A total of 20 healthy OF and 18 YF were recruited from the campus of Beijing Sport university, China (Table 1). None of our participants had any orthopedic or neurological disorders, acute pain, or other complaints that might have affected gait and they were all able to walk independently without a walking aid. All participants were informed about the research procedures, and the protocol was approved by the Ethics Committee of Sports Science Experiment of Beijing Sport University (approval number: 2021010H).

Participants wore three inertial sensors (Xsens MTw Awinda, the Netherland) on the heels and the lumbar region of the trunk, using the supplied elastic belt. These sensors had a sample rate of 100 samples and a range of −160 m/s² and +160 m/s². Data collection was synchronized between sensors. All participants wore the same model of shoes. They were asked to walk 100 meters on a straight running track at a self-selected speed, since gait variability is expected to be minimal at this speed for healthy people (27). In addition, although clinical gait tests are usually 4 or 10 meters, these tests do not represent daily-life gait very well (28). Therefore, 100 meters used in this study can well reflect the natural gait at a comfortable speed without participants being exhausted.

MATLAB (R2019b, MathWorks Inc, Natick, MA, USA) was used to analyze data without the first and last steps. Each gait cycle was identified from the sagittal plane angular velocity of foot sensors with three gait events: heel-strike (T_{heel_strike}), toe-off (T_{toe_off}), and foot-flat (T_{foot_flat}) (29). Stride time was defined as the duration between two consecutive T_{heel_strike}. Combined with the gait events of both feet, we got the initial double support (IDS) period and the terminal double support (TDS) period.

For the trunk sensor, sensor data were realigned to a coordinate system based on the accelerometer's orientation with respect to gravity (vertical, VT, axis) and optimization of left-right symmetry (mediolateral, ML, axis) (10, 30).

For the foot sensors, initial displacements were calculated by integrating linear accelerations twice for each gait cycle (in the global coordinate system), using the zero-velocity-update method to eliminate drift, assuming linearity of the drift (31). The hence obtained direction of displacement was not necessary along the x- or y-axis of the global coordinate system. To obtain meaningful stride lengths, we thus rotated the obtained positions, the acceleration, and angular velocity of the feet to a coordinate system that was aligned with the direction of walking (i.e., end position minus starting position), with the VT axis being VT. Then, walking speed was obtained by dividing the distance of the walking direction by the time.

For acceleration measures, maximum VT acceleration of feet and trunk was calculated to reflect the intensity of ground contact (32). It has been suggested that people stabilize their heads during walking (33). Although the trunk segment plays a key role in damping gait-related oscillations (33), the damping of oscillations by the trunk in the VT direction has been suggested to be minor (34, 35). Hence, such accelerations must be attenuated by the lower limbs. Thus, we calculated trunk-foot VT acceleration attenuation, which was used in our study, and was calculated by the difference in maximum VT acceleration between trunk and foot, which represents the impact absorption of the lower limbs. Acceleration amplitude (in the coordinate system prescribed by the walking direction, see above) for each direction [anteroposterior direction (AP), ML, and VT] was calculated as the range of acceleration in a gait cycle.

For the above measures of each person, after getting the mean and SD over all cycles (see Tables 2, 3), we obtained the coefficient of variation (CV) by dividing the SD by the mean (36) (see Supplementary Table 1).

We calculated the LDE of acceleration and angular velocity of each dimension separately (in the coordinate system prescribed by the walking direction, see above). The time series of 50 gait cycles was normalized into 5,000 samples, with an average of 100 samples per cycle. From these data, state spaces were reconstructed using the method of correlation integral (C-C method), which not only can determine both embedding dimension and delay time but also has good robustness to the noise in a small amount of data (37) (see Supplementary Tables 2, 3 for dimension and delay values). LDE was expressed as the mean logarithmic rate of divergence per stride using Rosenstein's method (38). Higher values of the LDE indicate lower local stability.

