Introduction

The ageing process is accompanied by a gradual deterioration of sensorimotor, neurologic, and musculoskeletal systems, resulting in changes in motion patterns and diminished motor control1. These changes contribute to a progressive reduction in functional mobility, movement smoothness, and attention eventually impacting independence in later stages of life2. Emerging evidence indicates that subclinical declines in neuromuscular control begin as early as middle age, preceding overt mobility limitations by decades3. Addressing these issues earlier—particularly during middle age—may significantly mitigate the deterioration of motor skills and prevent mobility-related limitations in older adulthood4,5. Middle adulthood (40–65 years) represents a critical window for early intervention, as compensatory mechanisms remain intact while age-related sensorimotor changes first manifest3. Simple and effective exercises for middle-aged people may improve changes due to ageing, and even reduce risk of fall in elderly6.

Different physical activities has been proposed for the ageing individuals7. Functional and rhythmic training has been widely explored as a strategy to enhance functional mobility, and attention8,9. An exercise regimen incorporating both forward and reverse stepping is considered a simple and highly beneficial exercise modality for the ageing population10. Walking gait serves as a fundamental form of forward functional and rhythmic training. On the other hand, reverse gait (reverse walking or stepping) specifically can magnify locomotion differences missed by forward gait analysis 11,12,13. Combining the benefits of both forward and backward movements, step aerobics may offer a more cautious and controlled variation of walking gait on uneven surfaces14. Furthermore, unlike reverse stair climbing training, it minimizes the fall risk during the reverse phase of the stepping cycle. Therefore, previous investigations prescribed step aerobics for enhancing dynamic balance, musculoskeletal function, and attention in the ageing population10,15,16.

A key component of rhythmic step aerobics is movement synchronization with an external rhythm, often dictated by a metronome. The significance of prescribing rhythmic exercise is that it engages the trainee’s attention, and as the rhythm increases, the exercise becomes even more challenging17. The middle-aged population could be expected to execute a controlled and coordinated performance as an adaptive response to training, even with challenges in the reverse phase of the stepping and temporal constraints18,19. While previous studies have described the kinetic behaviour of the rhythmic step aerobics, the kinematic response to training remains underexplored20,21 .

Kinematics response measured by quantitative metrics may help optimize and personalize step aerobics training. Particularly, step height and rhythm determine step training intensity22. The rhythm influences the time of final or initial contacts, and the stance/swing phase time is adjusted accordingly. Here, a suitable metric for evaluating the training effect is the swing-to-stance time ratio, which previously was suggested as a measure to assess stability control strategy23. To measure this, there is a growing interest in collecting kinematic data using a single inertial measurement unit (IMU) placed on the sacrum to represent the centre of mass (COM) dynamics 24,25,26. Therefore, the COM motion pattern could represent the entire body motion pattern during step exercises, thus allowing the assessment of the effect of the rhythmic step aerobics training program on the core dynamics and coordination and synchronization with rhythmic constraints.

On the other hand, the controlled and coordinated movement could be reflected and evaluated by the smoothness of the movement. Movement smoothness evaluation offers insight into the response to the training program from the kinematics point of view. Smoothness evaluation is generally based on jerk assessment27.It has been proposed that optimum smoothness in movement is achieved by minimizing the jerk cost function 28,29,30. The smoothness of the core dynamics motion could also be assessed in three dimension to provide a more detailed examination of the kinematic response to the training. However, such smoothness metric is not currently being used for trainability evaluation in step aerobics.

The present study addressed a distinct gap by focusing on a personalized, cyclic step aerobics intervention that systematically integrates both forward and backward stepping in a controlled, alternating pattern. Unlike prior studies, which have largely examined simple, unidirectional walking or repetitive gait cycles, our protocol required participants to execute repeated backward steps interleaved with forward steps, under rhythmic constraints and with limited visual feedback. This design introduces a higher level of motor complexity and cognitive demand, more closely reflecting the real-world challenges of dynamic balance and fall prevention in middle-aged and older adults.

Given the scarcity of research in this area, an exploratory approach is warranted to generate initial insights and assess the feasibility of using kinematics metrics for evaluating neuromuscular adaptation. These measures are critical for understanding motor adaptations, as middle-aged individuals often exhibit increased movement caution, potentially leading to long-term mobility decline. Given that middle-aged women often face unique physiological and lifestyle-related barriers to maintaining physical activity, such as hormonal changes, musculoskeletal concerns, and time constraints due to caregiving roles, this study specifically targeted this demographic to investigate how rhythmic step aerobics can serve as an accessible and effective intervention for improving mobility and movement control31,32. The study (1) established how rhythmic constraints influence motor adaptation by assessing changes in the swing-to-stance time ratio over the course of training, (2) analysed movement smoothness through jerk cost evaluation in three dimensions to determine improvements in controlled motion, and (3) examined whether these kinematic metrics may serve as valid indicators of trainability, providing insights into kinematics adaptation and functional mobility improvements.

Materials and methods

A 24-session progressive rhythmic step aerobics program was conducted on middle-aged women. The middle-aged volunteers for this study were selected based on their responses to a physical activity readiness questionnaire (PARQ). Any physical or neurological issues that could prevent participation in physical activity served as the exclusion criteria. Eleven middle-aged women (average age: 52.9 ± 4.77 yrs, average body mass: 67.85 ± 11.73 kg, and average height: 1.63 ± 0.05 m) were requested to complete the PARQ as the inclusion criteria, to assess potential health risks, including musculoskeletal, neurological, respiratory, blood pressure, and cardiac arrhythmia. Their medical practitioners prohibited none of the volunteers from engaging in physical activities. Moreover, the volunteers should not have had any prior experience in conducting rhythmic training.

