-off performance\u003c/h2\u003e \u003cp\u003eBy incorporating three walking conditions (Normal, Max, and AFB), the present design distinguished AFB-induced modulation of push-off from both baseline gait and voluntary maximal execution, clarifying that AFB enhances push-off within a submaximal, yet functionally relevant, operating range.\u003c/p\u003e \u003cp\u003ePitchV-based AFB immediately enhanced push-off\u0026ndash;related mechanical output by increasing ankle plantarflexor activity during late stance, particularly in the soleus. Because PitchV is closely associated with ankle plantarflexor power generation [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], these coordinated increases indicate a mechanically meaningful enhancement of push-off rather than a superficial alteration of gait pattern.\u003c/p\u003e \u003cp\u003eDuring normal walking, PitchV reached only 50%\u0026ndash;60% of the maximal value observed during maximal push-off walking, indicating substantial underutilization of available push-off capacity even in healthy young adults [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Such underutilization is considered an adaptive energy-saving strategy rather than a limitation of mechanical capacity [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. The present results extend this concept by showing that AFB can rapidly access this reserve, producing a 20%\u0026ndash;25% increase in push-off intensity.\u003c/p\u003e \u003cp\u003eThese observations are consistent with previous studies showing that VFB based on the ground reaction forces can immediately enhance push-off performance [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Importantly, the present approach achieves a comparable effect using a shoe-mounted IMU and AFB, eliminating the need for force plates or visual attention. From a clinical perspective, chronic underuse of push-off capacity may contribute to reduced lower limb muscle activation and increased fall risk with aging [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Although only immediate effects were examined, the ability to promote active use of push-off reserve capacity suggests potential value for early, preventive interventions aimed at preserving ankle function.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Integrated interpretation of direct and indirect pathways\u003c/h2\u003e \u003cp\u003eSEM clarified how push-off enhancement influenced MinTC through the interaction of direct and indirect pathways. Enhancement of push-off kinematics exerted a negative direct effect on MinTC, reflecting a transient lowering of the toe associated with increased plantarflexion during late stance. However, this effect was outweighed by a larger positive indirect effect mediated through early-swing kinematics, resulting in a net increase in toe clearance.\u003c/p\u003e \u003cp\u003eFrom a biomechanical perspective, push-off enhancement induces two sequential effects. First, increased ankle plantarflexion during late stance serves as the mechanical initiator of subsequent swing phase dynamics. This is followed by facilitated dorsiflexion during early swing, which elevates the foot trajectory. The dominance of the latter mechanism explains why overall MinTC increased despite the negative direct pathway. These findings demonstrate that the influence of push-off on toe clearance cannot be understood from late-stance mechanics alone, but must be interpreted within a phase-coupled framework spanning push-off and early swing.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e4.3. Biomechanical pathways supporting the push-off hypothesis\u003c/h2\u003e \u003cp\u003eBuilding on this phase-coupled interpretation, the present results provide biomechanical support for the push-off hypothesis by identifying two pathways linking enhanced push-off to MinTC. The first pathway involves increased forward propulsion during late stance, which facilitates swing initiation and contributes to elevation of the foot trajectory. This mechanism is consistent with previous research linking push-off intensity to swing leg dynamics and gait stability [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe second pathway, which emerged as the dominant mediator, involves a passive toe-lift mechanism initiated during late stance. Enhanced ankle plantarflexion stretches the antagonist tibialis anterior muscle\u0026ndash;tendon unit, storing elastic energy that is released during early swing [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. This elastic recoil enables rapid dorsiflexion immediately after toe-off, promoting toe lift and increasing MinTC [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. SEM strongly supported this mediating pathway, whereas the direct pathway from push-off kinematics to MinTC was negative.