Identification of Anaerobic Threshold during Dynamic Exercise in Healthy Men Using Kolmogorov-Sinai Entropy FMHSP Silva 1 , AC Silva Filho 2 , LO Murta Jr 1 , MAS Lavrador 1 , VRFS Marães 3 , MS Moura 3 , AM Catai 3 , E Silva 3 , BC Maciel 1 , L Gallo Jr 1 1 University of São Paulo, Ribeirão Preto, Brazil 2 University of Ribeirão Preto, Ribeirão Preto, Brasil 3 Federal University of São Carlos, São Carlos, Brazil Abstract During dynamic physical exercise there is a changing point in physiological state called Anaerobic Threshold (AT). Some respiratory and cardiovascular variables, including heart rate variability (HRV), experiment substantial changes at this point. In this work we measure the AT using Kolmogorov-Sinai Entropy applied to HRV time series. This procedure has two major advantage: a) it is non-invasive and b) it requests low cost equipments. The study also includes the comparison of AT values obtained by the mentioned method with another one obtained through a statistical analysis using the Auto Regressive Integrated Moving Average model. 1. Introduction During dynamic physical exercise (DE) there is a changing point in physiological state called Anaerobic Threshold (AT) [1]. Changes in cardio respiratory variables including heart rate variability occur at this point [1,2]. The search for low cost, non-invasive methods for AT identification, has raised interests from researchers that work in the signal processing applied to biological systems field. Auto Regressive Integrated Moving Average model (ARIMA) has been used for this purpose [3-5]. The general idea to be understood in the entropy concept is that it is impossible to use all the system energy involved in a work realization, because part of that energy is lost. Entropy is, in this sense, a measure of the inaccessible energy. The physicist Ludwig Boltzmann proposed a statistical entropy measure (H): ∑ = - = s N i i i P P K H 1 ) ( log (1) Where K is the Boltzmann constant (only depending on the units used), and P i is the ordinary probability of an element being in any one of the N s phase space states. Shannon, particularly, reached to the same Boltzmann expression with K = 1. Kolmogorov and Sinai proposed, in 1959, to apply the Shannon entropy to dynamic systems. For such end, they used the Correlation Integral (C m (ε)) [6-10]. The computed K-S entropy (H KS ) can be interpreted as a loss (or gain) of information by the system, between the m.p and (m+1). p instants, where p is the reconstruction step: (2) As m grows, the K 2 mean value defined as: (3) converges to H KS . This mean value is plotted in a diagram as a function of m, for different values of ε, and we look for its asymptotic value. The main goal of the present work is to evaluate the tool: Kolmogorov-Sinai entropy (K-S) when applied to HRV time series in different powers of dynamic exercise, in order to quantify the AT in healthy individuals. The results were compared to the AT values obtained using ARIMA model. 2. Methods Ten healthy male volunteers have been studied (23 ± 2.0 years) They exhibited a sedentary life style. Dynamic exercise tests (discontinuous steps) included two ) ( ) ( C ln p 1 lim lim H 1 m 0 KS ε ε ε + ∞ → → = m m C ) ( ) ( C ln p 1 K 1 m 2 ε ε + = m C 0276-6547/05 $20.00 © 2005 IEEE 731 Computers in Cardiology 2005;32:731-734.