Based on the inclusion criteria, nine individuals (using Cohen’s criteria, α = 0.1, and effect size = 0.8) were selected for the intervention (average age: 53.38 ± 5.26 yrs, average body mass: 64.56 ± 10.61 kg, average height: 1.62 ± 0.04 m)33consistent with recommendations for pilot studies in biomechanics and clinical research34,35. Simon’s two-stage design for pilot studies was considered additionally36. This approach provides 80% probability of detecting clinically meaningful effects (≥ 30% improvement) while allowing for 20% attrition - parameters appropriate for exploratory biomechanical investigations. Recruitment focused on middle-aged women without prior rhythmic training experience – a population with limited availability during COVID pandemic.

Due to limited accessibility to volunteers during the COVID-19 pandemic, participant recruitment was challenging. Several factors contributed to reduced participant availability during our study period, including lockdown restrictions, health concerns, and limited access to research facilities. Multiple pilot studies conducted during the pandemic faced similar recruitment challenges and adopted comparable sample sizes as a practical necessity34,35. To minimize confounding factors and ensure that observed changes were attributable to the intervention, participants were instructed to report their daily routines, any illness episodes, and to refrain from engaging in other high-intensity physical activities throughout the study period. Additionally, sleep records were monitored to control for potential effects of rest on performance. By systematically monitoring these lifestyle factors, we aimed to attribute pre- to post-test changes primarily to the SAT intervention.

Prior to the first testing session, a familiarization set was conducted to acquaint the volunteers with the testing procedures and the metronome beats. Participants were instructed to obtain at least eight hours of sleep the night before the experiment. To minimize the effects of fatigue, they completed a questionnaire detailing their activities over the preceding 48 h. Additionally, all participants were asked to consume a light breakfast (such as eggs and bread) on the morning of the test.

The purpose of the study and the testing protocols were fully explained to each participant. The written informed consent was obtained from all participants. The SSRI ethics committee of the Sports Sciences Research Institute approved the experiments, the approval ID was IR.SSRC.REC.1400.049. All the experiments methods were carried out in accordance with relevant SSRI ethics committee guidelines and regulations.

The exercise program comprised a 30-minute aerobic session with warm-up (dynamic stretch for five minutes plus 3 min of step aerobics), stepping exercises (four sets of four-minute stepping), active recovery, and cool-down (static stretch). Dynamic stretch consisted of full body dynamic stretch from standing, standing forward bend, side stretch, 180-degree upper body twist, and dynamic calf stretch (lunge position). Each movement was performed continuously and rhythmically for 30 s, ensuring dynamic activation and preparation of the major muscle groups for the main exercise session. Static stretch included full body overhead stretch, side stretch, upper body twist, calf stretch (lunge position), lunge stretch. Each stretch was performed in a controlled manner for ten seconds to promote flexibility and relaxation after exercise.Stepping rhythm, regulated by a metronome, maintained intensity between low and moderate levels (= 40–59% \(\:V{O}_{2,\:max}\)) using (1)22. The calculated rhythm for middle-aged females was approximately 80 ± 10 steps per minute at a fixed step height of 90 mm, which was adjustable based on the physical readiness of the individuals during the first session. The exercise program was developed in collaboration with sports scientists qualified by the National Federation of Fitness and had a history of training planning for national teams and clinical situations.

$$\:{VO}_{2}=0.2\times\:rhythm\left(\text{s}\text{t}\text{e}\text{p}/min\right)+1.33\times\:\left(1.8\times\:step\:height(m\right)\times\:rhythm\left(\text{s}\text{t}\text{e}\text{p}/min\right)$$
(1)

The stepping rhythm gradually intensified over 24 sessions, ultimately increasing to 115 ± 5 steps per minute. Data on stepping were obtained during the first, twelfth, and twenty-fourth sessions with the guidance of a personal trainer. The program aimed at thrice-weekly home sessions to enhance fitness and health.

A single IMU was fixed on the skin using double-sided adhesive tape on the Sacrum (S1 vertebrae). The sacrum represented the centre of mass (COM) since it is aligned to the vertical midline of the body, and it records the core’s dynamic information25,26,37. Single IMU solutions achieve 80–90% of multi-sensor accuracy while enabling home-based assessments38. Although a multi-sensor approach could capture compensatory movements of the upper limbs and trunk, it also increases participant burden and may constrain natural movement. Figure 1 depicts the recurring stepping cycle (forward-ascending and backward-descending steps). LPMS-B2 AHRS system (Life Performance Measurement Systems, Tokyo, Japan), integrating accelerometer, gyroscope, and magnetometer sensors, transmitted data wirelessly to a computer using Bluetooth and received and stored data via OpenMAT 1.3.5 software. The sensor was designed with a static accuracy of below 0.5°, a dynamic accuracy under 2° root mean squared, and a dynamic precision of ± 0.1°39,40. It operated at a sampling rate of 100 Hz. The accompanying software provided offset correction and misalignment calibration for both the gyroscope and accelerometer41. To ensure precise navigation and measurement control, a rapid calibration process was implemented, utilizing an ellipsoidal fitting technique that combines soft and hard iron compensation, aligned with the measurement principles of the three-axis magnetic sensor42.