\u003c/p\u003e \u003cp\u003eAlthough stretch reflexes may contribute to early-swing dorsiflexion, prior work indicates that within the normal walking speed range (1.0\u0026ndash;1.3 m/s), elastic energy storage and recoil in the muscle\u0026ndash;tendon unit outweigh reflex-mediated contributions to ankle dorsiflexion [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Therefore, the present findings emphasize a predominantly mechanical interpretation, in which elastic energy storage and release play a central role. By demonstrating that enhanced push-off simultaneously induces opposing effects on toe trajectory, with early-swing dorsiflexion predominating, this study provides quantitative validation of the push-off hypothesis.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec23\" class=\"Section2\"\u003e \u003ch2\u003e4.4. Implications for gait intervention strategies\u003c/h2\u003e \u003cp\u003eThe identified causal structure was robust to IIV and independent of stride length, supporting its relevance for intervention design. Conventional gait interventions often emphasize increasing walking speed or step length [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]; however, when push-off capacity is reduced, such strategies may promote proximal compensations that are metabolically inefficient and potentially destabilizing [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn contrast, PitchV-based AFB selectively enhanced ankle push-off while walking speed was controlled, strengthening the mechanical basis of gait without causing speed-dependent trade-offs. By directly targeting push-off capacity, this approach may reduce reliance on proximal compensations, a possibility that should be examined directly in future studies. It may also limit unnecessary increases in metabolic cost and avoid increases in fall risk associated with faster walking [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. Thus, push-off\u0026ndash;focused feedback interventions represent a biomechanically efficient alternative to speed- or step-length\u0026ndash;based strategies.\u003c/p\u003e \u003cp\u003eFinally, the magnitude of the effects linking PitchV to late-stance plantarflexion and early-swing dorsiflexion to MinTC varied across individuals. This variability indicates that push-off\u0026ndash;focused feedback may benefit from individual tuning of feedback targets, rather than limiting its potential as a scalable intervention.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec24\" class=\"Section2\"\u003e \u003ch2\u003e4.5. Limitations and future directions\u003c/h2\u003e \u003cp\u003eSeveral limitations should be acknowledged. First, the study was conducted in healthy young adults to minimize age-related confounding effects. Age-related declines in muscle strength and joint flexibility may attenuate the identified mechanisms in older adults, and push-off reserve capacity itself may be reduced. Second, walking was performed on a treadmill with controlled speed; effects during overground walking in unconstrained environments require further investigation. Third, although the toe-lift mechanism was interpreted primarily as mechanical, more detailed neuromuscular analyses and musculoskeletal modeling are needed to dissociate passive elastic contributions from active control. Fourth, MinTC was used as a surrogate marker of fall risk, and prospective studies incorporating fall-related outcomes are required to establish real-world relevance. Finally, only immediate effects of AFB were examined; whether repeated exposure induces motor learning or long-term adaptations remains unknown. Longitudinal intervention studies are therefore required.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eThis study demonstrated that AFB based on peak foot pitch angular velocity (PitchV), derived from a single shoe-mounted IMU, can immediately enhance push-off during walking. SEM revealed that push-off\u0026ndash;related kinematic changes are organized across gait phases, with early-swing ankle dorsiflexion emerging as a key mediator associated with MinTC.\u003c/p\u003e \u003cp\u003eThese findings provide biomechanical support for the push-off hypothesis and suggest that modulation of push-off mechanics influences tripping-related gait characteristics without increasing walking speed or stride length. By requiring only a wearable IMU and simple AFB, the proposed approach shows promise as a practical and scalable strategy for future gait interventions, particularly in older adults.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cp\u003eIMU, inertial measurement unit\u003c/p\u003e\n\u003cp\u003eMinTC, minimum toe clearance\u003c/p\u003e\n\u003cp\u003eAFB, auditory feedback\u003c/p\u003e\n\u003cp\u003eEMG, electromyogram\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthical approval statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe study was approved by the Ethics Committee of Tokyo University of Agriculture and Technology (Approval No. 251106-0417, December 1st, 2025).