Feet can be used as an indicator of the human aging process. Reduced walking and exercise and increasing body weight can lead to retardation of the foot muscles and to foot deformities and falls, as well as increasingly flatfooted structures [1
]. Reduced medial longitudinal arches in adults demonstrate many biomechanical inefficiencies and various gait abnormalities in the feet and ankles [4
]. For people with abnormal flat-footed structures, the ability to absorb shock and thus to maintain postural stability is reduced. This may result in inflammation of the plantar fascia, plantar lesions, and body pain, and may even lead to an increased risk of falling [4
]. In this way, the structure of the foot arch is important for posture [8
], and may be an important variable to assess during pre-participation physical examinations [3
]. Further study of foot structure, postural control, and the risk of lower extremity musculoskeletal injury may provide appropriate direction for clinical interventions for individuals with abnormal foot structures [10
]. Previous studies have examined the use of corrective aids to control abnormal foot gait biomechanics and alleviate the discomfort experienced by people with flat feet [11
]. However, the literature suggests that there is currently no set of effective and quantized assessment instruments for post-treatment evaluation [12
]. Clinicians therefore need to consider further evidence when selecting management options for flat feet.
Center of pressure (COP) displacement-based time-series analysis is the measure most often used to examine postural stability during upright standing on a force plate [15
], and has been designed to be a low-cost and portable measurement system for quantifying the dynamic properties of humans’ postural stability [18
]. In the real world, humans typically exhibit complex dynamic behavior, and knowledge of system variability is essential for understanding the intrinsic behavior of dynamic systems. Traditional COP-based measures use means of raw data as measurements. However, COP signals analyzed using the complexity index (CI)—calculated using entropy-based measures [19
]—have recently been considered to be a better measure for analyzing non-stationary human fluctuations in postural sway data.
Entropy concerns system randomness and regularity [21
], and has been applied to physiological and biological time-series data to assess the structural dynamics of a system across different time scales [22
]. Multiscale entropy (MSE) has potential applications in verifying physiological and physical time-series data [22
]. MSE is a univariate method that has the ability to detect intrinsic correlations. It is also used to measure the complexity of single-channel signals. However, only “sufficient” length and “regular” scale are reliably processed with MSE. Empirical mode decomposition (EMD) has been proposed by Huang et al. as a new signal-decomposition method for nonlinear and nonstationary signals [23
]. The EMD is data-driven and generates intrinsic multiple data scales from inputs, and it may be used for MSE analysis. Ahmed et al. proposed multivariate EMD (MEMD) as a means to generate intrinsic data scales, and it can be used for the subsequent multivariate MSE (MMSE) analysis of input multichannel data [24
]. MMSE offers assessments of multichannel observations. It is characterized with greater freedom in analysis than MSE. Entropy methods can be used in signal processing to separate useful signals from intrusive noise. For example, they can be used to evaluate data such as electroencephalogram (EEG) signals to detect an epileptic attack or to classify the signals as focal or non-focal [28
]. The CIs of the MSE and MMSE methods have been validated for use in postural sway dynamics analysis for both younger and older adults, with and without intervention [18
In the present study, differences in postural stability between healthy young adults with flat feet and those with normal feet were observed using both the traditional COP-based measures and the entropy-based measures MSE and MMSE. Different combinations of intrinsic mode functions (IMFs) in the entropy method with different parameters, experimental designs, or force-plate COP signals can generate different postural stability assessment results [18
]. We therefore tried to identify combinations of IMFs that could be used to evaluate differences in postural stability between flatfooted and normal foot young adults to identify the appropriate combinations of IMFs.
The aim of this study was to investigate the effectiveness of postural stability measurements for identifying differences between flatfooted and normal-footed participants. The effectiveness of traditional COP-based and entropy-based MSE and MMSE measures was compared based on a quiet-standing task on a force plate.
Entropy-based data analysis methods have been used to characterize a range of real-world dynamical, non-linear, and non-stationary biomedical time series. We compared MSE and MMSE results with COP-based measures to assess their capacity to identify differences in stability between groups of young adults with dissimilar foot arches. We found that: (1) based on traditional raw-data-based measures from COP signals, MDIST and RDIST exhibited significant differences in the ML direction with EO (Table 2
); (2) the CI values (an entropy-based MSE method using the same COP signals) exhibited significant differences in the AP direction with EC in the low-frequency IMF6
signals (Table 3
); (3) there were no significant differences in the MMSE (Table 5
); and (4) reconstructed combinations of IMFs for the entropy-based measures, IMF5,6
, and IMF5,6,7
revealed significant differences in stability in both directions for both EO and EC between the two groups (Table 6
). Thus, the traditional raw-data-based measures only revealed significant differences under EO conditions, whereas the entropy-based measures revealed differences under both EO and EC conditions.
