Effects of transcranial direct current stimulation (tDCS) on multiscale complexity of dual-task postural control in older adults

Abstract

Transcranial direct current stimulation (tDCS) targeting the prefrontal cortex reduces the size and speed of standing postural sway in younger adults, particularly when performing a cognitive dual task. Here, we hypothesized that tDCS would alter the complex dynamics of postural sway as quantified by multiscale entropy (MSE). Twenty healthy older adults completed two study visits. Center-of-pressure (COP) fluctuations were recorded during single-task (i.e., quiet standing) and dual-task (i.e., standing while performing serial subtractions) conditions, both before and after a 20-min session of real or sham tDCS. MSE was used to estimate COP complexity within each condition. The percentage change in complexity from single- to dual-task conditions (i.e., dual-task cost) was also calculated. Before tDCS, COP complexity was lower (p = 0.04) in the dual-task condition as compared to the single-task condition. Neither real nor sham tDCS altered complexity in the single-task condition. As compared to sham tDCS, real tDCS increased complexity in the dual-task condition (p = 0.02) and induced a trend toward improved serial subtraction performance (p = 0.09). Moreover, those subjects with lower dual-task COP complexity at baseline exhibited greater percentage increases in complexity following real tDCS (R = −0.39, p = 0.05). Real tDCS also reduced the dual-task cost to complexity (p = 0.02), while sham stimulation had no effect. A single session of tDCS targeting the prefrontal cortex increased standing postural sway complexity with concurrent non-postural cognitive task. This form of noninvasive brain stimulation may be a safe strategy to acutely improve postural control by enhancing the system’s capacity to adapt to stressors.

Appendix

Multiscale entropy

MSE was calculated according to the procedure proposed by Costa (2007). For a given one-dimensional discrete time series of length N = {x ₁,…, x _i ,…, x _N }, the set of consecutive coarse-grained time series $\left\{ {y(\tau )} \right\}$ constructed was given by

$$y_{j}^{{(\uptau)}} = 1/\uptau\sum\limits_{{i = (j - 1)\uptau + 1}}^{{j\uptau}} {x_{i} }$$

(2)

where x _i represents the original time series, τ is the scale factor, and 1 ≤ J ≤ N/τ. In other words, the coarse-grained series at different timescales are obtained by taking arithmetic averages of τ which neighbors original values without overlapping. Thus, the length of each coarse-grained series is given by N/τ, such that scale 1 reflects the original time series.

The sample entropy (SE) of each coarse-grained time series was then calculated. SE, which is related to approximate entropy (AE), calculates the irregularity of a given time series using the following steps:

• 1 For the coarse-gained time series y(i), we could form the vectors Y(i) as:

  $\left\{ {Y(i) = y(i),y(i + 1),{ \ldots },y(i + m - 1)} \right\},$

  where m is the pattern length parameter;

• 2 Define the distance between vector Y(i) and Y(j) as

  $$d (Y(i),Y(j)) = \hbox{max} \left( {\left| {\left. {y (i + k) - y(j + k)} \right|} \right.} \right),$$

  (3)

• 3 For each i ≤ N − m, calculate the quality

  $$B_{j}^{m} = ({\text{number}}\;{\text{of}}\;{\text{vector}}\,Y(i), i \ne j,{\text{such}}\;{\text{that}}\;d(Y(j)) < r)$$

  (4)

  the tolerance level r is set at a percentage of the SD of the time series.

• 4 Repeat steps (1)–(3) with embedding dimension m + 1;

• 5 SE is defined as:

  $${\text{SE}} - \lim_{N \to \infty } \ln \left( {{{\sum\limits_{i = 1}^{N - m} {B_{i}^{m} } } \mathord{\left/ {\vphantom {{\sum\limits_{i = 1}^{N - m} {B_{i}^{m} } } {\sum\nolimits_{i = 1}^{N - m} {B_{i}^{{^{m} + 1}} } }}} \right. \kern-0pt} {\sum\limits_{i = 1}^{N - m} {B_{i}^{{^{m} + 1}} } }}} \right)$$

  (5)

  When given a signal with finite length, Eq. 5 will be presented as

  $${\text{SE}} = \ln ({{B_{i}^{m + 1} } \mathord{\left/ {\vphantom {{B_{i}^{m + 1} } {B_{i}^{m} }}} \right. \kern-0pt} {B_{i}^{m} }}),$$

  (6)

Thus, SE reflects the conditional probability that a time series of length N/τ, repeating itself within given tolerance r for m points, will also repeat itself for m + 1 points without self-matches. Thus, both the tolerance level r and pattern length m need to be set in SE algorithm for the MSE calculation. Here, we choose a tolerance level of r = 0.15 × SD of the time series to avoid distortion due to the variability in signal magnitude (Costa et al. 2007). Additionally, we set m = 2 as traditionally recommended.