Introduction

Balance ability declines with age, resulting in a high risk of falls. In particular, older adults with lumbar spinal stenosis (LSS) often have increased balance impairment and a higher risk of falls due to symptoms such as neuropathic claudication, sensory disturbance, and motor disability1,2. A previous study exploring motion perception has shown that patients with LSS and impaired proprioception of the trunk and lower extremities exhibit large postural sway during standing, which is likely due to errors in feedback control3. In addition, alterations in sensory reweighting during postural control have been observed in patients with LSS; they rely less on proprioceptive cues and more on space cues (i.e., visual and vestibular inputs) than do healthy adults4. As somatosensory information is particularly important during postural control5,6, enhancing somatosensory function and allowing use of afferent information to appropriately adjust posture control would improve balance ability and reduce fall risk in patients with LSS.

We focused on stochastic resonance (SR) as a method for enhancing somatosensory function. SR is a phenomenon wherein subthreshold noise enhances the response of a nonlinear system to a weak input signal7,8,9,10. In previous studies applying the SR phenomenon to human postural control, subthreshold electrical stimulation with a white noise structure has been shown to reduce standing postural sway in healthy younger and older adults through enhanced somatosensory feedback7,9. Recent studies have also suggested that postural stability is more effectively achieved with the pink noise structure than with the typical white noise structure11,12. Given that beneficial effects of noise stimulation have been observed particularly in individuals with somatosensory deficits, including those associated with aging13, stroke, or diabetic neuropathy14, pink noise stimulation can be expected to show a substantial effect in patients with LSS. Pink noise stimulation could be a new treatment for patients with LSS to improve balance ability through the enhancement of afferent information due to the increased sensitivity of somatosensory receptors; however, no study has explored the effects of noise stimulation on the postural control system in patients with LSS.

Therefore, this study aimed to explore the effects of subthreshold electrical stimulation with a pink-noise structure on postural control in patients with LSS. Kinematic and kinetic data were used to explore the detailed mechanisms of noise-induced postural stabilization. We hypothesized that pink noise stimulation would reduce postural sway in patients with LSS, accompanied by improved feedback control, altered the segmental configurations of the lower limbs and trunk, and reduced the variability of the segment angles.

Methods

Participants

Sixteen patients with LSS (7 males and 9 females, mean ± standard deviation [SD]: age, 75 ± 10 years; height, 155.9 ± 9.1 cm; mass, 59.4 ± 13.9 kg) participated in our cross-sectional study; 11 patients had previously undergone treatment for LSS. The inclusion criteria were as follows: diagnosis of LSS by a medical doctor and ability to stand without assistance. The exclusion criteria were as follows: (1) severe neurologic, metabolic, or cardiovascular disease that may affect standing posture; (2) cognitive impairments preventing the understanding of the study description; and (3) implantable devices, such as cardiac pacemakers. Data were collected at the university hospital between February 1 and March 29, 2024. This study was performed in accordance with the principles of the Declaration of Helsinki, and all procedures and consent forms were approved by the Research Ethics Committee of Kansai Medical University (2023171). Prior to the experiments, all the patients provided written informed consent.

Procedure

Reflective markers were attached to both sides of the acromion, anterior superior iliac spine, posterior superior iliac spine, greater trochanter, medial epicondyle of the femur, lateral epicondyle of the femur, medial malleolus of the tibia, lateral malleolus of the fibula, first metatarsal, fifth metatarsal, and calcaneal bones. The participants were provided size-fit shoes to avoid injury. To provide electrical noise stimulation, we placed stimulation electrodes (Ag/AgCl, 18 × 36 mm; F-150-S; Nihon-Kohden Corp., Tokyo, Japan) in the medial and lateral joint spaces of both knees11,12.

Subsequently, the sensory threshold (ST) of each knee was determined according to previous studies11,12,15. To minimize fatigue in patients, the test was performed in a sitting position with the knee joints in mild extension. ST was defined as the largest noise intensity that the patients could not feel. The upper limit of the noise intensity was set to 0.32 mA; this intensity corresponded to the mean ST of healthy young adults11 and was employed to safely provide electrical noise stimulation to patients with sensory impairment. Therefore, for participants who could not sense the noise stimulation at 0.32 mA, ST was defined as 0.32 mA.