Fig. 1
figure 1

Illustration of the repetitive stepping cycle during a step aerobics training set, showing the progression of each step, including the forward and backward movements. The percentages represent the relative duration of each phase in the stepping cycle.

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Prior studies demonstrated that calibrated AHRS systems achieved < 2° RMSE in orientation tracking compared to Vicon for low-acceleration movements, making them suitable for COM kinematics in controlled environments43,44. While direct Vicon comparison would strengthen validation, the evidence from prior construct validation with the same SAT regimen support the current study40. While no gold-standard (e.g., Vicon) validation was possible during the pandemic, the task was designed in collaboration with clinical/sports experts, lending face and ecological validity.

To assess measurement reliability of the IMU across repeated testing sessions, test-retest reliability was assessed using intraclass correlation coefficient (ICC), and coefficient of variation (CV%). Specifically, the ICC (2,1) model, which is appropriate for absolute agreement in test-retest designs. Based on established guidelines, ICC values between 0.5 and 0.75 indicate moderate reliability, which is considered acceptable for early-phase, exploratory studies45. The CV% of jerk cost and stance-swing ratio was computed to assess variability, with values below 10% suggesting measurement consistency45.

Data analysis

Data analysis was divided into two sections: preprocessing and processing. Preprocessing involved filtering and detrending, event detection, rotation, and differentiation for jerk estimation.

Filtering reduced instrumentation noise using a second-order zero-lag Butterworth filter with a 10 Hz cutoff frequency filters acceleration data across all axes46. Non-stationarity was exhibited in the collected data, likely due to instrumentation noise47. Therefore, a nonlinear detrending technique was applied to ensure the stationarity of the data. Stationarity of residual detrended and dedrifted data was verified using the Augmented Dicky-Fuller (ADF) test (p-value < 0.05).

Event detection involved identifying three events: final contact (FC), initial contact (IC), and the first forward step. The continuous wavelet transform (CWT), a time-frequency transform, applied on the z-axis acceleration, determined IC and FC timings. Equation (2) represents the mathematical description of (CWT), denoted as T(a, b), on the given signal x(t)22.

$$\:T\left(a,b\right)=1/\sqrt{a}{\int\:}_{-{\infty\:}}^{+{\infty\:}}x\left(t\right){\psi\:}^{\text{*}}\left(t-b/a\right)dt=1/2\pi\:{\int\:}_{-{\infty\:}}^{{\infty\:}}\widehat{x}\left(\omega\:\right){\widehat{\psi\:}}_{a,b}^{\text{*}}\left(\omega\:\right)d\omega\:$$
(2)

Where, \(\:{\widehat{\psi\:}}_{a,b}^{*}\left(\omega\:\right)=\sqrt{a}{\widehat{\psi\:}}^{*}\left(a\omega\:\right){e}^{i\omega\:b}\) refers to the function of the mother wavelet. The wavelet transform is denoted by T(a, b), where a represents the wavelet scaling factor and b represents the localized time index. The symbol (*) denotes the complex conjugate. The scaling factor and the stepping frequency has an inverse correlation. Equation (3) determines the optimal scale for (CWT) analysis based on stepping frequency.

$$\:a\times\:{F}_{a}={F}_{c}/\varDelta\:$$
(3)

Where a represents scaling factor, \(\:{F}_{a}\) represents metronome-guided stepping frequency, \(\:{F}_{c}\) represents the mother wavelet’s central frequency, and \(\:\varDelta\:\) represents the sampling period. The sampling frequency of the IMU was 100 Hz, and the stepping frequency, dictated by the metronome, varied between 1.33 Hz and 2.16 Hz, corresponding to rhythms of 80 and 130 steps per minute, respectively, throughout the training period.

The initial contact (IC) and the final contact (FC) timings were determined using the data obtained after the first Gaussian continuous wavelet (CWT). The minima in this signal indicated the timing of the initial contact and the maxima indicated final contacts. This method was originally proposed and validated by McCamley et al. for detection movement events from the waist-mounted IMUs48. The original Gaussian wavelet approach by, which yielded initial contact (IC) and final contact (FC) root mean square errors (RMSE) of 0.02s and 0.03s respectively in healthy subjects, and 0.18s IC RMSE in more complex conditions with moderate phase distortion48. The Gaussian mother wavelet was selected for its superior time localization in detecting step transitions. The scale parameter a was tuned to match the metronome-guided stepping frequency, ensuring optimal alignment between wavelet oscillations and stepping rhythm49.

Rotation aligned sensor data with a global coordinate system using quaternion vectors. X and Y of the global frame were in the transverse plane, and the vertical direction aligned with the anatomical vertical axis. Equation (4) describes the rotating process using quaternion vectors50.

$$\:{R}_{q}\left(a\right)=q\otimes a \otimes{q}^{\text{*}}$$
(4)

In (4), \(\:{R}_{q}\) denotes the rotating operator in terms of quaternion vector, which was applied to filtered and detrended acceleration vector (\(\:a=\left[\begin{array}{ccc}{a}_{x}&\:{a}_{y}&\:{a}_{z}\end{array}\right]\)). The quarternion vector represented as \(\:q=\left[\begin{array}{cc}\begin{array}{cc}{q}_{1}&\:{q}_{2}\end{array}&\:\begin{array}{cc}{q}_{3}&\:{q}_{4}\end{array}\end{array}\right]\) was used to determine the axis and angle of rotation. \(\:{q}^{*}\) indicates the conjugate of q. The operator\(\:⨂\) denotes the quaternion multiplication. Differentiation yielded jerk data, further filtered with a 10 Hz Butterworth filter46.