There have been a number of studies that use COP signals to compare postural stability between younger and older adults. Priteo et al. used COP stabilogram metrics to assess postural stability under EO and EC conditions, and showed that there were more differences—which were generally statistically stronger—between these conditions for older adults than for younger adults [15
]. However, in the present study (which involved only young participants), differences were only revealed in the lower-frequency measures. Nonstationary COP signals can be decomposed to IMFs by using EMD and MEMD methods, and then evaluated using different combinations of the signals. Costa et al. found significant differences in complexity between older and younger adults by adding together the five highest-frequency IMFs [19
]. Yang and Jiang also revealed a difference in complexity for older and younger adults under EO and EC conditions—with or without allocated attention—by using the reconstructed COP signal IMF2,3
]. Similarly, Jiang et al. found significant differences in complexity for older adults before and after using vibratory insoles; however, they found no such differences for younger adults [20
]. Further, Wei et al. revealed statistically significant differences in complexity between younger and older adults using reconstructed IMF5
, and IMF3,4,5
signals via MSE, and before and after the use of vibratory insoles among older adults using reconstructed IMF4
, and IMF2,3,4
signals via MMSE [31
]. Huang et al. compared different COP systems using entropy measures, and found that IMF5,6
was more sensitive than IMF2,3
in distinguishing among young adults [18
]. These studies show that the postural stability of younger adults differs from that of older adults, and that in younger adults it is less likely that changes will be detected after interventions.
Entropy-based measures can be used to distinguish between different types of participants; however, the parameters used with these methods must be set to appropriate values. Examples of such parameters are the length of sequences to be compared, tolerance values, run times, and scale numbers for determining the CI values of the complexity algorithm [20
]. Ramdani et al. [38
] assessed postural stability between EO and EC in younger adults using the following parameters: m
= 3; and r
= 0.3, 0.25, 0.15, or 0.1. They found significant differences between the AP and ML directions, and evaluated the different frequencies taken from the COP signals [38
]. Jiang et al. found a significant difference in the AP direction between EO and EC in younger adults using the parameters m
= 2 and r
= 0.15, with IMF2,4,5
]. Previous studies applying entropy-based measures have observed significant differences in postural stability mainly in the higher-frequency signals (~1–30 Hz) [18
]. One study [40
] showed that the frequency range is <2 Hz in human-body COP signals, and another study [41
] used COP signals to show that visual input affects the lower frequencies. Further experimentation using appropriate parameters and specific IMF signal frequency ranges is required to verify the analysis results for different groups of participants, to evaluate how human balance control functions.
There are few studies comparing postural stability between flatfooted and normal-footed individuals. Dabholkar et al. [42
] compared dynamic balance between flatfooted and normal young females, using the Star Excursion Balance Test (SEBT), and found that the flatfooted individuals’ reach distance was significantly less. Han et al. [43
] showed that during walking, the COP pathway of flat feet may be different from that of normal feet, and that the plantar foot pressure of a flat foot was lower than that of a normal foot. Kim et al. [44
] examined differences in static and dynamic stability between flexible flat feet and normal feet in young people. They showed that the static stability of both MVELO measurements under single-leg standing (EO or EC) were significantly different between the two groups, and concluded that this might indicate the absence of a relationship between static and dynamic stability. In our study, however, we found no such difference for two-leg standing. Some recent studies have shown that the effects of aging on balance may be accentuated in the ML direction [17
]. Mediolateral balance assessment methods were shown to be reliable and effective for both younger and older adults. As the degree of flatfoot deformity increases, static postural stability decreases [47
]. Quantifying postural stability changes in the ML direction would be the next step in exploring the increased risk of falls that is associated with age. In this study, the COP-based measures in the ML direction revealed differences between dissimilar foot arches (Table 6
). Previous studies of flat feet have not specifically explored the direction of changes in postural stability [5
]. Among the methods used in these studies, COP-based assessments appear to be the easiest for clinicians to conduct and quantify for use in assessing improvements in, or identifying appropriate management for, individuals with flat feet.
There are a few limitations to this study that affect the application of entropy-based methods to COP. (1) The differences between the participant groups (Table 1
) with respect to gender, height, weight, and BMI distributions may have influenced the results. (2) We acknowledge that there are many possible combinations of IMFs with different variables for entropy-based analyses. Investigating a wider range of IMF combinations, and the effects of the combinations selected in this study, require further investigation. (3) The meaning of each IMF is currently unclear, and further research is needed to explore this.
In this paper, we used a basic EMD method to decompose nonstationary COP signals into IMFs, and then combined them using a trial-and-error approach to assess postural stability using MSE and MMSE analyses. In future research, we plan to analyze additional EMD methods. Recent studies have suggested that the original EMD method is prone to mode mixing and mode splitting; methods for stabilizing EMD include noise-assisted MEMD [48
] or using MEMD instead of EMD [49
]. The next stage in this investigatory process is therefore to try to verify the effects of treatment of flatfooted individuals using more-developed EMD and entropy-based methods to deepen the analysis of postural stability using COP signals. There are also other types of postural stability assessments that can be used. These COP-based measurements are a simple and effective means of assessing subtle changes in postural stability, which should be utilized in clinical practice in combination with various strategies for alleviating the symptoms of flatfoot.