After the ST tests, the participants performed a quiet standing task for 40 s (Fig. 1). During the task, they stood with their arms folded across their chest and their feet positioned as parallel as possible to the hip width. They were asked to stand relaxed while looking at a fixed point 2 m ahead. There were two noise conditions: No-STIM and PINK. In the No-STIM condition, no electrical stimulation was provided, whereas in the PINK condition, pink noise-like electrical stimulation (see the next section) was provided to both knee joints at 50% intensity of the individual ST11,12. The stimulation was imperceptible, and electrodes were attached to patients in both conditions; thus, participants were effectively blinded to the experimental condition. The task comprised five sets of each of the two noise conditions. The order of the two noise conditions was randomized within each set, resulting in a total of 10 trials (5 trials × 2 conditions). To minimize fatigue, an approximately 3-min break was taken between sets.

Fig. 1
figure 1

An illustration of the experimental setup. A motion capture system and force plate were used to measure kinematic and kinetic data, and a portable electrical stimulator was used to provide pink-noise-like stimulation with a 1/f structure.

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Portable electrical stimulator

In this study, we used a portable electrical stimulator (10 × 25 × 5 cm, 400 g) with the prospect of future studies exploring the combined effects of noise stimulation and exercise therapy. To avoid the risk of raised skin temperature and pain, the stimulator provides a pink noise-like stimulation11,12 created by combining a pink noise signal with a continuous square wave (duty cycle, 50%; pulse width, 0.1 ms). The details of the device were previously provided16. The device consisted of several major elements: an analog circuit that generated a pink noise voltage waveform, a microcomputer that measured the voltage and generated a pink noise-like voltage waveform, a voltage-to-current circuit, and a current mirror circuit that converted the pink noise-like voltage waveform into a current waveform. Prior to the experiments, we confirmed that the portable stimulator successfully outputted an electrical noise signal with a 1/f structure.

Data processing

Force plates (MG-1190; ANIMA Corp., Tokyo, Japan) and 12 infrared cameras with motion capture systems (Locus 3D MA-3000; ANIMA Corp.) were used to measure kinetic and kinematic data at 1,000 and 100 Hz, respectively, during the quiet standing tasks. The force plate signals were low-pass filtered at 15 Hz with a 4th order, zero-lag Butterworth filter11,12, and the motion capture signals were low-pass filtered at 6 Hz with a 4th order, zero-lag Butterworth filter17. Excluding the beginning and end of the measurement, data for 30 s of steady standing were used for further analysis11.

Using force plate signals, the foot center of pressure (CoP) was computed at 100 Hz; the root mean square (CoPrms) and mean velocity (CoPmv) in the anteroposterior (AP) direction were evaluated as the global amount of postural sway. Note that we focused on the AP direction because balance impairments in patients with LSS are largely in this direction1,18,19. CoPmv was calculated using the total path length and total time, and each CoP measure was normalized to the individuals foot length for further statistical analysis11,12,20.

To assess the function of feedback control during quiet standing, a stabilogram-diffusion analysis (SDA) was performed21,22. We first plotted the CoPrms displacement in the AP direction (〈Δy2〉) against a time interval (Δt) from 0.01 to 10 s. After separately creating these diffusion plots for all the trials, we ensemble-averaged the five plots for each noise condition and separated the short- and long-term regions at the transition where the slopes of the plots significantly changed. The long-term region is interpreted to mainly reflect closed-loop feedback control, and we computed the scaling exponent at the long-term region (Hyl) where a large effect of pink noise-like stimulation was observed in healthy younger adults12. The Hyl was calculated from the slope of the log–log diffusion plot (log 〈Δy2〉 vs log ∆t) in the long-term region and reflects the persistence of the CoP stochastic behavior. The reduction in Hyl is viewed as an increase in CoP behavior that returns to the equilibrium point following a perturbation21,22.