In the processing stage, the durations of both the swing and stance phases for each step were computed separately. The time ratio was calculated by dividing the duration of the stance phase (measured in seconds) by the duration of the swing phase (also measured in seconds). The ratio was distributed normally throughout the four-minute stepping based on Shapiro-wilk test results (p-value < 0.05). To assess temporal adaptation in detail, a step-separated repeated measures ANOVA was conducted for the stance-to-swing time ratio. Where a significant main effect of session was found, Bonferroni-adjusted post-hoc comparisons were performed to identify which sessions differed. This stepwise approach allowed us to capture unique adaptation patterns for each step, particularly distinguishing between forward and backward phases.

Furthermore a hierarchical clustering model using ward linkage was deployed to cluster the steps based on the session to highlight the differences51. Hierarchical clustering (Ward’s method) was chosen over alternative clustering approaches due to its ability to segment movement patterns without predefined clusters, making it particularly suitable for tracking neuromuscular adaptations over time. Unlike k-means, which assumes spherical clusters, hierarchical clustering allows progressive step segmentation, capturing the temporal nature of motor adaptations52. This approach does not involve predictive modeling or classification, but rather provides a visual and quantitative means to group similar movement patterns across training sessions, supporting the interpretation of adaptation trends.

The jerk cost function was employed to evaluate smoothness. This function quantified the level of smoothness exhibited by the COM trajectory throughout each step. Smoothness was assessed using the jerk cost function in (5)19,27,29,30,53,54.

$$\:JC={\int\:}_{{t}_{FC}}^{{t}_{IC}}{\left(j\right)}^{2}dt\:$$
(5)

Equation (5) defines the jerk cost function (JC). This equation represents the time of final contact (\(\:{t}_{FC}\)) and the time of initial contact (\(\:{t}_{IC}\)), where j is the COM jerk vector. The jerk cost value of each step was distributed normally on each set based on Shapiro-wilk test results (p-value < 0.05).

First, the two-dimensional jerk costs in the frontal, sagittal, and transverse planes aligned with the anatomical frame were determined. The smoothness evaluations were conducted for the first, twelfth, and twenty-fourth sessions to investigate the training response. The effectiveness of the training program on this value was assessed using a step-separated repeated measures ANOVA. Where a significant main effect of session was found, Bonferroni-adjusted post-hoc comparisons were performed to identify which sessions differed. A hierarchical clustering using ward linkage method was also applied to group the smoothness levels as a response to the training55.

Given the exploratory nature and small sample size of this pilot study, a dual analytic strategy was employed. First, parametric methods (ANOVA, linear mixed models) were used to facilitate comparison with previous kinematic studies and to explore potential patterns in the data. However, recognizing the limited statistical power and increased risk of Type I (false positive) and Type II (false negative) errors in small samples, these analyses were supplemented with Bayesian estimation, which is robust for small-sample inference56,57.

For all outcome variables (stance-to-swing time ratio and jerk cost in frontal, saggital and transverse planes, and three-dimensional), homogeneity of variance was assessed using Levene’s test, with p > 0.1 indicating that the assumption was met. Bayesian estimation was performed using weakly informative priors for group means and standard deviations, with posterior distributions of mean differences and 95% credible intervals computed via Markov Chain Monte Carlo sampling58. This approach provides direct probability statements about the likelihood of observed effects and is increasingly recommended for pilot studies and small samples59. All findings are interpreted as exploratory and hypothesis-generating, with emphasis on effect size and credible intervals rather than p-values59.

To assess the robustness of the temporal and smoothness metrics to signal processing parameters, a local sensitivity analysis was performed. For the wavelet-based event detection, the timing of final contact (FC) was recalculated after perturbing the wavelet scale parameter by ± 10% around its nominal value. The sensitivity was quantified as the change in detected FC timing per unit change in scale. For movement smoothness, jerk cost was recalculated after varying the filter cutoff frequency (± 1 Hz from nominal 10 Hz), and the sensitivity was computed as the change in jerk cost per Hz.

Linear mixed-effects models were used to analyse changes across sessions while accounting for within-subject correlations in our repeated measures design. Given the small sample size, linear mixed-effects model was not used for confirmatory inference but rather to support descriptive analysis and hypothesis generation. This approach aligns with current recommendations for pilot studies, where multilevel modeling can help characterize variance components and guide future research design60. Models included session as a fixed effect and subject-specific random intercepts to capture individual variability60,61:

$${y_{ij}}={\beta _0}+{\beta _1}Sessio{n_{ij}}+{u_{0j}}+{\varepsilon _{ij}}$$
(6)

Where \({y_{ij}}\) represents the outcome measure (stance-to-swing time ratio or jerk cost) for subject j ate session i, \({\beta _0}\)is the fixed intercept, \({\beta _1}\)represents the fixed effect of session, \({u_{0j}}\)is the subject-specific random intercept capturing baseline individual differences, and \({\varepsilon _{ij}}\)is the observational-level residual error. Models were fit using restricted maximum likelihood estimation, and significance was assessed using F-tests with Satterthwaite approximation. Intraclass correlation coefficients quantified between-subject variance proportions. Post-hoc comparisons used Bonferroni-adjusted p-values, with effect sizes reported as Cohen’s d and partial η-squared60,61.

