Postural control, foot sole sensation, leg strength, functional capacity and mobility were assessed within the Biomechanics Laboratory at Louisiana State University at baseline and every six weeks throughout the training program.
Postural control
Postural control was assessed by recording COP dynamics at 50 Hz during three, 30 sec trials of eyes-closed standing (arms at side, heels 5 cm apart, and feet abducted 10deg) on a stationary force platform (AMTI, Watertown, MA).
For this secondary analysis, we computed a COP complexity index using multi-scale entropy analysis [
22]. This metric estimates the degree of “information content” of a physiological signal. With respect to standing postural control, this metric is believed to reflect the combined influences of the numerous inputs (i.e., sensory, sensory integration, and motor elements) that interact with one another nonlinearly to regulate the body’s postural sway (i.e., COP) over time. Specifically, the metric characterizes the degree of irregularity within the signal over multiple temporal scales, such that greater multi-scale irregularity reflects higher information content, or complexity. It is suitable for relatively short, nonstationary time-series [
23,
29] and has high test-retest reliability in community-dwelling older adults [
27]. It also offers distinct advantage over traditional entropy metrics, which are limited to the estimation of regularity on a single time scale and thus, have no straightforward correspondence to physiologic complexity [
22].
Reliable entropy analysis requires the occurrence of multiple repetitions of a given dynamical pattern. Therefore, relatively low frequency non-stationarities were filtered using Empirical Mode Decomposition [
29,
30]. The EMD method decomposes a signal into
n "intrinsic mode functions," where each function is characterized by a dominant frequency equal to the sampling frequency divided by 2
n+1. Here, we restricted our analysis to intrinsic mode functions 1–3, thus filtering dynamical information on time scales larger than 320 ms (i.e., 2
3+1/50 sec, where 1/50 sec is the sampling interval).
To ensure that COP dynamics across the bandwidth of interest were distinguishable from noise, we recorded the COP fluctuations of a 75 Kg mass and compared its power in each principle direction to all acquired COP time-series. In all cases, the signal-to-noise ratios in the anterioposterior (AP) and mediolateral (ML) directions were greater than ten and less than one, respectively. For this reason, we only computed the complexity index (see below) from AP COP dynamics.
The complexity index was calculated for each filtered AP COP time-series using a three step process. First, the time-series was “coarse-grained” to produce multiple time-series that each capture system dynamics on a given time scale. The coarse-grained time-series for time scale
n is the sequence of mean center-of-pressure values produced by dividing the original time-series into non-overlapping windows with
n data points, and then calculating the mean value for each window. As entropy analysis (see second step) is a statistical measure, the length of time-series must be substantially longer than the time-scale of interest to ensure sufficient samples for the analysis [
31]. As such, each time-series was coarse-grained into scales 1 (i.e., 1500 data points) to 5 (i.e., 300 data points).
Second, the degree of irregularity associated with each coarse-grained time-series was calculated using sample entropy, such that greater entropy reflects greater irregularity at that time-scale [
31]. This conditional probability metric quantifies the likelihood that if a vector with
m data points matches a template of the same length, within a tolerance
r, the vector and template will still match when their length increases from
m to
m + 1 data points. Here, we used
m=2 and
r=15% of the standard deviation of the original signal [
22,
31,
32].
Third, the COP complexity index was calculated by plotting the sample entropy of each coarse-grained time-series as a function of time scale, and then calculating the area under the resultant curve [
28]. As such, time-series with greater irregularity over multiple temporal scales have more area beneath the curve and higher complexity.
In addition to the COP complexity index, the traditional balance measure of average COP speed was computed by dividing total path length by trial duration. COP area was calculated by computing the area of an ellipse enclosing 95% of the COP signal.
Statistical analysis
Statistical analyses were performed using JMP software (SAS Institute, Cary, NC). All 25 subjects were included in the analysis and descriptive statistics were used to summarize each variable. The effects of Tai Chi exercise on COP complexity, area and speed were analyzed with one-way, repeated-measure ANCOVAs with testing session (baseline, 6, 12, 18, and 24wk) as the within-subject factor. Covariates included subject characteristics known to influence postural control (i.e., age, sex, and BMI), foot sole sensation at baseline (i.e., the number of sites with intact sensation) and the number of completed practice sessions. Tukey’s post-hoc testing was used to compare factor means of significant models. As a secondary analysis, the relationship between changes in COP metrics and changes in foot sole sensation, leg strength (i.e., knee extensor and flexor peak torque), functional capacity (i.e., 6MW) and mobility (i.e., TUG) were calculated. Spearman or Pearson product correlations were used for ordinal and continuous data, respectively. Linear regression analyses were also performed to examine each relationship while controlling for age, sex and BMI. Significance level was set at α=0.05 for all analyses.