In addition, to evaluate the contribution of specific sway frequencies, we performed a discrete wavelet transform using the Haar wavelet (center frequency = 0.99). The Haar wavelet was chosen because of its sensitivity to abrupt postural changes and its widespread application in postural control research. Computational procedures were performed as described in previous studies23,24. Briefly, each CoP signal was decomposed into 11 discrete wavelet levels, and the relative energy at each level was calculated to quantify the contribution of different frequency bands. We computed the somatosensory energy index (SEI) by summing the relative wavelet energy at levels 6 to 8, which approximately correspond to the frequency range of 0.38–1.54 Hz23. The SEI reflects sway components associated with somatosensory feedback and was used to examine whether pink noise stimulation increased somatosensory-related activity within this frequency band.

Body movements during quiet standing were assessed using marker trajectories. After constructing the shank, thigh, and trunk segments, the AP tilt relative to the vertical line was calculated. Positive and negative angles were defined as anterior and posterior tilts, respectively. The mean and variability (SD) of each angle in the AP direction during standing were calculated for further analysis.

For each trial, outcome values (e.g., CoPrms, CoPmv, segment angles, Hyl, SEI) were calculated and then averaged across five trials per condition per participant. These per-participant averages were used for further statistical analysis.

Performance-based and self-reported measurements

For performance-based measures, we conducted the Timed Up and Go (TUG), 10-m walk, and muscle strength tests. In the TUG test25, we asked the participants to perform the following actions as quickly as possible: stand up from a chair, walk 3 m, walk back, and sit down. We measured the time required for performance using a digital stopwatch. In the 10-m walk test26, participants walked at a comfortable speed on a 10-m path to evaluate their gait speed (m/s). Each measurement was performed twice, and the average values were recorded.

We also measured the maximal isometric strength of the bilateral hip abductors, knee extensors, and plantar flexors using a handheld dynamometer (μTas F-100; ANIMA Corp.). The participants were seated with their knees and hips flexed at 90° for the knee extensor test and in a supine position with the target knee fully extended for the hip abductor test. In both tests, the sensor was placed 5 cm above the lateral malleolus, and the maximal isometric strength was measured27,28. In the plantar flexor tests, the participants were in a sitting position with the knees extended and plantar surfaces against the wall. The sensor was placed between the targeted metatarsophalangeal joint and wall to measure the maximal isometric strength29. All strength tests were performed twice on the right and left sides, and the largest torque divided by body mass (Nm/kg) was recorded on each side. For further analysis, we used the average values of the right and left sides.

For self-reported measures, the area and strength of numbness were assessed using a paper questionnaire. A numerical rating scale (NRS)30,31 was used to assess numbness strength, with scores ranging from 0 to 10. To assess the risk of falls, fall experiences over the past year were recorded32.

Statistical analysis

This study used nonparametric procedures due to violations of normality. To explore the effect of pink noise stimulation on postural sway during standing, Wilcoxon signed-rank tests were performed to compare the CoPrms and CoPmv values between the No-STIM and PINK conditions.

To further explore the mechanism of noise-induced changes in postural sway, the values of SEI, Hyl, and the average and variability of each segment angle (i.e., trunk, thigh, and shank angles) were compared between the No-STIM and PINK conditions using the Wilcoxon signed-rank test. Data from participants who completed the entire trial were used for statistical analyses. When we found a significant difference, we calculated the effect size (r) based on Cohen’s classification. For all analyses, we used SPSS version 26 (IBM, Armonk, NY, USA); statistical significance was set at 0.05.

Results

Of the 16 patients who consented to participate, the data of 14 patients were included in the final analysis. Two patients withdrew early due to severe postural instability, although they reported no discomfort related to the stimulation. The ST in this study was 0.19 ± 0.11 mA; in five patients, the ST was actually > 0.32 mA but was defined as 0.32 mA. None of the participants felt noise stimulation while standing. Table 1 presents the results of the performance-based and self-reported measures. Regarding the NRS, 12 of the 14 patients had numbness; the most common area of numbness was the plantar surface of the foot. The areas of numbness were classified into four major categories: entire plantar surface, entire forefoot, anteromedial side, and anterolateral side (Fig. 2).

