Mathematical Index and Model in Stabirometry

Hiroki Takada¹, Yoshiyuki Kitaoka² and Yuuki Shimizu³

¹Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
²Department of Mathematics, Meijo University, Tempaku-ku, Nagoya 468-8502, Japan
³Institute for Hydrospheric-Atmospheric Sciences, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan

(Received April 20, 2000; Accepted March 21, 2001)

Keywords: Sway of the Center-of-Gravity of the Body, Stabirometry, Fokker-Planck Equation (FPE), Stochastic Dynamical Equation (SDE), Form of a Potential Function

Abstract. We measured the sway of the center-of-gravity of the body with a stabirometer for five men aged of 19 to 25 years. There are standardized parameters on stabirometry (observation with the stabirometer) by SUZUKI et al. (1996). We have analyzed the measured data by paying attention to force acting on it. We could admit polarity and rhythm on the force and the kind of effect of visual information. We also constructed a mathematical model of the sway of the center-of-gravity of the body on some conditions. We obtained a stochastic dynamical equation system as a mathematical model corresponding to the sway of the center-of-gravity of the body. We compared the statokinesigram obtained from the numerical simulation of this SDE with that obtained from the measured data.