Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Restricted accessArticles

Stochastic two-delay differential model of delayed visual feedback effects on postural dynamics

Jason Boulet

Jason Boulet

Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

Centre for Neural Dynamics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

[email protected]

Google Scholar

Find this author on PubMed

,
Ramesh Balasubramaniam

Ramesh Balasubramaniam

Centre for Neural Dynamics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

Department of Kinesiology, McMaster University, Hamilton, Ontario L8S 4L8, Canada

Google Scholar

Find this author on PubMed

,
Andreas Daffertshofer

Andreas Daffertshofer

Research Institute MOVE, VU University Amsterdam, van der Boechorststraat 9, 1081 Amsterdam, The Netherlands

Google Scholar

Find this author on PubMed

and
André Longtin

André Longtin

Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

Centre for Neural Dynamics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

Google Scholar

Find this author on PubMed

    We report on experiments and modelling involving the ‘visuo-postural control loop’ in the upright stance. We experimentally manipulated an artificial delay to the visual feedback during standing, presented at delays ranging from 0 to 1 s in increments of 250 ms. Using stochastic delay differential equations, we explicitly modelled the centre-of-pressure (COP) and centre-of-mass (COM) dynamics with two independent delay terms for vision and proprioception. A novel ‘drifting fixed point’ hypothesis was used to describe the fluctuations of the COM with the COP being modelled as a faster, corrective process of the COM. The model was in good agreement with the data in terms of probability density functions, power spectral densities, short- and long-term correlations (Hurst exponents) as well the critical time between the two ranges.

    References