Table 1 Performance-based and self-reported measures
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Fig. 2
figure 2

Areas of numbness. A common area of numbness was the plantar surface of the feet, classified into four major categories: entire plantar surface, entire forefoot, anteromedial side, and anterolateral side.

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Figure 3 presents the results of the CoP-related measures. CoPrms and CoPmv in the PINK condition were significantly lower than those in the No-STIM condition (CoPrms p = 0.009, r = 0.47; CoPmv p = 0.030, r = 0.41), wherein 12 of the 14 patients received the noise benefits of CoPrms reduction. We also found a larger SEI in the PINK condition than that in the No-STIM condition (p = 0.003, r = 0.53). No significant difference between noise conditions was found in Hyl; however, in a secondary statistical analysis that focused on 12 patients who had a noise-induced reduction in CoPrms, a significant reduction in Hyl was found with noise stimulation (p = 0.037; r = 0.40).

Fig. 3
figure 3

Center of pressure (CoP)-related measures. The box plots of the root mean square of the CoP (CoPrms), mean velocity of the CoP (CoPmv), somatosensory energy index (SEI), and scaling exponent (Hyl) in the anteroposterior direction are represented. The CoPrms and CoPmv were normalized by the foot length. Black dots represent the patients with noise benefits (i.e., noise-induced reduction in CoPrms), and red dots represent those without the benefits. The horizontal line, box edges, and whiskers display the median, 25th and 75th percentiles, and minimum and maximum values except for the outliers, respectively. Significant differences are represented with one asterisk (p < 0.05). No-STIM: no stimulation condition, PINK: pink noise condition.

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Table 2 shows the results of the segmental configuration and variabilities. There were no significant differences in the average segment angles. Regarding the variabilities of the segment angle, pink noise stimulation significantly reduced the variability of the AP tilt of the trunk (p = 0.041; r = 0.39).

Table 2 Measures of segment angles.
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Discussion

This study aimed to explore the effects of subthreshold stimulation with pink noise on postural control in patients with LSS. We found that pink noise stimulation of the knee joints significantly reduced the typical measures of postural sway, i.e., CoPrms and CoPmv. Additionally, pink noise stimulation significantly increased the SEI, and Hyl was reduced in patients whose postural sway was reduced by noise stimulation. Furthermore, pink noise stimulation significantly reduced the variability of the AP tilt of the trunk, whereas such alterations were not observed in the shank and thigh segments. These findings partly support our hypothesis that pink noise reduces postural sway in patients with LSS, involving improved feedback controls, alternating segmental configurations, and reducing segment angle variability.

In a previous study that applied pink noise stimulation to healthy young adults, noise-induced CoPrms attenuation was observed in 63% of participants11. In the present study, such an effect was observed in 86% of patients. Similar observations were also found in the CoPmv, suggesting that pink noise stimulation may be more effective in patients with LSS than in healthy young adults. The reduction in CoPmv was modest, whereas the decrease in CoPrms (approximately 11%) approached the magnitude of difference previously reported between older adult fallers and non-fallers33, indicating a potentially meaningful improvement in postural control. Based on previous studies suggesting different features of the CoPrms and CoPmv20,34, noise-induced CoPrms and CoPmv reductions indicate a more effective postural control system and smaller amount of regulatory balancing activity related to postural stability, respectively. In other words, in patients with LSS, the stability level was increased by pink noise stimulation without involving large regulatory activity. To further examine potential moderators of the stimulation effect, we explored trends across ST and clinical measures (e.g., functional mobility and numbness characteristics), but found no clear patterns indicating that these baseline clinical factors influenced the observed benefits of noise stimulation. Nonetheless, these findings collectively demonstrate that pink noise stimulation can modulate postural control in patients with LSS, even in the absence of identifiable clinical predictors, highlighting its potential as a broadly applicable intervention for this population.