Results

Consistency and reliability of measurements are crucial in analyzing biomechanical variables over multiple sessions. In this exploratory pilot study, the stance-to-swing time ratio and jerk cost both exhibited moderate reliability (ICC = 0.5), with CVs of 10% and 23%, respectively. According to published guidelines, these ICC values indicate moderate reliability45. This level of reliability is common in pilot studies with small, homogeneous samples and is sufficient for generating hypotheses and informing methodological improvements for subsequent research. The observed variability, particularly in jerk cost, likely reflects both individual adaptation differences and the inherent measurement noise expected in early-phase studies.

A 3D plot of the first Gaussian CWT coefficients at different scales throughout time is shown in Fig. (2). The step’s initial and final contacts (IC and FC) are shown regardless of direction.

Fig. 2
figure 2

Continuous Wavelet Transform (CWT) coefficients at different scales over 5 s of stepping. The A represents the scale at which the forward and backward phases were interchanged. The B represents the scales at which the initial contacts occurred. The timing of initial and final contacts based on the CWT results was distinguished on the acceleration plot.

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Levene’s test indicated no significant difference in variances across sessions for both stance-to-swing time ratio and jerk cost in any plane (all p > 0.1), supporting the validity of parametric and Bayesian analyses. Given the exploratory pilot design, Bayesian estimation supplemented frequentist analyses to quantify uncertainty. All findings were interpreted as preliminary, with emphasis on effect sizes and credible intervals over statistical significance.

Bayesian estimation revealed that the most pronounced adaptations occurred during the third step (the first backward step). For this step, the jerk cost showed substantial reductions in both the sagittal plane (posterior mean: − 89.3, 95% credible interval: [–238.5, + 58.3]) and in three-dimensional analysis (posterior mean: − 95.1, 95% CI: [–243.9, + 55.2]), indicating a trend toward improved movement smoothness, although the credible intervals included zero, reflecting uncertainty due to the small sample size. For the first step (forward), the jerk cost also decreased across all planes, with the largest reduction observed in the sagittal plane (–189.1, 95% CI: [–338.9, − 47.8]) and in 3D (–201.3, 95% CI: [–350.2, − 55.7]), where the credible intervals did not include zero, suggesting more robust evidence for improved smoothness in these directions. In contrast, the second and fourth steps exhibited smaller or more uncertain changes, with all 95% credible intervals overlapping zero. The stance-to-swing time ratio increased slightly for all steps, but only the first step showed a credible interval that did not include zero (+ 0.18, 95% CI: [+ 0.01, + 0.32]). Overall, these Bayesian analysis results support the interpretation that the most consistent and meaningful kinematic adaptations were observed in the backward stepping phase, particularly for jerk cost and time ratio metrics, while changes in other steps and planes were less definitive.

Figure (3a) shows each step’s stance-to-swing phase time ratio in the first set of test sessions. The first set rhythm was constant across all the sessions. Results in Fig. (3a) and repeated measures ANOVA revealed a significant session effect for the third step (first step backward) (F(2,14) = 6.05, p = 0.008, η²=0.45). Post-hoc comparisons showed 0.62 mean difference between the first and twelfth sessions (95% CI: 0.18–1.06, p = 0.009, d = 1.21), 0.58 mean difference between twelfth and twenty-fourth sessions (95% CI: 0.14–1.02, p = 0.013, d = 1.09), and 1.20 mean difference between the first and the twenty-fourth sessions (95% CI: 0.76–1.64, p = 0.001, d = 2.30). Non-significant session effects were found for the two forward steps and the second backward step (fourth step). These results highlight that temporal adaptations to rhythmic step aerobics were most pronounced during the backward phase of the stepping cycle.

Fig. 3
figure 3

(a) Stance to swing time ratio in the first, twelfth and twenty-fourth sessions. (b) Represent the hierarchical clustering of steps based on the sessions.

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The jerk cost function evaluated the smoothness of COM movement during one set of test sessions. The findings are displayed in Fig. (4). The circle radius represents the measured smoothness level at a constant rhythm. The top row shows frontal, sagittal, and transverse two-dimensional data. The repeated ANOVA measure with post-hoc analysis was conducted to examine the effect of training on the smoothness of performance from the first to the twenty-fourth session (Table 1).

Fig. 4
figure 4

The resultant jerk cost in frontal, sagittal, and transverse planes. The radius of the circles corresponds to the jerk cost value, the horizontal axis is the testing sessions, and the vertical axis is the separated steps of the cycle.

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Table 1 Jerk cost results across steps and planes and three-dimensional analysis(First, S1, Twelfth, S12, and Twenty-Fourth, S24, Sessions), η²: Partial eta squared (effect size for ANOVA), Cohen’s d: Effect size for pairwise comparisons (|d| > 0.8 = large), p-adj: Bonferroni-adjusted p-value.
Full size table

Table 1 summarizes movement efficiency improvements across the sagittal (XZ), transverse (XY), frontal (YZ) planes, and three-dimensional space. Jerk cost analysis across all steps and planes revealed that the most pronounced and statistically robust adaptation occurred in the third step (first backward step) in three-dimensional (3D) analysis, with a significant reduction in jerk cost from the first to the twenty-fourth session (F(2,14) = 4.68, p = 0.028, d = 1.13). This finding was mirrored in the sagittal plane for the same step, which also showed a significant reduction (F(2,14) = 5.06, p = 0.022, d = 1.14). In contrast, the other steps did not exhibit statistically significant improvements in jerk cost in 3D or any plane. For the first step (forward), results were marginal, particularly in the frontal (F(2,14) = 3.38, p = 0.063, d = 1.27, p-adj = 0.042) and 3D (F(2,14) = 3.92, p = 0.044, d = 1.36, p-adj = 0.042) analyses, but these should be interpreted with caution given the borderline p-values and the multiple comparisons performed. For the third step, only the sagittal plane showed a significant result among the 2D analyses, while the frontal and transverse planes did not reach statistical significance despite large effect sizes in some cases. No significant changes were observed in the second and fourth steps across any planes or in 3D.