Normality was assessed using the Kolmogorov–Smirnov test. For measures of the left and right feet, differences were tested using two-way ANOVAs, with within-subject factor Foot (left and right) and between-subject factor Group (YF and OF). For other measures, we used Student's t-tests to compare between age groups. For LDE, which appeared not distributed normally, we compared between groups using the Mann–Whitney U test. For all measures, p < 0.05 was considered as a significant effect. Cohen's d effects were calculated for each variable as the difference between group means divided by the group pooled SD. Magnitudes of d = 0.01, 0.20, 0,50, 0.80, 1.20, and 2.0 were considered very small, small, medium, large, very large, and huge, separately (39–41).

In this study, we used inertial sensors to evaluate differences in acceleration intensity, variability, and stability of feet and trunk during gait between healthy YF and OF. Although older adults generally were suggested to walk slower due to physical limitations, such as muscle weakness or loss of flexibility (42), the OF in our study walked at a similar preferred speed and stride length as the YF.

We found a reduction in foot VT maximum acceleration in OF, which probably reflected a reduction of peak ground reaction forces. Such a reduction of ground reaction forces could result from a crouch-like gait, which has been shown in young adults to lead to a reduction of the peak ground reaction force (43, 44). Such a crouch-like gait may increase the metabolic cost of locomotion in the elderly (45). Although the trunk segment plays a key role in damping gait-related oscillations (33), the damping of oscillations by the trunk in the VT direction has been suggested to be minor (34, 35). In our study, we found a lower trunk-foot VT acceleration attenuation and a higher trunk acceleration amplitude in OF, which implies decreased cushioning (impact absorption) and hence less preservation of the stability of the head (46). Even though foot (VT) accelerations were lower in OF, suggesting less impact, the OF were not able to attenuate the higher accelerations in the trunk. This reduction in impact absorption may be caused by age-related neuromuscular changes, such as a reduced muscle strength of the triceps surae and quadriceps femoris (47), degraded stiffness and elastic modulus of the tendons (48), muscle co-contraction, and degraded absorption of the intervertebral disc (49). Considering that two-thirds of the weight of the human body is in the upper body, such higher trunk accelerations may be destabilizing, which may cause falls (50).

For stability, LDE calculated from trunk time-series data has been shown to better reflect differences in gait stability due to age than LDE calculated from data of other segments (51). In our study, OF showed significantly lower local dynamic stability (higher LDE) in ML acceleration, ML, and VT angular velocity. Among these, the LDE calculated from trunk ML angular velocity had the largest effect size. As stability in the ML direction needs more control than stability in the AP direction during gait (52, 53), decreased LDE of trunk angular velocity in ML direction could be an early indicator of gait stability problems.

All participants in this study walked under the same environmental conditions. Thus, any between-subject differences in variability arose from differences in (internal) neuromotor noise and not (external) environmental noise. No differences were found in the variability of spatiotemporal measures, which was consistent with a previous study showing that temporal gait variability of older non-fallers was not significantly different from young adults in terms of SD and CV (27).

Our OF walked with less variability of maximum VT acceleration of feet variability than YF (Table 3, Supplementary Table 1). However, the variability of ML and VT acceleration amplitude of the trunk was larger for the OF, which could suggest OF are at a higher risk of balance loss and falling (36).

All in all, our findings suggest that stability of the trunk might be a more sensitive indicator of locomotor impairment and potential future risk of falls than changes in variability of the trunk, as the LDE had higher effect sizes (54). Measures of the variability of acceleration of the feet showed even higher effect sizes and might thus be even more useful. However, here, it should be noted that these effects were opposite from theoretically expected, with the OF having lower (means and variability) acceleration of the foot.

All tests in our study were aimed at testing the same hypothesis, that is, OF are less stable and more variable than YF, hence, we did not use a correction for multiple testing. Nonetheless, not correcting may lead to Type I errors, and thus, some caution is warranted. Furthermore, the older participants in our study were quite fit and additional studies are needed to further investigate the applicability of acceleration attenuation when studying older adults. Future research can expand the sample size and conduct a multi-center study to obtain more representative results. Although we used only trunk and feet sensors for practical usefulness, the underlying mechanisms for the alterations in gait in the older women remain unclear and would require more detailed assessments of, e.g., whole-body kinematics and muscle activity.