Moreover, our findings provide evidence that pink noise stimulation facilitated somatosensory feedback control during quiet standing. Specifically, we found a noise-induced increase in the SEI, which captures the energy contribution in the somatosensory-relevant frequency range. A similar increase has also been reported in studies employing vibrotactile feedback in individuals with transfemoral amputations23, supporting the interpretation that noise stimulation enhances the engagement of somatosensory input. In parallel, Hyl significantly decreased in the 12 patients with the noise effect, indicating a greater tendency for the CoP trajectory to return to the equilibrium point following perturbations21,22. These results suggest that pink noise stimulation may enhance closed-loop postural control by increasing reliance on somatosensory input and reducing persistent sway behavior. Augmenting the weighting of somatosensory receptors may also promote postural stability even under challenging conditions in which other sensory modalities, such as vision, are less accessible or reliable.

Earlier studies using vibratory stimulation have also demonstrated beneficial effects in individuals with somatosensory deficits, including those associated with aging, stroke, or diabetic neuropathy: subthreshold vibration improved foot sensitivity35 and reduced postural sway through enhanced feedback control mechanisms14. Previous and current findings implied that both vibratory and electrical forms of noise stimulation effectively enhance somatosensory processing. A likely shared mechanism involves increased receptor membrane excitability via minor fluctuations in ion permeability. This results in partial depolarization, sensitizing afferent neurons to subthreshold inputs. However, given the substantial differences in modalities and receptor targets between vibratory and electrical stimulation, the optimal stimulus modality and anatomical target may vary depending on the patient population. Identifying these optimal conditions and exploring the specific neural pathways and underlying mechanisms modulated by noise stimulation may further advance the clinical application of SR-based interventions. Such efforts could support the development of noise-based stimulation as a promising strategy for individuals with sensory deficits including patients with LSS.

Noise-induced alterations have also been observed in segment movements; noise stimulation has been shown to reduce trunk variability, and we also found a relatively large variability in the trunk compared to the shank and thigh (Table 2). A previous study revealed that the impaired afferent input from the leg induced constant contractions of the proximal muscles (e.g., the gluteus muscles) as a compensatory strategy36. Such a compensatory motor pattern of the proximal elements for the distal elements would be organized in a way to stabilize the posture according to the principle of abundance37,38. By applying noise stimulation to patients with LSS, such a compensatory strategy of the proximal segments might no longer be necessary through the increased afferent input from the knee joints, resulting in reduced variability in the trunk. Another interpretation is that that pink noise stimulation improved the delayed perception of deviations from the trunk’s neutral position caused by impaired proprioceptive sensations (i.e., trunk kinesthesia)3. The SR effect on the trunk proprioception is still unclear; however, noise-enhanced proprioception of the knee joints might, at least in part, suppress the transmission of internal perturbations from the lower limb to the trunk, reducing trunk variability. While the reduction in trunk variability could theoretically be interpreted as a decrease in compensatory strategies, our CoP-based measurements collectively suggest that this change reflects an enhancement of postural control rather than a loss of adaptability.

The study had several limitations; first, the mechanisms underlying the pink noise effect remain unclear. More comprehensive evaluations of somatosensory and motor impairments would help elucidate the mechanism and develop more effective stimulation methods. Second, although reductions in sway measures were observed, the clinical significance of these changes remains unclear. This study did not include clinical balance assessments (e.g., Mini-BESTest39), which limits its ability to determine whether the observed changes in postural sway translate to meaningful improvements in functional balance or fall risk. Future studies should incorporate such assessments to clarify the practical relevance of noise-induced sway modulation. Third, the sample size was insufficient to reveal the physical characteristics of patients with a large pink noise effect. In addition, we applied a fixed upper limit for stimulation intensity to ensure safety in clinical settings. This may have prevented optimal SR, but the approach effectively minimized risk and still led to sway reductions in many patients. Finally, this pilot study included patients with LSS attending a single hospital; thus, it remains unclear whether similar results will be obtained in other patient populations. Further studies are warranted to address these limitations.

Conclusions

Subthreshold electrical stimulation with pink noise reduced the AP postural sway while standing in patients with LSS, which is likely related to enhanced feedback control and reduced variability of the trunk angle. The SR phenomenon caused by imperceptible pink noise stimulation may be useful for rehabilitation.