## 4 Discussion  
Understanding how individuals respond to different static and dynamic postural conditions and utilizing the best method to measure responses is important when comparing how a healthy nervous system responds versus how a brain-injured individual responds to the same conditions. Previous research that examined children and adults with mild traumatic brain injury, e.g., concussion, has suggested that the use of the center-of-pressure (COP) data can be useful in delineating a normal from an abnormal response to the perturbations of static and dynamic balance [10; 13; 14; 18; 47; 48; 49; 50]. Since it has been shown that the COP time series is non-linear, traditional methods of assessing various COP parameters, e.g., statistical use of means and standard deviation, have not been effective [10; 48]. Previous work using non-linear metrics, such as approximate and sample entropy, to study  
Figure 15: Histograms, i.e., count (vertical axis) of the difference between SampEn and ApEn, i.e., Sample–Approximate (horizontal axis). Values to the left of the vertical black line indicate that ApEn was larger, and values to the right of the vertical black line indicate that SampEn was larger. normal and pathological balance has been more useful [3; 18; 19; 51; 52; 53], with some interest in the selection of the input parameters, i.e., \(N\), \(m\), and \(r\), for the calculation of ApEn and SampEn. Previous work by [PERSON] et al. [16; 17; 38] discussed parameter selection processes relative to gait data [16; 38] and short data sets [17], but only [PERSON] et al. [52] examined a range of input parameters related to COP time series in healthy young and older adults. In our laboratory, [PERSON] et al. [21] measured the center of pressure of healthy college-aged participants under various quiet standing postures and used ApEn to characterize the time series, but their method was limited by an overly redundant data set and included the determination and use of only one tolerance window, \(r\), that was atypical. Based on the need described in the literature for more work investigating the diverse application of ApEn and SampEn analyses, and the methodological limitations of the previous research in our laboratory, the primary purpose of this study was to compare ApEn and SampEn under various difficult quiet standing conditions and examine the effects of different tolerance window values. The results revealed the following: (1) that even though SampEn tended to yield lower mean values than ApEn, both indices provided measures of unpredictability or irregularity of a COP time series in both the anterior-posterior and medial-lateral directions; (2) both ApEn and SampEn effectively differentiated a more stable quiet standing posture, i.e., eyes open feet together, from less stable standing postures, i.e., eyes-open and eyes-closed tandem standing postures; and (3), the selection of \(r\) had a relatively consistent effect with both entropic statistical analyses. Ours is the first study to examine and report ApEn and SampEn related to the non-linear dynamics of the center-of-pressure excursions for quiet tandem standing under eyes-open and -closed conditions. It has been demonstrated that high sampling rates result in reduced estimated entropy values, likely since higher rates are well above the frequency of the tested behavior creating an artificial increase in the number of matches [12; 38]. [PERSON] et al. [21] reported average ApEn estimates ranging from 0.005 to 0.030 for each 30 s COP time series sampled at 1200 Hz. By contrast, in this study, the estimates of average ApEn are higher and ranged from 0.1 to 0.6 for each 30 s COP time series sampled at 60 Hz. By low-pass filtering and decimating the data to 60 Hz, we minimized the effect of measurement noise above 30 Hz on the entropy estimates. Others have demonstrated the importance of how data management is handled and interpreted. For example, [PERSON] et al.