Analysis of Vertical Micro Acceleration While Standing Reveals Age-Related Changes

In this study, we investigated the fluctuation characteristics of micro vertical acceleration of center of mass (vCOMacc) in standing and examined the usefulness of vCOMacc as an aging marker for standing control abilities. Sixteen young and 18 older adults participated in this experiment. Data for vCOMacc were calculated as the vertical ground reaction force value divided by each participant’s body mass using a force plate. The COMacc frequency structure was determined using the continuous wavelet transform to analyze the relative frequency characteristics. For time domain analysis, we determined the root mean square (RMS) and maximum amplitude (MA) of the integrated power spectral density. We also analyzed the correlation between vCOMacc and lower limb muscle activity. The relative frequency band of vCOMacc was higher in older than young adults, and the time domain indicators were sufficient to distinguish the effects of aging. Regarding the relationship between vCOMacc during standing and muscle activity, a correlation was found with the soleus muscle in young adults, while it was moderately correlated with the gastrocnemius muscle in older adults. The cause of vCOM may be related to differences in muscle activity, and vCOMacc may be utilized to more easily assess the effects of aging in standing control.


Introduction
Stable posture control is essential for safety in daily life and may determine quality of life, especially for older adults. To evaluate bipedal standing ability, many studies use force plates to analyze center of pressure (COP) [1][2][3][4][5] or center of mass (COM) acceleration [6][7][8][9]. The COP trajectory has been shown to be able to predict the dynamic response of attitude control systems to perturbations of young or older adults even during a quiet stance [10,11]. Alternatively, anterior-posterior center of mass acceleration (apCOMacc) [6][7][8][9] can be used to analyze the aging, developmental, and disease characteristics in a controlled standing system. In this regard, such devices are useful devices that can be easily measured, leading to many studies, especially on sagittal plane trajectory [12][13][14]. On the other hand, vertical fluctuation is much smaller than horizontal fluctuation; thus, there is generally little interest in such variation characteristics [15]. However, it has been reported that the vertical ground reaction force (Fz) parameter allows the collection of data at a lower cost, because it only collects the weight load fluctuation of the individual; additionally, it is more robust against fluctuations between trials [16]. If an analysis method using only vertical acceleration can be proposed for balance control due to aging, clinical evaluation using a simpler and lower-cost device will be

Subjects
This study included 16 healthy young adults (age: 20.4 ± 0.6 years; height: 165.9 ± 8.3 cm; weight: 58.3 ± 6.3 kg) and 18 healthy older adults (age: 72.9 ± 3.6 years; height: 162.0 ± 8.2 cm; weight: 62.9 ± 8.6 kg), a total of 34 subjects. Exclusion criteria included a history of musculoskeletal injuries or diseases and neurological disorders. All subjects gave their informed oral and written consent for inclusion before they participated in the study. The study was conducted in accordance with the Declaration of Helsinki, and the protocol was approved by the ethics review board of Yamagata Prefectural University of Health Sciences (approval ID: 1310-16).

Measurements
Participants were requested to stand, with their eyes open, on a single force plate (60 × 90 cm, Type 9287A; Kistler, Winterthur, Switzerland). They were instructed to watch a target, which was placed at eye level, while keeping their arms and stance in a comfortable position. Anteriorposterior positioning of the feet was based upon a predetermined distance and was aligned using markers on the force plates. The force plate was used to extract both Fz data and anterior-posterior ground reaction force data (Fx) points. For the purpose of clarifying the relationship between vCOMacc and the muscle activity of the lower limbs, a surface electromyography (EMG) system (TrignoTM Wireless EMG, Delsys Inc., Boston, MA, USA) was used to collect muscle activity data. Prior to attaching the electrodes, skin impedance was reduced by wiping the skin with alcohol swabs. The EMG electrodes were placed on the soleus (So) and medial gastrocnemius muscles (MG) of both limbs. The EMG signals of lower limb muscle were in the range of 10-450 Hz when bandpass-filtered offline (fourth-order Butterworth filter). Each subject underwent three trials, with a sufficient resting period between each trial. All data were collected at a sampling frequency of 1000 Hz, and signals were loaded onto a personal computer for analysis. The duration of each trial was approximately 60 s. Only data from the last 55 s were subjected to subsequent analyses.

