Abstract—In this work, the anterior-posterior displacement of the center of pressure was modeled as a fractional Brownian motion to analyze the effect of fatigue of plantar flexor muscles by isometric contraction. A sample of 17 young, healthy adults was evaluated by stabilometric test, 2 min before and after a plantar flexion, sustained until exhaustion. For each test, the model was applied to four consecutive periods of 30 s and then averaged to estimate the parameters. The fatigue increased the stochastic activity in both persistent and antipersistent controls, and also increased the Hurst exponent of the long-term mechanism. As a conclusion, the used model suggests that peripheral fatigue increases the body sway and reduces the gain of the antipersistent mechanism. However, these changes are detectable only when more than one 30 s data segment is considered for analysis. Index Terms—Quiet Standing Control, Localized Fatigue, Fractional Brownian Motion. I. INTRODUCTION HE body sway control is a complex task that depends on different sensorial inputs including visual, vestibular, and proprioceptive [1]. In several studies, authors aim at inferring about the importance of each sensorial input, considering that the relative contribution of each subsystem can be estimated by its suppression effect [2]. Stabilometry is used for studying the movements of the center of pressure (COP) under feet, while the subject stays over a vertical force platform. The time series generated by decomposition of COP positions, in mediolateral (x) and anterior-posterior (y) directions, are named stabilograms. In a previous study, the triceps surae fatigue induction was related to increased anterior-posterior stabilogram dispersion, as well as an increased delay between stabilogram and the root mean square value of the gastrocnemius myoelectric signal [3]. The results were attributed to the triceps surae muscle activity as an important body sway controller in anterior-posterior direction. Indeed, the triceps surae fatigue did not show similar effects in Manuscript received April 1, 2010. This study was partially supported by the Brazilian Research Council (CNPq), José Bonifácio University Foundation (FUJB) and CAPES Foundation. R. G. T. Mello is with Sport and Physical Education Department, Naval School, Brazilian Navy, rogerfisiologia@ig.com.br. L. F. Oliveira is with Biomechanics Laboratory, School of Physical Education and Sports, Federal University of Rio de Janeiro. J. Nadal is with Biomedical Engineering Program, COPPE, Federal University of Rio de Janeiro, P. O. Box 68.510, 21941-972 Rio de Janeiro RJ, Brazil, jn@peb.ufrj.br. mediolateral direction. Several models were proposed to represent body sway control, and the inverted pendulum is the most used in classical studies [4]. Collins and De Luca [5] interpreted stabilograms as a stochastic and deterministic process composed by two phases, one in open-loop and another in closed-loop, using the concepts of the fractional Brownian motion based on statistical mechanics. The classical Brownian motion has Gaussian probability density function (pdf) and the spatial positions of the moving object are independent along the time. Several physical systems were modeled using this process, showing that correlation tends on limit to zero, when Δt → ∞ [6]. Originally, in 1828 Robert Brown showed the randomness of the pollen movements on water surface, which justify the attribution of his name to the phenomenon. Afterward, in 1905 Einstein studied the Brownian motion and showed that the mean square displacement of a random movement has relationship with the time as described by the follow equation [5]: ( ) t D t b Δ ⋅ ⋅ = > Δ < 2 2 (1) where ( ) > Δ < t b 2 is an average of the b(t) square displacement, Δt is the time interval between samples, and D is the diffusion coefficient. This relationship can be demonstrated considering the Gaussian pdf of the ramdom movement, with zero mean, at which ( ) > Δ < t b 2 corresponds to variance: () () () ( ) ∫ ∞ ∞ - Δ ⋅ ⋅ = Δ ⋅ Δ Δ ⋅ Δ = > Δ < t D b d t t b P t b t b 2 , 2 2 (2) where Δb = b(t)-b(t 0 ) and ) ), ( ( t t b P Δ Δ is the Gaussian pdf. Therefore, D has a direct relationship with data variance. Mandelbrot and Van Ness [7] introduced the fractional Brownian motion concept as a generalization of the b(t) random function. The reduced b variable defined by: H t D t b t b b ) / ( 2 ) ( ) ( 0 τ τ Δ ⋅ ⋅ ⋅ - = (3) where τ is an infinitesimal time interval, has Gaussian pdf with zero mean and unit variance. Therefore, in this generalization, the variance of Δt increment is calculated by: H H t t D t V ⋅ ⋅ Δ ∼         Δ ⋅ ⋅ = Δ 2 2 2 ) ( τ τ (4) Localized Fatigue Effects on Quiet Standing Control by Fractional Brownian Motion Roger G. T. Mello, Member, EMBS, Liliam F. Oliveira, and Jurandir Nadal, Member, IEEE T 32nd Annual International Conference of the IEEE EMBS Buenos Aires, Argentina, August 31 - September 4, 2010 978-1-4244-4124-2/10/$25.00 ©2010 IEEE 2415