To further analyse adaptation patterns, hierarchical clustering was applied to stance-to-swing ratio and smoothness data. Figure (3b) represents the results of the clustering method, along with the proximity and threshold dendrograms. The hierarchical clustering evaluation yielded a Silhouette Score of 0.403, indicating moderate cluster separation with some overlap. The Davies-Bouldin Index of 0.671 suggest well-separated clusters with good cohesion, while the Calinski-Harabasz Index of 11.113 reflects moderately well-formed clusters. These results indicate that the clustering provided tentative evidence of progressive adaptation patterns. The external validation metrics for the temporal metrics (Rand Index = 0.727, Adjusted Rand Index = 0.421, Normalized Mutual Information = 0.667) indicate moderate agreement between the hierarchical clustering results and the true session labels.

The clustering algorithm divided the steps in a way that distinguished the differences between forward and backward movements. In the second level, the clustering algorithm grouped the 12th and 24th sessions separately from the first session, reinforcing the notion that adaptation occurred progressively over time.

Figure (5) illustrates the clustering results for jerk cost values, showing data grouped into four distinguishable clusters. The circles represent smoothness, where a larger radius indicates more jerky movement and less smoothness, while smaller circles represent smoother movements. The clustering highlights variations in jerk cost across sessions, demonstrating the training program’s impact on reducing jerkiness and improving movement smoothness over time.

The hierarchical clustering approach applied on smoothness data in 3D space was evaluated using the Silhouette Score (0.26), Davies-Bouldin Index (0.99), and Calinski-Harabasz Index (38.33). The silhouette score indicates moderate clustering quality, with some overlap between clusters. The Davies-Bouldin Index suggests reasonable separation, though improvement is possible. The Calinski-Harabasz Index reflects moderately well-formed clusters. Overall, the clustering method provides a fair segmentation of the data. The hierarchical clustering analysis yielded a Rand Score of 0.684, an Adjusted Rand Score of 0.281, and a Normalized Mutual Information of 0.350. These values indicate moderate raw agreement but limited meaningful correspondence between the clustering results and the true session labels.

Perturbing the wavelet scale parameter by ± 10% resulted in a mean change of 6.2 ms in the detected final contact times, corresponding to a local sensitivity of 0.62 ms/% scale change. The maximum observed timing shift across all steps was 12 milliseconds. For jerk cost, increasing the filter cutoff frequency by 1 Hz led to a mean decrease of 13.5 jerk units (g²/s³), yielding a sensitivity of − 13.5 jerk units/Hz. These results indicate that both temporal event detection and smoothness metrics are modestly sensitive to their respective processing parameters.

The Linear Mixed-Effect Modelling analysis revealed several key insights regarding the temporal adaptation and smoothness metrics. In temporal adaptation (stance-to-swing time ratio) a significant increase was observed in the ratio for the third step (first step backward) across all sessions (p-value = 0.001). For the first and second forward steps and the fourth step (second backward step non-significant changes were observed. Between-subject variance accounted for 38.6% of the total variance, indicating moderate individual differences.

Relative to the smoothness metric, the linear mixed-effect model showed a significant reduction in the jerk cost values across all planes for the third step (first step backward), with largest effects in sagittal plane (β=-176.7, p = 0.001) and three-dimensional results (β=-219.8, p = 0.001). Non-significant changes were observed across all planed in the second forward and backward steps. ICC values between 0.42 and 0.51 indicated moderate-to-substantial between-subject variability.

Discussion

As an exploratory pilot study, our primary aim was to assess the feasibility and preliminary reliability of using IMU-derived kinematic metrics to track neuromuscular adaptation during step aerobics in middle-aged women. The problem addressed in this study was the lack of research on kinematic adaptations resulting from rhythmic step aerobics, particularly in backward stepping, despite its potential to improve mobility and stability. This gap is critical because backward stepping may be more sensitive to age-related declines and poses unique challenges requiring greater neuromuscular control.

The application of both parametric and Bayesian statistics in this pilot study is justified by recent literature advocating for robust, transparent reporting in small-sample research57,59. While parametric methods (ANOVA, LMM) are standard for kinematic research and facilitate comparison with prior work, Bayesian estimation was prioritized to address the increased risk of Type I and II errors, as it provides more reliable inference in small samples by incorporating prior information and directly quantifying uncertainty. Importantly, wide credible intervals—particularly those that include zero—should not be misinterpreted as evidence of no effect. Instead, they reflect the inherent uncertainty of small-sample exploratory studies. In this context, Bayesian estimation offers a more nuanced interpretation than binary significance testing by quantifying the degree of uncertainty.

The moderate ICC values observed (0.5 for both jerk cost and stance-to-swing ratio) are consistent with those reported in similar pilot and exploratory biomechanics studies, where small sample sizes and homogeneous cohorts often yield moderate reliability estimates45. While these values limit the strength of longitudinal conclusions at the individual level, they are sufficient for group-level trend analysis and for refining the methodology for future, larger-scale longitudinal studies. As recommended in the literature, ICC values in the moderate range should be interpreted with caution and primarily serve to guide further research and protocol optimization45.