Data Analysis
For both Fz and Fx data, analog offset (DC offsets; mean amplitude displacement from zero) were removed. vCOMacc and apCOMacc were obtained by dividing the ground reaction force (GRF) in the Fz and Fx directions by the participant's body mass. The vCOMacc data were subjected to filtering using a fourth-order Butterworth bandpass filter, which employed a zero-phase lag with a cutoff frequency of 0.1-20 Hz. The apCOMacc data were low-pass-filtered at a frequency of 10 Hz using a Butterworth filter [27].
We used the CWT method to analyze the effect of aging on the time domain and the frequency domain of COMacc. Continuous wavelet transform describes a mathematical technique that can be used to analyze a complex time-series signal with variable power or magnitude over a wide range of frequencies. The CWT, shown in Equation (1), was calculated using AutoSignal software (Systat Software Inc., San Jose, CA, USA). The CWT of a discrete sequence x n is defined as the convolution of x n with a scaled and translated version of ψ 0 (n).
where the complex conjugate is indicated by *, N is the data series length, and δt is the sampling interval. By varying the wavelet scale s and translating along the localized time index n, it is possible to construct an image showing the amplitude of any feature versus the scale and how this amplitude varies with time. The subscript zero on ψ (Equation (2)) was added to indicate that this value of ψ was also normalized.
where τ is the adjustable, nondimensional time parameter. For this study, the adjustable parameter σ was set to 8 in the AutoSignal environment. The global wavelet spectrum (Equation (3)), which is defined as the time average over a series of wavelet powers, can be expressed as where W n is the CWT coefficient, and n and N are the specific time ranges to average the CWT coefficients. A continuous wavelet (Morlet) time-frequency analysis, which determines the integrated power (time-integral squared amplitude (TISA)) across time [28][29][30], was performed. The TISA power is defined as TISA (Power) = ∆t × (Re 2 + Im 2 )/2 (4) where Re and Im are the real and imaginary parts of the transformed data, respectively, and ∆t is the sampling interval (Equation (4)).

Frequency Domain Analysis
The normalized power spectral density (power in frequency bin divided by the total amount of power) was averaged across a 2 Hz band recording, which ranged from 0 to 20 Hz for vCOMacc or 0 to 10 Hz for apCOMacc.

Time Domain Analysis
For each participant's COMacc and EMG data, the root mean square (RMS) was used to quantify the mean power of COMacc ( Figure 1). Measurements of the average power spectral density of COMacc and EMG data were calculated for each trial from the RMS as follows: where x(i) is the COMacc data for sample number i, and N is the number of samples. Moreover, the maximum amplitude (MA) of the COMacc integrated power was compared for both groups, which allowed for an evaluation of the instantaneous changes in COMacc and an examination of the effects of aging.

Time Domain Analysis
For each participant's COMacc and EMG data, the root mean square (RMS) was used to quantify the mean power of COMacc ( Figure 1). Measurements of the average power spectral density of COMacc and EMG data were calculated for each trial from the RMS as follows: where x(i) is the COMacc data for sample number i, and N is the number of samples. Moreover, the maximum amplitude (MA) of the COMacc integrated power was compared for both groups, which allowed for an evaluation of the instantaneous changes in COMacc and an examination of the effects of aging.

Statistical Analysis of COMacc Data
Statistical analysis of the mean power value within each frequency band for the two groups was performed using two-factor analysis of variance, with a statistical significance level set at p < 0.05. Time domain vCOMacc and apCOMacc data were statistically tested for both groups (young vs. older adults) using a non-paired t-test. The correlation between RMS vCOMacc or RMS apCOMacc and the correlation between each COM and EMG were estimated using Pearson's correlation coefficient (r) (* p < 0.05, ** p < 0.01).