\u003c/p\u003e\u003cp\u003e \u003ch2\u003eDeclaration of interest\u003c/h2\u003e \u003cp\u003eThe authors have no competing interests to declare that are relevant to the content of this article.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eData availability statement\u003c/h2\u003e \u003cp\u003eThe datasets used and/or analyzed in the present study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eWorld Health Organization, ed (2008) WHO global report on falls prevention in older age. 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J Am Geriatr Soc 59:1069\u0026ndash;1073. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1111/j.1532-5415.2011.03408.x\u003c/span\u003e\u003cspan address=\"10.1111/j.1532-5415.2011.03408.x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Tokyo University of Agriculture and Technology","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":"gait analysis, wearable sensors, biomechanics, fall prevention, structural equation modeling","lastPublishedDoi":"10.21203/rs.3.rs-8746981/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8746981/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cdiv id=\"ASec1\" class=\"AbstractSection\"\u003e \u003cdiv class=\"Heading\"\u003eBackground\u003c/div\u003e \u003cp\u003eReduced push-off during walking, particularly among older adults, compromises dynamic stability and increases tripping risk. Although push-off enhancement has been proposed as a target for fall prevention, the mechanisms linking increased push-off to minimum toe clearance (MinTC)\u0026mdash;a key determinant of tripping risk\u0026mdash;remain unclear, and practical interventions are limited. The objectives of this study were (1) elucidate the biomechanical pathways through which push-off enhancement is associated with changes in MinTC and (2) evaluate an inertial measurement unit (IMU)-based auditory feedback (AFB) approach for modulating push-off during walking.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"ASec2\" class=\"AbstractSection\"\u003e \u003cdiv class=\"Heading\"\u003eMethods\u003c/div\u003e \u003cp\u003eAn AFB system targeting push-off intensity by peak foot pitch angular velocity (PitchV) was developed using a single shoe-mounted IMU. Twenty-four young adults walked on a treadmill under normal walking, maximal push-off, and PitchV-based AFB conditions. Lower limb kinematics, electromyography, and MinTC were measured. Structural equation modeling (SEM) was used to examine phase-coupled causal pathways linking push-off\u0026ndash;related kinematic changes to MinTC, including the influence of stride length.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"ASec3\" class=\"AbstractSection\"\u003e \u003cdiv class=\"Heading\"\u003eResults\u003c/div\u003e \u003cp\u003ePitchV-based AFB increased push-off intensity relative to normal walking. SEM revealed two opposing effects of push-off on toe trajectory: a dominant positive indirect effect mediated by facilitated ankle dorsiflexion during early swing outweighing a smaller negative direct effect of late-stance ankle plantarflexion. This indirect pathway, consistent with a toe-lift mechanism, dominated the net association with MinTC. Importantly, the path coefficient linking PitchV to MinTC remained stable when stride length was included in the model.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"ASec4\" class=\"AbstractSection\"\u003e \u003cdiv class=\"Heading\"\u003eConclusion\u003c/div\u003e \u003cp\u003ePush-off enhancement is associated with improved toe clearance through coordinated cross-phase ankle plantarflexion\u0026ndash;dorsiflexion dynamics, providing mechanistic support for the \u003cem\u003epush-off hypothesis\u003c/em\u003e. The proposed IMU-based AFB offers a biomechanically targeted approach to gait modulation with potential relevance to reduce the risk of falls.\u003c/p\u003e \u003c/div\u003e","manuscriptTitle":"Biomechanical pathways linking push-off enhancement to toe clearance: Insights from a wearable auditory feedback system","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-03 11:57:36","doi":"10.21203/rs.3.rs-8746981/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":"0859eaae-fc04-4239-a48f-49264b45e5bb","owner":[],"postedDate":"February 3rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":62071802,"name":"Biomedical Engineering"},{"id":62071803,"name":"Physical Medicine \u0026 Rehab"}],"tags":[],"updatedAt":"2026-02-03T11:57:39+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-03 11:57:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8746981","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8746981","identity":"rs-8746981","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}