Modeling the basin of attraction as a two-dimensional manifold from experimental data: applications to balance in humans.
We present a method of modeling the basin of attraction as a three-dimensional function describing a two-dimensional manifold on which the dynamics of the system evolves from experimental time series data. Our method is based on the density of the data set and uses numerical optimization and data modeling tools. We also show how to obtain analytic curves that describe both the contours and the boundary of the basin. Our method is applied to the problem of regaining balance after perturbation from quiet vertical stance using data of an elite athlete. Our method goes beyond the statistical description of the experimental data, providing a function that describes the shape of the basin of attraction. To test its robustness, our method has also been applied to two different data sets of a second subject and no significant differences were found between the contours of the calculated basin of attraction for the different data sets. The proposed method has many uses in a wide variety of areas, not just human balance for which there are many applications in medicine, rehabilitation, and sport.
Zakynthinaki
Maria S
MS
Instituto de Ciencias Matemticas, CSIC-UAM-UC3M-UCM, c/Serrano 121, 28006 Madrid, Spain. mzakyn@mat.csic.es
Stirling
James R
JR
Martínez
Carlos A Cordente
CA
de Durana
Alfonso López Díaz
AL
Quintana
Manuel Sillero
MS
Romo
Gabriel Rodríguez
GR
Molinuevo
Javier Sampedro
JS
D000328:Adult; D000465:Algorithms; D001703:Biophysics / Q000379:methods; D006801:Humans; D008297:Male; D015233:Models, Statistical; D008962:Models, Theoretical; D009068:Movement; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D009991:Oscillometry / Q000379:methods; D004856:Postural Balance; D013269:Stochastic Processes