Jerk-based smoothness measures are sensitive to movement amplitude, duration, and the presence of hesitations, making them particularly responsive to even minor variations in motor performance62. While CV values below 10% are often considered indicative of good measurement precision in controlled laboratory settings, greater variability (CV > 10%) is expected when evaluating movement smoothness during dynamic, attention-demanding tasks in field studies or home environments. IMU-based assessments conducted in field studies, real-world settings tend to yield greater coefficients of variation compared to laboratory-based measurements, reflecting the increased variability inherent in natural movement contexts63. The field study approach better captures authentic movement behavior and adaptation outside the laboratory.

The findings suggest that rhythmic step aerobics may be associated with adaptations in stepping patterns, particularly in backward stepping (based on three-dimensional results). Participants tended to increase the stance phase duration, which could reflect an attempt to enhance stability in the absence of visual feedback. Additionally, smoothness improvements were most pronounced in the sagittal and transverse planes, which may point toward potential enhancement in neuromuscular coordination. The marginal findings underscore the importance of attending closely to methodological details and sources of variability in field-based studies.

Rhythmic step aerobics requires synchronization with an external rhythm, compelling participants to adjust their stance and swing phase durations to align with tempo variations. The rhythm dictated the time interval between the final contacts of each step. The individuals tried to synchronize their steps with this rhythm by adjusting the swing and stance time intervals. The adopted metric to assess these adjustments was the stance-to-swing time ratio. Figure 3b not only differentiates the forward from the backward movements in the first level but also potentially reflecting the effect of training in the second level by grouping 12th and 24th sessions separately from the first session. While these results suggest that the clustering captures aspects of temporal adaptation, the moderate agreement and clustering metrics indicate that these findings should be interpreted as preliminary and exploratory. The clustering assignments were compared to the true session labels, yielding moderate agreement.

On the other hand, Fig. 3a indicates that the stance-to-swing time ratio appeared relatively stable in forward phases across sessions, consistent with prior observations of overlearned forward motion patterns in adults. In contrast, the ratio tended to increase in backward phases, potentially reflecting a strategy to prolong stance duration for stability—a trend aligned with age-related compensatory mechanisms observed in reverse gait studies.

The findings of this exploratory study appear to be consistent with prior research highlighting the potential and significance of reverse walking in improving balance and stability in aging individuals. Studies show that backward walking is more sensitive to age-related mobility decline than forward walking, with older adults exhibiting greater deficits in velocity and stride length​11. These deficits make transitions to backward movement particularly challenging64,65. Additionally, maintaining gait velocity and stride length during backward walking presents greater difficulties for elderly individuals compared to younger adults64. In the present study, the observed tendency for increased stance phase duration during reverse stepping provides a stabilizing effect, aligning with research indicating that slower tempos in stepping tests require prolonged one-leg support times, particularly in older adults​23. However, further research with larger and more diverse cohorts is needed to confirm these trends and clarify their broader relevance.

Smoothness analysis, assessed via jerk cost evaluation, provided exploratory insights into potential motor adaptation patterns. The results suggested that participants demonstrated significant reductions in jerk cost, particularly in the backward steps (specifically in the sagittal plane and three-dimensional results). These trends appear generally consistent with the minimum jerk theory, which proposes that the central nervous system (CNS) might organize movement to reduce abrupt acceleration changes, potentially contributing smoother motion. Previous studies indicate that voluntary movements tend to minimize jerk, a pattern that seems broadly aligned with the smoothness trends observed in both forward and backward movements in this study66,67​.

Additionally, the CNS appears to prioritize the leading step in the backward step, reinforcing earlier models of motor control that emphasize stability during the initial movement phase. Research suggests that smoothness and stability serve as key metrics for movement organization, particularly in repetitive activities like walking and step aerobics, supporting the importance of core stability in maintaining efficient locomotion​66,67. It is worthy to mention that the observed reductions in jerk cost, while directionally meaningful, had wide credible intervals (e.g., sagittal plane: −189.1 [− 338.9, − 47.8]), highlighting substantial uncertainty inherent to pilot-scale biomechanical studies.

Figure (5) suggest tentative distinctions between the forward and backward movement in the first session. It clusters the smoothness of the first and third steps into two groups, which may indicate the effect of training on the smoothness evaluation (the moderate silhouette score (0.26) and overlap in cluster boundaries requires caution against overinterpretation). Walking and running are daily overlearned motion patterns, as is the step aerobics cycle’s forward phase54. The smoothness of these forward motion patterns reaches its optimum level in adulthood, and there are few variations in the executed smoothness during this stage of life.

Limited visual feedback from surroundings and aligning with gravity could result in the exhibition of a less smooth and more jerky movement in the fourth step. Unlike the third step, consistent effectiveness in terms of smoothness was not sustained throughout the fourth step. The results suggest that the CNS may not have focused as significantly on the smoothness of the COM movement during the fourth step.

Fig. 5
figure 5

Hierarchical clustering of jerk cost values across sessions. Data is grouped into four clusters, with different shades representing each. Larger circles indicate higher jerk cost (less smooth movement), while smaller circles indicate smoother movement. The clustering highlights variations across sessions demonstrating the training program’s effect on improving movement smoothness.

