Multiple timescales in postural dynamics associated with vision and a secondary task are revealed by wavelet analysis

Abstract

Discrete wavelet analysis is used to resolve the center of pressure time series data into several timescale components, providing new insights into postural control. Healthy young and elderly participants stood quietly with their eyes open or closed and either performed a secondary task or stood quietly. Without vision, both younger and older participants had reduced energy in the long timescales, supporting the concept that vision is used to control low frequency postural sway. Furthermore, energy was increased at timescales corresponding to closed-loop (somatosensory and vestibular) and open-loop mechanisms, consistent with the idea of a shift from visual control to other control mechanisms. However, a relatively greater increase was observed for older adults. With a secondary task a similar pattern was observed—increased energy at the short and moderate timescales, decreased energy at long timescales. The possibility of a common strategy—at the timescale level—in response to postural perturbations is considered.

Appendices

Appendix 1: Calculating the energy content of the signal

The energy content at the level “j” can be expressed in terms of the detail WCs at that scale as,

$$ E\left( j \right) = \sum\limits_{k = 0}^{K\left( j \right)} {\left( {T\left( {j,k} \right)} \right)^{2} } $$

(8)

Similarly, the total energy content of the signal can be found by summing the energy content of the approximated signal and the energy content over all J levels of the detail signals:

$$ E_{T} = \sum\limits_{k = 0}^{K\left( J \right)} {\left( {S\left( {J,k} \right)} \right)^{2} } + \sum\limits_{j = 1}^{J} {\sum\limits_{k = 0}^{K\left( j \right)} {\left( {T\left( {j,k} \right)} \right)^{2} } } , $$

(9)

where the energy at each discrete scale j = 1,…, J and discrete location k = 0,…, K(j) are summed. The energy content of the different scales can be expressed as a percentage of the total energy of the signal which is the sum of the decomposed scale energies

$$ E\% \left( j \right) = \left( {{\frac{E\left( j \right)}{{E_{T} }}}} \right)100\% . $$

(10)

Appendix 2: Energy content percentage for vision effect

The percentage of energy content for the vision effect was examined by comparing the quiet standing with eyes open (SEO) and quiet standing with eyes closed (SEC) conditions for each trial of a subject as,

$$ \Updelta E_{\text{EYE}} \% \left( j \right) = \left( {{\frac{{E_{\text{SEC}} \% \left( j \right) - E_{\text{SEO}} \% \left( j \right)}}{{E_{\text{SEO}} \% \left( j \right)}}}} \right)100\% $$

(11)

where E _SEO%(j) and E _SEC%(j) are the energy content percentages averaged over the three trials for the quiet standing with eyes open and quiet standing with eyes closed conditions, respectively. ∆E _EYE%(j),j = 1,…, 3 for one young individual (subject 14) are shown in Fig. 5c.

Appendix 3: Energy content percentage for tapping effect

The percentage of energy content for the tapping effect was examined by comparing the quiet standing with eyes open (SEO) and tapping with eyes open (TEO) conditions for each trial of a subject as

$$ \Updelta E_{\text{TAP}} \% \left( j \right) = \left( {{\frac{{E_{\text{TEO}} \% \left( j \right) - E_{\text{SEO}} \% \left( j \right)}}{{E_{\text{SEO}} \% \left( j \right)}}}} \right)100\% . $$

(12)

where E _SEO%(j) and E _TEO%(j) are the energy content percentages averaged over the three trials for the quiet standing with eyes open and tapping with eyes open cases, respectively. The calculation was conducted for each of the young and older subjects.