Statistical Analysis of COMacc Data
Statistical analysis of the mean power value within each frequency band for the two groups was performed using two-factor analysis of variance, with a statistical significance level set at p < 0.05. Time domain vCOMacc and apCOMacc data were statistically tested for both groups (young vs. older adults) using a non-paired t-test. The correlation between RMS vCOMacc or RMS apCOMacc and the correlation between each COM and EMG were estimated using Pearson's correlation coefficient (r) (* p < 0.05, ** p < 0.01). Figure 1 shows a representative time-series example of vCOMacc or apCOMacc from young adults (upper panel, a and c) and older adults (lower panel, b and d). Figure 2 shows typical examples of frequency domain and time domain analysis results for each COMacc using CWT. Approximately 90% of vCOMacc data in both young and older adults were present below 10 Hz; thus, those below 10 Hz were analyzed in this study.

Results
Geriatrics 2020, 5, x FOR PEER REVIEW 5 of 12 90% of vCOMacc data in both young and older adults were present below 10 Hz; thus, those below 10 Hz were analyzed in this study.

Frequency Domain
Analysis of the frequency structure of COMacc indicated that the power spectrum of vCOMacc was stronger within older adults, mainly with respect to the relative power observed across the 2-8 Hz band. In addition, almost every young adult displayed major peaks in the 4-6 Hz power spectrum, whereas older adults typically showed peaks in the vCOMacc spectrum between frequencies of 6 and 8 Hz (Figure 3, Table 1). Moreover, the main frequency band of apCOMacc in both groups was less than approximately 2 Hz, which was similar to previous reports ( Figure 3, Table 2) [7]. Examples of analysis in two-dimensional plots from continuous wavelet transform (CWT) of COMacc in young adults (panels (a,c)) and older adults (panels (b,d)). The power spectral density of the CWT shows the time-integrated square amplitude. Frequency domain analysis was normalized, and the power spectral densities were averaged across the 1 Hz band over the frequency range of 0-20 Hz for vCOMacc and 0-10 Hz for apCOMacc.

Frequency Domain
Analysis of the frequency structure of COMacc indicated that the power spectrum of vCOMacc was stronger within older adults, mainly with respect to the relative power observed across the 2-8 Hz band. In addition, almost every young adult displayed major peaks in the 4-6 Hz power spectrum, whereas older adults typically showed peaks in the vCOMacc spectrum between frequencies of 6 and 8 Hz (Figure 3, Table 1). Moreover, the main frequency band of apCOMacc in both groups was less than approximately 2 Hz, which was similar to previous reports ( Figure 3, Table 2) [7].  (panel b,d), respectively. The solid line represents the average in each frequency band of the group. The shaded area represents one standard deviation. Table 1. Summary of vertical center of mass acceleration (vCOMacc), integrated power spectral density (PSD), maximum amplitude (MA), root mean square (RMS), and correlation coefficient (r) for both age groups combined.

Young Adults
Older
Geriatrics 2020, 5, x FOR PEER REVIEW 7 of 12 Table 2. Summary of anterior-posterior center of mass acceleration (apCOMacc), integrated power spectral density, maximum amplitude, root mean square for both age groups combined. Values presented are means and standard deviations of the normalized power spectral density of each frequency band. Comparison of frequency band, MA, and RMS differences between both groups. †, Statistical analysis within each frequency band.

Correlation Analysis for vCOMacc and apCOMacc
There was no significant correlation between vCOMacc and apCOMacc in both young and older adults (young: r = 0.16, p = 0.56; older adults: r = 0.42, p = 0.08) ( Table 1). Tables 3 and 4 show the correlation between vCOMacc or apCOMacc and EMG for young adults and older adults, respectively. In young adults, a high correlation coefficient was obtained with COMacc for the frequency band above 4 Hz. In older adults, a negative correlation was found between vCOMacc and MG in the 0-2 Hz frequency band, while a positive correlation was found between apCOMacc and EMG in the 4-6 and 6-8 Hz frequency bands Table 3. Correlation between the power spectral density of vCOMacc or apCOMacc in young adults and the root mean square of lower limb muscle activity.