Full size image

Jerk cost and smoothness findings suggest that extended participation in the program could enhance movement efficiency, particularly in backward steps. The limited adaptation observed in forward steps could be related to their lower complexity in motor control adjustments, as participants were already accustomed to this motion pattern. While the observed trends appear to align with the minimum jerk theory—suggesting that participants may have refined their movement patterns over time to minimize abrupt acceleration changes, especially in backward stepping where increased motor control is required due to reduced visual feedback—these interpretations remain preliminary.

To further examine neuromuscular adaptation patterns, hierarchical clustering (Ward’s method) was applied to smoothness and stance-to-swing ratio data. The clustering analysis revealed distinct changes in movement execution over time, grouping early training sessions separately from later ones. Hierarchical clustering (Ward’s method) was chosen due to its ability to segment movement patterns without predefined clusters. Unlike k-means, which assumes spherical clusters, hierarchical clustering allows progressive step segmentation, making it more suitable for tracking neuromuscular adaptations​55. DBSCAN, though effective for density-based clustering, requires volunteer-specific tuning, making it less generalizable​55. Gaussian Mixture Models, while offering probabilistic clustering, rely on predefined distributions, limiting adaptability to movement variations​55. Ward’s method minimizes within-cluster variance, ensuring well-separated, compact clusters, enhancing interpretation​55. Given its ability to detect progressive changes and provide interpretable outputs, hierarchical clustering is a powerful tool for biomechanical analysis55​.

The moderate silhouette scores obtained (0.403) align with similar biomechanical studies and reflect the inherent variability of human movement rather than methodological limitations. These values suggest that the separation between clusters is modest and that there is substantial overlap in the movement patterns across sessions. The clustering method successfully distinguished between genuinely distinct cutting techniques, capturing both sport-specific and temporal adaptation patterns. This demonstrates the method’s sensitivity to detecting meaningful biomechanical differences, supporting its validity despite moderate internal validation metrics68. The findings should therefore be viewed as preliminary evidence of adaptation patterns. The current study used the visualization-based interpretation of the clustering results and support the results by the repeated ANOVA and linear mixed-effect model.

In summary, the time ratio analysis and smoothness evaluation provided preliminary evidence that the training program appeared to most prominently influence the backward phase of the stepping cycle. Backward descent is a challenging motion pattern due to limited visual feedback. Yet the effect of training during the reverse stepping is not symmetrical on both legs. Exploratory evidence suggests that kinematic metrics like jerk cost and temporal ratios could potentially serve as sensitive indicators of preclinical mobility impairment, detectable decades before functional limitations emerge3. The exercise could be effective as a rehab/prehab program if the leading step is alternated between the left and right feet every other minute (i.e. change the starting leg every minute). Hence, this allows for a smoother movement pattern of each foot and could encourage more balanced adaptation, though further research is needed to confirm these effects and establish optimal implementation protocols.

The use of a single sacrum-mounted IMU is supported by recent literature demonstrating that COM-based kinematic variables, such as jerk cost, can encompass information about both strength and dynamic balance, serving as valid proxies for motor control trainability in functional tasks40. The single-sensor design, while enabling home-based assessment, may underestimate COM deviations during extreme upper-body adjustments in reverse stepping. However, our test-retest reliability (ICC = 0.5) aligns with multi-sensor studies (ICC = 0.45–0.62), suggesting sufficient sensitivity for detecting training-induced adaptations38.

While this study provides valuable insights into the effects of rhythmic step aerobics on movement smoothness and motor adaptation, several limitations should be acknowledged. First, the small sample size and moderate measurement reliability, both of which are typical for pilot and exploratory research. Small sample sizes inherently increase the risk of both Type I and Type II errors, limit the precision of effect estimates, and reduce the external validity of findings69. However, the context of COVID-19 pandemic research and the established conventions for pilot studies provide important frameworks for understanding these limitations.The moderate ICC values reflect the constraints of early-phase studies and highlight the need for larger, more diverse cohorts in future work to establish clinical-grade reliability and generalizability. The findings should therefore be viewed as preliminary and hypothesis-generating, rather than definitive. Second, the study focused exclusively on healthy middle-aged women, which restricts the applicability of the results to other age groups or clinical populations. Future research should encompass a broader sample of middle-aged men and women, including individuals with neurological or musculoskeletal deficiencies, to enhance the generalizability of the findings. Third, the test-retest reliability of some measurement methods was moderate, as were the coefficients of variation (CV) for certain metrics, which may affect the robustness of some results. These limitations should be considered when interpreting findings and designing future studies to improve measurement reliability. Fourth, Single IMU configuration, while practical for real-world deployment, may underestimate complex trunk kinematics during backward stepping.

Conclusion

This exploratory, longitudinal pilot study provides preliminary evidence that rhythmic step aerobics may improve movement smoothness and temporal adaptation in middle-aged women. The moderate reliability of key kinematic metrics, as indicated by ICC values, is in line with expectations for pilot studies and underscores the need for further research with larger samples to confirm these findings and support broader clinical application.

The most pronounced adaptations were observed during the backward stepping phase, where increased stance duration and reduced jerk cost suggest improved stability and neuromuscular coordination. These findings highlight the backward phase as a sensitive target for detecting motor adaptation and underscore the potential of kinematic metrics, such as stance-to-swing ratio and smoothness, as practical indicators of trainability in prehabilitation and rehabilitation contexts.

Overall, this study contributes to the growing body of knowledge on personalized rhythmic exercise programs, underscoring their potential for improving movement smoothness, enhancing kinematic performance, and improving mobility, particularly in aging women.