Discussion
The purpose of this study was to apply wavelet spectral analysis to the study of postural control and to determine whether aging results in measurable changes in spectral properties during quiet standing.

Frequency Domain
vCOMacc revealed differing power spectral densities according to age, and the frequencies showed measurable differences between age groups. Specifically, the relative power spectral density was characterized by a high-frequency band in older adults. Physical tremors of the soleus muscle [31] or increased power of lower limb muscle activity in the high-frequency band [32] may be associated with vCOMacc in older adults; therefore, vCOMacc can be an indicator of age-related neurological or musculoskeletal decline. Worthy of note was the correlation between the gastrocnemius muscle and vCOMacc in the lower-frequency band. Previous studies reported that the lower-band oscillatory drive of the bilateral plantar flexors during a quiet stance is characteristic in older adults [33]. Such an increase in the low-frequency bands may be associated with poor motor unit firing rate [34], reduced vibrotactile sensitivity of the foot soles [35], and amplified vestibular motor response [36]. During quiet standing, the activation of calf muscles plays an important role in the postural control of standing balance [37,38], because the ankle joint torque controls the COM behavior [39]. Thus, if the behavior of MG activity can be estimated from a specific frequency band of vCOMacc, it may be possible to easily obtain more information from a simple bio signal.

Time Domain
The results obtained from the MA RMS and the integrated power spectral density RMS were enough to reliably distinguish young adults from older adults, as shown in Figure 2. A significant increase in the power spectral density of vCOMacc during standing may be associated with the age-related decrease in dynamic ballistic muscle strength [40] or in the number of motor units [41]. Additionally, a persistent increase in spectrum density in older adults may be associated with the sustained and enhanced muscle activity of the plantaris flexors [42,43], as well as a decline in cutaneous feedback and proprioception [44]. Otherwise, during standing, the body is constantly subjected to micro vibrations, which may be caused by myocardial contractions [45] or physiological tremors [46][47][48].
Previous studies also investigated the amplitude and structural variabilities of apCOMacc and EMG, showing an enhanced relationship between postural variability and responsible muscle activation [49] Similarly, this study also evaluated the relationship between the sagittal plane COM and the calf muscles, while a different correlation was found between vCOMacc and calf muscle. Thus, it is possible that vCOMacc allows the observation of different aspects of balance control.
Note that the correlation between apCOMacc RMS and vCOMacc RMS was low. When apCOMacc is the result of multilinked joint control of the lower limbs [50], this suggests that vCOMacc is an index that can evaluate aspects of the physical control mechanism differently from apCOMacc. As the details of the mechanism giving rise to such characteristics have not yet been clarified, this is a desirable subject for future studies.
The present study had some limitations. This study relied upon an uncomplicated experiment, which specifically analyzed time variation in vCOMacc. One of the major objectives of this study was to investigate whether we could use the obtained data to identify age-related changes in postural control. However, it was not possible to clarify the cause of age-related differences in vCOMacc fluctuation. Additional measurements (e.g., heart rate and electroencephalogram recordings) could provide potential sources of time-frequency differences across age groups. In addition, the number of subjects who participated in this experiment is small, which may affect the accuracy of the estimation obtained in this experiment. Therefore, this experiment is positioned as a preliminary experiment for further research in the future.
In conclusion, a micro acceleration analysis in quiet standing using time-frequency characteristics revealed differing power spectral densities according to age. Time-frequency analysis showed multiple spectral activity peaks during body oscillations within each frequency range, indicating that the underlying signal contained within vCOMacc is highly dynamic. Therefore, the use of time-frequency methods, which provide information on not only the frequency content but also the timing of these dynamic features of spectral activity, is recommended for further investigation. Furthermore, vCOMacc was able to reflect the activity dynamics of lower limb muscle activities in the standing position, suggesting that neurological information in standing control may be collected using a simple method.

Conflicts of Interest:
The authors declare no conflict of interest.